TSTP Solution File: SWW345+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SWW345+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 : n007.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 00:13:58 EDT 2023
% Result : Theorem 52.62s 52.39s
% Output : CNFRefutation 52.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW345+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n007.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
% 0.13/0.35 % DateTime : Sun Aug 27 21:05:57 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.57 start to proof:theBenchmark
% 52.14/52.23 %-------------------------------------------
% 52.14/52.23 % File :CSE---1.6
% 52.14/52.23 % Problem :theBenchmark
% 52.14/52.23 % Transform :cnf
% 52.14/52.23 % Format :tptp:raw
% 52.14/52.23 % Command :java -jar mcs_scs.jar %d %s
% 52.14/52.23
% 52.14/52.23 % Result :Theorem 48.680000s
% 52.14/52.23 % Output :CNFRefutation 48.680000s
% 52.14/52.23 %-------------------------------------------
% 52.14/52.24 %------------------------------------------------------------------------------
% 52.14/52.24 % File : SWW345+1 : TPTP v8.1.2. Released v5.2.0.
% 52.14/52.24 % Domain : Software Verification
% 52.14/52.24 % Problem : Hoare's Logic with Procedures 435211, 5000 axioms selected
% 52.14/52.24 % Version : Especial.
% 52.14/52.24 % English :
% 52.14/52.24
% 52.14/52.24 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 52.14/52.24 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 52.14/52.24 % Source : [Bla11]
% 52.14/52.24 % Names : hoare_435211.5000.p [Bla11]
% 52.14/52.24
% 52.14/52.24 % Status : Theorem
% 52.14/52.24 % Rating : 0.47 v7.5.0, 0.44 v7.4.0, 0.60 v7.3.0, 0.55 v7.2.0, 0.52 v7.1.0, 0.61 v7.0.0, 0.57 v6.4.0, 0.58 v6.3.0, 0.62 v6.2.0, 0.76 v6.1.0, 0.83 v5.5.0, 0.81 v5.4.0, 0.82 v5.3.0, 0.85 v5.2.0
% 52.14/52.24 % Syntax : Number of formulae : 5211 (1707 unt; 0 def)
% 52.14/52.24 % Number of atoms : 12610 (4532 equ)
% 52.14/52.24 % Maximal formula atoms : 13 ( 2 avg)
% 52.14/52.24 % Number of connectives : 8486 (1087 ~; 158 |; 710 &)
% 52.14/52.24 % ( 875 <=>;5656 =>; 0 <=; 0 <~>)
% 52.14/52.24 % Maximal formula depth : 22 ( 6 avg)
% 52.14/52.24 % Maximal term depth : 19 ( 2 avg)
% 52.14/52.24 % Number of predicates : 143 ( 142 usr; 1 prp; 0-7 aty)
% 52.14/52.24 % Number of functors : 393 ( 393 usr; 62 con; 0-10 aty)
% 52.14/52.24 % Number of variables : 16777 (16648 !; 129 ?)
% 52.14/52.24 % SPC : FOF_THM_RFO_SEQ
% 52.14/52.24
% 52.14/52.24 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 52.14/52.24 % 2011-03-01 12:14:09
% 52.14/52.24 %------------------------------------------------------------------------------
% 52.14/52.24 %----Relevant facts (4983)
% 52.14/52.24 fof(fact_ext,axiom,
% 52.14/52.24 ! [V_g_2,V_f_2] :
% 52.14/52.24 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 52.14/52.24 => V_f_2 = V_g_2 ) ).
% 52.14/52.24
% 52.14/52.24 fof(fact_triple__valid__def2,axiom,
% 52.14/52.24 ! [V_Q_2,V_c_2,V_P_2,V_n_2,T_b] :
% 52.14/52.24 ( 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))
% 52.14/52.24 <=> ! [B_Z,B_s] :
% 52.14/52.24 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
% 52.14/52.24 => ! [B_s_H] :
% 52.14/52.24 ( c_Natural_Oevaln(V_c_2,B_s,V_n_2,B_s_H)
% 52.14/52.24 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s_H)) ) ) ) ).
% 52.14/52.24
% 52.14/52.24 fof(fact_triple__valid__Suc,axiom,
% 52.14/52.24 ! [V_t,V_n,T_a] :
% 52.14/52.24 ( c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n),V_t)
% 52.14/52.24 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n,V_t) ) ).
% 52.14/52.24
% 52.14/52.24 fof(fact_evaln_OSkip,axiom,
% 52.14/52.24 ! [V_n,V_s] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_s) ).
% 52.14/52.24
% 52.14/52.24 fof(fact_evaln__elim__cases_I1_J,axiom,
% 52.14/52.24 ! [V_t,V_n,V_s] :
% 52.14/52.24 ( c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t)
% 52.14/52.24 => V_t = V_s ) ).
% 52.14/52.24
% 52.14/52.24 fof(fact_hoare__valids__def,axiom,
% 52.14/52.24 ! [V_tsa_2,V_Ga_2,T_b] :
% 52.14/52.24 ( c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,V_tsa_2)
% 52.14/52.24 <=> ! [B_n] :
% 52.14/52.24 ( ! [B_x] :
% 52.14/52.24 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_Ga_2))
% 52.14/52.24 => c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x) )
% 52.14/52.24 => ! [B_x] :
% 52.14/52.24 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_tsa_2))
% 52.14/52.24 => c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x) ) ) ) ).
% 52.14/52.24
% 52.14/52.24 fof(fact_evaln_OSemi,axiom,
% 52.14/52.24 ! [V_s2,V_c1,V_s1,V_n,V_s0,V_c0] :
% 52.14/52.24 ( c_Natural_Oevaln(V_c0,V_s0,V_n,V_s1)
% 52.14/52.24 => ( c_Natural_Oevaln(V_c1,V_s1,V_n,V_s2)
% 52.14/52.24 => c_Natural_Oevaln(c_Com_Ocom_OSemi(V_c0,V_c1),V_s0,V_n,V_s2) ) ) ).
% 52.14/52.24
% 52.14/52.24 fof(fact_evaln_OIfFalse,axiom,
% 52.14/52.24 ! [V_c0_2,V_s1_2,V_n_2,V_c1_2,V_s_2,V_b_2] :
% 52.14/52.25 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 52.14/52.25 => ( c_Natural_Oevaln(V_c1_2,V_s_2,V_n_2,V_s1_2)
% 52.14/52.25 => 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) ) ) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_evaln_OIfTrue,axiom,
% 52.14/52.25 ! [V_c1_2,V_s1_2,V_n_2,V_c0_2,V_s_2,V_b_2] :
% 52.14/52.25 ( hBOOL(hAPP(V_b_2,V_s_2))
% 52.14/52.25 => ( c_Natural_Oevaln(V_c0_2,V_s_2,V_n_2,V_s1_2)
% 52.14/52.25 => 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) ) ) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_evaln__elim__cases_I5_J,axiom,
% 52.14/52.25 ! [V_t_2,V_n_2,V_s_2,V_c2_2,V_c1_2,V_b_2] :
% 52.14/52.25 ( 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)
% 52.14/52.25 => ( ( hBOOL(hAPP(V_b_2,V_s_2))
% 52.14/52.25 => ~ c_Natural_Oevaln(V_c1_2,V_s_2,V_n_2,V_t_2) )
% 52.14/52.25 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 52.14/52.25 => ~ c_Natural_Oevaln(V_c2_2,V_s_2,V_n_2,V_t_2) ) ) ) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_evaln_OWhileFalse,axiom,
% 52.14/52.25 ! [V_n_2,V_c_2,V_s_2,V_b_2] :
% 52.14/52.25 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 52.14/52.25 => c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),V_s_2,V_n_2,V_s_2) ) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_evaln_OWhileTrue,axiom,
% 52.14/52.25 ! [V_s2_2,V_s1_2,V_n_2,V_c_2,V_s0_2,V_b_2] :
% 52.14/52.25 ( hBOOL(hAPP(V_b_2,V_s0_2))
% 52.14/52.25 => ( c_Natural_Oevaln(V_c_2,V_s0_2,V_n_2,V_s1_2)
% 52.14/52.25 => ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),V_s1_2,V_n_2,V_s2_2)
% 52.14/52.25 => c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),V_s0_2,V_n_2,V_s2_2) ) ) ) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_evaln_Oequations_I1_J,axiom,
% 52.14/52.25 ! [V_a2,V_a1] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_a1,V_a2,V_a1) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_triple_Oinject,axiom,
% 52.14/52.25 ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_b] :
% 52.14/52.25 ( 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)
% 52.14/52.25 <=> ( V_fun1_2 = V_fun1_H_2
% 52.14/52.25 & V_com_2 = V_com_H_2
% 52.14/52.25 & V_fun2_2 = V_fun2_H_2 ) ) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_triples__valid__Suc,axiom,
% 52.14/52.25 ! [V_n_2,V_tsa_2,T_b] :
% 52.14/52.25 ( ! [B_x] :
% 52.14/52.25 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_tsa_2))
% 52.14/52.25 => c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),B_x) )
% 52.14/52.25 => ! [B_x] :
% 52.14/52.25 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_tsa_2))
% 52.14/52.25 => c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,B_x) ) ) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_evaln__Suc,axiom,
% 52.14/52.25 ! [V_s_H,V_n,V_s,V_c] :
% 52.14/52.25 ( c_Natural_Oevaln(V_c,V_s,V_n,V_s_H)
% 52.14/52.25 => c_Natural_Oevaln(V_c,V_s,hAPP(c_Nat_OSuc,V_n),V_s_H) ) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_evaln_Oequations_I8_J,axiom,
% 52.14/52.25 ! [V_a6_2,V_a4_2,V_a2_2,V_a3_2,V_a1_2] :
% 52.14/52.25 ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),V_a2_2,V_a4_2,V_a6_2)
% 52.14/52.25 <=> ( ( V_a6_2 = V_a2_2
% 52.14/52.25 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
% 52.14/52.25 | ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 52.14/52.25 & ? [B_s1] :
% 52.14/52.25 ( c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,B_s1)
% 52.14/52.25 & c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),B_s1,V_a4_2,V_a6_2) ) ) ) ) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_evaln_Oequations_I7_J,axiom,
% 52.14/52.25 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2] :
% 52.14/52.25 ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),V_a2_2,V_a4_2,V_a2_2)
% 52.14/52.25 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 52.14/52.25 => ? [B_s1] :
% 52.14/52.25 ( c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,B_s1)
% 52.14/52.25 & c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),B_s1,V_a4_2,V_a2_2) ) ) ) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_evaln_Oequations_I6_J,axiom,
% 52.14/52.25 ! [V_a5_2,V_a4_2,V_a2_2,V_a3_2,V_a6_2,V_a1_2] :
% 52.14/52.25 ( 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)
% 52.14/52.25 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 52.14/52.25 & c_Natural_Oevaln(V_a6_2,V_a2_2,V_a4_2,V_a5_2) )
% 52.14/52.25 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 52.14/52.25 & c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,V_a5_2) ) ) ) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_evaln_Oequations_I5_J,axiom,
% 52.14/52.25 ! [V_a5_2,V_a4_2,V_a2_2,V_a6_2,V_a3_2,V_a1_2] :
% 52.14/52.25 ( 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)
% 52.14/52.25 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 52.14/52.25 & c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,V_a5_2) )
% 52.14/52.25 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 52.14/52.25 & c_Natural_Oevaln(V_a6_2,V_a2_2,V_a4_2,V_a5_2) ) ) ) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_evaln_Oequations_I4_J,axiom,
% 52.14/52.25 ! [V_a6_2,V_a3_2,V_a2_2,V_a5_2,V_a1_2] :
% 52.14/52.25 ( c_Natural_Oevaln(c_Com_Ocom_OSemi(V_a1_2,V_a5_2),V_a2_2,V_a3_2,V_a6_2)
% 52.14/52.25 <=> ? [B_s1] :
% 52.14/52.25 ( c_Natural_Oevaln(V_a1_2,V_a2_2,V_a3_2,B_s1)
% 52.14/52.25 & c_Natural_Oevaln(V_a5_2,B_s1,V_a3_2,V_a6_2) ) ) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_com_Osimps_I12_J,axiom,
% 52.14/52.25 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_com_Osimps_I13_J,axiom,
% 52.14/52.25 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ).
% 52.14/52.25
% 52.14/52.25 fof(fact_com_Osimps_I14_J,axiom,
% 52.14/52.25 ! [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) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_com_Osimps_I15_J,axiom,
% 52.14/52.25 ! [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 ).
% 52.14/52.25
% 52.14/52.25 fof(fact_com_Osimps_I44_J,axiom,
% 52.14/52.25 ! [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) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_com_Osimps_I45_J,axiom,
% 52.14/52.25 ! [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) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_com_Osimps_I16_J,axiom,
% 52.14/52.25 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_com_Osimps_I17_J,axiom,
% 52.14/52.25 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ).
% 52.14/52.25
% 52.14/52.25 fof(fact_com_Osimps_I46_J,axiom,
% 52.14/52.25 ! [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) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_com_Osimps_I47_J,axiom,
% 52.14/52.25 ! [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) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_com_Osimps_I53_J,axiom,
% 52.14/52.25 ! [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) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_com_Osimps_I5_J,axiom,
% 52.14/52.25 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] :
% 52.14/52.25 ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2)
% 52.14/52.25 <=> ( V_fun_2 = V_fun_H_2
% 52.14/52.25 & V_com_2 = V_com_H_2 ) ) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_com_Osimps_I4_J,axiom,
% 52.14/52.25 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] :
% 52.14/52.25 ( 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)
% 52.14/52.25 <=> ( V_fun_2 = V_fun_H_2
% 52.14/52.25 & V_com1_2 = V_com1_H_2
% 52.14/52.25 & V_com2_2 = V_com2_H_2 ) ) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_com_Osimps_I3_J,axiom,
% 52.14/52.25 ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] :
% 52.14/52.25 ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2)
% 52.14/52.25 <=> ( V_com1_2 = V_com1_H_2
% 52.14/52.25 & V_com2_2 = V_com2_H_2 ) ) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_com_Osimps_I52_J,axiom,
% 52.14/52.25 ! [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) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_triple_Osimps_I2_J,axiom,
% 52.14/52.25 ! [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) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_triple_Orecs,axiom,
% 52.14/52.25 ! [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) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_evaln__elim__cases_I4_J,axiom,
% 52.14/52.25 ! [V_t,V_n,V_s,V_c2,V_c1] :
% 52.14/52.25 ( c_Natural_Oevaln(c_Com_Ocom_OSemi(V_c1,V_c2),V_s,V_n,V_t)
% 52.14/52.25 => ~ ! [B_s1] :
% 52.14/52.25 ( c_Natural_Oevaln(V_c1,V_s,V_n,B_s1)
% 52.14/52.25 => ~ c_Natural_Oevaln(V_c2,B_s1,V_n,V_t) ) ) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_Suc__inject,axiom,
% 52.14/52.25 ! [V_y,V_x] :
% 52.14/52.25 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y)
% 52.14/52.25 => V_x = V_y ) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_nat_Oinject,axiom,
% 52.14/52.25 ! [V_nat_H_2,V_nat_2] :
% 52.14/52.25 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2)
% 52.14/52.25 <=> V_nat_2 = V_nat_H_2 ) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_Suc__n__not__n,axiom,
% 52.14/52.25 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ).
% 52.14/52.25
% 52.14/52.25 fof(fact_n__not__Suc__n,axiom,
% 52.14/52.25 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_evaln__WHILE__case,axiom,
% 52.14/52.25 ! [V_t_2,V_n_2,V_s_2,V_c_2,V_b_2] :
% 52.14/52.25 ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),V_s_2,V_n_2,V_t_2)
% 52.14/52.25 => ( ( V_t_2 = V_s_2
% 52.14/52.25 => hBOOL(hAPP(V_b_2,V_s_2)) )
% 52.14/52.25 => ~ ( hBOOL(hAPP(V_b_2,V_s_2))
% 52.14/52.25 => ! [B_s1] :
% 52.14/52.25 ( c_Natural_Oevaln(V_c_2,V_s_2,V_n_2,B_s1)
% 52.14/52.25 => ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),B_s1,V_n_2,V_t_2) ) ) ) ) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_com_Osimps_I64_J,axiom,
% 52.14/52.25 ! [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 ).
% 52.14/52.25
% 52.14/52.25 fof(fact_com_Osimps_I67_J,axiom,
% 52.14/52.25 ! [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) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_com_Osimps_I68_J,axiom,
% 52.14/52.25 ! [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) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_com_Osimps_I69_J,axiom,
% 52.14/52.25 ! [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) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_of__nat__aux_Osimps_I2_J,axiom,
% 52.14/52.25 ! [V_i_2,V_n_2,V_inc_2,T_b] :
% 52.14/52.25 ( class_Rings_Osemiring__1(T_b)
% 52.14/52.25 => 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)) ) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_nat__case__Suc,axiom,
% 52.14/52.25 ! [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) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_nat__rec__Suc,axiom,
% 52.14/52.25 ! [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)) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_com_Orecs_I1_J,axiom,
% 52.14/52.25 ! [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 ).
% 52.14/52.25
% 52.14/52.25 fof(fact_com_Orecs_I4_J,axiom,
% 52.14/52.25 ! [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)) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_com_Orecs_I5_J,axiom,
% 52.14/52.25 ! [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)) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_com_Orecs_I6_J,axiom,
% 52.14/52.25 ! [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)) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_WTs__elim__cases_I4_J,axiom,
% 52.14/52.25 ! [V_c2,V_c1] :
% 52.14/52.25 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c1,V_c2)))
% 52.14/52.25 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1))
% 52.14/52.25 => ~ hBOOL(hAPP(c_Com_OWT,V_c2)) ) ) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_com_Osimps_I66_J,axiom,
% 52.14/52.25 ! [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) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_com_Osimps_I71_J,axiom,
% 52.14/52.25 ! [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) ).
% 52.14/52.25
% 52.14/52.25 fof(fact_WTs__elim__cases_I5_J,axiom,
% 52.14/52.25 ! [V_c2_2,V_c1_2,V_b_2] :
% 52.14/52.25 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2)))
% 52.14/52.25 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1_2))
% 52.14/52.25 => ~ hBOOL(hAPP(c_Com_OWT,V_c2_2)) ) ) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_WTs__elim__cases_I6_J,axiom,
% 52.14/52.26 ! [V_c_2,V_b_2] :
% 52.14/52.26 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_c_2)))
% 52.14/52.26 => hBOOL(hAPP(c_Com_OWT,V_c_2)) ) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_WTs__elim__cases_I3_J,axiom,
% 52.14/52.26 ! [V_c_2,V_a_2,V_Y_2] :
% 52.14/52.26 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2)))
% 52.14/52.26 => hBOOL(hAPP(c_Com_OWT,V_c_2)) ) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I43_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I42_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_WT_Oequations_I3_J,axiom,
% 52.14/52.26 ! [V_a1_2,V_a3_2,V_a2_2] :
% 52.14/52.26 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_a2_2,V_a3_2,V_a1_2)))
% 52.14/52.26 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I7_J,axiom,
% 52.14/52.26 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_fun_2,V_pname_2,V_vname_2] :
% 52.14/52.26 ( 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)
% 52.14/52.26 <=> ( V_vname_2 = V_vname_H_2
% 52.14/52.26 & V_pname_2 = V_pname_H_2
% 52.14/52.26 & V_fun_2 = V_fun_H_2 ) ) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I2_J,axiom,
% 52.14/52.26 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] :
% 52.14/52.26 ( 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)
% 52.14/52.26 <=> ( V_loc_2 = V_loc_H_2
% 52.14/52.26 & V_fun_2 = V_fun_H_2
% 52.14/52.26 & V_com_2 = V_com_H_2 ) ) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Orecs_I8_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Orecs_I3_J,axiom,
% 52.14/52.26 ! [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)) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_WT_OLocal,axiom,
% 52.14/52.26 ! [V_a_2,V_Y_2,V_c_2] :
% 52.14/52.26 ( hBOOL(hAPP(c_Com_OWT,V_c_2))
% 52.14/52.26 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2))) ) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_While,axiom,
% 52.14/52.26 ! [V_b_2,V_c_2] :
% 52.14/52.26 ( hBOOL(hAPP(c_Com_OWT,V_c_2))
% 52.14/52.26 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_c_2))) ) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_WT_Oequations_I6_J,axiom,
% 52.14/52.26 ! [V_a1_2,V_a2_2] :
% 52.14/52.26 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_a2_2,V_a1_2)))
% 52.14/52.26 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_WT_OIf,axiom,
% 52.14/52.26 ! [V_b_2,V_c1_2,V_c0_2] :
% 52.14/52.26 ( hBOOL(hAPP(c_Com_OWT,V_c0_2))
% 52.14/52.26 => ( hBOOL(hAPP(c_Com_OWT,V_c1_2))
% 52.14/52.26 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2))) ) ) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_WT_Oequations_I5_J,axiom,
% 52.14/52.26 ! [V_a2_2,V_a1_2,V_a3_2] :
% 52.14/52.26 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_a3_2,V_a1_2,V_a2_2)))
% 52.14/52.26 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2))
% 52.14/52.26 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_WT_OSemi,axiom,
% 52.14/52.26 ! [V_c1,V_c0] :
% 52.14/52.26 ( hBOOL(hAPP(c_Com_OWT,V_c0))
% 52.14/52.26 => ( hBOOL(hAPP(c_Com_OWT,V_c1))
% 52.14/52.26 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c0,V_c1))) ) ) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_WT_Oequations_I4_J,axiom,
% 52.14/52.26 ! [V_a2_2,V_a1_2] :
% 52.14/52.26 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_a1_2,V_a2_2)))
% 52.14/52.26 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2))
% 52.14/52.26 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_WT_Oequations_I1_J,axiom,
% 52.14/52.26 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_WT_OSkip,axiom,
% 52.14/52.26 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I38_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I61_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I39_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I60_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I36_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I37_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I56_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I57_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I34_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I51_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I35_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I50_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I11_J,axiom,
% 52.14/52.26 ! [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 ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I21_J,axiom,
% 52.14/52.26 ! [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 ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I10_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I20_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_WTs__elim__cases_I8_J,axiom,
% 52.14/52.26 ! [V_a_2,V_P_2,V_X_2] :
% 52.14/52.26 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_P_2,V_a_2)))
% 52.14/52.26 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P_2))) ) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_def__nat__rec__Suc,axiom,
% 52.14/52.26 ! [V_n_2,V_h_2,V_c_2,T_b,V_f_2] :
% 52.14/52.26 ( ! [B_n] : hAPP(V_f_2,B_n) = hAPP(c_Nat_Onat_Onat__rec(T_b,V_c_2,V_h_2),B_n)
% 52.14/52.26 => 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)) ) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_WT_Oequations_I8_J,axiom,
% 52.14/52.26 ! [V_a3_2,V_a1_2,V_a2_2] :
% 52.14/52.26 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_a2_2,V_a1_2,V_a3_2)))
% 52.14/52.26 <=> hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a1_2))) ) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_WT_OCall,axiom,
% 52.14/52.26 ! [V_a_2,V_X_2,V_pn_2] :
% 52.14/52.26 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn_2)))
% 52.14/52.26 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_pn_2,V_a_2))) ) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_of__nat__aux_Osimps_I1_J,axiom,
% 52.14/52.26 ! [V_i_2,V_inc_2,T_b] :
% 52.14/52.26 ( class_Rings_Osemiring__1(T_b)
% 52.14/52.26 => 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 ) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I65_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Orecs_I2_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I70_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_nat__rec__0,axiom,
% 52.14/52.26 ! [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 ).
% 52.14/52.26
% 52.14/52.26 fof(fact_evalc__elim__cases_I1_J,axiom,
% 52.14/52.26 ! [V_t,V_s] :
% 52.14/52.26 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_t))
% 52.14/52.26 => V_t = V_s ) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_evalc_OSkip,axiom,
% 52.14/52.26 ! [V_s] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s)) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_evalc_OWhileFalse,axiom,
% 52.14/52.26 ! [V_c_2,V_s_2,V_b_2] :
% 52.14/52.26 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 52.14/52.26 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s_2),V_s_2)) ) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_evalc_OWhileTrue,axiom,
% 52.14/52.26 ! [V_s2_2,V_s1_2,V_c_2,V_s0_2,V_b_2] :
% 52.14/52.26 ( hBOOL(hAPP(V_b_2,V_s0_2))
% 52.14/52.26 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_2),V_s0_2),V_s1_2))
% 52.14/52.26 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s1_2),V_s2_2))
% 52.14/52.26 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s0_2),V_s2_2)) ) ) ) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_evalc_OIfFalse,axiom,
% 52.14/52.26 ! [V_c0_2,V_s1_2,V_c1_2,V_s_2,V_b_2] :
% 52.14/52.26 ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 52.14/52.26 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_s1_2))
% 52.14/52.26 => 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)) ) ) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_evalc_OIfTrue,axiom,
% 52.14/52.26 ! [V_c1_2,V_s1_2,V_c0_2,V_s_2,V_b_2] :
% 52.14/52.26 ( hBOOL(hAPP(V_b_2,V_s_2))
% 52.14/52.26 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0_2),V_s_2),V_s1_2))
% 52.14/52.26 => 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)) ) ) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_evalc__elim__cases_I5_J,axiom,
% 52.14/52.26 ! [V_t_2,V_s_2,V_c2_2,V_c1_2,V_b_2] :
% 52.14/52.26 ( 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))
% 52.14/52.26 => ( ( hBOOL(hAPP(V_b_2,V_s_2))
% 52.14/52.26 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_t_2)) )
% 52.14/52.26 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2))
% 52.14/52.26 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2_2),V_s_2),V_t_2)) ) ) ) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_evalc_OSemi,axiom,
% 52.14/52.26 ! [V_s2,V_c1,V_s1,V_s0,V_c0] :
% 52.14/52.26 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0),V_s0),V_s1))
% 52.14/52.26 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s1),V_s2))
% 52.14/52.26 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_s2)) ) ) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I1_J,axiom,
% 52.14/52.26 ! [V_fun_H_2,V_vname_H_2,V_fun_2,V_vname_2] :
% 52.14/52.26 ( c_Com_Ocom_OAss(V_vname_2,V_fun_2) = c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2)
% 52.14/52.26 <=> ( V_vname_2 = V_vname_H_2
% 52.14/52.26 & V_fun_2 = V_fun_H_2 ) ) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I6_J,axiom,
% 52.14/52.26 ! [V_pname_H_2,V_pname_2] :
% 52.14/52.26 ( hAPP(c_Com_Ocom_OBODY,V_pname_2) = hAPP(c_Com_Ocom_OBODY,V_pname_H_2)
% 52.14/52.26 <=> V_pname_2 = V_pname_H_2 ) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I30_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I31_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com__det,axiom,
% 52.14/52.26 ! [V_u,V_t,V_s,V_c] :
% 52.14/52.26 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t))
% 52.14/52.26 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_u))
% 52.14/52.26 => V_u = V_t ) ) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_Zero__not__Suc,axiom,
% 52.14/52.26 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_nat_Osimps_I2_J,axiom,
% 52.14/52.26 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_Suc__not__Zero,axiom,
% 52.14/52.26 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_nat_Osimps_I3_J,axiom,
% 52.14/52.26 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_Zero__neq__Suc,axiom,
% 52.14/52.26 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_Suc__neq__Zero,axiom,
% 52.14/52.26 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_evaln__evalc,axiom,
% 52.14/52.26 ! [V_t,V_n,V_s,V_c] :
% 52.14/52.26 ( c_Natural_Oevaln(V_c,V_s,V_n,V_t)
% 52.14/52.26 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) ) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_eval__eq,axiom,
% 52.14/52.26 ! [V_t_2,V_s_2,V_c_2] :
% 52.14/52.26 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_2),V_s_2),V_t_2))
% 52.14/52.26 <=> ? [B_n] : c_Natural_Oevaln(V_c_2,V_s_2,B_n,V_t_2) ) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_Body__triple__valid__0,axiom,
% 52.14/52.26 ! [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)) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_evalc_Oequations_I7_J,axiom,
% 52.14/52.26 ! [V_a2_2,V_a3_2,V_a1_2] :
% 52.14/52.26 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a2_2))
% 52.14/52.26 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 52.14/52.26 => ? [B_s1] :
% 52.14/52.26 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1))
% 52.14/52.26 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a2_2)) ) ) ) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_evalc_Oequations_I8_J,axiom,
% 52.14/52.26 ! [V_a5_2,V_a2_2,V_a3_2,V_a1_2] :
% 52.14/52.26 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a5_2))
% 52.14/52.26 <=> ( ( V_a5_2 = V_a2_2
% 52.14/52.26 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
% 52.14/52.26 | ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 52.14/52.26 & ? [B_s1] :
% 52.14/52.26 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1))
% 52.14/52.26 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a5_2)) ) ) ) ) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_evalc_Oequations_I5_J,axiom,
% 52.14/52.26 ! [V_a4_2,V_a2_2,V_a5_2,V_a3_2,V_a1_2] :
% 52.14/52.26 ( 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))
% 52.14/52.26 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 52.14/52.26 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) )
% 52.14/52.26 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 52.14/52.26 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) ) ) ) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_evalc_Oequations_I6_J,axiom,
% 52.14/52.26 ! [V_a4_2,V_a2_2,V_a3_2,V_a5_2,V_a1_2] :
% 52.14/52.26 ( 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))
% 52.14/52.26 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 52.14/52.26 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) )
% 52.14/52.26 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 52.14/52.26 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) ) ) ) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_evalc_Oequations_I4_J,axiom,
% 52.14/52.26 ! [V_a5_2,V_a2_2,V_a4_2,V_a1_2] :
% 52.14/52.26 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_a1_2,V_a4_2)),V_a2_2),V_a5_2))
% 52.14/52.26 <=> ? [B_s1] :
% 52.14/52.26 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a1_2),V_a2_2),B_s1))
% 52.14/52.26 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a4_2),B_s1),V_a5_2)) ) ) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_evalc_Oequations_I1_J,axiom,
% 52.14/52.26 ! [V_a] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_a),V_a)) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I59_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I58_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I55_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I54_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I49_J,axiom,
% 52.14/52.26 ! [V_com2,V_com1,V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I48_J,axiom,
% 52.14/52.26 ! [V_pname_H,V_com2,V_com1] : c_Com_Ocom_OSemi(V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I40_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I63_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I41_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I62_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I18_J,axiom,
% 52.14/52.26 ! [V_pname_H] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,V_pname_H) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I19_J,axiom,
% 52.14/52.26 ! [V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSKIP ).
% 52.14/52.26
% 52.14/52.26 fof(fact_WT_Oequations_I2_J,axiom,
% 52.14/52.26 ! [V_a2_2,V_a1_2] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(V_a1_2,V_a2_2))) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_WT_OAssign,axiom,
% 52.14/52.26 ! [V_a_2,V_X_2] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(V_X_2,V_a_2))) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I28_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I29_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I26_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I27_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_nat__case__0,axiom,
% 52.14/52.26 ! [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 ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I24_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I25_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I23_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I33_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I22_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I32_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I8_J,axiom,
% 52.14/52.26 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Osimps_I9_J,axiom,
% 52.14/52.26 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) != c_Com_Ocom_OSKIP ).
% 52.14/52.26
% 52.14/52.26 fof(fact_com_Orecs_I7_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_triple_Osize_I1_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_triple_Osize_I2_J,axiom,
% 52.14/52.26 ! [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) ).
% 52.14/52.26
% 52.14/52.26 fof(fact_evalc__elim__cases_I4_J,axiom,
% 52.14/52.26 ! [V_t,V_s,V_c2,V_c1] :
% 52.14/52.26 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1,V_c2)),V_s),V_t))
% 52.14/52.26 => ~ ! [B_s1] :
% 52.14/52.26 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s),B_s1))
% 52.14/52.26 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2),B_s1),V_t)) ) ) ).
% 52.14/52.27
% 52.14/52.27 fof(fact_com_Osize_I1_J,axiom,
% 52.14/52.27 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 52.14/52.27
% 52.14/52.27 fof(fact_com_Osize_I8_J,axiom,
% 52.14/52.27 ! [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) ).
% 52.14/52.27
% 52.14/52.27 fof(fact_com_Osize_I2_J,axiom,
% 52.14/52.27 ! [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) ).
% 52.14/52.27
% 52.14/52.27 fof(fact_com_Osize_I7_J,axiom,
% 52.14/52.27 ! [V_pname] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 52.14/52.27
% 52.14/52.27 fof(fact_com_Osize_I9_J,axiom,
% 52.14/52.27 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 52.14/52.27
% 52.14/52.27 fof(fact_com_Osize_I16_J,axiom,
% 52.14/52.27 ! [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) ).
% 52.14/52.27
% 52.14/52.27 fof(fact_com_Osize_I10_J,axiom,
% 52.14/52.27 ! [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) ).
% 52.14/52.27
% 52.14/52.27 fof(fact_com_Osize_I15_J,axiom,
% 52.14/52.27 ! [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) ).
% 52.14/52.27
% 52.14/52.27 fof(fact_com_Osize_I11_J,axiom,
% 52.14/52.27 ! [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))) ).
% 52.14/52.27
% 52.14/52.27 fof(fact_com_Osize_I12_J,axiom,
% 52.14/52.27 ! [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))) ).
% 52.14/52.27
% 52.14/52.27 fof(fact_com_Osize_I3_J,axiom,
% 52.14/52.27 ! [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))) ).
% 52.14/52.27
% 52.14/52.27 fof(fact_com_Osize_I4_J,axiom,
% 52.14/52.27 ! [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))) ).
% 52.14/52.27
% 52.14/52.27 fof(fact_com_Osize_I13_J,axiom,
% 52.14/52.27 ! [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))) ).
% 52.14/52.27
% 52.14/52.27 fof(fact_com_Osize_I5_J,axiom,
% 52.14/52.27 ! [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))) ).
% 52.14/52.27
% 52.14/52.27 fof(fact_com_Osize_I14_J,axiom,
% 52.14/52.27 ! [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))) ).
% 52.14/52.27
% 52.14/52.27 fof(fact_com_Osize_I6_J,axiom,
% 52.14/52.27 ! [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))) ).
% 52.14/52.27
% 52.14/52.27 fof(fact_evalc_OAssign,axiom,
% 52.23/52.27 ! [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)))) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_evalc__elim__cases_I2_J,axiom,
% 52.23/52.27 ! [V_t_2,V_s_2,V_a_2,V_X_2] :
% 52.23/52.27 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(V_X_2,V_a_2)),V_s_2),V_t_2))
% 52.23/52.27 => V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_evaln_OAssign,axiom,
% 52.23/52.27 ! [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))) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_evaln__elim__cases_I2_J,axiom,
% 52.23/52.27 ! [V_t_2,V_n_2,V_s_2,V_a_2,V_X_2] :
% 52.23/52.27 ( c_Natural_Oevaln(c_Com_Ocom_OAss(V_X_2,V_a_2),V_s_2,V_n_2,V_t_2)
% 52.23/52.27 => V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_nat__add__right__cancel,axiom,
% 52.23/52.27 ! [V_n_2,V_k_2,V_m_2] :
% 52.23/52.27 ( 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)
% 52.23/52.27 <=> V_m_2 = V_n_2 ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_nat__add__left__cancel,axiom,
% 52.23/52.27 ! [V_n_2,V_m_2,V_k_2] :
% 52.23/52.27 ( 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)
% 52.23/52.27 <=> V_m_2 = V_n_2 ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_nat__add__assoc,axiom,
% 52.23/52.27 ! [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)) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_nat__add__left__commute,axiom,
% 52.23/52.27 ! [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)) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_nat__add__commute,axiom,
% 52.23/52.27 ! [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) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_add__eq__self__zero,axiom,
% 52.23/52.27 ! [V_n,V_m] :
% 52.23/52.27 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m
% 52.23/52.27 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_add__is__0,axiom,
% 52.23/52.27 ! [V_n_2,V_m_2] :
% 52.23/52.27 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.27 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.27 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_Nat_Oadd__0__right,axiom,
% 52.23/52.27 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 52.23/52.27
% 52.23/52.27 fof(fact_plus__nat_Oadd__0,axiom,
% 52.23/52.27 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 52.23/52.27
% 52.23/52.27 fof(fact_add__Suc__right,axiom,
% 52.23/52.27 ! [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)) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_add__Suc,axiom,
% 52.23/52.27 ! [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)) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_add__Suc__shift,axiom,
% 52.23/52.27 ! [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)) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_add__is__1,axiom,
% 52.23/52.27 ! [V_n_2,V_m_2] :
% 52.23/52.27 ( 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))
% 52.23/52.27 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 52.23/52.27 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 52.23/52.27 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.27 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_one__is__add,axiom,
% 52.23/52.27 ! [V_n_2,V_m_2] :
% 52.23/52.27 ( 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)
% 52.23/52.27 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 52.23/52.27 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 52.23/52.27 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.27 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_evaln_Oequations_I2_J,axiom,
% 52.23/52.27 ! [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))) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_evalc_Oequations_I2_J,axiom,
% 52.23/52.27 ! [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)))) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_add__0__left,axiom,
% 52.23/52.27 ! [V_a,T_a] :
% 52.23/52.27 ( class_Groups_Omonoid__add(T_a)
% 52.23/52.27 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 52.23/52.27 ! [V_a,T_a] :
% 52.23/52.27 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.27 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_add__0,axiom,
% 52.23/52.27 ! [V_a,T_a] :
% 52.23/52.27 ( class_Groups_Ocomm__monoid__add(T_a)
% 52.23/52.27 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_double__zero__sym,axiom,
% 52.23/52.27 ! [V_a_2,T_b] :
% 52.23/52.27 ( class_Groups_Olinordered__ab__group__add(T_b)
% 52.23/52.27 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)
% 52.23/52.27 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_add__0__right,axiom,
% 52.23/52.27 ! [V_a,T_a] :
% 52.23/52.27 ( class_Groups_Omonoid__add(T_a)
% 52.23/52.27 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 52.23/52.27 ! [V_a,T_a] :
% 52.23/52.27 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.27 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_add_Ocomm__neutral,axiom,
% 52.23/52.27 ! [V_a,T_a] :
% 52.23/52.27 ( class_Groups_Ocomm__monoid__add(T_a)
% 52.23/52.27 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_add__0__iff,axiom,
% 52.23/52.27 ! [V_a_2,V_b_2,T_b] :
% 52.23/52.27 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 52.23/52.27 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)
% 52.23/52.27 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_double__eq__0__iff,axiom,
% 52.23/52.27 ! [V_a_2,T_b] :
% 52.23/52.27 ( class_Groups_Olinordered__ab__group__add(T_b)
% 52.23/52.27 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.27 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_nat_Osize_I2_J,axiom,
% 52.23/52.27 ! [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))) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_nat_Osize_I4_J,axiom,
% 52.23/52.27 ! [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))) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_nat__size,axiom,
% 52.23/52.27 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ).
% 52.23/52.27
% 52.23/52.27 fof(fact_nat_Osize_I3_J,axiom,
% 52.23/52.27 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) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_nat_Osize_I1_J,axiom,
% 52.23/52.27 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_zero__reorient,axiom,
% 52.23/52.27 ! [V_x_2,T_b] :
% 52.23/52.27 ( class_Groups_Ozero(T_b)
% 52.23/52.27 => ( c_Groups_Ozero__class_Ozero(T_b) = V_x_2
% 52.23/52.27 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_add__right__imp__eq,axiom,
% 52.23/52.27 ! [V_c,V_a,V_b,T_a] :
% 52.23/52.27 ( class_Groups_Ocancel__semigroup__add(T_a)
% 52.23/52.27 => ( 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)
% 52.23/52.27 => V_b = V_c ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_add__imp__eq,axiom,
% 52.23/52.27 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.27 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 52.23/52.27 => ( 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)
% 52.23/52.27 => V_b = V_c ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_add__left__imp__eq,axiom,
% 52.23/52.27 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.27 ( class_Groups_Ocancel__semigroup__add(T_a)
% 52.23/52.27 => ( 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)
% 52.23/52.27 => V_b = V_c ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 52.23/52.27 ! [V_d,V_c,V_b,V_a,T_a] :
% 52.23/52.27 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.27 => 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)) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_add__right__cancel,axiom,
% 52.23/52.27 ! [V_c_2,V_a_2,V_b_2,T_b] :
% 52.23/52.27 ( class_Groups_Ocancel__semigroup__add(T_b)
% 52.23/52.27 => ( 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)
% 52.23/52.27 <=> V_b_2 = V_c_2 ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_add__left__cancel,axiom,
% 52.23/52.27 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 52.23/52.27 ( class_Groups_Ocancel__semigroup__add(T_b)
% 52.23/52.27 => ( 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)
% 52.23/52.27 <=> V_b_2 = V_c_2 ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 52.23/52.27 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.27 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.27 => 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) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 52.23/52.27 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.27 ( class_Groups_Oab__semigroup__add(T_a)
% 52.23/52.27 => 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)) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 52.23/52.27 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.27 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.27 => 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)) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 52.23/52.27 ! [V_d,V_c,V_a,T_a] :
% 52.23/52.27 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.27 => 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) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 52.23/52.27 ! [V_d,V_c,V_a,T_a] :
% 52.23/52.27 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.27 => 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)) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 52.23/52.27 ! [V_c,V_a,T_a] :
% 52.23/52.27 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.27 => 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) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_bool_Osize_I2_J,axiom,
% 52.23/52.27 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_bool_Osize_I1_J,axiom,
% 52.23/52.27 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_bool_Osize_I4_J,axiom,
% 52.23/52.27 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_bool_Osize_I3_J,axiom,
% 52.23/52.27 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_Body__triple__valid__Suc,axiom,
% 52.23/52.27 ! [V_Q_2,V_pn_2,V_P_2,V_n_2,T_b] :
% 52.23/52.27 ( 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))
% 52.23/52.27 <=> 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)) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_def__nat__rec__0,axiom,
% 52.23/52.27 ! [V_h_2,V_c_2,T_b,V_f_2] :
% 52.23/52.27 ( ! [B_n] : hAPP(V_f_2,B_n) = hAPP(c_Nat_Onat_Onat__rec(T_b,V_c_2,V_h_2),B_n)
% 52.23/52.27 => hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_c_2 ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_evalc__WHILE__case,axiom,
% 52.23/52.27 ! [V_t_2,V_s_2,V_c_2,V_b_2] :
% 52.23/52.27 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s_2),V_t_2))
% 52.23/52.27 => ( ( V_t_2 = V_s_2
% 52.23/52.27 => hBOOL(hAPP(V_b_2,V_s_2)) )
% 52.23/52.27 => ~ ( hBOOL(hAPP(V_b_2,V_s_2))
% 52.23/52.27 => ! [B_s1] :
% 52.23/52.27 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_2),V_s_2),B_s1))
% 52.23/52.27 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),B_s1),V_t_2)) ) ) ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_pair__box_Osize_I1_J,axiom,
% 52.23/52.27 ! [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))) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_evalc__evaln,axiom,
% 52.23/52.27 ! [V_t,V_s,V_c] :
% 52.23/52.27 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t))
% 52.23/52.27 => ? [B_n] : c_Natural_Oevaln(V_c,V_s,B_n,V_t) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_sum_Osize_I1_J,axiom,
% 52.23/52.27 ! [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))) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_sum_Osize_I2_J,axiom,
% 52.23/52.27 ! [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))) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_evalc_OBody,axiom,
% 52.23/52.27 ! [V_s1,V_s0,V_pn] :
% 52.23/52.27 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_s0),V_s1))
% 52.23/52.27 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_pn)),V_s0),V_s1)) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_evalc__elim__cases_I6_J,axiom,
% 52.23/52.27 ! [V_s1,V_s,V_P] :
% 52.23/52.27 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_s1))
% 52.23/52.27 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P))),V_s),V_s1)) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_evaln_OBody,axiom,
% 52.23/52.27 ! [V_s1,V_n,V_s0,V_pn] :
% 52.23/52.27 ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn)),V_s0,V_n,V_s1)
% 52.23/52.27 => c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_pn),V_s0,hAPP(c_Nat_OSuc,V_n),V_s1) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_pair__box_Oinject,axiom,
% 52.23/52.27 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 52.23/52.27 ( 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)
% 52.23/52.27 <=> ( V_a_2 = V_a_H_2
% 52.23/52.27 & V_b_2 = V_b_H_2 ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_evalc_Oequations_I9_J,axiom,
% 52.23/52.27 ! [V_a3_2,V_a2_2,V_a1_2] :
% 52.23/52.27 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),V_a3_2))
% 52.23/52.27 <=> 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)) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_evaln_Oequations_I9_J,axiom,
% 52.23/52.27 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] :
% 52.23/52.27 ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_a1_2),V_a2_2,hAPP(c_Nat_OSuc,V_a3_2),V_a4_2)
% 52.23/52.27 <=> 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) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_pair__box_Osize_I2_J,axiom,
% 52.23/52.27 ! [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) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_pair__box_Orecs,axiom,
% 52.23/52.27 ! [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) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_pair__box_Osimps_I2_J,axiom,
% 52.23/52.27 ! [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) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_evaln__elim__cases_I6_J,axiom,
% 52.23/52.27 ! [V_s1,V_n,V_s,V_P] :
% 52.23/52.27 ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_P),V_s,V_n,V_s1)
% 52.23/52.27 => ~ ! [B_n] :
% 52.23/52.27 ( V_n = hAPP(c_Nat_OSuc,B_n)
% 52.23/52.27 => ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P)),V_s,B_n,V_s1) ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_Inl__not__Inr,axiom,
% 52.23/52.27 ! [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) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_sum_Osimps_I3_J,axiom,
% 52.23/52.27 ! [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) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_Inr__not__Inl,axiom,
% 52.23/52.27 ! [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) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_sum_Osimps_I4_J,axiom,
% 52.23/52.27 ! [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) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_sum_Osize_I3_J,axiom,
% 52.23/52.27 ! [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) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_sum_Osize_I4_J,axiom,
% 52.23/52.27 ! [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) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_sum_Osimps_I1_J,axiom,
% 52.23/52.27 ! [V_a_H_2,V_a_2,T_c,T_b] :
% 52.23/52.27 ( 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)
% 52.23/52.27 <=> V_a_2 = V_a_H_2 ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_Inr__inject,axiom,
% 52.23/52.27 ! [V_y,V_x,T_a,T_b] :
% 52.23/52.27 ( hAPP(c_Sum__Type_OInr(T_b,T_a),V_x) = hAPP(c_Sum__Type_OInr(T_b,T_a),V_y)
% 52.23/52.27 => V_x = V_y ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_sum_Osimps_I2_J,axiom,
% 52.23/52.27 ! [V_b_H_2,V_b_2,T_b,T_c] :
% 52.23/52.27 ( 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)
% 52.23/52.27 <=> V_b_2 = V_b_H_2 ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_Inl__inject,axiom,
% 52.23/52.27 ! [V_y,V_x,T_b,T_a] :
% 52.23/52.27 ( hAPP(c_Sum__Type_OInl(T_a,T_b),V_x) = hAPP(c_Sum__Type_OInl(T_a,T_b),V_y)
% 52.23/52.27 => V_x = V_y ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_Projl_Osimps,axiom,
% 52.23/52.27 ! [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 ).
% 52.23/52.27
% 52.23/52.27 fof(fact_Projr_Osimps,axiom,
% 52.23/52.27 ! [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 ).
% 52.23/52.27
% 52.23/52.27 fof(fact_sum_Orecs_I1_J,axiom,
% 52.23/52.27 ! [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) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_sum_Orecs_I2_J,axiom,
% 52.23/52.27 ! [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) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_Suml_Osimps,axiom,
% 52.23/52.27 ! [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) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_Sumr_Osimps,axiom,
% 52.23/52.27 ! [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) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_WT_OBody,axiom,
% 52.23/52.27 ! [V_pn] :
% 52.23/52.27 ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_ONone(tc_Com_Ocom)
% 52.23/52.27 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn))) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_WT_Oequations_I7_J,axiom,
% 52.23/52.27 ! [V_a_2] :
% 52.23/52.27 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a_2)))
% 52.23/52.27 <=> ? [B_y] : hAPP(c_Com_Obody,V_a_2) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_zero__less__Suc,axiom,
% 52.23/52.27 ! [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))) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_not0__implies__Suc,axiom,
% 52.23/52.27 ! [V_n] :
% 52.23/52.27 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.27 => ? [B_m] : V_n = hAPP(c_Nat_OSuc,B_m) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_nat__induct,axiom,
% 52.23/52.27 ! [V_n_2,V_P_2] :
% 52.23/52.27 ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 52.23/52.27 => ( ! [B_n] :
% 52.23/52.27 ( hBOOL(hAPP(V_P_2,B_n))
% 52.23/52.27 => hBOOL(hAPP(V_P_2,hAPP(c_Nat_OSuc,B_n))) )
% 52.23/52.27 => hBOOL(hAPP(V_P_2,V_n_2)) ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_less__zeroE,axiom,
% 52.23/52.27 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_lessI,axiom,
% 52.23/52.27 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_Suc__mono,axiom,
% 52.23/52.27 ! [V_n,V_m] :
% 52.23/52.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 52.23/52.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_nat__less__cases,axiom,
% 52.23/52.27 ! [V_P_2,V_n_2,V_m_2] :
% 52.23/52.27 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 52.23/52.27 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 52.23/52.27 => ( ( V_m_2 = V_n_2
% 52.23/52.27 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 52.23/52.27 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 52.23/52.27 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 52.23/52.27 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_less__not__refl3,axiom,
% 52.23/52.27 ! [V_t,V_s] :
% 52.23/52.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t))
% 52.23/52.27 => V_s != V_t ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_less__not__refl2,axiom,
% 52.23/52.27 ! [V_m,V_n] :
% 52.23/52.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 52.23/52.27 => V_m != V_n ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_less__irrefl__nat,axiom,
% 52.23/52.27 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_linorder__neqE__nat,axiom,
% 52.23/52.27 ! [V_y,V_x] :
% 52.23/52.27 ( V_x != V_y
% 52.23/52.27 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 52.23/52.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_nat__neq__iff,axiom,
% 52.23/52.27 ! [V_n_2,V_m_2] :
% 52.23/52.27 ( V_m_2 != V_n_2
% 52.23/52.27 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 52.23/52.27 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_less__not__refl,axiom,
% 52.23/52.27 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_Suml__inject,axiom,
% 52.23/52.27 ! [V_g_2,V_f_2,T_c,T_d,T_b] :
% 52.23/52.27 ( 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)
% 52.23/52.27 => V_f_2 = V_g_2 ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_Sumr__inject,axiom,
% 52.23/52.27 ! [V_g_2,V_f_2,T_b,T_d,T_c] :
% 52.23/52.27 ( 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)
% 52.23/52.27 => V_f_2 = V_g_2 ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_add__less__cancel__right,axiom,
% 52.23/52.27 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 52.23/52.27 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 52.23/52.27 => ( 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)))
% 52.23/52.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_add__less__cancel__left,axiom,
% 52.23/52.27 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 52.23/52.27 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 52.23/52.27 => ( 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)))
% 52.23/52.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_add__strict__right__mono,axiom,
% 52.23/52.27 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.27 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 52.23/52.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 52.23/52.27 => 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))) ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_add__strict__left__mono,axiom,
% 52.23/52.27 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.27 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 52.23/52.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 52.23/52.27 => 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))) ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_add__strict__mono,axiom,
% 52.23/52.27 ! [V_d,V_c,V_b,V_a,T_a] :
% 52.23/52.27 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 52.23/52.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 52.23/52.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 52.23/52.27 => 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))) ) ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_add__less__imp__less__right,axiom,
% 52.23/52.27 ! [V_b,V_c,V_a,T_a] :
% 52.23/52.27 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 52.23/52.27 => ( 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)))
% 52.23/52.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_add__less__imp__less__left,axiom,
% 52.23/52.27 ! [V_b,V_a,V_c,T_a] :
% 52.23/52.27 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 52.23/52.27 => ( 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)))
% 52.23/52.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_gr0I,axiom,
% 52.23/52.27 ! [V_n] :
% 52.23/52.27 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_gr__implies__not0,axiom,
% 52.23/52.27 ! [V_n,V_m] :
% 52.23/52.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 52.23/52.27 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_less__nat__zero__code,axiom,
% 52.23/52.27 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_neq0__conv,axiom,
% 52.23/52.27 ! [V_n_2] :
% 52.23/52.27 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_not__less0,axiom,
% 52.23/52.27 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_not__less__eq,axiom,
% 52.23/52.27 ! [V_n_2,V_m_2] :
% 52.23/52.27 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 52.23/52.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_less__Suc__eq,axiom,
% 52.23/52.27 ! [V_n_2,V_m_2] :
% 52.23/52.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 52.23/52.27 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 52.23/52.27 | V_m_2 = V_n_2 ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_Suc__less__eq,axiom,
% 52.23/52.27 ! [V_n_2,V_m_2] :
% 52.23/52.27 ( 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)))
% 52.23/52.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_not__less__less__Suc__eq,axiom,
% 52.23/52.27 ! [V_m_2,V_n_2] :
% 52.23/52.27 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 52.23/52.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 52.23/52.27 <=> V_n_2 = V_m_2 ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_less__antisym,axiom,
% 52.23/52.27 ! [V_m,V_n] :
% 52.23/52.27 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 52.23/52.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m)))
% 52.23/52.27 => V_m = V_n ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_less__SucI,axiom,
% 52.23/52.27 ! [V_n,V_m] :
% 52.23/52.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 52.23/52.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_Suc__lessI,axiom,
% 52.23/52.27 ! [V_n,V_m] :
% 52.23/52.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 52.23/52.27 => ( hAPP(c_Nat_OSuc,V_m) != V_n
% 52.23/52.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_less__trans__Suc,axiom,
% 52.23/52.27 ! [V_k,V_j,V_i] :
% 52.23/52.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 52.23/52.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 52.23/52.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_less__SucE,axiom,
% 52.23/52.27 ! [V_n,V_m] :
% 52.23/52.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 52.23/52.27 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 52.23/52.27 => V_m = V_n ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_Suc__lessD,axiom,
% 52.23/52.27 ! [V_n,V_m] :
% 52.23/52.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 52.23/52.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_Suc__less__SucD,axiom,
% 52.23/52.27 ! [V_n,V_m] :
% 52.23/52.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))
% 52.23/52.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_add__lessD1,axiom,
% 52.23/52.27 ! [V_k,V_j,V_i] :
% 52.23/52.27 ( 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))
% 52.23/52.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_less__add__eq__less,axiom,
% 52.23/52.27 ! [V_n,V_m,V_l,V_k] :
% 52.23/52.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 52.23/52.27 => ( 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)
% 52.23/52.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_add__less__mono,axiom,
% 52.23/52.27 ! [V_l,V_k,V_j,V_i] :
% 52.23/52.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 52.23/52.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 52.23/52.27 => 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))) ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_add__less__mono1,axiom,
% 52.23/52.27 ! [V_k,V_j,V_i] :
% 52.23/52.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 52.23/52.27 => 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))) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_trans__less__add2,axiom,
% 52.23/52.27 ! [V_m,V_j,V_i] :
% 52.23/52.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 52.23/52.27 => 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))) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_trans__less__add1,axiom,
% 52.23/52.27 ! [V_m,V_j,V_i] :
% 52.23/52.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 52.23/52.27 => 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))) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_nat__add__left__cancel__less,axiom,
% 52.23/52.27 ! [V_n_2,V_m_2,V_k_2] :
% 52.23/52.27 ( 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)))
% 52.23/52.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_not__add__less2,axiom,
% 52.23/52.27 ! [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)) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_not__add__less1,axiom,
% 52.23/52.27 ! [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)) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_add__neg__neg,axiom,
% 52.23/52.27 ! [V_b,V_a,T_a] :
% 52.23/52.27 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 52.23/52.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.27 => 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))) ) ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_add__pos__pos,axiom,
% 52.23/52.27 ! [V_b,V_a,T_a] :
% 52.23/52.27 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 52.23/52.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 52.23/52.27 => 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))) ) ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 52.23/52.27 ! [V_a_2,T_b] :
% 52.23/52.27 ( class_Groups_Olinordered__ab__group__add(T_b)
% 52.23/52.27 => ( 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)))
% 52.23/52.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_even__less__0__iff,axiom,
% 52.23/52.27 ! [V_a_2,T_b] :
% 52.23/52.27 ( class_Rings_Olinordered__idom(T_b)
% 52.23/52.27 => ( 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)))
% 52.23/52.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 52.23/52.27 ! [V_a_2,T_b] :
% 52.23/52.27 ( class_Groups_Olinordered__ab__group__add(T_b)
% 52.23/52.27 => ( 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),V_a_2),V_a_2)))
% 52.23/52.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_less__Suc__eq__0__disj,axiom,
% 52.23/52.27 ! [V_n_2,V_m_2] :
% 52.23/52.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 52.23/52.27 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.27 | ? [B_j] :
% 52.23/52.27 ( V_m_2 = hAPP(c_Nat_OSuc,B_j)
% 52.23/52.27 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_less__Suc0,axiom,
% 52.23/52.27 ! [V_n_2] :
% 52.23/52.27 ( 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))))
% 52.23/52.27 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_gr0__conv__Suc,axiom,
% 52.23/52.27 ! [V_n_2] :
% 52.23/52.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 52.23/52.27 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_add__gr__0,axiom,
% 52.23/52.27 ! [V_n_2,V_m_2] :
% 52.23/52.27 ( 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)))
% 52.23/52.27 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 52.23/52.27 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_less__iff__Suc__add,axiom,
% 52.23/52.27 ! [V_n_2,V_m_2] :
% 52.23/52.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 52.23/52.27 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_less__add__Suc2,axiom,
% 52.23/52.27 ! [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)))) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_less__add__Suc1,axiom,
% 52.23/52.27 ! [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)))) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_WT__bodiesD,axiom,
% 52.23/52.27 ! [V_b,V_pn] :
% 52.23/52.27 ( c_Com_OWT__bodies
% 52.23/52.27 => ( hAPP(c_Com_Obody,V_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b)
% 52.23/52.27 => hBOOL(hAPP(c_Com_OWT,V_b)) ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_option_Osize_I2_J,axiom,
% 52.23/52.27 ! [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))) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_pos__add__strict,axiom,
% 52.23/52.27 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.27 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 52.23/52.27 => 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))) ) ) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_option_Osize_I1_J,axiom,
% 52.23/52.27 ! [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) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_WTs__elim__cases_I7_J,axiom,
% 52.23/52.27 ! [V_P] :
% 52.23/52.27 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P)))
% 52.23/52.27 => ~ ! [B_y] : hAPP(c_Com_Obody,V_P) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_the_Osimps,axiom,
% 52.23/52.27 ! [V_x,T_a] : hAPP(c_Option_Othe(T_a),hAPP(c_Option_Ooption_OSome(T_a),V_x)) = V_x ).
% 52.23/52.27
% 52.23/52.27 fof(fact_option_Osimps_I2_J,axiom,
% 52.23/52.27 ! [V_a_H,T_a] : c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_option_Osimps_I3_J,axiom,
% 52.23/52.27 ! [V_a_H,T_a] : hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ).
% 52.23/52.27
% 52.23/52.27 fof(fact_not__Some__eq,axiom,
% 52.23/52.27 ! [T_b,V_x_2] :
% 52.23/52.27 ( ! [B_y] : V_x_2 != hAPP(c_Option_Ooption_OSome(T_b),B_y)
% 52.23/52.28 <=> V_x_2 = c_Option_Ooption_ONone(T_b) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_not__None__eq,axiom,
% 52.23/52.28 ! [T_b,V_x_2] :
% 52.23/52.28 ( V_x_2 != c_Option_Ooption_ONone(T_b)
% 52.23/52.28 <=> ? [B_y] : V_x_2 = hAPP(c_Option_Ooption_OSome(T_b),B_y) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_option_Osize_I4_J,axiom,
% 52.23/52.28 ! [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) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_linorder__neqE__linordered__idom,axiom,
% 52.23/52.28 ! [V_y,V_x,T_a] :
% 52.23/52.28 ( class_Rings_Olinordered__idom(T_a)
% 52.23/52.28 => ( V_x != V_y
% 52.23/52.28 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 52.23/52.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_option_Oinject,axiom,
% 52.23/52.28 ! [V_a_H_2,V_a_2,T_b] :
% 52.23/52.28 ( hAPP(c_Option_Ooption_OSome(T_b),V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_a_H_2)
% 52.23/52.28 <=> V_a_2 = V_a_H_2 ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_option_Osize_I3_J,axiom,
% 52.23/52.28 ! [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) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_termination__basic__simps_I2_J,axiom,
% 52.23/52.28 ! [V_y,V_z,V_x] :
% 52.23/52.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z))
% 52.23/52.28 => 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))) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_termination__basic__simps_I1_J,axiom,
% 52.23/52.28 ! [V_z,V_y,V_x] :
% 52.23/52.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 52.23/52.28 => 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))) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_option_Osimps_I5_J,axiom,
% 52.23/52.28 ! [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) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_option_Orecs_I2_J,axiom,
% 52.23/52.28 ! [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) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_option_Osimps_I4_J,axiom,
% 52.23/52.28 ! [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 ).
% 52.23/52.28
% 52.23/52.28 fof(fact_option_Orecs_I1_J,axiom,
% 52.23/52.28 ! [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 ).
% 52.23/52.28
% 52.23/52.28 fof(fact_is__none__code_I2_J,axiom,
% 52.23/52.28 ! [V_x,T_b] : ~ c_Option_Ois__none(T_b,hAPP(c_Option_Ooption_OSome(T_b),V_x)) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_is__none__def,axiom,
% 52.23/52.28 ! [V_x_2,T_b] :
% 52.23/52.28 ( c_Option_Ois__none(T_b,V_x_2)
% 52.23/52.28 <=> V_x_2 = c_Option_Ooption_ONone(T_b) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_is__none__code_I1_J,axiom,
% 52.23/52.28 ! [T_a] : c_Option_Ois__none(T_a,c_Option_Ooption_ONone(T_a)) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_of__nat__0__less__iff,axiom,
% 52.23/52.28 ! [V_n_2,T_b] :
% 52.23/52.28 ( class_Rings_Olinordered__semidom(T_b)
% 52.23/52.28 => ( 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)))
% 52.23/52.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_of__nat__eq__iff,axiom,
% 52.23/52.28 ! [V_n_2,V_m_2,T_b] :
% 52.23/52.28 ( class_Nat_Osemiring__char__0(T_b)
% 52.23/52.28 => ( 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)
% 52.23/52.28 <=> V_m_2 = V_n_2 ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_int__eq__0__conv,axiom,
% 52.23/52.28 ! [V_n_2] :
% 52.23/52.28 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.28 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_int__0,axiom,
% 52.23/52.28 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) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_zless__iff__Suc__zadd,axiom,
% 52.23/52.28 ! [V_z_2,V_w_2] :
% 52.23/52.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 52.23/52.28 <=> ? [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))) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_zless__int,axiom,
% 52.23/52.28 ! [V_n_2,V_m_2] :
% 52.23/52.28 ( 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)))
% 52.23/52.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_zadd__int__left,axiom,
% 52.23/52.28 ! [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) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_zadd__int,axiom,
% 52.23/52.28 ! [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)) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_zero__less__int__conv,axiom,
% 52.23/52.28 ! [V_n_2] :
% 52.23/52.28 ( 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)))
% 52.23/52.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_of__nat__less__0__iff,axiom,
% 52.23/52.28 ! [V_m,T_a] :
% 52.23/52.28 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.28 => ~ 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))) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_of__nat__0,axiom,
% 52.23/52.28 ! [T_a] :
% 52.23/52.28 ( class_Rings_Osemiring__1(T_a)
% 52.23/52.28 => 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) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_of__nat__less__imp__less,axiom,
% 52.23/52.28 ! [V_n,V_m,T_a] :
% 52.23/52.28 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.28 => ( 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)))
% 52.23/52.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_less__imp__of__nat__less,axiom,
% 52.23/52.28 ! [V_n,V_m,T_a] :
% 52.23/52.28 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 52.23/52.28 => 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))) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_of__nat__less__iff,axiom,
% 52.23/52.28 ! [V_n_2,V_m_2,T_b] :
% 52.23/52.28 ( class_Rings_Olinordered__semidom(T_b)
% 52.23/52.28 => ( 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)))
% 52.23/52.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_of__nat__add,axiom,
% 52.23/52.28 ! [V_n,V_m,T_a] :
% 52.23/52.28 ( class_Rings_Osemiring__1(T_a)
% 52.23/52.28 => 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)) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_less__imp__Suc__add,axiom,
% 52.23/52.28 ! [V_n,V_m] :
% 52.23/52.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 52.23/52.28 => ? [B_k] : V_n = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),B_k)) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_less__imp__add__positive,axiom,
% 52.23/52.28 ! [V_j,V_i] :
% 52.23/52.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 52.23/52.28 => ? [B_k] :
% 52.23/52.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_k))
% 52.23/52.28 & hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),B_k) = V_j ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_gr0__implies__Suc,axiom,
% 52.23/52.28 ! [V_n] :
% 52.23/52.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 52.23/52.28 => ? [B_m] : V_n = hAPP(c_Nat_OSuc,B_m) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_lift__Suc__mono__less__iff,axiom,
% 52.23/52.28 ! [V_m_2,V_n_2,V_f_2,T_b] :
% 52.23/52.28 ( class_Orderings_Oorder(T_b)
% 52.23/52.28 => ( ! [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))))
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_n_2)),hAPP(V_f_2,V_m_2)))
% 52.23/52.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_lift__Suc__mono__less,axiom,
% 52.23/52.28 ! [V_n_H_2,V_n_2,V_f_2,T_b] :
% 52.23/52.28 ( class_Orderings_Oorder(T_b)
% 52.23/52.28 => ( ! [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))))
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_n_H_2))
% 52.23/52.28 => 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))) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
% 52.23/52.28 ! [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)) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_transfer__int__nat__relations_I2_J,axiom,
% 52.23/52.28 ! [V_y_2,V_x_2] :
% 52.23/52.28 ( 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)))
% 52.23/52.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_transfer__int__nat__numerals_I1_J,axiom,
% 52.23/52.28 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)) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_order__less__irrefl,axiom,
% 52.23/52.28 ! [V_x,T_a] :
% 52.23/52.28 ( class_Orderings_Opreorder(T_a)
% 52.23/52.28 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_linorder__neq__iff,axiom,
% 52.23/52.28 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.28 ( class_Orderings_Olinorder(T_b)
% 52.23/52.28 => ( V_x_2 != V_y_2
% 52.23/52.28 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 52.23/52.28 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_int__less__0__conv,axiom,
% 52.23/52.28 ! [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))) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_int__int__eq,axiom,
% 52.23/52.28 ! [V_n_2,V_m_2] :
% 52.23/52.28 ( 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)
% 52.23/52.28 <=> V_m_2 = V_n_2 ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_transfer__int__nat__relations_I1_J,axiom,
% 52.23/52.28 ! [V_y_2,V_x_2] :
% 52.23/52.28 ( 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)
% 52.23/52.28 <=> V_x_2 = V_y_2 ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_zadd__0,axiom,
% 52.23/52.28 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ).
% 52.23/52.28
% 52.23/52.28 fof(fact_zadd__0__right,axiom,
% 52.23/52.28 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 52.23/52.28
% 52.23/52.28 fof(fact_zadd__assoc,axiom,
% 52.23/52.28 ! [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)) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_zadd__left__commute,axiom,
% 52.23/52.28 ! [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)) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_zadd__commute,axiom,
% 52.23/52.28 ! [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) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_zless__linear,axiom,
% 52.23/52.28 ! [V_y,V_x] :
% 52.23/52.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y))
% 52.23/52.28 | V_x = V_y
% 52.23/52.28 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_zadd__strict__right__mono,axiom,
% 52.23/52.28 ! [V_k,V_j,V_i] :
% 52.23/52.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 52.23/52.28 => 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))) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_linorder__cases,axiom,
% 52.23/52.28 ! [V_y,V_x,T_a] :
% 52.23/52.28 ( class_Orderings_Olinorder(T_a)
% 52.23/52.28 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 52.23/52.28 => ( V_x != V_y
% 52.23/52.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_order__less__asym,axiom,
% 52.23/52.28 ! [V_y,V_x,T_a] :
% 52.23/52.28 ( class_Orderings_Opreorder(T_a)
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 52.23/52.28 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_xt1_I10_J,axiom,
% 52.23/52.28 ! [V_z,V_x,V_y,T_a] :
% 52.23/52.28 ( class_Orderings_Oorder(T_a)
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 52.23/52.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_order__less__trans,axiom,
% 52.23/52.28 ! [V_z,V_y,V_x,T_a] :
% 52.23/52.28 ( class_Orderings_Opreorder(T_a)
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 52.23/52.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_xt1_I2_J,axiom,
% 52.23/52.28 ! [V_c,V_a,V_b,T_a] :
% 52.23/52.28 ( class_Orderings_Oorder(T_a)
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 52.23/52.28 => ( V_b = V_c
% 52.23/52.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_ord__less__eq__trans,axiom,
% 52.23/52.28 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.28 ( class_Orderings_Oord(T_a)
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 52.23/52.28 => ( V_b = V_c
% 52.23/52.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_xt1_I1_J,axiom,
% 52.23/52.28 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.28 ( class_Orderings_Oorder(T_a)
% 52.23/52.28 => ( V_a = V_b
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b))
% 52.23/52.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_ord__eq__less__trans,axiom,
% 52.23/52.28 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.28 ( class_Orderings_Oord(T_a)
% 52.23/52.28 => ( V_a = V_b
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 52.23/52.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_xt1_I9_J,axiom,
% 52.23/52.28 ! [V_a,V_b,T_a] :
% 52.23/52.28 ( class_Orderings_Oorder(T_a)
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 52.23/52.28 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_order__less__asym_H,axiom,
% 52.23/52.28 ! [V_b,V_a,T_a] :
% 52.23/52.28 ( class_Orderings_Opreorder(T_a)
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 52.23/52.28 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_order__less__imp__not__eq2,axiom,
% 52.23/52.28 ! [V_y,V_x,T_a] :
% 52.23/52.28 ( class_Orderings_Oorder(T_a)
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 52.23/52.28 => V_y != V_x ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_order__less__imp__not__eq,axiom,
% 52.23/52.28 ! [V_y,V_x,T_a] :
% 52.23/52.28 ( class_Orderings_Oorder(T_a)
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 52.23/52.28 => V_x != V_y ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_order__less__imp__not__less,axiom,
% 52.23/52.28 ! [V_y,V_x,T_a] :
% 52.23/52.28 ( class_Orderings_Opreorder(T_a)
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 52.23/52.28 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_order__less__not__sym,axiom,
% 52.23/52.28 ! [V_y,V_x,T_a] :
% 52.23/52.28 ( class_Orderings_Opreorder(T_a)
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 52.23/52.28 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_less__imp__neq,axiom,
% 52.23/52.28 ! [V_y,V_x,T_a] :
% 52.23/52.28 ( class_Orderings_Oorder(T_a)
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 52.23/52.28 => V_x != V_y ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_linorder__neqE,axiom,
% 52.23/52.28 ! [V_y,V_x,T_a] :
% 52.23/52.28 ( class_Orderings_Olinorder(T_a)
% 52.23/52.28 => ( V_x != V_y
% 52.23/52.28 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 52.23/52.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_linorder__antisym__conv3,axiom,
% 52.23/52.28 ! [V_x_2,V_y_2,T_b] :
% 52.23/52.28 ( class_Orderings_Olinorder(T_b)
% 52.23/52.28 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 52.23/52.28 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 52.23/52.28 <=> V_x_2 = V_y_2 ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_linorder__less__linear,axiom,
% 52.23/52.28 ! [V_y,V_x,T_a] :
% 52.23/52.28 ( class_Orderings_Olinorder(T_a)
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 52.23/52.28 | V_x = V_y
% 52.23/52.28 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_not__less__iff__gr__or__eq,axiom,
% 52.23/52.28 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.28 ( class_Orderings_Olinorder(T_b)
% 52.23/52.28 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 52.23/52.28 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 52.23/52.28 | V_x_2 = V_y_2 ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_zero__less__imp__eq__int,axiom,
% 52.23/52.28 ! [V_k] :
% 52.23/52.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 52.23/52.28 => ? [B_n] :
% 52.23/52.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 52.23/52.28 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_of__int__less__0__iff,axiom,
% 52.23/52.28 ! [V_z_2,T_b] :
% 52.23/52.28 ( class_Rings_Olinordered__idom(T_b)
% 52.23/52.28 => ( 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)))
% 52.23/52.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_of__int__0__less__iff,axiom,
% 52.23/52.28 ! [V_z_2,T_b] :
% 52.23/52.28 ( class_Rings_Olinordered__idom(T_b)
% 52.23/52.28 => ( 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)))
% 52.23/52.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_zmult__zless__mono2__lemma,axiom,
% 52.23/52.28 ! [V_k,V_j,V_i] :
% 52.23/52.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 52.23/52.28 => 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))) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_negative__zless__0,axiom,
% 52.23/52.28 ! [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))) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_split__nat,axiom,
% 52.23/52.28 ! [V_i_2,V_P_2] :
% 52.23/52.28 ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2)))
% 52.23/52.28 <=> ( ! [B_n] :
% 52.23/52.28 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
% 52.23/52.28 => hBOOL(hAPP(V_P_2,B_n)) )
% 52.23/52.28 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.28 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_zero__less__nat__eq,axiom,
% 52.23/52.28 ! [V_z_2] :
% 52.23/52.28 ( 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)))
% 52.23/52.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_negative__zless,axiom,
% 52.23/52.28 ! [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))) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_int__Suc,axiom,
% 52.23/52.28 ! [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)) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_odd__less__0,axiom,
% 52.23/52.28 ! [V_z_2] :
% 52.23/52.28 ( 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)))
% 52.23/52.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 52.23/52.28 ! [V_m,V_a,T_a] :
% 52.23/52.28 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.28 => 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) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 52.23/52.28 ! [V_a,V_m,T_a] :
% 52.23/52.28 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.28 => 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) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 52.23/52.28 ! [V_m,T_a] :
% 52.23/52.28 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.28 => 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) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_less__1__mult,axiom,
% 52.23/52.28 ! [V_n,V_m,T_a] :
% 52.23/52.28 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m))
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n))
% 52.23/52.28 => 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))) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_square__eq__iff,axiom,
% 52.23/52.28 ! [V_b_2,V_a_2,T_b] :
% 52.23/52.28 ( class_Rings_Oidom(T_b)
% 52.23/52.28 => ( 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)
% 52.23/52.28 <=> ( V_a_2 = V_b_2
% 52.23/52.28 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_square__eq__1__iff,axiom,
% 52.23/52.28 ! [V_x_2,T_b] :
% 52.23/52.28 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 52.23/52.28 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 52.23/52.28 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_b)
% 52.23/52.28 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_minus__mult__minus,axiom,
% 52.23/52.28 ! [V_b,V_a,T_a] :
% 52.23/52.28 ( class_Rings_Oring(T_a)
% 52.23/52.28 => 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) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_minus__mult__commute,axiom,
% 52.23/52.28 ! [V_b,V_a,T_a] :
% 52.23/52.28 ( class_Rings_Oring(T_a)
% 52.23/52.28 => 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)) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_minus__mult__left,axiom,
% 52.23/52.28 ! [V_b,V_a,T_a] :
% 52.23/52.28 ( class_Rings_Oring(T_a)
% 52.23/52.28 => 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) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_minus__mult__right,axiom,
% 52.23/52.28 ! [V_b,V_a,T_a] :
% 52.23/52.28 ( class_Rings_Oring(T_a)
% 52.23/52.28 => 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)) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 52.23/52.28 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 52.23/52.28 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.28 => 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)) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 52.23/52.28 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 52.23/52.28 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.28 => 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)) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 52.23/52.28 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 52.23/52.28 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.28 => 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))) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 52.23/52.28 ! [V_rx,V_ly,V_lx,T_a] :
% 52.23/52.28 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.28 => 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) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_zmult__assoc,axiom,
% 52.23/52.28 ! [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)) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 52.23/52.28 ! [V_rx,V_ly,V_lx,T_a] :
% 52.23/52.28 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.28 => 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)) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 52.23/52.28 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.28 ( class_Groups_Oab__semigroup__mult(T_a)
% 52.23/52.28 => 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)) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_neg__equal__iff__equal,axiom,
% 52.23/52.28 ! [V_b_2,V_a_2,T_b] :
% 52.23/52.28 ( class_Groups_Ogroup__add(T_b)
% 52.23/52.28 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 52.23/52.28 <=> V_a_2 = V_b_2 ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_of__int__eq__iff,axiom,
% 52.23/52.28 ! [V_z_2,V_w_2,T_b] :
% 52.23/52.28 ( class_Int_Oring__char__0(T_b)
% 52.23/52.28 => ( 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)
% 52.23/52.28 <=> V_w_2 = V_z_2 ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_minus__equation__iff,axiom,
% 52.23/52.28 ! [V_b_2,V_a_2,T_b] :
% 52.23/52.28 ( class_Groups_Ogroup__add(T_b)
% 52.23/52.28 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_b_2
% 52.23/52.28 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) = V_a_2 ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_zmult__zminus,axiom,
% 52.23/52.28 ! [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)) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 52.23/52.28 ! [V_ry,V_rx,V_lx,T_a] :
% 52.23/52.28 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.28 => 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) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 52.23/52.28 ! [V_ry,V_rx,V_lx,T_a] :
% 52.23/52.28 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.28 => 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)) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_equation__minus__iff,axiom,
% 52.23/52.28 ! [V_b_2,V_a_2,T_b] :
% 52.23/52.28 ( class_Groups_Ogroup__add(T_b)
% 52.23/52.28 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 52.23/52.28 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_zmult__commute,axiom,
% 52.23/52.28 ! [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) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 52.23/52.28 ! [V_b,V_a,T_a] :
% 52.23/52.28 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.28 => 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) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_zmult__1__right,axiom,
% 52.23/52.28 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 52.23/52.28
% 52.23/52.28 fof(fact_mult_Ocomm__neutral,axiom,
% 52.23/52.28 ! [V_a,T_a] :
% 52.23/52.28 ( class_Groups_Ocomm__monoid__mult(T_a)
% 52.23/52.28 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 52.23/52.28 ! [V_a,T_a] :
% 52.23/52.28 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.28 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_mult__1__right,axiom,
% 52.23/52.28 ! [V_a,T_a] :
% 52.23/52.28 ( class_Groups_Omonoid__mult(T_a)
% 52.23/52.28 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_one__reorient,axiom,
% 52.23/52.28 ! [V_x_2,T_b] :
% 52.23/52.28 ( class_Groups_Oone(T_b)
% 52.23/52.28 => ( c_Groups_Oone__class_Oone(T_b) = V_x_2
% 52.23/52.28 <=> V_x_2 = c_Groups_Oone__class_Oone(T_b) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_zmult__1,axiom,
% 52.23/52.28 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 52.23/52.28
% 52.23/52.28 fof(fact_mult__1,axiom,
% 52.23/52.28 ! [V_a,T_a] :
% 52.23/52.28 ( class_Groups_Ocomm__monoid__mult(T_a)
% 52.23/52.28 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 52.23/52.28 ! [V_a,T_a] :
% 52.23/52.28 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.28 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_mult__1__left,axiom,
% 52.23/52.28 ! [V_a,T_a] :
% 52.23/52.28 ( class_Groups_Omonoid__mult(T_a)
% 52.23/52.28 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_of__int__mult,axiom,
% 52.23/52.28 ! [V_z,V_w,T_a] :
% 52.23/52.28 ( class_Rings_Oring__1(T_a)
% 52.23/52.28 => 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)) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_of__int__minus,axiom,
% 52.23/52.28 ! [V_z,T_a] :
% 52.23/52.28 ( class_Rings_Oring__1(T_a)
% 52.23/52.28 => 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)) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_zminus__zminus,axiom,
% 52.23/52.28 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ).
% 52.23/52.28
% 52.23/52.28 fof(fact_minus__minus,axiom,
% 52.23/52.28 ! [V_a,T_a] :
% 52.23/52.28 ( class_Groups_Ogroup__add(T_a)
% 52.23/52.28 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
% 52.23/52.28 ! [V_x,T_a] :
% 52.23/52.28 ( class_Rings_Ocomm__ring__1(T_a)
% 52.23/52.28 => 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) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_of__int__1,axiom,
% 52.23/52.28 ! [T_a] :
% 52.23/52.28 ( class_Rings_Oring__1(T_a)
% 52.23/52.28 => 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) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_of__nat__mult,axiom,
% 52.23/52.28 ! [V_n,V_m,T_a] :
% 52.23/52.28 ( class_Rings_Osemiring__1(T_a)
% 52.23/52.28 => 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)) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_of__nat__1,axiom,
% 52.23/52.28 ! [T_a] :
% 52.23/52.28 ( class_Rings_Osemiring__1(T_a)
% 52.23/52.28 => 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) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_of__int__of__nat,axiom,
% 52.23/52.28 ! [V_k,T_a] :
% 52.23/52.28 ( class_Rings_Oring__1(T_a)
% 52.23/52.28 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.28 => 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)))) )
% 52.23/52.28 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.28 => 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)) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_nat__zminus__int,axiom,
% 52.23/52.28 ! [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) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_nat__1,axiom,
% 52.23/52.28 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_pos__zmult__eq__1__iff,axiom,
% 52.23/52.28 ! [V_n_2,V_m_2] :
% 52.23/52.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2))
% 52.23/52.28 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 52.23/52.28 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 52.23/52.28 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_minus__zero,axiom,
% 52.23/52.28 ! [T_a] :
% 52.23/52.28 ( class_Groups_Ogroup__add(T_a)
% 52.23/52.28 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_neg__0__equal__iff__equal,axiom,
% 52.23/52.28 ! [V_a_2,T_b] :
% 52.23/52.28 ( class_Groups_Ogroup__add(T_b)
% 52.23/52.28 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 52.23/52.28 <=> c_Groups_Ozero__class_Ozero(T_b) = V_a_2 ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_equal__neg__zero,axiom,
% 52.23/52.28 ! [V_a_2,T_b] :
% 52.23/52.28 ( class_Groups_Olinordered__ab__group__add(T_b)
% 52.23/52.28 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 52.23/52.28 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_neg__equal__0__iff__equal,axiom,
% 52.23/52.28 ! [V_a_2,T_b] :
% 52.23/52.28 ( class_Groups_Ogroup__add(T_b)
% 52.23/52.28 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.28 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_neg__equal__zero,axiom,
% 52.23/52.28 ! [V_a_2,T_b] :
% 52.23/52.28 ( class_Groups_Olinordered__ab__group__add(T_b)
% 52.23/52.28 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_a_2
% 52.23/52.28 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_neg__less__iff__less,axiom,
% 52.23/52.28 ! [V_a_2,V_b_2,T_b] :
% 52.23/52.28 ( class_Groups_Oordered__ab__group__add(T_b)
% 52.23/52.28 => ( 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)))
% 52.23/52.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_minus__less__iff,axiom,
% 52.23/52.28 ! [V_b_2,V_a_2,T_b] :
% 52.23/52.28 ( class_Groups_Oordered__ab__group__add(T_b)
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
% 52.23/52.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_less__minus__iff,axiom,
% 52.23/52.28 ! [V_b_2,V_a_2,T_b] :
% 52.23/52.28 ( class_Groups_Oordered__ab__group__add(T_b)
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
% 52.23/52.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_minus__add__distrib,axiom,
% 52.23/52.28 ! [V_b,V_a,T_a] :
% 52.23/52.28 ( class_Groups_Oab__group__add(T_a)
% 52.23/52.28 => 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)) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_minus__add,axiom,
% 52.23/52.28 ! [V_b,V_a,T_a] :
% 52.23/52.28 ( class_Groups_Ogroup__add(T_a)
% 52.23/52.28 => 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)) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_add__minus__cancel,axiom,
% 52.23/52.28 ! [V_b,V_a,T_a] :
% 52.23/52.28 ( class_Groups_Ogroup__add(T_a)
% 52.23/52.28 => 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 ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_minus__add__cancel,axiom,
% 52.23/52.28 ! [V_b,V_a,T_a] :
% 52.23/52.28 ( class_Groups_Ogroup__add(T_a)
% 52.23/52.28 => 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 ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 52.23/52.28 ! [V_a,T_a] :
% 52.23/52.28 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.28 => 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) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 52.23/52.28 ! [V_a,T_a] :
% 52.23/52.28 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.28 => 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) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_mult__zero__left,axiom,
% 52.23/52.28 ! [V_a,T_a] :
% 52.23/52.28 ( class_Rings_Omult__zero(T_a)
% 52.23/52.28 => 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) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_mult__zero__right,axiom,
% 52.23/52.28 ! [V_a,T_a] :
% 52.23/52.28 ( class_Rings_Omult__zero(T_a)
% 52.23/52.28 => 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) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_mult__eq__0__iff,axiom,
% 52.23/52.28 ! [V_b_2,V_a_2,T_b] :
% 52.23/52.28 ( class_Rings_Oring__no__zero__divisors(T_b)
% 52.23/52.28 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.28 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.28 | V_b_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_no__zero__divisors,axiom,
% 52.23/52.28 ! [V_b,V_a,T_a] :
% 52.23/52.28 ( class_Rings_Ono__zero__divisors(T_a)
% 52.23/52.28 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.28 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.28 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_divisors__zero,axiom,
% 52.23/52.28 ! [V_b,V_a,T_a] :
% 52.23/52.28 ( class_Rings_Ono__zero__divisors(T_a)
% 52.23/52.28 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.28 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.28 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_one__neq__zero,axiom,
% 52.23/52.28 ! [T_a] :
% 52.23/52.28 ( class_Rings_Ozero__neq__one(T_a)
% 52.23/52.28 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_zero__neq__one,axiom,
% 52.23/52.28 ! [T_a] :
% 52.23/52.28 ( class_Rings_Ozero__neq__one(T_a)
% 52.23/52.28 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_zminus__0,axiom,
% 52.23/52.28 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) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_nat__int,axiom,
% 52.23/52.28 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ).
% 52.23/52.28
% 52.23/52.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 52.23/52.28 ! [V_z,V_y,V_x,T_a] :
% 52.23/52.28 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.28 => 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)) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_crossproduct__noteq,axiom,
% 52.23/52.28 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 52.23/52.28 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 52.23/52.28 => ( ( V_a_2 != V_b_2
% 52.23/52.28 & V_c_2 != V_d_2 )
% 52.23/52.28 <=> 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)) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 52.23/52.28 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.28 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.28 => 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)) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 52.23/52.28 ! [V_b,V_m,V_a,T_a] :
% 52.23/52.28 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.28 => 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) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_crossproduct__eq,axiom,
% 52.23/52.28 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_b] :
% 52.23/52.28 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 52.23/52.28 => ( 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))
% 52.23/52.28 <=> ( V_w_2 = V_x_2
% 52.23/52.28 | V_y_2 = V_z_2 ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_comm__semiring__class_Odistrib,axiom,
% 52.23/52.28 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.28 ( class_Rings_Ocomm__semiring(T_a)
% 52.23/52.28 => 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)) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_combine__common__factor,axiom,
% 52.23/52.28 ! [V_c,V_b,V_e,V_a,T_a] :
% 52.23/52.28 ( class_Rings_Osemiring(T_a)
% 52.23/52.28 => 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) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_zminus__zadd__distrib,axiom,
% 52.23/52.28 ! [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)) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_zadd__zmult__distrib2,axiom,
% 52.23/52.28 ! [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)) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_zadd__zmult__distrib,axiom,
% 52.23/52.28 ! [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)) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_int__0__neq__1,axiom,
% 52.23/52.28 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_of__int__int__eq,axiom,
% 52.23/52.28 ! [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) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_one__less__nat__eq,axiom,
% 52.23/52.28 ! [V_z_2] :
% 52.23/52.28 ( 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)))
% 52.23/52.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_neg__0__less__iff__less,axiom,
% 52.23/52.28 ! [V_a_2,T_b] :
% 52.23/52.28 ( class_Groups_Oordered__ab__group__add(T_b)
% 52.23/52.28 => ( 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)))
% 52.23/52.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_neg__less__0__iff__less,axiom,
% 52.23/52.28 ! [V_a_2,T_b] :
% 52.23/52.28 ( class_Groups_Oordered__ab__group__add(T_b)
% 52.23/52.28 => ( 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)))
% 52.23/52.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_neg__less__nonneg,axiom,
% 52.23/52.28 ! [V_a_2,T_b] :
% 52.23/52.28 ( class_Groups_Olinordered__ab__group__add(T_b)
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
% 52.23/52.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_less__minus__self__iff,axiom,
% 52.23/52.28 ! [V_a_2,T_b] :
% 52.23/52.28 ( class_Rings_Olinordered__idom(T_b)
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 52.23/52.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_minus__unique,axiom,
% 52.23/52.28 ! [V_b,V_a,T_a] :
% 52.23/52.28 ( class_Groups_Ogroup__add(T_a)
% 52.23/52.28 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.28 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_ab__left__minus,axiom,
% 52.23/52.28 ! [V_a,T_a] :
% 52.23/52.28 ( class_Groups_Oab__group__add(T_a)
% 52.23/52.28 => 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) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_left__minus,axiom,
% 52.23/52.28 ! [V_a,T_a] :
% 52.23/52.28 ( class_Groups_Ogroup__add(T_a)
% 52.23/52.28 => 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) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_eq__neg__iff__add__eq__0,axiom,
% 52.23/52.28 ! [V_b_2,V_a_2,T_b] :
% 52.23/52.28 ( class_Groups_Ogroup__add(T_b)
% 52.23/52.28 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 52.23/52.28 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_right__minus,axiom,
% 52.23/52.28 ! [V_a,T_a] :
% 52.23/52.28 ( class_Groups_Ogroup__add(T_a)
% 52.23/52.28 => 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) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_nat__0,axiom,
% 52.23/52.28 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_transfer__nat__int__numerals_I1_J,axiom,
% 52.23/52.28 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_not__square__less__zero,axiom,
% 52.23/52.28 ! [V_a,T_a] :
% 52.23/52.28 ( class_Rings_Olinordered__ring(T_a)
% 52.23/52.28 => ~ 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))) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_mult__less__cancel__right__disj,axiom,
% 52.23/52.28 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 52.23/52.28 ( class_Rings_Olinordered__ring__strict(T_b)
% 52.23/52.28 => ( 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)))
% 52.23/52.28 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 52.23/52.28 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
% 52.23/52.28 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 52.23/52.28 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_mult__less__cancel__left__disj,axiom,
% 52.23/52.28 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 52.23/52.28 ( class_Rings_Olinordered__ring__strict(T_b)
% 52.23/52.28 => ( 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)))
% 52.23/52.28 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 52.23/52.28 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
% 52.23/52.28 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 52.23/52.28 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_mult__less__cancel__left__pos,axiom,
% 52.23/52.28 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 52.23/52.28 ( class_Rings_Olinordered__ring__strict(T_b)
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 52.23/52.28 => ( 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)))
% 52.23/52.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_mult__pos__pos,axiom,
% 52.23/52.28 ! [V_b,V_a,T_a] :
% 52.23/52.28 ( class_Rings_Olinordered__semiring__strict(T_a)
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 52.23/52.28 => 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))) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_mult__pos__neg,axiom,
% 52.23/52.28 ! [V_b,V_a,T_a] :
% 52.23/52.28 ( class_Rings_Olinordered__semiring__strict(T_a)
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.28 => 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))) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_mult__pos__neg2,axiom,
% 52.23/52.28 ! [V_b,V_a,T_a] :
% 52.23/52.28 ( class_Rings_Olinordered__semiring__strict(T_a)
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.28 => 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))) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_zero__less__mult__pos,axiom,
% 52.23/52.28 ! [V_b,V_a,T_a] :
% 52.23/52.28 ( class_Rings_Olinordered__semiring__strict(T_a)
% 52.23/52.28 => ( 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)))
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_zero__less__mult__pos2,axiom,
% 52.23/52.28 ! [V_a,V_b,T_a] :
% 52.23/52.28 ( class_Rings_Olinordered__semiring__strict(T_a)
% 52.23/52.28 => ( 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)))
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_mult__less__cancel__left__neg,axiom,
% 52.23/52.28 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 52.23/52.28 ( class_Rings_Olinordered__ring__strict(T_b)
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 52.23/52.28 => ( 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)))
% 52.23/52.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_mult__neg__pos,axiom,
% 52.23/52.28 ! [V_b,V_a,T_a] :
% 52.23/52.28 ( class_Rings_Olinordered__semiring__strict(T_a)
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 52.23/52.28 => 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))) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_mult__neg__neg,axiom,
% 52.23/52.28 ! [V_b,V_a,T_a] :
% 52.23/52.28 ( class_Rings_Olinordered__ring__strict(T_a)
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.28 => 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))) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_mult__strict__right__mono,axiom,
% 52.23/52.28 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.28 ( class_Rings_Olinordered__semiring__strict(T_a)
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 52.23/52.28 => 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))) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_mult__strict__left__mono,axiom,
% 52.23/52.28 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.28 ( class_Rings_Olinordered__semiring__strict(T_a)
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 52.23/52.28 => 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))) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_comm__mult__strict__left__mono,axiom,
% 52.23/52.28 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.28 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 52.23/52.28 => 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))) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_mult__strict__right__mono__neg,axiom,
% 52.23/52.28 ! [V_c,V_a,V_b,T_a] :
% 52.23/52.28 ( class_Rings_Olinordered__ring__strict(T_a)
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.28 => 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))) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_mult__strict__left__mono__neg,axiom,
% 52.23/52.28 ! [V_c,V_a,V_b,T_a] :
% 52.23/52.28 ( class_Rings_Olinordered__ring__strict(T_a)
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.28 => 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))) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_not__one__less__zero,axiom,
% 52.23/52.28 ! [T_a] :
% 52.23/52.28 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.28 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_zero__less__one,axiom,
% 52.23/52.28 ! [T_a] :
% 52.23/52.28 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_sum__squares__eq__zero__iff,axiom,
% 52.23/52.28 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.28 ( class_Rings_Olinordered__ring__strict(T_b)
% 52.23/52.28 => ( 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)
% 52.23/52.28 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.28 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_add__scale__eq__noteq,axiom,
% 52.23/52.28 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 52.23/52.28 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 52.23/52.28 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.28 => ( ( V_a = V_b
% 52.23/52.28 & V_c != V_d )
% 52.23/52.28 => 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)) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_less__add__one,axiom,
% 52.23/52.28 ! [V_a,T_a] :
% 52.23/52.28 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.28 => 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)))) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_zadd__zminus__inverse2,axiom,
% 52.23/52.28 ! [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) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_negative__eq__positive,axiom,
% 52.23/52.28 ! [V_m_2,V_n_2] :
% 52.23/52.28 ( 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)
% 52.23/52.28 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.28 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_not__int__zless__negative,axiom,
% 52.23/52.28 ! [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)))) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_zmult__zless__mono2,axiom,
% 52.23/52.28 ! [V_k,V_j,V_i] :
% 52.23/52.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 52.23/52.28 => 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))) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_int__0__less__1,axiom,
% 52.23/52.28 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))) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_odd__nonzero,axiom,
% 52.23/52.28 ! [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) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_zless__add1__eq,axiom,
% 52.23/52.28 ! [V_z_2,V_w_2] :
% 52.23/52.28 ( 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))))
% 52.23/52.28 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 52.23/52.28 | V_w_2 = V_z_2 ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_of__int__0,axiom,
% 52.23/52.28 ! [T_a] :
% 52.23/52.28 ( class_Rings_Oring__1(T_a)
% 52.23/52.28 => 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) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_of__int__0__eq__iff,axiom,
% 52.23/52.28 ! [V_z_2,T_b] :
% 52.23/52.28 ( class_Int_Oring__char__0(T_b)
% 52.23/52.28 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
% 52.23/52.28 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_of__int__eq__0__iff,axiom,
% 52.23/52.28 ! [V_z_2,T_b] :
% 52.23/52.28 ( class_Int_Oring__char__0(T_b)
% 52.23/52.28 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.28 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_of__int__less__iff,axiom,
% 52.23/52.28 ! [V_z_2,V_w_2,T_b] :
% 52.23/52.28 ( class_Rings_Olinordered__idom(T_b)
% 52.23/52.28 => ( 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)))
% 52.23/52.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_of__int__add,axiom,
% 52.23/52.28 ! [V_z,V_w,T_a] :
% 52.23/52.28 ( class_Rings_Oring__1(T_a)
% 52.23/52.28 => 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)) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_of__int__of__nat__eq,axiom,
% 52.23/52.28 ! [V_n,T_a] :
% 52.23/52.28 ( class_Rings_Oring__1(T_a)
% 52.23/52.28 => 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) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_zless__nat__conj,axiom,
% 52.23/52.28 ! [V_z_2,V_w_2] :
% 52.23/52.28 ( 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)))
% 52.23/52.28 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 52.23/52.28 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_nat__mono__iff,axiom,
% 52.23/52.28 ! [V_w_2,V_z_2] :
% 52.23/52.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 52.23/52.28 => ( 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)))
% 52.23/52.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_zless__nat__eq__int__zless,axiom,
% 52.23/52.28 ! [V_z_2,V_m_2] :
% 52.23/52.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2)))
% 52.23/52.28 <=> 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)) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_not__sum__squares__lt__zero,axiom,
% 52.23/52.28 ! [V_y,V_x,T_a] :
% 52.23/52.28 ( class_Rings_Olinordered__ring(T_a)
% 52.23/52.28 => ~ 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))) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_sum__squares__gt__zero__iff,axiom,
% 52.23/52.28 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.28 ( class_Rings_Olinordered__ring__strict(T_b)
% 52.23/52.28 => ( 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))))
% 52.23/52.28 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.28 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_zero__less__two,axiom,
% 52.23/52.28 ! [T_a] :
% 52.23/52.28 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.28 => 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)))) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_of__nat__Suc,axiom,
% 52.23/52.28 ! [V_m,T_a] :
% 52.23/52.28 ( class_Rings_Osemiring__1(T_a)
% 52.23/52.28 => 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)) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_int__Suc0__eq__1,axiom,
% 52.23/52.28 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) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_nat__aux__def,axiom,
% 52.23/52.28 ! [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) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_negD,axiom,
% 52.23/52.28 ! [V_x] :
% 52.23/52.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.28 => ? [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))) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_sgn__if,axiom,
% 52.23/52.28 ! [V_x,T_a] :
% 52.23/52.28 ( class_Groups_Osgn__if(T_a)
% 52.23/52.28 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.28 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) )
% 52.23/52.28 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.28 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 52.23/52.28 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) )
% 52.23/52.28 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 52.23/52.28 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_sgn__neg,axiom,
% 52.23/52.28 ! [V_a,T_a] :
% 52.23/52.28 ( class_Rings_Olinordered__idom(T_a)
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.28 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_sgn__1__neg,axiom,
% 52.23/52.28 ! [V_a_2,T_b] :
% 52.23/52.28 ( class_Rings_Olinordered__idom(T_b)
% 52.23/52.28 => ( 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))
% 52.23/52.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_zsgn__def,axiom,
% 52.23/52.28 ! [V_i] :
% 52.23/52.28 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.28 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 52.23/52.28 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.28 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 52.23/52.28 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 52.23/52.28 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 52.23/52.28 => 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)) ) ) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_Suc__nat__eq__nat__zadd1,axiom,
% 52.23/52.28 ! [V_z] :
% 52.23/52.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 52.23/52.28 => 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)) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_nat__less__iff,axiom,
% 52.23/52.28 ! [V_m_2,V_w_2] :
% 52.23/52.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 52.23/52.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2))
% 52.23/52.28 <=> 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))) ) ) ).
% 52.23/52.28
% 52.23/52.28 fof(fact_convex__bound__lt,axiom,
% 52.23/52.28 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 52.23/52.28 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 52.23/52.29 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 52.23/52.29 => 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)) ) ) ) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_sgn__1__pos,axiom,
% 52.23/52.29 ! [V_a_2,T_b] :
% 52.23/52.29 ( class_Rings_Olinordered__idom(T_b)
% 52.23/52.29 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b)
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_order__refl,axiom,
% 52.23/52.29 ! [V_x,T_a] :
% 52.23/52.29 ( class_Orderings_Opreorder(T_a)
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_le0,axiom,
% 52.23/52.29 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_negative__zle,axiom,
% 52.23/52.29 ! [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))) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__le__mono,axiom,
% 52.23/52.29 ! [V_l,V_k,V_j,V_i] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 52.23/52.29 => 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))) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__le__mono2,axiom,
% 52.23/52.29 ! [V_k,V_j,V_i] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 52.23/52.29 => 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))) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__le__mono1,axiom,
% 52.23/52.29 ! [V_k,V_j,V_i] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 52.23/52.29 => 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))) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_nat__mult__assoc,axiom,
% 52.23/52.29 ! [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)) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_nat__mult__eq__1__iff,axiom,
% 52.23/52.29 ! [V_n_2,V_m_2] :
% 52.23/52.29 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 52.23/52.29 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 52.23/52.29 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_nat__mult__commute,axiom,
% 52.23/52.29 ! [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) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_nat__mult__1__right,axiom,
% 52.23/52.29 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 52.23/52.29
% 52.23/52.29 fof(fact_nat__1__eq__mult__iff,axiom,
% 52.23/52.29 ! [V_n_2,V_m_2] :
% 52.23/52.29 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
% 52.23/52.29 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 52.23/52.29 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_nat__mult__1,axiom,
% 52.23/52.29 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 52.23/52.29
% 52.23/52.29 fof(fact_le__cube,axiom,
% 52.23/52.29 ! [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)))) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_le__square,axiom,
% 52.23/52.29 ! [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))) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__eq__self__implies__10,axiom,
% 52.23/52.29 ! [V_n,V_m] :
% 52.23/52.29 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 52.23/52.29 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 52.23/52.29 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_Suc__mult__le__cancel1,axiom,
% 52.23/52.29 ! [V_n_2,V_m_2,V_k_2] :
% 52.23/52.29 ( 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)))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_zle__refl,axiom,
% 52.23/52.29 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_zle__linear,axiom,
% 52.23/52.29 ! [V_w,V_z] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 52.23/52.29 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_zle__trans,axiom,
% 52.23/52.29 ! [V_k,V_j,V_i] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_zle__antisym,axiom,
% 52.23/52.29 ! [V_w,V_z] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
% 52.23/52.29 => V_z = V_w ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_sgn__sgn,axiom,
% 52.23/52.29 ! [V_a,T_a] :
% 52.23/52.29 ( class_Rings_Olinordered__idom(T_a)
% 52.23/52.29 => 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) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_le__fun__def,axiom,
% 52.23/52.29 ! [V_g_2,V_f_2,T_b,T_c] :
% 52.23/52.29 ( class_Orderings_Oord(T_c)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 52.23/52.29 <=> ! [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))) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_linorder__linear,axiom,
% 52.23/52.29 ! [V_y,V_x,T_a] :
% 52.23/52.29 ( class_Orderings_Olinorder(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 52.23/52.29 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_order__eq__iff,axiom,
% 52.23/52.29 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.29 ( class_Orderings_Oorder(T_b)
% 52.23/52.29 => ( V_x_2 = V_y_2
% 52.23/52.29 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 52.23/52.29 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_order__eq__refl,axiom,
% 52.23/52.29 ! [V_y,V_x,T_a] :
% 52.23/52.29 ( class_Orderings_Opreorder(T_a)
% 52.23/52.29 => ( V_x = V_y
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_le__funD,axiom,
% 52.23/52.29 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 52.23/52.29 ( class_Orderings_Oord(T_c)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 52.23/52.29 => 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))) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_order__antisym__conv,axiom,
% 52.23/52.29 ! [V_x_2,V_y_2,T_b] :
% 52.23/52.29 ( class_Orderings_Oorder(T_b)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 52.23/52.29 <=> V_x_2 = V_y_2 ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_ord__eq__le__trans,axiom,
% 52.23/52.29 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.29 ( class_Orderings_Oord(T_a)
% 52.23/52.29 => ( V_a = V_b
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_xt1_I3_J,axiom,
% 52.23/52.29 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.29 ( class_Orderings_Oorder(T_a)
% 52.23/52.29 => ( V_a = V_b
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_ord__le__eq__trans,axiom,
% 52.23/52.29 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.29 ( class_Orderings_Oord(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 52.23/52.29 => ( V_b = V_c
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_xt1_I4_J,axiom,
% 52.23/52.29 ! [V_c,V_a,V_b,T_a] :
% 52.23/52.29 ( class_Orderings_Oorder(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 52.23/52.29 => ( V_b = V_c
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_order__antisym,axiom,
% 52.23/52.29 ! [V_y,V_x,T_a] :
% 52.23/52.29 ( class_Orderings_Oorder(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 52.23/52.29 => V_x = V_y ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_order__trans,axiom,
% 52.23/52.29 ! [V_z,V_y,V_x,T_a] :
% 52.23/52.29 ( class_Orderings_Opreorder(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_xt1_I5_J,axiom,
% 52.23/52.29 ! [V_x,V_y,T_a] :
% 52.23/52.29 ( class_Orderings_Oorder(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 52.23/52.29 => V_x = V_y ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_xt1_I6_J,axiom,
% 52.23/52.29 ! [V_z,V_x,V_y,T_a] :
% 52.23/52.29 ( class_Orderings_Oorder(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_le__funE,axiom,
% 52.23/52.29 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 52.23/52.29 ( class_Orderings_Oord(T_c)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 52.23/52.29 => 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))) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_linorder__le__cases,axiom,
% 52.23/52.29 ! [V_y,V_x,T_a] :
% 52.23/52.29 ( class_Orderings_Olinorder(T_a)
% 52.23/52.29 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_of__nat__le__iff,axiom,
% 52.23/52.29 ! [V_n_2,V_m_2,T_b] :
% 52.23/52.29 ( class_Rings_Olinordered__semidom(T_b)
% 52.23/52.29 => ( 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)))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_zle__int,axiom,
% 52.23/52.29 ! [V_n_2,V_m_2] :
% 52.23/52.29 ( 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)))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_transfer__int__nat__relations_I3_J,axiom,
% 52.23/52.29 ! [V_y_2,V_x_2] :
% 52.23/52.29 ( 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)))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_of__int__le__iff,axiom,
% 52.23/52.29 ! [V_z_2,V_w_2,T_b] :
% 52.23/52.29 ( class_Rings_Olinordered__idom(T_b)
% 52.23/52.29 => ( 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)))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_one__le__mult__iff,axiom,
% 52.23/52.29 ! [V_n_2,V_m_2] :
% 52.23/52.29 ( 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)))
% 52.23/52.29 <=> ( 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))
% 52.23/52.29 & 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)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__le__cancel1,axiom,
% 52.23/52.29 ! [V_n_2,V_m_2,V_k_2] :
% 52.23/52.29 ( 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)))
% 52.23/52.29 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__le__cancel2,axiom,
% 52.23/52.29 ! [V_n_2,V_k_2,V_m_2] :
% 52.23/52.29 ( 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)))
% 52.23/52.29 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_transfer__nat__int__relations_I3_J,axiom,
% 52.23/52.29 ! [V_y_2,V_x_2] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 52.23/52.29 => ( 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)))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_xt1_I8_J,axiom,
% 52.23/52.29 ! [V_z,V_x,V_y,T_a] :
% 52.23/52.29 ( class_Orderings_Oorder(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_order__le__less__trans,axiom,
% 52.23/52.29 ! [V_z,V_y,V_x,T_a] :
% 52.23/52.29 ( class_Orderings_Opreorder(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_xt1_I7_J,axiom,
% 52.23/52.29 ! [V_z,V_x,V_y,T_a] :
% 52.23/52.29 ( class_Orderings_Oorder(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_order__less__le__trans,axiom,
% 52.23/52.29 ! [V_z,V_y,V_x,T_a] :
% 52.23/52.29 ( class_Orderings_Opreorder(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_xt1_I11_J,axiom,
% 52.23/52.29 ! [V_a,V_b,T_a] :
% 52.23/52.29 ( class_Orderings_Oorder(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 52.23/52.29 => ( V_a != V_b
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_order__le__neq__trans,axiom,
% 52.23/52.29 ! [V_b,V_a,T_a] :
% 52.23/52.29 ( class_Orderings_Oorder(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 52.23/52.29 => ( V_a != V_b
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_order__le__imp__less__or__eq,axiom,
% 52.23/52.29 ! [V_y,V_x,T_a] :
% 52.23/52.29 ( class_Orderings_Oorder(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 52.23/52.29 | V_x = V_y ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_linorder__antisym__conv2,axiom,
% 52.23/52.29 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.29 ( class_Orderings_Olinorder(T_b)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 52.23/52.29 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 52.23/52.29 <=> V_x_2 = V_y_2 ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_order__less__imp__le,axiom,
% 52.23/52.29 ! [V_y,V_x,T_a] :
% 52.23/52.29 ( class_Orderings_Opreorder(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_leD,axiom,
% 52.23/52.29 ! [V_x,V_y,T_a] :
% 52.23/52.29 ( class_Orderings_Olinorder(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 52.23/52.29 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_xt1_I12_J,axiom,
% 52.23/52.29 ! [V_b,V_a,T_a] :
% 52.23/52.29 ( class_Orderings_Oorder(T_a)
% 52.23/52.29 => ( V_a != V_b
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_order__neq__le__trans,axiom,
% 52.23/52.29 ! [V_b,V_a,T_a] :
% 52.23/52.29 ( class_Orderings_Oorder(T_a)
% 52.23/52.29 => ( V_a != V_b
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_linorder__antisym__conv1,axiom,
% 52.23/52.29 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.29 ( class_Orderings_Olinorder(T_b)
% 52.23/52.29 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 52.23/52.29 <=> V_x_2 = V_y_2 ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_not__leE,axiom,
% 52.23/52.29 ! [V_x,V_y,T_a] :
% 52.23/52.29 ( class_Orderings_Olinorder(T_a)
% 52.23/52.29 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_leI,axiom,
% 52.23/52.29 ! [V_y,V_x,T_a] :
% 52.23/52.29 ( class_Orderings_Olinorder(T_a)
% 52.23/52.29 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_order__le__less,axiom,
% 52.23/52.29 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.29 ( class_Orderings_Oorder(T_b)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 52.23/52.29 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 52.23/52.29 | V_x_2 = V_y_2 ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_less__le__not__le,axiom,
% 52.23/52.29 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.29 ( class_Orderings_Opreorder(T_b)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 52.23/52.29 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 52.23/52.29 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_order__less__le,axiom,
% 52.23/52.29 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.29 ( class_Orderings_Oorder(T_b)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 52.23/52.29 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 52.23/52.29 & V_x_2 != V_y_2 ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_linorder__le__less__linear,axiom,
% 52.23/52.29 ! [V_y,V_x,T_a] :
% 52.23/52.29 ( class_Orderings_Olinorder(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 52.23/52.29 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_linorder__not__le,axiom,
% 52.23/52.29 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.29 ( class_Orderings_Olinorder(T_b)
% 52.23/52.29 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_linorder__not__less,axiom,
% 52.23/52.29 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.29 ( class_Orderings_Olinorder(T_b)
% 52.23/52.29 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_add__le__imp__le__left,axiom,
% 52.23/52.29 ! [V_b,V_a,V_c,T_a] :
% 52.23/52.29 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 52.23/52.29 => ( 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)))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_add__le__imp__le__right,axiom,
% 52.23/52.29 ! [V_b,V_c,V_a,T_a] :
% 52.23/52.29 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 52.23/52.29 => ( 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)))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_add__mono,axiom,
% 52.23/52.29 ! [V_d,V_c,V_b,V_a,T_a] :
% 52.23/52.29 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 52.23/52.29 => 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))) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_add__left__mono,axiom,
% 52.23/52.29 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.29 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 52.23/52.29 => 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))) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_add__right__mono,axiom,
% 52.23/52.29 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.29 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 52.23/52.29 => 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))) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_add__le__cancel__left,axiom,
% 52.23/52.29 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 52.23/52.29 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 52.23/52.29 => ( 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)))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_add__le__cancel__right,axiom,
% 52.23/52.29 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 52.23/52.29 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 52.23/52.29 => ( 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)))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__0,axiom,
% 52.23/52.29 ! [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) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__0__right,axiom,
% 52.23/52.29 ! [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) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__is__0,axiom,
% 52.23/52.29 ! [V_n_2,V_m_2] :
% 52.23/52.29 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.29 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.29 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__cancel1,axiom,
% 52.23/52.29 ! [V_n_2,V_m_2,V_k_2] :
% 52.23/52.29 ( 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)
% 52.23/52.29 <=> ( V_m_2 = V_n_2
% 52.23/52.29 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__cancel2,axiom,
% 52.23/52.29 ! [V_n_2,V_k_2,V_m_2] :
% 52.23/52.29 ( 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)
% 52.23/52.29 <=> ( V_m_2 = V_n_2
% 52.23/52.29 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_Suc__mult__cancel1,axiom,
% 52.23/52.29 ! [V_n_2,V_m_2,V_k_2] :
% 52.23/52.29 ( 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)
% 52.23/52.29 <=> V_m_2 = V_n_2 ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 52.23/52.29 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_le__0__eq,axiom,
% 52.23/52.29 ! [V_n_2] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 52.23/52.29 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_le__minus__iff,axiom,
% 52.23/52.29 ! [V_b_2,V_a_2,T_b] :
% 52.23/52.29 ( class_Groups_Oordered__ab__group__add(T_b)
% 52.23/52.29 => ( 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)))
% 52.23/52.29 <=> 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))) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_minus__le__iff,axiom,
% 52.23/52.29 ! [V_b_2,V_a_2,T_b] :
% 52.23/52.29 ( class_Groups_Oordered__ab__group__add(T_b)
% 52.23/52.29 => ( 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))
% 52.23/52.29 <=> 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)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_neg__le__iff__le,axiom,
% 52.23/52.29 ! [V_a_2,V_b_2,T_b] :
% 52.23/52.29 ( class_Groups_Oordered__ab__group__add(T_b)
% 52.23/52.29 => ( 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)))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_le__imp__neg__le,axiom,
% 52.23/52.29 ! [V_b,V_a,T_a] :
% 52.23/52.29 ( class_Groups_Oordered__ab__group__add(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 52.23/52.29 => 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))) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_add__mult__distrib2,axiom,
% 52.23/52.29 ! [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)) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_add__mult__distrib,axiom,
% 52.23/52.29 ! [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)) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_Suc__leD,axiom,
% 52.23/52.29 ! [V_n,V_m] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_le__SucE,axiom,
% 52.23/52.29 ! [V_n,V_m] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 52.23/52.29 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 52.23/52.29 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_le__SucI,axiom,
% 52.23/52.29 ! [V_n,V_m] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_Suc__le__mono,axiom,
% 52.23/52.29 ! [V_m_2,V_n_2] :
% 52.23/52.29 ( 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)))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_le__Suc__eq,axiom,
% 52.23/52.29 ! [V_n_2,V_m_2] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 52.23/52.29 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 52.23/52.29 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_not__less__eq__eq,axiom,
% 52.23/52.29 ! [V_n_2,V_m_2] :
% 52.23/52.29 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_Suc__n__not__le__n,axiom,
% 52.23/52.29 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 52.23/52.29 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))) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_nat__less__le,axiom,
% 52.23/52.29 ! [V_n_2,V_m_2] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 52.23/52.29 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 52.23/52.29 & V_m_2 != V_n_2 ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_le__eq__less__or__eq,axiom,
% 52.23/52.29 ! [V_n_2,V_m_2] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 52.23/52.29 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 52.23/52.29 | V_m_2 = V_n_2 ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_less__imp__le__nat,axiom,
% 52.23/52.29 ! [V_n,V_m] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_le__neq__implies__less,axiom,
% 52.23/52.29 ! [V_n,V_m] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 52.23/52.29 => ( V_m != V_n
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_less__or__eq__imp__le,axiom,
% 52.23/52.29 ! [V_n,V_m] :
% 52.23/52.29 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 52.23/52.29 | V_m = V_n )
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_termination__basic__simps_I5_J,axiom,
% 52.23/52.29 ! [V_y,V_x] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_le__add2,axiom,
% 52.23/52.29 ! [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))) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_le__add1,axiom,
% 52.23/52.29 ! [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))) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_le__iff__add,axiom,
% 52.23/52.29 ! [V_n_2,V_m_2] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 52.23/52.29 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_nat__add__left__cancel__le,axiom,
% 52.23/52.29 ! [V_n_2,V_m_2,V_k_2] :
% 52.23/52.29 ( 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)))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_trans__le__add1,axiom,
% 52.23/52.29 ! [V_m,V_j,V_i] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 52.23/52.29 => 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))) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_trans__le__add2,axiom,
% 52.23/52.29 ! [V_m,V_j,V_i] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 52.23/52.29 => 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))) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_add__le__mono1,axiom,
% 52.23/52.29 ! [V_k,V_j,V_i] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 52.23/52.29 => 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))) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_add__le__mono,axiom,
% 52.23/52.29 ! [V_l,V_k,V_j,V_i] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 52.23/52.29 => 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))) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_add__leD2,axiom,
% 52.23/52.29 ! [V_n,V_k,V_m] :
% 52.23/52.29 ( 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))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_add__leD1,axiom,
% 52.23/52.29 ! [V_n,V_k,V_m] :
% 52.23/52.29 ( 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))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_add__leE,axiom,
% 52.23/52.29 ! [V_n,V_k,V_m] :
% 52.23/52.29 ( 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))
% 52.23/52.29 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 52.23/52.29 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_termination__basic__simps_I4_J,axiom,
% 52.23/52.29 ! [V_y,V_z,V_x] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z))
% 52.23/52.29 => 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))) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_termination__basic__simps_I3_J,axiom,
% 52.23/52.29 ! [V_z,V_y,V_x] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y))
% 52.23/52.29 => 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))) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_zless__le,axiom,
% 52.23/52.29 ! [V_w_2,V_z_2] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2))
% 52.23/52.29 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2))
% 52.23/52.29 & V_z_2 != V_w_2 ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_zadd__left__mono,axiom,
% 52.23/52.29 ! [V_k,V_j,V_i] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 52.23/52.29 => 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))) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_evaln__nonstrict,axiom,
% 52.23/52.29 ! [V_m,V_t,V_n,V_s,V_c] :
% 52.23/52.29 ( c_Natural_Oevaln(V_c,V_s,V_n,V_t)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 52.23/52.29 => c_Natural_Oevaln(V_c,V_s,V_m,V_t) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_nat__le__eq__zle,axiom,
% 52.23/52.29 ! [V_z_2,V_w_2] :
% 52.23/52.29 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 52.23/52.29 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
% 52.23/52.29 => ( 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)))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_nat__mult__distrib,axiom,
% 52.23/52.29 ! [V_z_H,V_z] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 52.23/52.29 => 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)) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom,
% 52.23/52.29 ! [V_y,V_x] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 52.23/52.29 => 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)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_of__int__le__0__iff,axiom,
% 52.23/52.29 ! [V_z_2,T_b] :
% 52.23/52.29 ( class_Rings_Olinordered__idom(T_b)
% 52.23/52.29 => ( 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)))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_of__int__0__le__iff,axiom,
% 52.23/52.29 ! [V_z_2,T_b] :
% 52.23/52.29 ( class_Rings_Olinordered__idom(T_b)
% 52.23/52.29 => ( 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)))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_sgn__0__0,axiom,
% 52.23/52.29 ! [V_a_2,T_b] :
% 52.23/52.29 ( class_Rings_Olinordered__idom(T_b)
% 52.23/52.29 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.29 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_sgn0,axiom,
% 52.23/52.29 ! [T_a] :
% 52.23/52.29 ( class_Groups_Osgn__if(T_a)
% 52.23/52.29 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_sgn__times,axiom,
% 52.23/52.29 ! [V_b,V_a,T_a] :
% 52.23/52.29 ( class_Rings_Olinordered__idom(T_a)
% 52.23/52.29 => 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)) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_nat__mult__distrib__neg,axiom,
% 52.23/52.29 ! [V_z_H,V_z] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.29 => 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))) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 52.23/52.29 ! [V_a_2,T_b] :
% 52.23/52.29 ( class_Groups_Olinordered__ab__group__add(T_b)
% 52.23/52.29 => ( 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)))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 52.23/52.29 ! [V_a_2,T_b] :
% 52.23/52.29 ( class_Groups_Olinordered__ab__group__add(T_b)
% 52.23/52.29 => ( 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)))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_add__nonneg__nonneg,axiom,
% 52.23/52.29 ! [V_b,V_a,T_a] :
% 52.23/52.29 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 52.23/52.29 => 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))) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_add__nonneg__eq__0__iff,axiom,
% 52.23/52.29 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.29 ( class_Groups_Oordered__comm__monoid__add(T_b)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_x_2))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_y_2))
% 52.23/52.29 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.29 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.29 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_add__increasing,axiom,
% 52.23/52.29 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.29 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 52.23/52.29 => 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))) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_add__increasing2,axiom,
% 52.23/52.29 ! [V_a,V_b,V_c,T_a] :
% 52.23/52.29 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 52.23/52.29 => 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))) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_add__nonpos__nonpos,axiom,
% 52.23/52.29 ! [V_b,V_a,T_a] :
% 52.23/52.29 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.29 => 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))) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_split__mult__neg__le,axiom,
% 52.23/52.29 ! [V_b,V_a,T_a] :
% 52.23/52.29 ( class_Rings_Oordered__cancel__semiring(T_a)
% 52.23/52.29 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.29 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) )
% 52.23/52.29 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.29 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) )
% 52.23/52.29 => 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))) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_split__mult__pos__le,axiom,
% 52.23/52.29 ! [V_b,V_a,T_a] :
% 52.23/52.29 ( class_Rings_Oordered__ring(T_a)
% 52.23/52.29 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.29 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
% 52.23/52.29 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.29 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 52.23/52.29 => 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))) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__mono,axiom,
% 52.23/52.29 ! [V_d,V_c,V_b,V_a,T_a] :
% 52.23/52.29 ( class_Rings_Oordered__semiring(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 52.23/52.29 => 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))) ) ) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__mono_H,axiom,
% 52.23/52.29 ! [V_d,V_c,V_b,V_a,T_a] :
% 52.23/52.29 ( class_Rings_Oordered__semiring(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 52.23/52.29 => 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))) ) ) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__left__mono__neg,axiom,
% 52.23/52.29 ! [V_c,V_a,V_b,T_a] :
% 52.23/52.29 ( class_Rings_Oordered__ring(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.29 => 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))) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__right__mono__neg,axiom,
% 52.23/52.29 ! [V_c,V_a,V_b,T_a] :
% 52.23/52.29 ( class_Rings_Oordered__ring(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.29 => 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))) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_comm__mult__left__mono,axiom,
% 52.23/52.29 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.29 ( class_Rings_Oordered__comm__semiring(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 52.23/52.29 => 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))) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__left__mono,axiom,
% 52.23/52.29 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.29 ( class_Rings_Oordered__semiring(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 52.23/52.29 => 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))) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__right__mono,axiom,
% 52.23/52.29 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.29 ( class_Rings_Oordered__semiring(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 52.23/52.29 => 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))) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__nonpos__nonpos,axiom,
% 52.23/52.29 ! [V_b,V_a,T_a] :
% 52.23/52.29 ( class_Rings_Oordered__ring(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.29 => 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))) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__nonpos__nonneg,axiom,
% 52.23/52.29 ! [V_b,V_a,T_a] :
% 52.23/52.29 ( class_Rings_Oordered__cancel__semiring(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 52.23/52.29 => 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))) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__nonneg__nonpos2,axiom,
% 52.23/52.29 ! [V_b,V_a,T_a] :
% 52.23/52.29 ( class_Rings_Oordered__cancel__semiring(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.29 => 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))) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__nonneg__nonpos,axiom,
% 52.23/52.29 ! [V_b,V_a,T_a] :
% 52.23/52.29 ( class_Rings_Oordered__cancel__semiring(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.29 => 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))) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__nonneg__nonneg,axiom,
% 52.23/52.29 ! [V_b,V_a,T_a] :
% 52.23/52.29 ( class_Rings_Oordered__cancel__semiring(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 52.23/52.29 => 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))) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__le__0__iff,axiom,
% 52.23/52.29 ! [V_b_2,V_a_2,T_b] :
% 52.23/52.29 ( class_Rings_Olinordered__ring__strict(T_b)
% 52.23/52.29 => ( 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)))
% 52.23/52.29 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 52.23/52.29 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 52.23/52.29 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 52.23/52.29 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_zero__le__mult__iff,axiom,
% 52.23/52.29 ! [V_b_2,V_a_2,T_b] :
% 52.23/52.29 ( class_Rings_Olinordered__ring__strict(T_b)
% 52.23/52.29 => ( 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)))
% 52.23/52.29 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 52.23/52.29 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 52.23/52.29 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 52.23/52.29 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_zero__le__square,axiom,
% 52.23/52.29 ! [V_a,T_a] :
% 52.23/52.29 ( class_Rings_Olinordered__ring(T_a)
% 52.23/52.29 => 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))) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_add__less__le__mono,axiom,
% 52.23/52.29 ! [V_d,V_c,V_b,V_a,T_a] :
% 52.23/52.29 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 52.23/52.29 => 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))) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_add__le__less__mono,axiom,
% 52.23/52.29 ! [V_d,V_c,V_b,V_a,T_a] :
% 52.23/52.29 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 52.23/52.29 => 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))) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_zero__le__one,axiom,
% 52.23/52.29 ! [T_a] :
% 52.23/52.29 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.29 => 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))) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_not__one__le__zero,axiom,
% 52.23/52.29 ! [T_a] :
% 52.23/52.29 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.29 => ~ 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))) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_neg__0__le__iff__le,axiom,
% 52.23/52.29 ! [V_a_2,T_b] :
% 52.23/52.29 ( class_Groups_Oordered__ab__group__add(T_b)
% 52.23/52.29 => ( 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)))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_le__minus__self__iff,axiom,
% 52.23/52.29 ! [V_a_2,T_b] :
% 52.23/52.29 ( class_Groups_Olinordered__ab__group__add(T_b)
% 52.23/52.29 => ( 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)))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_neg__le__0__iff__le,axiom,
% 52.23/52.29 ! [V_a_2,T_b] :
% 52.23/52.29 ( class_Groups_Oordered__ab__group__add(T_b)
% 52.23/52.29 => ( 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)))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_minus__le__self__iff,axiom,
% 52.23/52.29 ! [V_a_2,T_b] :
% 52.23/52.29 ( class_Groups_Olinordered__ab__group__add(T_b)
% 52.23/52.29 => ( 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))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__eq__1__iff,axiom,
% 52.23/52.29 ! [V_n_2,V_m_2] :
% 52.23/52.29 ( 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))
% 52.23/52.29 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 52.23/52.29 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_of__nat__0__le__iff,axiom,
% 52.23/52.29 ! [V_n,T_a] :
% 52.23/52.29 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.29 => 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))) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_zero__le__imp__of__nat,axiom,
% 52.23/52.29 ! [V_m,T_a] :
% 52.23/52.29 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.29 => 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))) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_nat__0__less__mult__iff,axiom,
% 52.23/52.29 ! [V_n_2,V_m_2] :
% 52.23/52.29 ( 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)))
% 52.23/52.29 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 52.23/52.29 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__less__cancel1,axiom,
% 52.23/52.29 ! [V_n_2,V_m_2,V_k_2] :
% 52.23/52.29 ( 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)))
% 52.23/52.29 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 52.23/52.29 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__less__cancel2,axiom,
% 52.23/52.29 ! [V_n_2,V_k_2,V_m_2] :
% 52.23/52.29 ( 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)))
% 52.23/52.29 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 52.23/52.29 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__less__mono1,axiom,
% 52.23/52.29 ! [V_k,V_j,V_i] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 52.23/52.29 => 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))) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__less__mono2,axiom,
% 52.23/52.29 ! [V_k,V_j,V_i] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 52.23/52.29 => 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))) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_Suc__mult__less__cancel1,axiom,
% 52.23/52.29 ! [V_n_2,V_m_2,V_k_2] :
% 52.23/52.29 ( 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)))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__Suc__right,axiom,
% 52.23/52.29 ! [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)) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__Suc,axiom,
% 52.23/52.29 ! [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)) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_One__nat__def,axiom,
% 52.23/52.29 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_less__eq__Suc__le,axiom,
% 52.23/52.29 ! [V_m_2,V_n_2] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_less__Suc__eq__le,axiom,
% 52.23/52.29 ! [V_n_2,V_m_2] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_Suc__le__eq,axiom,
% 52.23/52.29 ! [V_n_2,V_m_2] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_le__imp__less__Suc,axiom,
% 52.23/52.29 ! [V_n,V_m] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_Suc__leI,axiom,
% 52.23/52.29 ! [V_n,V_m] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_le__less__Suc__eq,axiom,
% 52.23/52.29 ! [V_n_2,V_m_2] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 52.23/52.29 <=> V_n_2 = V_m_2 ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_Suc__le__lessD,axiom,
% 52.23/52.29 ! [V_n,V_m] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_Suc__eq__plus1__left,axiom,
% 52.23/52.29 ! [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) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_Suc__eq__plus1,axiom,
% 52.23/52.29 ! [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)) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 52.23/52.29 ! [V_y,V_x] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 52.23/52.29 => 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))) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_zero__zle__int,axiom,
% 52.23/52.29 ! [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))) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
% 52.23/52.29 ! [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))) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
% 52.23/52.29 ! [V_P_2] :
% 52.23/52.29 ( ? [B_x] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 52.23/52.29 & hBOOL(hAPP(V_P_2,B_x)) )
% 52.23/52.29 <=> ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
% 52.23/52.29 ! [V_P_2] :
% 52.23/52.29 ( ! [B_x] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 52.23/52.29 => hBOOL(hAPP(V_P_2,B_x)) )
% 52.23/52.29 <=> ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 52.23/52.29 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))) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_ex__nat,axiom,
% 52.23/52.29 ! [V_P_2] :
% 52.23/52.29 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 52.23/52.29 <=> ? [B_x] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 52.23/52.29 & hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_all__nat,axiom,
% 52.23/52.29 ! [V_P_2] :
% 52.23/52.29 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 52.23/52.29 <=> ! [B_x] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 52.23/52.29 => hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_transfer__nat__int__relations_I1_J,axiom,
% 52.23/52.29 ! [V_y_2,V_x_2] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 52.23/52.29 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2)
% 52.23/52.29 <=> V_x_2 = V_y_2 ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_eq__nat__nat__iff,axiom,
% 52.23/52.29 ! [V_z_H_2,V_z_2] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2))
% 52.23/52.29 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2)
% 52.23/52.29 <=> V_z_2 = V_z_H_2 ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_zadd__zless__mono,axiom,
% 52.23/52.29 ! [V_z,V_z_H,V_w,V_w_H] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 52.23/52.29 => 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))) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 52.23/52.29 ! [V_y,V_x] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 52.23/52.29 => 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))) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_zmult__int,axiom,
% 52.23/52.29 ! [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)) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_int__mult,axiom,
% 52.23/52.29 ! [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)) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
% 52.23/52.29 ! [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)) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_zle__iff__zadd,axiom,
% 52.23/52.29 ! [V_z_2,V_w_2] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
% 52.23/52.29 <=> ? [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)) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_int__1,axiom,
% 52.23/52.29 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) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_transfer__int__nat__numerals_I2_J,axiom,
% 52.23/52.29 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)) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_transfer__nat__int__numerals_I2_J,axiom,
% 52.23/52.29 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_add__pos__nonneg,axiom,
% 52.23/52.29 ! [V_b,V_a,T_a] :
% 52.23/52.29 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 52.23/52.29 => 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))) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_add__nonneg__pos,axiom,
% 52.23/52.29 ! [V_b,V_a,T_a] :
% 52.23/52.29 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 52.23/52.29 => 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))) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_add__strict__increasing,axiom,
% 52.23/52.29 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.29 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 52.23/52.29 => 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))) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_add__strict__increasing2,axiom,
% 52.23/52.29 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.29 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 52.23/52.29 => 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))) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_add__neg__nonpos,axiom,
% 52.23/52.29 ! [V_b,V_a,T_a] :
% 52.23/52.29 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.29 => 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))) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_add__nonpos__neg,axiom,
% 52.23/52.29 ! [V_b,V_a,T_a] :
% 52.23/52.29 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.29 => 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))) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__left__le__imp__le,axiom,
% 52.23/52.29 ! [V_b,V_a,V_c,T_a] :
% 52.23/52.29 ( class_Rings_Olinordered__semiring__strict(T_a)
% 52.23/52.29 => ( 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)))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__right__le__imp__le,axiom,
% 52.23/52.29 ! [V_b,V_c,V_a,T_a] :
% 52.23/52.29 ( class_Rings_Olinordered__semiring__strict(T_a)
% 52.23/52.29 => ( 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)))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__less__imp__less__left,axiom,
% 52.23/52.29 ! [V_b,V_a,V_c,T_a] :
% 52.23/52.29 ( class_Rings_Olinordered__semiring__strict(T_a)
% 52.23/52.29 => ( 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)))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__left__less__imp__less,axiom,
% 52.23/52.29 ! [V_b,V_a,V_c,T_a] :
% 52.23/52.29 ( class_Rings_Olinordered__semiring(T_a)
% 52.23/52.29 => ( 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)))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__less__imp__less__right,axiom,
% 52.23/52.29 ! [V_b,V_c,V_a,T_a] :
% 52.23/52.29 ( class_Rings_Olinordered__semiring__strict(T_a)
% 52.23/52.29 => ( 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)))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__right__less__imp__less,axiom,
% 52.23/52.29 ! [V_b,V_c,V_a,T_a] :
% 52.23/52.29 ( class_Rings_Olinordered__semiring(T_a)
% 52.23/52.29 => ( 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)))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__le__less__imp__less,axiom,
% 52.23/52.29 ! [V_d,V_c,V_b,V_a,T_a] :
% 52.23/52.29 ( class_Rings_Olinordered__semiring__strict(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 52.23/52.29 => 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))) ) ) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__less__le__imp__less,axiom,
% 52.23/52.29 ! [V_d,V_c,V_b,V_a,T_a] :
% 52.23/52.29 ( class_Rings_Olinordered__semiring__strict(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 52.23/52.29 => 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))) ) ) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__strict__mono_H,axiom,
% 52.23/52.29 ! [V_d,V_c,V_b,V_a,T_a] :
% 52.23/52.29 ( class_Rings_Olinordered__semiring__strict(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 52.23/52.29 => 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))) ) ) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__strict__mono,axiom,
% 52.23/52.29 ! [V_d,V_c,V_b,V_a,T_a] :
% 52.23/52.29 ( class_Rings_Olinordered__semiring__strict(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 52.23/52.29 => 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))) ) ) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__le__cancel__left__neg,axiom,
% 52.23/52.29 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 52.23/52.29 ( class_Rings_Olinordered__ring__strict(T_b)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 52.23/52.29 => ( 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)))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__le__cancel__left__pos,axiom,
% 52.23/52.29 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 52.23/52.29 ( class_Rings_Olinordered__ring__strict(T_b)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 52.23/52.29 => ( 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)))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_sum__squares__le__zero__iff,axiom,
% 52.23/52.29 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.29 ( class_Rings_Olinordered__ring__strict(T_b)
% 52.23/52.29 => ( 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)))
% 52.23/52.29 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.29 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_sum__squares__ge__zero,axiom,
% 52.23/52.29 ! [V_y,V_x,T_a] :
% 52.23/52.29 ( class_Rings_Olinordered__ring(T_a)
% 52.23/52.29 => 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)))) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__left__le__one__le,axiom,
% 52.23/52.29 ! [V_y,V_x,T_a] :
% 52.23/52.29 ( class_Rings_Olinordered__idom(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 52.23/52.29 => 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)) ) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_mult__right__le__one__le,axiom,
% 52.23/52.29 ! [V_y,V_x,T_a] :
% 52.23/52.29 ( class_Rings_Olinordered__idom(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 52.23/52.29 => 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)) ) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_sgn__less,axiom,
% 52.23/52.29 ! [V_a_2,T_b] :
% 52.23/52.29 ( class_Rings_Olinordered__idom(T_b)
% 52.23/52.29 => ( 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)))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_sgn__greater,axiom,
% 52.23/52.29 ! [V_a_2,T_b] :
% 52.23/52.29 ( class_Rings_Olinordered__idom(T_b)
% 52.23/52.29 => ( 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)))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_one__less__mult,axiom,
% 52.23/52.29 ! [V_m,V_n] :
% 52.23/52.29 ( 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))
% 52.23/52.29 => ( 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))
% 52.23/52.29 => 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))) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_n__less__n__mult__m,axiom,
% 52.23/52.29 ! [V_m,V_n] :
% 52.23/52.29 ( 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))
% 52.23/52.29 => ( 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))
% 52.23/52.29 => 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))) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_n__less__m__mult__n,axiom,
% 52.23/52.29 ! [V_m,V_n] :
% 52.23/52.29 ( 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))
% 52.23/52.29 => ( 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))
% 52.23/52.29 => 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))) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_int__le__0__conv,axiom,
% 52.23/52.29 ! [V_n_2] :
% 52.23/52.29 ( 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)))
% 52.23/52.29 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_nat__le__0,axiom,
% 52.23/52.29 ! [V_z] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.29 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_nat__0__iff,axiom,
% 52.23/52.29 ! [V_i_2] :
% 52.23/52.29 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_int__one__le__iff__zero__less,axiom,
% 52.23/52.29 ! [V_z_2] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_int__nat__eq,axiom,
% 52.23/52.29 ! [V_z] :
% 52.23/52.29 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 52.23/52.29 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z )
% 52.23/52.29 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 52.23/52.29 => 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) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_int__eq__iff,axiom,
% 52.23/52.29 ! [V_z_2,V_m_2] :
% 52.23/52.29 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2
% 52.23/52.29 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2)
% 52.23/52.29 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_nat__0__le,axiom,
% 52.23/52.29 ! [V_z] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 52.23/52.29 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_zless__imp__add1__zle,axiom,
% 52.23/52.29 ! [V_z,V_w] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z))
% 52.23/52.29 => 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)) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_add1__zle__eq,axiom,
% 52.23/52.29 ! [V_z_2,V_w_2] :
% 52.23/52.29 ( 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))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_zle__add1__eq__le,axiom,
% 52.23/52.29 ! [V_z_2,V_w_2] :
% 52.23/52.29 ( 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))))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_int__zle__neg,axiom,
% 52.23/52.29 ! [V_m_2,V_n_2] :
% 52.23/52.29 ( 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))))
% 52.23/52.29 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.29 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_negative__zle__0,axiom,
% 52.23/52.29 ! [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))) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_convex__bound__le,axiom,
% 52.23/52.29 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 52.23/52.29 ( class_Rings_Olinordered__semiring__1(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 52.23/52.29 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 52.23/52.29 => 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)) ) ) ) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_transfer__nat__int__relations_I2_J,axiom,
% 52.23/52.29 ! [V_y_2,V_x_2] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 52.23/52.29 => ( 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)))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_nat__less__eq__zless,axiom,
% 52.23/52.29 ! [V_z_2,V_w_2] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 52.23/52.29 => ( 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)))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_nat__eq__iff2,axiom,
% 52.23/52.29 ! [V_w_2,V_m_2] :
% 52.23/52.29 ( V_m_2 = hAPP(c_Int_Onat,V_w_2)
% 52.23/52.29 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 52.23/52.29 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 52.23/52.29 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 52.23/52.29 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_nat__eq__iff,axiom,
% 52.23/52.29 ! [V_m_2,V_w_2] :
% 52.23/52.29 ( hAPP(c_Int_Onat,V_w_2) = V_m_2
% 52.23/52.29 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 52.23/52.29 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 52.23/52.29 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 52.23/52.29 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_nat__add__distrib,axiom,
% 52.23/52.29 ! [V_z_H,V_z] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 52.23/52.29 => 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)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom,
% 52.23/52.29 ! [V_y,V_x] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 52.23/52.29 => 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)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_le__imp__0__less,axiom,
% 52.23/52.29 ! [V_z] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 52.23/52.29 => 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))) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_not__zle__0__negative,axiom,
% 52.23/52.29 ! [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))))) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_of__nat__nat,axiom,
% 52.23/52.29 ! [V_z,T_a] :
% 52.23/52.29 ( class_Rings_Oring__1(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 52.23/52.29 => 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) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_sgn__pos,axiom,
% 52.23/52.29 ! [V_a,T_a] :
% 52.23/52.29 ( class_Rings_Olinordered__idom(T_a)
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.29 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_self__quotient__aux2,axiom,
% 52.23/52.29 ! [V_q,V_r,V_a] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 52.23/52.29 => ( 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))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_self__quotient__aux1,axiom,
% 52.23/52.29 ! [V_q,V_r,V_a] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 52.23/52.29 => ( 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))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_q__pos__lemma,axiom,
% 52.23/52.29 ! [V_r_H,V_q_H,V_b_H] :
% 52.23/52.29 ( 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)))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_q__neg__lemma,axiom,
% 52.23/52.29 ! [V_r_H,V_q_H,V_b_H] :
% 52.23/52.29 ( 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)))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_unique__quotient__lemma,axiom,
% 52.23/52.29 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 52.23/52.29 ( 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)))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_zdiv__mono2__lemma,axiom,
% 52.23/52.29 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 52.23/52.29 ( 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)
% 52.23/52.29 => ( 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)))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_unique__quotient__lemma__neg,axiom,
% 52.23/52.29 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 52.23/52.29 ( 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)))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 52.23/52.29 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 52.23/52.29 ( 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)
% 52.23/52.29 => ( 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)))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_nat__mult__le__cancel1,axiom,
% 52.23/52.29 ! [V_n_2,V_m_2,V_k_2] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 52.23/52.29 => ( 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)))
% 52.23/52.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_le__refl,axiom,
% 52.23/52.29 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_nat__le__linear,axiom,
% 52.23/52.29 ! [V_n,V_m] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 52.23/52.29 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_eq__imp__le,axiom,
% 52.23/52.29 ! [V_n,V_m] :
% 52.23/52.29 ( V_m = V_n
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_le__trans,axiom,
% 52.23/52.29 ! [V_k,V_j,V_i] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k))
% 52.23/52.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ).
% 52.23/52.29
% 52.23/52.29 fof(fact_le__antisym,axiom,
% 52.23/52.29 ! [V_n,V_m] :
% 52.23/52.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 52.23/52.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 52.23/52.30 => V_m = V_n ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_less__fun__def,axiom,
% 52.23/52.30 ! [V_g_2,V_f_2,T_b,T_c] :
% 52.23/52.30 ( class_Orderings_Oord(T_c)
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 52.23/52.30 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 52.23/52.30 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2)) ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 52.23/52.30 ! [V_n_2,V_m_2,V_k_2] :
% 52.23/52.30 ( 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)
% 52.23/52.30 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.30 | V_m_2 = V_n_2 ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_left__add__mult__distrib,axiom,
% 52.23/52.30 ! [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) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_nat__mult__eq__cancel1,axiom,
% 52.23/52.30 ! [V_n_2,V_m_2,V_k_2] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 52.23/52.30 => ( 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)
% 52.23/52.30 <=> V_m_2 = V_n_2 ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_nat__mult__less__cancel1,axiom,
% 52.23/52.30 ! [V_n_2,V_m_2,V_k_2] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 52.23/52.30 => ( 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)))
% 52.23/52.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_transfer__morphism__nat__int,axiom,
% 52.23/52.30 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))) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_compl__le__compl__iff,axiom,
% 52.23/52.30 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.30 ( class_Lattices_Oboolean__algebra(T_b)
% 52.23/52.30 => ( 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)))
% 52.23/52.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_compl__mono,axiom,
% 52.23/52.30 ! [V_y,V_x,T_a] :
% 52.23/52.30 ( class_Lattices_Oboolean__algebra(T_a)
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 52.23/52.30 => 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))) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_ex__least__nat__less,axiom,
% 52.23/52.30 ! [V_n_2,V_P_2] :
% 52.23/52.30 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 52.23/52.30 => ( hBOOL(hAPP(V_P_2,V_n_2))
% 52.23/52.30 => ? [B_k] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2))
% 52.23/52.30 & ! [B_i] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k))
% 52.23/52.30 => ~ hBOOL(hAPP(V_P_2,B_i)) )
% 52.23/52.30 & 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)))) ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_divmod__int__rel__mod__eq,axiom,
% 52.23/52.30 ! [V_y,V_q_1,V_b_1,V_a_1] :
% 52.23/52.30 ( 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)
% 52.23/52.30 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 52.23/52.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) )
% 52.23/52.30 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y))
% 52.23/52.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 52.23/52.30 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.30 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zmult2__lemma__aux2,axiom,
% 52.23/52.30 ! [V_q,V_r,V_b,V_c] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.30 => 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))) ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zmult2__lemma__aux1,axiom,
% 52.23/52.30 ! [V_q,V_r,V_b,V_c] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.30 => 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))) ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zmult2__lemma__aux4,axiom,
% 52.23/52.30 ! [V_q,V_b,V_r,V_c] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 52.23/52.30 => 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))) ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__mod__trivial,axiom,
% 52.23/52.30 ! [V_b,V_a,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__0,axiom,
% 52.23/52.30 ! [V_a,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__by__0,axiom,
% 52.23/52.30 ! [V_a,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__self,axiom,
% 52.23/52.30 ! [V_a,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__add__self2,axiom,
% 52.23/52.30 ! [V_b,V_a,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__add__self1,axiom,
% 52.23/52.30 ! [V_a,V_b,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__add__right__eq,axiom,
% 52.23/52.30 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__add__left__eq,axiom,
% 52.23/52.30 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__add__eq,axiom,
% 52.23/52.30 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zmod__simps_I2_J,axiom,
% 52.23/52.30 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zmod__simps_I1_J,axiom,
% 52.23/52.30 ! [V_b,V_c,V_a,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__add__cong,axiom,
% 52.23/52.30 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 52.23/52.30 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 52.23/52.30 => 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) ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__mult__right__eq,axiom,
% 52.23/52.30 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__mult__left__eq,axiom,
% 52.23/52.30 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__mult__eq,axiom,
% 52.23/52.30 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__mult__mult1,axiom,
% 52.23/52.30 ! [V_b,V_a,V_c,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => 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)) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__mult__mult2,axiom,
% 52.23/52.30 ! [V_b,V_c,V_a,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zmod__simps_I4_J,axiom,
% 52.23/52.30 ! [V_b,V_c,V_a,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__mult__cong,axiom,
% 52.23/52.30 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 52.23/52.30 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 52.23/52.30 => 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) ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__minus__eq,axiom,
% 52.23/52.30 ! [V_b,V_a,T_a] :
% 52.23/52.30 ( class_Divides_Oring__div(T_a)
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__minus__cong,axiom,
% 52.23/52.30 ! [V_a_H,V_b,V_a,T_a] :
% 52.23/52.30 ( class_Divides_Oring__div(T_a)
% 52.23/52.30 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)
% 52.23/52.30 => 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) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zmod__zero,axiom,
% 52.23/52.30 ! [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) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zmod__self,axiom,
% 52.23/52.30 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zmod__simps_I3_J,axiom,
% 52.23/52.30 ! [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) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zmod__zmult1__eq,axiom,
% 52.23/52.30 ! [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) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zminus__zmod,axiom,
% 52.23/52.30 ! [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) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zmod__zminus__zminus,axiom,
% 52.23/52.30 ! [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)) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zmod__zminus2,axiom,
% 52.23/52.30 ! [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)) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__mult__self2__is__0,axiom,
% 52.23/52.30 ! [V_b,V_a,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__mult__self1__is__0,axiom,
% 52.23/52.30 ! [V_a,V_b,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__mult__self2,axiom,
% 52.23/52.30 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__mult__self1,axiom,
% 52.23/52.30 ! [V_b,V_c,V_a,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__by__1,axiom,
% 52.23/52.30 ! [V_a,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zmod__le__nonneg__dividend,axiom,
% 52.23/52.30 ! [V_k,V_m] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 52.23/52.30 => 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)) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
% 52.23/52.30 ! [V_y,V_x] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 52.23/52.30 => 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))) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_neg__mod__bound,axiom,
% 52.23/52.30 ! [V_a,V_b] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.30 => 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))) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_pos__mod__bound,axiom,
% 52.23/52.30 ! [V_a,V_b] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 52.23/52.30 => 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)) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zmod__eq__0__iff,axiom,
% 52.23/52.30 ! [V_d_2,V_m_2] :
% 52.23/52.30 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.30 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zmod__zminus2__not__zero,axiom,
% 52.23/52.30 ! [V_l,V_k] :
% 52.23/52.30 ( 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)
% 52.23/52.30 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zmod__zminus1__not__zero,axiom,
% 52.23/52.30 ! [V_l,V_k] :
% 52.23/52.30 ( 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)
% 52.23/52.30 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__neg__neg__trivial,axiom,
% 52.23/52.30 ! [V_b,V_a] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 52.23/52.30 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_neg__mod__conj,axiom,
% 52.23/52.30 ! [V_a,V_b] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.30 => ( 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)))
% 52.23/52.30 & 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))) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_neg__mod__sign,axiom,
% 52.23/52.30 ! [V_a,V_b] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.30 => 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))) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__pos__pos__trivial,axiom,
% 52.23/52.30 ! [V_b,V_a] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 52.23/52.30 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_pos__mod__conj,axiom,
% 52.23/52.30 ! [V_a,V_b] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 52.23/52.30 => ( 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)))
% 52.23/52.30 & 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)) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_pos__mod__sign,axiom,
% 52.23/52.30 ! [V_a,V_b] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 52.23/52.30 => 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))) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mult__left__idem,axiom,
% 52.23/52.30 ! [V_b,V_a,T_a] :
% 52.23/52.30 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mult__idem,axiom,
% 52.23/52.30 ! [V_x,T_a] :
% 52.23/52.30 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 52.23/52.30 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_times_Oidem,axiom,
% 52.23/52.30 ! [V_a,T_a] :
% 52.23/52.30 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 52.23/52.30 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_compl__eq__compl__iff,axiom,
% 52.23/52.30 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.30 ( class_Lattices_Oboolean__algebra(T_b)
% 52.23/52.30 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)
% 52.23/52.30 <=> V_x_2 = V_y_2 ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_uminus__apply,axiom,
% 52.23/52.30 ! [V_x_2,V_A_2,T_c,T_b] :
% 52.23/52.30 ( class_Groups_Ouminus(T_b)
% 52.23/52.30 => 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)) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_double__compl,axiom,
% 52.23/52.30 ! [V_x,T_a] :
% 52.23/52.30 ( class_Lattices_Oboolean__algebra(T_a)
% 52.23/52.30 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__pos__neg__trivial,axiom,
% 52.23/52.30 ! [V_b,V_a] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 52.23/52.30 => ( 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)))
% 52.23/52.30 => 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) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_split__zmod,axiom,
% 52.23/52.30 ! [V_k_2,V_n_2,V_P_2] :
% 52.23/52.30 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 52.23/52.30 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.30 => hBOOL(hAPP(V_P_2,V_n_2)) )
% 52.23/52.30 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 52.23/52.30 => ! [B_i,B_j] :
% 52.23/52.30 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 52.23/52.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 52.23/52.30 & 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) )
% 52.23/52.30 => hBOOL(hAPP(V_P_2,B_j)) ) )
% 52.23/52.30 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.30 => ! [B_i,B_j] :
% 52.23/52.30 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 52.23/52.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.30 & 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) )
% 52.23/52.30 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zmult2__lemma__aux3,axiom,
% 52.23/52.30 ! [V_q,V_b,V_r,V_c] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 52.23/52.30 => 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))) ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_z3mod__def,axiom,
% 52.23/52.30 ! [V_k,V_l] :
% 52.23/52.30 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 52.23/52.30 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) )
% 52.23/52.30 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 52.23/52.30 => 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)) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_split__pos__lemma,axiom,
% 52.23/52.30 ! [V_n_2,V_P_2,V_k_2] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 52.23/52.30 => ( 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)))
% 52.23/52.30 <=> ! [B_i,B_j] :
% 52.23/52.30 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 52.23/52.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 52.23/52.30 & 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) )
% 52.23/52.30 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_split__neg__lemma,axiom,
% 52.23/52.30 ! [V_n_2,V_P_2,V_k_2] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.30 => ( 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)))
% 52.23/52.30 <=> ! [B_i,B_j] :
% 52.23/52.30 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 52.23/52.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.30 & 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) )
% 52.23/52.30 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zmod__zmult2__eq,axiom,
% 52.23/52.30 ! [V_b,V_a,V_c] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 52.23/52.30 => 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)) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
% 52.23/52.30 ! [V_y,V_x] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 52.23/52.30 => 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))) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_split__zdiv,axiom,
% 52.23/52.30 ! [V_k_2,V_n_2,V_P_2] :
% 52.23/52.30 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)))
% 52.23/52.30 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.30 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 52.23/52.30 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 52.23/52.30 => ! [B_i] :
% 52.23/52.30 ( ? [B_j] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 52.23/52.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 52.23/52.30 & 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) )
% 52.23/52.30 => hBOOL(hAPP(V_P_2,B_i)) ) )
% 52.23/52.30 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.30 => ! [B_i] :
% 52.23/52.30 ( ? [B_j] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 52.23/52.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.30 & 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) )
% 52.23/52.30 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_divmod__int__rel__div__eq,axiom,
% 52.23/52.30 ! [V_r_1,V_y,V_b_1,V_a_1] :
% 52.23/52.30 ( 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)
% 52.23/52.30 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1))
% 52.23/52.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) )
% 52.23/52.30 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1))
% 52.23/52.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 52.23/52.30 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.30 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_split__div_H,axiom,
% 52.23/52.30 ! [V_n_2,V_m_2,V_P_2] :
% 52.23/52.30 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))
% 52.23/52.30 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.30 & hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 52.23/52.30 | ? [B_q] :
% 52.23/52.30 ( 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))
% 52.23/52.30 & 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))))
% 52.23/52.30 & hBOOL(hAPP(V_P_2,B_q)) ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_div__add1__eq,axiom,
% 52.23/52.30 ! [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)) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
% 52.23/52.30 ! [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)) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zdiv__int,axiom,
% 52.23/52.30 ! [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)) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__mult2__eq,axiom,
% 52.23/52.30 ! [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)) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_div__mult1__eq,axiom,
% 52.23/52.30 ! [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)) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_div__le__mono,axiom,
% 52.23/52.30 ! [V_k,V_n,V_m] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 52.23/52.30 => 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))) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_div__le__dividend,axiom,
% 52.23/52.30 ! [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)) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zdiv__zero,axiom,
% 52.23/52.30 ! [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) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__Suc__eq__Suc__mod,axiom,
% 52.23/52.30 ! [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) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_div__mult2__eq,axiom,
% 52.23/52.30 ! [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) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__less,axiom,
% 52.23/52.30 ! [V_n,V_m] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 52.23/52.30 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__less__eq__dividend,axiom,
% 52.23/52.30 ! [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)) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__mult__distrib,axiom,
% 52.23/52.30 ! [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)) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__mult__distrib2,axiom,
% 52.23/52.30 ! [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)) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zdiv__zminus2,axiom,
% 52.23/52.30 ! [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) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zdiv__zminus__zminus,axiom,
% 52.23/52.30 ! [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) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_div__0,axiom,
% 52.23/52.30 ! [V_a,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_div__by__0,axiom,
% 52.23/52.30 ! [V_a,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_div__by__1,axiom,
% 52.23/52.30 ! [V_a,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_nat__div__distrib,axiom,
% 52.23/52.30 ! [V_y,V_x] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 52.23/52.30 => 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)) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom,
% 52.23/52.30 ! [V_y,V_x] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 52.23/52.30 => 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)) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_div__1,axiom,
% 52.23/52.30 ! [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 ).
% 52.23/52.30
% 52.23/52.30 fof(fact_div__less,axiom,
% 52.23/52.30 ! [V_n,V_m] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 52.23/52.30 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_nat__mult__div__cancel__disj,axiom,
% 52.23/52.30 ! [V_n,V_m,V_k] :
% 52.23/52.30 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.30 => 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) )
% 52.23/52.30 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.30 => 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) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__Suc,axiom,
% 52.23/52.30 ! [V_n,V_m] :
% 52.23/52.30 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n
% 52.23/52.30 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 52.23/52.30 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n
% 52.23/52.30 => 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)) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__1,axiom,
% 52.23/52.30 ! [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) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
% 52.23/52.30 ! [V_y,V_x] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 52.23/52.30 => 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))) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__less__divisor,axiom,
% 52.23/52.30 ! [V_m,V_n] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 52.23/52.30 => 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)) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_pos__imp__zdiv__neg__iff,axiom,
% 52.23/52.30 ! [V_a_2,V_b_2] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 52.23/52.30 => ( 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)))
% 52.23/52.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_neg__imp__zdiv__neg__iff,axiom,
% 52.23/52.30 ! [V_a_2,V_b_2] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.30 => ( 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)))
% 52.23/52.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_div__neg__pos__less0,axiom,
% 52.23/52.30 ! [V_b,V_a] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 52.23/52.30 => 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))) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zdiv__self,axiom,
% 52.23/52.30 ! [V_a] :
% 52.23/52.30 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.30 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__eq__0__iff,axiom,
% 52.23/52.30 ! [V_d_2,V_m_2] :
% 52.23/52.30 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.30 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_DIVISION__BY__ZERO,axiom,
% 52.23/52.30 ! [V_a] :
% 52.23/52.30 ( 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)
% 52.23/52.30 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zmod__zdiv__trivial,axiom,
% 52.23/52.30 ! [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) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__mult__self3,axiom,
% 52.23/52.30 ! [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) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zdiv__zadd1__eq,axiom,
% 52.23/52.30 ! [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)) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom,
% 52.23/52.30 ! [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)) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zmod__int,axiom,
% 52.23/52.30 ! [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)) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_div__mult__mult1,axiom,
% 52.23/52.30 ! [V_b,V_a,V_c,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.30 => 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) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_div__mult__mult2,axiom,
% 52.23/52.30 ! [V_b,V_a,V_c,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.30 => 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) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_div__mult__self1__is__id,axiom,
% 52.23/52.30 ! [V_a,V_b,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.30 => 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 ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_div__mult__self2__is__id,axiom,
% 52.23/52.30 ! [V_a,V_b,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.30 => 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 ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_div__mult__mult1__if,axiom,
% 52.23/52.30 ! [V_b,V_a,V_c,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.30 => 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) )
% 52.23/52.30 & ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.30 => 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) ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_div__self,axiom,
% 52.23/52.30 ! [V_a,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.30 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__div__trivial,axiom,
% 52.23/52.30 ! [V_b,V_a,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_div__le__mono2,axiom,
% 52.23/52.30 ! [V_k,V_n,V_m] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 52.23/52.30 => 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))) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_div__mult__self__is__m,axiom,
% 52.23/52.30 ! [V_m,V_n] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 52.23/52.30 => 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 ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_div__mult__self1__is__m,axiom,
% 52.23/52.30 ! [V_m,V_n] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 52.23/52.30 => 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 ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_nat__mult__div__cancel1,axiom,
% 52.23/52.30 ! [V_n,V_m,V_k] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_div__less__dividend,axiom,
% 52.23/52.30 ! [V_m,V_n] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 52.23/52.30 => 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)) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zdiv__eq__0__iff,axiom,
% 52.23/52.30 ! [V_k_2,V_i_2] :
% 52.23/52.30 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.30 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.30 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2))
% 52.23/52.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) )
% 52.23/52.30 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
% 52.23/52.30 ! [V_a_2,V_b_2] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 52.23/52.30 => ( 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)))
% 52.23/52.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_pos__imp__zdiv__pos__iff,axiom,
% 52.23/52.30 ! [V_i_2,V_k_2] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 52.23/52.30 => ( 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)))
% 52.23/52.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
% 52.23/52.30 ! [V_b_2,V_a_2] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
% 52.23/52.30 => ( 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)))
% 52.23/52.30 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2))
% 52.23/52.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zdiv__mono2,axiom,
% 52.23/52.30 ! [V_b,V_b_H,V_a] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 52.23/52.30 => 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))) ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_div__nonneg__neg__le0,axiom,
% 52.23/52.30 ! [V_b,V_a] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.30 => 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))) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_div__pos__pos__trivial,axiom,
% 52.23/52.30 ! [V_b,V_a] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 52.23/52.30 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
% 52.23/52.30 ! [V_a_2,V_b_2] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.30 => ( 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)))
% 52.23/52.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_div__nonpos__pos__le0,axiom,
% 52.23/52.30 ! [V_b,V_a] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 52.23/52.30 => 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))) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zdiv__mono2__neg,axiom,
% 52.23/52.30 ! [V_b,V_b_H,V_a] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 52.23/52.30 => 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))) ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_div__neg__neg__trivial,axiom,
% 52.23/52.30 ! [V_b,V_a] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 52.23/52.30 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zdiv__mono1,axiom,
% 52.23/52.30 ! [V_b,V_a_H,V_a] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 52.23/52.30 => 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))) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zdiv__mono1__neg,axiom,
% 52.23/52.30 ! [V_b,V_a_H,V_a] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.30 => 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))) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__le__divisor,axiom,
% 52.23/52.30 ! [V_m,V_n] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 52.23/52.30 => 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)) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_int__div__less__self,axiom,
% 52.23/52.30 ! [V_k,V_x] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
% 52.23/52.30 => 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)) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zdiv__zmult2__eq,axiom,
% 52.23/52.30 ! [V_b,V_a,V_c] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__mult__self4,axiom,
% 52.23/52.30 ! [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) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zdiv__zmod__equality2,axiom,
% 52.23/52.30 ! [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) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zdiv__zmod__equality,axiom,
% 52.23/52.30 ! [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) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zdiv__zmult1__eq,axiom,
% 52.23/52.30 ! [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)) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zmod__zdiv__equality,axiom,
% 52.23/52.30 ! [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)) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_div__mult__self1,axiom,
% 52.23/52.30 ! [V_c,V_a,V_b,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.30 => 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)) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_div__mult__self2,axiom,
% 52.23/52.30 ! [V_c,V_a,V_b,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.30 => 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)) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_div__add__self1,axiom,
% 52.23/52.30 ! [V_a,V_b,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.30 => 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)) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_div__add__self2,axiom,
% 52.23/52.30 ! [V_a,V_b,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.30 => 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)) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_div__mod__equality,axiom,
% 52.23/52.30 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_div__mod__equality2,axiom,
% 52.23/52.30 ! [V_c,V_a,V_b,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__div__equality,axiom,
% 52.23/52.30 ! [V_b,V_a,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => 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 ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__div__equality2,axiom,
% 52.23/52.30 ! [V_a,V_b,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => 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 ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
% 52.23/52.30 ! [V_b,V_a,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => 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 ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_split__div,axiom,
% 52.23/52.30 ! [V_k_2,V_n_2,V_P_2] :
% 52.23/52.30 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2)))
% 52.23/52.30 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.30 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 52.23/52.30 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.30 => ! [B_i,B_j] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 52.23/52.30 => ( 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)
% 52.23/52.30 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__lemma,axiom,
% 52.23/52.30 ! [V_q,V_b,V_r,V_c] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b))
% 52.23/52.30 => 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))) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_split__mod,axiom,
% 52.23/52.30 ! [V_k_2,V_n_2,V_P_2] :
% 52.23/52.30 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
% 52.23/52.30 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.30 => hBOOL(hAPP(V_P_2,V_n_2)) )
% 52.23/52.30 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.30 => ! [B_i,B_j] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 52.23/52.30 => ( 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)
% 52.23/52.30 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_Suc__times__mod__eq,axiom,
% 52.23/52.30 ! [V_m,V_k] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k))
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_nat__mod__distrib,axiom,
% 52.23/52.30 ! [V_y,V_x] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 52.23/52.30 => 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)) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom,
% 52.23/52.30 ! [V_y,V_x] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 52.23/52.30 => 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)) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_split__div__lemma,axiom,
% 52.23/52.30 ! [V_m_2,V_q_2,V_n_2] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 52.23/52.30 => ( ( 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))
% 52.23/52.30 & 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)))) )
% 52.23/52.30 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_z3div__def,axiom,
% 52.23/52.30 ! [V_k,V_l] :
% 52.23/52.30 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 52.23/52.30 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) )
% 52.23/52.30 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 52.23/52.30 => 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))) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zdiv__zminus1__eq__if,axiom,
% 52.23/52.30 ! [V_a,V_b] :
% 52.23/52.30 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.30 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.30 => 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)) )
% 52.23/52.30 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.30 => 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)) ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zdiv__zminus2__eq__if,axiom,
% 52.23/52.30 ! [V_a,V_b] :
% 52.23/52.30 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.30 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.30 => 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)) )
% 52.23/52.30 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.30 => 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)) ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_le__div__geq,axiom,
% 52.23/52.30 ! [V_m,V_n] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 52.23/52.30 => 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)) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__div__decomp,axiom,
% 52.23/52.30 ! [V_b,V_a,T_a] :
% 52.23/52.30 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.30 => 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)) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom,
% 52.23/52.30 ! [V_y,V_x] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 52.23/52.30 => 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)) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_incr__mult__lemma,axiom,
% 52.23/52.30 ! [V_k_2,V_P_2,V_d_2] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 52.23/52.30 => ( ! [B_x] :
% 52.23/52.30 ( hBOOL(hAPP(V_P_2,B_x))
% 52.23/52.30 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) )
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 52.23/52.30 => ! [B_x] :
% 52.23/52.30 ( hBOOL(hAPP(V_P_2,B_x))
% 52.23/52.30 => 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)))) ) ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_field__le__mult__one__interval,axiom,
% 52.23/52.30 ! [V_y,V_x,T_a] :
% 52.23/52.30 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 52.23/52.30 => ( ! [B_z] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a)))
% 52.23/52.30 => 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)) ) )
% 52.23/52.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__commute,axiom,
% 52.23/52.30 ! [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) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__eq__diff__eq,axiom,
% 52.23/52.30 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 52.23/52.30 ( class_Groups_Oab__group__add(T_b)
% 52.23/52.30 => ( 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)
% 52.23/52.30 => ( V_a_2 = V_b_2
% 52.23/52.30 <=> V_c_2 = V_d_2 ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_of__int__diff,axiom,
% 52.23/52.30 ! [V_z,V_w,T_a] :
% 52.23/52.30 ( class_Rings_Oring__1(T_a)
% 52.23/52.30 => 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)) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_minus__apply,axiom,
% 52.23/52.30 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 52.23/52.30 ( class_Groups_Ominus(T_b)
% 52.23/52.30 => 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)) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_of__nat__diff,axiom,
% 52.23/52.30 ! [V_m,V_n,T_a] :
% 52.23/52.30 ( class_Rings_Oring__1(T_a)
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 52.23/52.30 => 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)) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zdiff__int,axiom,
% 52.23/52.30 ! [V_m,V_n] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 52.23/52.30 => 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)) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__eq__diff__less__eq,axiom,
% 52.23/52.30 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 52.23/52.30 ( class_Groups_Oordered__ab__group__add(T_b)
% 52.23/52.30 => ( 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)
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 52.23/52.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_right__minus__eq,axiom,
% 52.23/52.30 ! [V_b_2,V_a_2,T_b] :
% 52.23/52.30 ( class_Groups_Ogroup__add(T_b)
% 52.23/52.30 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.30 <=> V_a_2 = V_b_2 ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_eq__iff__diff__eq__0,axiom,
% 52.23/52.30 ! [V_b_2,V_a_2,T_b] :
% 52.23/52.30 ( class_Groups_Oab__group__add(T_b)
% 52.23/52.30 => ( V_a_2 = V_b_2
% 52.23/52.30 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__self,axiom,
% 52.23/52.30 ! [V_a,T_a] :
% 52.23/52.30 ( class_Groups_Ogroup__add(T_a)
% 52.23/52.30 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__0__right,axiom,
% 52.23/52.30 ! [V_a,T_a] :
% 52.23/52.30 ( class_Groups_Ogroup__add(T_a)
% 52.23/52.30 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__eq__diff__less,axiom,
% 52.23/52.30 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 52.23/52.30 ( class_Groups_Oordered__ab__group__add(T_b)
% 52.23/52.30 => ( 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)
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 52.23/52.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2)) ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_add__diff__cancel,axiom,
% 52.23/52.30 ! [V_b,V_a,T_a] :
% 52.23/52.30 ( class_Groups_Ogroup__add(T_a)
% 52.23/52.30 => 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 ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__add__cancel,axiom,
% 52.23/52.30 ! [V_b,V_a,T_a] :
% 52.23/52.30 ( class_Groups_Ogroup__add(T_a)
% 52.23/52.30 => 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 ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_minus__diff__eq,axiom,
% 52.23/52.30 ! [V_b,V_a,T_a] :
% 52.23/52.30 ( class_Groups_Oab__group__add(T_a)
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__diff__right__eq,axiom,
% 52.23/52.30 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.30 ( class_Divides_Oring__div(T_a)
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__diff__left__eq,axiom,
% 52.23/52.30 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.30 ( class_Divides_Oring__div(T_a)
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__diff__eq,axiom,
% 52.23/52.30 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.30 ( class_Divides_Oring__div(T_a)
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__diff__cong,axiom,
% 52.23/52.30 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 52.23/52.30 ( class_Divides_Oring__div(T_a)
% 52.23/52.30 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 52.23/52.30 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 52.23/52.30 => 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) ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__0__eq__0,axiom,
% 52.23/52.30 ! [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) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_minus__nat_Odiff__0,axiom,
% 52.23/52.30 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__self__eq__0,axiom,
% 52.23/52.30 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diffs0__imp__equal,axiom,
% 52.23/52.30 ! [V_n,V_m] :
% 52.23/52.30 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.30 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.30 => V_m = V_n ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_Suc__diff__diff,axiom,
% 52.23/52.30 ! [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) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__Suc__Suc,axiom,
% 52.23/52.30 ! [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) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_less__imp__diff__less,axiom,
% 52.23/52.30 ! [V_n,V_k,V_j] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 52.23/52.30 => 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)) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__less__mono2,axiom,
% 52.23/52.30 ! [V_l,V_n,V_m] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l))
% 52.23/52.30 => 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))) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__if,axiom,
% 52.23/52.30 ! [V_n,V_m] :
% 52.23/52.30 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 52.23/52.30 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m )
% 52.23/52.30 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 52.23/52.30 => 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) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__geq,axiom,
% 52.23/52.30 ! [V_n,V_m] :
% 52.23/52.30 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__add__inverse2,axiom,
% 52.23/52.30 ! [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 ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__add__inverse,axiom,
% 52.23/52.30 ! [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 ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__diff__left,axiom,
% 52.23/52.30 ! [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)) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__cancel,axiom,
% 52.23/52.30 ! [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) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__cancel2,axiom,
% 52.23/52.30 ! [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) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_le__diff__iff,axiom,
% 52.23/52.30 ! [V_n_2,V_m_2,V_k_2] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 52.23/52.30 => ( 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)))
% 52.23/52.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_Nat_Odiff__diff__eq,axiom,
% 52.23/52.30 ! [V_n,V_m,V_k] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 52.23/52.30 => 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) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_eq__diff__iff,axiom,
% 52.23/52.30 ! [V_n_2,V_m_2,V_k_2] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 52.23/52.30 => ( 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)
% 52.23/52.30 <=> V_m_2 = V_n_2 ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__diff__cancel,axiom,
% 52.23/52.30 ! [V_n,V_i] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n))
% 52.23/52.30 => 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 ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__le__mono,axiom,
% 52.23/52.30 ! [V_l,V_n,V_m] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 52.23/52.30 => 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))) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__le__mono2,axiom,
% 52.23/52.30 ! [V_l,V_n,V_m] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 52.23/52.30 => 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))) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__le__self,axiom,
% 52.23/52.30 ! [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)) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_le__mod__geq,axiom,
% 52.23/52.30 ! [V_m,V_n] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zdiff__zmult__distrib2,axiom,
% 52.23/52.30 ! [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)) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zdiff__zmult__distrib,axiom,
% 52.23/52.30 ! [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)) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__mult__distrib,axiom,
% 52.23/52.30 ! [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)) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__mult__distrib2,axiom,
% 52.23/52.30 ! [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)) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zdiff__zmod__right,axiom,
% 52.23/52.30 ! [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) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zdiff__zmod__left,axiom,
% 52.23/52.30 ! [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) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_nat__diff__distrib,axiom,
% 52.23/52.30 ! [V_z,V_z_H] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 52.23/52.30 => 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)) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zdiff__int__split,axiom,
% 52.23/52.30 ! [V_y_2,V_x_2,V_P_2] :
% 52.23/52.30 ( 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))))
% 52.23/52.30 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2))
% 52.23/52.30 => 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)))) )
% 52.23/52.30 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 52.23/52.30 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_le__iff__diff__le__0,axiom,
% 52.23/52.30 ! [V_b_2,V_a_2,T_b] :
% 52.23/52.30 ( class_Groups_Oordered__ab__group__add(T_b)
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 52.23/52.30 <=> 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))) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_less__iff__diff__less__0,axiom,
% 52.23/52.30 ! [V_b_2,V_a_2,T_b] :
% 52.23/52.30 ( class_Groups_Oordered__ab__group__add(T_b)
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 52.23/52.30 <=> 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))) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_eq__add__iff1,axiom,
% 52.23/52.30 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 52.23/52.30 ( class_Rings_Oring(T_b)
% 52.23/52.30 => ( 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)
% 52.23/52.30 <=> 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 ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_eq__add__iff2,axiom,
% 52.23/52.30 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 52.23/52.30 ( class_Rings_Oring(T_b)
% 52.23/52.30 => ( 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)
% 52.23/52.30 <=> 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) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__0,axiom,
% 52.23/52.30 ! [V_a,T_a] :
% 52.23/52.30 ( class_Groups_Ogroup__add(T_a)
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__def,axiom,
% 52.23/52.30 ! [V_b,V_a,T_a] :
% 52.23/52.30 ( class_Groups_Ogroup__add(T_a)
% 52.23/52.30 => 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)) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_ab__diff__minus,axiom,
% 52.23/52.30 ! [V_b,V_a,T_a] :
% 52.23/52.30 ( class_Groups_Oab__group__add(T_a)
% 52.23/52.30 => 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)) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
% 52.23/52.30 ! [V_y,V_x,T_a] :
% 52.23/52.30 ( class_Rings_Ocomm__ring__1(T_a)
% 52.23/52.30 => 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)) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__minus__eq__add,axiom,
% 52.23/52.30 ! [V_b,V_a,T_a] :
% 52.23/52.30 ( class_Groups_Ogroup__add(T_a)
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_less__bin__lemma,axiom,
% 52.23/52.30 ! [V_l_2,V_k_2] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
% 52.23/52.30 <=> 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))) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zero__less__diff,axiom,
% 52.23/52.30 ! [V_m_2,V_n_2] :
% 52.23/52.30 ( 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)))
% 52.23/52.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__less,axiom,
% 52.23/52.30 ! [V_m,V_n] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 52.23/52.30 => 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)) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__less__Suc,axiom,
% 52.23/52.30 ! [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))) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__add__0,axiom,
% 52.23/52.30 ! [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) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__is__0__eq,axiom,
% 52.23/52.30 ! [V_n_2,V_m_2] :
% 52.23/52.30 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__is__0__eq_H,axiom,
% 52.23/52.30 ! [V_n,V_m] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 52.23/52.30 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_less__diff__conv,axiom,
% 52.23/52.30 ! [V_k_2,V_j_2,V_i_2] :
% 52.23/52.30 ( 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)))
% 52.23/52.30 <=> 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)) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_add__diff__inverse,axiom,
% 52.23/52.30 ! [V_n,V_m] :
% 52.23/52.30 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 52.23/52.30 => 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 ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_Suc__diff__le,axiom,
% 52.23/52.30 ! [V_m,V_n] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 52.23/52.30 => 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)) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_less__diff__iff,axiom,
% 52.23/52.30 ! [V_n_2,V_m_2,V_k_2] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 52.23/52.30 => ( 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)))
% 52.23/52.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__less__mono,axiom,
% 52.23/52.30 ! [V_c,V_b,V_a] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a))
% 52.23/52.30 => 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))) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__add__assoc2,axiom,
% 52.23/52.30 ! [V_i,V_j,V_k] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_add__diff__assoc2,axiom,
% 52.23/52.30 ! [V_i,V_j,V_k] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__add__assoc,axiom,
% 52.23/52.30 ! [V_i,V_j,V_k] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 52.23/52.30 => 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)) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_le__imp__diff__is__add,axiom,
% 52.23/52.30 ! [V_k_2,V_j_2,V_i_2] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 52.23/52.30 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2
% 52.23/52.30 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_le__add__diff__inverse2,axiom,
% 52.23/52.30 ! [V_m,V_n] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 52.23/52.30 => 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 ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_le__diff__conv2,axiom,
% 52.23/52.30 ! [V_i_2,V_j_2,V_k_2] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2))
% 52.23/52.30 => ( 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)))
% 52.23/52.30 <=> 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)) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_add__diff__assoc,axiom,
% 52.23/52.30 ! [V_i,V_j,V_k] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_le__add__diff__inverse,axiom,
% 52.23/52.30 ! [V_m,V_n] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 52.23/52.30 => 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 ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_le__add__diff,axiom,
% 52.23/52.30 ! [V_m,V_n,V_k] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 52.23/52.30 => 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))) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_le__diff__conv,axiom,
% 52.23/52.30 ! [V_i_2,V_k_2,V_j_2] :
% 52.23/52.30 ( 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))
% 52.23/52.30 <=> 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))) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__diff__right,axiom,
% 52.23/52.30 ! [V_i,V_j,V_k] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__int__def,axiom,
% 52.23/52.30 ! [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)) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__int__def__symmetric,axiom,
% 52.23/52.30 ! [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) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__Suc__eq__diff__pred,axiom,
% 52.23/52.30 ! [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) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__Suc__1,axiom,
% 52.23/52.30 ! [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 ).
% 52.23/52.30
% 52.23/52.30 fof(fact_div__mod__equality_H,axiom,
% 52.23/52.30 ! [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)) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mult__div__cancel,axiom,
% 52.23/52.30 ! [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)) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_Divides_Omod__div__equality_H,axiom,
% 52.23/52.30 ! [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)) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_tsub__eq,axiom,
% 52.23/52.30 ! [V_x,V_y] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 52.23/52.30 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
% 52.23/52.30 ! [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)) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_le__add__iff1,axiom,
% 52.23/52.30 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 52.23/52.30 ( class_Rings_Oordered__ring(T_b)
% 52.23/52.30 => ( 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)))
% 52.23/52.30 <=> 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)) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_le__add__iff2,axiom,
% 52.23/52.30 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 52.23/52.30 ( class_Rings_Oordered__ring(T_b)
% 52.23/52.30 => ( 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)))
% 52.23/52.30 <=> 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))) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_less__add__iff1,axiom,
% 52.23/52.30 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 52.23/52.30 ( class_Rings_Oordered__ring(T_b)
% 52.23/52.30 => ( 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)))
% 52.23/52.30 <=> 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)) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_less__add__iff2,axiom,
% 52.23/52.30 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 52.23/52.30 ( class_Rings_Oordered__ring(T_b)
% 52.23/52.30 => ( 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)))
% 52.23/52.30 <=> 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))) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__Suc__less,axiom,
% 52.23/52.30 ! [V_i,V_n] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 52.23/52.30 => 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)) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_Suc__pred,axiom,
% 52.23/52.30 ! [V_n] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 52.23/52.30 => 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 ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_nat__diff__split,axiom,
% 52.23/52.30 ! [V_b_2,V_a_2,V_P_2] :
% 52.23/52.30 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 52.23/52.30 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 52.23/52.30 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 52.23/52.30 & ! [B_d] :
% 52.23/52.30 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 52.23/52.30 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_nat__diff__split__asm,axiom,
% 52.23/52.30 ! [V_b_2,V_a_2,V_P_2] :
% 52.23/52.30 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 52.23/52.30 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 52.23/52.30 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 52.23/52.30 | ? [B_d] :
% 52.23/52.30 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 52.23/52.30 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zle__diff1__eq,axiom,
% 52.23/52.30 ! [V_z_2,V_w_2] :
% 52.23/52.30 ( 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))))
% 52.23/52.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__Suc__diff__eq2,axiom,
% 52.23/52.30 ! [V_m,V_j,V_k] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 52.23/52.30 => 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)) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_diff__Suc__diff__eq1,axiom,
% 52.23/52.30 ! [V_m,V_j,V_k] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 52.23/52.30 => 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)) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_nat__le__add__iff1,axiom,
% 52.23/52.30 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 52.23/52.30 => ( 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)))
% 52.23/52.30 <=> 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)) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_nat__diff__add__eq1,axiom,
% 52.23/52.30 ! [V_n,V_m,V_u,V_i,V_j] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_nat__eq__add__iff1,axiom,
% 52.23/52.30 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 52.23/52.30 => ( 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)
% 52.23/52.30 <=> 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 ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_nat__le__add__iff2,axiom,
% 52.23/52.30 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 52.23/52.30 => ( 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)))
% 52.23/52.30 <=> 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))) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_nat__diff__add__eq2,axiom,
% 52.23/52.30 ! [V_n,V_m,V_u,V_j,V_i] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 52.23/52.30 => 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)) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_nat__eq__add__iff2,axiom,
% 52.23/52.30 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 52.23/52.30 => ( 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)
% 52.23/52.30 <=> 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) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zmod__zminus2__eq__if,axiom,
% 52.23/52.30 ! [V_b,V_a] :
% 52.23/52.30 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.30 => 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) )
% 52.23/52.30 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.30 => 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) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zmod__zminus1__eq__if,axiom,
% 52.23/52.30 ! [V_b,V_a] :
% 52.23/52.30 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.30 => 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) )
% 52.23/52.30 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.30 => 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)) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zmod__zdiv__equality_H,axiom,
% 52.23/52.30 ! [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)) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zmult__div__cancel,axiom,
% 52.23/52.30 ! [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)) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_tsub__def,axiom,
% 52.23/52.30 ! [V_x,V_y] :
% 52.23/52.30 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 52.23/52.30 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) )
% 52.23/52.30 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 52.23/52.30 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_Suc__diff__1,axiom,
% 52.23/52.30 ! [V_n] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 52.23/52.30 => 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 ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_Suc__pred_H,axiom,
% 52.23/52.30 ! [V_n] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 52.23/52.30 => 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))) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_nat__less__add__iff1,axiom,
% 52.23/52.30 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 52.23/52.30 => ( 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)))
% 52.23/52.30 <=> 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)) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_nat__less__add__iff2,axiom,
% 52.23/52.30 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 52.23/52.30 => ( 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)))
% 52.23/52.30 <=> 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))) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_add__eq__if,axiom,
% 52.23/52.30 ! [V_n,V_m] :
% 52.23/52.30 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.30 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n )
% 52.23/52.30 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.30 => 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)) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_div__if,axiom,
% 52.23/52.30 ! [V_m,V_n] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 52.23/52.30 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 52.23/52.30 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 52.23/52.30 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 52.23/52.30 => 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)) ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_div__geq,axiom,
% 52.23/52.30 ! [V_m,V_n] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 52.23/52.30 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 52.23/52.30 => 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)) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mult__eq__if,axiom,
% 52.23/52.30 ! [V_n,V_m] :
% 52.23/52.30 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.30 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 52.23/52.30 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.30 => 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)) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_int__power__div__base,axiom,
% 52.23/52.30 ! [V_k,V_m] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 52.23/52.30 => 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)))) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_decr__mult__lemma,axiom,
% 52.23/52.30 ! [V_k_2,V_P_2,V_d_2] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 52.23/52.30 => ( ! [B_x] :
% 52.23/52.30 ( hBOOL(hAPP(V_P_2,B_x))
% 52.23/52.30 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) )
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 52.23/52.30 => ! [B_x] :
% 52.23/52.30 ( hBOOL(hAPP(V_P_2,B_x))
% 52.23/52.30 => 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)))) ) ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_incr__lemma,axiom,
% 52.23/52.30 ! [V_x,V_z,V_d] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 52.23/52.30 => 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)))) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_decr__lemma,axiom,
% 52.23/52.30 ! [V_z,V_x,V_d] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 52.23/52.30 => 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)) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_nat__mod__eq__lemma,axiom,
% 52.23/52.30 ! [V_y,V_n,V_x] :
% 52.23/52.30 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n)
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x))
% 52.23/52.30 => ? [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)) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_mod__induct__0,axiom,
% 52.23/52.30 ! [V_i_2,V_P_2,V_p_2] :
% 52.23/52.30 ( ! [B_i] :
% 52.23/52.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2))
% 52.23/52.30 => ( hBOOL(hAPP(V_P_2,B_i))
% 52.23/52.30 => hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) )
% 52.23/52.30 => ( hBOOL(hAPP(V_P_2,V_i_2))
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
% 52.23/52.30 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_expand__Suc,axiom,
% 52.23/52.30 ! [V_v] :
% 52.23/52.30 ( 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)))
% 52.23/52.30 => 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))) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_nat__gcd_Osimps,axiom,
% 52.23/52.30 ! [V_x,V_y] :
% 52.23/52.30 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.30 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x )
% 52.23/52.30 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.30 => 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)) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_of__int__power,axiom,
% 52.23/52.30 ! [V_n,V_z,T_a] :
% 52.23/52.30 ( class_Rings_Oring__1(T_a)
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_of__int__number__of__eq,axiom,
% 52.23/52.30 ! [V_v,T_a] :
% 52.23/52.30 ( class_Int_Onumber__ring(T_a)
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_eq__number__of,axiom,
% 52.23/52.30 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.30 ( ( class_Int_Onumber__ring(T_b)
% 52.23/52.30 & class_Int_Oring__char__0(T_b) )
% 52.23/52.30 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 52.23/52.30 <=> V_x_2 = V_y_2 ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_number__of__reorient,axiom,
% 52.23/52.30 ! [V_x_2,V_w_2,T_b] :
% 52.23/52.30 ( class_Int_Onumber(T_b)
% 52.23/52.30 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2
% 52.23/52.30 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_abs__idempotent,axiom,
% 52.23/52.30 ! [V_a,T_a] :
% 52.23/52.30 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_zero__le__zpower__abs,axiom,
% 52.23/52.30 ! [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))) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_abs__le__D1,axiom,
% 52.23/52.30 ! [V_b,V_a,T_a] :
% 52.23/52.30 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 52.23/52.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 52.23/52.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_abs__ge__self,axiom,
% 52.23/52.30 ! [V_a,T_a] :
% 52.23/52.30 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 52.23/52.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_abs__zero,axiom,
% 52.23/52.30 ! [T_a] :
% 52.23/52.30 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 52.23/52.30 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_abs__eq__0,axiom,
% 52.23/52.30 ! [V_a_2,T_b] :
% 52.23/52.30 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 52.23/52.30 => ( hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.30 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_abs__add__abs,axiom,
% 52.23/52.30 ! [V_b,V_a,T_a] :
% 52.23/52.30 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 52.23/52.30 => 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)) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_abs__mult__self,axiom,
% 52.23/52.30 ! [V_a,T_a] :
% 52.23/52.30 ( class_Rings_Olinordered__idom(T_a)
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_abs__mult,axiom,
% 52.23/52.30 ! [V_b,V_a,T_a] :
% 52.23/52.30 ( class_Rings_Olinordered__idom(T_a)
% 52.23/52.30 => 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)) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_abs__minus__commute,axiom,
% 52.23/52.30 ! [V_b,V_a,T_a] :
% 52.23/52.30 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 52.23/52.30 => 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)) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_abs__one,axiom,
% 52.23/52.30 ! [T_a] :
% 52.23/52.30 ( class_Rings_Olinordered__idom(T_a)
% 52.23/52.30 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_abs__minus__cancel,axiom,
% 52.23/52.30 ! [V_a,T_a] :
% 52.23/52.30 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 52.23/52.30 ! [V_q,V_y,V_x,T_a] :
% 52.23/52.30 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.30 => 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)) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_abs__of__nat,axiom,
% 52.23/52.30 ! [V_n,T_a] :
% 52.23/52.30 ( class_Rings_Olinordered__idom(T_a)
% 52.23/52.30 => 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) ) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_abs__int__eq,axiom,
% 52.23/52.30 ! [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) ).
% 52.23/52.30
% 52.23/52.30 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 52.23/52.30 ! [V_q,V_p,V_x,T_a] :
% 52.23/52.30 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.30 => 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)) ) ).
% 52.23/52.30
% 52.23/52.31 fof(fact_zpower__zpower,axiom,
% 52.23/52.31 ! [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)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 52.23/52.31 ! [V_x,T_a] :
% 52.23/52.31 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.31 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_zpower__zmod,axiom,
% 52.23/52.31 ! [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) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_of__nat__number__of__lemma,axiom,
% 52.23/52.31 ! [V_v,T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => ( ( 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)))
% 52.23/52.31 => 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) )
% 52.23/52.31 & ( ~ 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)))
% 52.23/52.31 => 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) ) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_number__of__eq,axiom,
% 52.23/52.31 ! [V_k,T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_abs__number__of,axiom,
% 52.23/52.31 ! [V_x,T_a] :
% 52.23/52.31 ( ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 & class_Rings_Olinordered__idom(T_a) )
% 52.23/52.31 => ( ( 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)))
% 52.23/52.31 => 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)) )
% 52.23/52.31 & ( ~ 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)))
% 52.23/52.31 => 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) ) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_zero__less__zpower__abs__iff,axiom,
% 52.23/52.31 ! [V_n_2,V_x_2] :
% 52.23/52.31 ( 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)))
% 52.23/52.31 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.31 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_abs__of__nonneg,axiom,
% 52.23/52.31 ! [V_a,T_a] :
% 52.23/52.31 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.31 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_abs__le__zero__iff,axiom,
% 52.23/52.31 ! [V_a_2,T_b] :
% 52.23/52.31 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 52.23/52.31 => ( 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)))
% 52.23/52.31 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_abs__ge__zero,axiom,
% 52.23/52.31 ! [V_a,T_a] :
% 52.23/52.31 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 52.23/52.31 => 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))) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_abs__not__less__zero,axiom,
% 52.23/52.31 ! [V_a,T_a] :
% 52.23/52.31 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 52.23/52.31 => ~ 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))) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_zero__less__abs__iff,axiom,
% 52.23/52.31 ! [V_a_2,T_b] :
% 52.23/52.31 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 52.23/52.31 => ( 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)))
% 52.23/52.31 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_abs__of__pos,axiom,
% 52.23/52.31 ! [V_a,T_a] :
% 52.23/52.31 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.31 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_abs__triangle__ineq,axiom,
% 52.23/52.31 ! [V_b,V_a,T_a] :
% 52.23/52.31 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 52.23/52.31 => 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)))) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_abs__mult__less,axiom,
% 52.23/52.31 ! [V_d,V_b,V_c,V_a,T_a] :
% 52.23/52.31 ( class_Rings_Olinordered__idom(T_a)
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c))
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d))
% 52.23/52.31 => 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))) ) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_abs__triangle__ineq2__sym,axiom,
% 52.23/52.31 ! [V_b,V_a,T_a] :
% 52.23/52.31 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 52.23/52.31 => 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)))) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_abs__triangle__ineq2,axiom,
% 52.23/52.31 ! [V_b,V_a,T_a] :
% 52.23/52.31 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 52.23/52.31 => 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)))) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_abs__triangle__ineq3,axiom,
% 52.23/52.31 ! [V_b,V_a,T_a] :
% 52.23/52.31 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 52.23/52.31 => 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)))) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_abs__ge__minus__self,axiom,
% 52.23/52.31 ! [V_a,T_a] :
% 52.23/52.31 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 52.23/52.31 => 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))) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_abs__le__iff,axiom,
% 52.23/52.31 ! [V_b_2,V_a_2,T_b] :
% 52.23/52.31 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 52.23/52.31 => ( 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))
% 52.23/52.31 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 52.23/52.31 & 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)) ) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_abs__leI,axiom,
% 52.23/52.31 ! [V_b,V_a,T_a] :
% 52.23/52.31 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))
% 52.23/52.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_abs__le__D2,axiom,
% 52.23/52.31 ! [V_b,V_a,T_a] :
% 52.23/52.31 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 52.23/52.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_abs__less__iff,axiom,
% 52.23/52.31 ! [V_b_2,V_a_2,T_b] :
% 52.23/52.31 ( class_Rings_Olinordered__idom(T_b)
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
% 52.23/52.31 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 52.23/52.31 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_le__number__of__eq__not__less,axiom,
% 52.23/52.31 ! [V_w_2,V_v_2,T_b] :
% 52.23/52.31 ( ( class_Int_Onumber(T_b)
% 52.23/52.31 & class_Orderings_Olinorder(T_b) )
% 52.23/52.31 => ( 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)))
% 52.23/52.31 <=> ~ 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))) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_left__distrib__number__of,axiom,
% 52.23/52.31 ! [V_v,V_b,V_a,T_b] :
% 52.23/52.31 ( ( class_Int_Onumber(T_b)
% 52.23/52.31 & class_Rings_Osemiring(T_b) )
% 52.23/52.31 => 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))) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_right__distrib__number__of,axiom,
% 52.23/52.31 ! [V_c,V_b,V_v,T_b] :
% 52.23/52.31 ( ( class_Int_Onumber(T_b)
% 52.23/52.31 & class_Rings_Osemiring(T_b) )
% 52.23/52.31 => 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)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
% 52.23/52.31 ! [V_q,V_x,T_a] :
% 52.23/52.31 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.31 => 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)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
% 52.23/52.31 ! [V_q,V_x,T_a] :
% 52.23/52.31 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.31 => 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)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
% 52.23/52.31 ! [V_q,V_x,T_a] :
% 52.23/52.31 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.31 => 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)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_left__diff__distrib__number__of,axiom,
% 52.23/52.31 ! [V_v,V_b,V_a,T_b] :
% 52.23/52.31 ( ( class_Int_Onumber(T_b)
% 52.23/52.31 & class_Rings_Oring(T_b) )
% 52.23/52.31 => 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))) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_right__diff__distrib__number__of,axiom,
% 52.23/52.31 ! [V_c,V_b,V_v,T_b] :
% 52.23/52.31 ( ( class_Int_Onumber(T_b)
% 52.23/52.31 & class_Rings_Oring(T_b) )
% 52.23/52.31 => 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)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_le__number__of,axiom,
% 52.23/52.31 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.31 ( ( class_Int_Onumber__ring(T_b)
% 52.23/52.31 & class_Rings_Olinordered__idom(T_b) )
% 52.23/52.31 => ( 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)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 52.23/52.31 ! [V_x,T_a] :
% 52.23/52.31 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.31 => 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) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 52.23/52.31 ! [V_q,V_p,V_x,T_a] :
% 52.23/52.31 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.31 => 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)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_less__number__of,axiom,
% 52.23/52.31 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.31 ( ( class_Int_Onumber__ring(T_b)
% 52.23/52.31 & class_Rings_Olinordered__idom(T_b) )
% 52.23/52.31 => ( 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)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_number__of__add,axiom,
% 52.23/52.31 ! [V_w,V_v,T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => 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)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_add__number__of__eq,axiom,
% 52.23/52.31 ! [V_w,V_v,T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => 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)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_add__number__of__left,axiom,
% 52.23/52.31 ! [V_z,V_w,V_v,T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => 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) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 52.23/52.31 ! [V_n,V_x] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 52.23/52.31 => 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))) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_mult__number__of__left,axiom,
% 52.23/52.31 ! [V_z,V_w,V_v,T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => 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) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_arith__simps_I32_J,axiom,
% 52.23/52.31 ! [V_w,V_v,T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => 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)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_number__of__mult,axiom,
% 52.23/52.31 ! [V_w,V_v,T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => 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)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_abs__zmult__eq__1,axiom,
% 52.23/52.31 ! [V_n,V_m] :
% 52.23/52.31 ( 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)
% 52.23/52.31 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_number__of__diff,axiom,
% 52.23/52.31 ! [V_w,V_v,T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => 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)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_zpower__zadd__distrib,axiom,
% 52.23/52.31 ! [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)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_number__of__minus,axiom,
% 52.23/52.31 ! [V_w,T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => 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)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_arith__simps_I30_J,axiom,
% 52.23/52.31 ! [V_w,T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => 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)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_mult__sgn__abs,axiom,
% 52.23/52.31 ! [V_x,T_a] :
% 52.23/52.31 ( class_Rings_Olinordered__idom(T_a)
% 52.23/52.31 => 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 ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_abs__sgn,axiom,
% 52.23/52.31 ! [V_k,T_a] :
% 52.23/52.31 ( class_Rings_Olinordered__idom(T_a)
% 52.23/52.31 => 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)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_abs__mult__pos,axiom,
% 52.23/52.31 ! [V_y,V_x,T_a] :
% 52.23/52.31 ( class_Rings_Olinordered__idom(T_a)
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 52.23/52.31 => 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)) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_abs__eq__mult,axiom,
% 52.23/52.31 ! [V_b,V_a,T_a] :
% 52.23/52.31 ( class_Rings_Oordered__ring__abs(T_a)
% 52.23/52.31 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.31 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
% 52.23/52.31 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 52.23/52.31 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 52.23/52.31 => 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)) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_abs__diff__triangle__ineq,axiom,
% 52.23/52.31 ! [V_d,V_c,V_b,V_a,T_a] :
% 52.23/52.31 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 52.23/52.31 => 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))))) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_abs__triangle__ineq4,axiom,
% 52.23/52.31 ! [V_b,V_a,T_a] :
% 52.23/52.31 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 52.23/52.31 => 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)))) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_abs__of__nonpos,axiom,
% 52.23/52.31 ! [V_a,T_a] :
% 52.23/52.31 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.31 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_abs__minus__le__zero,axiom,
% 52.23/52.31 ! [V_a,T_a] :
% 52.23/52.31 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 52.23/52.31 => 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))) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_abs__if,axiom,
% 52.23/52.31 ! [V_a,T_a] :
% 52.23/52.31 ( class_Groups_Oabs__if(T_a)
% 52.23/52.31 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.31 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) )
% 52.23/52.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.31 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_abs__of__neg,axiom,
% 52.23/52.31 ! [V_a,T_a] :
% 52.23/52.31 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.31 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_zabs__less__one__iff,axiom,
% 52.23/52.31 ! [V_z_2] :
% 52.23/52.31 ( 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)))
% 52.23/52.31 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_add__number__of__diff1,axiom,
% 52.23/52.31 ! [V_c,V_w,V_v,T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => 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) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_zabs__def,axiom,
% 52.23/52.31 ! [V_i] :
% 52.23/52.31 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.31 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) )
% 52.23/52.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.31 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_minus__number__of__mult,axiom,
% 52.23/52.31 ! [V_z,V_w,T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => 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) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_nat__abs__mult__distrib,axiom,
% 52.23/52.31 ! [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))) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_diff__number__of__eq,axiom,
% 52.23/52.31 ! [V_w,V_v,T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => 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))) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_add__number__of__diff2,axiom,
% 52.23/52.31 ! [V_w,V_c,V_v,T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => 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) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__strict__mono,axiom,
% 52.23/52.31 ! [V_n,V_b,V_a,T_a] :
% 52.23/52.31 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 52.23/52.31 => 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))) ) ) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_one__less__power,axiom,
% 52.23/52.31 ! [V_n,V_a,T_a] :
% 52.23/52.31 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 52.23/52.31 => 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))) ) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__increasing__iff,axiom,
% 52.23/52.31 ! [V_y_2,V_x_2,V_b_2,T_b] :
% 52.23/52.31 ( class_Rings_Olinordered__semidom(T_b)
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
% 52.23/52.31 => ( 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)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__le__imp__le__exp,axiom,
% 52.23/52.31 ! [V_n,V_m,V_a,T_a] :
% 52.23/52.31 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 52.23/52.31 => ( 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)))
% 52.23/52.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__decreasing,axiom,
% 52.23/52.31 ! [V_a,V_N,V_n,T_a] :
% 52.23/52.31 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 52.23/52.31 => 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))) ) ) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__strict__decreasing,axiom,
% 52.23/52.31 ! [V_a,V_N,V_n,T_a] :
% 52.23/52.31 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 52.23/52.31 => 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))) ) ) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__Suc__less__one,axiom,
% 52.23/52.31 ! [V_n,V_a,T_a] :
% 52.23/52.31 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 52.23/52.31 => 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))) ) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_number__of__is__id,axiom,
% 52.23/52.31 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ).
% 52.23/52.31
% 52.23/52.31 fof(fact_less__eq__number__of__int__code,axiom,
% 52.23/52.31 ! [V_l_2,V_k_2] :
% 52.23/52.31 ( 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)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_less__number__of__int__code,axiom,
% 52.23/52.31 ! [V_l_2,V_k_2] :
% 52.23/52.31 ( 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)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_plus__numeral__code_I9_J,axiom,
% 52.23/52.31 ! [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)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_times__numeral__code_I5_J,axiom,
% 52.23/52.31 ! [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)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_minus__numeral__code_I5_J,axiom,
% 52.23/52.31 ! [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)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__Suc__0,axiom,
% 52.23/52.31 ! [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)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_nat__power__eq__Suc__0__iff,axiom,
% 52.23/52.31 ! [V_m_2,V_x_2] :
% 52.23/52.31 ( 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))
% 52.23/52.31 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.31 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_nat__power__less__imp__less,axiom,
% 52.23/52.31 ! [V_n,V_m,V_i] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))
% 52.23/52.31 => ( 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)))
% 52.23/52.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_nat__zero__less__power__iff,axiom,
% 52.23/52.31 ! [V_n_2,V_x_2] :
% 52.23/52.31 ( 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)))
% 52.23/52.31 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))
% 52.23/52.31 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_int__number__of__def,axiom,
% 52.23/52.31 ! [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) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_nat__one__le__power,axiom,
% 52.23/52.31 ! [V_n,V_i] :
% 52.23/52.31 ( 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))
% 52.23/52.31 => 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))) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_nat__number__of,axiom,
% 52.23/52.31 ! [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) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_nat__number__of__def,axiom,
% 52.23/52.31 ! [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)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
% 52.23/52.31 ! [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)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_int__power,axiom,
% 52.23/52.31 ! [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) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_zpower__int,axiom,
% 52.23/52.31 ! [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)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_minus__numeral__code_I6_J,axiom,
% 52.23/52.31 ! [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))) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__eq__if,axiom,
% 52.23/52.31 ! [V_p,V_m] :
% 52.23/52.31 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.31 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 52.23/52.31 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.31 => 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)))) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_int__eq__iff__number__of,axiom,
% 52.23/52.31 ! [V_v_2,V_m_2] :
% 52.23/52.31 ( 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)
% 52.23/52.31 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))
% 52.23/52.31 & 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))) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_nat__power__eq,axiom,
% 52.23/52.31 ! [V_n,V_z] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 52.23/52.31 => 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) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom,
% 52.23/52.31 ! [V_n,V_x] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 52.23/52.31 => 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)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_field__power__not__zero,axiom,
% 52.23/52.31 ! [V_n,V_a,T_a] :
% 52.23/52.31 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 52.23/52.31 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.31 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__commutes,axiom,
% 52.23/52.31 ! [V_n,V_a,T_a] :
% 52.23/52.31 ( class_Groups_Omonoid__mult(T_a)
% 52.23/52.31 => 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)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__mult__distrib,axiom,
% 52.23/52.31 ! [V_n,V_b,V_a,T_a] :
% 52.23/52.31 ( class_Groups_Ocomm__monoid__mult(T_a)
% 52.23/52.31 => 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)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__one,axiom,
% 52.23/52.31 ! [V_n,T_a] :
% 52.23/52.31 ( class_Groups_Omonoid__mult(T_a)
% 52.23/52.31 => 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) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_of__nat__power,axiom,
% 52.23/52.31 ! [V_n,V_m,T_a] :
% 52.23/52.31 ( class_Rings_Osemiring__1(T_a)
% 52.23/52.31 => 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) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__mult,axiom,
% 52.23/52.31 ! [V_n,V_m,V_a,T_a] :
% 52.23/52.31 ( class_Groups_Omonoid__mult(T_a)
% 52.23/52.31 => 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) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_one__div__nat__number__of,axiom,
% 52.23/52.31 ! [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))) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__abs,axiom,
% 52.23/52.31 ! [V_n,V_a,T_a] :
% 52.23/52.31 ( class_Rings_Olinordered__idom(T_a)
% 52.23/52.31 => 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) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__one__right,axiom,
% 52.23/52.31 ! [V_a,T_a] :
% 52.23/52.31 ( class_Groups_Omonoid__mult(T_a)
% 52.23/52.31 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_zero__le__power,axiom,
% 52.23/52.31 ! [V_n,V_a,T_a] :
% 52.23/52.31 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.31 => 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))) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__mono,axiom,
% 52.23/52.31 ! [V_n,V_b,V_a,T_a] :
% 52.23/52.31 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.31 => 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))) ) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_zero__less__power,axiom,
% 52.23/52.31 ! [V_n,V_a,T_a] :
% 52.23/52.31 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.31 => 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))) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__eq__0__iff,axiom,
% 52.23/52.31 ! [V_n_2,V_a_2,T_b] :
% 52.23/52.31 ( ( class_Power_Opower(T_b)
% 52.23/52.31 & class_Rings_Omult__zero(T_b)
% 52.23/52.31 & class_Rings_Ono__zero__divisors(T_b)
% 52.23/52.31 & class_Rings_Ozero__neq__one(T_b) )
% 52.23/52.31 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.31 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.31 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_one__le__power,axiom,
% 52.23/52.31 ! [V_n,V_a,T_a] :
% 52.23/52.31 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 52.23/52.31 => 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))) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__0__Suc,axiom,
% 52.23/52.31 ! [V_n,T_a] :
% 52.23/52.31 ( ( class_Power_Opower(T_a)
% 52.23/52.31 & class_Rings_Osemiring__0(T_a) )
% 52.23/52.31 => 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) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__inject__exp,axiom,
% 52.23/52.31 ! [V_n_2,V_m_2,V_a_2,T_b] :
% 52.23/52.31 ( class_Rings_Olinordered__semidom(T_b)
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2))
% 52.23/52.31 => ( 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)
% 52.23/52.31 <=> V_m_2 = V_n_2 ) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__Suc,axiom,
% 52.23/52.31 ! [V_n,V_a,T_a] :
% 52.23/52.31 ( class_Power_Opower(T_a)
% 52.23/52.31 => 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)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__Suc2,axiom,
% 52.23/52.31 ! [V_n,V_a,T_a] :
% 52.23/52.31 ( class_Groups_Omonoid__mult(T_a)
% 52.23/52.31 => 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) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__0,axiom,
% 52.23/52.31 ! [V_a,T_a] :
% 52.23/52.31 ( class_Power_Opower(T_a)
% 52.23/52.31 => 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) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__add,axiom,
% 52.23/52.31 ! [V_n,V_m,V_a,T_a] :
% 52.23/52.31 ( class_Groups_Omonoid__mult(T_a)
% 52.23/52.31 => 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)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_abs__power__minus,axiom,
% 52.23/52.31 ! [V_n,V_a,T_a] :
% 52.23/52.31 ( class_Rings_Olinordered__idom(T_a)
% 52.23/52.31 => 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)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__less__imp__less__base,axiom,
% 52.23/52.31 ! [V_b,V_n,V_a,T_a] :
% 52.23/52.31 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.31 => ( 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)))
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 52.23/52.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__le__imp__le__base,axiom,
% 52.23/52.31 ! [V_b,V_n,V_a,T_a] :
% 52.23/52.31 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.31 => ( 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))))
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 52.23/52.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__inject__base,axiom,
% 52.23/52.31 ! [V_b,V_n,V_a,T_a] :
% 52.23/52.31 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.31 => ( 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))
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 52.23/52.31 => V_a = V_b ) ) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__gt1__lemma,axiom,
% 52.23/52.31 ! [V_n,V_a,T_a] :
% 52.23/52.31 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 52.23/52.31 => 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)))) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__less__power__Suc,axiom,
% 52.23/52.31 ! [V_n,V_a,T_a] :
% 52.23/52.31 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 52.23/52.31 => 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)))) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__0__left,axiom,
% 52.23/52.31 ! [V_n,T_a] :
% 52.23/52.31 ( ( class_Power_Opower(T_a)
% 52.23/52.31 & class_Rings_Osemiring__0(T_a) )
% 52.23/52.31 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.31 => 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) )
% 52.23/52.31 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.31 => 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) ) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__gt1,axiom,
% 52.23/52.31 ! [V_n,V_a,T_a] :
% 52.23/52.31 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 52.23/52.31 => 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)))) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__strict__increasing,axiom,
% 52.23/52.31 ! [V_a,V_N,V_n,T_a] :
% 52.23/52.31 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 52.23/52.31 => 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))) ) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__less__imp__less__exp,axiom,
% 52.23/52.31 ! [V_n,V_m,V_a,T_a] :
% 52.23/52.31 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 52.23/52.31 => ( 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)))
% 52.23/52.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__strict__increasing__iff,axiom,
% 52.23/52.31 ! [V_y_2,V_x_2,V_b_2,T_b] :
% 52.23/52.31 ( class_Rings_Olinordered__semidom(T_b)
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
% 52.23/52.31 => ( 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)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_zero__le__power__abs,axiom,
% 52.23/52.31 ! [V_n,V_a,T_a] :
% 52.23/52.31 ( class_Rings_Olinordered__idom(T_a)
% 52.23/52.31 => 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))) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__increasing,axiom,
% 52.23/52.31 ! [V_a,V_N,V_n,T_a] :
% 52.23/52.31 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 52.23/52.31 => 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))) ) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__minus,axiom,
% 52.23/52.31 ! [V_n,V_a,T_a] :
% 52.23/52.31 ( class_Rings_Oring__1(T_a)
% 52.23/52.31 => 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)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__Suc__less,axiom,
% 52.23/52.31 ! [V_n,V_a,T_a] :
% 52.23/52.31 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 52.23/52.31 => 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))) ) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__eq__imp__eq__base,axiom,
% 52.23/52.31 ! [V_b,V_n,V_a,T_a] :
% 52.23/52.31 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.31 => ( 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)
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 52.23/52.31 => V_a = V_b ) ) ) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_Nitpick_Onat__lcm__def,axiom,
% 52.23/52.31 ! [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)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_Nitpick_Oint__gcd__def,axiom,
% 52.23/52.31 ! [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)))) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_one__mod__nat__number__of,axiom,
% 52.23/52.31 ! [V_v_H] :
% 52.23/52.31 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 52.23/52.31 => 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)) )
% 52.23/52.31 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 52.23/52.31 => 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))) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__power__power,axiom,
% 52.23/52.31 ! [T_b] :
% 52.23/52.31 ( class_Power_Opower(T_b)
% 52.23/52.31 => 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)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_div__nat__number__of,axiom,
% 52.23/52.31 ! [V_v_H,V_v] :
% 52.23/52.31 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 52.23/52.31 => 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) )
% 52.23/52.31 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 52.23/52.31 => 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))) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_mod__nat__number__of,axiom,
% 52.23/52.31 ! [V_v_H,V_v] :
% 52.23/52.31 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 52.23/52.31 => 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) )
% 52.23/52.31 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 52.23/52.31 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 52.23/52.31 => 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) )
% 52.23/52.31 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 52.23/52.31 => 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))) ) ) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_Nitpick_Oint__lcm__def,axiom,
% 52.23/52.31 ! [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)))) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_not__neg__0,axiom,
% 52.23/52.31 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_not__neg__int,axiom,
% 52.23/52.31 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_not__neg__1,axiom,
% 52.23/52.31 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_not__neg__eq__ge__0,axiom,
% 52.23/52.31 ! [V_x_2] :
% 52.23/52.31 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_neg__def,axiom,
% 52.23/52.31 ! [V_Z_2] :
% 52.23/52.31 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_neg__nat,axiom,
% 52.23/52.31 ! [V_z] :
% 52.23/52.31 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 52.23/52.31 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_not__neg__nat,axiom,
% 52.23/52.31 ! [V_z] :
% 52.23/52.31 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 52.23/52.31 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power_Opower_Opower__0,axiom,
% 52.23/52.31 ! [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 ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power_Opower_Opower__Suc,axiom,
% 52.23/52.31 ! [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)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_neg__imp__number__of__eq__0,axiom,
% 52.23/52.31 ! [V_v] :
% 52.23/52.31 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 52.23/52.31 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_neg__zminus__int,axiom,
% 52.23/52.31 ! [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))))) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_eq__nat__number__of,axiom,
% 52.23/52.31 ! [V_v_H_2,V_v_2] :
% 52.23/52.31 ( 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)
% 52.23/52.31 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 52.23/52.31 => 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))) )
% 52.23/52.31 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 52.23/52.31 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 52.23/52.31 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 52.23/52.31 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 52.23/52.31 => V_v_2 = V_v_H_2 ) ) ) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_nat__number__of__add__left,axiom,
% 52.23/52.31 ! [V_k,V_v_H,V_v] :
% 52.23/52.31 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 52.23/52.31 => 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) )
% 52.23/52.31 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 52.23/52.31 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 52.23/52.31 => 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) )
% 52.23/52.31 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 52.23/52.31 => 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) ) ) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_int__nat__number__of,axiom,
% 52.23/52.31 ! [V_v] :
% 52.23/52.31 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 52.23/52.31 => 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) )
% 52.23/52.31 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 52.23/52.31 => 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) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_of__nat__number__of__eq,axiom,
% 52.23/52.31 ! [V_v,T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 52.23/52.31 => 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) )
% 52.23/52.31 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 52.23/52.31 => 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) ) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__nat__number__of__number__of,axiom,
% 52.23/52.31 ! [V_w,V_v] :
% 52.23/52.31 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 52.23/52.31 => 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)) )
% 52.23/52.31 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 52.23/52.31 => 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))) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power__nat__number__of,axiom,
% 52.23/52.31 ! [V_n,V_v] :
% 52.23/52.31 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 52.23/52.31 => 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) )
% 52.23/52.31 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 52.23/52.31 => 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)) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_Suc__nat__number__of__add,axiom,
% 52.23/52.31 ! [V_n,V_v] :
% 52.23/52.31 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 52.23/52.31 => 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) )
% 52.23/52.31 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 52.23/52.31 => 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) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_Suc__nat__number__of,axiom,
% 52.23/52.31 ! [V_v] :
% 52.23/52.31 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 52.23/52.31 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 52.23/52.31 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 52.23/52.31 => 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)) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_zmod__minus1,axiom,
% 52.23/52.31 ! [V_b] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 52.23/52.31 => 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)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_div__pos__neg__trivial,axiom,
% 52.23/52.31 ! [V_b,V_a] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 52.23/52.31 => ( 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)))
% 52.23/52.31 => 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) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_nat0__intermed__int__val,axiom,
% 52.23/52.31 ! [V_k_2,V_f_2,V_n_2] :
% 52.23/52.31 ( ! [B_i] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 52.23/52.31 => 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))) )
% 52.23/52.31 => ( 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))
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 52.23/52.31 => ? [B_i] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 52.23/52.31 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_int__val__lemma,axiom,
% 52.23/52.31 ! [V_k_2,V_f_2,V_n_2] :
% 52.23/52.31 ( ! [B_i] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 52.23/52.31 => 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))) )
% 52.23/52.31 => ( 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))
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 52.23/52.31 => ? [B_i] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 52.23/52.31 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_eq__number__of__eq,axiom,
% 52.23/52.31 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_b)
% 52.23/52.31 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 52.23/52.31 <=> 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)))) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_diff__bin__simps_I2_J,axiom,
% 52.23/52.31 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_nonzero__number__of__Min,axiom,
% 52.23/52.31 ! [T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I24_J,axiom,
% 52.23/52.31 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I7_J,axiom,
% 52.23/52.31 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_iszero__def,axiom,
% 52.23/52.31 ! [V_z_2,T_b] :
% 52.23/52.31 ( class_Rings_Osemiring__1(T_b)
% 52.23/52.31 => ( c_Int_Oiszero(T_b,V_z_2)
% 52.23/52.31 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_iszero__0,axiom,
% 52.23/52.31 ! [T_a] :
% 52.23/52.31 ( class_Rings_Osemiring__1(T_a)
% 52.23/52.31 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_not__iszero__1,axiom,
% 52.23/52.31 ! [T_a] :
% 52.23/52.31 ( class_Rings_Osemiring__1(T_a)
% 52.23/52.31 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_bin__less__0__simps_I2_J,axiom,
% 52.23/52.31 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_Int_OMin__def,axiom,
% 52.23/52.31 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_mult__Min,axiom,
% 52.23/52.31 ! [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) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_neg__number__of__Min,axiom,
% 52.23/52.31 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_mult__minus1__right,axiom,
% 52.23/52.31 ! [V_z,T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => 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) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_mult__minus1,axiom,
% 52.23/52.31 ! [V_z,T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => 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) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_arith__simps_I31_J,axiom,
% 52.23/52.31 ! [T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => 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) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_number__of__Min,axiom,
% 52.23/52.31 ! [T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => 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)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_abs__minus__one,axiom,
% 52.23/52.31 ! [T_a] :
% 52.23/52.31 ( ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 & class_Rings_Olinordered__idom(T_a) )
% 52.23/52.31 => 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) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_zmod__minus1__right,axiom,
% 52.23/52.31 ! [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) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_zmult__eq__1__iff,axiom,
% 52.23/52.31 ! [V_n_2,V_m_2] :
% 52.23/52.31 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 52.23/52.31 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 52.23/52.31 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 52.23/52.31 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
% 52.23/52.31 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
% 52.23/52.31 ! [V_n,V_m] :
% 52.23/52.31 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 52.23/52.31 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 52.23/52.31 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_of__int__m1,axiom,
% 52.23/52.31 ! [T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => 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) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_zdiv__minus1__right,axiom,
% 52.23/52.31 ! [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) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_succ__def,axiom,
% 52.23/52.31 ! [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)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_abs__power__minus__one,axiom,
% 52.23/52.31 ! [V_n,T_a] :
% 52.23/52.31 ( ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 & class_Rings_Olinordered__idom(T_a) )
% 52.23/52.31 => 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) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_div__eq__minus1,axiom,
% 52.23/52.31 ! [V_b] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 52.23/52.31 => 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) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_number__of__succ,axiom,
% 52.23/52.31 ! [V_k,T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => 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)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_nat__1__add__number__of,axiom,
% 52.23/52.31 ! [V_v] :
% 52.23/52.31 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 52.23/52.31 => 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) )
% 52.23/52.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 52.23/52.31 => 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)) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_nat__number__of__add__1,axiom,
% 52.23/52.31 ! [V_v] :
% 52.23/52.31 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 52.23/52.31 => 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) )
% 52.23/52.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 52.23/52.31 => 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)) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_eq__special_I3_J,axiom,
% 52.23/52.31 ! [V_x_2,T_b] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_b)
% 52.23/52.31 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.31 <=> 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)))) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_eq__special_I1_J,axiom,
% 52.23/52.31 ! [V_y_2,T_b] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_b)
% 52.23/52.31 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 52.23/52.31 <=> 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)))) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_neg__number__of__pred__iff__0,axiom,
% 52.23/52.31 ! [V_v_2] :
% 52.23/52.31 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))))
% 52.23/52.31 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_nat__number__of__mult__left,axiom,
% 52.23/52.31 ! [V_k,V_v_H,V_v] :
% 52.23/52.31 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 52.23/52.31 => 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) )
% 52.23/52.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 52.23/52.31 => 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) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_mult__nat__number__of,axiom,
% 52.23/52.31 ! [V_v_H,V_v] :
% 52.23/52.31 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 52.23/52.31 => 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) )
% 52.23/52.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 52.23/52.31 => 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)) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_pred__Pls,axiom,
% 52.23/52.31 c_Int_Opred(c_Int_OPls) = c_Int_OMin ).
% 52.23/52.31
% 52.23/52.31 fof(fact_Pls__def,axiom,
% 52.23/52.31 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I19_J,axiom,
% 52.23/52.31 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I2_J,axiom,
% 52.23/52.31 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_add__Pls,axiom,
% 52.23/52.31 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ).
% 52.23/52.31
% 52.23/52.31 fof(fact_add__Pls__right,axiom,
% 52.23/52.31 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 52.23/52.31
% 52.23/52.31 fof(fact_mult__Pls,axiom,
% 52.23/52.31 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ).
% 52.23/52.31
% 52.23/52.31 fof(fact_diff__bin__simps_I1_J,axiom,
% 52.23/52.31 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 52.23/52.31
% 52.23/52.31 fof(fact_minus__Pls,axiom,
% 52.23/52.31 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I37_J,axiom,
% 52.23/52.31 c_Int_OPls != c_Int_OMin ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I40_J,axiom,
% 52.23/52.31 c_Int_OMin != c_Int_OPls ).
% 52.23/52.31
% 52.23/52.31 fof(fact_succ__pred,axiom,
% 52.23/52.31 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ).
% 52.23/52.31
% 52.23/52.31 fof(fact_semiring__norm_I112_J,axiom,
% 52.23/52.31 ! [T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_number__of__Pls,axiom,
% 52.23/52.31 ! [T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_add__numeral__0,axiom,
% 52.23/52.31 ! [V_a,T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => 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 ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_add__numeral__0__right,axiom,
% 52.23/52.31 ! [V_a,T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => 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 ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_bin__less__0__simps_I1_J,axiom,
% 52.23/52.31 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_nat__number__of__Pls,axiom,
% 52.23/52.31 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_semiring__norm_I113_J,axiom,
% 52.23/52.31 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_zero__is__num__zero,axiom,
% 52.23/52.31 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_Suc__diff__number__of,axiom,
% 52.23/52.31 ! [V_m,V_v] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v))
% 52.23/52.31 => 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))) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I20_J,axiom,
% 52.23/52.31 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I23_J,axiom,
% 52.23/52.31 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I3_J,axiom,
% 52.23/52.31 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I6_J,axiom,
% 52.23/52.31 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_eq__number__of__Pls__Min,axiom,
% 52.23/52.31 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) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_not__neg__number__of__Pls,axiom,
% 52.23/52.31 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_iszero__Numeral0,axiom,
% 52.23/52.31 ! [T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_succ__Min,axiom,
% 52.23/52.31 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ).
% 52.23/52.31
% 52.23/52.31 fof(fact_le__iff__pred__less,axiom,
% 52.23/52.31 ! [V_l_2,V_k_2] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_pred__def,axiom,
% 52.23/52.31 ! [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)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_add__Min__right,axiom,
% 52.23/52.31 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_add__Min,axiom,
% 52.23/52.31 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_nat__number__of__diff__1,axiom,
% 52.23/52.31 ! [V_v] :
% 52.23/52.31 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 52.23/52.31 => 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) )
% 52.23/52.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 52.23/52.31 => 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)) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_eq__0__number__of,axiom,
% 52.23/52.31 ! [V_v_2] :
% 52.23/52.31 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_eq__number__of__0,axiom,
% 52.23/52.31 ! [V_v_2] :
% 52.23/52.31 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_number__of2,axiom,
% 52.23/52.31 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))) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_less__nat__number__of,axiom,
% 52.23/52.31 ! [V_v_H_2,V_v_2] :
% 52.23/52.31 ( 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)))
% 52.23/52.31 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
% 52.23/52.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) )
% 52.23/52.31 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_le__nat__number__of,axiom,
% 52.23/52.31 ! [V_v_H_2,V_v_2] :
% 52.23/52.31 ( 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)))
% 52.23/52.31 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2))
% 52.23/52.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_le__special_I3_J,axiom,
% 52.23/52.31 ! [V_x_2,T_b] :
% 52.23/52.31 ( ( class_Int_Onumber__ring(T_b)
% 52.23/52.31 & class_Rings_Olinordered__idom(T_b) )
% 52.23/52.31 => ( 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)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_le__special_I1_J,axiom,
% 52.23/52.31 ! [V_y_2,T_b] :
% 52.23/52.31 ( ( class_Int_Onumber__ring(T_b)
% 52.23/52.31 & class_Rings_Olinordered__idom(T_b) )
% 52.23/52.31 => ( 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)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_less__special_I1_J,axiom,
% 52.23/52.31 ! [V_y_2,T_b] :
% 52.23/52.31 ( ( class_Int_Onumber__ring(T_b)
% 52.23/52.31 & class_Rings_Olinordered__idom(T_b) )
% 52.23/52.31 => ( 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)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_less__special_I3_J,axiom,
% 52.23/52.31 ! [V_x_2,T_b] :
% 52.23/52.31 ( ( class_Int_Onumber__ring(T_b)
% 52.23/52.31 & class_Rings_Olinordered__idom(T_b) )
% 52.23/52.31 => ( 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)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_less__0__number__of,axiom,
% 52.23/52.31 ! [V_v_2] :
% 52.23/52.31 ( 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)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_add__nat__number__of,axiom,
% 52.23/52.31 ! [V_v_H,V_v] :
% 52.23/52.31 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 52.23/52.31 => 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) )
% 52.23/52.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 52.23/52.31 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 52.23/52.31 => 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) )
% 52.23/52.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 52.23/52.31 => 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)) ) ) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_number__of__pred,axiom,
% 52.23/52.31 ! [V_w,T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => 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)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_eq__special_I4_J,axiom,
% 52.23/52.31 ! [V_x_2,T_b] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_b)
% 52.23/52.31 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 52.23/52.31 <=> 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))))) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_eq__special_I2_J,axiom,
% 52.23/52.31 ! [V_y_2,T_b] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_b)
% 52.23/52.31 => ( c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 52.23/52.31 <=> 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)))) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_diff__special_I2_J,axiom,
% 52.23/52.31 ! [V_v,T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => 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)))) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_diff__special_I1_J,axiom,
% 52.23/52.31 ! [V_w,T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => 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))) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_Suc__div__eq__add3__div__number__of,axiom,
% 52.23/52.31 ! [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)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_Suc__div__eq__add3__div,axiom,
% 52.23/52.31 ! [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) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I51_J,axiom,
% 52.23/52.31 ! [V_l_2,V_k_2] :
% 52.23/52.31 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
% 52.23/52.31 <=> V_k_2 = V_l_2 ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I34_J,axiom,
% 52.23/52.31 ! [V_l_2,V_k_2] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_less__eq__int__code_I16_J,axiom,
% 52.23/52.31 ! [V_k2_2,V_k1_2] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I17_J,axiom,
% 52.23/52.31 ! [V_l_2,V_k_2] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_less__int__code_I16_J,axiom,
% 52.23/52.31 ! [V_k2_2,V_k1_2] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I39_J,axiom,
% 52.23/52.31 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I46_J,axiom,
% 52.23/52.31 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ).
% 52.23/52.31
% 52.23/52.31 fof(fact_Bit1__Min,axiom,
% 52.23/52.31 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I43_J,axiom,
% 52.23/52.31 ! [V_l_2] :
% 52.23/52.31 ( c_Int_OMin = c_Int_OBit1(V_l_2)
% 52.23/52.31 <=> c_Int_OMin = V_l_2 ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I47_J,axiom,
% 52.23/52.31 ! [V_k_2] :
% 52.23/52.31 ( c_Int_OBit1(V_k_2) = c_Int_OMin
% 52.23/52.31 <=> V_k_2 = c_Int_OMin ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_bin__less__0__simps_I4_J,axiom,
% 52.23/52.31 ! [V_w_2] :
% 52.23/52.31 ( 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)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I22_J,axiom,
% 52.23/52.31 ! [V_k_2] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I12_J,axiom,
% 52.23/52.31 ! [V_k_2] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_Bit1__def,axiom,
% 52.23/52.31 ! [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) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I26_J,axiom,
% 52.23/52.31 ! [V_k_2] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I30_J,axiom,
% 52.23/52.31 ! [V_k_2] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I9_J,axiom,
% 52.23/52.31 ! [V_k_2] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I13_J,axiom,
% 52.23/52.31 ! [V_k_2] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_neg__number__of__Bit1,axiom,
% 52.23/52.31 ! [V_w_2] :
% 52.23/52.31 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2))))
% 52.23/52.31 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_minus__Bit1,axiom,
% 52.23/52.31 ! [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))) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_iszero__number__of__Bit1,axiom,
% 52.23/52.31 ! [V_w,T_a] :
% 52.23/52.31 ( ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 & class_Int_Oring__char__0(T_a) )
% 52.23/52.31 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_succ__Pls,axiom,
% 52.23/52.31 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_number__of__Bit1,axiom,
% 52.23/52.31 ! [V_w,T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => 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)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_mult__numeral__1__right,axiom,
% 52.23/52.31 ! [V_a,T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => 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 ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_mult__numeral__1,axiom,
% 52.23/52.31 ! [V_a,T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => 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 ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_semiring__norm_I110_J,axiom,
% 52.23/52.31 ! [T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_numeral__1__eq__1,axiom,
% 52.23/52.31 ! [T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I29_J,axiom,
% 52.23/52.31 ! [V_k_2] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I5_J,axiom,
% 52.23/52.31 ! [V_k_2] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_one__is__num__one,axiom,
% 52.23/52.31 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_Numeral1__eq1__nat,axiom,
% 52.23/52.31 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_nat__numeral__1__eq__1,axiom,
% 52.23/52.31 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_diff__bin__simps_I4_J,axiom,
% 52.23/52.31 ! [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)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_minus__Min,axiom,
% 52.23/52.31 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_not__iszero__Numeral1,axiom,
% 52.23/52.31 ! [T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_numeral__1__eq__Suc__0,axiom,
% 52.23/52.31 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)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_numeral__3__eq__3,axiom,
% 52.23/52.31 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)))) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_power3__eq__cube,axiom,
% 52.23/52.31 ! [V_a,T_a] :
% 52.23/52.31 ( class_Groups_Omonoid__mult(T_a)
% 52.23/52.31 => 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) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
% 52.23/52.31 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))))) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_Suc3__eq__add__3,axiom,
% 52.23/52.31 ! [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) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_transfer__int__nat__numerals_I4_J,axiom,
% 52.23/52.31 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)))) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_transfer__nat__int__numerals_I4_J,axiom,
% 52.23/52.31 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)))) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_le__special_I4_J,axiom,
% 52.23/52.31 ! [V_x_2,T_b] :
% 52.23/52.31 ( ( class_Int_Onumber__ring(T_b)
% 52.23/52.31 & class_Rings_Olinordered__idom(T_b) )
% 52.23/52.31 => ( 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)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_le__special_I2_J,axiom,
% 52.23/52.31 ! [V_y_2,T_b] :
% 52.23/52.31 ( ( class_Int_Onumber__ring(T_b)
% 52.23/52.31 & class_Rings_Olinordered__idom(T_b) )
% 52.23/52.31 => ( 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)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_less__special_I4_J,axiom,
% 52.23/52.31 ! [V_x_2,T_b] :
% 52.23/52.31 ( ( class_Int_Onumber__ring(T_b)
% 52.23/52.31 & class_Rings_Olinordered__idom(T_b) )
% 52.23/52.31 => ( 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)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_less__special_I2_J,axiom,
% 52.23/52.31 ! [V_y_2,T_b] :
% 52.23/52.31 ( ( class_Int_Onumber__ring(T_b)
% 52.23/52.31 & class_Rings_Olinordered__idom(T_b) )
% 52.23/52.31 => ( 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)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_add__special_I2_J,axiom,
% 52.23/52.31 ! [V_w,T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => 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)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_add__special_I3_J,axiom,
% 52.23/52.31 ! [V_v,T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => 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))) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_Suc__diff__eq__diff__pred,axiom,
% 52.23/52.31 ! [V_m,V_n] :
% 52.23/52.31 ( 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))
% 52.23/52.31 => 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)))) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_mod__Suc__eq__mod__add3,axiom,
% 52.23/52.31 ! [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)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_Suc__mod__eq__add3__mod,axiom,
% 52.23/52.31 ! [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) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom,
% 52.23/52.31 ! [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)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_div__Suc__eq__div__add3,axiom,
% 52.23/52.31 ! [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)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_zmod__number__of__Bit1,axiom,
% 52.23/52.31 ! [V_v,V_w] :
% 52.23/52.31 ( ( 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)))
% 52.23/52.31 => 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)) )
% 52.23/52.31 & ( ~ 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)))
% 52.23/52.31 => 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)) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_neg__zmod__mult__2,axiom,
% 52.23/52.31 ! [V_b,V_a] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.31 => 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)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_pos__zdiv__mult__2,axiom,
% 52.23/52.31 ! [V_b,V_a] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 52.23/52.31 => 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) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_neg__zdiv__mult__2,axiom,
% 52.23/52.31 ! [V_b,V_a] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.31 => 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) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_pos__zmod__mult__2,axiom,
% 52.23/52.31 ! [V_b,V_a] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 52.23/52.31 => 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))) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_of__nat__double,axiom,
% 52.23/52.31 ! [V_x,T_a] :
% 52.23/52.31 ( class_Rings_Osemiring__1(T_a)
% 52.23/52.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 52.23/52.31 => 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))) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I48_J,axiom,
% 52.23/52.31 ! [V_l_2,V_k_2] :
% 52.23/52.31 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
% 52.23/52.31 <=> V_k_2 = V_l_2 ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_less__eq__int__code_I13_J,axiom,
% 52.23/52.31 ! [V_k2_2,V_k1_2] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I31_J,axiom,
% 52.23/52.31 ! [V_l_2,V_k_2] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_less__int__code_I13_J,axiom,
% 52.23/52.31 ! [V_k2_2,V_k1_2] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I14_J,axiom,
% 52.23/52.31 ! [V_l_2,V_k_2] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I44_J,axiom,
% 52.23/52.31 ! [V_k_2] :
% 52.23/52.31 ( c_Int_OBit0(V_k_2) = c_Int_OPls
% 52.23/52.31 <=> V_k_2 = c_Int_OPls ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I38_J,axiom,
% 52.23/52.31 ! [V_l_2] :
% 52.23/52.31 ( c_Int_OPls = c_Int_OBit0(V_l_2)
% 52.23/52.31 <=> c_Int_OPls = V_l_2 ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_Bit0__Pls,axiom,
% 52.23/52.31 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I50_J,axiom,
% 52.23/52.31 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I49_J,axiom,
% 52.23/52.31 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_Bit0__def,axiom,
% 52.23/52.31 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_add__Bit0__Bit0,axiom,
% 52.23/52.31 ! [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)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_mult__Bit0,axiom,
% 52.23/52.31 ! [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)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_diff__bin__simps_I7_J,axiom,
% 52.23/52.31 ! [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)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_minus__Bit0,axiom,
% 52.23/52.31 ! [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)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I45_J,axiom,
% 52.23/52.31 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I42_J,axiom,
% 52.23/52.31 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_bin__less__0__simps_I3_J,axiom,
% 52.23/52.31 ! [V_w_2] :
% 52.23/52.31 ( 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)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I27_J,axiom,
% 52.23/52.31 ! [V_k_2] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I21_J,axiom,
% 52.23/52.31 ! [V_k_2] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_less__eq__int__code_I14_J,axiom,
% 52.23/52.31 ! [V_k2_2,V_k1_2] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I32_J,axiom,
% 52.23/52.31 ! [V_l_2,V_k_2] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I10_J,axiom,
% 52.23/52.31 ! [V_k_2] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I4_J,axiom,
% 52.23/52.31 ! [V_k_2] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_less__int__code_I15_J,axiom,
% 52.23/52.31 ! [V_k2_2,V_k1_2] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I16_J,axiom,
% 52.23/52.31 ! [V_l_2,V_k_2] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_add__Bit1__Bit0,axiom,
% 52.23/52.31 ! [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)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_add__Bit0__Bit1,axiom,
% 52.23/52.31 ! [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)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_diff__bin__simps_I3_J,axiom,
% 52.23/52.31 ! [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)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_diff__bin__simps_I10_J,axiom,
% 52.23/52.31 ! [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)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_diff__bin__simps_I9_J,axiom,
% 52.23/52.31 ! [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)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I28_J,axiom,
% 52.23/52.31 ! [V_k_2] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I8_J,axiom,
% 52.23/52.31 ! [V_k_2] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_zdiv__number__of__Bit0,axiom,
% 52.23/52.31 ! [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)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_neg__number__of__Bit0,axiom,
% 52.23/52.31 ! [V_w_2] :
% 52.23/52.31 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2))))
% 52.23/52.31 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_pred__Bit1,axiom,
% 52.23/52.31 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_pred__Bit0,axiom,
% 52.23/52.31 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_pred__Min,axiom,
% 52.23/52.31 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_iszero__number__of__Bit0,axiom,
% 52.23/52.31 ! [V_w_2,T_b] :
% 52.23/52.31 ( ( class_Int_Onumber__ring(T_b)
% 52.23/52.31 & class_Int_Oring__char__0(T_b) )
% 52.23/52.31 => ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2)))
% 52.23/52.31 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_succ__Bit0,axiom,
% 52.23/52.31 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_succ__Bit1,axiom,
% 52.23/52.31 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_number__of__Bit0,axiom,
% 52.23/52.31 ! [V_w,T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => 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)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I15_J,axiom,
% 52.23/52.31 ! [V_l_2,V_k_2] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_less__int__code_I14_J,axiom,
% 52.23/52.31 ! [V_k2_2,V_k1_2] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I33_J,axiom,
% 52.23/52.31 ! [V_l_2,V_k_2] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_less__eq__int__code_I15_J,axiom,
% 52.23/52.31 ! [V_k2_2,V_k1_2] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_mult__Bit1,axiom,
% 52.23/52.31 ! [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) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I25_J,axiom,
% 52.23/52.31 ! [V_k_2] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_rel__simps_I11_J,axiom,
% 52.23/52.31 ! [V_k_2] :
% 52.23/52.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 52.23/52.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_diff__bin__simps_I6_J,axiom,
% 52.23/52.31 ! [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)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_diff__bin__simps_I5_J,axiom,
% 52.23/52.31 ! [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)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_diff__bin__simps_I8_J,axiom,
% 52.23/52.31 ! [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)) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_add__Bit1__Bit1,axiom,
% 52.23/52.31 ! [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))) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_double__number__of__Bit0,axiom,
% 52.23/52.31 ! [V_w,T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.31 => 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)) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_number__of1,axiom,
% 52.23/52.31 ! [V_n] :
% 52.23/52.31 ( 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)))
% 52.23/52.31 => ( 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))))
% 52.23/52.31 & 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)))) ) ) ).
% 52.23/52.31
% 52.23/52.31 fof(fact_mult__2,axiom,
% 52.23/52.31 ! [V_z,T_a] :
% 52.23/52.31 ( class_Int_Onumber__ring(T_a)
% 52.23/52.32 => 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) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_mult__2__right,axiom,
% 52.23/52.32 ! [V_z,T_a] :
% 52.23/52.32 ( class_Int_Onumber__ring(T_a)
% 52.23/52.32 => 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) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_one__add__one__is__two,axiom,
% 52.23/52.32 ! [T_a] :
% 52.23/52.32 ( class_Int_Onumber__ring(T_a)
% 52.23/52.32 => 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))) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_zero__power2,axiom,
% 52.23/52.32 ! [T_a] :
% 52.23/52.32 ( class_Rings_Osemiring__1(T_a)
% 52.23/52.32 => 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) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_zero__eq__power2,axiom,
% 52.23/52.32 ! [V_a_2,T_b] :
% 52.23/52.32 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 52.23/52.32 => ( 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)
% 52.23/52.32 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_numeral__2__eq__2,axiom,
% 52.23/52.32 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))) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_semiring__norm_I115_J,axiom,
% 52.23/52.32 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))) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 52.23/52.32 ! [V_x,T_a] :
% 52.23/52.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.32 => 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)))) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_power2__eq__square,axiom,
% 52.23/52.32 ! [V_a,T_a] :
% 52.23/52.32 ( class_Groups_Omonoid__mult(T_a)
% 52.23/52.32 => 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) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
% 52.23/52.32 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))))) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_add__2__eq__Suc,axiom,
% 52.23/52.32 ! [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)) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_add__2__eq__Suc_H,axiom,
% 52.23/52.32 ! [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)) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_one__power2,axiom,
% 52.23/52.32 ! [T_a] :
% 52.23/52.32 ( class_Rings_Osemiring__1(T_a)
% 52.23/52.32 => 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) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_power2__minus,axiom,
% 52.23/52.32 ! [V_a,T_a] :
% 52.23/52.32 ( class_Rings_Oring__1(T_a)
% 52.23/52.32 => 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)))) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_nat__mult__2__right,axiom,
% 52.23/52.32 ! [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) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_nat__mult__2,axiom,
% 52.23/52.32 ! [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) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_power__even__eq,axiom,
% 52.23/52.32 ! [V_n,V_a,T_a] :
% 52.23/52.32 ( class_Groups_Omonoid__mult(T_a)
% 52.23/52.32 => 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)))) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_transfer__int__nat__numerals_I3_J,axiom,
% 52.23/52.32 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)))) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_transfer__nat__int__numerals_I3_J,axiom,
% 52.23/52.32 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)))) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_power2__abs,axiom,
% 52.23/52.32 ! [V_a,T_a] :
% 52.23/52.32 ( class_Rings_Olinordered__idom(T_a)
% 52.23/52.32 => 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)))) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_abs__power2,axiom,
% 52.23/52.32 ! [V_a,T_a] :
% 52.23/52.32 ( class_Rings_Olinordered__idom(T_a)
% 52.23/52.32 => 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)))) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_nat__1__add__1,axiom,
% 52.23/52.32 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))) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_mod2__Suc__Suc,axiom,
% 52.23/52.32 ! [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)))) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_div2__Suc__Suc,axiom,
% 52.23/52.32 ! [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))))) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_zmod__number__of__Bit0,axiom,
% 52.23/52.32 ! [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))) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_add__self__div__2,axiom,
% 52.23/52.32 ! [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 ).
% 52.23/52.32
% 52.23/52.32 fof(fact_zero__le__power2,axiom,
% 52.23/52.32 ! [V_a,T_a] :
% 52.23/52.32 ( class_Rings_Olinordered__idom(T_a)
% 52.23/52.32 => 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)))))) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_power2__le__imp__le,axiom,
% 52.23/52.32 ! [V_y,V_x,T_a] :
% 52.23/52.32 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.32 => ( 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))))))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 52.23/52.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_power2__eq__imp__eq,axiom,
% 52.23/52.32 ! [V_y,V_x,T_a] :
% 52.23/52.32 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.32 => ( 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))))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 52.23/52.32 => V_x = V_y ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_zero__less__power2,axiom,
% 52.23/52.32 ! [V_a_2,T_b] :
% 52.23/52.32 ( class_Rings_Olinordered__idom(T_b)
% 52.23/52.32 => ( 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))))))
% 52.23/52.32 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_power2__less__0,axiom,
% 52.23/52.32 ! [V_a,T_a] :
% 52.23/52.32 ( class_Rings_Olinordered__idom(T_a)
% 52.23/52.32 => ~ 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))) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_sum__power2__eq__zero__iff,axiom,
% 52.23/52.32 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.32 ( class_Rings_Olinordered__idom(T_b)
% 52.23/52.32 => ( 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)
% 52.23/52.32 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.32 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_power2__eq__square__number__of,axiom,
% 52.23/52.32 ! [V_w,T_b] :
% 52.23/52.32 ( ( class_Groups_Omonoid__mult(T_b)
% 52.23/52.32 & class_Int_Onumber(T_b) )
% 52.23/52.32 => 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)) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_less__2__cases,axiom,
% 52.23/52.32 ! [V_n] :
% 52.23/52.32 ( 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)))))
% 52.23/52.32 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.32 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_nat__2,axiom,
% 52.23/52.32 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))) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_power2__eq__1__iff,axiom,
% 52.23/52.32 ! [V_a_2,T_b] :
% 52.23/52.32 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 52.23/52.32 => ( 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)
% 52.23/52.32 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_b)
% 52.23/52.32 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 52.23/52.32 ! [V_n,V_x,T_a] :
% 52.23/52.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.32 => 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)) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_power__minus__even,axiom,
% 52.23/52.32 ! [V_n,V_a,T_a] :
% 52.23/52.32 ( class_Rings_Oring__1(T_a)
% 52.23/52.32 => 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)) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_power2__less__imp__less,axiom,
% 52.23/52.32 ! [V_y,V_x,T_a] :
% 52.23/52.32 ( class_Rings_Olinordered__semidom(T_a)
% 52.23/52.32 => ( 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))))))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 52.23/52.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_sum__power2__le__zero__iff,axiom,
% 52.23/52.32 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.32 ( class_Rings_Olinordered__idom(T_b)
% 52.23/52.32 => ( 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)))
% 52.23/52.32 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.32 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_sum__power2__ge__zero,axiom,
% 52.23/52.32 ! [V_y,V_x,T_a] :
% 52.23/52.32 ( class_Rings_Olinordered__idom(T_a)
% 52.23/52.32 => 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))))))) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_not__sum__power2__lt__zero,axiom,
% 52.23/52.32 ! [V_y,V_x,T_a] :
% 52.23/52.32 ( class_Rings_Olinordered__idom(T_a)
% 52.23/52.32 => ~ 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))) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_sum__power2__gt__zero__iff,axiom,
% 52.23/52.32 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.32 ( class_Rings_Olinordered__idom(T_b)
% 52.23/52.32 => ( 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)))))))
% 52.23/52.32 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.32 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_power2__sum,axiom,
% 52.23/52.32 ! [V_y,V_x,T_a] :
% 52.23/52.32 ( class_Int_Onumber__ring(T_a)
% 52.23/52.32 => 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)) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_zero__le__even__power_H,axiom,
% 52.23/52.32 ! [V_n,V_a,T_a] :
% 52.23/52.32 ( class_Rings_Olinordered__idom(T_a)
% 52.23/52.32 => 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)))) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
% 52.23/52.32 ! [V_n,V_x,T_a] :
% 52.23/52.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.32 => 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))) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_power__odd__eq,axiom,
% 52.23/52.32 ! [V_n,V_a,T_a] :
% 52.23/52.32 ( class_Groups_Omonoid__mult(T_a)
% 52.23/52.32 => 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))))) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_power__minus1__even,axiom,
% 52.23/52.32 ! [V_n,T_a] :
% 52.23/52.32 ( class_Rings_Oring__1(T_a)
% 52.23/52.32 => 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) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_zdiv__number__of__Bit1,axiom,
% 52.23/52.32 ! [V_v,V_w] :
% 52.23/52.32 ( ( 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)))
% 52.23/52.32 => 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)) )
% 52.23/52.32 & ( ~ 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)))
% 52.23/52.32 => 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)) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_mod2__gr__0,axiom,
% 52.23/52.32 ! [V_m_2] :
% 52.23/52.32 ( 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))))))
% 52.23/52.32 <=> 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) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_div__2__gt__zero,axiom,
% 52.23/52.32 ! [V_n] :
% 52.23/52.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 52.23/52.32 => 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)))))) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_power2__diff,axiom,
% 52.23/52.32 ! [V_y,V_x,T_a] :
% 52.23/52.32 ( class_Int_Onumber__ring(T_a)
% 52.23/52.32 => 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)) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_odd__0__le__power__imp__0__le,axiom,
% 52.23/52.32 ! [V_n,V_a,T_a] :
% 52.23/52.32 ( class_Rings_Olinordered__idom(T_a)
% 52.23/52.32 => ( 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)))))
% 52.23/52.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_odd__power__less__zero,axiom,
% 52.23/52.32 ! [V_n,V_a,T_a] :
% 52.23/52.32 ( class_Rings_Olinordered__idom(T_a)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.32 => 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))) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_power__minus1__odd,axiom,
% 52.23/52.32 ! [V_n,T_a] :
% 52.23/52.32 ( class_Rings_Oring__1(T_a)
% 52.23/52.32 => 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)) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_power__m1__even,axiom,
% 52.23/52.32 ! [V_n,T_a] :
% 52.23/52.32 ( class_Int_Onumber__ring(T_a)
% 52.23/52.32 => 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) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_power__m1__odd,axiom,
% 52.23/52.32 ! [V_n,T_a] :
% 52.23/52.32 ( class_Int_Onumber__ring(T_a)
% 52.23/52.32 => 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) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_Suc__n__div__2__gt__zero,axiom,
% 52.23/52.32 ! [V_n] :
% 52.23/52.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 52.23/52.32 => 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)))))) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_int__of__code,axiom,
% 52.23/52.32 ! [V_k] :
% 52.23/52.32 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 52.23/52.32 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 52.23/52.32 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 52.23/52.32 => ( ( 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)
% 52.23/52.32 => 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)))))) )
% 52.23/52.32 & ( 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)
% 52.23/52.32 => 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)) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_one__code__numeral__code,axiom,
% 52.23/52.32 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)) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_half__gt__zero__iff,axiom,
% 52.23/52.32 ! [V_r_2,T_b] :
% 52.23/52.32 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 52.23/52.32 & class_Int_Onumber__ring(T_b) )
% 52.23/52.32 => ( 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))))))
% 52.23/52.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2)) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_half__gt__zero,axiom,
% 52.23/52.32 ! [V_r,T_a] :
% 52.23/52.32 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 52.23/52.32 & class_Int_Onumber__ring(T_a) )
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r))
% 52.23/52.32 => 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)))))) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom,
% 52.23/52.32 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_nat__intermed__int__val,axiom,
% 52.23/52.32 ! [V_k_2,V_f_2,V_n_2,V_m_2] :
% 52.23/52.32 ( ! [B_i] :
% 52.23/52.32 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 52.23/52.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) )
% 52.23/52.32 => 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))) )
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 52.23/52.32 => ? [B_i] :
% 52.23/52.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 52.23/52.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 52.23/52.32 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_code__numeral__zero__minus__one,axiom,
% 52.23/52.32 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) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__zero,axiom,
% 52.23/52.32 ! [V_a,T_a] :
% 52.23/52.32 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 52.23/52.32 => 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) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__zero__left,axiom,
% 52.23/52.32 ! [V_a,T_a] :
% 52.23/52.32 ( class_Rings_Odivision__ring(T_a)
% 52.23/52.32 => 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) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_add__divide__distrib,axiom,
% 52.23/52.32 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.32 ( class_Rings_Odivision__ring(T_a)
% 52.23/52.32 => 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)) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_times__divide__times__eq,axiom,
% 52.23/52.32 ! [V_w,V_z,V_y,V_x,T_a] :
% 52.23/52.32 ( class_Fields_Ofield__inverse__zero(T_a)
% 52.23/52.32 => 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)) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_times__divide__eq__right,axiom,
% 52.23/52.32 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.32 ( class_Rings_Odivision__ring(T_a)
% 52.23/52.32 => 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) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_diff__divide__distrib,axiom,
% 52.23/52.32 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.32 ( class_Rings_Odivision__ring(T_a)
% 52.23/52.32 => 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)) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__1,axiom,
% 52.23/52.32 ! [V_a,T_a] :
% 52.23/52.32 ( class_Rings_Odivision__ring(T_a)
% 52.23/52.32 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_minus__divide__divide,axiom,
% 52.23/52.32 ! [V_b,V_a,T_a] :
% 52.23/52.32 ( class_Fields_Ofield__inverse__zero(T_a)
% 52.23/52.32 => 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) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_minus__divide__right,axiom,
% 52.23/52.32 ! [V_b,V_a,T_a] :
% 52.23/52.32 ( class_Fields_Ofield__inverse__zero(T_a)
% 52.23/52.32 => 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)) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_minus__divide__left,axiom,
% 52.23/52.32 ! [V_b,V_a,T_a] :
% 52.23/52.32 ( class_Rings_Odivision__ring(T_a)
% 52.23/52.32 => 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) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_power__divide,axiom,
% 52.23/52.32 ! [V_n,V_b,V_a,T_a] :
% 52.23/52.32 ( class_Fields_Ofield__inverse__zero(T_a)
% 52.23/52.32 => 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)) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_abs__divide,axiom,
% 52.23/52.32 ! [V_b,V_a,T_a] :
% 52.23/52.32 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 52.23/52.32 => 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)) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom,
% 52.23/52.32 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom,
% 52.23/52.32 ! [V_y,V_x] :
% 52.23/52.32 ( c_Nat__Transfer_Ois__nat(V_x)
% 52.23/52.32 => ( c_Nat__Transfer_Ois__nat(V_y)
% 52.23/52.32 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom,
% 52.23/52.32 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom,
% 52.23/52.32 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom,
% 52.23/52.32 ! [V_y,V_x] :
% 52.23/52.32 ( c_Nat__Transfer_Ois__nat(V_x)
% 52.23/52.32 => ( c_Nat__Transfer_Ois__nat(V_y)
% 52.23/52.32 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom,
% 52.23/52.32 ! [V_y,V_x] :
% 52.23/52.32 ( c_Nat__Transfer_Ois__nat(V_x)
% 52.23/52.32 => ( c_Nat__Transfer_Ois__nat(V_y)
% 52.23/52.32 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom,
% 52.23/52.32 ! [V_y,V_x] :
% 52.23/52.32 ( c_Nat__Transfer_Ois__nat(V_x)
% 52.23/52.32 => ( c_Nat__Transfer_Ois__nat(V_y)
% 52.23/52.32 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom,
% 52.23/52.32 ! [V_n,V_x] :
% 52.23/52.32 ( c_Nat__Transfer_Ois__nat(V_x)
% 52.23/52.32 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_zero__le__divide__iff,axiom,
% 52.23/52.32 ! [V_b_2,V_a_2,T_b] :
% 52.23/52.32 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 52.23/52.32 => ( 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)))
% 52.23/52.32 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 52.23/52.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 52.23/52.32 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 52.23/52.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__le__0__iff,axiom,
% 52.23/52.32 ! [V_b_2,V_a_2,T_b] :
% 52.23/52.32 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 52.23/52.32 => ( 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)))
% 52.23/52.32 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 52.23/52.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 52.23/52.32 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 52.23/52.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__right__mono,axiom,
% 52.23/52.32 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.32 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 52.23/52.32 => 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))) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__right__mono__neg,axiom,
% 52.23/52.32 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.32 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.32 => 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))) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__strict__right__mono__neg,axiom,
% 52.23/52.32 ! [V_c,V_a,V_b,T_a] :
% 52.23/52.32 ( class_Fields_Olinordered__field(T_a)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.32 => 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))) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__strict__right__mono,axiom,
% 52.23/52.32 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.32 ( class_Fields_Olinordered__field(T_a)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 52.23/52.32 => 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))) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__neg__neg,axiom,
% 52.23/52.32 ! [V_y,V_x,T_a] :
% 52.23/52.32 ( class_Fields_Olinordered__field(T_a)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.32 => 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))) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__neg__pos,axiom,
% 52.23/52.32 ! [V_y,V_x,T_a] :
% 52.23/52.32 ( class_Fields_Olinordered__field(T_a)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 52.23/52.32 => 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))) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__pos__neg,axiom,
% 52.23/52.32 ! [V_y,V_x,T_a] :
% 52.23/52.32 ( class_Fields_Olinordered__field(T_a)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.32 => 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))) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__pos__pos,axiom,
% 52.23/52.32 ! [V_y,V_x,T_a] :
% 52.23/52.32 ( class_Fields_Olinordered__field(T_a)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 52.23/52.32 => 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))) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__less__0__iff,axiom,
% 52.23/52.32 ! [V_b_2,V_a_2,T_b] :
% 52.23/52.32 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 52.23/52.32 => ( 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)))
% 52.23/52.32 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 52.23/52.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 52.23/52.32 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 52.23/52.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_zero__less__divide__iff,axiom,
% 52.23/52.32 ! [V_b_2,V_a_2,T_b] :
% 52.23/52.32 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 52.23/52.32 => ( 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)))
% 52.23/52.32 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 52.23/52.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 52.23/52.32 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 52.23/52.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_eq__divide__eq,axiom,
% 52.23/52.32 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 52.23/52.32 ( class_Fields_Ofield__inverse__zero(T_b)
% 52.23/52.32 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
% 52.23/52.32 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.32 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 )
% 52.23/52.32 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.32 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__eq__eq,axiom,
% 52.23/52.32 ! [V_a_2,V_c_2,V_b_2,T_b] :
% 52.23/52.32 ( class_Fields_Ofield__inverse__zero(T_b)
% 52.23/52.32 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
% 52.23/52.32 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.32 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) )
% 52.23/52.32 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.32 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_mult__divide__mult__cancel__right,axiom,
% 52.23/52.32 ! [V_b,V_a,V_c,T_a] :
% 52.23/52.32 ( class_Fields_Ofield__inverse__zero(T_a)
% 52.23/52.32 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.32 => 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) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_mult__divide__mult__cancel__left,axiom,
% 52.23/52.32 ! [V_b,V_a,V_c,T_a] :
% 52.23/52.32 ( class_Fields_Ofield__inverse__zero(T_a)
% 52.23/52.32 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.32 => 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) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_frac__eq__eq,axiom,
% 52.23/52.32 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] :
% 52.23/52.32 ( class_Fields_Ofield(T_b)
% 52.23/52.32 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.32 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.32 => ( 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)
% 52.23/52.32 <=> 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) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_eq__divide__imp,axiom,
% 52.23/52.32 ! [V_b,V_a,V_c,T_a] :
% 52.23/52.32 ( class_Rings_Odivision__ring(T_a)
% 52.23/52.32 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.32 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b
% 52.23/52.32 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__eq__imp,axiom,
% 52.23/52.32 ! [V_a,V_b,V_c,T_a] :
% 52.23/52.32 ( class_Rings_Odivision__ring(T_a)
% 52.23/52.32 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.32 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
% 52.23/52.32 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_nonzero__divide__eq__eq,axiom,
% 52.23/52.32 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 52.23/52.32 ( class_Rings_Odivision__ring(T_b)
% 52.23/52.32 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.32 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
% 52.23/52.32 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_nonzero__eq__divide__eq,axiom,
% 52.23/52.32 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 52.23/52.32 ( class_Rings_Odivision__ring(T_b)
% 52.23/52.32 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.32 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
% 52.23/52.32 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_right__inverse__eq,axiom,
% 52.23/52.32 ! [V_a_2,V_b_2,T_b] :
% 52.23/52.32 ( class_Rings_Odivision__ring(T_b)
% 52.23/52.32 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.32 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_b)
% 52.23/52.32 <=> V_a_2 = V_b_2 ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__self,axiom,
% 52.23/52.32 ! [V_a,T_a] :
% 52.23/52.32 ( class_Rings_Odivision__ring(T_a)
% 52.23/52.32 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.32 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__self__if,axiom,
% 52.23/52.32 ! [V_a,T_a] :
% 52.23/52.32 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 52.23/52.32 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.32 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) )
% 52.23/52.32 & ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.32 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_nonzero__minus__divide__divide,axiom,
% 52.23/52.32 ! [V_a,V_b,T_a] :
% 52.23/52.32 ( class_Rings_Odivision__ring(T_a)
% 52.23/52.32 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.32 => 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) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_nonzero__minus__divide__right,axiom,
% 52.23/52.32 ! [V_a,V_b,T_a] :
% 52.23/52.32 ( class_Rings_Odivision__ring(T_a)
% 52.23/52.32 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.32 => 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)) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_nonzero__power__divide,axiom,
% 52.23/52.32 ! [V_n,V_a,V_b,T_a] :
% 52.23/52.32 ( class_Fields_Ofield(T_a)
% 52.23/52.32 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.32 => 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)) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_nonzero__abs__divide,axiom,
% 52.23/52.32 ! [V_a,V_b,T_a] :
% 52.23/52.32 ( class_Fields_Olinordered__field(T_a)
% 52.23/52.32 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.32 => 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)) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_power__one__over,axiom,
% 52.23/52.32 ! [V_n,V_a,T_a] :
% 52.23/52.32 ( class_Fields_Ofield__inverse__zero(T_a)
% 52.23/52.32 => 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) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom,
% 52.23/52.32 ! [V_y,V_x] :
% 52.23/52.32 ( c_Nat__Transfer_Ois__nat(V_x)
% 52.23/52.32 => ( c_Nat__Transfer_Ois__nat(V_y)
% 52.23/52.32 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__nonpos__neg,axiom,
% 52.23/52.32 ! [V_y,V_x,T_a] :
% 52.23/52.32 ( class_Fields_Olinordered__field(T_a)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.32 => 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))) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__nonpos__pos,axiom,
% 52.23/52.32 ! [V_y,V_x,T_a] :
% 52.23/52.32 ( class_Fields_Olinordered__field(T_a)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 52.23/52.32 => 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))) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_frac__le,axiom,
% 52.23/52.32 ! [V_z,V_w,V_y,V_x,T_a] :
% 52.23/52.32 ( class_Fields_Olinordered__field(T_a)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 52.23/52.32 => 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))) ) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_frac__less,axiom,
% 52.23/52.32 ! [V_z,V_w,V_y,V_x,T_a] :
% 52.23/52.32 ( class_Fields_Olinordered__field(T_a)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 52.23/52.32 => 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))) ) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_frac__less2,axiom,
% 52.23/52.32 ! [V_z,V_w,V_y,V_x,T_a] :
% 52.23/52.32 ( class_Fields_Olinordered__field(T_a)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z))
% 52.23/52.32 => 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))) ) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__nonneg__neg,axiom,
% 52.23/52.32 ! [V_y,V_x,T_a] :
% 52.23/52.32 ( class_Fields_Olinordered__field(T_a)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.32 => 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))) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__nonneg__pos,axiom,
% 52.23/52.32 ! [V_y,V_x,T_a] :
% 52.23/52.32 ( class_Fields_Olinordered__field(T_a)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 52.23/52.32 => 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))) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__strict__left__mono__neg,axiom,
% 52.23/52.32 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.32 ( class_Fields_Olinordered__field(T_a)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.32 => ( 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)))
% 52.23/52.32 => 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))) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__strict__left__mono,axiom,
% 52.23/52.32 ! [V_c,V_a,V_b,T_a] :
% 52.23/52.32 ( class_Fields_Olinordered__field(T_a)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 52.23/52.32 => ( 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)))
% 52.23/52.32 => 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))) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_neg__divide__less__eq,axiom,
% 52.23/52.32 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 52.23/52.32 ( class_Fields_Olinordered__field(T_b)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 52.23/52.32 => ( 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))
% 52.23/52.32 <=> 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)) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_neg__less__divide__eq,axiom,
% 52.23/52.32 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 52.23/52.32 ( class_Fields_Olinordered__field(T_b)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 52.23/52.32 => ( 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)))
% 52.23/52.32 <=> 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))) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_mult__imp__less__div__pos,axiom,
% 52.23/52.32 ! [V_x,V_z,V_y,T_a] :
% 52.23/52.32 ( class_Fields_Olinordered__field(T_a)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 52.23/52.32 => ( 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))
% 52.23/52.32 => 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))) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_mult__imp__div__pos__less,axiom,
% 52.23/52.32 ! [V_z,V_x,V_y,T_a] :
% 52.23/52.32 ( class_Fields_Olinordered__field(T_a)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 52.23/52.32 => ( 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)))
% 52.23/52.32 => 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)) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_pos__divide__less__eq,axiom,
% 52.23/52.32 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 52.23/52.32 ( class_Fields_Olinordered__field(T_b)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 52.23/52.32 => ( 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))
% 52.23/52.32 <=> 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))) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_pos__less__divide__eq,axiom,
% 52.23/52.32 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 52.23/52.32 ( class_Fields_Olinordered__field(T_b)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 52.23/52.32 => ( 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)))
% 52.23/52.32 <=> 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)) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__less__eq,axiom,
% 52.23/52.32 ! [V_a_2,V_c_2,V_b_2,T_b] :
% 52.23/52.32 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 52.23/52.32 => ( 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))
% 52.23/52.32 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 52.23/52.32 => 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))) )
% 52.23/52.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 52.23/52.32 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 52.23/52.32 => 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)) )
% 52.23/52.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 52.23/52.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_less__divide__eq,axiom,
% 52.23/52.32 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 52.23/52.32 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 52.23/52.32 => ( 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)))
% 52.23/52.32 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 52.23/52.32 => 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)) )
% 52.23/52.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 52.23/52.32 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 52.23/52.32 => 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))) )
% 52.23/52.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 52.23/52.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_is__nat__def,axiom,
% 52.23/52.32 ! [V_x_2] :
% 52.23/52.32 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 52.23/52.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_add__num__frac,axiom,
% 52.23/52.32 ! [V_x,V_z,V_y,T_a] :
% 52.23/52.32 ( class_Fields_Ofield__inverse__zero(T_a)
% 52.23/52.32 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.32 => 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) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_add__divide__eq__iff,axiom,
% 52.23/52.32 ! [V_y,V_x,V_z,T_a] :
% 52.23/52.32 ( class_Fields_Ofield(T_a)
% 52.23/52.32 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.32 => 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) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_add__frac__num,axiom,
% 52.23/52.32 ! [V_z,V_x,V_y,T_a] :
% 52.23/52.32 ( class_Fields_Ofield__inverse__zero(T_a)
% 52.23/52.32 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.32 => 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) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__add__eq__iff,axiom,
% 52.23/52.32 ! [V_y,V_x,V_z,T_a] :
% 52.23/52.32 ( class_Fields_Ofield(T_a)
% 52.23/52.32 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.32 => 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) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_add__frac__eq,axiom,
% 52.23/52.32 ! [V_w,V_x,V_z,V_y,T_a] :
% 52.23/52.32 ( class_Fields_Ofield(T_a)
% 52.23/52.32 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.32 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.32 => 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)) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_diff__frac__eq,axiom,
% 52.23/52.32 ! [V_w,V_x,V_z,V_y,T_a] :
% 52.23/52.32 ( class_Fields_Ofield(T_a)
% 52.23/52.32 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.32 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.32 => 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)) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__diff__eq__iff,axiom,
% 52.23/52.32 ! [V_y,V_x,V_z,T_a] :
% 52.23/52.32 ( class_Fields_Ofield(T_a)
% 52.23/52.32 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.32 => 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) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_diff__divide__eq__iff,axiom,
% 52.23/52.32 ! [V_y,V_x,V_z,T_a] :
% 52.23/52.32 ( class_Fields_Ofield(T_a)
% 52.23/52.32 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.32 => 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) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_eq__divide__eq__number__of1,axiom,
% 52.23/52.32 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 52.23/52.32 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 52.23/52.32 & class_Int_Onumber(T_b) )
% 52.23/52.32 => ( 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))
% 52.23/52.32 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.32 => 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 )
% 52.23/52.32 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.32 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_eq__divide__eq__number__of,axiom,
% 52.23/52.32 ! [V_c_2,V_b_2,V_w_2,T_b] :
% 52.23/52.32 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 52.23/52.32 & class_Int_Onumber(T_b) )
% 52.23/52.32 => ( 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)
% 52.23/52.32 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.32 => 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 )
% 52.23/52.32 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.32 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__eq__eq__number__of,axiom,
% 52.23/52.32 ! [V_w_2,V_c_2,V_b_2,T_b] :
% 52.23/52.32 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 52.23/52.32 & class_Int_Onumber(T_b) )
% 52.23/52.32 => ( 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)
% 52.23/52.32 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.32 => 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) )
% 52.23/52.32 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.32 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__eq__eq__number__of1,axiom,
% 52.23/52.32 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 52.23/52.32 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 52.23/52.32 & class_Int_Onumber(T_b) )
% 52.23/52.32 => ( 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
% 52.23/52.32 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.32 => 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)) )
% 52.23/52.32 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.32 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_gt__half__sum,axiom,
% 52.23/52.32 ! [V_b,V_a,T_a] :
% 52.23/52.32 ( class_Fields_Olinordered__field(T_a)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 52.23/52.32 => 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)) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_less__half__sum,axiom,
% 52.23/52.32 ! [V_b,V_a,T_a] :
% 52.23/52.32 ( class_Fields_Olinordered__field(T_a)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 52.23/52.32 => 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))))) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__Numeral0,axiom,
% 52.23/52.32 ! [V_x,T_a] :
% 52.23/52.32 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 52.23/52.32 & class_Int_Onumber__ring(T_a) )
% 52.23/52.32 => 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) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_abs__div__pos,axiom,
% 52.23/52.32 ! [V_x,V_y,T_a] :
% 52.23/52.32 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 52.23/52.32 => 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)) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__numeral__1,axiom,
% 52.23/52.32 ! [V_a,T_a] :
% 52.23/52.32 ( ( class_Fields_Ofield(T_a)
% 52.23/52.32 & class_Int_Onumber__ring(T_a) )
% 52.23/52.32 => 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 ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__Numeral1,axiom,
% 52.23/52.32 ! [V_x,T_a] :
% 52.23/52.32 ( ( class_Fields_Ofield(T_a)
% 52.23/52.32 & class_Int_Onumber__ring(T_a) )
% 52.23/52.32 => 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 ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__minus1,axiom,
% 52.23/52.32 ! [V_x,T_a] :
% 52.23/52.32 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 52.23/52.32 & class_Int_Onumber__ring(T_a) )
% 52.23/52.32 => 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) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_zero__code__numeral__code,axiom,
% 52.23/52.32 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) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_le__divide__eq,axiom,
% 52.23/52.32 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 52.23/52.32 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 52.23/52.32 => ( 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)))
% 52.23/52.32 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 52.23/52.32 => 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)) )
% 52.23/52.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 52.23/52.32 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 52.23/52.32 => 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))) )
% 52.23/52.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 52.23/52.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__le__eq,axiom,
% 52.23/52.32 ! [V_a_2,V_c_2,V_b_2,T_b] :
% 52.23/52.32 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 52.23/52.32 => ( 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))
% 52.23/52.32 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 52.23/52.32 => 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))) )
% 52.23/52.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 52.23/52.32 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 52.23/52.32 => 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)) )
% 52.23/52.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 52.23/52.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_pos__le__divide__eq,axiom,
% 52.23/52.32 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 52.23/52.32 ( class_Fields_Olinordered__field(T_b)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 52.23/52.32 => ( 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)))
% 52.23/52.32 <=> 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)) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_pos__divide__le__eq,axiom,
% 52.23/52.32 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 52.23/52.32 ( class_Fields_Olinordered__field(T_b)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 52.23/52.32 => ( 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))
% 52.23/52.32 <=> 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))) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_mult__imp__div__pos__le,axiom,
% 52.23/52.32 ! [V_z,V_x,V_y,T_a] :
% 52.23/52.32 ( class_Fields_Olinordered__field(T_a)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 52.23/52.32 => ( 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)))
% 52.23/52.32 => 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)) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_mult__imp__le__div__pos,axiom,
% 52.23/52.32 ! [V_x,V_z,V_y,T_a] :
% 52.23/52.32 ( class_Fields_Olinordered__field(T_a)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 52.23/52.32 => ( 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))
% 52.23/52.32 => 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))) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_neg__le__divide__eq,axiom,
% 52.23/52.32 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 52.23/52.32 ( class_Fields_Olinordered__field(T_b)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 52.23/52.32 => ( 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)))
% 52.23/52.32 <=> 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))) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_neg__divide__le__eq,axiom,
% 52.23/52.32 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 52.23/52.32 ( class_Fields_Olinordered__field(T_b)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 52.23/52.32 => ( 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))
% 52.23/52.32 <=> 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)) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__left__mono,axiom,
% 52.23/52.32 ! [V_c,V_a,V_b,T_a] :
% 52.23/52.32 ( class_Fields_Olinordered__field(T_a)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 52.23/52.32 => ( 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)))
% 52.23/52.32 => 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))) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__left__mono__neg,axiom,
% 52.23/52.32 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.32 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 52.23/52.32 => ( 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)))
% 52.23/52.32 => 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))) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__less__eq__number__of1,axiom,
% 52.23/52.32 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 52.23/52.32 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 52.23/52.32 & class_Int_Onumber(T_b) )
% 52.23/52.32 => ( 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))
% 52.23/52.32 <=> ( ( 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)))
% 52.23/52.32 => 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)))) )
% 52.23/52.32 & ( ~ 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)))
% 52.23/52.32 => ( ( 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)))
% 52.23/52.32 => 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)) )
% 52.23/52.32 & ( ~ 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)))
% 52.23/52.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__less__eq__number__of,axiom,
% 52.23/52.32 ! [V_w_2,V_c_2,V_b_2,T_b] :
% 52.23/52.32 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 52.23/52.32 & class_Int_Onumber(T_b) )
% 52.23/52.32 => ( 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)))
% 52.23/52.32 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 52.23/52.32 => 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))) )
% 52.23/52.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 52.23/52.32 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 52.23/52.32 => 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)) )
% 52.23/52.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 52.23/52.32 => 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))) ) ) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_less__divide__eq__number__of,axiom,
% 52.23/52.32 ! [V_c_2,V_b_2,V_w_2,T_b] :
% 52.23/52.32 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 52.23/52.32 & class_Int_Onumber(T_b) )
% 52.23/52.32 => ( 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)))
% 52.23/52.32 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 52.23/52.32 => 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)) )
% 52.23/52.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 52.23/52.32 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 52.23/52.32 => 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))) )
% 52.23/52.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 52.23/52.32 => 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))) ) ) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_less__divide__eq__number__of1,axiom,
% 52.23/52.32 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 52.23/52.32 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 52.23/52.32 & class_Int_Onumber(T_b) )
% 52.23/52.32 => ( 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))))
% 52.23/52.32 <=> ( ( 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)))
% 52.23/52.32 => 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)) )
% 52.23/52.32 & ( ~ 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)))
% 52.23/52.32 => ( ( 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)))
% 52.23/52.32 => 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)))) )
% 52.23/52.32 & ( ~ 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)))
% 52.23/52.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_power__diff,axiom,
% 52.23/52.32 ! [V_m,V_n,V_a,T_a] :
% 52.23/52.32 ( class_Fields_Ofield(T_a)
% 52.23/52.32 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 52.23/52.32 => 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)) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_minus1__divide,axiom,
% 52.23/52.32 ! [V_x,T_a] :
% 52.23/52.32 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 52.23/52.32 & class_Int_Onumber__ring(T_a) )
% 52.23/52.32 => 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)) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom,
% 52.23/52.32 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_le__divide__eq__number__of1,axiom,
% 52.23/52.32 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 52.23/52.32 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 52.23/52.32 & class_Int_Onumber(T_b) )
% 52.23/52.32 => ( 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))))
% 52.23/52.32 <=> ( ( 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)))
% 52.23/52.32 => 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)) )
% 52.23/52.32 & ( ~ 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)))
% 52.23/52.32 => ( ( 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)))
% 52.23/52.32 => 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)))) )
% 52.23/52.32 & ( ~ 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)))
% 52.23/52.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_le__divide__eq__number__of,axiom,
% 52.23/52.32 ! [V_c_2,V_b_2,V_w_2,T_b] :
% 52.23/52.32 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 52.23/52.32 & class_Int_Onumber(T_b) )
% 52.23/52.32 => ( 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)))
% 52.23/52.32 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 52.23/52.32 => 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)) )
% 52.23/52.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 52.23/52.32 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 52.23/52.32 => 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))) )
% 52.23/52.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 52.23/52.32 => 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))) ) ) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__le__eq__number__of,axiom,
% 52.23/52.32 ! [V_w_2,V_c_2,V_b_2,T_b] :
% 52.23/52.32 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 52.23/52.32 & class_Int_Onumber(T_b) )
% 52.23/52.32 => ( 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)))
% 52.23/52.32 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 52.23/52.32 => 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))) )
% 52.23/52.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 52.23/52.32 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 52.23/52.32 => 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)) )
% 52.23/52.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 52.23/52.32 => 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))) ) ) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divide__le__eq__number__of1,axiom,
% 52.23/52.32 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 52.23/52.32 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 52.23/52.32 & class_Int_Onumber(T_b) )
% 52.23/52.32 => ( 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))
% 52.23/52.32 <=> ( ( 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)))
% 52.23/52.32 => 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)))) )
% 52.23/52.32 & ( ~ 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)))
% 52.23/52.32 => ( ( 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)))
% 52.23/52.32 => 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)) )
% 52.23/52.32 & ( ~ 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)))
% 52.23/52.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_nat__of__aux__code,axiom,
% 52.23/52.32 ! [V_n,V_i] :
% 52.23/52.32 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 52.23/52.32 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n )
% 52.23/52.32 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 52.23/52.32 => 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)) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_code__numeral_Osize_I1_J,axiom,
% 52.23/52.32 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) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_code__numeral_Osize_I3_J,axiom,
% 52.23/52.32 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) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_code__numeral_Osimps_I4_J,axiom,
% 52.23/52.32 ! [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 ).
% 52.23/52.32
% 52.23/52.32 fof(fact_log_Osimps,axiom,
% 52.23/52.32 ! [V_i,V_b] :
% 52.23/52.32 ( ( ( 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)))
% 52.23/52.32 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 52.23/52.32 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 52.23/52.32 & ( ~ ( 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)))
% 52.23/52.32 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 52.23/52.32 => 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))) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_field__le__epsilon,axiom,
% 52.23/52.32 ! [V_y,V_x,T_a] :
% 52.23/52.32 ( class_Fields_Olinordered__field(T_a)
% 52.23/52.32 => ( ! [B_e] :
% 52.23/52.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e))
% 52.23/52.32 => 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))) )
% 52.23/52.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_minus__shift__def,axiom,
% 52.23/52.32 ! [V_r,V_l,V_k] :
% 52.23/52.32 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 52.23/52.32 => 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) )
% 52.23/52.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 52.23/52.32 => 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) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_inc__shift__def,axiom,
% 52.23/52.32 ! [V_k,V_v] :
% 52.23/52.32 ( ( V_v = V_k
% 52.23/52.32 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 52.23/52.32 & ( V_v != V_k
% 52.23/52.32 => 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)) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_code__numeral_Osize_I4_J,axiom,
% 52.23/52.32 ! [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))) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_code__numeral_Osize_I2_J,axiom,
% 52.23/52.32 ! [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))) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_minus__code__numeral__code,axiom,
% 52.23/52.32 ! [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) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_subtract__code__numeral__def,axiom,
% 52.23/52.32 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_code__numeral_Oinject,axiom,
% 52.23/52.32 ! [V_code__numeral_H_2,V_code__numeral_2] :
% 52.23/52.32 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2)
% 52.23/52.32 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_code__numeral_Osimps_I2_J,axiom,
% 52.23/52.32 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_code__numeral_Osimps_I3_J,axiom,
% 52.23/52.32 ! [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) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_code__numeral_Osimps_I5_J,axiom,
% 52.23/52.32 ! [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) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_Suc__code__numeral__minus__one,axiom,
% 52.23/52.32 ! [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 ).
% 52.23/52.32
% 52.23/52.32 fof(fact_negDivAlg__eqn__1__number__of,axiom,
% 52.23/52.32 ! [V_w] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 => ( ( 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))))
% 52.23/52.32 => 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))) )
% 52.23/52.32 & ( ~ 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))))
% 52.23/52.32 => 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)))) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_diff__nat__number__of,axiom,
% 52.23/52.32 ! [V_v_2,V_v_H_2] :
% 52.23/52.32 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 52.23/52.32 => 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) )
% 52.23/52.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 52.23/52.32 => 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)) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_code__numeral_Orecs_I2_J,axiom,
% 52.23/52.32 ! [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)) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divmod__nat__step,axiom,
% 52.23/52.32 ! [V_m,V_n] :
% 52.23/52.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 52.23/52.32 => 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)) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_code__numeral__not__eq__zero,axiom,
% 52.23/52.32 ! [V_i_2] :
% 52.23/52.32 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 52.23/52.32 <=> 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)) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_beyond__def,axiom,
% 52.23/52.32 ! [V_l,V_k] :
% 52.23/52.32 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 52.23/52.32 => c_Quickcheck_Obeyond(V_k,V_l) = V_l )
% 52.23/52.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 52.23/52.32 => c_Quickcheck_Obeyond(V_k,V_l) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divmod__nat__zero,axiom,
% 52.23/52.32 ! [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) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_Code__Numeral_Oof__nat__inject,axiom,
% 52.23/52.32 ! [V_m_2,V_n_2] :
% 52.23/52.32 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2)
% 52.23/52.32 <=> V_n_2 = V_m_2 ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_Code__Numeral_Oof__nat__code,axiom,
% 52.23/52.32 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_fun__Compl__def,axiom,
% 52.23/52.32 ! [V_x_2,V_A_2,T_c,T_b] :
% 52.23/52.32 ( class_Groups_Ouminus(T_b)
% 52.23/52.32 => 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)) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_fun__diff__def,axiom,
% 52.23/52.32 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 52.23/52.32 ( class_Groups_Ominus(T_b)
% 52.23/52.32 => 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)) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_less__eq__nat_Osimps_I2_J,axiom,
% 52.23/52.32 ! [V_n_2,V_m_2] :
% 52.23/52.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 52.23/52.32 <=> 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)) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divmod__nat__base,axiom,
% 52.23/52.32 ! [V_n,V_m] :
% 52.23/52.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 52.23/52.32 => 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) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_less__eq__Suc__le__raw,axiom,
% 52.23/52.32 ! [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)) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_diff__Suc,axiom,
% 52.23/52.32 ! [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)) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_nat__number__of__Bit0,axiom,
% 52.23/52.32 ! [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))) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_times__code__numeral__code,axiom,
% 52.23/52.32 ! [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)) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divmod__nat__div__mod,axiom,
% 52.23/52.32 ! [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)) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_power__number__of__even,axiom,
% 52.23/52.32 ! [V_w_2,V_z_2,T_b] :
% 52.23/52.32 ( class_Int_Onumber__ring(T_b)
% 52.23/52.32 => 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))) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_zpower__number__of__even,axiom,
% 52.23/52.32 ! [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))) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_beyond__zero,axiom,
% 52.23/52.32 ! [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) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_power__number__of__even__number__of,axiom,
% 52.23/52.32 ! [V_w_2,V_v_2,T_b] :
% 52.23/52.32 ( class_Int_Onumber__ring(T_b)
% 52.23/52.32 => 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))) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_diff__nat__eq__if,axiom,
% 52.23/52.32 ! [V_z_2,V_z_H_2] :
% 52.23/52.32 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 52.23/52.32 => 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) )
% 52.23/52.32 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 52.23/52.32 => 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)) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_negDivAlg__div__mod,axiom,
% 52.23/52.32 ! [V_l,V_k] :
% 52.23/52.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 52.23/52.32 => 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)) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_negDivAlg__minus1,axiom,
% 52.23/52.32 ! [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))) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_semiring__1__class_Oof__nat__code,axiom,
% 52.23/52.32 ! [V_n_2,T_b] :
% 52.23/52.32 ( class_Rings_Osemiring__1(T_b)
% 52.23/52.32 => 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)) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_adjust__eq,axiom,
% 52.23/52.32 ! [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))) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_zero__code__numeral__def,axiom,
% 52.23/52.32 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_one__code__numeral__def,axiom,
% 52.23/52.32 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_less__code__numeral__code,axiom,
% 52.23/52.32 ! [V_m_2,V_n_2] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_Suc__eq__number__of,axiom,
% 52.23/52.32 ! [V_v_2,V_n_2] :
% 52.23/52.32 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 52.23/52.32 <=> 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))))) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_eq__number__of__Suc,axiom,
% 52.23/52.32 ! [V_n_2,V_v_2] :
% 52.23/52.32 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2)
% 52.23/52.32 <=> 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))))) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_nat__case__number__of,axiom,
% 52.23/52.32 ! [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))) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_nat__rec__number__of,axiom,
% 52.23/52.32 ! [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)))) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_plus__code__numeral__code,axiom,
% 52.23/52.32 ! [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)) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_less__eq__code__numeral__code,axiom,
% 52.23/52.32 ! [V_m_2,V_n_2] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_nat__number__of__Bit1,axiom,
% 52.23/52.32 ! [V_w_2] :
% 52.23/52.32 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 52.23/52.32 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 52.23/52.32 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 52.23/52.32 => 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)))) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_less__Suc__number__of,axiom,
% 52.23/52.32 ! [V_v_2,V_n_2] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 <=> 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))))) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_less__number__of__Suc,axiom,
% 52.23/52.32 ! [V_n_2,V_v_2] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 <=> 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)))) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_le__Suc__number__of,axiom,
% 52.23/52.32 ! [V_v_2,V_n_2] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 <=> 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))))) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_le__number__of__Suc,axiom,
% 52.23/52.32 ! [V_n_2,V_v_2] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 <=> 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)))) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_subtract__code__numeral__code,axiom,
% 52.23/52.32 ! [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)) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_nat__case__add__eq__if,axiom,
% 52.23/52.32 ! [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)))) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_nat__rec__add__eq__if,axiom,
% 52.23/52.32 ! [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))))) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_power__number__of__odd,axiom,
% 52.23/52.32 ! [V_z_2,V_w_2,T_b] :
% 52.23/52.32 ( class_Int_Onumber__ring(T_b)
% 52.23/52.32 => ( ( 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)))
% 52.23/52.32 => 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))) )
% 52.23/52.32 & ( ~ 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)))
% 52.23/52.32 => 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) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_zpower__number__of__odd,axiom,
% 52.23/52.32 ! [V_z_2,V_w_2] :
% 52.23/52.32 ( ( 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)))
% 52.23/52.32 => 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))) )
% 52.23/52.32 & ( ~ 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)))
% 52.23/52.32 => 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) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_negDivAlg_Osimps,axiom,
% 52.23/52.32 ! [V_b,V_a] :
% 52.23/52.32 ( ( ( 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)))
% 52.23/52.32 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 52.23/52.32 => 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)) )
% 52.23/52.32 & ( ~ ( 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)))
% 52.23/52.32 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 52.23/52.32 => 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))) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_power__number__of__odd__number__of,axiom,
% 52.23/52.32 ! [V_v_2,V_w_2,T_b] :
% 52.23/52.32 ( class_Int_Onumber__ring(T_b)
% 52.23/52.32 => ( ( 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)))
% 52.23/52.32 => 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))) )
% 52.23/52.32 & ( ~ 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)))
% 52.23/52.32 => 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) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_code__numeral_Orecs_I1_J,axiom,
% 52.23/52.32 ! [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 ).
% 52.23/52.32
% 52.23/52.32 fof(fact_negDivAlg__eqn,axiom,
% 52.23/52.32 ! [V_a,V_b] :
% 52.23/52.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 52.23/52.32 => ( ( 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)))
% 52.23/52.32 => 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)) )
% 52.23/52.32 & ( ~ 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)))
% 52.23/52.32 => 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))) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_negDivAlg__eqn__number__of,axiom,
% 52.23/52.32 ! [V_w,V_v] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 => ( ( 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))))
% 52.23/52.32 => 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))) )
% 52.23/52.32 & ( ~ 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))))
% 52.23/52.32 => 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)))) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_norm__frac_Osimps,axiom,
% 52.23/52.32 ! [V_a_2,V_b_2] :
% 52.23/52.32 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.32 => 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)) )
% 52.23/52.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.32 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.32 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 52.23/52.32 => 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)) )
% 52.23/52.32 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.32 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 52.23/52.32 => 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))) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_posDivAlg__eqn__1__number__of,axiom,
% 52.23/52.32 ! [V_w] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 => ( ( 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)))
% 52.23/52.32 => 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)) )
% 52.23/52.32 & ( ~ 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)))
% 52.23/52.32 => 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)))) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_posDivAlg_Osimps,axiom,
% 52.23/52.32 ! [V_b,V_a] :
% 52.23/52.32 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 52.23/52.32 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 52.23/52.32 => 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) )
% 52.23/52.32 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 52.23/52.32 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 52.23/52.32 => 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))) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_adjust__def,axiom,
% 52.23/52.32 ! [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))))))) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_posDivAlg__eqn__number__of,axiom,
% 52.23/52.32 ! [V_w,V_v] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 => ( ( 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)))
% 52.23/52.32 => 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)) )
% 52.23/52.32 & ( ~ 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)))
% 52.23/52.32 => 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)))) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_posDivAlg__eqn,axiom,
% 52.23/52.32 ! [V_a,V_b] :
% 52.23/52.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 52.23/52.32 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 52.23/52.32 => 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) )
% 52.23/52.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 52.23/52.32 => 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))) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_posDivAlg__0,axiom,
% 52.23/52.32 ! [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)) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_posDivAlg__div__mod,axiom,
% 52.23/52.32 ! [V_l,V_k] :
% 52.23/52.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 52.23/52.32 => 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)) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_of__int__num,axiom,
% 52.23/52.32 ! [V_k_2,T_b] :
% 52.23/52.32 ( class_Rings_Oring__1(T_b)
% 52.23/52.32 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.32 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b) )
% 52.23/52.32 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.32 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.32 => 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))) )
% 52.23/52.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.32 => 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))))) ) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_MGT__def,axiom,
% 52.23/52.32 ! [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)) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divmod__nat__rel__mult1__eq,axiom,
% 52.23/52.32 ! [V_a,V_r,V_q,V_c,V_b] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 52.23/52.32 => 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)))) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divmod__nat__rel__mult2__eq,axiom,
% 52.23/52.32 ! [V_c,V_r,V_q,V_b,V_a] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 52.23/52.32 => 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)))) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_negDivAlg_Opsimps,axiom,
% 52.23/52.32 ! [V_b_2,V_a_2] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 => ( ( ( 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)))
% 52.23/52.32 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 52.23/52.32 => 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)) )
% 52.23/52.32 & ( ~ ( 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)))
% 52.23/52.32 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 52.23/52.32 => 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))) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_accp__downward,axiom,
% 52.23/52.32 ! [V_a_2,V_b_2,V_r_2,T_b] :
% 52.23/52.32 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_b_2))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 52.23/52.32 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_accp_Oequations,axiom,
% 52.23/52.32 ! [V_a_2,V_r_2,T_b] :
% 52.23/52.32 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 52.23/52.32 <=> ! [B_x] :
% 52.23/52.32 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 52.23/52.32 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_accp_Osimps,axiom,
% 52.23/52.32 ! [V_a_2,V_r_2,T_b] :
% 52.23/52.32 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 52.23/52.32 <=> ! [B_x] :
% 52.23/52.32 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 52.23/52.32 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divmod__nat__rel__unique,axiom,
% 52.23/52.32 ! [V_qr_H,V_qr,V_n,V_m] :
% 52.23/52.32 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 52.23/52.32 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H))
% 52.23/52.32 => V_qr = V_qr_H ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_accp__subset,axiom,
% 52.23/52.32 ! [V_R2_2,V_R1_2,T_b] :
% 52.23/52.32 ( 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))
% 52.23/52.32 => 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))) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divmod__nat__eq,axiom,
% 52.23/52.32 ! [V_qr,V_n,V_m] :
% 52.23/52.32 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 52.23/52.32 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divmod__nat__rel__divmod__nat,axiom,
% 52.23/52.32 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_mod__eq,axiom,
% 52.23/52.32 ! [V_r,V_q,V_n,V_m] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_div__eq,axiom,
% 52.23/52.32 ! [V_r,V_q,V_n,V_m] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divmod__nat__rel,axiom,
% 52.23/52.32 ! [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)))) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divmod__int__mod__div,axiom,
% 52.23/52.32 ! [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)) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divmod__nat__rel__add1__eq,axiom,
% 52.23/52.32 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 => ( 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)))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 52.23/52.32 => 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)))) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_posDivAlg_Opsimps,axiom,
% 52.23/52.32 ! [V_b_2,V_a_2] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 52.23/52.32 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 52.23/52.32 => 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) )
% 52.23/52.32 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 52.23/52.32 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 52.23/52.32 => 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))) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_norm__frac_Opsimps,axiom,
% 52.23/52.32 ! [V_b_2,V_a_2] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.32 => 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)) )
% 52.23/52.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.32 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.32 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 52.23/52.32 => 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)) )
% 52.23/52.32 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.32 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 52.23/52.32 => 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))) ) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_Nitpick_OFrac__def,axiom,
% 52.23/52.32 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)))) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divmod__int__def,axiom,
% 52.23/52.32 ! [V_b,V_a] :
% 52.23/52.32 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 52.23/52.32 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 52.23/52.32 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) )
% 52.23/52.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 52.23/52.32 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.32 => 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)) )
% 52.23/52.32 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.32 => 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))) ) ) ) ) )
% 52.23/52.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 52.23/52.32 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 52.23/52.32 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) )
% 52.23/52.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 52.23/52.32 => 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))) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_negDivAlg_Opinduct,axiom,
% 52.23/52.32 ! [V_P_2,V_a1_2,V_a0_2] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 => ( ! [B_a,B_b] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 => ( ( ~ ( 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)))
% 52.23/52.32 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 52.23/52.32 => 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))) )
% 52.23/52.32 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 52.23/52.32 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_negateSnd__eq,axiom,
% 52.23/52.32 ! [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)) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_splitI,axiom,
% 52.23/52.32 ! [T_c,T_b,V_b_2,V_a_2,V_f_2] :
% 52.23/52.32 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2))
% 52.23/52.32 => 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))) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_prod__caseI,axiom,
% 52.23/52.32 ! [T_c,T_b,V_b_2,V_a_2,V_f1_2] :
% 52.23/52.32 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2))
% 52.23/52.32 => 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))) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_posDivAlg_Opinduct,axiom,
% 52.23/52.32 ! [V_P_2,V_a1_2,V_a0_2] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 => ( ! [B_a,B_b] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b))
% 52.23/52.32 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 52.23/52.32 => 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))) )
% 52.23/52.32 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 52.23/52.32 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_nat__gcd_Opsimps,axiom,
% 52.23/52.32 ! [V_y_2,V_x_2] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.32 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 )
% 52.23/52.32 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.32 => 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)) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divmod__int__pdivmod,axiom,
% 52.23/52.32 ! [V_l_2,V_k_2] :
% 52.23/52.32 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.32 => 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)) )
% 52.23/52.32 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.32 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.32 => 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) )
% 52.23/52.32 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.32 => 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)))) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_apsnd__conv,axiom,
% 52.23/52.32 ! [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)) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_split__paired__All,axiom,
% 52.23/52.32 ! [T_c,T_b,V_P_2] :
% 52.23/52.32 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 52.23/52.32 <=> ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_Pair__eq,axiom,
% 52.23/52.32 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 52.23/52.32 ( 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)
% 52.23/52.32 <=> ( V_a_2 = V_a_H_2
% 52.23/52.32 & V_b_2 = V_b_H_2 ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_Pair__inject,axiom,
% 52.23/52.32 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] :
% 52.23/52.32 ( 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)
% 52.23/52.32 => ~ ( V_a = V_a_H
% 52.23/52.32 => V_b != V_b_H ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_negateSnd__def,axiom,
% 52.23/52.32 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_split__weak__cong,axiom,
% 52.23/52.32 ! [V_c_2,T_d,T_c,T_b,V_q_2,V_p_2] :
% 52.23/52.32 ( V_p_2 = V_q_2
% 52.23/52.32 => 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) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_prod_Osimps_I2_J,axiom,
% 52.23/52.32 ! [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) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_split__conv,axiom,
% 52.23/52.32 ! [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) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_splitD,axiom,
% 52.23/52.32 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_split__eta,axiom,
% 52.23/52.32 ! [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 ).
% 52.23/52.32
% 52.23/52.32 fof(fact_split__twice,axiom,
% 52.23/52.32 ! [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) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_pdivmod__def,axiom,
% 52.23/52.32 ! [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))) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_pdivmod__posDivAlg,axiom,
% 52.23/52.32 ! [V_k,V_l] :
% 52.23/52.32 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.32 => 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)) )
% 52.23/52.32 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.32 => 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)) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divmod__int__code,axiom,
% 52.23/52.32 ! [V_l_2,V_k_2] :
% 52.23/52.32 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.32 => 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)) )
% 52.23/52.32 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.32 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.32 => 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) )
% 52.23/52.32 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.32 => 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)))) ) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_div__mod__code__numeral__def,axiom,
% 52.23/52.32 ! [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)) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_zmult2__lemma,axiom,
% 52.23/52.32 ! [V_c,V_r,V_q,V_b,V_a] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 52.23/52.32 => 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)))) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_mod__pos__neg__1__number__of,axiom,
% 52.23/52.32 ! [V_w] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 => 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))))) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divmod__int__rel__def,axiom,
% 52.23/52.32 ! [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))))))) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_norm__frac_Opinduct,axiom,
% 52.23/52.32 ! [V_P_2,V_a1_2,V_a0_2] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 => ( ! [B_a,B_b] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.32 => 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))) )
% 52.23/52.32 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 52.23/52.32 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_splitD_H,axiom,
% 52.23/52.32 ! [V_c_2,V_b_2,V_a_2,V_R_2,T_d,T_c,T_b] :
% 52.23/52.32 ( 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))
% 52.23/52.32 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_c_2)) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_snd__conv,axiom,
% 52.23/52.32 ! [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 ).
% 52.23/52.32
% 52.23/52.32 fof(fact_snd__eqD,axiom,
% 52.23/52.32 ! [V_a,V_y,V_x,T_a,T_b] :
% 52.23/52.32 ( 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
% 52.23/52.32 => V_y = V_a ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_apsnd__eq__conv,axiom,
% 52.23/52.32 ! [V_g_2,V_x_2,V_f_2,T_b,T_c,T_d] :
% 52.23/52.32 ( 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)
% 52.23/52.32 <=> 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)) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_snd__apsnd,axiom,
% 52.23/52.32 ! [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)) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_snd__def,axiom,
% 52.23/52.32 ! [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) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_mod__int__def,axiom,
% 52.23/52.32 ! [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)) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divmod__int__rel__0,axiom,
% 52.23/52.32 ! [V_b] :
% 52.23/52.32 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.32 => 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)))) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_self__remainder,axiom,
% 52.23/52.32 ! [V_r,V_q,V_a] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.32 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_unique__quotient,axiom,
% 52.23/52.32 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 => ( 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)))
% 52.23/52.32 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.32 => V_q = V_q_H ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_unique__remainder,axiom,
% 52.23/52.32 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 => ( 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)))
% 52.23/52.32 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.32 => V_r = V_r_H ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divmod__int__rel__neg,axiom,
% 52.23/52.32 ! [V_qr,V_b,V_a] :
% 52.23/52.32 ( 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))
% 52.23/52.32 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divmod__int__correct,axiom,
% 52.23/52.32 ! [V_a,V_b] :
% 52.23/52.32 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.32 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_self__quotient,axiom,
% 52.23/52.32 ! [V_r,V_q,V_a] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.32 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divmod__int__rel__mod,axiom,
% 52.23/52.32 ! [V_r,V_q,V_b,V_a] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.32 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divmod__int__rel__div,axiom,
% 52.23/52.32 ! [V_r,V_q,V_b,V_a] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.32 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_negDivAlg__correct,axiom,
% 52.23/52.32 ! [V_b,V_a] :
% 52.23/52.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 52.23/52.32 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_mod__neg__pos,axiom,
% 52.23/52.32 ! [V_b,V_a] :
% 52.23/52.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 52.23/52.32 => 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)) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divmod__int__rel__div__mod,axiom,
% 52.23/52.32 ! [V_a,V_b] :
% 52.23/52.32 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.32 => 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)))) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_posDivAlg__correct,axiom,
% 52.23/52.32 ! [V_b,V_a] :
% 52.23/52.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 52.23/52.32 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_mod__pos__pos,axiom,
% 52.23/52.32 ! [V_b,V_a] :
% 52.23/52.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 52.23/52.32 => 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)) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_mod__pos__pos__1__number__of,axiom,
% 52.23/52.32 ! [V_w] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 => 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))) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_zadd1__lemma,axiom,
% 52.23/52.32 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 => ( 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)))
% 52.23/52.32 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.32 => 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)))) ) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_zminus1__lemma,axiom,
% 52.23/52.32 ! [V_r_2,V_q_2,V_b_2,V_a_2] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 => 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))))) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_mod__pos__neg,axiom,
% 52.23/52.32 ! [V_b,V_a] :
% 52.23/52.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.32 => 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)))) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divmod__nat__if,axiom,
% 52.23/52.32 ! [V_m_2,V_n_2] :
% 52.23/52.32 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.32 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 52.23/52.32 => 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) )
% 52.23/52.32 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.32 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 52.23/52.32 => 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)) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_divmod__int__relI,axiom,
% 52.23/52.32 ! [V_r,V_q,V_b,V_a] :
% 52.23/52.32 ( 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)
% 52.23/52.32 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 52.23/52.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) )
% 52.23/52.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 52.23/52.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 52.23/52.32 => 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))) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_mod__neg__neg,axiom,
% 52.23/52.32 ! [V_b,V_a] :
% 52.23/52.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.32 => 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)))) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_zmult1__lemma,axiom,
% 52.23/52.32 ! [V_a,V_r,V_q,V_c,V_b] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.32 => 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)))) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_equalityI,axiom,
% 52.23/52.32 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 52.23/52.32 => V_A_2 = V_B_2 ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_div__pos__neg__1__number__of,axiom,
% 52.23/52.32 ! [V_w] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 => 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))))) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_nat__gcd_Opinduct,axiom,
% 52.23/52.32 ! [V_P_2,V_a1_2,V_a0_2] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 => ( ! [B_x,B_y] :
% 52.23/52.32 ( 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)))
% 52.23/52.32 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.32 => hBOOL(hAPP(hAPP(V_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) )
% 52.23/52.32 => hBOOL(hAPP(hAPP(V_P_2,B_x),B_y)) ) )
% 52.23/52.32 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_div__neg__neg,axiom,
% 52.23/52.32 ! [V_b,V_a] :
% 52.23/52.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.32 => 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)))) ) ) ).
% 52.23/52.32
% 52.23/52.32 fof(fact_min__number__of__Suc,axiom,
% 52.23/52.33 ! [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)))) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__0L,axiom,
% 52.23/52.33 ! [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) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__0R,axiom,
% 52.23/52.33 ! [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) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__Suc__Suc,axiom,
% 52.23/52.33 ! [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)) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__le__iff__disj,axiom,
% 52.23/52.33 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_b)
% 52.23/52.33 => ( 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))
% 52.23/52.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 52.23/52.33 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Oinf__le1,axiom,
% 52.23/52.33 ! [V_y,V_x,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => 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)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Oinf__le2,axiom,
% 52.23/52.33 ! [V_y,V_x,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => 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)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Ole__iff__inf,axiom,
% 52.23/52.33 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_b)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 52.23/52.33 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Ole__inf__iff,axiom,
% 52.23/52.33 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_b)
% 52.23/52.33 => ( 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)))
% 52.23/52.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 52.23/52.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Ole__infI1,axiom,
% 52.23/52.33 ! [V_b,V_x,V_a,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 52.23/52.33 => 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)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Ole__infI2,axiom,
% 52.23/52.33 ! [V_a,V_x,V_b,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 52.23/52.33 => 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)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Oinf__absorb1,axiom,
% 52.23/52.33 ! [V_y,V_x,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 52.23/52.33 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Oinf__absorb2,axiom,
% 52.23/52.33 ! [V_x,V_y,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 52.23/52.33 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Ole__infI,axiom,
% 52.23/52.33 ! [V_b,V_a,V_x,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 52.23/52.33 => 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))) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Oinf__greatest,axiom,
% 52.23/52.33 ! [V_z,V_y,V_x,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 52.23/52.33 => 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))) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Oinf__mono,axiom,
% 52.23/52.33 ! [V_d,V_b,V_c,V_a,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 52.23/52.33 => 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))) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Ole__infE,axiom,
% 52.23/52.33 ! [V_b,V_a,V_x,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => ( 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)))
% 52.23/52.33 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 52.23/52.33 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__diff__distrib__left,axiom,
% 52.23/52.33 ! [V_z,V_y,V_x,T_a] :
% 52.23/52.33 ( class_Groups_Oordered__ab__group__add(T_a)
% 52.23/52.33 => 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)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Oless__infI1,axiom,
% 52.23/52.33 ! [V_b,V_x,V_a,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 52.23/52.33 => 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)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Oless__infI2,axiom,
% 52.23/52.33 ! [V_a,V_x,V_b,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 52.23/52.33 => 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)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__less__iff__disj,axiom,
% 52.23/52.33 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_b)
% 52.23/52.33 => ( 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))
% 52.23/52.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 52.23/52.33 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__less__iff__conj,axiom,
% 52.23/52.33 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_b)
% 52.23/52.33 => ( 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)))
% 52.23/52.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 52.23/52.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__add__distrib__left,axiom,
% 52.23/52.33 ! [V_z,V_y,V_x,T_a] :
% 52.23/52.33 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 52.23/52.33 => 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)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Oinf__assoc,axiom,
% 52.23/52.33 ! [V_z,V_y,V_x,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => 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)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Oinf_Oassoc,axiom,
% 52.23/52.33 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => 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)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Oinf__left__commute,axiom,
% 52.23/52.33 ! [V_z,V_y,V_x,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => 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)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Oinf_Oleft__commute,axiom,
% 52.23/52.33 ! [V_c,V_a,V_b,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => 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)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Oinf__left__idem,axiom,
% 52.23/52.33 ! [V_y,V_x,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => 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) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Oinf_Oleft__idem,axiom,
% 52.23/52.33 ! [V_b,V_a,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => 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) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Oinf__commute,axiom,
% 52.23/52.33 ! [V_y,V_x,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => 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) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Oinf_Ocommute,axiom,
% 52.23/52.33 ! [V_b,V_a,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => 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) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Oinf_Oidem,axiom,
% 52.23/52.33 ! [V_a,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__diff,axiom,
% 52.23/52.33 ! [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) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_fst__eqD,axiom,
% 52.23/52.33 ! [V_a,V_y,V_x,T_b,T_a] :
% 52.23/52.33 ( 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
% 52.23/52.33 => V_x = V_a ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_fst__conv,axiom,
% 52.23/52.33 ! [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 ).
% 52.23/52.33
% 52.23/52.33 fof(fact_prod__eqI,axiom,
% 52.23/52.33 ! [V_q,V_p,T_b,T_a] :
% 52.23/52.33 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q)
% 52.23/52.33 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q)
% 52.23/52.33 => V_p = V_q ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_Pair__fst__snd__eq,axiom,
% 52.23/52.33 ! [T_c,T_b,V_t_2,V_s_2] :
% 52.23/52.33 ( V_s_2 = V_t_2
% 52.23/52.33 <=> ( hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2)
% 52.23/52.33 & hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_fst__apsnd,axiom,
% 52.23/52.33 ! [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) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_fst__def,axiom,
% 52.23/52.33 ! [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) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__number__of,axiom,
% 52.23/52.33 ! [V_v,V_u,T_b] :
% 52.23/52.33 ( ( class_Int_Onumber(T_b)
% 52.23/52.33 & class_Orderings_Oord(T_b) )
% 52.23/52.33 => ( ( 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)))
% 52.23/52.33 => 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) )
% 52.23/52.33 & ( ~ 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)))
% 52.23/52.33 => 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) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_surjective__pairing,axiom,
% 52.23/52.33 ! [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)) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_pair__collapse,axiom,
% 52.23/52.33 ! [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 ).
% 52.23/52.33
% 52.23/52.33 fof(fact_prod__case__beta,axiom,
% 52.23/52.33 ! [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)) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_div__int__def,axiom,
% 52.23/52.33 ! [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)) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_mod__nat__def,axiom,
% 52.23/52.33 ! [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)) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_split__beta,axiom,
% 52.23/52.33 ! [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)) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_split__comp__eq,axiom,
% 52.23/52.33 ! [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)) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_split__def,axiom,
% 52.23/52.33 ! [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)) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_double__diff,axiom,
% 52.23/52.33 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 52.23/52.33 => 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 ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_Diff__mono,axiom,
% 52.23/52.33 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_b] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2))
% 52.23/52.33 => 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))) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_Diff__subset,axiom,
% 52.23/52.33 ! [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_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_Compl__anti__mono,axiom,
% 52.23/52.33 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.33 => 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))) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_Compl__subset__Compl__iff,axiom,
% 52.23/52.33 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.33 ( 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)))
% 52.23/52.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_equalityE,axiom,
% 52.23/52.33 ! [T_b,V_B_2,V_A_2] :
% 52.23/52.33 ( V_A_2 = V_B_2
% 52.23/52.33 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.33 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_subset__trans,axiom,
% 52.23/52.33 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 52.23/52.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_equalityD2,axiom,
% 52.23/52.33 ! [T_b,V_B_2,V_A_2] :
% 52.23/52.33 ( V_A_2 = V_B_2
% 52.23/52.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_equalityD1,axiom,
% 52.23/52.33 ! [T_b,V_B_2,V_A_2] :
% 52.23/52.33 ( V_A_2 = V_B_2
% 52.23/52.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_set__eq__subset,axiom,
% 52.23/52.33 ! [T_b,V_B_2,V_A_2] :
% 52.23/52.33 ( V_A_2 = V_B_2
% 52.23/52.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_subset__refl,axiom,
% 52.23/52.33 ! [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)) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_subset__psubset__trans,axiom,
% 52.23/52.33 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 52.23/52.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_psubset__subset__trans,axiom,
% 52.23/52.33 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 52.23/52.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_psubset__imp__subset,axiom,
% 52.23/52.33 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_subset__iff__psubset__eq,axiom,
% 52.23/52.33 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.33 | V_A_2 = V_B_2 ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_psubset__eq,axiom,
% 52.23/52.33 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.33 & V_A_2 != V_B_2 ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__Suc1,axiom,
% 52.23/52.33 ! [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) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__Suc2,axiom,
% 52.23/52.33 ! [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) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_div__neg__pos,axiom,
% 52.23/52.33 ! [V_b,V_a] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 52.23/52.33 => 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)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_div__pos__pos,axiom,
% 52.23/52.33 ! [V_b,V_a] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 52.23/52.33 => 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)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_div__pos__pos__1__number__of,axiom,
% 52.23/52.33 ! [V_w] :
% 52.23/52.33 ( 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)))
% 52.23/52.33 => 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))) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_div__pos__neg,axiom,
% 52.23/52.33 ! [V_b,V_a] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 52.23/52.33 => 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)))) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__Suc__number__of,axiom,
% 52.23/52.33 ! [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)))) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_prod__size__simp,axiom,
% 52.23/52.33 ! [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))) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_conjI__realizer,axiom,
% 52.23/52.33 ! [T_c,T_b,V_q_2,V_Q_2,V_p_2,V_P_2] :
% 52.23/52.33 ( hBOOL(hAPP(V_P_2,V_p_2))
% 52.23/52.33 => ( hBOOL(hAPP(V_Q_2,V_q_2))
% 52.23/52.33 => ( 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))))
% 52.23/52.33 & 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)))) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_exI__realizer,axiom,
% 52.23/52.33 ! [T_b,T_c,V_x_2,V_y_2,V_P_2] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2))
% 52.23/52.33 => 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)))) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__ord__min,axiom,
% 52.23/52.33 ! [T_b] :
% 52.23/52.33 ( class_Orderings_Oord(T_b)
% 52.23/52.33 => c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_prod_Orecs,axiom,
% 52.23/52.33 ! [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) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_Compl__eq__Compl__iff,axiom,
% 52.23/52.33 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.33 ( 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)
% 52.23/52.33 <=> V_A_2 = V_B_2 ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_double__complement,axiom,
% 52.23/52.33 ! [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 ).
% 52.23/52.33
% 52.23/52.33 fof(fact_Diff__idemp,axiom,
% 52.23/52.33 ! [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) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_psubset__trans,axiom,
% 52.23/52.33 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 52.23/52.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_div__nat__def,axiom,
% 52.23/52.33 ! [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)) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_divmod__nat__rel__def,axiom,
% 52.23/52.33 ! [V_qr_2,V_n_2,V_m_2] :
% 52.23/52.33 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2))
% 52.23/52.33 <=> ( 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))
% 52.23/52.33 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.33 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 52.23/52.33 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.33 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 52.23/52.33 => ( 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)))
% 52.23/52.33 & 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)) ) )
% 52.23/52.33 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 52.23/52.33 => ( 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)))
% 52.23/52.33 & 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))) ) ) ) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_range,axiom,
% 52.23/52.33 ! [V_s,V_k] :
% 52.23/52.33 ( 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))
% 52.23/52.33 => 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)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_New__DSequence_Opos__not__seq__def,axiom,
% 52.23/52.33 ! [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))) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_max__number__of__Suc,axiom,
% 52.23/52.33 ! [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)))) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_max__Suc__number__of,axiom,
% 52.23/52.33 ! [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)))) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_apsnd__apfst,axiom,
% 52.23/52.33 ! [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))) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_max__diff__distrib__left,axiom,
% 52.23/52.33 ! [V_z,V_y,V_x,T_a] :
% 52.23/52.33 ( class_Groups_Oordered__ab__group__add(T_a)
% 52.23/52.33 => 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)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_less__max__iff__disj,axiom,
% 52.23/52.33 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_b)
% 52.23/52.33 => ( 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)))
% 52.23/52.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 52.23/52.33 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_max__less__iff__conj,axiom,
% 52.23/52.33 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_b)
% 52.23/52.33 => ( 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))
% 52.23/52.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 52.23/52.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Oless__supI2,axiom,
% 52.23/52.33 ! [V_a,V_b,V_x,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 52.23/52.33 => 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))) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Oless__supI1,axiom,
% 52.23/52.33 ! [V_b,V_a,V_x,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 52.23/52.33 => 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))) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Osup__inf__absorb,axiom,
% 52.23/52.33 ! [V_y,V_x,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => 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 ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Oinf__sup__absorb,axiom,
% 52.23/52.33 ! [V_y,V_x,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => 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 ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Osup__inf__distrib1,axiom,
% 52.23/52.33 ! [V_z,V_y,V_x,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => 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)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Oinf__sup__distrib1,axiom,
% 52.23/52.33 ! [V_z,V_y,V_x,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => 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)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Osup__inf__distrib2,axiom,
% 52.23/52.33 ! [V_x,V_z,V_y,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => 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)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Oinf__sup__distrib2,axiom,
% 52.23/52.33 ! [V_x,V_z,V_y,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => 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)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_max__0L,axiom,
% 52.23/52.33 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 52.23/52.33
% 52.23/52.33 fof(fact_max__0R,axiom,
% 52.23/52.33 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ).
% 52.23/52.33
% 52.23/52.33 fof(fact_max__Suc__Suc,axiom,
% 52.23/52.33 ! [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)) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_le__max__iff__disj,axiom,
% 52.23/52.33 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_b)
% 52.23/52.33 => ( 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)))
% 52.23/52.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2))
% 52.23/52.33 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_le__maxI1,axiom,
% 52.23/52.33 ! [V_y,V_x,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => 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))) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_le__maxI2,axiom,
% 52.23/52.33 ! [V_x,V_y,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => 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))) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Ole__iff__sup,axiom,
% 52.23/52.33 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_b)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 52.23/52.33 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Ole__sup__iff,axiom,
% 52.23/52.33 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_b)
% 52.23/52.33 => ( 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))
% 52.23/52.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 52.23/52.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Ole__supI1,axiom,
% 52.23/52.33 ! [V_b,V_a,V_x,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 52.23/52.33 => 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))) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Ole__supI2,axiom,
% 52.23/52.33 ! [V_a,V_b,V_x,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 52.23/52.33 => 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))) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Osup__absorb2,axiom,
% 52.23/52.33 ! [V_y,V_x,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 52.23/52.33 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Osup__absorb1,axiom,
% 52.23/52.33 ! [V_x,V_y,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 52.23/52.33 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Ole__supI,axiom,
% 52.23/52.33 ! [V_b,V_x,V_a,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 52.23/52.33 => 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)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Osup__least,axiom,
% 52.23/52.33 ! [V_z,V_x,V_y,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 52.23/52.33 => 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)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Osup__mono,axiom,
% 52.23/52.33 ! [V_d,V_b,V_c,V_a,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 52.23/52.33 => 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))) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Ole__supE,axiom,
% 52.23/52.33 ! [V_x,V_b,V_a,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => ( 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))
% 52.23/52.33 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 52.23/52.33 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_max__add__distrib__left,axiom,
% 52.23/52.33 ! [V_z,V_y,V_x,T_a] :
% 52.23/52.33 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 52.23/52.33 => 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)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Osup__assoc,axiom,
% 52.23/52.33 ! [V_z,V_y,V_x,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => 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)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Osup_Oassoc,axiom,
% 52.23/52.33 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => 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)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Osup__left__commute,axiom,
% 52.23/52.33 ! [V_z,V_y,V_x,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => 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)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Osup_Oleft__commute,axiom,
% 52.23/52.33 ! [V_c,V_a,V_b,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => 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)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Osup__left__idem,axiom,
% 52.23/52.33 ! [V_y,V_x,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => 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) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Osup_Oleft__idem,axiom,
% 52.23/52.33 ! [V_b,V_a,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => 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) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Osup__commute,axiom,
% 52.23/52.33 ! [V_y,V_x,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => 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) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Osup_Ocommute,axiom,
% 52.23/52.33 ! [V_b,V_a,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => 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) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Osup_Oidem,axiom,
% 52.23/52.33 ! [V_a,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_apfst__conv,axiom,
% 52.23/52.33 ! [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) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_apfst__eq__conv,axiom,
% 52.23/52.33 ! [V_g_2,V_x_2,V_f_2,T_c,T_b,T_d] :
% 52.23/52.33 ( 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)
% 52.23/52.33 <=> 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)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_fst__apfst,axiom,
% 52.23/52.33 ! [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)) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_snd__apfst,axiom,
% 52.23/52.33 ! [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) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_max__number__of,axiom,
% 52.23/52.33 ! [V_v,V_u,T_b] :
% 52.23/52.33 ( ( class_Int_Onumber(T_b)
% 52.23/52.33 & class_Orderings_Oord(T_b) )
% 52.23/52.33 => ( ( 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)))
% 52.23/52.33 => 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) )
% 52.23/52.33 & ( ~ 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)))
% 52.23/52.33 => 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) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Odistrib__inf__le,axiom,
% 52.23/52.33 ! [V_z,V_y,V_x,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => 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)))) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_min__max_Odistrib__sup__le,axiom,
% 52.23/52.33 ! [V_z,V_y,V_x,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => 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)))) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_minus__max__eq__min,axiom,
% 52.23/52.33 ! [V_y,V_x,T_a] :
% 52.23/52.33 ( class_Groups_Olinordered__ab__group__add(T_a)
% 52.23/52.33 => 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)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_minus__min__eq__max,axiom,
% 52.23/52.33 ! [V_y,V_x,T_a] :
% 52.23/52.33 ( class_Groups_Olinordered__ab__group__add(T_a)
% 52.23/52.33 => 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)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_nat__minus__add__max,axiom,
% 52.23/52.33 ! [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) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_apsnd__apfst__commute,axiom,
% 52.23/52.33 ! [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)) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_max__Suc1,axiom,
% 52.23/52.33 ! [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) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_max__Suc2,axiom,
% 52.23/52.33 ! [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) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_apfst__apsnd,axiom,
% 52.23/52.33 ! [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))) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dual__min,axiom,
% 52.23/52.33 ! [T_b] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_b)
% 52.23/52.33 => 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) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_max__ord__max,axiom,
% 52.23/52.33 ! [T_b] :
% 52.23/52.33 ( class_Orderings_Oord(T_b)
% 52.23/52.33 => c_Orderings_Oord__class_Omax(T_b) = c_Orderings_Oord_Omax(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_code__numeral__decr,axiom,
% 52.23/52.33 ! [V_k] :
% 52.23/52.33 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 52.23/52.33 => 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))) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_Nitpick_Ozero__frac__def,axiom,
% 52.23/52.33 ! [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))) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_pos__not__random__dseq__def,axiom,
% 52.23/52.33 ! [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)) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_Code__Numeral_Onat__of__inject,axiom,
% 52.23/52.33 ! [V_l_2,V_k_2] :
% 52.23/52.33 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2)
% 52.23/52.33 <=> V_k_2 = V_l_2 ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_code__numeral_Onat__of__inject,axiom,
% 52.23/52.33 ! [V_y_2,V_x_2] :
% 52.23/52.33 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2)
% 52.23/52.33 <=> V_x_2 = V_y_2 ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_nat__of__of__nat,axiom,
% 52.23/52.33 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ).
% 52.23/52.33
% 52.23/52.33 fof(fact_of__nat__nat__of,axiom,
% 52.23/52.33 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ).
% 52.23/52.33
% 52.23/52.33 fof(fact_nat__of__inverse,axiom,
% 52.23/52.33 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ).
% 52.23/52.33
% 52.23/52.33 fof(fact_less__code__numeral__def,axiom,
% 52.23/52.33 ! [V_m_2,V_n_2] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 52.23/52.33 <=> 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))) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_nat__of__number,axiom,
% 52.23/52.33 ! [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) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_less__eq__code__numeral__def,axiom,
% 52.23/52.33 ! [V_m_2,V_n_2] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 52.23/52.33 <=> 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))) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_nat__of__code,axiom,
% 52.23/52.33 ! [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)) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_nat__of__aux__def,axiom,
% 52.23/52.33 ! [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) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_Min_Oidem,axiom,
% 52.23/52.33 ! [V_x,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_Max_Oidem,axiom,
% 52.23/52.33 ! [V_x,T_a] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_a)
% 52.23/52.33 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dual__max,axiom,
% 52.23/52.33 ! [T_b] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_b)
% 52.23/52.33 => 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) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_Suc__code__numeral__def,axiom,
% 52.23/52.33 ! [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))) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_minus__code__numeral__def,axiom,
% 52.23/52.33 ! [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))) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_plus__code__numeral__def,axiom,
% 52.23/52.33 ! [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))) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_div__code__numeral__def,axiom,
% 52.23/52.33 ! [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))) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_times__code__numeral__def,axiom,
% 52.23/52.33 ! [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))) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_mod__code__numeral__def,axiom,
% 52.23/52.33 ! [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))) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_Nitpick_Oone__frac__def,axiom,
% 52.23/52.33 ! [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))) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_Nitpick_Onumber__of__frac__def,axiom,
% 52.23/52.33 ! [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))) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_Nitpick_Ofrac__def,axiom,
% 52.23/52.33 ! [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)) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_surjective__sum,axiom,
% 52.23/52.33 ! [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 ).
% 52.23/52.33
% 52.23/52.33 fof(fact_iterate_Osimps,axiom,
% 52.23/52.33 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 52.23/52.33 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 52.23/52.33 => 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) )
% 52.23/52.33 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 52.23/52.33 => 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)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_sum__case__KK,axiom,
% 52.23/52.33 ! [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 ).
% 52.23/52.33
% 52.23/52.33 fof(fact_scomp__scomp,axiom,
% 52.23/52.33 ! [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)) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_sum__case__inject,axiom,
% 52.23/52.33 ! [V_g2_2,V_g1_2,V_f2_2,V_f1_2,T_c,T_d,T_b] :
% 52.23/52.33 ( 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)
% 52.23/52.33 => ~ ( V_f1_2 = V_g1_2
% 52.23/52.33 => V_f2_2 != V_g2_2 ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_sum__case__weak__cong,axiom,
% 52.23/52.33 ! [V_g_2,V_f_2,T_c,T_d,T_b,V_t_2,V_s_2] :
% 52.23/52.33 ( V_s_2 = V_t_2
% 52.23/52.33 => 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) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_scomp__Pair,axiom,
% 52.23/52.33 ! [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 ).
% 52.23/52.33
% 52.23/52.33 fof(fact_Pair__scomp,axiom,
% 52.23/52.33 ! [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) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_scomp__apply,axiom,
% 52.23/52.33 ! [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)) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_sum_Osimps_I6_J,axiom,
% 52.23/52.33 ! [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) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_sum_Osimps_I5_J,axiom,
% 52.23/52.33 ! [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) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_scomp__def,axiom,
% 52.23/52.33 ! [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)) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_scomp__unfold,axiom,
% 52.23/52.33 ! [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))) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_Nitpick_Oplus__frac__def,axiom,
% 52.23/52.33 ! [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))) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_internal__split__def,axiom,
% 52.23/52.33 ! [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) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_transfer__morphism__int__nat,axiom,
% 52.23/52.33 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)) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_New__DSequence_Opos__decr__bind__def,axiom,
% 52.23/52.33 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 52.23/52.33 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 52.23/52.33 => 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) )
% 52.23/52.33 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 52.23/52.33 => 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)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom,
% 52.23/52.33 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 52.23/52.33 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 52.23/52.33 => 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) )
% 52.23/52.33 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 52.23/52.33 => 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)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_internal__split__conv,axiom,
% 52.23/52.33 ! [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) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_Nitpick_Otimes__frac__def,axiom,
% 52.23/52.33 ! [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))) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_Nitpick_Oof__frac__def,axiom,
% 52.23/52.33 ! [V_q,T_a,T_b] :
% 52.23/52.33 ( ( class_Rings_Oinverse(T_b)
% 52.23/52.33 & class_Rings_Oring__1(T_b) )
% 52.23/52.33 => 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))) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_Nitpick_Oinverse__frac__def,axiom,
% 52.23/52.33 ! [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)) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_Nitpick_Ouminus__frac__def,axiom,
% 52.23/52.33 ! [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))) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom,
% 52.23/52.33 ! [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)) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_Nitpick_Oless__frac__def,axiom,
% 52.23/52.33 ! [V_r_2,V_q_2,T_b] :
% 52.23/52.33 ( c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2)
% 52.23/52.33 <=> 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))) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_Nitpick_Oless__eq__frac__def,axiom,
% 52.23/52.33 ! [V_r_2,V_q_2,T_b] :
% 52.23/52.33 ( c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2)
% 52.23/52.33 <=> 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))) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom,
% 52.23/52.33 ! [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)) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_New__DSequence_Oneg__bind__def,axiom,
% 52.23/52.33 ! [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)) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_New__DSequence_Opos__empty__def,axiom,
% 52.23/52.33 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_pos__empty__def,axiom,
% 52.23/52.33 ! [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) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_neg__bind__def,axiom,
% 52.23/52.33 ! [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)) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_New__DSequence_Opos__bind__def,axiom,
% 52.23/52.33 ! [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)) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_predicate2D,axiom,
% 52.23/52.33 ! [V_y_2,V_x_2,V_Q_2,V_P_2,T_c,T_b] :
% 52.23/52.33 ( 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))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 52.23/52.33 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_rev__predicate2D,axiom,
% 52.23/52.33 ! [V_Q_2,T_c,T_b,V_y_2,V_x_2,V_P_2] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 52.23/52.33 => ( 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))
% 52.23/52.33 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_predicate1D,axiom,
% 52.23/52.33 ! [V_x_2,V_Q_2,V_P_2,T_b] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2))
% 52.23/52.33 => ( hBOOL(hAPP(V_P_2,V_x_2))
% 52.23/52.33 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_rev__predicate1D,axiom,
% 52.23/52.33 ! [V_Q_2,T_b,V_x_2,V_P_2] :
% 52.23/52.33 ( hBOOL(hAPP(V_P_2,V_x_2))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2))
% 52.23/52.33 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_pos__bind__def,axiom,
% 52.23/52.33 ! [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)) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_The__split,axiom,
% 52.23/52.33 ! [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))) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_Random_Osimps,axiom,
% 52.23/52.33 ! [V_size_2,V_g_2,T_b,V_nrandom_2] :
% 52.23/52.33 ( ( 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)))
% 52.23/52.33 => 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)) )
% 52.23/52.33 & ( ~ 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)))
% 52.23/52.33 => 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))))))) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_exE__realizer,axiom,
% 52.23/52.33 ! [T_d,V_f_2,V_Q_2,V_p_2,T_b,T_c,V_P_2] :
% 52.23/52.33 ( 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)))
% 52.23/52.33 => ( ! [B_x,B_y] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(V_P_2,B_y),B_x))
% 52.23/52.33 => hBOOL(hAPP(V_Q_2,hAPP(hAPP(V_f_2,B_x),B_y))) )
% 52.23/52.33 => 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))) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_curry__def,axiom,
% 52.23/52.33 ! [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)) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_curryI,axiom,
% 52.23/52.33 ! [V_b_2,V_a_2,T_c,T_b,V_f_2] :
% 52.23/52.33 ( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
% 52.23/52.33 => hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_curryD,axiom,
% 52.23/52.33 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
% 52.23/52.33 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_curryE,axiom,
% 52.23/52.33 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
% 52.23/52.33 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_curry__conv,axiom,
% 52.23/52.33 ! [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)) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_split__curry,axiom,
% 52.23/52.33 ! [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 ).
% 52.23/52.33
% 52.23/52.33 fof(fact_curry__split,axiom,
% 52.23/52.33 ! [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 ).
% 52.23/52.33
% 52.23/52.33 fof(fact_split__paired__The,axiom,
% 52.23/52.33 ! [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)))) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_The__split__eq,axiom,
% 52.23/52.33 ! [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) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_divmod__nat__def,axiom,
% 52.23/52.33 ! [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)) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_Random__Sequence_Oempty__def,axiom,
% 52.23/52.33 ! [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)) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_Random__Sequence_Osingle__def,axiom,
% 52.23/52.33 ! [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)) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_the__eq__trivial,axiom,
% 52.23/52.33 ! [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 ).
% 52.23/52.33
% 52.23/52.33 fof(fact_the__sym__eq__trivial,axiom,
% 52.23/52.33 ! [V_x_2,T_b] : c_HOL_OThe(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 52.23/52.33
% 52.23/52.33 fof(fact_Powp__def,axiom,
% 52.23/52.33 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.33 ( hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2))
% 52.23/52.33 <=> ! [B_x] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 52.23/52.33 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_Powp__mono,axiom,
% 52.23/52.33 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.33 => 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))) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_power__dvd__imp__le,axiom,
% 52.23/52.33 ! [V_n,V_m,V_i] :
% 52.23/52.33 ( 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)))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_i))
% 52.23/52.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__mult__cancel2,axiom,
% 52.23/52.33 ! [V_n_2,V_m_2] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 52.23/52.33 => ( 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))
% 52.23/52.33 <=> V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__mult__cancel1,axiom,
% 52.23/52.33 ! [V_n_2,V_m_2] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 52.23/52.33 => ( 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))
% 52.23/52.33 <=> V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_zdvd__mult__cancel1,axiom,
% 52.23/52.33 ! [V_n_2,V_m_2] :
% 52.23/52.33 ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.33 => ( 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))
% 52.23/52.33 <=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_arith__series__int,axiom,
% 52.23/52.33 ! [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)))) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd_Oorder__refl,axiom,
% 52.23/52.33 ! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x)) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__0__right,axiom,
% 52.23/52.33 ! [V_a,T_a] :
% 52.23/52.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.33 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__1__left,axiom,
% 52.23/52.33 ! [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)) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_setsum__abs,axiom,
% 52.23/52.33 ! [V_A_2,V_f_2,T_c,T_b] :
% 52.23/52.33 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 52.23/52.33 => 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))) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_setsum__abs__ge__zero,axiom,
% 52.23/52.33 ! [V_A_2,V_f_2,T_c,T_b] :
% 52.23/52.33 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 52.23/52.33 => 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))) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_zdvd__antisym__abs,axiom,
% 52.23/52.33 ! [V_b,V_a] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a),V_b))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_b),V_a))
% 52.23/52.33 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_a) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_b) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_nat__dvd__1__iff__1,axiom,
% 52.23/52.33 ! [V_m_2] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
% 52.23/52.33 <=> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__if__abs__eq,axiom,
% 52.23/52.33 ! [V_k,V_l,T_a] :
% 52.23/52.33 ( class_Rings_Olinordered__idom(T_a)
% 52.23/52.33 => ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_l) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k)
% 52.23/52.33 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_l),V_k)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_abs__dvd__iff,axiom,
% 52.23/52.33 ! [V_k_2,V_m_2,T_b] :
% 52.23/52.33 ( class_Rings_Olinordered__idom(T_b)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_m_2)),V_k_2))
% 52.23/52.33 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__abs__iff,axiom,
% 52.23/52.33 ! [V_k_2,V_m_2,T_b] :
% 52.23/52.33 ( class_Rings_Olinordered__idom(T_b)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_k_2)))
% 52.23/52.33 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__power__same,axiom,
% 52.23/52.33 ! [V_n,V_y,V_x,T_a] :
% 52.23/52.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
% 52.23/52.33 => 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))) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_one__dvd,axiom,
% 52.23/52.33 ! [V_a,T_a] :
% 52.23/52.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.33 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__0__left,axiom,
% 52.23/52.33 ! [V_a,T_a] :
% 52.23/52.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 52.23/52.33 => V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__add,axiom,
% 52.23/52.33 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
% 52.23/52.33 => 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))) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd_Oeq__iff,axiom,
% 52.23/52.33 ! [V_y_2,V_x_2] :
% 52.23/52.33 ( V_x_2 = V_y_2
% 52.23/52.33 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 52.23/52.33 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd_Ole__less,axiom,
% 52.23/52.33 ! [V_y_2,V_x_2] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 52.23/52.33 <=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 52.23/52.33 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) )
% 52.23/52.33 | V_x_2 = V_y_2 ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd_Oless__le,axiom,
% 52.23/52.33 ! [V_y_2,V_x_2] :
% 52.23/52.33 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 52.23/52.33 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) )
% 52.23/52.33 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 52.23/52.33 & V_x_2 != V_y_2 ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd_Oneq__le__trans,axiom,
% 52.23/52.33 ! [V_b,V_a] :
% 52.23/52.33 ( V_a != V_b
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 52.23/52.33 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd_Oeq__refl,axiom,
% 52.23/52.33 ! [V_y,V_x] :
% 52.23/52.33 ( V_x = V_y
% 52.23/52.33 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd_Oantisym__conv,axiom,
% 52.23/52.33 ! [V_x_2,V_y_2] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 52.23/52.33 <=> V_x_2 = V_y_2 ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd_Ole__imp__less__or__eq,axiom,
% 52.23/52.33 ! [V_y,V_x] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 52.23/52.33 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 52.23/52.33 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 52.23/52.33 | V_x = V_y ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd_Ole__neq__trans,axiom,
% 52.23/52.33 ! [V_b,V_a] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 52.23/52.33 => ( V_a != V_b
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 52.23/52.33 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd_Oord__eq__le__trans,axiom,
% 52.23/52.33 ! [V_c,V_b,V_a] :
% 52.23/52.33 ( V_a = V_b
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))
% 52.23/52.33 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd_Oord__le__eq__trans,axiom,
% 52.23/52.33 ! [V_c,V_b,V_a] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 52.23/52.33 => ( V_b = V_c
% 52.23/52.33 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__antisym,axiom,
% 52.23/52.33 ! [V_n,V_m] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m))
% 52.23/52.33 => V_m = V_n ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd_Oantisym,axiom,
% 52.23/52.33 ! [V_y,V_x] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 52.23/52.33 => V_x = V_y ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd_Oorder__trans,axiom,
% 52.23/52.33 ! [V_z,V_y,V_x] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 52.23/52.33 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd_Oord__eq__less__trans,axiom,
% 52.23/52.33 ! [V_c,V_b,V_a] :
% 52.23/52.33 ( V_a = V_b
% 52.23/52.33 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))
% 52.23/52.33 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_b)) )
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c))
% 52.23/52.33 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd_Ole__less__trans,axiom,
% 52.23/52.33 ! [V_z,V_y,V_x] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 52.23/52.33 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 52.23/52.33 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y)) )
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
% 52.23/52.33 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd_Oless__imp__neq,axiom,
% 52.23/52.33 ! [V_y,V_x] :
% 52.23/52.33 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 52.23/52.33 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 52.23/52.33 => V_x != V_y ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd_Oless__not__sym,axiom,
% 52.23/52.33 ! [V_y,V_x] :
% 52.23/52.33 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 52.23/52.33 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 52.23/52.33 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 52.23/52.33 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd_Oless__imp__le,axiom,
% 52.23/52.33 ! [V_y,V_x] :
% 52.23/52.33 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 52.23/52.33 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 52.23/52.33 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd_Oless__imp__not__less,axiom,
% 52.23/52.33 ! [V_y,V_x] :
% 52.23/52.33 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 52.23/52.33 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 52.23/52.33 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 52.23/52.33 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd_Oless__imp__not__eq,axiom,
% 52.23/52.33 ! [V_y,V_x] :
% 52.23/52.33 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 52.23/52.33 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 52.23/52.33 => V_x != V_y ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd_Oless__imp__not__eq2,axiom,
% 52.23/52.33 ! [V_y,V_x] :
% 52.23/52.33 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 52.23/52.33 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 52.23/52.33 => V_y != V_x ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd_Oord__less__eq__trans,axiom,
% 52.23/52.33 ! [V_c,V_b,V_a] :
% 52.23/52.33 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 52.23/52.33 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) )
% 52.23/52.33 => ( V_b = V_c
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c))
% 52.23/52.33 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd_Oless__le__trans,axiom,
% 52.23/52.33 ! [V_z,V_y,V_x] :
% 52.23/52.33 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 52.23/52.33 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
% 52.23/52.33 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd_Oless__asym_H,axiom,
% 52.23/52.33 ! [V_b,V_a] :
% 52.23/52.33 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 52.23/52.33 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) )
% 52.23/52.33 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
% 52.23/52.33 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd_Oless__trans,axiom,
% 52.23/52.33 ! [V_z,V_y,V_x] :
% 52.23/52.33 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 52.23/52.33 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 52.23/52.33 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 52.23/52.33 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y)) )
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
% 52.23/52.33 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd_Oless__asym,axiom,
% 52.23/52.33 ! [V_y,V_x] :
% 52.23/52.33 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 52.23/52.33 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 52.23/52.33 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 52.23/52.33 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_lessThan__eq__iff,axiom,
% 52.23/52.33 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_b)
% 52.23/52.33 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)
% 52.23/52.33 <=> V_x_2 = V_y_2 ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__refl,axiom,
% 52.23/52.33 ! [V_a,T_a] :
% 52.23/52.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.33 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_a)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__trans,axiom,
% 52.23/52.33 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c))
% 52.23/52.33 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__mod__imp__dvd,axiom,
% 52.23/52.33 ! [V_n,V_m,V_k,T_a] :
% 52.23/52.33 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n)))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))
% 52.23/52.33 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__mod,axiom,
% 52.23/52.33 ! [V_n,V_m,V_k,T_a] :
% 52.23/52.33 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))
% 52.23/52.33 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n))) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_mod__mod__cancel,axiom,
% 52.23/52.33 ! [V_a,V_b,V_c,T_a] :
% 52.23/52.33 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
% 52.23/52.33 => 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) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__mod__iff,axiom,
% 52.23/52.33 ! [V_m_2,V_n_2,V_k_2,T_b] :
% 52.23/52.33 ( class_Divides_Osemiring__div(T_b)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_n_2))
% 52.23/52.33 => ( 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)))
% 52.23/52.33 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_m_2)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_zdvd__int,axiom,
% 52.23/52.33 ! [V_y_2,V_x_2] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 52.23/52.33 <=> 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))) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_transfer__int__nat__relations_I4_J,axiom,
% 52.23/52.33 ! [V_y_2,V_x_2] :
% 52.23/52.33 ( 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)))
% 52.23/52.33 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__triv__left,axiom,
% 52.23/52.33 ! [V_b,V_a,T_a] :
% 52.23/52.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.33 => 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))) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__triv__right,axiom,
% 52.23/52.33 ! [V_b,V_a,T_a] :
% 52.23/52.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.33 => 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))) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__mult2,axiom,
% 52.23/52.33 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 52.23/52.33 => 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))) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__mult,axiom,
% 52.23/52.33 ! [V_b,V_c,V_a,T_a] :
% 52.23/52.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
% 52.23/52.33 => 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))) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_mult__dvd__mono,axiom,
% 52.23/52.33 ! [V_d,V_c,V_b,V_a,T_a] :
% 52.23/52.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_d))
% 52.23/52.33 => 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))) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvdI,axiom,
% 52.23/52.33 ! [V_k,V_b,V_a,T_a] :
% 52.23/52.33 ( class_Rings_Odvd(T_a)
% 52.23/52.33 => ( V_a = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k)
% 52.23/52.33 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_a)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__mult__left,axiom,
% 52.23/52.33 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.33 => ( 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))
% 52.23/52.33 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__mult__right,axiom,
% 52.23/52.33 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.33 => ( 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))
% 52.23/52.33 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_div__dvd__div,axiom,
% 52.23/52.33 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 52.23/52.33 ( class_Divides_Osemiring__div(T_b)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_c_2))
% 52.23/52.33 => ( 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)))
% 52.23/52.33 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_b_2),V_c_2)) ) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_zdvd__zmod__imp__zdvd,axiom,
% 52.23/52.33 ! [V_n,V_m,V_k] :
% 52.23/52.33 ( 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)))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n))
% 52.23/52.33 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_zdvd__zmod,axiom,
% 52.23/52.33 ! [V_n,V_m,V_f] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),V_m))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),V_n))
% 52.23/52.33 => 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))) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_uminus__dvd__conv_I2_J,axiom,
% 52.23/52.33 ! [V_t_2,V_d_2] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))
% 52.23/52.33 <=> 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))) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_uminus__dvd__conv_I1_J,axiom,
% 52.23/52.33 ! [V_t_2,V_d_2] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))
% 52.23/52.33 <=> 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)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_zdvd__zdiffD,axiom,
% 52.23/52.33 ! [V_n,V_m,V_k] :
% 52.23/52.33 ( 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)))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n))
% 52.23/52.33 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__reduce,axiom,
% 52.23/52.33 ! [V_n_2,V_k_2] :
% 52.23/52.33 ( 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)))
% 52.23/52.33 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_n_2)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_of__nat__setsum,axiom,
% 52.23/52.33 ! [V_A_2,V_f_2,T_c,T_b] :
% 52.23/52.33 ( class_Rings_Osemiring__1(T_b)
% 52.23/52.33 => 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) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__minus__iff,axiom,
% 52.23/52.33 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.33 ( class_Rings_Ocomm__ring__1(T_b)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)))
% 52.23/52.33 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_minus__dvd__iff,axiom,
% 52.23/52.33 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.33 ( class_Rings_Ocomm__ring__1(T_b)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),V_y_2))
% 52.23/52.33 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__diff,axiom,
% 52.23/52.33 ! [V_z,V_y,V_x,T_a] :
% 52.23/52.33 ( class_Rings_Ocomm__ring__1(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_z))
% 52.23/52.33 => 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))) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_setsum__lessThan__Suc,axiom,
% 52.23/52.33 ! [V_n_2,V_f_2,T_b] :
% 52.23/52.33 ( class_Groups_Ocomm__monoid__add(T_b)
% 52.23/52.33 => 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)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_of__int__setsum,axiom,
% 52.23/52.33 ! [V_A_2,V_f_2,T_c,T_b] :
% 52.23/52.33 ( class_Rings_Oring__1(T_b)
% 52.23/52.33 => 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) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__diff__nat,axiom,
% 52.23/52.33 ! [V_n,V_m,V_k] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
% 52.23/52.33 => 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))) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_setsum__commute,axiom,
% 52.23/52.33 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 52.23/52.33 ( class_Groups_Ocomm__monoid__add(T_b)
% 52.23/52.33 => 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) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_setsum__0,axiom,
% 52.23/52.33 ! [V_A_2,T_c,T_b] :
% 52.23/52.33 ( class_Groups_Ocomm__monoid__add(T_b)
% 52.23/52.33 => 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) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_setsum__addf,axiom,
% 52.23/52.33 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 52.23/52.33 ( class_Groups_Ocomm__monoid__add(T_b)
% 52.23/52.33 => 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)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_setsum__right__distrib,axiom,
% 52.23/52.33 ! [V_A_2,V_f_2,T_c,V_r_2,T_b] :
% 52.23/52.33 ( class_Rings_Osemiring__0(T_b)
% 52.23/52.33 => 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) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_setsum__left__distrib,axiom,
% 52.23/52.33 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 52.23/52.33 ( class_Rings_Osemiring__0(T_b)
% 52.23/52.33 => 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) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_setsum__product,axiom,
% 52.23/52.33 ! [V_B_2,V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 52.23/52.33 ( class_Rings_Osemiring__0(T_b)
% 52.23/52.33 => 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) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_setsum__subtractf,axiom,
% 52.23/52.33 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 52.23/52.33 ( class_Groups_Oab__group__add(T_b)
% 52.23/52.33 => 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)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_setsum__negf,axiom,
% 52.23/52.33 ! [V_A_2,V_f_2,T_c,T_b] :
% 52.23/52.33 ( class_Groups_Oab__group__add(T_b)
% 52.23/52.33 => 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)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_setsum__divide__distrib,axiom,
% 52.23/52.33 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 52.23/52.33 ( class_Fields_Ofield(T_b)
% 52.23/52.33 => 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) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_abs__setsum__abs,axiom,
% 52.23/52.33 ! [V_A_2,V_f_2,T_c,T_b] :
% 52.23/52.33 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 52.23/52.33 => 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) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_transfer__nat__int__relations_I4_J,axiom,
% 52.23/52.33 ! [V_y_2,V_x_2] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 52.23/52.33 => ( 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)))
% 52.23/52.33 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_int__dvd__iff,axiom,
% 52.23/52.33 ! [V_z_2,V_m_2] :
% 52.23/52.33 ( 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))
% 52.23/52.33 <=> 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)))) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__int__iff,axiom,
% 52.23/52.33 ! [V_m_2,V_z_2] :
% 52.23/52.33 ( 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)))
% 52.23/52.33 <=> 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)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_lessThan__subset__iff,axiom,
% 52.23/52.33 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_b)
% 52.23/52.33 => ( 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)))
% 52.23/52.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__mult__cancel__left,axiom,
% 52.23/52.33 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 52.23/52.33 ( class_Rings_Oidom(T_b)
% 52.23/52.33 => ( 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)))
% 52.23/52.33 <=> ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.33 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__mult__cancel__right,axiom,
% 52.23/52.33 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 52.23/52.33 ( class_Rings_Oidom(T_b)
% 52.23/52.33 => ( 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)))
% 52.23/52.33 <=> ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.33 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__imp__mod__0,axiom,
% 52.23/52.33 ! [V_b,V_a,T_a] :
% 52.23/52.33 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 52.23/52.33 => c_Divides_Odiv__class_Omod(T_a,V_b,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__eq__mod__eq__0,axiom,
% 52.23/52.33 ! [V_b_2,V_a_2,T_b] :
% 52.23/52.33 ( class_Divides_Osemiring__div(T_b)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 52.23/52.33 <=> c_Divides_Odiv__class_Omod(T_b,V_b_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_lessThan__strict__subset__iff,axiom,
% 52.23/52.33 ! [V_n_2,V_m_2,T_b] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_b)
% 52.23/52.33 => ( 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)))
% 52.23/52.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_n_2)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_div__add,axiom,
% 52.23/52.33 ! [V_y,V_x,V_z,T_a] :
% 52.23/52.33 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_x))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_y))
% 52.23/52.33 => 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)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__mult__div__cancel,axiom,
% 52.23/52.33 ! [V_b,V_a,T_a] :
% 52.23/52.33 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 52.23/52.33 => 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 ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_div__mult__swap,axiom,
% 52.23/52.33 ! [V_a,V_b,V_c,T_a] :
% 52.23/52.33 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
% 52.23/52.33 => 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) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__div__mult__self,axiom,
% 52.23/52.33 ! [V_b,V_a,T_a] :
% 52.23/52.33 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 52.23/52.33 => 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 ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__div__mult,axiom,
% 52.23/52.33 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.33 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 52.23/52.33 => 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) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_div__mult__div__if__dvd,axiom,
% 52.23/52.33 ! [V_w,V_z,V_x,V_y,T_a] :
% 52.23/52.33 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_w))
% 52.23/52.33 => 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)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__div__neg,axiom,
% 52.23/52.33 ! [V_x,V_y,T_a] :
% 52.23/52.33 ( class_Divides_Oring__div(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 52.23/52.33 => 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)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__neg__div,axiom,
% 52.23/52.33 ! [V_x,V_y,T_a] :
% 52.23/52.33 ( class_Divides_Oring__div(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 52.23/52.33 => 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)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_power__le__dvd,axiom,
% 52.23/52.33 ! [V_m,V_b,V_n,V_a,T_a] :
% 52.23/52.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.33 => ( 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))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 52.23/52.33 => 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)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__power__le,axiom,
% 52.23/52.33 ! [V_m,V_n,V_y,V_x,T_a] :
% 52.23/52.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 52.23/52.33 => 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))) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_le__imp__power__dvd,axiom,
% 52.23/52.33 ! [V_a,V_n,V_m,T_a] :
% 52.23/52.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 52.23/52.33 => 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))) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_div__power,axiom,
% 52.23/52.33 ! [V_n,V_x,V_y,T_a] :
% 52.23/52.33 ( class_Divides_Osemiring__div(T_a)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 52.23/52.33 => 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)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_zdvd__antisym__nonneg,axiom,
% 52.23/52.33 ! [V_n,V_m] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_n))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m))
% 52.23/52.33 => V_m = V_n ) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_zdvd__not__zless,axiom,
% 52.23/52.33 ! [V_n,V_m] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_m),V_n))
% 52.23/52.33 => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_zdvd__mono,axiom,
% 52.23/52.33 ! [V_t_2,V_m_2,V_k_2] :
% 52.23/52.33 ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m_2),V_t_2))
% 52.23/52.33 <=> 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))) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_zdvd__mult__cancel,axiom,
% 52.23/52.33 ! [V_n,V_m,V_k] :
% 52.23/52.33 ( 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)))
% 52.23/52.33 => ( V_k != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.33 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_zdvd__reduce,axiom,
% 52.23/52.33 ! [V_m_2,V_n_2,V_k_2] :
% 52.23/52.33 ( 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))))
% 52.23/52.33 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),V_n_2)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_zdvd__period,axiom,
% 52.23/52.33 ! [V_c_2,V_t_2,V_x_2,V_d_2,V_a_2] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),V_d_2))
% 52.23/52.33 => ( 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)))
% 52.23/52.33 <=> 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))) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__1__iff__1,axiom,
% 52.23/52.33 ! [V_m_2] :
% 52.23/52.33 ( 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))))
% 52.23/52.33 <=> V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_nat__dvd__not__less,axiom,
% 52.23/52.33 ! [V_n,V_m] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 52.23/52.33 => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_nat__mult__dvd__cancel__disj,axiom,
% 52.23/52.33 ! [V_n_2,V_m_2,V_k_2] :
% 52.23/52.33 ( 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)))
% 52.23/52.33 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.33 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_zdvd__mult__div__cancel,axiom,
% 52.23/52.33 ! [V_m,V_n] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m))
% 52.23/52.33 => 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 ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_zmod__eq__dvd__iff,axiom,
% 52.23/52.33 ! [V_y_2,V_n_2,V_x_2] :
% 52.23/52.33 ( 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)
% 52.23/52.33 <=> 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))) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__diffD1,axiom,
% 52.23/52.33 ! [V_n,V_m,V_k] :
% 52.23/52.33 ( 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)))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 52.23/52.33 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__diffD,axiom,
% 52.23/52.33 ! [V_n,V_m,V_k] :
% 52.23/52.33 ( 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)))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 52.23/52.33 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_zdvd1__eq,axiom,
% 52.23/52.33 ! [V_x_2] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_x_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))
% 52.23/52.33 <=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_abs__div,axiom,
% 52.23/52.33 ! [V_x,V_y] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_y),V_x))
% 52.23/52.33 => 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)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_nat__dvd__iff,axiom,
% 52.23/52.33 ! [V_m_2,V_z_2] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),V_m_2))
% 52.23/52.33 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 52.23/52.33 => 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))) )
% 52.23/52.33 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 52.23/52.33 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_arith__series__general,axiom,
% 52.23/52.33 ! [V_n_2,V_d_2,V_a_2,T_b] :
% 52.23/52.33 ( class_Rings_Ocomm__semiring__1(T_b)
% 52.23/52.33 => 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)))) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_unity__coeff__ex,axiom,
% 52.23/52.33 ! [V_l_2,V_P_2,T_b] :
% 52.23/52.33 ( ( class_Rings_Odvd(T_b)
% 52.23/52.33 & class_Rings_Osemiring__0(T_b) )
% 52.23/52.33 => ( ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x)))
% 52.23/52.33 <=> ? [B_x] :
% 52.23/52.33 ( 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))))
% 52.23/52.33 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_inf__period_I3_J,axiom,
% 52.23/52.33 ! [V_t_2,V_D_2,V_d_2,T_b] :
% 52.23/52.33 ( ( class_Rings_Ocomm__ring(T_b)
% 52.23/52.33 & class_Rings_Odvd(T_b) )
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
% 52.23/52.33 => ! [B_x,B_k] :
% 52.23/52.33 ( 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)))
% 52.23/52.33 <=> 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))) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_inf__period_I4_J,axiom,
% 52.23/52.33 ! [V_t_2,V_D_2,V_d_2,T_b] :
% 52.23/52.33 ( ( class_Rings_Ocomm__ring(T_b)
% 52.23/52.33 & class_Rings_Odvd(T_b) )
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
% 52.23/52.33 => ! [B_x,B_k] :
% 52.23/52.33 ( 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)))
% 52.23/52.33 <=> 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))) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__eq__mod__eq__0__number__of,axiom,
% 52.23/52.33 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.33 ( ( class_Divides_Osemiring__div(T_b)
% 52.23/52.33 & class_Int_Onumber(T_b) )
% 52.23/52.33 => ( 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)))
% 52.23/52.33 <=> 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) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__div__div__eq__mult,axiom,
% 52.23/52.33 ! [V_d_2,V_b_2,V_c_2,V_a_2,T_b] :
% 52.23/52.33 ( class_Divides_Osemiring__div(T_b)
% 52.23/52.33 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.33 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_c_2),V_d_2))
% 52.23/52.33 => ( 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)
% 52.23/52.33 <=> 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) ) ) ) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__div__eq__mult,axiom,
% 52.23/52.33 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 52.23/52.33 ( class_Divides_Osemiring__div(T_b)
% 52.23/52.33 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 52.23/52.33 => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = V_c_2
% 52.23/52.33 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2) ) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_zdvd__imp__le,axiom,
% 52.23/52.33 ! [V_n,V_z] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z),V_n))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_n))
% 52.23/52.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_n)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_zdvd__iff__zmod__eq__0__number__of,axiom,
% 52.23/52.33 ! [V_y_2,V_x_2] :
% 52.23/52.33 ( 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)))
% 52.23/52.33 <=> 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) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__imp__le,axiom,
% 52.23/52.33 ! [V_n,V_k] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 52.23/52.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__mult__cancel,axiom,
% 52.23/52.33 ! [V_n,V_m,V_k] :
% 52.23/52.33 ( 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)))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 52.23/52.33 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_nat__mult__dvd__cancel1,axiom,
% 52.23/52.33 ! [V_n_2,V_m_2,V_k_2] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 52.23/52.33 => ( 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)))
% 52.23/52.33 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__imp__le__int,axiom,
% 52.23/52.33 ! [V_d,V_i] :
% 52.23/52.33 ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d),V_i))
% 52.23/52.33 => 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))) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd__power,axiom,
% 52.23/52.33 ! [V_x,V_n,T_a] :
% 52.23/52.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 52.23/52.33 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 52.23/52.33 | V_x = c_Groups_Oone__class_Oone(T_a) )
% 52.23/52.33 => 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))) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd_Ostrict__monoD,axiom,
% 52.23/52.33 ! [V_y_2,V_x_2,V_f_2,T_b] :
% 52.23/52.33 ( class_Orderings_Oorder(T_b)
% 52.23/52.33 => ( 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)
% 52.23/52.33 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 52.23/52.33 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) )
% 52.23/52.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_arith__series__nat,axiom,
% 52.23/52.33 ! [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)))) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd_OmonoD,axiom,
% 52.23/52.33 ! [V_y_2,V_x_2,V_f_2,T_b] :
% 52.23/52.33 ( class_Orderings_Oorder(T_b)
% 52.23/52.33 => ( c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 52.23/52.33 => 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))) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_setsum__natinterval__difff,axiom,
% 52.23/52.33 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 52.23/52.33 ( class_Groups_Oab__group__add(T_b)
% 52.23/52.33 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 52.23/52.33 => 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)))) )
% 52.23/52.33 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 52.23/52.33 => 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) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_gauss__sum,axiom,
% 52.23/52.33 ! [V_n_2,T_b] :
% 52.23/52.33 ( class_Rings_Ocomm__semiring__1(T_b)
% 52.23/52.33 => 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))) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_setsum__shift__lb__Suc0__0,axiom,
% 52.23/52.33 ! [V_k_2,V_f_2] :
% 52.23/52.33 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.33 => 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)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_dvd_Ostrict__mono__mono,axiom,
% 52.23/52.33 ! [V_f_2,T_b] :
% 52.23/52.33 ( class_Orderings_Oorder(T_b)
% 52.23/52.33 => ( 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)
% 52.23/52.33 => c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_atLeastatMost__subset__iff,axiom,
% 52.23/52.33 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 52.23/52.33 ( class_Orderings_Oorder(T_b)
% 52.23/52.33 => ( 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)))
% 52.23/52.33 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 52.23/52.33 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2))
% 52.23/52.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom,
% 52.23/52.33 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 52.23/52.33 ( class_Groups_Ocomm__monoid__add(T_b)
% 52.23/52.33 => 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)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom,
% 52.23/52.33 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
% 52.23/52.33 ( class_Groups_Ocomm__monoid__add(T_b)
% 52.23/52.33 => 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)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_int__setsum,axiom,
% 52.23/52.33 ! [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) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom,
% 52.23/52.33 ! [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)) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_atLeastatMost__psubset__iff,axiom,
% 52.23/52.33 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 52.23/52.33 ( class_Orderings_Oorder(T_b)
% 52.23/52.33 => ( 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)))
% 52.23/52.33 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 52.23/52.33 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2))
% 52.23/52.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
% 52.23/52.33 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_a_2))
% 52.23/52.33 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2)) ) ) )
% 52.23/52.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_setsum__head__Suc,axiom,
% 52.23/52.33 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 52.23/52.33 ( class_Groups_Ocomm__monoid__add(T_b)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 52.23/52.33 => 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))) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_setsum__cl__ivl__Suc,axiom,
% 52.23/52.33 ! [V_f_2,V_m_2,V_n_2,T_b] :
% 52.23/52.33 ( class_Groups_Ocomm__monoid__add(T_b)
% 52.23/52.33 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 52.23/52.33 => 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) )
% 52.23/52.33 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 52.23/52.33 => 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))) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_setsum__ub__add__nat,axiom,
% 52.23/52.33 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_b] :
% 52.23/52.33 ( class_Groups_Ocomm__monoid__add(T_b)
% 52.23/52.33 => ( 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))))
% 52.23/52.33 => 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)))) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_all__nat__less,axiom,
% 52.23/52.33 ! [V_P_2,V_n_2] :
% 52.23/52.33 ( ! [B_m] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 52.23/52.33 => hBOOL(hAPP(V_P_2,B_m)) )
% 52.23/52.33 <=> ! [B_x] :
% 52.23/52.33 ( 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)))
% 52.23/52.33 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_ex__nat__less,axiom,
% 52.23/52.33 ! [V_P_2,V_n_2] :
% 52.23/52.33 ( ? [B_m] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 52.23/52.33 & hBOOL(hAPP(V_P_2,B_m)) )
% 52.23/52.33 <=> ? [B_x] :
% 52.23/52.33 ( 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)))
% 52.23/52.33 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_sum__diff__distrib,axiom,
% 52.23/52.33 ! [V_n_2,V_P_2,V_Q_2] :
% 52.23/52.33 ( ! [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)))
% 52.23/52.33 => 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)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_geometric__sum,axiom,
% 52.23/52.33 ! [V_n_2,V_x_2,T_b] :
% 52.23/52.33 ( class_Fields_Ofield(T_b)
% 52.23/52.33 => ( V_x_2 != c_Groups_Oone__class_Oone(T_b)
% 52.23/52.33 => 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))) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_ex__nat__less__eq,axiom,
% 52.23/52.33 ! [V_P_2,V_n_2] :
% 52.23/52.33 ( ? [B_m] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 52.23/52.33 & hBOOL(hAPP(V_P_2,B_m)) )
% 52.23/52.33 <=> ? [B_x] :
% 52.23/52.33 ( 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)))
% 52.23/52.33 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_all__nat__less__eq,axiom,
% 52.23/52.33 ! [V_P_2,V_n_2] :
% 52.23/52.33 ( ! [B_m] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 52.23/52.33 => hBOOL(hAPP(V_P_2,B_m)) )
% 52.23/52.33 <=> ! [B_x] :
% 52.23/52.33 ( 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)))
% 52.23/52.33 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_atLeastLessThan__inj_I2_J,axiom,
% 52.23/52.33 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_b)
% 52.23/52.33 => ( 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)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
% 52.23/52.33 => V_b_2 = V_d_2 ) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_atLeastLessThan__inj_I1_J,axiom,
% 52.23/52.33 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_b)
% 52.23/52.33 => ( 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)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
% 52.23/52.33 => V_a_2 = V_c_2 ) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_atLeastLessThan__eq__iff,axiom,
% 52.23/52.33 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_b)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
% 52.23/52.33 => ( 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)
% 52.23/52.33 <=> ( V_a_2 = V_c_2
% 52.23/52.33 & V_b_2 = V_d_2 ) ) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
% 52.23/52.33 ! [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) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_atLeast0LessThan,axiom,
% 52.23/52.33 ! [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) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_atLeastLessThan__subset__iff,axiom,
% 52.23/52.33 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_b)
% 52.23/52.33 => ( 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)))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
% 52.23/52.33 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2))
% 52.23/52.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
% 52.23/52.33 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 52.23/52.33 ( class_Groups_Ocomm__monoid__add(T_b)
% 52.23/52.33 => 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)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_setsum__shift__bounds__nat__ivl,axiom,
% 52.23/52.33 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
% 52.23/52.33 ( class_Groups_Ocomm__monoid__add(T_b)
% 52.23/52.33 => 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)) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_ivl__diff,axiom,
% 52.23/52.33 ! [V_m_2,V_n_2,V_i_2,T_b] :
% 52.23/52.33 ( class_Orderings_Olinorder(T_b)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_n_2))
% 52.23/52.33 => 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) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_setsum__add__nat__ivl,axiom,
% 52.23/52.33 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
% 52.23/52.33 ( class_Groups_Ocomm__monoid__add(T_b)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 52.23/52.33 => 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)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_setsum__diff__nat__ivl,axiom,
% 52.23/52.33 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
% 52.23/52.33 ( class_Groups_Oab__group__add(T_b)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 52.23/52.33 => 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)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
% 52.23/52.33 ! [V_k_2,V_f_2,T_b] :
% 52.23/52.33 ( class_Groups_Ocomm__monoid__add(T_b)
% 52.23/52.33 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.33 => 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)) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_setsum__head__upt__Suc,axiom,
% 52.23/52.33 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 52.23/52.33 ( class_Groups_Ocomm__monoid__add(T_b)
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 52.23/52.33 => 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))) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_setsum__op__ivl__Suc,axiom,
% 52.23/52.33 ! [V_f_2,V_m_2,V_n_2,T_b] :
% 52.23/52.33 ( class_Groups_Ocomm__monoid__add(T_b)
% 52.23/52.33 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 52.23/52.33 => 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) )
% 52.23/52.33 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 52.23/52.33 => 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)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_bset_I6_J,axiom,
% 52.23/52.33 ! [V_t_2,V_B_2,V_D_2] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 52.23/52.33 => ! [B_x] :
% 52.23/52.33 ( ! [B_xa] :
% 52.23/52.33 ( 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)))
% 52.23/52.33 => ! [B_xb] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 52.23/52.33 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 52.23/52.33 => 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)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_aset_I8_J,axiom,
% 52.23/52.33 ! [V_t_2,V_A_2,V_D_2] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 52.23/52.33 => ! [B_x] :
% 52.23/52.33 ( ! [B_xa] :
% 52.23/52.33 ( 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)))
% 52.23/52.33 => ! [B_xb] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 52.23/52.33 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 52.23/52.33 => 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))) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_periodic__finite__ex,axiom,
% 52.23/52.33 ! [V_P_2,V_d_2] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 52.23/52.33 => ( ! [B_x,B_k] :
% 52.23/52.33 ( hBOOL(hAPP(V_P_2,B_x))
% 52.23/52.33 <=> 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)))) )
% 52.23/52.33 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 52.23/52.33 <=> ? [B_x] :
% 52.23/52.33 ( 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)))
% 52.23/52.33 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_aset_I7_J,axiom,
% 52.23/52.33 ! [V_t_2,V_A_2,V_D_2] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 52.23/52.33 => ! [B_x] :
% 52.23/52.33 ( ! [B_xa] :
% 52.23/52.33 ( 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)))
% 52.23/52.33 => ! [B_xb] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 52.23/52.33 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 52.23/52.33 => 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))) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 52.23/52.33 ! [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) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_bset_I5_J,axiom,
% 52.23/52.33 ! [V_t_2,V_B_2,V_D_2] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 52.23/52.33 => ! [B_x] :
% 52.23/52.33 ( ! [B_xa] :
% 52.23/52.33 ( 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)))
% 52.23/52.33 => ! [B_xb] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 52.23/52.33 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 52.23/52.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 52.23/52.33 => 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)) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_aset_I10_J,axiom,
% 52.23/52.33 ! [V_t_2,V_A_2,V_D_2,V_d_2] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2))
% 52.23/52.33 => ! [B_x] :
% 52.23/52.33 ( ! [B_xa] :
% 52.23/52.33 ( 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)))
% 52.23/52.33 => ! [B_xb] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 52.23/52.33 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 52.23/52.33 => ( ~ 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)))
% 52.23/52.33 => ~ 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))) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_bset_I10_J,axiom,
% 52.23/52.33 ! [V_t_2,V_B_2,V_D_2,V_d_2] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2))
% 52.23/52.33 => ! [B_x] :
% 52.23/52.33 ( ! [B_xa] :
% 52.23/52.33 ( 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)))
% 52.23/52.33 => ! [B_xb] :
% 52.23/52.33 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 52.23/52.33 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 52.23/52.33 => ( ~ 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)))
% 52.23/52.33 => ~ 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))) ) ) ) ).
% 52.23/52.33
% 52.23/52.33 fof(fact_aset_I9_J,axiom,
% 52.23/52.33 ! [V_t_2,V_A_2,V_D_2,V_d_2] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2))
% 52.23/52.34 => ! [B_x] :
% 52.23/52.34 ( ! [B_xa] :
% 52.23/52.34 ( 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)))
% 52.23/52.34 => ! [B_xb] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 52.23/52.34 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 52.23/52.34 => ( 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)))
% 52.23/52.34 => 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))) ) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_bset_I9_J,axiom,
% 52.23/52.34 ! [V_t_2,V_B_2,V_D_2,V_d_2] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2))
% 52.23/52.34 => ! [B_x] :
% 52.23/52.34 ( ! [B_xa] :
% 52.23/52.34 ( 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)))
% 52.23/52.34 => ! [B_xb] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 52.23/52.34 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 52.23/52.34 => ( 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)))
% 52.23/52.34 => 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))) ) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_image__atLeastZeroLessThan__int,axiom,
% 52.23/52.34 ! [V_u_2] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))
% 52.23/52.34 => 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))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_setsum__head,axiom,
% 52.23/52.34 ! [V_P_2,V_n_2,V_m_2,T_b] :
% 52.23/52.34 ( class_Groups_Ocomm__monoid__add(T_b)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 52.23/52.34 => 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))) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_dvd_Ostrict__monoI,axiom,
% 52.23/52.34 ! [V_f_2,T_b] :
% 52.23/52.34 ( class_Orderings_Oorder(T_b)
% 52.23/52.34 => ( ! [B_x,B_y] :
% 52.23/52.34 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_x),B_y))
% 52.23/52.34 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_y),B_x)) )
% 52.23/52.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),hAPP(V_f_2,B_y))) )
% 52.23/52.34 => 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) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_image__uminus__atLeastLessThan,axiom,
% 52.23/52.34 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.34 ( class_Groups_Oordered__ab__group__add(T_b)
% 52.23/52.34 => 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)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_image__uminus__greaterThanAtMost,axiom,
% 52.23/52.34 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.34 ( class_Groups_Oordered__ab__group__add(T_b)
% 52.23/52.34 => 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)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_subset__image__iff,axiom,
% 52.23/52.34 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
% 52.23/52.34 ( 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)))
% 52.23/52.34 <=> ? [B_AA] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2))
% 52.23/52.34 & V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_image__mono,axiom,
% 52.23/52.34 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.34 => 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))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_transfer__nat__int__set__relations_I5_J,axiom,
% 52.23/52.34 ! [V_B_2,V_A_2] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.34 <=> 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))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_image__image,axiom,
% 52.23/52.34 ! [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) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_transfer__nat__int__set__relations_I4_J,axiom,
% 52.23/52.34 ! [V_B_2,V_A_2] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.34 <=> 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))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_transfer__nat__int__set__relations_I3_J,axiom,
% 52.23/52.34 ! [V_B_2,V_A_2] :
% 52.23/52.34 ( V_A_2 = V_B_2
% 52.23/52.34 <=> 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) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_image__diff__subset,axiom,
% 52.23/52.34 ! [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)))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_image__uminus__atLeastAtMost,axiom,
% 52.23/52.34 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.34 ( class_Groups_Oordered__ab__group__add(T_b)
% 52.23/52.34 => 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)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom,
% 52.23/52.34 ! [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) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom,
% 52.23/52.34 ! [V_A_2,V_f_2,T_b] :
% 52.23/52.34 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 52.23/52.34 & class_Groups_Ocomm__monoid__mult(T_b) )
% 52.23/52.34 => 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)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom,
% 52.23/52.34 ! [V_n_2,V_m_2] :
% 52.23/52.34 ( c_Nat__Transfer_Ois__nat(V_m_2)
% 52.23/52.34 => ( c_Nat__Transfer_Ois__nat(V_n_2)
% 52.23/52.34 => 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))) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_setsum__SucD,axiom,
% 52.23/52.34 ! [V_n_2,V_A_2,V_f_2,T_b] :
% 52.23/52.34 ( 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)
% 52.23/52.34 => ? [B_x] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.23/52.34 & 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))) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_setsum__ivl__cong,axiom,
% 52.23/52.34 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_c_2,V_a_2,T_b,T_c] :
% 52.23/52.34 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 52.23/52.34 & class_Orderings_Oord(T_b) )
% 52.23/52.34 => ( V_a_2 = V_c_2
% 52.23/52.34 => ( V_b_2 = V_d_2
% 52.23/52.34 => ( ! [B_x] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),B_x))
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2))
% 52.23/52.34 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) )
% 52.23/52.34 => 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)) ) ) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_card__atLeastAtMost__int,axiom,
% 52.23/52.34 ! [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))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_image__uminus__lessThan,axiom,
% 52.23/52.34 ! [V_x_2,T_b] :
% 52.23/52.34 ( class_Groups_Oordered__ab__group__add(T_b)
% 52.23/52.34 => 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)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_card__greaterThanAtMost__int,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_greaterThan__eq__iff,axiom,
% 52.23/52.34 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.34 ( class_Orderings_Olinorder(T_b)
% 52.23/52.34 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)
% 52.23/52.34 <=> V_x_2 = V_y_2 ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_image__Suc__atLeastLessThan,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_image__Suc__atLeastAtMost,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_image__add__atLeastLessThan,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_image__add__atLeastAtMost,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_card__eq__setsum,axiom,
% 52.23/52.34 ! [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) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_transfer__int__nat__set__return__embed,axiom,
% 52.23/52.34 ! [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 ).
% 52.23/52.34
% 52.23/52.34 fof(fact_greaterThan__subset__iff,axiom,
% 52.23/52.34 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.34 ( class_Orderings_Olinorder(T_b)
% 52.23/52.34 => ( 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)))
% 52.23/52.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_setsum__constant,axiom,
% 52.23/52.34 ! [V_A_2,V_y_2,T_c,T_b] :
% 52.23/52.34 ( class_Rings_Osemiring__1(T_b)
% 52.23/52.34 => 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) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_card__atLeastZeroLessThan__int,axiom,
% 52.23/52.34 ! [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) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_card__atLeastLessThan__int,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom,
% 52.23/52.34 ! [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))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 52.23/52.34 ! [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) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_image__add__int__atLeastLessThan,axiom,
% 52.23/52.34 ! [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) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_image__uminus__greaterThan,axiom,
% 52.23/52.34 ! [V_x_2,T_b] :
% 52.23/52.34 ( class_Groups_Oordered__ab__group__add(T_b)
% 52.23/52.34 => 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)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_card__greaterThanLessThan__int,axiom,
% 52.23/52.34 ! [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)))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Body__sound__lemma,axiom,
% 52.23/52.34 ! [V_Procs_2,V_Q_2,V_P_2,V_Ga_2,T_b] :
% 52.23/52.34 ( 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))
% 52.23/52.34 => 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)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom,
% 52.23/52.34 ! [V_f_2,V_A_2,T_b] :
% 52.23/52.34 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 52.23/52.34 & class_Groups_Ocomm__monoid__mult(T_b) )
% 52.23/52.34 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 52.23/52.34 => 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)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_transfer__int__nat__set__relations_I4_J,axiom,
% 52.23/52.34 ! [V_B_2,V_A_2] :
% 52.23/52.34 ( c_Nat__Transfer_Onat__set(V_A_2)
% 52.23/52.34 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.34 <=> 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))) ) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_sup1CI,axiom,
% 52.23/52.34 ! [T_b,V_A_2,V_x_2,V_B_2] :
% 52.23/52.34 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2))
% 52.23/52.34 => hBOOL(hAPP(V_A_2,V_x_2)) )
% 52.23/52.34 => 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)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_sup1E,axiom,
% 52.23/52.34 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 52.23/52.34 ( 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))
% 52.23/52.34 => ( ~ hBOOL(hAPP(V_A_2,V_x_2))
% 52.23/52.34 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom,
% 52.23/52.34 ! [V_A_2] :
% 52.23/52.34 ( c_Nat__Transfer_Onat__set(V_A_2)
% 52.23/52.34 => 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)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_image__Un,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_card__lessThan,axiom,
% 52.23/52.34 ! [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 ).
% 52.23/52.34
% 52.23/52.34 fof(fact_less__supI1,axiom,
% 52.23/52.34 ! [V_b,V_a,V_x,T_a] :
% 52.23/52.34 ( class_Lattices_Osemilattice__sup(T_a)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 52.23/52.34 => 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))) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_less__supI2,axiom,
% 52.23/52.34 ! [V_a,V_b,V_x,T_a] :
% 52.23/52.34 ( class_Lattices_Osemilattice__sup(T_a)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 52.23/52.34 => 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))) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Un__mono,axiom,
% 52.23/52.34 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 52.23/52.34 => 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))) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Un__least,axiom,
% 52.23/52.34 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 52.23/52.34 => 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)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Un__absorb2,axiom,
% 52.23/52.34 ! [V_A_2,V_B_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 52.23/52.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Un__absorb1,axiom,
% 52.23/52.34 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_subset__Un__eq,axiom,
% 52.23/52.34 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.34 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Un__upper2,axiom,
% 52.23/52.34 ! [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))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Un__upper1,axiom,
% 52.23/52.34 ! [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))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_inf__sup__ord_I3_J,axiom,
% 52.23/52.34 ! [V_y,V_x,T_a] :
% 52.23/52.34 ( class_Lattices_Olattice(T_a)
% 52.23/52.34 => 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))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_sup__ge1,axiom,
% 52.23/52.34 ! [V_y,V_x,T_a] :
% 52.23/52.34 ( class_Lattices_Osemilattice__sup(T_a)
% 52.23/52.34 => 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))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_inf__sup__ord_I4_J,axiom,
% 52.23/52.34 ! [V_x,V_y,T_a] :
% 52.23/52.34 ( class_Lattices_Olattice(T_a)
% 52.23/52.34 => 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))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_sup__ge2,axiom,
% 52.23/52.34 ! [V_x,V_y,T_a] :
% 52.23/52.34 ( class_Lattices_Osemilattice__sup(T_a)
% 52.23/52.34 => 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))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_le__iff__sup,axiom,
% 52.23/52.34 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.34 ( class_Lattices_Osemilattice__sup(T_b)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 52.23/52.34 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_le__sup__iff,axiom,
% 52.23/52.34 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 52.23/52.34 ( class_Lattices_Osemilattice__sup(T_b)
% 52.23/52.34 => ( 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))
% 52.23/52.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 52.23/52.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_le__supI1,axiom,
% 52.23/52.34 ! [V_b,V_a,V_x,T_a] :
% 52.23/52.34 ( class_Lattices_Osemilattice__sup(T_a)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 52.23/52.34 => 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))) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_le__supI2,axiom,
% 52.23/52.34 ! [V_a,V_b,V_x,T_a] :
% 52.23/52.34 ( class_Lattices_Osemilattice__sup(T_a)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 52.23/52.34 => 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))) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_sup__absorb2,axiom,
% 52.23/52.34 ! [V_y,V_x,T_a] :
% 52.23/52.34 ( class_Lattices_Osemilattice__sup(T_a)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 52.23/52.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_sup__absorb1,axiom,
% 52.23/52.34 ! [V_x,V_y,T_a] :
% 52.23/52.34 ( class_Lattices_Osemilattice__sup(T_a)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 52.23/52.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_le__supI,axiom,
% 52.23/52.34 ! [V_b,V_x,V_a,T_a] :
% 52.23/52.34 ( class_Lattices_Osemilattice__sup(T_a)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 52.23/52.34 => 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)) ) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_sup__least,axiom,
% 52.23/52.34 ! [V_z,V_x,V_y,T_a] :
% 52.23/52.34 ( class_Lattices_Osemilattice__sup(T_a)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 52.23/52.34 => 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)) ) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_sup__mono,axiom,
% 52.23/52.34 ! [V_d,V_b,V_c,V_a,T_a] :
% 52.23/52.34 ( class_Lattices_Osemilattice__sup(T_a)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 52.23/52.34 => 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))) ) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_le__supE,axiom,
% 52.23/52.34 ! [V_x,V_b,V_a,T_a] :
% 52.23/52.34 ( class_Lattices_Osemilattice__sup(T_a)
% 52.23/52.34 => ( 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))
% 52.23/52.34 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 52.23/52.34 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_sup__max,axiom,
% 52.23/52.34 ! [T_b] :
% 52.23/52.34 ( ( class_Lattices_Osemilattice__sup(T_b)
% 52.23/52.34 & class_Orderings_Olinorder(T_b) )
% 52.23/52.34 => c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Sup__fin_Oidem,axiom,
% 52.23/52.34 ! [V_x,T_a] :
% 52.23/52.34 ( class_Lattices_Olattice(T_a)
% 52.23/52.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Un__Diff,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Un__Diff__cancel2,axiom,
% 52.23/52.34 ! [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) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Un__Diff__cancel,axiom,
% 52.23/52.34 ! [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) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_sup__fun__def,axiom,
% 52.23/52.34 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 52.23/52.34 ( class_Lattices_Olattice(T_b)
% 52.23/52.34 => 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)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_sup__apply,axiom,
% 52.23/52.34 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 52.23/52.34 ( class_Lattices_Olattice(T_b)
% 52.23/52.34 => 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)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_sup__assoc,axiom,
% 52.23/52.34 ! [V_z,V_y,V_x,T_a] :
% 52.23/52.34 ( class_Lattices_Osemilattice__sup(T_a)
% 52.23/52.34 => 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)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_inf__sup__aci_I6_J,axiom,
% 52.23/52.34 ! [V_z,V_y,V_x,T_a] :
% 52.23/52.34 ( class_Lattices_Olattice(T_a)
% 52.23/52.34 => 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)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_sup_Oassoc,axiom,
% 52.23/52.34 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.34 ( class_Lattices_Osemilattice__sup(T_a)
% 52.23/52.34 => 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)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_sup__left__commute,axiom,
% 52.23/52.34 ! [V_z,V_y,V_x,T_a] :
% 52.23/52.34 ( class_Lattices_Osemilattice__sup(T_a)
% 52.23/52.34 => 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)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_inf__sup__aci_I7_J,axiom,
% 52.23/52.34 ! [V_z,V_y,V_x,T_a] :
% 52.23/52.34 ( class_Lattices_Olattice(T_a)
% 52.23/52.34 => 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)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_sup_Oleft__commute,axiom,
% 52.23/52.34 ! [V_c,V_a,V_b,T_a] :
% 52.23/52.34 ( class_Lattices_Osemilattice__sup(T_a)
% 52.23/52.34 => 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)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_sup__left__idem,axiom,
% 52.23/52.34 ! [V_y,V_x,T_a] :
% 52.23/52.34 ( class_Lattices_Osemilattice__sup(T_a)
% 52.23/52.34 => 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) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_inf__sup__aci_I8_J,axiom,
% 52.23/52.34 ! [V_y,V_x,T_a] :
% 52.23/52.34 ( class_Lattices_Olattice(T_a)
% 52.23/52.34 => 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) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_sup_Oleft__idem,axiom,
% 52.23/52.34 ! [V_b,V_a,T_a] :
% 52.23/52.34 ( class_Lattices_Osemilattice__sup(T_a)
% 52.23/52.34 => 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) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_sup__commute,axiom,
% 52.23/52.34 ! [V_y,V_x,T_a] :
% 52.23/52.34 ( class_Lattices_Osemilattice__sup(T_a)
% 52.23/52.34 => 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) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_inf__sup__aci_I5_J,axiom,
% 52.23/52.34 ! [V_y,V_x,T_a] :
% 52.23/52.34 ( class_Lattices_Olattice(T_a)
% 52.23/52.34 => 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) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_sup_Ocommute,axiom,
% 52.23/52.34 ! [V_b,V_a,T_a] :
% 52.23/52.34 ( class_Lattices_Osemilattice__sup(T_a)
% 52.23/52.34 => 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) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_sup__idem,axiom,
% 52.23/52.34 ! [V_x,T_a] :
% 52.23/52.34 ( class_Lattices_Osemilattice__sup(T_a)
% 52.23/52.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_sup_Oidem,axiom,
% 52.23/52.34 ! [V_a,T_a] :
% 52.23/52.34 ( class_Lattices_Osemilattice__sup(T_a)
% 52.23/52.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_ball__Un,axiom,
% 52.23/52.34 ! [V_P_2,V_B_2,V_A_2,T_b] :
% 52.23/52.34 ( ! [B_x] :
% 52.23/52.34 ( 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)))
% 52.23/52.34 => hBOOL(hAPP(V_P_2,B_x)) )
% 52.23/52.34 <=> ( ! [B_x] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.23/52.34 => hBOOL(hAPP(V_P_2,B_x)) )
% 52.23/52.34 & ! [B_x] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 52.23/52.34 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_bex__Un,axiom,
% 52.23/52.34 ! [V_P_2,V_B_2,V_A_2,T_b] :
% 52.23/52.34 ( ? [B_x] :
% 52.23/52.34 ( 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)))
% 52.23/52.34 & hBOOL(hAPP(V_P_2,B_x)) )
% 52.23/52.34 <=> ( ? [B_x] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.23/52.34 & hBOOL(hAPP(V_P_2,B_x)) )
% 52.23/52.34 | ? [B_x] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 52.23/52.34 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Un__assoc,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Un__left__commute,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Un__left__absorb,axiom,
% 52.23/52.34 ! [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) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Un__commute,axiom,
% 52.23/52.34 ! [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) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Un__absorb,axiom,
% 52.23/52.34 ! [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 ).
% 52.23/52.34
% 52.23/52.34 fof(fact_sup1I2,axiom,
% 52.23/52.34 ! [V_A_2,T_b,V_x_2,V_B_2] :
% 52.23/52.34 ( hBOOL(hAPP(V_B_2,V_x_2))
% 52.23/52.34 => 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)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_sup1I1,axiom,
% 52.23/52.34 ! [V_B_2,T_b,V_x_2,V_A_2] :
% 52.23/52.34 ( hBOOL(hAPP(V_A_2,V_x_2))
% 52.23/52.34 => 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)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_transfer__int__nat__set__relations_I3_J,axiom,
% 52.23/52.34 ! [V_B_2,V_A_2] :
% 52.23/52.34 ( c_Nat__Transfer_Onat__set(V_A_2)
% 52.23/52.34 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 52.23/52.34 => ( V_A_2 = V_B_2
% 52.23/52.34 <=> 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) ) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_ivl__disj__un_I15_J,axiom,
% 52.23/52.34 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 52.23/52.34 ( class_Orderings_Olinorder(T_b)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 52.23/52.34 => 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) ) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_ivl__disj__un_I16_J,axiom,
% 52.23/52.34 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 52.23/52.34 ( class_Orderings_Olinorder(T_b)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 52.23/52.34 => 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) ) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_ivl__disj__un_I17_J,axiom,
% 52.23/52.34 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 52.23/52.34 ( class_Orderings_Olinorder(T_b)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 52.23/52.34 => 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) ) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Diff__subset__conv,axiom,
% 52.23/52.34 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 52.23/52.34 ( 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))
% 52.23/52.34 <=> 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))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Diff__partition,axiom,
% 52.23/52.34 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.34 => 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 ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_card__atLeastLessThan,axiom,
% 52.23/52.34 ! [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) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_ivl__disj__un_I20_J,axiom,
% 52.23/52.34 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 52.23/52.34 ( class_Orderings_Olinorder(T_b)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 52.23/52.34 => 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) ) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Compl__Diff__eq,axiom,
% 52.23/52.34 ! [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) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_ivl__disj__un_I18_J,axiom,
% 52.23/52.34 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 52.23/52.34 ( class_Orderings_Olinorder(T_b)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 52.23/52.34 => 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) ) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_ivl__disj__un_I19_J,axiom,
% 52.23/52.34 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 52.23/52.34 ( class_Orderings_Olinorder(T_b)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 52.23/52.34 => 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) ) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_card__greaterThanAtMost,axiom,
% 52.23/52.34 ! [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) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_nat__set__def,axiom,
% 52.23/52.34 ! [V_S_2] :
% 52.23/52.34 ( c_Nat__Transfer_Onat__set(V_S_2)
% 52.23/52.34 <=> ! [B_x] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2))
% 52.23/52.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_image__uminus__greaterThanLessThan,axiom,
% 52.23/52.34 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.34 ( class_Groups_Oordered__ab__group__add(T_b)
% 52.23/52.34 => 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)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom,
% 52.23/52.34 ! [V_y_2,V_x_2] :
% 52.23/52.34 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 52.23/52.34 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_card__atLeastAtMost,axiom,
% 52.23/52.34 ! [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) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_ivl__disj__un_I21_J,axiom,
% 52.23/52.34 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 52.23/52.34 ( class_Orderings_Olinorder(T_b)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 52.23/52.34 => 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) ) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_ivl__disj__un_I8_J,axiom,
% 52.23/52.34 ! [V_u_2,V_l_2,T_b] :
% 52.23/52.34 ( class_Orderings_Olinorder(T_b)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 52.23/52.34 => 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) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_ivl__disj__un_I22_J,axiom,
% 52.23/52.34 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 52.23/52.34 ( class_Orderings_Olinorder(T_b)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 52.23/52.34 => 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) ) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_ivl__disj__un_I11_J,axiom,
% 52.23/52.34 ! [V_u_2,V_l_2,T_b] :
% 52.23/52.34 ( class_Orderings_Olinorder(T_b)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 52.23/52.34 => 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) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_subset__card__intvl__is__intvl,axiom,
% 52.23/52.34 ! [V_k_2,V_A_2] :
% 52.23/52.34 ( 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)))))
% 52.23/52.34 => 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))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom,
% 52.23/52.34 ! [V_y_2,V_x_2] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 52.23/52.34 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_transfer__nat__int__set__return__embed,axiom,
% 52.23/52.34 ! [V_A_2] :
% 52.23/52.34 ( c_Nat__Transfer_Onat__set(V_A_2)
% 52.23/52.34 => 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 ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 52.23/52.34 ! [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) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_transfer__int__nat__set__relations_I5_J,axiom,
% 52.23/52.34 ! [V_B_2,V_A_2] :
% 52.23/52.34 ( c_Nat__Transfer_Onat__set(V_A_2)
% 52.23/52.34 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.34 <=> 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))) ) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_hoare__derivs_OBody,axiom,
% 52.23/52.34 ! [V_Procs_2,V_Q_2,V_P_2,V_Ga_2,T_b] :
% 52.23/52.34 ( 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))
% 52.23/52.34 => 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)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom,
% 52.23/52.34 ! [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))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_ivl__disj__un_I12_J,axiom,
% 52.23/52.34 ! [V_u_2,V_l_2,T_b] :
% 52.23/52.34 ( class_Orderings_Olinorder(T_b)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 52.23/52.34 => 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) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_ivl__disj__un_I7_J,axiom,
% 52.23/52.34 ! [V_u_2,V_l_2,T_b] :
% 52.23/52.34 ( class_Orderings_Olinorder(T_b)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 52.23/52.34 => 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) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom,
% 52.23/52.34 ! [V_B_2,V_A_2] :
% 52.23/52.34 ( c_Nat__Transfer_Onat__set(V_A_2)
% 52.23/52.34 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 52.23/52.34 => 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)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_sup__nat__def,axiom,
% 52.23/52.34 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_cut,axiom,
% 52.23/52.34 ! [V_Ga_2,V_tsa_2,V_G_H_2,T_b] :
% 52.23/52.34 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_tsa_2)
% 52.23/52.34 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_G_H_2)
% 52.23/52.34 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_atMost__eq__iff,axiom,
% 52.23/52.34 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.34 ( class_Orderings_Olinorder(T_b)
% 52.23/52.34 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)
% 52.23/52.34 <=> V_x_2 = V_y_2 ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_atLeast__eq__iff,axiom,
% 52.23/52.34 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.34 ( class_Orderings_Olinorder(T_b)
% 52.23/52.34 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)
% 52.23/52.34 <=> V_x_2 = V_y_2 ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_thin,axiom,
% 52.23/52.34 ! [V_Ga_2,V_tsa_2,V_G_H_2,T_b] :
% 52.23/52.34 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_tsa_2)
% 52.23/52.34 => ( 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))
% 52.23/52.34 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_weaken,axiom,
% 52.23/52.34 ! [V_tsa_2,V_ts_H_2,V_Ga_2,T_b] :
% 52.23/52.34 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_H_2)
% 52.23/52.34 => ( 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))
% 52.23/52.34 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_asm,axiom,
% 52.23/52.34 ! [V_Ga_2,V_tsa_2,T_b] :
% 52.23/52.34 ( 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))
% 52.23/52.34 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_card__atMost,axiom,
% 52.23/52.34 ! [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) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_image__uminus__atMost,axiom,
% 52.23/52.34 ! [V_x_2,T_b] :
% 52.23/52.34 ( class_Groups_Oordered__ab__group__add(T_b)
% 52.23/52.34 => 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)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_image__uminus__atLeast,axiom,
% 52.23/52.34 ! [V_x_2,T_b] :
% 52.23/52.34 ( class_Groups_Oordered__ab__group__add(T_b)
% 52.23/52.34 => 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)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_atLeast__Suc__greaterThan,axiom,
% 52.23/52.34 ! [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) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom,
% 52.23/52.34 ! [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))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom,
% 52.23/52.34 ! [V_B_2,V_A_2] :
% 52.23/52.34 ( c_Nat__Transfer_Onat__set(V_A_2)
% 52.23/52.34 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 52.23/52.34 => 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))) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_atLeast0AtMost,axiom,
% 52.23/52.34 ! [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) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_card__greaterThanLessThan,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_lessThan__Suc__atMost,axiom,
% 52.23/52.34 ! [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) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom,
% 52.23/52.34 ! [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) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_atLeast__subset__iff,axiom,
% 52.23/52.34 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.34 ( class_Orderings_Oorder(T_b)
% 52.23/52.34 => ( 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)))
% 52.23/52.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_atMost__subset__iff,axiom,
% 52.23/52.34 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.34 ( class_Orderings_Oorder(T_b)
% 52.23/52.34 => ( 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)))
% 52.23/52.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_atLeastLessThan__add__Un,axiom,
% 52.23/52.34 ! [V_k_2,V_j_2,V_i_2] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 52.23/52.34 => 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))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Compl__lessThan,axiom,
% 52.23/52.34 ! [V_k_2,T_b] :
% 52.23/52.34 ( class_Orderings_Olinorder(T_b)
% 52.23/52.34 => 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) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Compl__atLeast,axiom,
% 52.23/52.34 ! [V_k_2,T_b] :
% 52.23/52.34 ( class_Orderings_Olinorder(T_b)
% 52.23/52.34 => 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) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Compl__atMost,axiom,
% 52.23/52.34 ! [V_k_2,T_b] :
% 52.23/52.34 ( class_Orderings_Olinorder(T_b)
% 52.23/52.34 => 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) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Compl__greaterThan,axiom,
% 52.23/52.34 ! [V_k_2,T_b] :
% 52.23/52.34 ( class_Orderings_Olinorder(T_b)
% 52.23/52.34 => 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) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_setsum__atMost__Suc,axiom,
% 52.23/52.34 ! [V_n_2,V_f_2,T_b] :
% 52.23/52.34 ( class_Groups_Ocomm__monoid__add(T_b)
% 52.23/52.34 => 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))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_ivl__disj__un_I14_J,axiom,
% 52.23/52.34 ! [V_u_2,V_l_2,T_b] :
% 52.23/52.34 ( class_Orderings_Olinorder(T_b)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 52.23/52.34 => 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) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_ivl__disj__un_I9_J,axiom,
% 52.23/52.34 ! [V_u_2,V_l_2,T_b] :
% 52.23/52.34 ( class_Orderings_Olinorder(T_b)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 52.23/52.34 => 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) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_ivl__disj__un_I10_J,axiom,
% 52.23/52.34 ! [V_u_2,V_l_2,T_b] :
% 52.23/52.34 ( class_Orderings_Olinorder(T_b)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 52.23/52.34 => 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) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_ivl__disj__un_I13_J,axiom,
% 52.23/52.34 ! [V_u_2,V_l_2,T_b] :
% 52.23/52.34 ( class_Orderings_Olinorder(T_b)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 52.23/52.34 => 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) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom,
% 52.23/52.34 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 52.23/52.34 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 52.23/52.34 & class_Groups_Ocomm__monoid__mult(T_b) )
% 52.23/52.34 => ( V_A_2 = V_B_2
% 52.23/52.34 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 52.23/52.34 => ( ! [B_x] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 52.23/52.34 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 52.23/52.34 => 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) ) ) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UN__le__eq__Un0,axiom,
% 52.23/52.34 ! [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))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_dvd_OatLeastatMost__psubset__iff,axiom,
% 52.23/52.34 ! [V_d_2,V_c_2,V_b_2,V_a_2] :
% 52.23/52.34 ( 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)))
% 52.23/52.34 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 52.23/52.34 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2))
% 52.23/52.34 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2))
% 52.23/52.34 & ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2))
% 52.23/52.34 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_c_2)) )
% 52.23/52.34 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2))
% 52.23/52.34 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_d_2),V_b_2)) ) ) ) )
% 52.23/52.34 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_d_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_dvd_OmonoI,axiom,
% 52.23/52.34 ! [V_f_2,T_b] :
% 52.23/52.34 ( class_Orderings_Oorder(T_b)
% 52.23/52.34 => ( ! [B_x,B_y] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_x),B_y))
% 52.23/52.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_f_2,B_y))) )
% 52.23/52.34 => c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_SUP1__iff,axiom,
% 52.23/52.34 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 52.23/52.34 ( 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))
% 52.23/52.34 <=> ? [B_x] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.23/52.34 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UN__le__add__shift,axiom,
% 52.23/52.34 ! [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) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_dvd_OatLeastatMost__subset__iff,axiom,
% 52.23/52.34 ! [V_d_2,V_c_2,V_b_2,V_a_2] :
% 52.23/52.34 ( 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)))
% 52.23/52.34 <=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 52.23/52.34 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2))
% 52.23/52.34 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2)) ) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_SUP__subset,axiom,
% 52.23/52.34 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 52.23/52.34 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.34 => 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))) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UN__extend__simps_I6_J,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UN__simps_I6_J,axiom,
% 52.23/52.34 ! [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) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_SUPR__apply,axiom,
% 52.23/52.34 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 52.23/52.34 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 52.23/52.34 => 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)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_ball__UN,axiom,
% 52.23/52.34 ! [V_P_2,V_B_2,V_A_2,T_c,T_b] :
% 52.23/52.34 ( ! [B_x] :
% 52.23/52.34 ( 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)))
% 52.23/52.34 => hBOOL(hAPP(V_P_2,B_x)) )
% 52.23/52.34 <=> ! [B_x] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 52.23/52.34 => ! [B_xa] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x)))
% 52.23/52.34 => hBOOL(hAPP(V_P_2,B_xa)) ) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_SUP__commute,axiom,
% 52.23/52.34 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 52.23/52.34 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 52.23/52.34 => 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))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UN__UN__flatten,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UN__simps_I9_J,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UN__extend__simps_I9_J,axiom,
% 52.23/52.34 ! [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) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_SUP__le__iff,axiom,
% 52.23/52.34 ! [V_u_2,V_M_2,V_A_2,T_c,T_b] :
% 52.23/52.34 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 52.23/52.34 => ( 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))
% 52.23/52.34 <=> ! [B_x] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 52.23/52.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_less__SUP__iff,axiom,
% 52.23/52.34 ! [V_f_2,V_A_2,T_c,V_a_2,T_b] :
% 52.23/52.34 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 52.23/52.34 & class_Orderings_Olinorder(T_b) )
% 52.23/52.34 => ( 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)))
% 52.23/52.34 <=> ? [B_x] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 52.23/52.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UN__subset__iff,axiom,
% 52.23/52.34 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] :
% 52.23/52.34 ( 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))
% 52.23/52.34 <=> ! [B_x] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 52.23/52.34 => 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)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UN__extend__simps_I10_J,axiom,
% 52.23/52.34 ! [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) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_image__UN,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UN__simps_I10_J,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UN__Un,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UN__Un__distrib,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_greaterThan__0,axiom,
% 52.23/52.34 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))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_upto_Opinduct,axiom,
% 52.23/52.34 ! [V_P_2,V_a1_2,V_a0_2] :
% 52.23/52.34 ( 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)))
% 52.23/52.34 => ( ! [B_i,B_j] :
% 52.23/52.34 ( 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)))
% 52.23/52.34 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j))
% 52.23/52.34 => 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)) )
% 52.23/52.34 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) )
% 52.23/52.34 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_image__ident,axiom,
% 52.23/52.34 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 52.23/52.34
% 52.23/52.34 fof(fact_lessThan__Suc__eq__insert__0,axiom,
% 52.23/52.34 ! [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))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_top1I,axiom,
% 52.23/52.34 ! [V_x_2,T_b] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_top__apply,axiom,
% 52.23/52.34 ! [V_x_2,T_c,T_b] :
% 52.23/52.34 ( class_Orderings_Otop(T_b)
% 52.23/52.34 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_insert__code,axiom,
% 52.23/52.34 ! [V_x_2,V_A_2,V_y_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2))
% 52.23/52.34 <=> ( V_y_2 = V_x_2
% 52.23/52.34 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_insert__commute,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_insert__absorb2,axiom,
% 52.23/52.34 ! [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) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_image__insert,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_subset__UNIV,axiom,
% 52.23/52.34 ! [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)))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_subset__insertI,axiom,
% 52.23/52.34 ! [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))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_subset__insertI2,axiom,
% 52.23/52.34 ! [V_b_2,V_B_2,V_A_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.34 => 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))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_insert__mono,axiom,
% 52.23/52.34 ! [V_a_2,V_D_2,V_C_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))
% 52.23/52.34 => 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))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Un__UNIV__left,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Un__UNIV__right,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Un__insert__right,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Un__insert__left,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_range__composition,axiom,
% 52.23/52.34 ! [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)))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_top__greatest,axiom,
% 52.23/52.34 ! [V_x,T_a] :
% 52.23/52.34 ( class_Orderings_Otop(T_a)
% 52.23/52.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_sup__top__right,axiom,
% 52.23/52.34 ! [V_x,T_a] :
% 52.23/52.34 ( class_Lattices_Obounded__lattice__top(T_a)
% 52.23/52.34 => 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) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_sup__top__left,axiom,
% 52.23/52.34 ! [V_x,T_a] :
% 52.23/52.34 ( class_Lattices_Obounded__lattice__top(T_a)
% 52.23/52.34 => 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) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UN__lessThan__UNIV,axiom,
% 52.23/52.34 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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UN__atMost__UNIV,axiom,
% 52.23/52.34 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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UN__atLeast__UNIV,axiom,
% 52.23/52.34 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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_surj__Compl__image__subset,axiom,
% 52.23/52.34 ! [V_A_2,V_f_2,T_b,T_c] :
% 52.23/52.34 ( 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))
% 52.23/52.34 => 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)))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Compl__partition2,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Compl__partition,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_lessThan__Suc,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Compl__eq__Diff__UNIV,axiom,
% 52.23/52.34 ! [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) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_atMost__Suc,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UN__insert,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_atLeast__0,axiom,
% 52.23/52.34 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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_compl__sup__top,axiom,
% 52.23/52.34 ! [V_x,T_a] :
% 52.23/52.34 ( class_Lattices_Oboolean__algebra(T_a)
% 52.23/52.34 => 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) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_sup__compl__top,axiom,
% 52.23/52.34 ! [V_x,T_a] :
% 52.23/52.34 ( class_Lattices_Oboolean__algebra(T_a)
% 52.23/52.34 => 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) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_atLeastAtMostSuc__conv,axiom,
% 52.23/52.34 ! [V_n_2,V_m_2] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 52.23/52.34 => 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)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UN__UN__finite__eq,axiom,
% 52.23/52.34 ! [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) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UN__finite2__subset,axiom,
% 52.23/52.34 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 52.23/52.34 ( ! [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)))
% 52.23/52.34 => 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))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
% 52.23/52.34 ! [V_x_2,V_y_2,V_c_2] :
% 52.23/52.34 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2))
% 52.23/52.34 => 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)) )
% 52.23/52.34 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2))
% 52.23/52.34 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 52.23/52.34 => 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))) )
% 52.23/52.34 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 52.23/52.34 => 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)) ) ) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UN__finite2__eq,axiom,
% 52.23/52.34 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 52.23/52.34 ( ! [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)
% 52.23/52.34 => 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) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UN__finite__subset,axiom,
% 52.23/52.34 ! [V_C_2,V_A_2,T_b] :
% 52.23/52.34 ( ! [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))
% 52.23/52.34 => 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)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_empty__subsetI,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_singleton__inject,axiom,
% 52.23/52.34 ! [V_b_2,V_a_2,T_b] :
% 52.23/52.34 ( 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)))
% 52.23/52.34 => V_a_2 = V_b_2 ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_doubleton__eq__iff,axiom,
% 52.23/52.34 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 52.23/52.34 ( 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))))
% 52.23/52.34 <=> ( ( V_a_2 = V_c_2
% 52.23/52.34 & V_b_2 = V_d_2 )
% 52.23/52.34 | ( V_a_2 = V_d_2
% 52.23/52.34 & V_b_2 = V_c_2 ) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_insert__not__empty,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_empty__not__insert,axiom,
% 52.23/52.34 ! [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) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UNIV__not__empty,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Un__empty,axiom,
% 52.23/52.34 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.34 ( 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))
% 52.23/52.34 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.34 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Un__empty__right,axiom,
% 52.23/52.34 ! [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 ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Un__empty__left,axiom,
% 52.23/52.34 ! [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 ).
% 52.23/52.34
% 52.23/52.34 fof(fact_subset__empty,axiom,
% 52.23/52.34 ! [V_A_2,T_b] :
% 52.23/52.34 ( 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))))
% 52.23/52.34 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_not__psubset__empty,axiom,
% 52.23/52.34 ! [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)))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_image__is__empty,axiom,
% 52.23/52.34 ! [V_A_2,V_f_2,T_b,T_c] :
% 52.23/52.34 ( 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))
% 52.23/52.34 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_image__empty,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_empty__is__image,axiom,
% 52.23/52.34 ! [V_A_2,V_f_2,T_c,T_b] :
% 52.23/52.34 ( 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)
% 52.23/52.34 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_ball__empty,axiom,
% 52.23/52.34 ! [V_P_2,T_b,B_x] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 52.23/52.34 => hBOOL(hAPP(V_P_2,B_x)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_empty__Diff,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Diff__empty,axiom,
% 52.23/52.34 ! [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 ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Diff__cancel,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_bot__apply,axiom,
% 52.23/52.34 ! [V_x_2,T_c,T_b] :
% 52.23/52.34 ( class_Orderings_Obot(T_b)
% 52.23/52.34 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_bot__fun__def,axiom,
% 52.23/52.34 ! [V_x_2,T_c,T_b] :
% 52.23/52.34 ( class_Orderings_Obot(T_b)
% 52.23/52.34 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_bot__least,axiom,
% 52.23/52.34 ! [V_x,T_a] :
% 52.23/52.34 ( class_Orderings_Obot(T_a)
% 52.23/52.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_SUP__const,axiom,
% 52.23/52.34 ! [V_M_2,T_b,V_A_2,T_c] :
% 52.23/52.34 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 52.23/52.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.34 => 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 ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UNION__empty__conv_I1_J,axiom,
% 52.23/52.34 ! [V_B_2,V_A_2,T_c,T_b] :
% 52.23/52.34 ( 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)
% 52.23/52.34 <=> ! [B_x] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 52.23/52.34 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UN__empty2,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UN__constant,axiom,
% 52.23/52.34 ! [V_c_2,T_c,T_b,V_A_2] :
% 52.23/52.34 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.34 => 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)) )
% 52.23/52.34 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.34 => 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 ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UNION__empty__conv_I2_J,axiom,
% 52.23/52.34 ! [V_B_2,V_A_2,T_b,T_c] :
% 52.23/52.34 ( 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))
% 52.23/52.34 <=> ! [B_x] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 52.23/52.34 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_sup__bot__left,axiom,
% 52.23/52.34 ! [V_x,T_a] :
% 52.23/52.34 ( class_Lattices_Obounded__lattice__bot(T_a)
% 52.23/52.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_sup__bot__right,axiom,
% 52.23/52.34 ! [V_x,T_a] :
% 52.23/52.34 ( class_Lattices_Obounded__lattice__bot(T_a)
% 52.23/52.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_sup__eq__bot__iff,axiom,
% 52.23/52.34 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.34 ( class_Lattices_Obounded__lattice__bot(T_b)
% 52.23/52.34 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_b)
% 52.23/52.34 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_b)
% 52.23/52.34 & V_y_2 = c_Orderings_Obot__class_Obot(T_b) ) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_setsum__empty,axiom,
% 52.23/52.34 ! [V_f_2,T_c,T_b] :
% 52.23/52.34 ( class_Groups_Ocomm__monoid__add(T_b)
% 52.23/52.34 => 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) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_setsum_Oempty,axiom,
% 52.23/52.34 ! [V_g_2,T_c,T_b] :
% 52.23/52.34 ( class_Groups_Ocomm__monoid__add(T_b)
% 52.23/52.34 => 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) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_subset__singletonD,axiom,
% 52.23/52.34 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.34 ( 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)))))
% 52.23/52.34 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.34 | V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_insert__is__Un,axiom,
% 52.23/52.34 ! [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) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_atLeastatMost__empty__iff2,axiom,
% 52.23/52.34 ! [V_b_2,V_a_2,T_b] :
% 52.23/52.34 ( class_Orderings_Oorder(T_b)
% 52.23/52.34 => ( 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)
% 52.23/52.34 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_atLeastatMost__empty__iff,axiom,
% 52.23/52.34 ! [V_b_2,V_a_2,T_b] :
% 52.23/52.34 ( class_Orderings_Oorder(T_b)
% 52.23/52.34 => ( 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))
% 52.23/52.34 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_atLeastatMost__empty,axiom,
% 52.23/52.34 ! [V_a_2,V_b_2,T_b] :
% 52.23/52.34 ( class_Orderings_Oorder(T_b)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
% 52.23/52.34 => 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)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Diff__insert,axiom,
% 52.23/52.34 ! [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)))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Diff__insert2,axiom,
% 52.23/52.34 ! [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) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_insert__Diff__single,axiom,
% 52.23/52.34 ! [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) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_atLeastLessThan__empty,axiom,
% 52.23/52.34 ! [V_a_2,V_b_2,T_b] :
% 52.23/52.34 ( class_Orderings_Oorder(T_b)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
% 52.23/52.34 => 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)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_atLeastLessThan__empty__iff2,axiom,
% 52.23/52.34 ! [V_b_2,V_a_2,T_b] :
% 52.23/52.34 ( class_Orderings_Oorder(T_b)
% 52.23/52.34 => ( 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)
% 52.23/52.34 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_atLeastLessThan__empty__iff,axiom,
% 52.23/52.34 ! [V_b_2,V_a_2,T_b] :
% 52.23/52.34 ( class_Orderings_Oorder(T_b)
% 52.23/52.34 => ( 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))
% 52.23/52.34 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Diff__UNIV,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_atLeastAtMost__singleton_H,axiom,
% 52.23/52.34 ! [V_b_2,V_a_2,T_b] :
% 52.23/52.34 ( class_Orderings_Oorder(T_b)
% 52.23/52.34 => ( V_a_2 = V_b_2
% 52.23/52.34 => 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))) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_atLeastAtMost__singleton__iff,axiom,
% 52.23/52.34 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 52.23/52.34 ( class_Orderings_Oorder(T_b)
% 52.23/52.34 => ( 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)))
% 52.23/52.34 <=> ( V_a_2 = V_b_2
% 52.23/52.34 & V_b_2 = V_c_2 ) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_atLeastAtMost__singleton,axiom,
% 52.23/52.34 ! [V_a_2,T_b] :
% 52.23/52.34 ( class_Orderings_Oorder(T_b)
% 52.23/52.34 => 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))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_subset__Compl__self__eq,axiom,
% 52.23/52.34 ! [V_A_2,T_b] :
% 52.23/52.34 ( 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)))
% 52.23/52.34 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Compl__empty__eq,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Compl__UNIV__eq,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_atLeastLessThan0,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_greaterThanAtMost__empty,axiom,
% 52.23/52.34 ! [V_k_2,V_l_2,T_b] :
% 52.23/52.34 ( class_Orderings_Oorder(T_b)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 52.23/52.34 => 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)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_greaterThanAtMost__empty__iff2,axiom,
% 52.23/52.34 ! [V_l_2,V_k_2,T_b] :
% 52.23/52.34 ( class_Orderings_Oorder(T_b)
% 52.23/52.34 => ( 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)
% 52.23/52.34 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_greaterThanAtMost__empty__iff,axiom,
% 52.23/52.34 ! [V_l_2,V_k_2,T_b] :
% 52.23/52.34 ( class_Orderings_Oorder(T_b)
% 52.23/52.34 => ( 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))
% 52.23/52.34 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_greaterThanLessThan__empty,axiom,
% 52.23/52.34 ! [V_k_2,V_l_2,T_b] :
% 52.23/52.34 ( class_Orderings_Oorder(T_b)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 52.23/52.34 => 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)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_lessThan__0,axiom,
% 52.23/52.34 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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_image__constant__conv,axiom,
% 52.23/52.34 ! [V_c_2,T_c,T_b,V_A_2] :
% 52.23/52.34 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.34 => 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)) )
% 52.23/52.34 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.34 => 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))) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UN__extend__simps_I1_J,axiom,
% 52.23/52.34 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 52.23/52.34 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.34 => 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))) )
% 52.23/52.34 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.34 => 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)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UN__singleton,axiom,
% 52.23/52.34 ! [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 ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UN__simps_I1_J,axiom,
% 52.23/52.34 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 52.23/52.34 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.34 => 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)) )
% 52.23/52.34 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.34 => 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)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_dvd_OatLeastatMost__empty,axiom,
% 52.23/52.34 ! [V_a_2,V_b_2] :
% 52.23/52.34 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2))
% 52.23/52.34 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) )
% 52.23/52.34 => 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)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_dvd_OatLeastatMost__empty__iff,axiom,
% 52.23/52.34 ! [V_b_2,V_a_2] :
% 52.23/52.34 ( 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))
% 52.23/52.34 <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_dvd_OatLeastatMost__empty__iff2,axiom,
% 52.23/52.34 ! [V_b_2,V_a_2] :
% 52.23/52.34 ( 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)
% 52.23/52.34 <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UN__extend__simps_I2_J,axiom,
% 52.23/52.34 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 52.23/52.34 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.34 => 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 )
% 52.23/52.34 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.34 => 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)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UN__extend__simps_I3_J,axiom,
% 52.23/52.34 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 52.23/52.34 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.34 => 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 )
% 52.23/52.34 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.34 => 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)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UN__simps_I2_J,axiom,
% 52.23/52.34 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 52.23/52.34 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.34 => 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)) )
% 52.23/52.34 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.34 => 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) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UN__simps_I3_J,axiom,
% 52.23/52.34 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 52.23/52.34 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.34 => 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)) )
% 52.23/52.34 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.34 => 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)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_compl__top__eq,axiom,
% 52.23/52.34 ! [T_a] :
% 52.23/52.34 ( class_Lattices_Oboolean__algebra(T_a)
% 52.23/52.34 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_compl__bot__eq,axiom,
% 52.23/52.34 ! [T_a] :
% 52.23/52.34 ( class_Lattices_Oboolean__algebra(T_a)
% 52.23/52.34 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UNIV__option__conv,axiom,
% 52.23/52.34 ! [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)))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_single__Diff__lessThan,axiom,
% 52.23/52.34 ! [V_k_2,T_b] :
% 52.23/52.34 ( class_Orderings_Oorder(T_b)
% 52.23/52.34 => 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))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_image__eq__UN,axiom,
% 52.23/52.34 ! [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)))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_atLeastLessThan__singleton,axiom,
% 52.23/52.34 ! [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))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_atMost__0,axiom,
% 52.23/52.34 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))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_dvd_OatLeastAtMost__singleton__iff,axiom,
% 52.23/52.34 ! [V_c_2,V_b_2,V_a_2] :
% 52.23/52.34 ( 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)))
% 52.23/52.34 <=> ( V_a_2 = V_b_2
% 52.23/52.34 & V_b_2 = V_c_2 ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_dvd_OatLeastAtMost__singleton,axiom,
% 52.23/52.34 ! [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))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_dvd_OatLeastAtMost__singleton_H,axiom,
% 52.23/52.34 ! [V_b_2,V_a_2] :
% 52.23/52.34 ( V_a_2 = V_b_2
% 52.23/52.34 => 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))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_atLeast__Suc,axiom,
% 52.23/52.34 ! [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)))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_greaterThan__Suc,axiom,
% 52.23/52.34 ! [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)))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_card__UNIV__bool,axiom,
% 52.23/52.34 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))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_ivl__disj__un_I2_J,axiom,
% 52.23/52.34 ! [V_u_2,T_b] :
% 52.23/52.34 ( class_Orderings_Olinorder(T_b)
% 52.23/52.34 => 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) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_atLeastLessThanSuc,axiom,
% 52.23/52.34 ! [V_n_2,V_m_2] :
% 52.23/52.34 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 52.23/52.34 => 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)) )
% 52.23/52.34 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 52.23/52.34 => 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)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_ivl__disj__un_I1_J,axiom,
% 52.23/52.34 ! [V_l_2,T_b] :
% 52.23/52.34 ( class_Orderings_Olinorder(T_b)
% 52.23/52.34 => 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) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_ivl__disj__un_I6_J,axiom,
% 52.23/52.34 ! [V_u_2,V_l_2,T_b] :
% 52.23/52.34 ( class_Orderings_Olinorder(T_b)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 52.23/52.34 => 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) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_ivl__disj__un_I5_J,axiom,
% 52.23/52.34 ! [V_u_2,V_l_2,T_b] :
% 52.23/52.34 ( class_Orderings_Olinorder(T_b)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 52.23/52.34 => 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) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_ivl__disj__un_I3_J,axiom,
% 52.23/52.34 ! [V_u_2,V_l_2,T_b] :
% 52.23/52.34 ( class_Orderings_Olinorder(T_b)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 52.23/52.34 => 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) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_ivl__disj__un_I4_J,axiom,
% 52.23/52.34 ! [V_u_2,V_l_2,T_b] :
% 52.23/52.34 ( class_Orderings_Olinorder(T_b)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 52.23/52.34 => 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) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_the__elem__def,axiom,
% 52.23/52.34 ! [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))))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_card_Oempty,axiom,
% 52.23/52.34 ! [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) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_dvd_OgreaterThanLessThan__empty,axiom,
% 52.23/52.34 ! [V_k_2,V_l_2] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
% 52.23/52.34 => 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)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_the__elem__eq,axiom,
% 52.23/52.34 ! [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 ).
% 52.23/52.34
% 52.23/52.34 fof(fact_derivs__insertD,axiom,
% 52.23/52.34 ! [V_tsa_2,V_t_2,V_Ga_2,T_b] :
% 52.23/52.34 ( 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))
% 52.23/52.34 => ( 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))))
% 52.23/52.34 & c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_hoare__derivs_Oinsert,axiom,
% 52.23/52.34 ! [V_tsa_2,V_t_2,V_Ga_2,T_b] :
% 52.23/52.34 ( 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))))
% 52.23/52.34 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2)
% 52.23/52.34 => 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)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom,
% 52.23/52.34 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_empty,axiom,
% 52.23/52.34 ! [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))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_hoare__derivs_Oequations_I1_J,axiom,
% 52.23/52.34 ! [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))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_bot__nat__def,axiom,
% 52.23/52.34 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_card__UNIV__unit,axiom,
% 52.23/52.34 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) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Comp,axiom,
% 52.23/52.34 ! [V_R_2,V_d_2,V_Q_2,V_c_2,V_P_2,V_Ga_2,T_b] :
% 52.23/52.34 ( 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))))
% 52.23/52.34 => ( 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))))
% 52.23/52.34 => 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)))) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_hoare__derivs_OSkip,axiom,
% 52.23/52.34 ! [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)))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_hoare__derivs_Oequations_I7_J,axiom,
% 52.23/52.34 ! [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)))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
% 52.23/52.34 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))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom,
% 52.23/52.34 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))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_LoopF,axiom,
% 52.23/52.34 ! [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)))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_simp__from__to,axiom,
% 52.23/52.34 ! [V_i_2,V_j_2] :
% 52.23/52.34 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 52.23/52.34 => 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)) )
% 52.23/52.34 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 52.23/52.34 => 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)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Ass,axiom,
% 52.23/52.34 ! [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)))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_hoare__derivs_Oequations_I8_J,axiom,
% 52.23/52.34 ! [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)))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_weak__Body,axiom,
% 52.23/52.34 ! [V_Q_2,V_pn_2,V_P_2,V_Ga_2,T_b] :
% 52.23/52.34 ( 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))))
% 52.23/52.34 => 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)))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_BodyN,axiom,
% 52.23/52.34 ! [V_Ga_2,V_Q_2,V_pn_2,V_P_2,T_b] :
% 52.23/52.34 ( 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))))
% 52.23/52.34 => 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)))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Body1,axiom,
% 52.23/52.34 ! [V_pn_2,V_Procs_2,V_Q_2,V_P_2,V_Ga_2,T_b] :
% 52.23/52.34 ( 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))
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),V_pn_2),V_Procs_2))
% 52.23/52.34 => 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)))) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_nat__def,axiom,
% 52.23/52.34 ! [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)))))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Option_Oset_Osimps_I2_J,axiom,
% 52.23/52.34 ! [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))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_dvd_OatLeastLessThan__empty__iff2,axiom,
% 52.23/52.34 ! [V_b_2,V_a_2] :
% 52.23/52.34 ( 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)
% 52.23/52.34 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 52.23/52.34 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_equalityCE,axiom,
% 52.23/52.34 ! [V_c_2,T_b,V_B_2,V_A_2] :
% 52.23/52.34 ( V_A_2 = V_B_2
% 52.23/52.34 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 52.23/52.34 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) )
% 52.23/52.34 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 52.23/52.34 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_SUP2__I,axiom,
% 52.23/52.34 ! [T_d,T_c,V_c_2,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
% 52.23/52.34 => 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)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_emptyE,axiom,
% 52.23/52.34 ! [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)))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_insertE,axiom,
% 52.23/52.34 ! [V_A_2,V_b_2,V_a_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
% 52.23/52.34 => ( V_a_2 != V_b_2
% 52.23/52.34 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_insertCI,axiom,
% 52.23/52.34 ! [V_b_2,V_B_2,V_a_2,T_b] :
% 52.23/52.34 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 52.23/52.34 => V_a_2 = V_b_2 )
% 52.23/52.34 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_subsetD,axiom,
% 52.23/52.34 ! [V_c_2,V_B_2,V_A_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 52.23/52.34 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UNIV__I,axiom,
% 52.23/52.34 ! [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)))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_image__eqI,axiom,
% 52.23/52.34 ! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_b_2] :
% 52.23/52.34 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 52.23/52.34 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UnCI,axiom,
% 52.23/52.34 ! [V_A_2,V_B_2,V_c_2,T_b] :
% 52.23/52.34 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 52.23/52.34 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
% 52.23/52.34 => 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))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UnE,axiom,
% 52.23/52.34 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 52.23/52.34 ( 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)))
% 52.23/52.34 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 52.23/52.34 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_DiffI,axiom,
% 52.23/52.34 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 52.23/52.34 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 52.23/52.34 => 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))) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_DiffE,axiom,
% 52.23/52.34 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 52.23/52.34 ( 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)))
% 52.23/52.34 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 52.23/52.34 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_ComplI,axiom,
% 52.23/52.34 ! [V_A_2,V_c_2,T_b] :
% 52.23/52.34 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 52.23/52.34 => 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))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UN__I,axiom,
% 52.23/52.34 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
% 52.23/52.34 => 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))) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_SUP1__I,axiom,
% 52.23/52.34 ! [T_c,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 52.23/52.34 => 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)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_mem__splitI,axiom,
% 52.23/52.34 ! [T_d,T_c,V_b_2,V_a_2,V_c_2,V_z_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,V_a_2),V_b_2)))
% 52.23/52.34 => 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)))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_pair__imageI,axiom,
% 52.23/52.34 ! [V_f_2,T_d,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 52.23/52.34 ( 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))
% 52.23/52.34 => 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))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_insert__absorb,axiom,
% 52.23/52.34 ! [V_A_2,V_a_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.23/52.34 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_insertI2,axiom,
% 52.23/52.34 ! [V_b_2,V_B_2,V_a_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 52.23/52.34 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_insert__ident,axiom,
% 52.23/52.34 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 52.23/52.34 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.34 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 52.23/52.34 => ( 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)
% 52.23/52.34 <=> V_A_2 = V_B_2 ) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_insert__iff,axiom,
% 52.23/52.34 ! [V_A_2,V_b_2,V_a_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
% 52.23/52.34 <=> ( V_a_2 = V_b_2
% 52.23/52.34 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_insertI1,axiom,
% 52.23/52.34 ! [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))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_all__not__in__conv,axiom,
% 52.23/52.34 ! [V_A_2,T_b] :
% 52.23/52.34 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.23/52.34 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_ex__in__conv,axiom,
% 52.23/52.34 ! [V_A_2,T_b] :
% 52.23/52.34 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.23/52.34 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_empty__iff,axiom,
% 52.23/52.34 ! [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)))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_equals0D,axiom,
% 52.23/52.34 ! [V_a_2,T_b,V_A_2] :
% 52.23/52.34 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.34 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_DiffD2,axiom,
% 52.23/52.34 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 52.23/52.34 ( 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)))
% 52.23/52.34 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_DiffD1,axiom,
% 52.23/52.34 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 52.23/52.34 ( 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)))
% 52.23/52.34 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Diff__iff,axiom,
% 52.23/52.34 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 52.23/52.34 ( 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)))
% 52.23/52.34 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 52.23/52.34 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_image__iff,axiom,
% 52.23/52.34 ! [V_A_2,V_f_2,T_c,V_z_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 52.23/52.34 <=> ? [B_x] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 52.23/52.34 & V_z_2 = hAPP(V_f_2,B_x) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_imageI,axiom,
% 52.23/52.34 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.34 => 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))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_rev__image__eqI,axiom,
% 52.23/52.34 ! [T_c,V_f_2,V_b_2,V_A_2,V_x_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.34 => ( V_b_2 = hAPP(V_f_2,V_x_2)
% 52.23/52.34 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UnI2,axiom,
% 52.23/52.34 ! [V_A_2,V_B_2,V_c_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 52.23/52.34 => 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))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UnI1,axiom,
% 52.23/52.34 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 52.23/52.34 => 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))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Un__iff,axiom,
% 52.23/52.34 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 52.23/52.34 ( 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)))
% 52.23/52.34 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 52.23/52.34 | hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_set__mp,axiom,
% 52.23/52.34 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.34 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_set__rev__mp,axiom,
% 52.23/52.34 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.34 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_in__mono,axiom,
% 52.23/52.34 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.34 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Compl__iff,axiom,
% 52.23/52.34 ! [V_A_2,V_c_2,T_b] :
% 52.23/52.34 ( 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)))
% 52.23/52.34 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_ComplD,axiom,
% 52.23/52.34 ! [V_A_2,V_c_2,T_b] :
% 52.23/52.34 ( 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)))
% 52.23/52.34 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_ComplE,axiom,
% 52.23/52.34 ! [V_A_2,V_c_2,T_b] :
% 52.23/52.34 ( 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)))
% 52.23/52.34 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_pred__equals__eq,axiom,
% 52.23/52.34 ! [V_S_2,V_R_2,T_b] :
% 52.23/52.34 ( 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)
% 52.23/52.34 <=> V_R_2 = V_S_2 ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_eq__mem,axiom,
% 52.23/52.34 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2)))
% 52.23/52.34 <=> V_x_2 = V_y_2 ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_mem__def,axiom,
% 52.23/52.34 ! [V_A_2,V_x_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.34 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_eqset__imp__iff,axiom,
% 52.23/52.34 ! [V_x_2,T_b,V_B_2,V_A_2] :
% 52.23/52.34 ( V_A_2 = V_B_2
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.34 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_eqelem__imp__iff,axiom,
% 52.23/52.34 ! [V_A_2,T_b,V_y_2,V_x_2] :
% 52.23/52.34 ( V_x_2 = V_y_2
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.34 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_eq__mem__trans,axiom,
% 52.23/52.34 ! [V_A_2,T_b,V_b_2,V_a_2] :
% 52.23/52.34 ( V_a_2 = V_b_2
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 52.23/52.34 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_elem__set,axiom,
% 52.23/52.34 ! [V_xo_2,V_x_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Option_Oset(T_b,V_xo_2)))
% 52.23/52.34 <=> V_xo_2 = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Rep__Integ__inject,axiom,
% 52.23/52.34 ! [V_y_2,V_x_2] :
% 52.23/52.34 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2)
% 52.23/52.34 <=> V_x_2 = V_y_2 ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_ord_OatLeastLessThan__iff,axiom,
% 52.23/52.34 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 52.23/52.34 ( 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)))
% 52.23/52.34 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 52.23/52.34 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_psubsetD,axiom,
% 52.23/52.34 ! [V_c_2,V_B_2,V_A_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 52.23/52.34 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_bot__empty__eq,axiom,
% 52.23/52.34 ! [V_x_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2))
% 52.23/52.34 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_ord_OatLeastAtMost__iff,axiom,
% 52.23/52.34 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_b] :
% 52.23/52.34 ( 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)))
% 52.23/52.34 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 52.23/52.34 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_pred__subset__eq,axiom,
% 52.23/52.34 ! [V_S_2,V_R_2,T_b] :
% 52.23/52.34 ( 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)))
% 52.23/52.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_sup__Un__eq,axiom,
% 52.23/52.34 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 52.23/52.34 ( 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))
% 52.23/52.34 <=> 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))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UN__iff,axiom,
% 52.23/52.34 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 52.23/52.34 ( 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)))
% 52.23/52.34 <=> ? [B_x] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 52.23/52.34 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_singletonE,axiom,
% 52.23/52.34 ! [V_a_2,V_b_2,T_b] :
% 52.23/52.34 ( 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)))))
% 52.23/52.34 => V_b_2 = V_a_2 ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_singleton__iff,axiom,
% 52.23/52.34 ! [V_a_2,V_b_2,T_b] :
% 52.23/52.34 ( 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)))))
% 52.23/52.34 <=> V_b_2 = V_a_2 ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_subset__insert,axiom,
% 52.23/52.34 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 52.23/52.34 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.34 => ( 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)))
% 52.23/52.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_insert__subset,axiom,
% 52.23/52.34 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 52.23/52.34 ( 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))
% 52.23/52.34 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 52.23/52.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_insert__image,axiom,
% 52.23/52.34 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.34 => 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) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_range__eqI,axiom,
% 52.23/52.34 ! [T_c,T_b,V_x_2,V_f_2,V_b_2] :
% 52.23/52.34 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 52.23/52.34 => 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))))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_rangeI,axiom,
% 52.23/52.34 ! [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))))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_insert__Diff__if,axiom,
% 52.23/52.34 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 52.23/52.34 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 52.23/52.34 => 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) )
% 52.23/52.34 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 52.23/52.34 => 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)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_insert__Diff1,axiom,
% 52.23/52.34 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 52.23/52.34 => 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) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_lessThan__iff,axiom,
% 52.23/52.34 ! [V_k_2,V_i_2,T_b] :
% 52.23/52.34 ( class_Orderings_Oord(T_b)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)))
% 52.23/52.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_ord_OgreaterThanLessThan__iff,axiom,
% 52.23/52.34 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_b] :
% 52.23/52.34 ( 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)))
% 52.23/52.34 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 52.23/52.34 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_atMost__iff,axiom,
% 52.23/52.34 ! [V_k_2,V_i_2,T_b] :
% 52.23/52.34 ( class_Orderings_Oord(T_b)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)))
% 52.23/52.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_atLeast__iff,axiom,
% 52.23/52.34 ! [V_k_2,V_i_2,T_b] :
% 52.23/52.34 ( class_Orderings_Oord(T_b)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)))
% 52.23/52.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_greaterThan__iff,axiom,
% 52.23/52.34 ! [V_k_2,V_i_2,T_b] :
% 52.23/52.34 ( class_Orderings_Oord(T_b)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)))
% 52.23/52.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_le__SUPI,axiom,
% 52.23/52.34 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 52.23/52.34 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 52.23/52.34 => 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))) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UN__insert__distrib,axiom,
% 52.23/52.34 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 52.23/52.34 => 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)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UN__upper,axiom,
% 52.23/52.34 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.23/52.34 => 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))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_SUP__UN__eq,axiom,
% 52.23/52.34 ! [V_x_2,V_r_2,T_c,T_b] :
% 52.23/52.34 ( 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))
% 52.23/52.34 <=> 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))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_UN__absorb,axiom,
% 52.23/52.34 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 52.23/52.34 => 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) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_insert__Diff,axiom,
% 52.23/52.34 ! [V_A_2,V_a_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.23/52.34 => 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 ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Diff__insert__absorb,axiom,
% 52.23/52.34 ! [V_A_2,V_x_2,T_b] :
% 52.23/52.34 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.34 => 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 ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_image__constant,axiom,
% 52.23/52.34 ! [V_c_2,T_c,V_A_2,V_x_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.34 => 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))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_subset__insert__iff,axiom,
% 52.23/52.34 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 52.23/52.34 ( 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)))
% 52.23/52.34 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.34 => 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)) )
% 52.23/52.34 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_diff__single__insert,axiom,
% 52.23/52.34 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 52.23/52.34 ( 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))
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.34 => 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))) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_psubset__insert__iff,axiom,
% 52.23/52.34 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 52.23/52.34 ( 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)))
% 52.23/52.34 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 52.23/52.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
% 52.23/52.34 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 52.23/52.34 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.34 => 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)) )
% 52.23/52.34 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_setsum__diff1__nat,axiom,
% 52.23/52.34 ! [V_f_2,V_A_2,V_a_2,T_b] :
% 52.23/52.34 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.23/52.34 => 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)) )
% 52.23/52.34 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.23/52.34 => 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) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_set__empty__eq,axiom,
% 52.23/52.34 ! [V_xo_2,T_b] :
% 52.23/52.34 ( c_Option_Oset(T_b,V_xo_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.34 <=> V_xo_2 = c_Option_Ooption_ONone(T_b) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_Option_Oset_Osimps_I1_J,axiom,
% 52.23/52.34 ! [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)) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_dvd_OatLeastLessThan__empty,axiom,
% 52.23/52.34 ! [V_a_2,V_b_2] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2))
% 52.23/52.34 => 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)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_dvd_OatLeastLessThan__empty__iff,axiom,
% 52.23/52.34 ! [V_b_2,V_a_2] :
% 52.23/52.34 ( 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))
% 52.23/52.34 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 52.23/52.34 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom,
% 52.23/52.34 ! [V_f_2,V_A_2,T_b] :
% 52.23/52.34 ( ! [B_x] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.23/52.34 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 52.23/52.34 => 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)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_fold__graph_H_Ointros_I2_J,axiom,
% 52.23/52.34 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.34 => ( 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)
% 52.23/52.34 => 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)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_flat__lub__def,axiom,
% 52.23/52.34 ! [V_b_2,V_A_2,T_b] :
% 52.23/52.34 ( ( 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)))))
% 52.23/52.34 => c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = V_b_2 )
% 52.23/52.34 & ( ~ 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)))))
% 52.23/52.34 => 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)))))) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_card__Diff__singleton__if,axiom,
% 52.23/52.34 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.34 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.34 => 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)) )
% 52.23/52.34 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.34 => 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) ) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_finite__atLeastLessThan,axiom,
% 52.23/52.34 ! [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))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_finite__atLeastAtMost__int,axiom,
% 52.23/52.34 ! [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))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_finite__atLeastAtMost,axiom,
% 52.23/52.34 ! [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))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_finite__lessThan,axiom,
% 52.23/52.34 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_finite__atMost,axiom,
% 52.23/52.34 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_finite__atLeastLessThan__int,axiom,
% 52.23/52.34 ! [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))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_finite__greaterThanAtMost,axiom,
% 52.23/52.34 ! [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))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_finite__greaterThanAtMost__int,axiom,
% 52.23/52.34 ! [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))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_finite__greaterThanLessThan__int,axiom,
% 52.23/52.34 ! [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))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_finite__greaterThanLessThan,axiom,
% 52.23/52.34 ! [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))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_finite_OemptyI,axiom,
% 52.23/52.34 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_finite_OinsertI,axiom,
% 52.23/52.34 ! [V_a_2,V_A_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.34 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_finite__imageI,axiom,
% 52.23/52.34 ! [V_h_2,T_c,V_F_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 52.23/52.34 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_finite__Diff,axiom,
% 52.23/52.34 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.34 => 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))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_finite__UNIV,axiom,
% 52.23/52.34 ! [T_b] :
% 52.23/52.34 ( class_Finite__Set_Ofinite(T_b)
% 52.23/52.34 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_infinite__UNIV__nat,axiom,
% 52.23/52.34 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_finite__Plus__UNIV__iff,axiom,
% 52.23/52.34 ! [T_c,T_b] :
% 52.23/52.34 ( 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))))
% 52.23/52.34 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 52.23/52.34 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_finite__insert,axiom,
% 52.23/52.34 ! [V_A_2,V_a_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)))
% 52.23/52.34 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_finite__fun__UNIVD2,axiom,
% 52.23/52.34 ! [T_c,T_b] :
% 52.23/52.34 ( 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))))
% 52.23/52.34 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_finite__Prod__UNIV,axiom,
% 52.23/52.34 ! [T_c,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 52.23/52.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
% 52.23/52.34 => 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)))) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_finite_Oequations_I1_J,axiom,
% 52.23/52.34 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_finite__UN,axiom,
% 52.23/52.34 ! [V_B_2,T_c,V_A_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.34 => ( 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)))
% 52.23/52.34 <=> ! [B_x] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.23/52.34 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_transfer__nat__int__set__relations_I2_J,axiom,
% 52.23/52.34 ! [V_A_2,V_x_2] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2))
% 52.23/52.34 <=> 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))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_SUP2__iff,axiom,
% 52.23/52.34 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 52.23/52.34 ( 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))
% 52.23/52.34 <=> ? [B_x] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.23/52.34 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_finite__nat__set__iff__bounded,axiom,
% 52.23/52.34 ! [V_N_2] :
% 52.23/52.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 52.23/52.34 <=> ? [B_m] :
% 52.23/52.34 ! [B_x] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 52.23/52.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_finite__nat__set__iff__bounded__le,axiom,
% 52.23/52.34 ! [V_N_2] :
% 52.23/52.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 52.23/52.34 <=> ? [B_m] :
% 52.23/52.34 ! [B_x] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 52.23/52.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_finite__Un,axiom,
% 52.23/52.34 ! [V_Ga_2,V_F_2,T_b] :
% 52.23/52.34 ( 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)))
% 52.23/52.34 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 52.23/52.34 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_finite__UnI,axiom,
% 52.23/52.34 ! [V_Ga_2,V_F_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 52.23/52.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2))
% 52.23/52.34 => 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))) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_rev__finite__subset,axiom,
% 52.23/52.34 ! [V_A_2,V_B_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.34 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_finite__subset,axiom,
% 52.23/52.34 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.34 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_transfer__nat__int__set__relations_I1_J,axiom,
% 52.23/52.34 ! [V_A_2] :
% 52.23/52.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2))
% 52.23/52.34 <=> 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))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_finite__code,axiom,
% 52.23/52.34 ! [V_A_2,T_b] :
% 52.23/52.34 ( class_Finite__Set_Ofinite(T_b)
% 52.23/52.34 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_finite,axiom,
% 52.23/52.34 ! [V_A_2,T_b] :
% 52.23/52.34 ( class_Finite__Set_Ofinite(T_b)
% 52.23/52.34 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_finite__Diff2,axiom,
% 52.23/52.34 ! [V_A_2,V_B_2,T_b] :
% 52.23/52.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.34 => ( 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)))
% 52.23/52.34 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_bot__empty__eq2,axiom,
% 52.23/52.34 ! [V_y_2,V_x_2,T_c,T_b] :
% 52.23/52.34 ( 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))
% 52.23/52.34 <=> 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)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)))) ) ).
% 52.23/52.34
% 52.23/52.34 fof(fact_pred__equals__eq2,axiom,
% 52.23/52.34 ! [V_S_2,V_R_2,T_c,T_b] :
% 52.23/52.35 ( 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)
% 52.23/52.35 <=> V_R_2 = V_S_2 ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_sup__Un__eq2,axiom,
% 52.23/52.35 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 52.23/52.35 ( 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))
% 52.23/52.35 <=> 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))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_finite__option__UNIV,axiom,
% 52.23/52.35 ! [T_b] :
% 52.23/52.35 ( 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))))
% 52.23/52.35 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_transfer__int__nat__set__relations_I1_J,axiom,
% 52.23/52.35 ! [V_A_2] :
% 52.23/52.35 ( c_Nat__Transfer_Onat__set(V_A_2)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2))
% 52.23/52.35 <=> 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))) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setsum_Oinfinite,axiom,
% 52.23/52.35 ! [V_g_2,V_A_2,T_b,T_c] :
% 52.23/52.35 ( class_Groups_Ocomm__monoid__add(T_c)
% 52.23/52.35 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => 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) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setsum__infinite,axiom,
% 52.23/52.35 ! [V_f_2,V_A_2,T_b,T_c] :
% 52.23/52.35 ( class_Groups_Ocomm__monoid__add(T_c)
% 52.23/52.35 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => 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) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_finite__surj,axiom,
% 52.23/52.35 ! [V_f_2,V_B_2,T_c,V_A_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( 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)))
% 52.23/52.35 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_finite__Diff__insert,axiom,
% 52.23/52.35 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 52.23/52.35 ( 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))))
% 52.23/52.35 <=> 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))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_card__infinite,axiom,
% 52.23/52.35 ! [V_A_2,T_b] :
% 52.23/52.35 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_transfer__int__nat__set__relations_I2_J,axiom,
% 52.23/52.35 ! [V_A_2,V_x_2] :
% 52.23/52.35 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 52.23/52.35 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 52.23/52.35 <=> 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))) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
% 52.23/52.35 ! [V_A_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 52.23/52.35 => ( 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)))
% 52.23/52.35 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_finite__compl,axiom,
% 52.23/52.35 ! [V_A_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 52.23/52.35 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setsum__eq__0__iff,axiom,
% 52.23/52.35 ! [V_f_2,V_F_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 52.23/52.35 => ( 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)
% 52.23/52.35 <=> ! [B_x] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 52.23/52.35 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_code__numeral_Oof__nat__inject,axiom,
% 52.23/52.35 ! [V_y_2,V_x_2] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 52.23/52.35 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2)
% 52.23/52.35 <=> V_x_2 = V_y_2 ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_nat__of,axiom,
% 52.23/52.35 ! [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)))) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2] :
% 52.23/52.35 ( c_Nat__Transfer_Onat__set(V_A_2)
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 52.23/52.35 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_SUP__UN__eq2,axiom,
% 52.23/52.35 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 52.23/52.35 ( 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))
% 52.23/52.35 <=> 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))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_fold__graph_H_Ointros_I1_J,axiom,
% 52.23/52.35 ! [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) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_fold__graph_H_Oequations_I1_J,axiom,
% 52.23/52.35 ! [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) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setsum_Odistrib,axiom,
% 52.23/52.35 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 52.23/52.35 ( class_Groups_Ocomm__monoid__add(T_c)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => 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)) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_finite__atLeastZeroLessThan__int,axiom,
% 52.23/52.35 ! [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))) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_finite__range__imageI,axiom,
% 52.23/52.35 ! [V_f_2,T_d,V_g_2,T_c,T_b] :
% 52.23/52.35 ( 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)))))
% 52.23/52.35 => 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))))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_pred__subset__eq2,axiom,
% 52.23/52.35 ! [V_S_2,V_R_2,T_c,T_b] :
% 52.23/52.35 ( 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)))
% 52.23/52.35 <=> 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)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_card__eq__0__iff,axiom,
% 52.23/52.35 ! [V_A_2,T_b] :
% 52.23/52.35 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.35 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_card__ge__0__finite,axiom,
% 52.23/52.35 ! [V_A_2,T_b] :
% 52.23/52.35 ( 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)))
% 52.23/52.35 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_card__insert__le,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => 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)))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2] :
% 52.23/52.35 ( c_Nat__Transfer_Onat__set(V_A_2)
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 52.23/52.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_card__seteq,axiom,
% 52.23/52.35 ! [V_A_2,V_B_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.35 => ( 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)))
% 52.23/52.35 => V_A_2 = V_B_2 ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_card__mono,axiom,
% 52.23/52.35 ! [V_A_2,V_B_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.35 => 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))) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_card__image__le,axiom,
% 52.23/52.35 ! [V_f_2,T_c,V_A_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => 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))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setsum__eq__Suc0__iff,axiom,
% 52.23/52.35 ! [V_f_2,V_A_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( 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))
% 52.23/52.35 <=> ? [B_x] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.23/52.35 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 52.23/52.35 & ! [B_xa] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 52.23/52.35 => ( B_x != B_xa
% 52.23/52.35 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_psubset__card__mono,axiom,
% 52.23/52.35 ! [V_A_2,V_B_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.35 => 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))) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setsum__eq__1__iff,axiom,
% 52.23/52.35 ! [V_f_2,V_A_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( 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)
% 52.23/52.35 <=> ? [B_x] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.23/52.35 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 52.23/52.35 & ! [B_xa] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 52.23/52.35 => ( B_x != B_xa
% 52.23/52.35 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setsum__delta_H,axiom,
% 52.23/52.35 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 52.23/52.35 ( class_Groups_Ocomm__monoid__add(T_c)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 52.23/52.35 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 52.23/52.35 => 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) )
% 52.23/52.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 52.23/52.35 => 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) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setsum__delta,axiom,
% 52.23/52.35 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 52.23/52.35 ( class_Groups_Ocomm__monoid__add(T_c)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 52.23/52.35 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 52.23/52.35 => 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) )
% 52.23/52.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 52.23/52.35 => 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) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_of__nat__inverse,axiom,
% 52.23/52.35 ! [V_y_2] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 52.23/52.35 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setsum__insert,axiom,
% 52.23/52.35 ! [V_f_2,V_a_2,V_F_2,T_b,T_c] :
% 52.23/52.35 ( class_Groups_Ocomm__monoid__add(T_c)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 52.23/52.35 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2))
% 52.23/52.35 => 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)) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setsum_Oinsert,axiom,
% 52.23/52.35 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 52.23/52.35 ( class_Groups_Ocomm__monoid__add(T_c)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => 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)) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_card__insert__if,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => 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) )
% 52.23/52.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => 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)) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_card__insert__disjoint,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => 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)) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_card__gt__0__iff,axiom,
% 52.23/52.35 ! [V_A_2,T_b] :
% 52.23/52.35 ( 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)))
% 52.23/52.35 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_finite__UNIV__card__ge__0,axiom,
% 52.23/52.35 ! [T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 52.23/52.35 => 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))))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setsum__diff,axiom,
% 52.23/52.35 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 52.23/52.35 ( class_Groups_Oab__group__add(T_c)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 52.23/52.35 => 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)) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_card__Diff__subset,axiom,
% 52.23/52.35 ! [V_A_2,V_B_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 52.23/52.35 => 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)) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_diff__card__le__card__Diff,axiom,
% 52.23/52.35 ! [V_A_2,V_B_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.35 => 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)))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_card__psubset,axiom,
% 52.23/52.35 ! [V_A_2,V_B_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.35 => ( 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)))
% 52.23/52.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setsum__diff__nat,axiom,
% 52.23/52.35 ! [V_f_2,V_A_2,V_B_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 52.23/52.35 => 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)) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setsum_Oinsert__remove,axiom,
% 52.23/52.35 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 52.23/52.35 ( class_Groups_Ocomm__monoid__add(T_c)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => 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)))))) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_card__insert,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => 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)))))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_card__Diff1__le,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => 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))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_card_Oinsert,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => 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)) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setsum__diff1_H,axiom,
% 52.23/52.35 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 52.23/52.35 ( class_Groups_Ocomm__monoid__add(T_c)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.23/52.35 => 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)))))) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setsum_Oremove,axiom,
% 52.23/52.35 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 52.23/52.35 ( class_Groups_Ocomm__monoid__add(T_c)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => 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)))))) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setsum__diff1__ring,axiom,
% 52.23/52.35 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 52.23/52.35 ( class_Rings_Oring(T_c)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.23/52.35 => 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)) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setsum__diff1,axiom,
% 52.23/52.35 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 52.23/52.35 ( class_Groups_Oab__group__add(T_c)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.23/52.35 => 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)) )
% 52.23/52.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.23/52.35 => 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) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_card__Suc__Diff1,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => 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) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_card__Diff1__less,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => 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))) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_card__Diff2__less,axiom,
% 52.23/52.35 ! [V_y_2,V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 52.23/52.35 => 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))) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_card__Diff__insert,axiom,
% 52.23/52.35 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.23/52.35 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 52.23/52.35 => 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)) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_card_Oinsert__remove,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => 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)))))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_card_Oremove,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => 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)))))) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_card__Diff__singleton,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => 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)) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_in__rel__def,axiom,
% 52.23/52.35 ! [V_y_2,V_x_2,V_R_2,T_c,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2))
% 52.23/52.35 <=> 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)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_finite__fun__UNIVD1,axiom,
% 52.23/52.35 ! [T_c,T_b] :
% 52.23/52.35 ( 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))))
% 52.23/52.35 => ( 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))
% 52.23/52.35 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Nitpick_Orefl_H__def,axiom,
% 52.23/52.35 ! [V_r_2,T_b] :
% 52.23/52.35 ( c_Nitpick_Orefl_H(T_b,V_r_2)
% 52.23/52.35 <=> ! [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)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_in__measure,axiom,
% 52.23/52.35 ! [V_f_2,V_y_2,V_x_2,T_b] :
% 52.23/52.35 ( hBOOL(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)))
% 52.23/52.35 <=> 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))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_sup2CI,axiom,
% 52.23/52.35 ! [T_c,T_b,V_A_2,V_y_2,V_x_2,V_B_2] :
% 52.23/52.35 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 52.23/52.35 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) )
% 52.23/52.35 => 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)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_sup2E,axiom,
% 52.23/52.35 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 52.23/52.35 ( 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))
% 52.23/52.35 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 52.23/52.35 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_bot2E,axiom,
% 52.23/52.35 ! [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)) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_infinite__UNIV__int,axiom,
% 52.23/52.35 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_sup2I2,axiom,
% 52.23/52.35 ! [V_A_2,T_c,T_b,V_y_2,V_x_2,V_B_2] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 52.23/52.35 => 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)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_sup2I1,axiom,
% 52.23/52.35 ! [V_B_2,T_c,T_b,V_y_2,V_x_2,V_A_2] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 52.23/52.35 => 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)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_less__by__empty,axiom,
% 52.23/52.35 ! [V_B_2,T_b,V_A_2] :
% 52.23/52.35 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 52.23/52.35 => 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)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_aset_I6_J,axiom,
% 52.23/52.35 ! [V_A_2,V_t_2,V_D_2] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 52.23/52.35 => ( 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))
% 52.23/52.35 => ! [B_x] :
% 52.23/52.35 ( ! [B_xa] :
% 52.23/52.35 ( 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)))
% 52.23/52.35 => ! [B_xb] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 52.23/52.35 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 52.23/52.35 => 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)) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_bset_I8_J,axiom,
% 52.23/52.35 ! [V_B_2,V_t_2,V_D_2] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 52.23/52.35 => ( 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))
% 52.23/52.35 => ! [B_x] :
% 52.23/52.35 ( ! [B_xa] :
% 52.23/52.35 ( 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)))
% 52.23/52.35 => ! [B_xb] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 52.23/52.35 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 52.23/52.35 => 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))) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_dvd_OlessThan__iff,axiom,
% 52.23/52.35 ! [V_k_2,V_i_2] :
% 52.23/52.35 ( 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)))
% 52.23/52.35 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2))
% 52.23/52.35 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_ord_OlessThan__iff,axiom,
% 52.23/52.35 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2)))
% 52.23/52.35 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_dvd_OgreaterThan__iff,axiom,
% 52.23/52.35 ! [V_k_2,V_i_2] :
% 52.23/52.35 ( 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)))
% 52.23/52.35 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2))
% 52.23/52.35 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_aset_I4_J,axiom,
% 52.23/52.35 ! [V_A_2,V_t_2,V_D_2] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 52.23/52.35 => ! [B_x] :
% 52.23/52.35 ( ! [B_xa] :
% 52.23/52.35 ( 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)))
% 52.23/52.35 => ! [B_xb] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 52.23/52.35 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 52.23/52.35 => ( B_x != V_t_2
% 52.23/52.35 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_bset_I4_J,axiom,
% 52.23/52.35 ! [V_B_2,V_t_2,V_D_2] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 52.23/52.35 => ! [B_x] :
% 52.23/52.35 ( ! [B_xa] :
% 52.23/52.35 ( 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)))
% 52.23/52.35 => ! [B_xb] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 52.23/52.35 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 52.23/52.35 => ( B_x != V_t_2
% 52.23/52.35 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_ord_OgreaterThan__iff,axiom,
% 52.23/52.35 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2)))
% 52.23/52.35 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_bset_I3_J,axiom,
% 52.23/52.35 ! [V_B_2,V_t_2,V_D_2] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 52.23/52.35 => ( 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))
% 52.23/52.35 => ( ! [B_x] :
% 52.23/52.35 ( 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)))
% 52.23/52.35 => ! [B_xa] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2))
% 52.23/52.35 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) )
% 52.23/52.35 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_aset_I3_J,axiom,
% 52.23/52.35 ! [V_A_2,V_t_2,V_D_2] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 52.23/52.35 => ( 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))
% 52.23/52.35 => ( ! [B_x] :
% 52.23/52.35 ( 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)))
% 52.23/52.35 => ! [B_xa] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2))
% 52.23/52.35 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) )
% 52.23/52.35 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_aset_I5_J,axiom,
% 52.23/52.35 ! [V_A_2,V_t_2,V_D_2] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 52.23/52.35 => ! [B_x] :
% 52.23/52.35 ( ! [B_xa] :
% 52.23/52.35 ( 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)))
% 52.23/52.35 => ! [B_xb] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 52.23/52.35 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 52.23/52.35 => 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)) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_bset_I7_J,axiom,
% 52.23/52.35 ! [V_B_2,V_t_2,V_D_2] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 52.23/52.35 => ! [B_x] :
% 52.23/52.35 ( ! [B_xa] :
% 52.23/52.35 ( 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)))
% 52.23/52.35 => ! [B_xb] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 52.23/52.35 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 52.23/52.35 => 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))) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_dvd_OatLeast__iff,axiom,
% 52.23/52.35 ! [V_k_2,V_i_2] :
% 52.23/52.35 ( 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)))
% 52.23/52.35 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_dvd_OatMost__iff,axiom,
% 52.23/52.35 ! [V_k_2,V_i_2] :
% 52.23/52.35 ( 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)))
% 52.23/52.35 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_ord_OatMost__iff,axiom,
% 52.23/52.35 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2)))
% 52.23/52.35 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_ord_OatLeast__iff,axiom,
% 52.23/52.35 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2)))
% 52.23/52.35 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_finite__pointwise,axiom,
% 52.23/52.35 ! [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] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_U_2))
% 52.23/52.35 => ( ! [B_p] :
% 52.23/52.35 ( 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))))
% 52.23/52.35 => 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)))) )
% 52.23/52.35 => ( 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))
% 52.23/52.35 => 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)) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_folding__one_Oremove,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 52.23/52.35 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 52.23/52.35 => hAPP(V_F_2,V_A_2) = V_x_2 )
% 52.23/52.35 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 52.23/52.35 => 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)))))) ) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_folding__image__simple_Oremove,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 52.23/52.35 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 52.23/52.35 => 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)))))) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_folding__image__simple_Oempty,axiom,
% 52.23/52.35 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 52.23/52.35 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 52.23/52.35 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_folding__one_Osingleton,axiom,
% 52.23/52.35 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 52.23/52.35 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 52.23/52.35 => 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 ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_folding__image__simple_Oinsert,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 52.23/52.35 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 52.23/52.35 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 52.23/52.35 => 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)) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_folding__one_Oinsert,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 52.23/52.35 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => 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)) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_folding__one_Oinsert__remove,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 52.23/52.35 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 52.23/52.35 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 52.23/52.35 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 52.23/52.35 => 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)))))) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_folding__image__simple_Oinsert__remove,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 52.23/52.35 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 52.23/52.35 => 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)))))) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setsum__mono2,axiom,
% 52.23/52.35 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 52.23/52.35 ( class_Groups_Oordered__comm__monoid__add(T_c)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.35 => ( ! [B_b] :
% 52.23/52.35 ( 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)))
% 52.23/52.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_b))) )
% 52.23/52.35 => 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))) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_mlex__leq,axiom,
% 52.23/52.35 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 52.23/52.35 ( 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)))
% 52.23/52.35 => ( hBOOL(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))
% 52.23/52.35 => hBOOL(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))) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_mlex__less,axiom,
% 52.23/52.35 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 52.23/52.35 ( 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)))
% 52.23/52.35 => hBOOL(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))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setsum__bounded,axiom,
% 52.23/52.35 ! [V_K_2,V_f_2,V_A_2,T_b,T_c] :
% 52.23/52.35 ( ( class_Groups_Oordered__ab__semigroup__add(T_c)
% 52.23/52.35 & class_Rings_Osemiring__1(T_c) )
% 52.23/52.35 => ( ! [B_i] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2))
% 52.23/52.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2)) )
% 52.23/52.35 => 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))) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_card__Suc__eq,axiom,
% 52.23/52.35 ! [V_k_2,V_A_2,T_b] :
% 52.23/52.35 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Nat_OSuc,V_k_2)
% 52.23/52.35 <=> ? [B_b,B_B] :
% 52.23/52.35 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B)
% 52.23/52.35 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B))
% 52.23/52.35 & hAPP(c_Finite__Set_Ocard(T_b),B_B) = V_k_2
% 52.23/52.35 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.23/52.35 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setsum__mono3,axiom,
% 52.23/52.35 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 52.23/52.35 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 52.23/52.35 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.35 => ( ! [B_x] :
% 52.23/52.35 ( 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)))
% 52.23/52.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 52.23/52.35 => 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))) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_ord_OgreaterThanAtMost__iff,axiom,
% 52.23/52.35 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 52.23/52.35 ( 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)))
% 52.23/52.35 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 52.23/52.35 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Nats__number__of,axiom,
% 52.23/52.35 ! [V_w_2,T_b] :
% 52.23/52.35 ( class_Int_Onumber__ring(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
% 52.23/52.35 => 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))) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_dvd_OgreaterThanAtMost__empty__iff2,axiom,
% 52.23/52.35 ! [V_l_2,V_k_2] :
% 52.23/52.35 ( 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)
% 52.23/52.35 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2))
% 52.23/52.35 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Nats__0,axiom,
% 52.23/52.35 ! [T_b] :
% 52.23/52.35 ( class_Rings_Osemiring__1(T_b)
% 52.23/52.35 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Nats__add,axiom,
% 52.23/52.35 ! [V_b_2,V_a_2,T_b] :
% 52.23/52.35 ( class_Rings_Osemiring__1(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 52.23/52.35 => 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))) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Nats__mult,axiom,
% 52.23/52.35 ! [V_b_2,V_a_2,T_b] :
% 52.23/52.35 ( class_Rings_Osemiring__1(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 52.23/52.35 => 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))) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Nats__1,axiom,
% 52.23/52.35 ! [T_b] :
% 52.23/52.35 ( class_Rings_Osemiring__1(T_b)
% 52.23/52.35 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_of__nat__in__Nats,axiom,
% 52.23/52.35 ! [V_n_2,T_b] :
% 52.23/52.35 ( class_Rings_Osemiring__1(T_b)
% 52.23/52.35 => 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))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_dvd_OgreaterThanAtMost__empty,axiom,
% 52.23/52.35 ! [V_k_2,V_l_2] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
% 52.23/52.35 => 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)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_dvd_OgreaterThanAtMost__empty__iff,axiom,
% 52.23/52.35 ! [V_l_2,V_k_2] :
% 52.23/52.35 ( 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))
% 52.23/52.35 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2))
% 52.23/52.35 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Ints__odd__less__0,axiom,
% 52.23/52.35 ! [V_a_2,T_b] :
% 52.23/52.35 ( class_Rings_Olinordered__idom(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 52.23/52.35 => ( 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)))
% 52.23/52.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Sup__fin_Oremove,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Lattices_Olattice(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 52.23/52.35 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_2 )
% 52.23/52.35 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 52.23/52.35 => 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)))))) ) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Max_Oremove,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 52.23/52.35 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 )
% 52.23/52.35 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 52.23/52.35 => 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)))))) ) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Max_Osingleton,axiom,
% 52.23/52.35 ! [V_x_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => 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 ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Sup__fin_Osingleton,axiom,
% 52.23/52.35 ! [V_x_2,T_b] :
% 52.23/52.35 ( class_Lattices_Olattice(T_b)
% 52.23/52.35 => 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 ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Ints__0,axiom,
% 52.23/52.35 ! [T_b] :
% 52.23/52.35 ( class_Rings_Oring__1(T_b)
% 52.23/52.35 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Ints__add,axiom,
% 52.23/52.35 ! [V_b_2,V_a_2,T_b] :
% 52.23/52.35 ( class_Rings_Oring__1(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 52.23/52.35 => 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))) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Ints__mult,axiom,
% 52.23/52.35 ! [V_b_2,V_a_2,T_b] :
% 52.23/52.35 ( class_Rings_Oring__1(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 52.23/52.35 => 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))) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Ints__diff,axiom,
% 52.23/52.35 ! [V_b_2,V_a_2,T_b] :
% 52.23/52.35 ( class_Rings_Oring__1(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 52.23/52.35 => 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))) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Ints__number__of,axiom,
% 52.23/52.35 ! [V_w_2,T_b] :
% 52.23/52.35 ( class_Int_Onumber__ring(T_b)
% 52.23/52.35 => 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))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Ints__1,axiom,
% 52.23/52.35 ! [T_b] :
% 52.23/52.35 ( class_Rings_Oring__1(T_b)
% 52.23/52.35 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Ints__minus,axiom,
% 52.23/52.35 ! [V_a_2,T_b] :
% 52.23/52.35 ( class_Rings_Oring__1(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 52.23/52.35 => 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))) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Ints__of__nat,axiom,
% 52.23/52.35 ! [V_n_2,T_b] :
% 52.23/52.35 ( class_Rings_Oring__1(T_b)
% 52.23/52.35 => 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))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Ints__power,axiom,
% 52.23/52.35 ! [V_n_2,V_a_2,T_b] :
% 52.23/52.35 ( class_Rings_Oring__1(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 52.23/52.35 => 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))) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Ints__of__int,axiom,
% 52.23/52.35 ! [V_z_2,T_b] :
% 52.23/52.35 ( class_Rings_Oring__1(T_b)
% 52.23/52.35 => 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))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Max__ge,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => 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))) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Max__in,axiom,
% 52.23/52.35 ! [V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Sup__fin_Oin__idem,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Lattices_Olattice(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => 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) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Max_Oin__idem,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => 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) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Ints__double__eq__0__iff,axiom,
% 52.23/52.35 ! [V_a_2,T_b] :
% 52.23/52.35 ( class_Int_Oring__char__0(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 52.23/52.35 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 52.23/52.35 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Max__mono,axiom,
% 52.23/52.35 ! [V_N_2,V_M_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 52.23/52.35 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 52.23/52.35 => 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))) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Sup__fin_Oinsert__idem,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Lattices_Olattice(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => 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)) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Max__insert,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => 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)) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Sup__fin_Osubset__idem,axiom,
% 52.23/52.35 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Lattices_Olattice(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 52.23/52.35 => 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) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Sup__fin_Ounion__idem,axiom,
% 52.23/52.35 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Lattices_Olattice(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.35 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => 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)) ) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Max_Osubset__idem,axiom,
% 52.23/52.35 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 52.23/52.35 => 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) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Max__Un,axiom,
% 52.23/52.35 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.35 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => 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)) ) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Ints__odd__nonzero,axiom,
% 52.23/52.35 ! [V_a_2,T_b] :
% 52.23/52.35 ( class_Int_Oring__char__0(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 52.23/52.35 => 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) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Sup__fin_Oinsert,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Lattices_Olattice(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => 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)) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Max_Oinsert,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => 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)) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Sup__fin_Oinsert__remove,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Lattices_Olattice(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 52.23/52.35 => 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 )
% 52.23/52.35 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 52.23/52.35 => 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)))))) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Max_Oinsert__remove,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 52.23/52.35 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 52.23/52.35 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 52.23/52.35 => 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)))))) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Max_Oclosed,axiom,
% 52.23/52.35 ! [V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => ( ! [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))))))
% 52.23/52.35 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Sup__fin_Oclosed,axiom,
% 52.23/52.35 ! [V_A_2,T_b] :
% 52.23/52.35 ( class_Lattices_Olattice(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => ( ! [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))))))
% 52.23/52.35 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Min_Oremove,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 52.23/52.35 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 )
% 52.23/52.35 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 52.23/52.35 => 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)))))) ) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Min_Osingleton,axiom,
% 52.23/52.35 ! [V_x_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => 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 ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Min__le,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => 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)) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Min__in,axiom,
% 52.23/52.35 ! [V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Min_Oin__idem,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => 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) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Min__antimono,axiom,
% 52.23/52.35 ! [V_N_2,V_M_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 52.23/52.35 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 52.23/52.35 => 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))) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Min__insert,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => 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)) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Min_Osubset__idem,axiom,
% 52.23/52.35 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 52.23/52.35 => 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) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Min__Un,axiom,
% 52.23/52.35 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.35 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => 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)) ) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Min_Oinsert,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => 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)) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Min_Oinsert__remove,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 52.23/52.35 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 52.23/52.35 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 52.23/52.35 => 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)))))) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_minus__Max__eq__Min,axiom,
% 52.23/52.35 ! [V_S_2,T_b] :
% 52.23/52.35 ( class_Groups_Olinordered__ab__group__add(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 52.23/52.35 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => 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)) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_minus__Min__eq__Max,axiom,
% 52.23/52.35 ! [V_S_2,T_b] :
% 52.23/52.35 ( class_Groups_Olinordered__ab__group__add(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 52.23/52.35 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => 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)) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Min_Oclosed,axiom,
% 52.23/52.35 ! [V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => ( ! [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))))))
% 52.23/52.35 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_iso__tuple__UNIV__I,axiom,
% 52.23/52.35 ! [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)))) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_fold__graph_H_Oequations_I2_J,axiom,
% 52.23/52.35 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_c,T_b] :
% 52.23/52.35 ( 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))
% 52.23/52.35 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 )
% 52.23/52.35 | ? [B_x,B_y] :
% 52.23/52.35 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y)
% 52.23/52.35 & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2))
% 52.23/52.35 & 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) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_in__lex__prod,axiom,
% 52.23/52.35 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 52.23/52.35 ( 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)))
% 52.23/52.35 <=> ( hBOOL(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))
% 52.23/52.35 | ( V_a_2 = V_a_H_2
% 52.23/52.35 & 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)) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_card__Plus__conv__if,axiom,
% 52.23/52.35 ! [V_B_2,T_c,V_A_2,T_b] :
% 52.23/52.35 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 52.23/52.35 => 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)) )
% 52.23/52.35 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 52.23/52.35 => 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) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_in__finite__psubset,axiom,
% 52.23/52.35 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.35 ( 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)))
% 52.23/52.35 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.35 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_InrI,axiom,
% 52.23/52.35 ! [V_A_2,T_c,V_B_2,V_b_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_B_2))
% 52.23/52.35 => 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))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_InlI,axiom,
% 52.23/52.35 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.23/52.35 => 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))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Plus__eq__empty__conv,axiom,
% 52.23/52.35 ! [V_B_2,V_A_2,T_c,T_b] :
% 52.23/52.35 ( 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))
% 52.23/52.35 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Plus__def,axiom,
% 52.23/52.35 ! [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)) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_finite__Plus__iff,axiom,
% 52.23/52.35 ! [V_B_2,V_A_2,T_c,T_b] :
% 52.23/52.35 ( 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)))
% 52.23/52.35 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_finite__Plus,axiom,
% 52.23/52.35 ! [V_B_2,T_c,V_A_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 52.23/52.35 => 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))) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_finite__PlusD_I1_J,axiom,
% 52.23/52.35 ! [V_B_2,V_A_2,T_c,T_b] :
% 52.23/52.35 ( 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)))
% 52.23/52.35 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_finite__PlusD_I2_J,axiom,
% 52.23/52.35 ! [V_B_2,V_A_2,T_c,T_b] :
% 52.23/52.35 ( 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)))
% 52.23/52.35 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_UNIV__Plus__UNIV,axiom,
% 52.23/52.35 ! [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)) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_card__Plus,axiom,
% 52.23/52.35 ! [V_B_2,T_c,V_A_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 52.23/52.35 => 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)) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_same__fstI,axiom,
% 52.23/52.35 ! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_P_2] :
% 52.23/52.35 ( hBOOL(hAPP(V_P_2,V_x_2))
% 52.23/52.35 => ( 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)))
% 52.23/52.35 => 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))) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_min__max_OSup__fin_Oremove,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 52.23/52.35 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = V_x_2 )
% 52.23/52.35 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 52.23/52.35 => 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)))))) ) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_min__max_OInf__fin_Oremove,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 52.23/52.35 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = V_x_2 )
% 52.23/52.35 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 52.23/52.35 => 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)))))) ) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_min__max_OInf__le__Sup,axiom,
% 52.23/52.35 ! [V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => 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))) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_min__max_OInf__fin_Oin__idem,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => 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) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_min__max_OSup__fin_Oin__idem,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => 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) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_min__max_OInf__fin_Osingleton,axiom,
% 52.23/52.35 ! [V_x_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => 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 ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_min__max_OSup__fin_Osingleton,axiom,
% 52.23/52.35 ! [V_x_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => 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 ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => 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)) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => 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)) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
% 52.23/52.35 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 52.23/52.35 => 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) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
% 52.23/52.35 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 52.23/52.35 => 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) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_min__max_Osup__Inf__absorb,axiom,
% 52.23/52.35 ! [V_a_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.23/52.35 => 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 ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_min__max_Oinf__Sup__absorb,axiom,
% 52.23/52.35 ! [V_a_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.23/52.35 => 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 ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
% 52.23/52.35 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.35 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => 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)) ) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
% 52.23/52.35 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.35 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => 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)) ) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_min__max_OInf__fin_Oinsert,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => 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)) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_min__max_OSup__fin_Oinsert,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => 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)) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 52.23/52.35 => 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 )
% 52.23/52.35 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 52.23/52.35 => 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)))))) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 52.23/52.35 => 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 )
% 52.23/52.35 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 52.23/52.35 => 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)))))) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_min__max_OSup__fin_Oclosed,axiom,
% 52.23/52.35 ! [V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => ( ! [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))))))
% 52.23/52.35 => 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)) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_min__max_OInf__fin_Oclosed,axiom,
% 52.23/52.35 ! [V_A_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => ( ! [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))))))
% 52.23/52.35 => 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)) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_folding__one_Oclosed,axiom,
% 52.23/52.35 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 52.23/52.35 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => ( ! [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))))))
% 52.23/52.35 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_fun__upd__image,axiom,
% 52.23/52.35 ! [V_y_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 52.23/52.35 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => 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)))))) )
% 52.23/52.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => 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) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setprod__gen__delta,axiom,
% 52.23/52.35 ! [V_c_2,V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 52.23/52.35 ( class_Groups_Ocomm__monoid__mult(T_c)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 52.23/52.35 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 52.23/52.35 => 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)))) )
% 52.23/52.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 52.23/52.35 => 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)) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setsum__nonneg__0,axiom,
% 52.23/52.35 ! [V_i_2,V_f_2,V_s_2,T_b,T_c] :
% 52.23/52.35 ( class_Groups_Oordered__ab__group__add(T_c)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 52.23/52.35 => ( ! [B_i] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 52.23/52.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 52.23/52.35 => ( 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)
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 52.23/52.35 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_fun__upd__triv,axiom,
% 52.23/52.35 ! [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 ).
% 52.23/52.35
% 52.23/52.35 fof(fact_abs__setprod,axiom,
% 52.23/52.35 ! [V_A_2,V_f_2,T_c,T_b] :
% 52.23/52.35 ( class_Fields_Olinordered__field(T_b)
% 52.23/52.35 => 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) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setprod__1,axiom,
% 52.23/52.35 ! [V_A_2,T_c,T_b] :
% 52.23/52.35 ( class_Groups_Ocomm__monoid__mult(T_b)
% 52.23/52.35 => 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) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_of__int__setprod,axiom,
% 52.23/52.35 ! [V_A_2,V_f_2,T_c,T_b] :
% 52.23/52.35 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 52.23/52.35 & class_Rings_Oring__1(T_b) )
% 52.23/52.35 => 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) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom,
% 52.23/52.35 ! [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)) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_of__nat__setprod,axiom,
% 52.23/52.35 ! [V_A_2,V_f_2,T_c,T_b] :
% 52.23/52.35 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 52.23/52.35 & class_Rings_Osemiring__1(T_b) )
% 52.23/52.35 => 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) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_int__setprod,axiom,
% 52.23/52.35 ! [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) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setprod__timesf,axiom,
% 52.23/52.35 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 52.23/52.35 ( class_Groups_Ocomm__monoid__mult(T_b)
% 52.23/52.35 => 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)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_fun__upd__idem,axiom,
% 52.23/52.35 ! [T_b,T_c,V_y_2,V_x_2,V_f_2] :
% 52.23/52.35 ( hAPP(V_f_2,V_x_2) = V_y_2
% 52.23/52.35 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,T_b),V_f_2),V_x_2),V_y_2) = V_f_2 ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_fun__upd__other,axiom,
% 52.23/52.35 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 52.23/52.35 ( V_z_2 != V_x_2
% 52.23/52.35 => 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) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_fun__upd__twist,axiom,
% 52.23/52.35 ! [V_d_2,V_b_2,V_m_2,T_c,T_b,V_c_2,V_a_2] :
% 52.23/52.35 ( V_a_2 != V_c_2
% 52.23/52.35 => 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) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_fun__upd__apply,axiom,
% 52.23/52.35 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 52.23/52.35 ( ( V_z_2 = V_x_2
% 52.23/52.35 => 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 )
% 52.23/52.35 & ( V_z_2 != V_x_2
% 52.23/52.35 => 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) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_fun__upd__same,axiom,
% 52.23/52.35 ! [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 ).
% 52.23/52.35
% 52.23/52.35 fof(fact_fun__upd__upd,axiom,
% 52.23/52.35 ! [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) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_fun__upd__idem__iff,axiom,
% 52.23/52.35 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 52.23/52.35 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2) = V_f_2
% 52.23/52.35 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_fun__upd__def,axiom,
% 52.23/52.35 ! [V_b_2,V_f_2,T_c,T_b,V_a_2,V_x_2] :
% 52.23/52.35 ( ( V_x_2 = V_a_2
% 52.23/52.35 => 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 )
% 52.23/52.35 & ( V_x_2 != V_a_2
% 52.23/52.35 => 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) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom,
% 52.23/52.35 ! [V_A_2,V_f_2,T_b] :
% 52.23/52.35 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 52.23/52.35 & class_Groups_Ocomm__monoid__mult(T_b) )
% 52.23/52.35 => 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)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setprod__zero,axiom,
% 52.23/52.35 ! [V_f_2,V_A_2,T_b,T_c] :
% 52.23/52.35 ( class_Rings_Ocomm__semiring__1(T_c)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( ? [B_x] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.23/52.35 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 52.23/52.35 => 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) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setprod__zero__iff,axiom,
% 52.23/52.35 ! [V_f_2,V_A_2,T_b,T_c] :
% 52.23/52.35 ( ( class_Rings_Ocomm__semiring__1(T_c)
% 52.23/52.35 & class_Rings_Ono__zero__divisors(T_c) )
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( 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)
% 52.23/52.35 <=> ? [B_x] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.23/52.35 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setprod__empty,axiom,
% 52.23/52.35 ! [V_f_2,T_c,T_b] :
% 52.23/52.35 ( class_Groups_Ocomm__monoid__mult(T_b)
% 52.23/52.35 => 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) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setprod_Oempty,axiom,
% 52.23/52.35 ! [V_g_2,T_c,T_b] :
% 52.23/52.35 ( class_Groups_Ocomm__monoid__mult(T_b)
% 52.23/52.35 => 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) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setprod__infinite,axiom,
% 52.23/52.35 ! [V_f_2,V_A_2,T_b,T_c] :
% 52.23/52.35 ( class_Groups_Ocomm__monoid__mult(T_c)
% 52.23/52.35 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => 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) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setprod_Oinfinite,axiom,
% 52.23/52.35 ! [V_g_2,V_A_2,T_b,T_c] :
% 52.23/52.35 ( class_Groups_Ocomm__monoid__mult(T_c)
% 52.23/52.35 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => 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) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setprod__eq__1__iff,axiom,
% 52.23/52.35 ! [V_f_2,V_F_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 52.23/52.35 => ( 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)
% 52.23/52.35 <=> ! [B_x] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 52.23/52.35 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom,
% 52.23/52.35 ! [V_f_2,V_A_2,T_b] :
% 52.23/52.35 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 52.23/52.35 & class_Groups_Ocomm__monoid__mult(T_b) )
% 52.23/52.35 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 52.23/52.35 => 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)) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setprod_Odistrib,axiom,
% 52.23/52.35 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 52.23/52.35 ( class_Groups_Ocomm__monoid__mult(T_c)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => 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)) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setprod__dividef,axiom,
% 52.23/52.35 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 52.23/52.35 ( class_Fields_Ofield__inverse__zero(T_c)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => 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)) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_dvd__setprod,axiom,
% 52.23/52.35 ! [V_f_2,V_i_2,V_A_2,T_b,T_c] :
% 52.23/52.35 ( class_Rings_Ocomm__semiring__1(T_c)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 52.23/52.35 => 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))) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setprod__pos__nat__iff,axiom,
% 52.23/52.35 ! [V_f_2,V_S_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 52.23/52.35 => ( 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)))
% 52.23/52.35 <=> ! [B_x] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 52.23/52.35 => 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))) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setprod__dvd__setprod__subset,axiom,
% 52.23/52.35 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 52.23/52.35 ( ( class_Groups_Ocomm__monoid__mult(T_c)
% 52.23/52.35 & class_Rings_Odvd(T_c) )
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.35 => 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))) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setprod__delta,axiom,
% 52.23/52.35 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 52.23/52.35 ( class_Groups_Ocomm__monoid__mult(T_c)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 52.23/52.35 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 52.23/52.35 => 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) )
% 52.23/52.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 52.23/52.35 => 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) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setprod__delta_H,axiom,
% 52.23/52.35 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 52.23/52.35 ( class_Groups_Ocomm__monoid__mult(T_c)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 52.23/52.35 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 52.23/52.35 => 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) )
% 52.23/52.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 52.23/52.35 => 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) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setprod__constant,axiom,
% 52.23/52.35 ! [V_y_2,V_A_2,T_b,T_c] :
% 52.23/52.35 ( class_Groups_Ocomm__monoid__mult(T_c)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => 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)) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setprod__insert,axiom,
% 52.23/52.35 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 52.23/52.35 ( class_Groups_Ocomm__monoid__mult(T_c)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.23/52.35 => 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)) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setprod_Oinsert,axiom,
% 52.23/52.35 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 52.23/52.35 ( class_Groups_Ocomm__monoid__mult(T_c)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => 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)) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setprod_Oinsert__remove,axiom,
% 52.23/52.35 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 52.23/52.35 ( class_Groups_Ocomm__monoid__mult(T_c)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => 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)))))) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setprod_Oremove,axiom,
% 52.23/52.35 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 52.23/52.35 ( class_Groups_Ocomm__monoid__mult(T_c)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => 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)))))) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setprod__diff1,axiom,
% 52.23/52.35 ! [V_a_2,V_f_2,V_A_2,T_b,T_c] :
% 52.23/52.35 ( class_Fields_Ofield(T_c)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_c)
% 52.23/52.35 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.23/52.35 => 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)) )
% 52.23/52.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.23/52.35 => 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) ) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_finite__range__updI,axiom,
% 52.23/52.35 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 52.23/52.35 ( 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)))))
% 52.23/52.35 => 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))))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_image__map__upd,axiom,
% 52.23/52.35 ! [V_y_2,V_m_2,T_c,V_A_2,V_x_2,T_b] :
% 52.23/52.35 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => 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) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_map__upd__nonempty,axiom,
% 52.23/52.35 ! [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)) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_map__upd__Some__unfold,axiom,
% 52.23/52.35 ! [V_y_2,V_x_2,V_b_2,V_a_2,V_m_2,T_b,T_c] :
% 52.23/52.35 ( 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)
% 52.23/52.35 <=> ( ( V_x_2 = V_a_2
% 52.23/52.35 & V_b_2 = V_y_2 )
% 52.23/52.35 | ( V_x_2 != V_a_2
% 52.23/52.35 & hAPP(V_m_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_map__upd__triv,axiom,
% 52.23/52.35 ! [T_c,V_x_2,T_b,V_k_2,V_t_2] :
% 52.23/52.35 ( hAPP(V_t_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
% 52.23/52.35 => 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 ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_map__upd__eqD1,axiom,
% 52.23/52.35 ! [V_y_2,V_n_2,V_x_2,V_a_2,V_m_2,T_c,T_b] :
% 52.23/52.35 ( 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))
% 52.23/52.35 => V_x_2 = V_y_2 ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_empty__upd__none,axiom,
% 52.23/52.35 ! [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) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom,
% 52.23/52.35 ! [V_f_2,V_A_2,T_b] :
% 52.23/52.35 ( ! [B_x] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.23/52.35 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 52.23/52.35 => 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)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_ran__map__upd,axiom,
% 52.23/52.35 ! [V_b_2,T_c,T_b,V_a_2,V_m_2] :
% 52.23/52.35 ( hAPP(V_m_2,V_a_2) = c_Option_Ooption_ONone(T_b)
% 52.23/52.35 => 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)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_fun__upd__None__restrict,axiom,
% 52.23/52.35 ! [V_m_2,T_c,V_D_2,V_x_2,T_b] :
% 52.23/52.35 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 52.23/52.35 => 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))))) )
% 52.23/52.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 52.23/52.35 => 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) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_restrict__in,axiom,
% 52.23/52.35 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => 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) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_restrict__map__empty,axiom,
% 52.23/52.35 ! [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) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_restrict__out,axiom,
% 52.23/52.35 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] :
% 52.23/52.35 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_c) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_restrict__map__insert,axiom,
% 52.23/52.35 ! [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)) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_restrict__map__def,axiom,
% 52.23/52.35 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] :
% 52.23/52.35 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => 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) )
% 52.23/52.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_c) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_restrict__map__to__empty,axiom,
% 52.23/52.35 ! [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) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_ranI,axiom,
% 52.23/52.35 ! [T_c,V_b_2,T_b,V_a_2,V_m_2] :
% 52.23/52.35 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_b_2)
% 52.23/52.35 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Map_Oran(T_c,T_b,V_m_2))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_fun__upd__restrict,axiom,
% 52.23/52.35 ! [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) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_ran__empty,axiom,
% 52.23/52.35 ! [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)) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_restrict__fun__upd,axiom,
% 52.23/52.35 ! [V_y_2,V_m_2,T_c,V_D_2,V_x_2,T_b] :
% 52.23/52.35 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 52.23/52.35 => 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) )
% 52.23/52.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 52.23/52.35 => 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) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_fun__upd__restrict__conv,axiom,
% 52.23/52.35 ! [V_y_2,V_m_2,T_c,V_D_2,V_x_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 52.23/52.35 => 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) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_restrict__complement__singleton__eq,axiom,
% 52.23/52.35 ! [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)) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_restrict__upd__same,axiom,
% 52.23/52.35 ! [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))))) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setsum__nonneg__leq__bound,axiom,
% 52.23/52.35 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_b,T_c] :
% 52.23/52.35 ( class_Groups_Oordered__ab__group__add(T_c)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 52.23/52.35 => ( ! [B_i] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 52.23/52.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 52.23/52.35 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = V_B_2
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 52.23/52.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_pair__lessI2,axiom,
% 52.23/52.35 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2))
% 52.23/52.35 => 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)) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_min__max_OSup__fin_Ohom__commute,axiom,
% 52.23/52.35 ! [V_N_2,V_h_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( ! [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))
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 52.23/52.35 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => 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)) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_pair__lessI1,axiom,
% 52.23/52.35 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 52.23/52.35 => 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)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_pair__leqI2,axiom,
% 52.23/52.35 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2))
% 52.23/52.35 => 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)) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_smin__insertI,axiom,
% 52.23/52.35 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 52.23/52.35 => ( 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))
% 52.23/52.35 => ( 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))
% 52.23/52.35 => 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)) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_smax__insertI,axiom,
% 52.23/52.35 ! [V_X_2,V_x_2,V_Y_2,V_y_2] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2))
% 52.23/52.35 => ( 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))
% 52.23/52.35 => ( 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))
% 52.23/52.35 => 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)) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_smin__emptyI,axiom,
% 52.23/52.35 ! [V_X_2] :
% 52.23/52.35 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 52.23/52.35 => 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)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_smax__emptyI,axiom,
% 52.23/52.35 ! [V_Y_2] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2))
% 52.23/52.35 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 52.23/52.35 => 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)) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_pair__leqI1,axiom,
% 52.23/52.35 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 52.23/52.35 => 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)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_wmax__insertI,axiom,
% 52.23/52.35 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))
% 52.23/52.35 => ( 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))
% 52.23/52.35 => ( 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))
% 52.23/52.35 => 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)) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_wmin__insertI,axiom,
% 52.23/52.35 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 52.23/52.35 => ( 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))
% 52.23/52.35 => ( 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))
% 52.23/52.35 => 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)) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_wmax__emptyI,axiom,
% 52.23/52.35 ! [V_X_2] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2))
% 52.23/52.35 => 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)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_wmin__emptyI,axiom,
% 52.23/52.35 ! [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)) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_min__weak__def,axiom,
% 52.23/52.35 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)))) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_max__weak__def,axiom,
% 52.23/52.35 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)))) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_max__rpair__set,axiom,
% 52.23/52.35 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)) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_max__strict__def,axiom,
% 52.23/52.35 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_max__ext__additive,axiom,
% 52.23/52.35 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_b] :
% 52.23/52.35 ( 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)))
% 52.23/52.35 => ( 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)))
% 52.23/52.35 => 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))) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_min__strict__def,axiom,
% 52.23/52.35 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_min__rpair__set,axiom,
% 52.23/52.35 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)) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_max__extp__max__ext__eq,axiom,
% 52.23/52.35 ! [V_xa_2,V_x_2,V_R_2,T_b] :
% 52.23/52.35 ( 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)
% 52.23/52.35 <=> 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))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_less__than__iff,axiom,
% 52.23/52.35 ! [V_y_2,V_x_2] :
% 52.23/52.35 ( 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))
% 52.23/52.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_intrel__iff,axiom,
% 52.23/52.35 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 52.23/52.35 ( 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))
% 52.23/52.35 <=> 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) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_pair__less__def,axiom,
% 52.23/52.35 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_mlex__prod__def,axiom,
% 52.23/52.35 ! [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))) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_rp__inv__image__rp,axiom,
% 52.23/52.35 ! [V_f_2,T_c,V_P_2,T_b] :
% 52.23/52.35 ( c_FunDef_Oreduction__pair(T_b,V_P_2)
% 52.23/52.35 => c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_P_2),V_f_2)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_min__max_OInf__fin_Ohom__commute,axiom,
% 52.23/52.35 ! [V_N_2,V_h_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( ! [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))
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 52.23/52.35 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => 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)) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_rp__inv__image__def,axiom,
% 52.23/52.35 ! [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))) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_in__inv__image,axiom,
% 52.23/52.35 ! [V_f_2,V_r_2,T_c,V_y_2,V_x_2,T_b] :
% 52.23/52.35 ( hBOOL(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)))
% 52.23/52.35 <=> 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)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Max_Ohom__commute,axiom,
% 52.23/52.35 ! [V_N_2,V_h_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( ! [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))
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 52.23/52.35 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => 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)) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Min_Ohom__commute,axiom,
% 52.23/52.35 ! [V_N_2,V_h_2,T_b] :
% 52.23/52.35 ( class_Orderings_Olinorder(T_b)
% 52.23/52.35 => ( ! [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))
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 52.23/52.35 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => 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)) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_measure__def,axiom,
% 52.23/52.35 ! [T_b] : c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_irrefl__def,axiom,
% 52.23/52.35 ! [V_r_2,T_b] :
% 52.23/52.35 ( c_Relation_Oirrefl(T_b,V_r_2)
% 52.23/52.35 <=> ! [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)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Field__insert,axiom,
% 52.23/52.35 ! [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)) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Id__on__def,axiom,
% 52.23/52.35 ! [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)))) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Id__on__def_H,axiom,
% 52.23/52.35 ! [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)) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Id__on__empty,axiom,
% 52.23/52.35 ! [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)) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Field__empty,axiom,
% 52.23/52.35 ! [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)) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_mono__Field,axiom,
% 52.23/52.35 ! [V_s_2,V_r_2,T_b] :
% 52.23/52.35 ( 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))
% 52.23/52.35 => 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))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Field__Un,axiom,
% 52.23/52.35 ! [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)) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_finite__Field,axiom,
% 52.23/52.35 ! [V_r_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 52.23/52.35 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_OField(T_b),V_r_2))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Id__on__eqI,axiom,
% 52.23/52.35 ! [V_A_2,T_b,V_b_2,V_a_2] :
% 52.23/52.35 ( V_a_2 = V_b_2
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.23/52.35 => hBOOL(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))) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Id__on__iff,axiom,
% 52.23/52.35 ! [V_A_2,V_y_2,V_x_2,T_b] :
% 52.23/52.35 ( hBOOL(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)))
% 52.23/52.35 <=> ( V_x_2 = V_y_2
% 52.23/52.35 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Id__onE,axiom,
% 52.23/52.35 ! [V_A_2,V_c_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_c_2),c_Relation_OId__on(T_b,V_A_2)))
% 52.23/52.35 => ~ ! [B_x] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.23/52.35 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Sup__fin_Ohom__commute,axiom,
% 52.23/52.35 ! [V_N_2,V_h_2,T_b] :
% 52.23/52.35 ( class_Lattices_Olattice(T_b)
% 52.23/52.35 => ( ! [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))
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 52.23/52.35 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => 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)) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setprod__mono__one__left,axiom,
% 52.23/52.35 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 52.23/52.35 ( class_Groups_Ocomm__monoid__mult(T_c)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 52.23/52.35 => ( ! [B_x] :
% 52.23/52.35 ( 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)))
% 52.23/52.35 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 52.23/52.35 => 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) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setprod__mono__one__right,axiom,
% 52.23/52.35 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 52.23/52.35 ( class_Groups_Ocomm__monoid__mult(T_c)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 52.23/52.35 => ( ! [B_x] :
% 52.23/52.35 ( 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)))
% 52.23/52.35 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 52.23/52.35 => 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) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setsum__mono__zero__right,axiom,
% 52.23/52.35 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 52.23/52.35 ( class_Groups_Ocomm__monoid__add(T_c)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 52.23/52.35 => ( ! [B_x] :
% 52.23/52.35 ( 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)))
% 52.23/52.35 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 52.23/52.35 => 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) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setsum__mono__zero__left,axiom,
% 52.23/52.35 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 52.23/52.35 ( class_Groups_Ocomm__monoid__add(T_c)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 52.23/52.35 => ( ! [B_x] :
% 52.23/52.35 ( 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)))
% 52.23/52.35 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 52.23/52.35 => 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) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_card__Pow,axiom,
% 52.23/52.35 ! [V_A_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => 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)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_finite__empty__induct,axiom,
% 52.23/52.35 ! [V_P_2,V_A_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(V_P_2,V_A_2))
% 52.23/52.35 => ( ! [B_a,B_A] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
% 52.23/52.35 => ( hBOOL(hAPP(V_P_2,B_A))
% 52.23/52.35 => 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)))))) ) ) )
% 52.23/52.35 => hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_escape,axiom,
% 52.23/52.35 ! [V_Q_2,V_c_2,V_Ga_2,T_b,V_P_2] :
% 52.23/52.35 ( ! [B_Z,B_s] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
% 52.23/52.35 => 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)))) )
% 52.23/52.35 => 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)))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_PowI,axiom,
% 52.23/52.35 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.35 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Pow__insert,axiom,
% 52.23/52.35 ! [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))) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Pow__empty,axiom,
% 52.23/52.35 ! [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))) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Pow__bottom,axiom,
% 52.23/52.35 ! [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))) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Pow__not__empty,axiom,
% 52.23/52.35 ! [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)) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Pow__top,axiom,
% 52.23/52.35 ! [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))) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Pow__iff,axiom,
% 52.23/52.35 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 52.23/52.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_PowD,axiom,
% 52.23/52.35 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 52.23/52.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Cantors__paradox,axiom,
% 52.23/52.35 ! [V_A_2,T_b] :
% 52.23/52.35 ~ ? [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) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_image__Pow__surj,axiom,
% 52.23/52.35 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 52.23/52.35 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_B_2
% 52.23/52.35 => 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) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Pow__UNIV,axiom,
% 52.23/52.35 ! [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)) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_finite__Pow__iff,axiom,
% 52.23/52.35 ! [V_A_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)))
% 52.23/52.35 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Pow__mono,axiom,
% 52.23/52.35 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.35 => 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))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Un__Pow__subset,axiom,
% 52.23/52.35 ! [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)))) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_UN__Pow__subset,axiom,
% 52.23/52.35 ! [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)))) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Powp__Pow__eq,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,T_b] :
% 52.23/52.35 ( 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))
% 52.23/52.35 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_image__Pow__mono,axiom,
% 52.23/52.35 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 52.23/52.35 ( 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))
% 52.23/52.35 => 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))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_folding__one__idem_Ounion__idem,axiom,
% 52.23/52.35 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 52.23/52.35 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.35 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => 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)) ) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_finite__subset__induct,axiom,
% 52.23/52.35 ! [V_P_2,V_A_2,V_F_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 52.23/52.35 => ( ! [B_a,B_F] :
% 52.23/52.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 52.23/52.35 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F))
% 52.23/52.35 => ( hBOOL(hAPP(V_P_2,B_F))
% 52.23/52.35 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F))) ) ) ) )
% 52.23/52.35 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_folding__one__idem_Osubset__idem,axiom,
% 52.23/52.35 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 52.23/52.35 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 52.23/52.35 => 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) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_folding__one__idem_Oidem,axiom,
% 52.23/52.35 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 52.23/52.35 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 52.23/52.35 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_folding__one__idem_Oin__idem,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 52.23/52.35 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_folding__one__idem_Oinsert__idem,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 52.23/52.35 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => 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)) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setsum__strict__mono,axiom,
% 52.23/52.35 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 52.23/52.35 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 52.23/52.35 & class_Groups_Oordered__cancel__ab__semigroup__add(T_c) )
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.35 => ( ! [B_x] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.23/52.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 52.23/52.35 => 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))) ) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_equiv__intrel__iff,axiom,
% 52.23/52.35 ! [V_y_2,V_x_2] :
% 52.23/52.35 ( 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))))
% 52.23/52.35 <=> 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)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_setsum__Plus,axiom,
% 52.23/52.35 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 52.23/52.35 ( class_Groups_Ocomm__monoid__add(T_d)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 52.23/52.35 => 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)) ) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Image__empty,axiom,
% 52.23/52.35 ! [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)) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Image__Un,axiom,
% 52.23/52.35 ! [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)) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Image__UN,axiom,
% 52.23/52.35 ! [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)) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_image__compose,axiom,
% 52.23/52.35 ! [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)) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_K__record__comp,axiom,
% 52.23/52.35 ! [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 ).
% 52.23/52.35
% 52.23/52.35 fof(fact_o__eq__dest__lhs,axiom,
% 52.23/52.35 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
% 52.23/52.35 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = V_c_2
% 52.23/52.35 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_o__def,axiom,
% 52.23/52.35 ! [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)) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_o__assoc,axiom,
% 52.23/52.35 ! [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) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_o__apply,axiom,
% 52.23/52.35 ! [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)) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_o__eq__dest,axiom,
% 52.23/52.35 ! [V_v_2,V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
% 52.23/52.35 ( 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)
% 52.23/52.35 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,hAPP(V_d_2,V_v_2)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_o__eq__elim,axiom,
% 52.23/52.35 ! [V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
% 52.23/52.35 ( 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)
% 52.23/52.35 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_c_2,hAPP(V_d_2,B_v)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_apfst__compose,axiom,
% 52.23/52.35 ! [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) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_apsnd__compose,axiom,
% 52.23/52.35 ! [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) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_comp__cong,axiom,
% 52.23/52.35 ! [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] :
% 52.23/52.35 ( 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))
% 52.23/52.35 => 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) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_fun__upd__comp,axiom,
% 52.23/52.35 ! [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)) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_comp__surj,axiom,
% 52.23/52.35 ! [V_g_2,T_d,V_f_2,T_b,T_c] :
% 52.23/52.35 ( 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))
% 52.23/52.35 => ( 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))
% 52.23/52.35 => 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)) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Image__mono,axiom,
% 52.23/52.35 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_c,T_b] :
% 52.23/52.35 ( 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))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2))
% 52.23/52.35 => 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))) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Un__Image,axiom,
% 52.23/52.35 ! [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)) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Image__iff,axiom,
% 52.23/52.35 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 52.23/52.35 <=> ? [B_x] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 52.23/52.35 & 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)) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_rev__ImageI,axiom,
% 52.23/52.35 ! [V_r_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.23/52.35 => ( 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))
% 52.23/52.35 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Image__eq__UN,axiom,
% 52.23/52.35 ! [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))))) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Image__singleton__iff,axiom,
% 52.23/52.35 ! [V_a_2,V_r_2,T_c,V_b_2,T_b] :
% 52.23/52.35 ( 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))))))
% 52.23/52.35 <=> 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)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_of__int,axiom,
% 52.23/52.35 ! [V_j_2,V_i_2,T_b] :
% 52.23/52.35 ( class_Rings_Oring__1(T_b)
% 52.23/52.35 => 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)) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_One__int__def,axiom,
% 52.23/52.35 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))))) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_mult,axiom,
% 52.23/52.35 ! [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))))) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_UN__o,axiom,
% 52.23/52.35 ! [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) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Rep__Integ__inverse,axiom,
% 52.23/52.35 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ).
% 52.23/52.35
% 52.23/52.35 fof(fact_split__comp,axiom,
% 52.23/52.35 ! [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)) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_number__of__code__numeral__def,axiom,
% 52.23/52.35 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) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_int__of__def,axiom,
% 52.23/52.35 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) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_minus,axiom,
% 52.23/52.35 ! [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))))) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Zero__int__def,axiom,
% 52.23/52.35 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))))) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_int__def,axiom,
% 52.23/52.35 ! [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))))) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_add,axiom,
% 52.23/52.35 ! [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))))) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_nat,axiom,
% 52.23/52.35 ! [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) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_minus__int__def,axiom,
% 52.23/52.35 ! [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))))))) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_less,axiom,
% 52.23/52.35 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 52.23/52.35 ( 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)))))))
% 52.23/52.35 <=> 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))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_le,axiom,
% 52.23/52.35 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 52.23/52.35 ( 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)))))))
% 52.23/52.35 <=> 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))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Loop__sound__lemma,axiom,
% 52.23/52.35 ! [V_c_2,V_b_2,V_P_2,V_Ga_2,T_b] :
% 52.23/52.35 ( 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))))
% 52.23/52.35 => 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)))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Nitpick_Odenom__def,axiom,
% 52.23/52.35 ! [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)) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Nitpick_Onum__def,axiom,
% 52.23/52.35 ! [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)) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_peek__and__def,axiom,
% 52.23/52.35 ! [V_s_2,V_Z_2,V_p_2,V_P_2,T_b] :
% 52.23/52.35 ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_b,V_P_2,V_p_2),V_Z_2),V_s_2))
% 52.23/52.35 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_Z_2),V_s_2))
% 52.23/52.35 & hBOOL(hAPP(V_p_2,V_s_2)) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_Loop,axiom,
% 52.23/52.35 ! [V_c_2,V_b_2,V_P_2,V_Ga_2,T_b] :
% 52.23/52.35 ( 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))))
% 52.23/52.35 => 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)))) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_hoare__derivs_OIf,axiom,
% 52.23/52.35 ! [V_d_2,V_Q_2,V_c_2,V_b_2,V_P_2,V_Ga_2,T_b] :
% 52.23/52.35 ( 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))))
% 52.23/52.35 => ( 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))))
% 52.23/52.35 => 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)))) ) ) ).
% 52.23/52.35
% 52.23/52.35 fof(fact_folding_Oremove,axiom,
% 52.23/52.35 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 52.23/52.35 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 52.23/52.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.35 => 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)) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_eq__Abs__Integ,axiom,
% 52.23/52.36 ! [V_z_2] :
% 52.23/52.36 ~ ! [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))))) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_folding_Oinsert__remove,axiom,
% 52.23/52.36 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 52.23/52.36 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.36 => 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)) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_folding_Ocommute__comps_I1_J,axiom,
% 52.23/52.36 ! [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] :
% 52.23/52.36 ( c_Finite__Set_Ofolding(T_b,T_c,V_fa_2,V_F_2)
% 52.23/52.36 => 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) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_folding_Ocommute__comp,axiom,
% 52.23/52.36 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_c,T_b] :
% 52.23/52.36 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_folding_Ocommute__left__comp,axiom,
% 52.23/52.36 ! [V_g_2,V_x_2,V_y_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 52.23/52.36 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_folding_Ocommute__left__comp_H_H,axiom,
% 52.23/52.36 ! [V_g_2,T_d,V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 52.23/52.36 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.36 => 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)) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_folding_Ocommute__comp_H_H,axiom,
% 52.23/52.36 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 52.23/52.36 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.36 => 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)) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_folding_Ocommute__left__comp_H,axiom,
% 52.23/52.36 ! [V_g_2,V_x_2,T_d,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 52.23/52.36 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.36 => 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)) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_folding_Ocommute__comp_H,axiom,
% 52.23/52.36 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 52.23/52.36 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.36 => 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)) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_folding_Oinsert,axiom,
% 52.23/52.36 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 52.23/52.36 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.36 => 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)) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_setsum__reindex__nonzero,axiom,
% 52.23/52.36 ! [T_c,V_h_2,V_f_2,V_S_2,T_b,T_d] :
% 52.23/52.36 ( class_Groups_Ocomm__monoid__add(T_d)
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 52.23/52.36 => ( ! [B_x] :
% 52.23/52.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 52.23/52.36 => ! [B_y] :
% 52.23/52.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2))
% 52.23/52.36 => ( B_x != B_y
% 52.23/52.36 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 52.23/52.36 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) )
% 52.23/52.36 => 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) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Random__Sequence_Omap__def,axiom,
% 52.23/52.36 ! [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)) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_quotient__def,axiom,
% 52.23/52.36 ! [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)))) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_quotient__is__empty,axiom,
% 52.23/52.36 ! [V_r_2,V_A_2,T_b] :
% 52.23/52.36 ( 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))
% 52.23/52.36 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_quotient__is__empty2,axiom,
% 52.23/52.36 ! [V_r_2,V_A_2,T_b] :
% 52.23/52.36 ( 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)
% 52.23/52.36 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_quotient__empty,axiom,
% 52.23/52.36 ! [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)) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_quotientI,axiom,
% 52.23/52.36 ! [V_r_2,V_A_2,V_x_2,T_b] :
% 52.23/52.36 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.36 => 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))) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_singleton__quotient,axiom,
% 52.23/52.36 ! [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))) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_subset__equiv__class,axiom,
% 52.23/52.36 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_b] :
% 52.23/52.36 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 52.23/52.36 => ( 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))))))
% 52.23/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 52.23/52.36 => hBOOL(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)) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_quotientE,axiom,
% 52.23/52.36 ! [V_r_2,V_A_2,V_X_2,T_b] :
% 52.23/52.36 ( 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)))
% 52.23/52.36 => ~ ! [B_x] :
% 52.23/52.36 ( 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))))
% 52.23/52.36 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_eq__equiv__class__iff2,axiom,
% 52.23/52.36 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 52.23/52.36 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 52.23/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 52.23/52.36 => ( 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)
% 52.23/52.36 <=> hBOOL(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)) ) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_equiv__intrel,axiom,
% 52.23/52.36 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) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_equiv__class__self,axiom,
% 52.23/52.36 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 52.23/52.36 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 52.23/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.23/52.36 => 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)))))) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_equiv__class__eq,axiom,
% 52.23/52.36 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
% 52.23/52.36 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 52.23/52.36 => ( hBOOL(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))
% 52.23/52.36 => 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)))) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_quotient__eqI,axiom,
% 52.23/52.36 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 52.23/52.36 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 52.23/52.36 => ( 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)))
% 52.23/52.36 => ( 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)))
% 52.23/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 52.23/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 52.23/52.36 => ( hBOOL(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))
% 52.23/52.36 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_quotient__eq__iff,axiom,
% 52.23/52.36 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 52.23/52.36 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 52.23/52.36 => ( 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)))
% 52.23/52.36 => ( 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)))
% 52.23/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 52.23/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 52.23/52.36 => ( V_X_2 = V_Y_2
% 52.23/52.36 <=> hBOOL(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)) ) ) ) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_equiv__class__eq__iff,axiom,
% 52.23/52.36 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 52.23/52.36 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 52.23/52.36 => ( hBOOL(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))
% 52.23/52.36 <=> ( 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))))
% 52.23/52.36 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.36 & hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_eq__equiv__class,axiom,
% 52.23/52.36 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_b] :
% 52.23/52.36 ( 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))))
% 52.23/52.36 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 52.23/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 52.23/52.36 => hBOOL(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)) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_eq__equiv__class__iff,axiom,
% 52.23/52.36 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 52.23/52.36 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 52.23/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.23/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 52.23/52.36 => ( 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))))
% 52.23/52.36 <=> hBOOL(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)) ) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_equiv__class__subset,axiom,
% 52.23/52.36 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
% 52.23/52.36 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 52.23/52.36 => ( hBOOL(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))
% 52.23/52.36 => 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)))))) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_UN__equiv__class,axiom,
% 52.23/52.36 ! [V_a_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 52.23/52.36 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 52.23/52.36 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 52.23/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.23/52.36 => 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) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_UN__equiv__class2,axiom,
% 52.23/52.36 ! [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] :
% 52.23/52.36 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 52.23/52.36 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 52.23/52.36 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 52.23/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a1_2),V_A1_2))
% 52.23/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a2_2),V_A2_2))
% 52.23/52.36 => 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) ) ) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_equiv__class__nondisjoint,axiom,
% 52.23/52.36 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_b] :
% 52.23/52.36 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 52.23/52.36 => ( 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)))))))
% 52.23/52.36 => hBOOL(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)) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf1I,axiom,
% 52.23/52.36 ! [T_b,V_B_2,V_x_2,V_A_2] :
% 52.23/52.36 ( hBOOL(hAPP(V_A_2,V_x_2))
% 52.23/52.36 => ( hBOOL(hAPP(V_B_2,V_x_2))
% 52.23/52.36 => 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)) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf1E,axiom,
% 52.23/52.36 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 52.23/52.36 ( 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))
% 52.23/52.36 => ~ ( hBOOL(hAPP(V_A_2,V_x_2))
% 52.23/52.36 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_IntI,axiom,
% 52.23/52.36 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 52.23/52.36 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 52.23/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 52.23/52.36 => 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))) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_IntE,axiom,
% 52.23/52.36 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 52.23/52.36 ( 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)))
% 52.23/52.36 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 52.23/52.36 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_finite__Int,axiom,
% 52.23/52.36 ! [V_Ga_2,V_F_2,T_b] :
% 52.23/52.36 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 52.23/52.36 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) )
% 52.23/52.36 => 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))) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf__eq__top__iff,axiom,
% 52.23/52.36 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.36 ( class_Lattices_Obounded__lattice__top(T_b)
% 52.23/52.36 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b)
% 52.23/52.36 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_b)
% 52.23/52.36 & V_y_2 = c_Orderings_Otop__class_Otop(T_b) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf__top__right,axiom,
% 52.23/52.36 ! [V_x,T_a] :
% 52.23/52.36 ( class_Lattices_Obounded__lattice__top(T_a)
% 52.23/52.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf__top__left,axiom,
% 52.23/52.36 ! [V_x,T_a] :
% 52.23/52.36 ( class_Lattices_Obounded__lattice__top(T_a)
% 52.23/52.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Int__UNIV__right,axiom,
% 52.23/52.36 ! [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 ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Int__UNIV__left,axiom,
% 52.23/52.36 ! [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 ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf__Int__eq,axiom,
% 52.23/52.36 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 52.23/52.36 ( 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))
% 52.23/52.36 <=> 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))) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Int__iff,axiom,
% 52.23/52.36 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 52.23/52.36 ( 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)))
% 52.23/52.36 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 52.23/52.36 & hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_IntD1,axiom,
% 52.23/52.36 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 52.23/52.36 ( 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)))
% 52.23/52.36 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_IntD2,axiom,
% 52.23/52.36 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 52.23/52.36 ( 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)))
% 52.23/52.36 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_sup__inf__distrib2,axiom,
% 52.23/52.36 ! [V_x,V_z,V_y,T_a] :
% 52.23/52.36 ( class_Lattices_Odistrib__lattice(T_a)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf__sup__distrib2,axiom,
% 52.23/52.36 ! [V_x,V_z,V_y,T_a] :
% 52.23/52.36 ( class_Lattices_Odistrib__lattice(T_a)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_sup__inf__distrib1,axiom,
% 52.23/52.36 ! [V_z,V_y,V_x,T_a] :
% 52.23/52.36 ( class_Lattices_Odistrib__lattice(T_a)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf__sup__distrib1,axiom,
% 52.23/52.36 ! [V_z,V_y,V_x,T_a] :
% 52.23/52.36 ( class_Lattices_Odistrib__lattice(T_a)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_sup__inf__absorb,axiom,
% 52.23/52.36 ! [V_y,V_x,T_a] :
% 52.23/52.36 ( class_Lattices_Olattice(T_a)
% 52.23/52.36 => 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 ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf__sup__absorb,axiom,
% 52.23/52.36 ! [V_y,V_x,T_a] :
% 52.23/52.36 ( class_Lattices_Olattice(T_a)
% 52.23/52.36 => 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 ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Un__Int__crazy,axiom,
% 52.23/52.36 ! [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)) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Un__Int__distrib2,axiom,
% 52.23/52.36 ! [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)) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Int__Un__distrib2,axiom,
% 52.23/52.36 ! [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)) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Un__Int__distrib,axiom,
% 52.23/52.36 ! [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)) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Int__Un__distrib,axiom,
% 52.23/52.36 ! [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)) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Int__empty__left,axiom,
% 52.23/52.36 ! [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)) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Int__empty__right,axiom,
% 52.23/52.36 ! [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)) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_disjoint__iff__not__equal,axiom,
% 52.23/52.36 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.36 ( 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))
% 52.23/52.36 <=> ! [B_x] :
% 52.23/52.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.23/52.36 => ! [B_xa] :
% 52.23/52.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2))
% 52.23/52.36 => B_x != B_xa ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf__bot__left,axiom,
% 52.23/52.36 ! [V_x,T_a] :
% 52.23/52.36 ( class_Lattices_Obounded__lattice__bot(T_a)
% 52.23/52.36 => 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) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf__bot__right,axiom,
% 52.23/52.36 ! [V_x,T_a] :
% 52.23/52.36 ( class_Lattices_Obounded__lattice__bot(T_a)
% 52.23/52.36 => 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) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_insert__inter__insert,axiom,
% 52.23/52.36 ! [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)) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_restrict__restrict,axiom,
% 52.23/52.36 ! [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)) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Diff__Int2,axiom,
% 52.23/52.36 ! [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) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Diff__Int__distrib2,axiom,
% 52.23/52.36 ! [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)) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Int__Diff,axiom,
% 52.23/52.36 ! [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)) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Diff__Int__distrib,axiom,
% 52.23/52.36 ! [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)) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom,
% 52.23/52.36 ! [V_B_2,V_A_2] :
% 52.23/52.36 ( c_Nat__Transfer_Onat__set(V_A_2)
% 52.23/52.36 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 52.23/52.36 => 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)) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf1D1,axiom,
% 52.23/52.36 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 52.23/52.36 ( 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))
% 52.23/52.36 => hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf1D2,axiom,
% 52.23/52.36 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 52.23/52.36 ( 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))
% 52.23/52.36 => hBOOL(hAPP(V_B_2,V_x_2)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Int__absorb,axiom,
% 52.23/52.36 ! [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 ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Int__commute,axiom,
% 52.23/52.36 ! [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) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Int__left__absorb,axiom,
% 52.23/52.36 ! [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) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Int__left__commute,axiom,
% 52.23/52.36 ! [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)) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Int__assoc,axiom,
% 52.23/52.36 ! [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)) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf_Oidem,axiom,
% 52.23/52.36 ! [V_a,T_a] :
% 52.23/52.36 ( class_Lattices_Osemilattice__inf(T_a)
% 52.23/52.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf__idem,axiom,
% 52.23/52.36 ! [V_x,T_a] :
% 52.23/52.36 ( class_Lattices_Osemilattice__inf(T_a)
% 52.23/52.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf_Ocommute,axiom,
% 52.23/52.36 ! [V_b,V_a,T_a] :
% 52.23/52.36 ( class_Lattices_Osemilattice__inf(T_a)
% 52.23/52.36 => 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) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf__sup__aci_I1_J,axiom,
% 52.23/52.36 ! [V_y,V_x,T_a] :
% 52.23/52.36 ( class_Lattices_Olattice(T_a)
% 52.23/52.36 => 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) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf__commute,axiom,
% 52.23/52.36 ! [V_y,V_x,T_a] :
% 52.23/52.36 ( class_Lattices_Osemilattice__inf(T_a)
% 52.23/52.36 => 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) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf_Oleft__idem,axiom,
% 52.23/52.36 ! [V_b,V_a,T_a] :
% 52.23/52.36 ( class_Lattices_Osemilattice__inf(T_a)
% 52.23/52.36 => 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) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf__sup__aci_I4_J,axiom,
% 52.23/52.36 ! [V_y,V_x,T_a] :
% 52.23/52.36 ( class_Lattices_Olattice(T_a)
% 52.23/52.36 => 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) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf__left__idem,axiom,
% 52.23/52.36 ! [V_y,V_x,T_a] :
% 52.23/52.36 ( class_Lattices_Osemilattice__inf(T_a)
% 52.23/52.36 => 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) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf_Oleft__commute,axiom,
% 52.23/52.36 ! [V_c,V_a,V_b,T_a] :
% 52.23/52.36 ( class_Lattices_Osemilattice__inf(T_a)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf__sup__aci_I3_J,axiom,
% 52.23/52.36 ! [V_z,V_y,V_x,T_a] :
% 52.23/52.36 ( class_Lattices_Olattice(T_a)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf__left__commute,axiom,
% 52.23/52.36 ! [V_z,V_y,V_x,T_a] :
% 52.23/52.36 ( class_Lattices_Osemilattice__inf(T_a)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf_Oassoc,axiom,
% 52.23/52.36 ! [V_c,V_b,V_a,T_a] :
% 52.23/52.36 ( class_Lattices_Osemilattice__inf(T_a)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf__sup__aci_I2_J,axiom,
% 52.23/52.36 ! [V_z,V_y,V_x,T_a] :
% 52.23/52.36 ( class_Lattices_Olattice(T_a)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf__assoc,axiom,
% 52.23/52.36 ! [V_z,V_y,V_x,T_a] :
% 52.23/52.36 ( class_Lattices_Osemilattice__inf(T_a)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf__apply,axiom,
% 52.23/52.36 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 52.23/52.36 ( class_Lattices_Olattice(T_b)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf__fun__def,axiom,
% 52.23/52.36 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 52.23/52.36 ( class_Lattices_Olattice(T_b)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf__min,axiom,
% 52.23/52.36 ! [T_b] :
% 52.23/52.36 ( ( class_Lattices_Osemilattice__inf(T_b)
% 52.23/52.36 & class_Orderings_Olinorder(T_b) )
% 52.23/52.36 => c_Lattices_Osemilattice__inf__class_Oinf(T_b) = c_Orderings_Oord__class_Omin(T_b) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Inf__fin_Oidem,axiom,
% 52.23/52.36 ! [V_x,T_a] :
% 52.23/52.36 ( class_Lattices_Olattice(T_a)
% 52.23/52.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_less__infI2,axiom,
% 52.23/52.36 ! [V_a,V_x,V_b,T_a] :
% 52.23/52.36 ( class_Lattices_Osemilattice__inf(T_a)
% 52.23/52.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 52.23/52.36 => 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)) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_less__infI1,axiom,
% 52.23/52.36 ! [V_b,V_x,V_a,T_a] :
% 52.23/52.36 ( class_Lattices_Osemilattice__inf(T_a)
% 52.23/52.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 52.23/52.36 => 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)) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_le__infE,axiom,
% 52.23/52.36 ! [V_b,V_a,V_x,T_a] :
% 52.23/52.36 ( class_Lattices_Osemilattice__inf(T_a)
% 52.23/52.36 => ( 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)))
% 52.23/52.36 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 52.23/52.36 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf__mono,axiom,
% 52.23/52.36 ! [V_d,V_b,V_c,V_a,T_a] :
% 52.23/52.36 ( class_Lattices_Osemilattice__inf(T_a)
% 52.23/52.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 52.23/52.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 52.23/52.36 => 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))) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf__greatest,axiom,
% 52.23/52.36 ! [V_z,V_y,V_x,T_a] :
% 52.23/52.36 ( class_Lattices_Osemilattice__inf(T_a)
% 52.23/52.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 52.23/52.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 52.23/52.36 => 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))) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_le__infI,axiom,
% 52.23/52.36 ! [V_b,V_a,V_x,T_a] :
% 52.23/52.36 ( class_Lattices_Osemilattice__inf(T_a)
% 52.23/52.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 52.23/52.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 52.23/52.36 => 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))) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf__absorb2,axiom,
% 52.23/52.36 ! [V_x,V_y,T_a] :
% 52.23/52.36 ( class_Lattices_Osemilattice__inf(T_a)
% 52.23/52.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 52.23/52.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf__absorb1,axiom,
% 52.23/52.36 ! [V_y,V_x,T_a] :
% 52.23/52.36 ( class_Lattices_Osemilattice__inf(T_a)
% 52.23/52.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 52.23/52.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_le__infI2,axiom,
% 52.23/52.36 ! [V_a,V_x,V_b,T_a] :
% 52.23/52.36 ( class_Lattices_Osemilattice__inf(T_a)
% 52.23/52.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 52.23/52.36 => 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)) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_le__infI1,axiom,
% 52.23/52.36 ! [V_b,V_x,V_a,T_a] :
% 52.23/52.36 ( class_Lattices_Osemilattice__inf(T_a)
% 52.23/52.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 52.23/52.36 => 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)) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_le__inf__iff,axiom,
% 52.23/52.36 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 52.23/52.36 ( class_Lattices_Osemilattice__inf(T_b)
% 52.23/52.36 => ( 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)))
% 52.23/52.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 52.23/52.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_le__iff__inf,axiom,
% 52.23/52.36 ! [V_y_2,V_x_2,T_b] :
% 52.23/52.36 ( class_Lattices_Osemilattice__inf(T_b)
% 52.23/52.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 52.23/52.36 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf__le2,axiom,
% 52.23/52.36 ! [V_y,V_x,T_a] :
% 52.23/52.36 ( class_Lattices_Osemilattice__inf(T_a)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf__sup__ord_I2_J,axiom,
% 52.23/52.36 ! [V_y,V_x,T_a] :
% 52.23/52.36 ( class_Lattices_Olattice(T_a)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf__le1,axiom,
% 52.23/52.36 ! [V_y,V_x,T_a] :
% 52.23/52.36 ( class_Lattices_Osemilattice__inf(T_a)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf__sup__ord_I1_J,axiom,
% 52.23/52.36 ! [V_y,V_x,T_a] :
% 52.23/52.36 ( class_Lattices_Olattice(T_a)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Int__lower1,axiom,
% 52.23/52.36 ! [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)) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Int__lower2,axiom,
% 52.23/52.36 ! [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)) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Int__absorb2,axiom,
% 52.23/52.36 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.23/52.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Int__absorb1,axiom,
% 52.23/52.36 ! [V_A_2,V_B_2,T_b] :
% 52.23/52.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 52.23/52.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Int__greatest,axiom,
% 52.23/52.36 ! [V_B_2,V_A_2,V_C_2,T_b] :
% 52.23/52.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2))
% 52.23/52.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2))
% 52.23/52.36 => 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))) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Int__mono,axiom,
% 52.23/52.36 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 52.23/52.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 52.23/52.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 52.23/52.36 => 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))) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Pow__Int__eq,axiom,
% 52.23/52.36 ! [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)) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_UN__simps_I5_J,axiom,
% 52.23/52.36 ! [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)) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_UN__simps_I4_J,axiom,
% 52.23/52.36 ! [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) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_UN__extend__simps_I5_J,axiom,
% 52.23/52.36 ! [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)) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Int__UN__distrib,axiom,
% 52.23/52.36 ! [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)) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_UN__extend__simps_I4_J,axiom,
% 52.23/52.36 ! [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)) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Int__UN__distrib2,axiom,
% 52.23/52.36 ! [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))) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_distrib__sup__le,axiom,
% 52.23/52.36 ! [V_z,V_y,V_x,T_a] :
% 52.23/52.36 ( class_Lattices_Olattice(T_a)
% 52.23/52.36 => 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)))) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_distrib__inf__le,axiom,
% 52.23/52.36 ! [V_z,V_y,V_x,T_a] :
% 52.23/52.36 ( class_Lattices_Olattice(T_a)
% 52.23/52.36 => 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)))) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf__compl__bot,axiom,
% 52.23/52.36 ! [V_x,T_a] :
% 52.23/52.36 ( class_Lattices_Oboolean__algebra(T_a)
% 52.23/52.36 => 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) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_compl__inf__bot,axiom,
% 52.23/52.36 ! [V_x,T_a] :
% 52.23/52.36 ( class_Lattices_Oboolean__algebra(T_a)
% 52.23/52.36 => 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) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_diff__eq,axiom,
% 52.23/52.36 ! [V_y,V_x,T_a] :
% 52.23/52.36 ( class_Lattices_Oboolean__algebra(T_a)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_compl__inf,axiom,
% 52.23/52.36 ! [V_y,V_x,T_a] :
% 52.23/52.36 ( class_Lattices_Oboolean__algebra(T_a)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_compl__sup,axiom,
% 52.23/52.36 ! [V_y,V_x,T_a] :
% 52.23/52.36 ( class_Lattices_Oboolean__algebra(T_a)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Int__insert__left__if1,axiom,
% 52.23/52.36 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 52.23/52.36 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Int__insert__right__if1,axiom,
% 52.23/52.36 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 52.23/52.36 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Int__insert__left__if0,axiom,
% 52.23/52.36 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 52.23/52.36 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 52.23/52.36 => 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) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Int__insert__right__if0,axiom,
% 52.23/52.36 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 52.23/52.36 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.23/52.36 => 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) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Int__insert__left,axiom,
% 52.23/52.36 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 52.23/52.36 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 52.23/52.36 => 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)) )
% 52.23/52.36 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 52.23/52.36 => 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) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Int__insert__right,axiom,
% 52.23/52.36 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 52.23/52.36 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.23/52.36 => 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)) )
% 52.23/52.36 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.23/52.36 => 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) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_image__Int__subset,axiom,
% 52.23/52.36 ! [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)))) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Diff__disjoint,axiom,
% 52.23/52.36 ! [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)) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Diff__triv,axiom,
% 52.23/52.36 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.36 ( 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))
% 52.23/52.36 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Un__Int__assoc__eq,axiom,
% 52.23/52.36 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 52.23/52.36 ( 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))
% 52.23/52.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Diff__Int,axiom,
% 52.23/52.36 ! [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)) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Diff__Un,axiom,
% 52.23/52.36 ! [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)) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Un__Diff__Int,axiom,
% 52.23/52.36 ! [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 ).
% 52.23/52.36
% 52.23/52.36 fof(fact_ivl__disj__int_I11_J,axiom,
% 52.23/52.36 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 52.23/52.36 ( class_Orderings_Oorder(T_b)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom,
% 52.23/52.36 ! [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))) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Compl__disjoint,axiom,
% 52.23/52.36 ! [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)) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Compl__disjoint2,axiom,
% 52.23/52.36 ! [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)) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Image__Int__subset,axiom,
% 52.23/52.36 ! [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)))) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Compl__Int,axiom,
% 52.23/52.36 ! [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)) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Compl__Un,axiom,
% 52.23/52.36 ! [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)) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Diff__eq,axiom,
% 52.23/52.36 ! [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)) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Diff__Compl,axiom,
% 52.23/52.36 ! [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) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_ivl__disj__int_I14_J,axiom,
% 52.23/52.36 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 52.23/52.36 ( class_Orderings_Oorder(T_b)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Image__Id__on,axiom,
% 52.23/52.36 ! [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) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom,
% 52.23/52.36 ! [V_B_2,V_A_2] :
% 52.23/52.36 ( c_Nat__Transfer_Onat__set(V_A_2)
% 52.23/52.36 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 52.23/52.36 => 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))) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_congruent2__implies__congruent,axiom,
% 52.23/52.36 ! [V_a_2,V_f_2,V_r2_2,T_d,T_c,V_r1_2,V_A_2,T_b] :
% 52.23/52.36 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r1_2)
% 52.23/52.36 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 52.23/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.23/52.36 => c_Equiv__Relations_Ocongruent(T_c,T_d,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_inf__Sup__absorb,axiom,
% 52.23/52.36 ! [V_a_2,V_A_2,T_b] :
% 52.23/52.36 ( class_Lattices_Olattice(T_b)
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.23/52.36 => 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 ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_disjoint__eq__subset__Compl,axiom,
% 52.23/52.36 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.36 ( 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))
% 52.23/52.36 <=> 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))) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_ivl__disj__int_I15_J,axiom,
% 52.23/52.36 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 52.23/52.36 ( class_Orderings_Oorder(T_b)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Int__atLeastAtMost,axiom,
% 52.23/52.36 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 52.23/52.36 ( class_Orderings_Olinorder(T_b)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Int__atLeastLessThan,axiom,
% 52.23/52.36 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 52.23/52.36 ( class_Orderings_Olinorder(T_b)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_ivl__disj__int_I4_J,axiom,
% 52.23/52.36 ! [V_u_2,V_l_2,T_b] :
% 52.23/52.36 ( class_Orderings_Oorder(T_b)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_ivl__disj__int_I2_J,axiom,
% 52.23/52.36 ! [V_u_2,V_l_2,T_b] :
% 52.23/52.36 ( class_Orderings_Oorder(T_b)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_ivl__disj__int_I16_J,axiom,
% 52.23/52.36 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 52.23/52.36 ( class_Orderings_Oorder(T_b)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_ivl__disj__int_I12_J,axiom,
% 52.23/52.36 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 52.23/52.36 ( class_Orderings_Oorder(T_b)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_ivl__disj__int_I13_J,axiom,
% 52.23/52.36 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 52.23/52.36 ( class_Orderings_Oorder(T_b)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Int__greaterThanAtMost,axiom,
% 52.23/52.36 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 52.23/52.36 ( class_Orderings_Olinorder(T_b)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_ivl__disj__int_I9_J,axiom,
% 52.23/52.36 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 52.23/52.36 ( class_Orderings_Oorder(T_b)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Int__greaterThanLessThan,axiom,
% 52.23/52.36 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 52.23/52.36 ( class_Orderings_Olinorder(T_b)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Int__atLeastAtMostL1,axiom,
% 52.23/52.36 ! [V_d_2,V_b_2,V_a_2,T_b] :
% 52.23/52.36 ( class_Orderings_Olinorder(T_b)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Int__atLeastAtMostR1,axiom,
% 52.23/52.36 ! [V_d_2,V_c_2,V_b_2,T_b] :
% 52.23/52.36 ( class_Orderings_Olinorder(T_b)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_ivl__disj__int_I8_J,axiom,
% 52.23/52.36 ! [V_u_2,V_l_2,T_b] :
% 52.23/52.36 ( class_Orderings_Oorder(T_b)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_ivl__disj__int_I7_J,axiom,
% 52.23/52.36 ! [V_u_2,V_l_2,T_b] :
% 52.23/52.36 ( class_Orderings_Oorder(T_b)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Int__atLeastAtMostL2,axiom,
% 52.23/52.36 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 52.23/52.36 ( class_Orderings_Olinorder(T_b)
% 52.23/52.36 => 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) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Int__atLeastAtMostR2,axiom,
% 52.23/52.36 ! [V_d_2,V_c_2,V_a_2,T_b] :
% 52.23/52.36 ( class_Orderings_Olinorder(T_b)
% 52.23/52.36 => 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) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_ivl__disj__int_I3_J,axiom,
% 52.23/52.36 ! [V_u_2,V_l_2,T_b] :
% 52.23/52.36 ( class_Orderings_Oorder(T_b)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_ivl__disj__int_I10_J,axiom,
% 52.23/52.36 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 52.23/52.36 ( class_Orderings_Oorder(T_b)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_ivl__disj__int_I1_J,axiom,
% 52.23/52.36 ! [V_u_2,V_l_2,T_b] :
% 52.23/52.36 ( class_Orderings_Oorder(T_b)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_ivl__disj__int_I6_J,axiom,
% 52.23/52.36 ! [V_u_2,V_l_2,T_b] :
% 52.23/52.36 ( class_Orderings_Oorder(T_b)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_ivl__disj__int_I5_J,axiom,
% 52.23/52.36 ! [V_u_2,V_l_2,T_b] :
% 52.23/52.36 ( class_Orderings_Oorder(T_b)
% 52.23/52.36 => 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)) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_folding__image__simple_Ounion__inter,axiom,
% 52.23/52.36 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 52.23/52.36 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 52.23/52.36 => 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)) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_compl__unique,axiom,
% 52.23/52.36 ! [V_y,V_x,T_a] :
% 52.23/52.36 ( class_Lattices_Oboolean__algebra(T_a)
% 52.23/52.36 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a)
% 52.23/52.36 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a)
% 52.23/52.36 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_setsum__Un__Int,axiom,
% 52.23/52.36 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 52.23/52.36 ( class_Groups_Ocomm__monoid__add(T_c)
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.36 => 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)) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_setprod_Ounion__inter,axiom,
% 52.23/52.36 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 52.23/52.36 ( class_Groups_Ocomm__monoid__mult(T_c)
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.36 => 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)) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_setprod__Un__Int,axiom,
% 52.23/52.36 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 52.23/52.36 ( class_Groups_Ocomm__monoid__mult(T_c)
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.36 => 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)) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_card__Un__Int,axiom,
% 52.23/52.36 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.36 => 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))) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_card_Ounion__inter,axiom,
% 52.23/52.36 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.36 => 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)) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_card__Diff__subset__Int,axiom,
% 52.23/52.36 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.36 ( 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)))
% 52.23/52.36 => 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))) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_setsum__restrict__set,axiom,
% 52.23/52.36 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 52.23/52.36 ( class_Groups_Ocomm__monoid__add(T_c)
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.36 => 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) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_folding_Ounion__inter,axiom,
% 52.23/52.36 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 52.23/52.36 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.36 => 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)) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_quotient__disj,axiom,
% 52.23/52.36 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 52.23/52.36 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 52.23/52.36 => ( 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)))
% 52.23/52.36 => ( 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)))
% 52.23/52.36 => ( V_X_2 = V_Y_2
% 52.23/52.36 | 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)) ) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_atMost__Int__atLeast,axiom,
% 52.23/52.36 ! [V_n_2,T_b] :
% 52.23/52.36 ( class_Orderings_Oorder(T_b)
% 52.23/52.36 => 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))) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_folding__image__simple_Ounion__disjoint,axiom,
% 52.23/52.36 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 52.23/52.36 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 52.23/52.36 => ( 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))
% 52.23/52.36 => 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)) ) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_folding__one_Ounion__disjoint,axiom,
% 52.23/52.36 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 52.23/52.36 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.36 => ( 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))
% 52.23/52.36 => 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)) ) ) ) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_folding__one_Ounion__inter,axiom,
% 52.23/52.36 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 52.23/52.36 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.36 => ( 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))
% 52.23/52.36 => 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)) ) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_congruent__def,axiom,
% 52.23/52.36 ! [V_f_2,V_r_2,T_c,T_b] :
% 52.23/52.36 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 52.23/52.36 <=> ! [B_x] :
% 52.23/52.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 52.23/52.36 => 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)) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_setsum__Un__disjoint,axiom,
% 52.23/52.36 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 52.23/52.36 ( class_Groups_Ocomm__monoid__add(T_c)
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.36 => ( 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))
% 52.23/52.36 => 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)) ) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_setsum__Un,axiom,
% 52.23/52.36 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 52.23/52.36 ( class_Groups_Oab__group__add(T_c)
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.36 => 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))) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_setprod_Ounion__disjoint,axiom,
% 52.23/52.36 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 52.23/52.36 ( class_Groups_Ocomm__monoid__mult(T_c)
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.36 => ( 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))
% 52.23/52.36 => 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)) ) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_setprod__Un__disjoint,axiom,
% 52.23/52.36 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 52.23/52.36 ( class_Groups_Ocomm__monoid__mult(T_c)
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.36 => ( 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))
% 52.23/52.36 => 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)) ) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_card__Un__disjoint,axiom,
% 52.23/52.36 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.36 => ( 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))
% 52.23/52.36 => 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)) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Sup__fin_Ounion__inter,axiom,
% 52.23/52.36 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.36 ( class_Lattices_Olattice(T_b)
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.36 => ( 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))
% 52.23/52.36 => 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)) ) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Sup__fin_Ounion__disjoint,axiom,
% 52.23/52.36 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.36 ( class_Lattices_Olattice(T_b)
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.36 => ( 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))
% 52.23/52.36 => 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)) ) ) ) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Min_Ounion__inter,axiom,
% 52.23/52.36 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.36 ( class_Orderings_Olinorder(T_b)
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.36 => ( 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))
% 52.23/52.36 => 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)) ) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Min_Ounion__disjoint,axiom,
% 52.23/52.36 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.36 ( class_Orderings_Olinorder(T_b)
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.36 => ( 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))
% 52.23/52.36 => 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)) ) ) ) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Max_Ounion__disjoint,axiom,
% 52.23/52.36 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.36 ( class_Orderings_Olinorder(T_b)
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.36 => ( 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))
% 52.23/52.36 => 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)) ) ) ) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_Max_Ounion__inter,axiom,
% 52.23/52.36 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.36 ( class_Orderings_Olinorder(T_b)
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.36 => ( 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))
% 52.23/52.36 => 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)) ) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
% 52.23/52.36 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.36 ( class_Orderings_Olinorder(T_b)
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.36 => ( 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))
% 52.23/52.36 => 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)) ) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom,
% 52.23/52.36 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.36 ( class_Orderings_Olinorder(T_b)
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.36 => ( 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))
% 52.23/52.36 => 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)) ) ) ) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom,
% 52.23/52.36 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.36 ( class_Orderings_Olinorder(T_b)
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.23/52.36 => ( 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))
% 52.23/52.36 => 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)) ) ) ) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_min__max_OSup__fin_Ounion__inter,axiom,
% 52.23/52.36 ! [V_B_2,V_A_2,T_b] :
% 52.23/52.36 ( class_Orderings_Olinorder(T_b)
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.36 => ( 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))
% 52.23/52.36 => 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)) ) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_congruent2D,axiom,
% 52.23/52.36 ! [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] :
% 52.23/52.36 ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 52.23/52.36 => ( 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))
% 52.23/52.36 => ( 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))
% 52.23/52.36 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_setsum__Un__nat,axiom,
% 52.23/52.36 ! [V_f_2,V_B_2,V_A_2,T_b] :
% 52.23/52.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.23/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.23/52.36 => 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))) ) ) ).
% 52.23/52.36
% 52.23/52.36 fof(fact_folding_Ounion,axiom,
% 52.58/52.36 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.58/52.36 => ( 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))
% 52.58/52.36 => 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)) ) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_congruentD,axiom,
% 52.58/52.36 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_c,T_b] :
% 52.58/52.36 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 52.58/52.36 => ( 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))
% 52.58/52.36 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_congruent2__implies__congruent__UN,axiom,
% 52.58/52.36 ! [V_a_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
% 52.58/52.36 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 52.58/52.36 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 52.58/52.36 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 52.58/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A2_2))
% 52.58/52.36 => 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)) ) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_UN__equiv__class__inject,axiom,
% 52.58/52.36 ! [V_Y_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 52.58/52.36 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 52.58/52.36 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 52.58/52.36 => ( 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)
% 52.58/52.36 => ( 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)))
% 52.58/52.36 => ( 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)))
% 52.58/52.36 => ( ! [B_x] :
% 52.58/52.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.58/52.36 => ! [B_y] :
% 52.58/52.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 52.58/52.36 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 52.58/52.36 => 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)) ) ) )
% 52.58/52.36 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_UN__equiv__class__type2,axiom,
% 52.58/52.36 ! [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] :
% 52.58/52.36 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 52.58/52.36 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 52.58/52.36 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 52.58/52.36 => ( 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)))
% 52.58/52.36 => ( 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)))
% 52.58/52.36 => ( ! [B_x1] :
% 52.58/52.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x1),V_A1_2))
% 52.58/52.36 => ! [B_x2] :
% 52.58/52.36 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x2),V_A2_2))
% 52.58/52.36 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) )
% 52.58/52.36 => 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)) ) ) ) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_UN__equiv__class__type,axiom,
% 52.58/52.36 ! [V_B_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 52.58/52.36 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 52.58/52.36 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 52.58/52.36 => ( 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)))
% 52.58/52.36 => ( ! [B_x] :
% 52.58/52.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.58/52.36 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) )
% 52.58/52.36 => 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)) ) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inf__nat__def,axiom,
% 52.58/52.36 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inf__Int__eq2,axiom,
% 52.58/52.36 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 52.58/52.36 ( 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))
% 52.58/52.36 <=> 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))) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_card_Ounion__inter__neutral,axiom,
% 52.58/52.36 ! [V_B_2,V_A_2,T_b] :
% 52.58/52.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.58/52.36 => ( ( ? [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)))
% 52.58/52.36 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 52.58/52.36 => 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)) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_setprod__Un,axiom,
% 52.58/52.36 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 52.58/52.36 ( class_Fields_Ofield(T_c)
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.58/52.36 => ( ! [B_x] :
% 52.58/52.36 ( 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)))
% 52.58/52.36 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c) )
% 52.58/52.36 => 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))) ) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_Integ__def,axiom,
% 52.58/52.36 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) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inf2I,axiom,
% 52.58/52.36 ! [T_c,T_b,V_B_2,V_y_2,V_x_2,V_A_2] :
% 52.58/52.36 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 52.58/52.36 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 52.58/52.36 => 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)) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inf2E,axiom,
% 52.58/52.36 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 52.58/52.36 ( 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))
% 52.58/52.36 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 52.58/52.36 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inf2D1,axiom,
% 52.58/52.36 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 52.58/52.36 ( 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))
% 52.58/52.36 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inf2D2,axiom,
% 52.58/52.36 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 52.58/52.36 ( 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))
% 52.58/52.36 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_Rep__Integ,axiom,
% 52.58/52.36 ! [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)) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_setprod_Ounion__inter__neutral,axiom,
% 52.58/52.36 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 52.58/52.36 ( class_Groups_Ocomm__monoid__mult(T_c)
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.58/52.36 => ( ! [B_x] :
% 52.58/52.36 ( 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)))
% 52.58/52.36 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 52.58/52.36 => 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)) ) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_setprod__Un__one,axiom,
% 52.58/52.36 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 52.58/52.36 ( class_Groups_Ocomm__monoid__mult(T_c)
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 52.58/52.36 => ( ! [B_x] :
% 52.58/52.36 ( 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)))
% 52.58/52.36 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 52.58/52.36 => 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)) ) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_setsum_Ounion__inter__neutral,axiom,
% 52.58/52.36 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 52.58/52.36 ( class_Groups_Ocomm__monoid__add(T_c)
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.58/52.36 => ( ! [B_x] :
% 52.58/52.36 ( 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)))
% 52.58/52.36 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 52.58/52.36 => 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)) ) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_setsum__Un__zero,axiom,
% 52.58/52.36 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 52.58/52.36 ( class_Groups_Ocomm__monoid__add(T_c)
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 52.58/52.36 => ( ! [B_x] :
% 52.58/52.36 ( 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)))
% 52.58/52.36 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 52.58/52.36 => 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)) ) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_refl__on__def_H,axiom,
% 52.58/52.36 ! [V_r_2,V_A_2,T_b] :
% 52.58/52.36 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 52.58/52.36 <=> ( ! [B_x] :
% 52.58/52.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 52.58/52.36 => 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)) )
% 52.58/52.36 & ! [B_x] :
% 52.58/52.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.58/52.36 => 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)) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_Inf__fin_Oremove,axiom,
% 52.58/52.36 ! [V_x_2,V_A_2,T_b] :
% 52.58/52.36 ( class_Lattices_Olattice(T_b)
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.58/52.36 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 52.58/52.36 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_2 )
% 52.58/52.36 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 52.58/52.36 => 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)))))) ) ) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_refl__on__Id__on,axiom,
% 52.58/52.36 ! [V_A_2,T_b] : c_Relation_Orefl__on(T_b,V_A_2,c_Relation_OId__on(T_b,V_A_2)) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_Inf__fin_Osingleton,axiom,
% 52.58/52.36 ! [V_x_2,T_b] :
% 52.58/52.36 ( class_Lattices_Olattice(T_b)
% 52.58/52.36 => 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 ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_refl__on__empty,axiom,
% 52.58/52.36 ! [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))) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_refl__on__Un,axiom,
% 52.58/52.36 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 52.58/52.36 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 52.58/52.36 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 52.58/52.36 => 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)) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_refl__on__Int,axiom,
% 52.58/52.36 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 52.58/52.36 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 52.58/52.36 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 52.58/52.36 => 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)) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_sup__Inf__absorb,axiom,
% 52.58/52.36 ! [V_a_2,V_A_2,T_b] :
% 52.58/52.36 ( class_Lattices_Olattice(T_b)
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.58/52.36 => 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 ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_Inf__fin_Oin__idem,axiom,
% 52.58/52.36 ! [V_x_2,V_A_2,T_b] :
% 52.58/52.36 ( class_Lattices_Olattice(T_b)
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.58/52.36 => 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) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_refl__onD2,axiom,
% 52.58/52.36 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 52.58/52.36 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 52.58/52.36 => ( hBOOL(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))
% 52.58/52.36 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_refl__onD1,axiom,
% 52.58/52.36 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 52.58/52.36 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 52.58/52.36 => ( hBOOL(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))
% 52.58/52.36 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_refl__onD,axiom,
% 52.58/52.36 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 52.58/52.36 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 52.58/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.58/52.36 => hBOOL(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)) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_Inf__fin_Oinsert__idem,axiom,
% 52.58/52.36 ! [V_x_2,V_A_2,T_b] :
% 52.58/52.36 ( class_Lattices_Olattice(T_b)
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.36 => 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)) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_Inf__fin_Osubset__idem,axiom,
% 52.58/52.36 ! [V_B_2,V_A_2,T_b] :
% 52.58/52.36 ( class_Lattices_Olattice(T_b)
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 52.58/52.36 => 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) ) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_Inf__fin_Ounion__idem,axiom,
% 52.58/52.36 ! [V_B_2,V_A_2,T_b] :
% 52.58/52.36 ( class_Lattices_Olattice(T_b)
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.58/52.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.36 => 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)) ) ) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_Inf__le__Sup,axiom,
% 52.58/52.36 ! [V_A_2,T_b] :
% 52.58/52.36 ( class_Lattices_Olattice(T_b)
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.36 => 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))) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_Inf__fin_Oinsert,axiom,
% 52.58/52.36 ! [V_x_2,V_A_2,T_b] :
% 52.58/52.36 ( class_Lattices_Olattice(T_b)
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.58/52.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.36 => 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)) ) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_Inf__fin_Oinsert__remove,axiom,
% 52.58/52.36 ! [V_x_2,V_A_2,T_b] :
% 52.58/52.36 ( class_Lattices_Olattice(T_b)
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 52.58/52.36 => 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 )
% 52.58/52.36 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 52.58/52.36 => 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)))))) ) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_Inf__fin_Ounion__inter,axiom,
% 52.58/52.36 ! [V_B_2,V_A_2,T_b] :
% 52.58/52.36 ( class_Lattices_Olattice(T_b)
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.58/52.36 => ( 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))
% 52.58/52.36 => 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)) ) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_Inf__fin_Ounion__disjoint,axiom,
% 52.58/52.36 ! [V_B_2,V_A_2,T_b] :
% 52.58/52.36 ( class_Lattices_Olattice(T_b)
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.58/52.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.36 => ( 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))
% 52.58/52.36 => 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)) ) ) ) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_Inf__fin_Oclosed,axiom,
% 52.58/52.36 ! [V_A_2,T_b] :
% 52.58/52.36 ( class_Lattices_Olattice(T_b)
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.36 => ( ! [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))))))
% 52.58/52.36 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_equiv__imp__dvd__card,axiom,
% 52.58/52.36 ! [V_k_2,V_r_2,V_A_2,T_b] :
% 52.58/52.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 52.58/52.36 => ( ! [B_x] :
% 52.58/52.36 ( 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)))
% 52.58/52.36 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_b),B_x))) )
% 52.58/52.36 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_folding__idem_Ounion__idem,axiom,
% 52.58/52.36 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.58/52.36 => 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)) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_folding__idem_Oidem__left__comp,axiom,
% 52.58/52.36 ! [V_g_2,V_x_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 52.58/52.36 => 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) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_folding__idem_Oidem__comp,axiom,
% 52.58/52.36 ! [V_x_2,V_F_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 52.58/52.36 => 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) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_folding__idem_Oin__comp__idem,axiom,
% 52.58/52.36 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.58/52.36 => 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) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_folding__idem_Oinsert__idem,axiom,
% 52.58/52.36 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => 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)) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_folding__idem_Osubset__comp__idem,axiom,
% 52.58/52.36 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 52.58/52.36 => 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) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_equivp__equiv,axiom,
% 52.58/52.36 ! [V_A_2,T_b] :
% 52.58/52.36 ( c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2)
% 52.58/52.36 <=> 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)) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_card__quotient__disjoint,axiom,
% 52.58/52.36 ! [V_r_2,V_A_2,T_b] :
% 52.58/52.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => ( 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)
% 52.58/52.36 => 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) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_type__definition__Integ,axiom,
% 52.58/52.36 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) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__on__empty,axiom,
% 52.58/52.36 ! [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))) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__uminus,axiom,
% 52.58/52.36 ! [V_A_2,T_b] :
% 52.58/52.36 ( class_Groups_Oordered__ab__group__add(T_b)
% 52.58/52.36 => c_Fun_Oinj__on(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b),V_A_2) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__on__strict__subset,axiom,
% 52.58/52.36 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 52.58/52.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.58/52.36 => 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))) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__onD,axiom,
% 52.58/52.36 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 52.58/52.36 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 52.58/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.58/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 52.58/52.36 => V_x_2 = V_y_2 ) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__on__iff,axiom,
% 52.58/52.36 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 52.58/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.58/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 52.58/52.36 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 52.58/52.36 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__on__contraD,axiom,
% 52.58/52.36 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 52.58/52.36 => ( V_x_2 != V_y_2
% 52.58/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.58/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 52.58/52.36 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__on__Un__image__eq__iff,axiom,
% 52.58/52.36 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( 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))
% 52.58/52.36 => ( 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)
% 52.58/52.36 <=> V_A_2 = V_B_2 ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__comp,axiom,
% 52.58/52.36 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 52.58/52.36 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
% 52.58/52.36 => 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))) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__on__imageI,axiom,
% 52.58/52.36 ! [V_A_2,V_f_2,V_g_2,T_d,T_c,T_b] :
% 52.58/52.36 ( 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)
% 52.58/52.36 => 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)) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_comp__inj__on,axiom,
% 52.58/52.36 ! [V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 52.58/52.36 => ( 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))
% 52.58/52.36 => 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) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_comp__inj__on__iff,axiom,
% 52.58/52.36 ! [V_f_H_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 52.58/52.36 => ( 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))
% 52.58/52.36 <=> 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) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_card__image,axiom,
% 52.58/52.36 ! [V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 52.58/52.36 => 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) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__on__diff,axiom,
% 52.58/52.36 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 52.58/52.36 => 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)) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__on__id2,axiom,
% 52.58/52.36 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_COMBI(T_b),V_A_2) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__on__def,axiom,
% 52.58/52.36 ! [V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 52.58/52.36 <=> ! [B_x] :
% 52.58/52.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.58/52.36 => ! [B_xa] :
% 52.58/52.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 52.58/52.36 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
% 52.58/52.36 => B_x = B_xa ) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_subset__inj__on,axiom,
% 52.58/52.36 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 52.58/52.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.58/52.36 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_finite__imageD,axiom,
% 52.58/52.36 ! [V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 52.58/52.36 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2)
% 52.58/52.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__on__imageI2,axiom,
% 52.58/52.36 ! [V_A_2,V_f_2,V_f_H_2,T_d,T_c,T_b] :
% 52.58/52.36 ( 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)
% 52.58/52.36 => c_Fun_Oinj__on(T_b,T_d,V_f_2,V_A_2) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_identity__equivp,axiom,
% 52.58/52.36 ! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_equivp__def,axiom,
% 52.58/52.36 ! [V_R_2,T_b] :
% 52.58/52.36 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 52.58/52.36 <=> ! [B_x,B_y] :
% 52.58/52.36 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
% 52.58/52.36 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_equivp__reflp,axiom,
% 52.58/52.36 ! [V_x_2,V_R_2,T_b] :
% 52.58/52.36 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 52.58/52.36 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_equivp__symp,axiom,
% 52.58/52.36 ! [V_y_2,V_x_2,V_R_2,T_b] :
% 52.58/52.36 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 52.58/52.36 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 52.58/52.36 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_equivp__transp,axiom,
% 52.58/52.36 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
% 52.58/52.36 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 52.58/52.36 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 52.58/52.36 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
% 52.58/52.36 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__image__eq__iff,axiom,
% 52.58/52.36 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 52.58/52.36 => ( 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)
% 52.58/52.36 <=> V_A_2 = V_B_2 ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_injD,axiom,
% 52.58/52.36 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 52.58/52.36 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 52.58/52.36 => V_x_2 = V_y_2 ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__eq,axiom,
% 52.58/52.36 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 52.58/52.36 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 52.58/52.36 <=> V_x_2 = V_y_2 ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__fun,axiom,
% 52.58/52.36 ! [T_d,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 52.58/52.36 => 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))) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__on__Int,axiom,
% 52.58/52.36 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 52.58/52.36 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 52.58/52.36 => 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)) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__image__mem__iff,axiom,
% 52.58/52.36 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 52.58/52.36 => ( 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)))
% 52.58/52.36 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_range__ex1__eq,axiom,
% 52.58/52.36 ! [V_b_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 52.58/52.36 => ( 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)))))
% 52.58/52.36 <=> ? [B_x] :
% 52.58/52.36 ( V_b_2 = hAPP(V_f_2,B_x)
% 52.58/52.36 & ! [B_y] :
% 52.58/52.36 ( V_b_2 = hAPP(V_f_2,B_y)
% 52.58/52.36 => B_y = B_x ) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__on__iff__surj,axiom,
% 52.58/52.36 ! [V_A_H_2,T_c,T_b,V_A_2] :
% 52.58/52.36 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.36 => ( ? [B_f] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 52.58/52.36 & 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)) )
% 52.58/52.36 <=> ? [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) = V_A_2 ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_endo__inj__surj,axiom,
% 52.58/52.36 ! [V_f_2,V_A_2,T_b] :
% 52.58/52.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => ( 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))
% 52.58/52.36 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2)
% 52.58/52.36 => hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2) = V_A_2 ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_finite__surj__inj,axiom,
% 52.58/52.36 ! [V_f_2,V_A_2,T_b] :
% 52.58/52.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => ( 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)))
% 52.58/52.36 => c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_finite__UNIV__inj__surj,axiom,
% 52.58/52.36 ! [V_f_2,T_b] :
% 52.58/52.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 52.58/52.36 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 52.58/52.36 => 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)) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_finite__UNIV__surj__inj,axiom,
% 52.58/52.36 ! [V_f_2,T_b] :
% 52.58/52.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 52.58/52.36 => ( 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))
% 52.58/52.36 => c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__image__subset__iff,axiom,
% 52.58/52.36 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 52.58/52.36 => ( 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)))
% 52.58/52.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__on__image__Int,axiom,
% 52.58/52.36 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 52.58/52.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 52.58/52.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 52.58/52.36 => 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)) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_image__Int,axiom,
% 52.58/52.36 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 52.58/52.36 => 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)) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_eq__card__imp__inj__on,axiom,
% 52.58/52.36 ! [V_f_2,T_c,V_A_2,T_b] :
% 52.58/52.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => ( 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)
% 52.58/52.36 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__on__iff__eq__card,axiom,
% 52.58/52.36 ! [V_f_2,T_c,V_A_2,T_b] :
% 52.58/52.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 52.58/52.36 <=> 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) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__on__image__set__diff,axiom,
% 52.58/52.36 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 52.58/52.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 52.58/52.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 52.58/52.36 => 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)) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_image__set__diff,axiom,
% 52.58/52.36 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 52.58/52.36 => 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)) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_setsum__reindex,axiom,
% 52.58/52.36 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 52.58/52.36 ( class_Groups_Ocomm__monoid__add(T_d)
% 52.58/52.36 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 52.58/52.36 => 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) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_pigeonhole,axiom,
% 52.58/52.36 ! [V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( 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)))
% 52.58/52.36 => ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__on__fun__updI,axiom,
% 52.58/52.36 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 52.58/52.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 52.58/52.36 => 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) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_setprod__reindex,axiom,
% 52.58/52.36 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 52.58/52.36 ( class_Groups_Ocomm__monoid__mult(T_d)
% 52.58/52.36 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 52.58/52.36 => 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) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_setprod__reindex__cong,axiom,
% 52.58/52.36 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 52.58/52.36 ( class_Groups_Ocomm__monoid__mult(T_d)
% 52.58/52.36 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 52.58/52.36 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 52.58/52.36 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)
% 52.58/52.36 => 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) ) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__singleton,axiom,
% 52.58/52.36 ! [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))) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_setsum_Oreindex,axiom,
% 52.58/52.36 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 52.58/52.36 ( class_Groups_Ocomm__monoid__add(T_c)
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 52.58/52.36 => 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) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_card__bij__eq,axiom,
% 52.58/52.36 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 52.58/52.36 => ( 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))
% 52.58/52.36 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
% 52.58/52.36 => ( 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))
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 52.58/52.36 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_setprod_Oreindex,axiom,
% 52.58/52.36 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 52.58/52.36 ( class_Groups_Ocomm__monoid__mult(T_c)
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 52.58/52.36 => 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) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__image__Compl__subset,axiom,
% 52.58/52.36 ! [V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 52.58/52.36 => 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)))) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__on__insert,axiom,
% 52.58/52.36 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))
% 52.58/52.36 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 52.58/52.36 & ~ 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))))))) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__on__Un,axiom,
% 52.58/52.36 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( 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))
% 52.58/52.36 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 52.58/52.36 & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 52.58/52.36 & 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)) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__on__iff__card__le,axiom,
% 52.58/52.36 ! [V_B_2,T_c,V_A_2,T_b] :
% 52.58/52.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 52.58/52.36 => ( ? [B_f] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 52.58/52.36 & 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)) )
% 52.58/52.36 <=> 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))) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_card__inj__on__le,axiom,
% 52.58/52.36 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 52.58/52.36 => ( 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))
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 52.58/52.36 => 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))) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_quotient__diff1,axiom,
% 52.58/52.36 ! [V_a_2,V_A_2,V_r_2,T_b] :
% 52.58/52.36 ( 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)
% 52.58/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.58/52.36 => 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)) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_type__definition_OAbs__image,axiom,
% 52.58/52.36 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 52.58/52.36 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 52.58/52.36 => 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)) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_type__definition_ORep__range,axiom,
% 52.58/52.36 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 52.58/52.36 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 52.58/52.36 => 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 ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_folding__image_Oreindex,axiom,
% 52.58/52.36 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 52.58/52.36 => ( c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2)
% 52.58/52.36 => 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) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__Inr,axiom,
% 52.58/52.36 ! [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) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__Suc,axiom,
% 52.58/52.36 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__Some,axiom,
% 52.58/52.36 ! [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) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__Inl,axiom,
% 52.58/52.36 ! [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) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__on__add__nat,axiom,
% 52.58/52.36 ! [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) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__of__nat,axiom,
% 52.58/52.36 ! [T_b] :
% 52.58/52.36 ( class_Nat_Osemiring__char__0(T_b)
% 52.58/52.36 => 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))) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__int,axiom,
% 52.58/52.36 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))) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_swap__inj__on,axiom,
% 52.58/52.36 ! [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) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_folding__image_Odistrib,axiom,
% 52.58/52.36 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 52.58/52.36 => 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)) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_type__definition_ORep__inverse,axiom,
% 52.58/52.36 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 52.58/52.36 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 52.58/52.36 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_type__definition_ORep__inject,axiom,
% 52.58/52.36 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 52.58/52.36 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 52.58/52.36 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2)
% 52.58/52.36 <=> V_x_2 = V_y_2 ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_type__definition__code__numeral,axiom,
% 52.58/52.36 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))) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_type__definition_OAbs__inject,axiom,
% 52.58/52.36 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 52.58/52.36 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 52.58/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 52.58/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 52.58/52.36 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2)
% 52.58/52.36 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_type__definition_OAbs__inverse,axiom,
% 52.58/52.36 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 52.58/52.36 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 52.58/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 52.58/52.36 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_type__definition_ORep,axiom,
% 52.58/52.36 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 52.58/52.36 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 52.58/52.36 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_the__inv__into__comp,axiom,
% 52.58/52.36 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
% 52.58/52.36 ( 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))
% 52.58/52.36 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
% 52.58/52.36 => ( 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))))
% 52.58/52.36 => 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) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_the__inv__into__into,axiom,
% 52.58/52.36 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 52.58/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 52.58/52.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.58/52.36 => 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)) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_fold__Un__disjoint,axiom,
% 52.58/52.36 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 52.58/52.36 ( class_Groups_Ocomm__monoid__mult(T_c)
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.58/52.36 => ( 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))
% 52.58/52.36 => 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)) ) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_fold__image__empty,axiom,
% 52.58/52.36 ! [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 ).
% 52.58/52.36
% 52.58/52.36 fof(fact_folding__image__simple_Oeq__fold__g,axiom,
% 52.58/52.36 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 52.58/52.36 => 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) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_folding__image_Oeq__fold,axiom,
% 52.58/52.36 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 52.58/52.36 => 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) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_the__inv__into__f__eq,axiom,
% 52.58/52.36 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 52.58/52.36 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 52.58/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.58/52.36 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_the__inv__into__f__f,axiom,
% 52.58/52.36 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 52.58/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.58/52.36 => 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 ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_the__inv__f__f,axiom,
% 52.58/52.36 ! [V_x_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 52.58/52.36 => 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 ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__on__the__inv__into,axiom,
% 52.58/52.36 ! [V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 52.58/52.36 => 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)) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_the__inv__into__onto,axiom,
% 52.58/52.36 ! [V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 52.58/52.36 => 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 ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_fold__image__distrib,axiom,
% 52.58/52.36 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 52.58/52.36 ( class_Groups_Ocomm__monoid__mult(T_c)
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => 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)) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_the__inv__into__def,axiom,
% 52.58/52.36 ! [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))) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_fold__image__insert,axiom,
% 52.58/52.36 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_b,T_c] :
% 52.58/52.36 ( class_Groups_Oab__semigroup__mult(T_c)
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.58/52.36 => 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)) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_setsum_OF__eq,axiom,
% 52.58/52.36 ! [V_g_2,V_A_2,T_b,T_c] :
% 52.58/52.36 ( class_Groups_Ocomm__monoid__add(T_c)
% 52.58/52.36 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => 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) )
% 52.58/52.36 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => 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) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_setsum_Oeq__fold,axiom,
% 52.58/52.36 ! [V_g_2,V_A_2,T_b,T_c] :
% 52.58/52.36 ( class_Groups_Ocomm__monoid__add(T_c)
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => 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) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_setprod_OF__eq,axiom,
% 52.58/52.36 ! [V_g_2,V_A_2,T_b,T_c] :
% 52.58/52.36 ( class_Groups_Ocomm__monoid__mult(T_c)
% 52.58/52.36 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => 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) )
% 52.58/52.36 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => 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) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_setprod_Oeq__fold,axiom,
% 52.58/52.36 ! [V_g_2,V_A_2,T_b,T_c] :
% 52.58/52.36 ( class_Groups_Ocomm__monoid__mult(T_c)
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => 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) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_f__the__inv__into__f,axiom,
% 52.58/52.36 ! [V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 52.58/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 52.58/52.36 => 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 ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_fold__image__Un__Int,axiom,
% 52.58/52.36 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 52.58/52.36 ( class_Groups_Ocomm__monoid__mult(T_c)
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.58/52.36 => 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))) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_fold__image__reindex,axiom,
% 52.58/52.36 ! [V_z_2,V_g_2,V_h_2,T_c,V_A_2,T_b,T_d] :
% 52.58/52.36 ( class_Groups_Oab__semigroup__mult(T_d)
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => ( c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2)
% 52.58/52.36 => 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) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_image__eq__fold__image,axiom,
% 52.58/52.36 ! [V_f_2,T_c,V_A_2,T_b] :
% 52.58/52.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => 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) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_card_Oeq__fold__g,axiom,
% 52.58/52.36 ! [V_A_2,T_b] :
% 52.58/52.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => 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) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_card__def,axiom,
% 52.58/52.36 ! [V_A_2,T_b] :
% 52.58/52.36 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => 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) )
% 52.58/52.36 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.36 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_comm__monoid__big_OF__eq,axiom,
% 52.58/52.36 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 52.58/52.36 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 52.58/52.36 => 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) )
% 52.58/52.36 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 52.58/52.36 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_fold__image__Un__one,axiom,
% 52.58/52.36 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 52.58/52.36 ( class_Groups_Ocomm__monoid__mult(T_c)
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 52.58/52.36 => ( ! [B_x] :
% 52.58/52.36 ( 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)))
% 52.58/52.36 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 52.58/52.36 => 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)) ) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__vimage__singleton,axiom,
% 52.58/52.36 ! [V_a_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 52.58/52.36 => 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))))) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_vimageI,axiom,
% 52.58/52.36 ! [T_c,V_B_2,T_b,V_b_2,V_a_2,V_f_2] :
% 52.58/52.36 ( hAPP(V_f_2,V_a_2) = V_b_2
% 52.58/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_B_2))
% 52.58/52.36 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_vimage__Int,axiom,
% 52.58/52.36 ! [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)) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_vimage__UNIV,axiom,
% 52.58/52.36 ! [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)) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_vimage__compose,axiom,
% 52.58/52.36 ! [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)) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_vimage__UN,axiom,
% 52.58/52.36 ! [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)) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_vimage__mono,axiom,
% 52.58/52.36 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 52.58/52.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.58/52.36 => 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))) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_vimage__code,axiom,
% 52.58/52.36 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2))
% 52.58/52.36 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_vimage__Compl,axiom,
% 52.58/52.36 ! [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)) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_vimage__ident,axiom,
% 52.58/52.36 ! [V_Y_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 52.58/52.36
% 52.58/52.36 fof(fact_vimage__empty,axiom,
% 52.58/52.36 ! [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)) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_vimage__Un,axiom,
% 52.58/52.36 ! [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)) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_vimage__eq,axiom,
% 52.58/52.36 ! [V_B_2,V_f_2,T_c,V_a_2,T_b] :
% 52.58/52.36 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)))
% 52.58/52.36 <=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_vimageD,axiom,
% 52.58/52.36 ! [V_A_2,V_f_2,T_c,V_a_2,T_b] :
% 52.58/52.36 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)))
% 52.58/52.36 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2)) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_vimageI2,axiom,
% 52.58/52.36 ! [T_c,V_A_2,V_a_2,V_f_2,T_b] :
% 52.58/52.36 ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2))
% 52.58/52.36 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_surj__image__vimage__eq,axiom,
% 52.58/52.36 ! [V_A_2,V_f_2,T_b,T_c] :
% 52.58/52.36 ( 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))
% 52.58/52.36 => 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 ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_image__vimage__subset,axiom,
% 52.58/52.36 ! [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)) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_vimage__Diff,axiom,
% 52.58/52.36 ! [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)) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_vimage__singleton__eq,axiom,
% 52.58/52.36 ! [V_b_2,V_f_2,T_c,V_a_2,T_b] :
% 52.58/52.36 ( 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))))))
% 52.58/52.36 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_vimage__insert,axiom,
% 52.58/52.36 ! [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)) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_finite__vimageD,axiom,
% 52.58/52.36 ! [V_F_2,V_h_2,T_c,T_b] :
% 52.58/52.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
% 52.58/52.36 => ( 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))
% 52.58/52.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_vimage__subsetD,axiom,
% 52.58/52.36 ! [V_A_2,V_B_2,V_f_2,T_b,T_c] :
% 52.58/52.36 ( 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))
% 52.58/52.36 => ( 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))
% 52.58/52.36 => 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))) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_image__vimage__eq,axiom,
% 52.58/52.36 ! [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)))) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_finite__vimageI,axiom,
% 52.58/52.36 ! [V_h_2,T_c,V_F_2,T_b] :
% 52.58/52.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 52.58/52.36 => ( c_Fun_Oinj__on(T_c,T_b,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 52.58/52.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_b,V_h_2),V_F_2))) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_inj__vimage__image__eq,axiom,
% 52.58/52.36 ! [V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 52.58/52.36 => 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 ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_vimage__const,axiom,
% 52.58/52.36 ! [T_c,V_A_2,V_c_2,T_b] :
% 52.58/52.36 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 52.58/52.36 => 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)) )
% 52.58/52.36 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 52.58/52.36 => 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)) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_vimage__eq__UN,axiom,
% 52.58/52.36 ! [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))))) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_vimage__subsetI,axiom,
% 52.58/52.36 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 52.58/52.36 => ( 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)))
% 52.58/52.36 => 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)) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_vimage__if,axiom,
% 52.58/52.36 ! [V_B_2,T_c,V_d_2,V_A_2,V_c_2,T_b] :
% 52.58/52.36 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 52.58/52.36 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 52.58/52.36 => 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)) )
% 52.58/52.36 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 52.58/52.36 => 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 ) ) )
% 52.58/52.36 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 52.58/52.36 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 52.58/52.36 => 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) )
% 52.58/52.36 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 52.58/52.36 => 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)) ) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_comm__monoid__big_Oinfinite,axiom,
% 52.58/52.36 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 52.58/52.36 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 52.58/52.36 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_Inf__fin_Ohom__commute,axiom,
% 52.58/52.36 ! [V_N_2,V_h_2,T_b] :
% 52.58/52.36 ( class_Lattices_Olattice(T_b)
% 52.58/52.36 => ( ! [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))
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 52.58/52.36 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.36 => 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)) ) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_ImageE,axiom,
% 52.58/52.36 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
% 52.58/52.36 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 52.58/52.36 => ~ ! [B_x] :
% 52.58/52.36 ( 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))
% 52.58/52.36 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_strong__setprod__reindex__cong,axiom,
% 52.58/52.36 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 52.58/52.36 ( class_Groups_Ocomm__monoid__mult(T_d)
% 52.58/52.36 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 52.58/52.36 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 52.58/52.36 => ( ! [B_x] :
% 52.58/52.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.58/52.36 => 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) )
% 52.58/52.36 => 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) ) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom,
% 52.58/52.36 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 52.58/52.36 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 52.58/52.36 & class_Groups_Ocomm__monoid__mult(T_b) )
% 52.58/52.36 => ( V_A_2 = V_B_2
% 52.58/52.36 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 52.58/52.36 => ( ! [B_x] :
% 52.58/52.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 52.58/52.36 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 52.58/52.36 => 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) ) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_dom__eq__singleton__conv,axiom,
% 52.58/52.36 ! [V_x_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( 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)))
% 52.58/52.36 <=> ? [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)) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_fold__graph__permute__diff,axiom,
% 52.58/52.36 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_b] :
% 52.58/52.36 ( class_Groups_Oab__semigroup__mult(T_b)
% 52.58/52.36 => ( 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))
% 52.58/52.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.58/52.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 52.58/52.36 => 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)) ) ) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_fold__graph_Oequations_I1_J,axiom,
% 52.58/52.36 ! [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)) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_fold__graph_OemptyI,axiom,
% 52.58/52.36 ! [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)) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_empty__fold__graphE,axiom,
% 52.58/52.36 ! [V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( 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))
% 52.58/52.36 => V_x_2 = V_z_2 ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_finite__dom__body,axiom,
% 52.58/52.36 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_fold__graph__imp__finite,axiom,
% 52.58/52.36 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 52.58/52.36 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 52.58/52.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_domIff,axiom,
% 52.58/52.36 ! [V_m_2,T_c,V_a_2,T_b] :
% 52.58/52.36 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_c,V_m_2)))
% 52.58/52.36 <=> hAPP(V_m_2,V_a_2) != c_Option_Ooption_ONone(T_c) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_domI,axiom,
% 52.58/52.36 ! [T_c,V_b_2,T_b,V_a_2,V_m_2] :
% 52.58/52.36 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_b_2)
% 52.58/52.36 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Map_Odom(T_c,T_b,V_m_2))) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_insert__dom,axiom,
% 52.58/52.36 ! [T_c,V_y_2,T_b,V_x_2,V_f_2] :
% 52.58/52.36 ( hAPP(V_f_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
% 52.58/52.36 => 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) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_dom__restrict,axiom,
% 52.58/52.36 ! [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) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_fold__graph_OinsertI,axiom,
% 52.58/52.36 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 52.58/52.36 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.58/52.36 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 52.58/52.36 => 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))) ) ) ).
% 52.58/52.36
% 52.58/52.36 fof(fact_dom__eq__empty__conv,axiom,
% 52.58/52.36 ! [V_f_2,T_c,T_b] :
% 52.58/52.36 ( c_Map_Odom(T_b,T_c,V_f_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 <=> V_f_2 = hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_dom__empty,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_dom__const,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_dom__minus,axiom,
% 52.58/52.37 ! [V_A_2,T_c,T_b,V_x_2,V_f_2] :
% 52.58/52.37 ( hAPP(V_f_2,V_x_2) = c_Option_Ooption_ONone(T_b)
% 52.58/52.37 => 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) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_fold__graph__insert__swap,axiom,
% 52.58/52.37 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_b] :
% 52.58/52.37 ( class_Groups_Oab__semigroup__mult(T_b)
% 52.58/52.37 => ( 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))
% 52.58/52.37 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 52.58/52.37 => 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))) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Diff1__fold__graph,axiom,
% 52.58/52.37 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 52.58/52.37 ( 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))
% 52.58/52.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.58/52.37 => 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))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_dom__fun__upd,axiom,
% 52.58/52.37 ! [V_x_2,V_f_2,T_c,T_b,V_y_2] :
% 52.58/52.37 ( ( V_y_2 = c_Option_Ooption_ONone(T_b)
% 52.58/52.37 => 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)))) )
% 52.58/52.37 & ( V_y_2 != c_Option_Ooption_ONone(T_b)
% 52.58/52.37 => 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)) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_fold1Set_Ointros,axiom,
% 52.58/52.37 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2))
% 52.58/52.37 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.58/52.37 => 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)) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_ran__restrictD,axiom,
% 52.58/52.37 ! [V_A_2,V_m_2,T_c,V_y_2,T_b] :
% 52.58/52.37 ( 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))))
% 52.58/52.37 => ? [B_x] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 52.58/52.37 & hAPP(V_m_2,B_x) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_accp__acc__eq,axiom,
% 52.58/52.37 ! [V_x_2,V_r_2,T_b] :
% 52.58/52.37 ( 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))
% 52.58/52.37 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_fold1Set__nonempty,axiom,
% 52.58/52.37 ! [V_x_2,V_A_2,V_f_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2))
% 52.58/52.37 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_empty__fold1SetE,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_acc__subset,axiom,
% 52.58/52.37 ! [V_R2_2,V_R1_2,T_b] :
% 52.58/52.37 ( 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))
% 52.58/52.37 => 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))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_fold1Set__sing,axiom,
% 52.58/52.37 ! [V_b_2,V_a_2,V_f_2,T_b] :
% 52.58/52.37 ( 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))
% 52.58/52.37 <=> V_a_2 = V_b_2 ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_acc_Osimps,axiom,
% 52.58/52.37 ! [V_r_2,V_a_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 52.58/52.37 <=> ! [B_x] :
% 52.58/52.37 ( 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))
% 52.58/52.37 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_acc__downward,axiom,
% 52.58/52.37 ! [V_a_2,V_r_2,V_b_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 52.58/52.37 => ( hBOOL(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))
% 52.58/52.37 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_max__extp_Oequations,axiom,
% 52.58/52.37 ! [V_a2_2,V_a1_2,V_R_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
% 52.58/52.37 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 52.58/52.37 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 52.58/52.37 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 & ! [B_x] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 52.58/52.37 => ? [B_xa] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 52.58/52.37 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_max__ext_Ointros,axiom,
% 52.58/52.37 ! [V_R_2,V_Y_2,V_X_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
% 52.58/52.37 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 => ( ! [B_x] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2))
% 52.58/52.37 => ? [B_xa] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2))
% 52.58/52.37 & 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)) ) )
% 52.58/52.37 => 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))) ) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_conseq2,axiom,
% 52.58/52.37 ! [V_Q_2,V_Q_H_2,V_c_2,V_P_2,V_Ga_2,T_b] :
% 52.58/52.37 ( 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))))
% 52.58/52.37 => ( ! [B_Z,B_s] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s))
% 52.58/52.37 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s)) )
% 52.58/52.37 => 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)))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_conseq1,axiom,
% 52.58/52.37 ! [V_P_2,V_Q_2,V_c_2,V_P_H_2,V_Ga_2,T_b] :
% 52.58/52.37 ( 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))))
% 52.58/52.37 => ( ! [B_Z,B_s] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s))
% 52.58/52.37 => hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s)) )
% 52.58/52.37 => 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)))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_fold1Set_Oequations,axiom,
% 52.58/52.37 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_b] :
% 52.58/52.37 ( 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))
% 52.58/52.37 <=> ? [B_a,B_A] :
% 52.58/52.37 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 52.58/52.37 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2))
% 52.58/52.37 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_insert__fold1SetE,axiom,
% 52.58/52.37 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_b] :
% 52.58/52.37 ( 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))
% 52.58/52.37 => ~ ! [B_a,B_A] :
% 52.58/52.37 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2))
% 52.58/52.37 => hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_image__split__eq__Sigma,axiom,
% 52.58/52.37 ! [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))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_fold1__Un,axiom,
% 52.58/52.37 ! [V_B_2,V_A_2,T_b] :
% 52.58/52.37 ( class_Groups_Oab__semigroup__mult(T_b)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.58/52.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 => ( 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))
% 52.58/52.37 => 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)) ) ) ) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_fold1__antimono,axiom,
% 52.58/52.37 ! [V_B_2,V_A_2,T_b] :
% 52.58/52.37 ( class_Orderings_Olinorder(T_b)
% 52.58/52.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.58/52.37 => 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))) ) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_SigmaI,axiom,
% 52.58/52.37 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.58/52.37 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
% 52.58/52.37 => 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))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Sigma__empty1,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Times__eq__cancel2,axiom,
% 52.58/52.37 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 52.58/52.37 => ( 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))
% 52.58/52.37 <=> V_A_2 = V_B_2 ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Sigma__Diff__distrib2,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Times__Diff__distrib1,axiom,
% 52.58/52.37 ! [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))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Sigma__Diff__distrib1,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_card__cartesian__product,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_setsum__cartesian__product,axiom,
% 52.58/52.37 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 52.58/52.37 ( class_Groups_Ocomm__monoid__add(T_b)
% 52.58/52.37 => 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))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Sigma__empty2,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Times__empty,axiom,
% 52.58/52.37 ! [V_B_2,V_A_2,T_c,T_b] :
% 52.58/52.37 ( 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))
% 52.58/52.37 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Compl__Times__UNIV1,axiom,
% 52.58/52.37 ! [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))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Compl__Times__UNIV2,axiom,
% 52.58/52.37 ! [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)))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_setprod__cartesian__product,axiom,
% 52.58/52.37 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 52.58/52.37 ( class_Groups_Ocomm__monoid__mult(T_b)
% 52.58/52.37 => 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))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Sigma__Un__distrib2,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Times__Un__distrib1,axiom,
% 52.58/52.37 ! [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))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Sigma__Un__distrib1,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_swap__product,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_fold1__singleton,axiom,
% 52.58/52.37 ! [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 ).
% 52.58/52.37
% 52.58/52.37 fof(fact_fold1__singleton__def,axiom,
% 52.58/52.37 ! [V_a_2,V_f_2,T_b,V_g_2] :
% 52.58/52.37 ( V_g_2 = c_Finite__Set_Ofold1(T_b,V_f_2)
% 52.58/52.37 => 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 ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_finite__cartesian__product,axiom,
% 52.58/52.37 ! [V_B_2,T_c,V_A_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 52.58/52.37 => 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)))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_equiv__type,axiom,
% 52.58/52.37 ! [V_r_2,V_A_2,T_b] :
% 52.58/52.37 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 52.58/52.37 => 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)))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Sigma__Int__distrib1,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Times__Int__distrib1,axiom,
% 52.58/52.37 ! [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))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Sigma__Int__distrib2,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Id__on__subset__Times,axiom,
% 52.58/52.37 ! [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)))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_UNIV__Times__UNIV,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_mem__Sigma__iff,axiom,
% 52.58/52.37 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 52.58/52.37 ( 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)))
% 52.58/52.37 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.58/52.37 & hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_SigmaD1,axiom,
% 52.58/52.37 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 52.58/52.37 ( 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)))
% 52.58/52.37 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_SigmaD2,axiom,
% 52.58/52.37 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 52.58/52.37 ( 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)))
% 52.58/52.37 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_SigmaE2,axiom,
% 52.58/52.37 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 52.58/52.37 ( 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)))
% 52.58/52.37 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.58/52.37 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_folding__one_Oeq__fold,axiom,
% 52.58/52.37 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 52.58/52.37 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_card__cartesian__product__singleton,axiom,
% 52.58/52.37 ! [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) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Times__subset__cancel2,axiom,
% 52.58/52.37 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 52.58/52.37 => ( 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))))
% 52.58/52.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Image__subset,axiom,
% 52.58/52.37 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 52.58/52.37 ( 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))))
% 52.58/52.37 => 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)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_finite__cartesian__productD1,axiom,
% 52.58/52.37 ! [V_B_2,V_A_2,T_c,T_b] :
% 52.58/52.37 ( 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))))
% 52.58/52.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 52.58/52.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_finite__cartesian__productD2,axiom,
% 52.58/52.37 ! [V_B_2,V_A_2,T_c,T_b] :
% 52.58/52.37 ( 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))))
% 52.58/52.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_fst__image__times,axiom,
% 52.58/52.37 ! [V_A_2,T_c,T_b,V_B_2] :
% 52.58/52.37 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 => 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)) )
% 52.58/52.37 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 => 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 ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_snd__image__times,axiom,
% 52.58/52.37 ! [V_B_2,T_c,T_b,V_A_2] :
% 52.58/52.37 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 => 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)) )
% 52.58/52.37 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 => 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 ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_fold1__def,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Sup__fin_OF__eq,axiom,
% 52.58/52.37 ! [V_A_2,T_b] :
% 52.58/52.37 ( class_Lattices_Olattice(T_b)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => 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) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Inf__fin_OF__eq,axiom,
% 52.58/52.37 ! [V_A_2,T_b] :
% 52.58/52.37 ( class_Lattices_Olattice(T_b)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => 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) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Min_OF__eq,axiom,
% 52.58/52.37 ! [V_A_2,T_b] :
% 52.58/52.37 ( class_Orderings_Olinorder(T_b)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => 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) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Max_OF__eq,axiom,
% 52.58/52.37 ! [V_A_2,T_b] :
% 52.58/52.37 ( class_Orderings_Olinorder(T_b)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => 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) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_min__max_OInf__fin_OF__eq,axiom,
% 52.58/52.37 ! [V_A_2,T_b] :
% 52.58/52.37 ( class_Orderings_Olinorder(T_b)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => 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) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_min__max_OSup__fin_OF__eq,axiom,
% 52.58/52.37 ! [V_A_2,T_b] :
% 52.58/52.37 ( class_Orderings_Olinorder(T_b)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => 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) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_refl__on__def,axiom,
% 52.58/52.37 ! [V_r_2,V_A_2,T_b] :
% 52.58/52.37 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 52.58/52.37 <=> ( 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))))
% 52.58/52.37 & ! [B_x] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.58/52.37 => 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)) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_insert__times__insert,axiom,
% 52.58/52.37 ! [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)))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_finite__equiv__class,axiom,
% 52.58/52.37 ! [V_X_2,V_r_2,V_A_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => ( 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))))
% 52.58/52.37 => ( 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)))
% 52.58/52.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_UN__Times__distrib,axiom,
% 52.58/52.37 ! [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))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Sigma__def,axiom,
% 52.58/52.37 ! [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))))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_fold1__belowI,axiom,
% 52.58/52.37 ! [V_a_2,V_A_2,T_b] :
% 52.58/52.37 ( class_Lattices_Osemilattice__inf(T_b)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.58/52.37 => 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)) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_finite__quotient,axiom,
% 52.58/52.37 ! [V_r_2,V_A_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => ( 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))))
% 52.58/52.37 => 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))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_below__fold1__iff,axiom,
% 52.58/52.37 ! [V_x_2,V_A_2,T_b] :
% 52.58/52.37 ( class_Lattices_Osemilattice__inf(T_b)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 => ( 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)))
% 52.58/52.37 <=> ! [B_x] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.58/52.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_min__max_Ofold1__belowI,axiom,
% 52.58/52.37 ! [V_a_2,V_A_2,T_b] :
% 52.58/52.37 ( class_Orderings_Olinorder(T_b)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.58/52.37 => 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)) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_fold1__insert__idem,axiom,
% 52.58/52.37 ! [V_x_2,V_A_2,T_b] :
% 52.58/52.37 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 52.58/52.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => 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)) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_min__max_Obelow__fold1__iff,axiom,
% 52.58/52.37 ! [V_x_2,V_A_2,T_b] :
% 52.58/52.37 ( class_Orderings_Olinorder(T_b)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 => ( 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)))
% 52.58/52.37 <=> ! [B_x] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.58/52.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_fold1__below__iff,axiom,
% 52.58/52.37 ! [V_x_2,V_A_2,T_b] :
% 52.58/52.37 ( class_Orderings_Olinorder(T_b)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 => ( 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))
% 52.58/52.37 <=> ? [B_x] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.58/52.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_fold1__Un2,axiom,
% 52.58/52.37 ! [V_B_2,V_A_2,T_b] :
% 52.58/52.37 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.58/52.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 => 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)) ) ) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_fold1__strict__below__iff,axiom,
% 52.58/52.37 ! [V_x_2,V_A_2,T_b] :
% 52.58/52.37 ( class_Orderings_Olinorder(T_b)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 => ( 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))
% 52.58/52.37 <=> ? [B_x] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.58/52.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_strict__below__fold1__iff,axiom,
% 52.58/52.37 ! [V_x_2,V_A_2,T_b] :
% 52.58/52.37 ( class_Orderings_Olinorder(T_b)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 => ( 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)))
% 52.58/52.37 <=> ! [B_x] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.58/52.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_vimage__Times,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_fold1__insert,axiom,
% 52.58/52.37 ! [V_x_2,V_A_2,T_b] :
% 52.58/52.37 ( class_Groups_Oab__semigroup__mult(T_b)
% 52.58/52.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.58/52.37 => 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)) ) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_semilattice__big_OF__eq,axiom,
% 52.58/52.37 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 52.58/52.37 ( c_Big__Operators_Osemilattice__big(T_b,V_f_2,V_F_2)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Ex__inj__on__UNION__Sigma,axiom,
% 52.58/52.37 ! [V_A_2,V_I_2,T_c,T_b] :
% 52.58/52.37 ? [B_f] :
% 52.58/52.37 ( 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))
% 52.58/52.37 & 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))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_refl__onI,axiom,
% 52.58/52.37 ! [V_A_2,V_r_2,T_b] :
% 52.58/52.37 ( 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))))
% 52.58/52.37 => ( ! [B_x] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.58/52.37 => 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)) )
% 52.58/52.37 => c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_setprod__Sigma,axiom,
% 52.58/52.37 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 52.58/52.37 ( class_Groups_Ocomm__monoid__mult(T_d)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => ( ! [B_x] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.58/52.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 52.58/52.37 => 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)) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_setsum__Sigma,axiom,
% 52.58/52.37 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 52.58/52.37 ( class_Groups_Ocomm__monoid__add(T_d)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => ( ! [B_x] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.58/52.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 52.58/52.37 => 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)) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_fold__image__Sigma,axiom,
% 52.58/52.37 ! [V_g_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 52.58/52.37 ( class_Groups_Ocomm__monoid__mult(T_d)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => ( ! [B_x] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.58/52.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 52.58/52.37 => 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)) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_card__SigmaI,axiom,
% 52.58/52.37 ! [V_B_2,T_c,V_A_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => ( ! [B_x] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.58/52.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 52.58/52.37 => 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) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_fold1__in,axiom,
% 52.58/52.37 ! [V_A_2,T_b] :
% 52.58/52.37 ( class_Groups_Oab__semigroup__mult(T_b)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 => ( ! [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))))))
% 52.58/52.37 => 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)) ) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_finite__SigmaI,axiom,
% 52.58/52.37 ! [V_B_2,T_c,V_A_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => ( ! [B_a] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 52.58/52.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 52.58/52.37 => 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))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_hom__fold1__commute,axiom,
% 52.58/52.37 ! [V_N_2,V_h_2,T_b] :
% 52.58/52.37 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 52.58/52.37 => ( ! [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))
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 52.58/52.37 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 => 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)) ) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_SigmaE,axiom,
% 52.58/52.37 ! [V_B_2,V_A_2,V_c_2,T_c,T_b] :
% 52.58/52.37 ( 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)))
% 52.58/52.37 => ~ ! [B_x] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.58/52.37 => ! [B_y] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x)))
% 52.58/52.37 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_map__pair__surj,axiom,
% 52.58/52.37 ! [V_g_2,T_d,T_e,V_f_2,T_b,T_c] :
% 52.58/52.37 ( 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))
% 52.58/52.37 => ( 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))
% 52.58/52.37 => 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)) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_map__pair__inj__on,axiom,
% 52.58/52.37 ! [V_B_2,V_g_2,T_e,T_d,V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.37 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 52.58/52.37 => ( c_Fun_Oinj__on(T_d,T_e,V_g_2,V_B_2)
% 52.58/52.37 => 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))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_map__pair__imageI,axiom,
% 52.58/52.37 ! [V_g_2,V_f_2,T_e,T_d,V_R_2,V_b_2,V_a_2,T_c,T_b] :
% 52.58/52.37 ( 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))
% 52.58/52.37 => 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))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_map__pair_Ocomp,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_map__pair__compose,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_map__pair_Ocompositionality,axiom,
% 52.58/52.37 ! [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) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_snd__comp__map__pair,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_fst__comp__map__pair,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_map__pair__simp,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_map__pair__ident,axiom,
% 52.58/52.37 ! [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 ).
% 52.58/52.37
% 52.58/52.37 fof(fact_snd__prod__fun,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_fst__map__pair,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_map__pair__def,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_map__pair__surj__on,axiom,
% 52.58/52.37 ! [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] :
% 52.58/52.37 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
% 52.58/52.37 => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_B_2) = V_B_H_2
% 52.58/52.37 => 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)) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_prod__fun__imageE,axiom,
% 52.58/52.37 ! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_c_2,T_c,T_b] :
% 52.58/52.37 ( 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)))
% 52.58/52.37 => ~ ! [B_x,B_y] :
% 52.58/52.37 ( 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))
% 52.58/52.37 => ~ 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)) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_setprod__pos__nat,axiom,
% 52.58/52.37 ! [V_f_2,V_S_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 52.58/52.37 => ( ! [B_x] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 52.58/52.37 => 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))) )
% 52.58/52.37 => 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))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_folding__one__idem_Ohom__commute,axiom,
% 52.58/52.37 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_b] :
% 52.58/52.37 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 52.58/52.37 => ( ! [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))
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 52.58/52.37 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 => 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)) ) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Rep__Integ__induct,axiom,
% 52.58/52.37 ! [V_P_2,V_y_2] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 52.58/52.37 => ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Int_ORep__Integ,B_x)))
% 52.58/52.37 => hBOOL(hAPP(V_P_2,V_y_2)) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Rep__Integ__cases,axiom,
% 52.58/52.37 ! [V_y_2] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 52.58/52.37 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom,
% 52.58/52.37 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 52.58/52.37 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 52.58/52.37 => ( ! [B_x] :
% 52.58/52.37 ( 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)))
% 52.58/52.37 => hAPP(V_g_2,B_x) = V_z_2 )
% 52.58/52.37 => 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)) ) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_fun__left__comm__idem__remove,axiom,
% 52.58/52.37 ! [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))))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_card__less__Suc2,axiom,
% 52.58/52.37 ! [V_i_2,V_M_2] :
% 52.58/52.37 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 52.58/52.37 => 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))))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_CollectI,axiom,
% 52.58/52.37 ! [T_b,V_a_2,V_P_2] :
% 52.58/52.37 ( hBOOL(hAPP(V_P_2,V_a_2))
% 52.58/52.37 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_finite__Collect__conjI,axiom,
% 52.58/52.37 ! [V_Q_2,V_P_2,T_b] :
% 52.58/52.37 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 52.58/52.37 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2))) )
% 52.58/52.37 => 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)))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_finite__Collect__less__nat,axiom,
% 52.58/52.37 ! [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)))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_finite__Collect__le__nat,axiom,
% 52.58/52.37 ! [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)))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom,
% 52.58/52.37 ! [V_x_2,V_f_2,T_c,T_b] :
% 52.58/52.37 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 52.58/52.37 => 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) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_insert__compr__raw,axiom,
% 52.58/52.37 ! [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))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_insert__compr,axiom,
% 52.58/52.37 ! [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))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_SetCompr__Sigma__eq,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Collect__split,axiom,
% 52.58/52.37 ! [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))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_vimage__Collect__eq,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Collect__neg__eq,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_finite__Collect__disjI,axiom,
% 52.58/52.37 ! [V_Q_2,V_P_2,T_b] :
% 52.58/52.37 ( 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))))
% 52.58/52.37 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 52.58/52.37 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Collect__conj__eq,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_fun__left__comm__idem__inf,axiom,
% 52.58/52.37 ! [T_b] :
% 52.58/52.37 ( class_Lattices_Osemilattice__inf(T_b)
% 52.58/52.37 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_UNIV__def,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_fun__left__comm__idem__insert,axiom,
% 52.58/52.37 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Collect__def,axiom,
% 52.58/52.37 ! [V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),V_P_2) = V_P_2 ).
% 52.58/52.37
% 52.58/52.37 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom,
% 52.58/52.37 ! [V_z_2,V_x_2,V_f_2,T_c,T_b] :
% 52.58/52.37 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 52.58/52.37 => 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) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom,
% 52.58/52.37 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 52.58/52.37 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 52.58/52.37 => 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)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_insert__Collect,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_empty__def,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Collect__empty__eq,axiom,
% 52.58/52.37 ! [V_P_2,T_b] :
% 52.58/52.37 ( hAPP(c_Set_OCollect(T_b),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_empty__Collect__eq,axiom,
% 52.58/52.37 ! [V_P_2,T_b] :
% 52.58/52.37 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_P_2)
% 52.58/52.37 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Collect__disj__eq,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_fun__left__comm__idem__sup,axiom,
% 52.58/52.37 ! [T_b] :
% 52.58/52.37 ( class_Lattices_Osemilattice__sup(T_b)
% 52.58/52.37 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_fun__left__comm__idem,axiom,
% 52.58/52.37 ! [T_b] :
% 52.58/52.37 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 52.58/52.37 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Collect__mem__eq,axiom,
% 52.58/52.37 ! [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 ).
% 52.58/52.37
% 52.58/52.37 fof(fact_mem__Collect__eq,axiom,
% 52.58/52.37 ! [V_P_2,V_a_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 52.58/52.37 <=> hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_CollectD,axiom,
% 52.58/52.37 ! [V_P_2,V_a_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 52.58/52.37 => hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_CollectE,axiom,
% 52.58/52.37 ! [V_P_2,V_a_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 52.58/52.37 => hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom,
% 52.58/52.37 ! [T_b] :
% 52.58/52.37 ( class_Orderings_Olinorder(T_b)
% 52.58/52.37 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom,
% 52.58/52.37 ! [T_b] :
% 52.58/52.37 ( class_Orderings_Olinorder(T_b)
% 52.58/52.37 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Un__def,axiom,
% 52.58/52.37 ! [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))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Int__Collect,axiom,
% 52.58/52.37 ! [V_P_2,V_A_2,V_x_2,T_b] :
% 52.58/52.37 ( 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))))
% 52.58/52.37 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.58/52.37 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Int__def,axiom,
% 52.58/52.37 ! [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))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_singleton__conv2,axiom,
% 52.58/52.37 ! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(c_fequal,V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_singleton__conv,axiom,
% 52.58/52.37 ! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Collect__conv__if2,axiom,
% 52.58/52.37 ! [T_b,V_a_2,V_P_2] :
% 52.58/52.37 ( ( hBOOL(hAPP(V_P_2,V_a_2))
% 52.58/52.37 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) )
% 52.58/52.37 & ( ~ hBOOL(hAPP(V_P_2,V_a_2))
% 52.58/52.37 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Collect__conv__if,axiom,
% 52.58/52.37 ! [T_b,V_a_2,V_P_2] :
% 52.58/52.37 ( ( hBOOL(hAPP(V_P_2,V_a_2))
% 52.58/52.37 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) )
% 52.58/52.37 & ( ~ hBOOL(hAPP(V_P_2,V_a_2))
% 52.58/52.37 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_set__diff__eq,axiom,
% 52.58/52.37 ! [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)))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_finite__Collect__not,axiom,
% 52.58/52.37 ! [V_P_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 52.58/52.37 => ( 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))))
% 52.58/52.37 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_insert__def,axiom,
% 52.58/52.37 ! [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) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Compl__eq,axiom,
% 52.58/52.37 ! [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))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_vimage__def,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Collect__imp__eq,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_dom__def,axiom,
% 52.58/52.37 ! [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)))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_finite__M__bounded__by__nat,axiom,
% 52.58/52.37 ! [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))))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_setsum__setsum__restrict,axiom,
% 52.58/52.37 ! [V_R_2,V_f_2,V_T_2,T_c,V_S_2,T_b,T_d] :
% 52.58/52.37 ( class_Groups_Ocomm__monoid__add(T_d)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 52.58/52.37 => 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) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_if__image__distrib,axiom,
% 52.58/52.37 ! [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))))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_dom__if,axiom,
% 52.58/52.37 ! [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)))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_nat__seg__image__imp__finite,axiom,
% 52.58/52.37 ! [V_n_2,V_f_2,T_b,V_A_2] :
% 52.58/52.37 ( 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)))
% 52.58/52.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_setsum__restrict__set_H,axiom,
% 52.58/52.37 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 52.58/52.37 ( class_Groups_Ocomm__monoid__add(T_c)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => 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) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_setsum__image__gen,axiom,
% 52.58/52.37 ! [V_f_2,T_d,V_g_2,V_S_2,T_b,T_c] :
% 52.58/52.37 ( class_Groups_Ocomm__monoid__add(T_c)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 52.58/52.37 => 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)) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Image__singleton,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_setsum__cases,axiom,
% 52.58/52.37 ! [V_g_2,V_f_2,V_P_2,V_A_2,T_b,T_c] :
% 52.58/52.37 ( class_Groups_Ocomm__monoid__add(T_c)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => 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))))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_card__less__Suc,axiom,
% 52.58/52.37 ! [V_i_2,V_M_2] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 52.58/52.37 => 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))))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_card__less,axiom,
% 52.58/52.37 ! [V_i_2,V_M_2] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 52.58/52.37 => 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) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_dom__override__on,axiom,
% 52.58/52.37 ! [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))))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_setsum__multicount,axiom,
% 52.58/52.37 ! [V_k_2,V_R_2,V_T_2,T_c,V_S_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 52.58/52.37 => ( ! [B_x] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2))
% 52.58/52.37 => 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 )
% 52.58/52.37 => 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)) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_finite__Collect__subsets,axiom,
% 52.58/52.37 ! [V_A_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => 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)))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Pow__def,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_override__on__apply__notin,axiom,
% 52.58/52.37 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 52.58/52.37 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.58/52.37 => 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) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_override__on__apply__in,axiom,
% 52.58/52.37 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.58/52.37 => 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) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_override__on__emptyset,axiom,
% 52.58/52.37 ! [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 ).
% 52.58/52.37
% 52.58/52.37 fof(fact_inj__graph,axiom,
% 52.58/52.37 ! [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))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
% 52.58/52.37 ! [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))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_override__on__def,axiom,
% 52.58/52.37 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 52.58/52.37 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.58/52.37 => 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) )
% 52.58/52.37 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.58/52.37 => 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) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_finite__psubset__def,axiom,
% 52.58/52.37 ! [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)))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_inv__image__def,axiom,
% 52.58/52.37 ! [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))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
% 52.58/52.37 ! [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)))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom,
% 52.58/52.37 ! [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)))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Nitpick_Oprod__def,axiom,
% 52.58/52.37 ! [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)))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_int__ge__less__than2__def,axiom,
% 52.58/52.37 ! [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)))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_int__ge__less__than__def,axiom,
% 52.58/52.37 ! [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)))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_reflp__def,axiom,
% 52.58/52.37 ! [V_r_2,T_b] :
% 52.58/52.37 ( c_Predicate_Oreflp(T_b,V_r_2)
% 52.58/52.37 <=> 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))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_reflpE,axiom,
% 52.58/52.37 ! [V_x_2,V_r_2,T_b] :
% 52.58/52.37 ( c_Predicate_Oreflp(T_b,V_r_2)
% 52.58/52.37 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_min__max_Oinf__Sup2__distrib,axiom,
% 52.58/52.37 ! [V_B_2,V_A_2,T_b] :
% 52.58/52.37 ( class_Orderings_Olinorder(T_b)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.58/52.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 => 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))))))) ) ) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_min__max_Osup__Inf2__distrib,axiom,
% 52.58/52.37 ! [V_B_2,V_A_2,T_b] :
% 52.58/52.37 ( class_Orderings_Olinorder(T_b)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.58/52.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 => 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))))))) ) ) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_finite__image__set,axiom,
% 52.58/52.37 ! [V_f_2,T_c,V_P_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 52.58/52.37 => 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))))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_finite__Collect__bounded__ex,axiom,
% 52.58/52.37 ! [V_Q_2,T_c,V_P_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 52.58/52.37 => ( 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)))))
% 52.58/52.37 <=> ! [B_y] :
% 52.58/52.37 ( hBOOL(hAPP(V_P_2,B_y))
% 52.58/52.37 => 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)))) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_ran__def,axiom,
% 52.58/52.37 ! [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)))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Pow__Compl,axiom,
% 52.58/52.37 ! [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))))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_add__Max__commute,axiom,
% 52.58/52.37 ! [V_k_2,V_N_2,T_b] :
% 52.58/52.37 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 52.58/52.37 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 => 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))))) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_add__Min__commute,axiom,
% 52.58/52.37 ! [V_k_2,V_N_2,T_b] :
% 52.58/52.37 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 52.58/52.37 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 => 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))))) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_sup__Inf2__distrib,axiom,
% 52.58/52.37 ! [V_B_2,V_A_2,T_b] :
% 52.58/52.37 ( class_Lattices_Odistrib__lattice(T_b)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.58/52.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 => 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))))))) ) ) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_sup__Inf1__distrib,axiom,
% 52.58/52.37 ! [V_x_2,V_A_2,T_b] :
% 52.58/52.37 ( class_Lattices_Odistrib__lattice(T_b)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 => 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))))) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_inf__Sup1__distrib,axiom,
% 52.58/52.37 ! [V_x_2,V_A_2,T_b] :
% 52.58/52.37 ( class_Lattices_Odistrib__lattice(T_b)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 => 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))))) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_inf__Sup2__distrib,axiom,
% 52.58/52.37 ! [V_B_2,V_A_2,T_b] :
% 52.58/52.37 ( class_Lattices_Odistrib__lattice(T_b)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.58/52.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 => 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))))))) ) ) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_min__max_Osup__Inf1__distrib,axiom,
% 52.58/52.37 ! [V_x_2,V_A_2,T_b] :
% 52.58/52.37 ( class_Orderings_Olinorder(T_b)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 => 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))))) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_min__max_Oinf__Sup1__distrib,axiom,
% 52.58/52.37 ! [V_x_2,V_A_2,T_b] :
% 52.58/52.37 ( class_Orderings_Olinorder(T_b)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 => 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))))) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_setsum__mult__setsum__if__inj,axiom,
% 52.58/52.37 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] :
% 52.58/52.37 ( class_Rings_Osemiring__0(T_d)
% 52.58/52.37 => ( 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)))
% 52.58/52.37 => 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))))))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_setsum__multicount__gen,axiom,
% 52.58/52.37 ! [V_k_2,V_R_2,V_t_2,T_c,V_s_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2))
% 52.58/52.37 => ( ! [B_x] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2))
% 52.58/52.37 => 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) )
% 52.58/52.37 => 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) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_inj__on__id,axiom,
% 52.58/52.37 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_Fun_Oid(T_b),V_A_2) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_map__pair_Oidentity,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_map__pair_Oid,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_of__int__eq__id,axiom,
% 52.58/52.37 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_id__def,axiom,
% 52.58/52.37 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ).
% 52.58/52.37
% 52.58/52.37 fof(fact_id__apply,axiom,
% 52.58/52.37 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ).
% 52.58/52.37
% 52.58/52.37 fof(fact_apfst__id,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_apsnd__id,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_vimage__id,axiom,
% 52.58/52.37 ! [V_A_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_Fun_Oid(T_b)),V_A_2) = V_A_2 ).
% 52.58/52.37
% 52.58/52.37 fof(fact_o__eq__id__dest,axiom,
% 52.58/52.37 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
% 52.58/52.37 ( 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)
% 52.58/52.37 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_id__o,axiom,
% 52.58/52.37 ! [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 ).
% 52.58/52.37
% 52.58/52.37 fof(fact_o__id,axiom,
% 52.58/52.37 ! [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 ).
% 52.58/52.37
% 52.58/52.37 fof(fact_surj__id,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_image__id,axiom,
% 52.58/52.37 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),V_Y_2) = V_Y_2 ).
% 52.58/52.37
% 52.58/52.37 fof(fact_folding_Oempty,axiom,
% 52.58/52.37 ! [V_F_2,V_f_2,T_c,T_b] :
% 52.58/52.37 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 52.58/52.37 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_apfst__def,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_apsnd__def,axiom,
% 52.58/52.37 ! [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) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_split__Pair,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_setsum__reindex__id,axiom,
% 52.58/52.37 ! [V_B_2,V_f_2,T_b,T_c] :
% 52.58/52.37 ( class_Groups_Ocomm__monoid__add(T_c)
% 52.58/52.37 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 52.58/52.37 => 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)) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_setprod__reindex__id,axiom,
% 52.58/52.37 ! [V_B_2,V_f_2,T_b,T_c] :
% 52.58/52.37 ( class_Groups_Ocomm__monoid__mult(T_c)
% 52.58/52.37 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 52.58/52.37 => 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)) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_finite__conv__nat__seg__image,axiom,
% 52.58/52.37 ! [V_A_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 <=> ? [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))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rel__comp__def,axiom,
% 52.58/52.37 ! [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))))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rel__compI,axiom,
% 52.58/52.37 ! [V_s_2,V_c_2,T_d,V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 52.58/52.37 ( 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))
% 52.58/52.37 => ( 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))
% 52.58/52.37 => 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))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rel__comp__UNION__distrib,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rel__comp__UNION__distrib2,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_O__assoc,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rel__comp__mono,axiom,
% 52.58/52.37 ! [V_s_2,V_s_H_2,T_d,V_r_2,V_r_H_2,T_c,T_b] :
% 52.58/52.37 ( 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))
% 52.58/52.37 => ( 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))
% 52.58/52.37 => 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))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rel__comp__distrib,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rel__comp__distrib2,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rel__comp__empty2,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rel__comp__empty1,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_union__comp__emptyL,axiom,
% 52.58/52.37 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 52.58/52.37 ( 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))
% 52.58/52.37 => ( 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))
% 52.58/52.37 => 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)) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_union__comp__emptyR,axiom,
% 52.58/52.37 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 52.58/52.37 ( 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))
% 52.58/52.37 => ( 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))
% 52.58/52.37 => 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)) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rel__comp__subset__Sigma,axiom,
% 52.58/52.37 ! [V_C_2,V_s_2,T_d,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 52.58/52.37 ( 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))))
% 52.58/52.37 => ( 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))))
% 52.58/52.37 => 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)))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_max__ext__compat,axiom,
% 52.58/52.37 ! [V_S_2,V_R_2,T_b] :
% 52.58/52.37 ( 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))
% 52.58/52.37 => 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))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_min__ext__compat,axiom,
% 52.58/52.37 ! [V_S_2,V_R_2,T_b] :
% 52.58/52.37 ( 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))
% 52.58/52.37 => 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))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_pred__comp__rel__comp__eq,axiom,
% 52.58/52.37 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 52.58/52.37 ( 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)
% 52.58/52.37 <=> 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))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_reduction__pairI,axiom,
% 52.58/52.37 ! [V_S_2,V_R_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_Owf(T_b,V_R_2)
% 52.58/52.37 => ( 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))
% 52.58/52.37 => 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)) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__less__than,axiom,
% 52.58/52.37 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_pred__comp_Ointros,axiom,
% 52.58/52.37 ! [T_d,T_c,T_b,V_c_2,V_s_2,V_b_2,V_a_2,V_r_2] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 52.58/52.37 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_c_2))
% 52.58/52.37 => c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2,V_a_2,V_c_2) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__empty,axiom,
% 52.58/52.37 ! [T_b] : c_Wellfounded_Owf(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__inv__image,axiom,
% 52.58/52.37 ! [V_f_2,T_c,V_r_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 52.58/52.37 => c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__lex__prod,axiom,
% 52.58/52.37 ! [V_rb_2,T_c,V_ra_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_Owf(T_b,V_ra_2)
% 52.58/52.37 => ( c_Wellfounded_Owf(T_c,V_rb_2)
% 52.58/52.37 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2)) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__measure,axiom,
% 52.58/52.37 ! [V_f_2,T_b] : c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__comp__self,axiom,
% 52.58/52.37 ! [V_R_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_Owf(T_b,V_R_2)
% 52.58/52.37 <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__no__loop,axiom,
% 52.58/52.37 ! [V_R_2,T_b] :
% 52.58/52.37 ( 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))
% 52.58/52.37 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__union__merge,axiom,
% 52.58/52.37 ! [V_S_2,V_R_2,T_b] :
% 52.58/52.37 ( 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))
% 52.58/52.37 <=> 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)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__less,axiom,
% 52.58/52.37 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)))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__int__ge__less__than2,axiom,
% 52.58/52.37 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__not__refl,axiom,
% 52.58/52.37 ! [V_a_2,V_r_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 52.58/52.37 => ~ hBOOL(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)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__not__sym,axiom,
% 52.58/52.37 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 52.58/52.37 => ( hBOOL(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))
% 52.58/52.37 => ~ hBOOL(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)) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__asym,axiom,
% 52.58/52.37 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 52.58/52.37 => ( hBOOL(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))
% 52.58/52.37 => ~ hBOOL(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)) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__irrefl,axiom,
% 52.58/52.37 ! [V_a_2,V_r_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 52.58/52.37 => ~ hBOOL(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)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__mlex,axiom,
% 52.58/52.37 ! [V_f_2,V_R_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_Owf(T_b,V_R_2)
% 52.58/52.37 => c_Wellfounded_Owf(T_b,c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_min__ext__wf,axiom,
% 52.58/52.37 ! [V_r_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 52.58/52.37 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_b,V_r_2)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_pred__comp_Oequations,axiom,
% 52.58/52.37 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 52.58/52.37 ( c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2,V_a1_2,V_a3_2)
% 52.58/52.37 <=> ? [B_b] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b))
% 52.58/52.37 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__subset,axiom,
% 52.58/52.37 ! [V_p_2,V_r_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 52.58/52.37 => ( 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))
% 52.58/52.37 => c_Wellfounded_Owf(T_b,V_p_2) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__pair__less,axiom,
% 52.58/52.37 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__finite__psubset,axiom,
% 52.58/52.37 ! [T_b] : c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_max__ext__wf,axiom,
% 52.58/52.37 ! [V_r_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 52.58/52.37 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_b,V_r_2)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__Int2,axiom,
% 52.58/52.37 ! [V_r_H_2,V_r_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 52.58/52.37 => 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)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__Int1,axiom,
% 52.58/52.37 ! [V_r_H_2,V_r_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 52.58/52.37 => 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)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__acc__iff,axiom,
% 52.58/52.37 ! [V_r_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 52.58/52.37 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_acc__wfD,axiom,
% 52.58/52.37 ! [V_x_2,V_r_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 52.58/52.37 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__int__ge__less__than,axiom,
% 52.58/52.37 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__iff__no__infinite__down__chain,axiom,
% 52.58/52.37 ! [V_r_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 52.58/52.37 <=> ~ ? [B_f] :
% 52.58/52.37 ! [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)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wfE__pf,axiom,
% 52.58/52.37 ! [V_A_2,V_R_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_Owf(T_b,V_R_2)
% 52.58/52.37 => ( 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)))
% 52.58/52.37 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__union__compatible,axiom,
% 52.58/52.37 ! [V_S_2,V_R_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_Owf(T_b,V_R_2)
% 52.58/52.37 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 52.58/52.37 => ( 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))
% 52.58/52.37 => 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)) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf,axiom,
% 52.58/52.37 ! [T_b] :
% 52.58/52.37 ( class_Orderings_Owellorder(T_b)
% 52.58/52.37 => 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)))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_reduction__pair__def,axiom,
% 52.58/52.37 ! [V_P_2,T_b] :
% 52.58/52.37 ( c_FunDef_Oreduction__pair(T_b,V_P_2)
% 52.58/52.37 <=> ( 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))
% 52.58/52.37 & 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))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_reduction__pair__lemma,axiom,
% 52.58/52.37 ! [V_S_2,V_R_2,V_P_2,T_b] :
% 52.58/52.37 ( c_FunDef_Oreduction__pair(T_b,V_P_2)
% 52.58/52.37 => ( 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)))
% 52.58/52.37 => ( 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)))
% 52.58/52.37 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 52.58/52.37 => 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)) ) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__map__pair__image,axiom,
% 52.58/52.37 ! [V_f_2,T_c,V_r_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 52.58/52.37 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 52.58/52.37 => 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)) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__lenlex,axiom,
% 52.58/52.37 ! [V_r_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 52.58/52.37 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olenlex(T_b,V_r_2)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__if__measure,axiom,
% 52.58/52.37 ! [T_b,V_g_2,V_f_2,V_P_2] :
% 52.58/52.37 ( ! [B_x] :
% 52.58/52.37 ( hBOOL(hAPP(V_P_2,B_x))
% 52.58/52.37 => 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))) )
% 52.58/52.37 => 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))))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_pred__nat__def,axiom,
% 52.58/52.37 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))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__lex,axiom,
% 52.58/52.37 ! [V_r_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 52.58/52.37 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olex(T_b,V_r_2)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__pred__nat,axiom,
% 52.58/52.37 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_lex__def,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__lexn,axiom,
% 52.58/52.37 ! [V_n_2,V_r_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 52.58/52.37 => c_Wellfounded_Owf(tc_List_Olist(T_b),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_lexn_Osimps_I1_J,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__same__fst,axiom,
% 52.58/52.37 ! [T_b,V_R_2,T_c,V_P_2] :
% 52.58/52.37 ( ! [B_x] :
% 52.58/52.37 ( hBOOL(hAPP(V_P_2,B_x))
% 52.58/52.37 => c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x)) )
% 52.58/52.37 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_P_2,V_R_2)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Range__Collect__split,axiom,
% 52.58/52.37 ! [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))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_RangeI,axiom,
% 52.58/52.37 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 52.58/52.37 ( 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))
% 52.58/52.37 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Range__Id__on,axiom,
% 52.58/52.37 ! [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 ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Range__empty,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Range__empty__iff,axiom,
% 52.58/52.37 ! [V_r_2,T_b,T_c] :
% 52.58/52.37 ( hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Range__Un__eq,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_finite__Range,axiom,
% 52.58/52.37 ! [V_r_2,T_c,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 52.58/52.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_snd__eq__Range,axiom,
% 52.58/52.37 ! [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) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Range__iff,axiom,
% 52.58/52.37 ! [V_r_2,T_c,V_a_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 52.58/52.37 <=> ? [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)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Range__insert,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Range__Int__subset,axiom,
% 52.58/52.37 ! [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)))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Range__Diff__subset,axiom,
% 52.58/52.37 ! [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)))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_RangeP__Range__eq,axiom,
% 52.58/52.37 ! [V_x_2,V_r_2,T_c,T_b] :
% 52.58/52.37 ( 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))
% 52.58/52.37 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_RangeE,axiom,
% 52.58/52.37 ! [V_r_2,T_c,V_b_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 52.58/52.37 => ~ ! [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)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_RangeP_Ointros,axiom,
% 52.58/52.37 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 52.58/52.37 => hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_b_2)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_RangeP_Oequations,axiom,
% 52.58/52.37 ! [V_a2_2,V_r_2,T_c,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2))
% 52.58/52.37 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__Un,axiom,
% 52.58/52.37 ! [V_s_2,V_r_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 52.58/52.37 => ( c_Wellfounded_Owf(T_b,V_s_2)
% 52.58/52.37 => ( 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))
% 52.58/52.37 => 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)) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wfP__def,axiom,
% 52.58/52.37 ! [V_r_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 52.58/52.37 <=> 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))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wfP__empty,axiom,
% 52.58/52.37 ! [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))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_DomainI,axiom,
% 52.58/52.37 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 52.58/52.37 ( 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))
% 52.58/52.37 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_accp__wfPD,axiom,
% 52.58/52.37 ! [V_x_2,V_r_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 52.58/52.37 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_x_2)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wfP__accp__iff,axiom,
% 52.58/52.37 ! [V_r_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 52.58/52.37 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Domain__Id__on,axiom,
% 52.58/52.37 ! [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 ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wfP__subset,axiom,
% 52.58/52.37 ! [V_p_2,V_r_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 52.58/52.37 => ( 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))
% 52.58/52.37 => c_Wellfounded_OwfP(T_b,V_p_2) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Domain__empty,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Domain__empty__iff,axiom,
% 52.58/52.37 ! [V_r_2,T_c,T_b] :
% 52.58/52.37 ( hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Domain__mono,axiom,
% 52.58/52.37 ! [V_s_2,V_r_2,T_c,T_b] :
% 52.58/52.37 ( 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))
% 52.58/52.37 => 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))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Domain__Un__eq,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_finite__Domain,axiom,
% 52.58/52.37 ! [V_r_2,T_c,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 52.58/52.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_fst__eq__Domain,axiom,
% 52.58/52.37 ! [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) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Domain__iff,axiom,
% 52.58/52.37 ! [V_r_2,T_c,V_a_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 52.58/52.37 <=> ? [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)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Domain__insert,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Domain__Int__subset,axiom,
% 52.58/52.37 ! [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)))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Domain__Diff__subset,axiom,
% 52.58/52.37 ! [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)))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Field__def,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__in__rel,axiom,
% 52.58/52.37 ! [V_R_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_Owf(T_b,V_R_2)
% 52.58/52.37 => c_Wellfounded_OwfP(T_b,c_FunDef_Oin__rel(T_b,T_b,V_R_2)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wfP__wf__eq,axiom,
% 52.58/52.37 ! [V_r_2,T_b] :
% 52.58/52.37 ( 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))
% 52.58/52.37 <=> c_Wellfounded_Owf(T_b,V_r_2) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Domain__Collect__split,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_DomainP__Domain__eq,axiom,
% 52.58/52.37 ! [V_x_2,V_r_2,T_c,T_b] :
% 52.58/52.37 ( 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))
% 52.58/52.37 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_DomainE,axiom,
% 52.58/52.37 ! [V_r_2,T_c,V_a_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 52.58/52.37 => ~ ! [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)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_DomainP_Ointros,axiom,
% 52.58/52.37 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 52.58/52.37 => hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a_2)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_DomainP_Oequations,axiom,
% 52.58/52.37 ! [V_a1_2,V_r_2,T_c,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2))
% 52.58/52.37 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wfP__acyclicP,axiom,
% 52.58/52.37 ! [V_r_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 52.58/52.37 => 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))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_neg__map__def,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__acyclic,axiom,
% 52.58/52.37 ! [V_r_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 52.58/52.37 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_acyclic__subset,axiom,
% 52.58/52.37 ! [V_r_2,V_s_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_Oacyclic(T_b,V_s_2)
% 52.58/52.37 => ( 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))
% 52.58/52.37 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_finite__acyclic__wf,axiom,
% 52.58/52.37 ! [V_r_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 52.58/52.37 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 52.58/52.37 => c_Wellfounded_Owf(T_b,V_r_2) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__iff__acyclic__if__finite,axiom,
% 52.58/52.37 ! [V_r_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 52.58/52.37 => ( c_Wellfounded_Owf(T_b,V_r_2)
% 52.58/52.37 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_neg__single__def,axiom,
% 52.58/52.37 ! [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) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_pos__map__def,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_New__DSequence_Oneg__single__def,axiom,
% 52.58/52.37 ! [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) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_pos__single__def,axiom,
% 52.58/52.37 ! [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) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_New__DSequence_Opos__single__def,axiom,
% 52.58/52.37 ! [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) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Nitpick_Owf_H__def,axiom,
% 52.58/52.37 ! [V_r_2,T_b] :
% 52.58/52.37 ( c_Nitpick_Owf_H(T_b,V_r_2)
% 52.58/52.37 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 52.58/52.37 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 52.58/52.37 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_pigeonhole__infinite,axiom,
% 52.58/52.37 ! [V_f_2,T_c,V_A_2,T_b] :
% 52.58/52.37 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 52.58/52.37 => ? [B_x] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.58/52.37 & ~ 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)))))) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Abs__Integ__cases,axiom,
% 52.58/52.37 ! [V_x_2] :
% 52.58/52.37 ~ ! [B_y] :
% 52.58/52.37 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y)
% 52.58/52.37 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Abs__Integ__induct,axiom,
% 52.58/52.37 ! [V_x_2,V_P_2] :
% 52.58/52.37 ( ! [B_y] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg))
% 52.58/52.37 => hBOOL(hAPP(V_P_2,hAPP(c_Int_OAbs__Integ,B_y))) )
% 52.58/52.37 => hBOOL(hAPP(V_P_2,V_x_2)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_finite__UN__I,axiom,
% 52.58/52.37 ! [V_B_2,T_c,V_A_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => ( ! [B_a] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 52.58/52.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 52.58/52.37 => 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))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_inj__on__diff__nat,axiom,
% 52.58/52.37 ! [V_k_2,V_N_2] :
% 52.58/52.37 ( ! [B_x] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 52.58/52.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) )
% 52.58/52.37 => 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) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wfP__SUP,axiom,
% 52.58/52.37 ! [T_b,V_r_2,T_c] :
% 52.58/52.37 ( ! [B_i] : c_Wellfounded_OwfP(T_c,hAPP(V_r_2,B_i))
% 52.58/52.37 => ( ! [B_i,B_j] :
% 52.58/52.37 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j)
% 52.58/52.37 => 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)) )
% 52.58/52.37 => 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)) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_finite__map__freshness,axiom,
% 52.58/52.37 ! [V_f_2,T_c,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Map_Odom(T_b,T_c,V_f_2)))
% 52.58/52.37 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 52.58/52.37 => ? [B_x] : hAPP(V_f_2,B_x) = c_Option_Ooption_ONone(T_c) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_mem__splitI2,axiom,
% 52.58/52.37 ! [V_c_2,V_z_2,T_d,T_c,T_b,V_p_2] :
% 52.58/52.37 ( ! [B_a,B_b] :
% 52.58/52.37 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)
% 52.58/52.37 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_c_2,B_a),B_b))) )
% 52.58/52.37 => 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))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_mem__splitE,axiom,
% 52.58/52.37 ! [V_p_2,V_c_2,T_d,T_c,V_z_2,T_b] :
% 52.58/52.37 ( 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)))
% 52.58/52.37 => ~ ! [B_x,B_y] :
% 52.58/52.37 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y)
% 52.58/52.37 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,B_x),B_y))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Eps__split,axiom,
% 52.58/52.37 ! [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))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_some__sym__eq__trivial,axiom,
% 52.58/52.37 ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 52.58/52.37
% 52.58/52.37 fof(fact_some__eq__trivial,axiom,
% 52.58/52.37 ! [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 ).
% 52.58/52.37
% 52.58/52.37 fof(fact_some__eq__ex,axiom,
% 52.58/52.37 ! [T_b,V_P_2] :
% 52.58/52.37 ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2)))
% 52.58/52.37 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_someI__ex,axiom,
% 52.58/52.37 ! [T_b,V_P_2] :
% 52.58/52.37 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 52.58/52.37 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_tfl__some,axiom,
% 52.58/52.37 ! [T_b,B_P] :
% 52.58/52.37 ( ? [B_x] : hBOOL(hAPP(B_P,B_x))
% 52.58/52.37 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_b,B_P))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_someI,axiom,
% 52.58/52.37 ! [T_b,V_x_2,V_P_2] :
% 52.58/52.37 ( hBOOL(hAPP(V_P_2,V_x_2))
% 52.58/52.37 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_exE__some,axiom,
% 52.58/52.37 ! [T_b,V_c_2,V_P_2] :
% 52.58/52.37 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 52.58/52.37 => ( V_c_2 = c_Hilbert__Choice_OEps(T_b,V_P_2)
% 52.58/52.37 => hBOOL(hAPP(V_P_2,V_c_2)) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_split__paired__Eps,axiom,
% 52.58/52.37 ! [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)))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Eps__split__eq,axiom,
% 52.58/52.37 ! [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) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wfI__pf,axiom,
% 52.58/52.37 ! [V_R_2,T_b] :
% 52.58/52.37 ( ! [B_A] :
% 52.58/52.37 ( 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)))
% 52.58/52.37 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 52.58/52.37 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Sigma__mono,axiom,
% 52.58/52.37 ! [V_D_2,V_B_2,T_c,V_C_2,V_A_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 52.58/52.37 => ( ! [B_x] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.58/52.37 => 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))) )
% 52.58/52.37 => 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))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_not__acc__down,axiom,
% 52.58/52.37 ! [V_R_2,V_x_2,T_b] :
% 52.58/52.37 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_R_2)))
% 52.58/52.37 => ~ ! [B_z] :
% 52.58/52.37 ( 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))
% 52.58/52.37 => hBOOL(hAPP(hAPP(c_member(T_b),B_z),c_Wellfounded_Oacc(T_b,V_R_2))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_acc_OaccI,axiom,
% 52.58/52.37 ! [V_r_2,V_x_2,T_b] :
% 52.58/52.37 ( ! [B_y] :
% 52.58/52.37 ( 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))
% 52.58/52.37 => hBOOL(hAPP(hAPP(c_member(T_b),B_y),c_Wellfounded_Oacc(T_b,V_r_2))) )
% 52.58/52.37 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_fold__image__1,axiom,
% 52.58/52.37 ! [V_f_2,V_S_2,T_b,T_c] :
% 52.58/52.37 ( class_Groups_Ocomm__monoid__mult(T_c)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 52.58/52.37 => ( ! [B_x] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 52.58/52.37 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 52.58/52.37 => 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) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_card_Oneutral,axiom,
% 52.58/52.37 ! [V_A_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.58/52.37 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 52.58/52.37 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_max__ext_Osimps,axiom,
% 52.58/52.37 ! [V_R_2,V_a2_2,V_a1_2,T_b] :
% 52.58/52.37 ( 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)))
% 52.58/52.37 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 52.58/52.37 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 52.58/52.37 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.37 & ! [B_x] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 52.58/52.37 => ? [B_xa] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 52.58/52.37 & 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)) ) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_fold__image__cong,axiom,
% 52.58/52.37 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 52.58/52.37 ( class_Groups_Oab__semigroup__mult(T_c)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => ( ! [B_x] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.58/52.37 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
% 52.58/52.37 => 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) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_setprod__dvd__setprod__subset2,axiom,
% 52.58/52.37 ! [V_g_2,V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 52.58/52.37 ( class_Rings_Ocomm__semiring__1(T_c)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 52.58/52.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.58/52.37 => ( ! [B_x] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.58/52.37 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 52.58/52.37 => 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))) ) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Min__eqI,axiom,
% 52.58/52.37 ! [V_x_2,V_A_2,T_b] :
% 52.58/52.37 ( class_Orderings_Olinorder(T_b)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => ( ! [B_y] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 52.58/52.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y)) )
% 52.58/52.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.58/52.37 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Max__eqI,axiom,
% 52.58/52.37 ! [V_x_2,V_A_2,T_b] :
% 52.58/52.37 ( class_Orderings_Olinorder(T_b)
% 52.58/52.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.37 => ( ! [B_y] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 52.58/52.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_y),V_x_2)) )
% 52.58/52.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.58/52.37 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__no__infinite__down__chainE,axiom,
% 52.58/52.37 ! [V_f_2,V_r_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 52.58/52.37 => ~ ! [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)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_setsum__reindex__cong,axiom,
% 52.58/52.37 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 52.58/52.37 ( class_Groups_Ocomm__monoid__add(T_d)
% 52.58/52.37 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 52.58/52.37 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 52.58/52.37 => ( ! [B_a] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 52.58/52.37 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) )
% 52.58/52.37 => 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) ) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_less__eq,axiom,
% 52.58/52.37 ! [V_n_2,V_m_2] :
% 52.58/52.37 ( 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)))
% 52.58/52.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__trancl,axiom,
% 52.58/52.37 ! [V_r_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 52.58/52.37 => c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_less__than__def,axiom,
% 52.58/52.37 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_acyclic__def,axiom,
% 52.58/52.37 ! [V_r_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 52.58/52.37 <=> ! [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))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_trancl_Or__into__trancl,axiom,
% 52.58/52.37 ! [V_r_2,V_b_2,V_a_2,T_b] :
% 52.58/52.37 ( hBOOL(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))
% 52.58/52.37 => hBOOL(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))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_trancl__subset__Field2,axiom,
% 52.58/52.37 ! [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))))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_r__into__trancl_H,axiom,
% 52.58/52.37 ! [V_r_2,V_p_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 52.58/52.37 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_trancl__empty,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_trancl__domain,axiom,
% 52.58/52.37 ! [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) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_trancl__range,axiom,
% 52.58/52.37 ! [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) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_finite__trancl,axiom,
% 52.58/52.37 ! [V_r_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 52.58/52.37 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_trancl__trans,axiom,
% 52.58/52.37 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 52.58/52.37 ( hBOOL(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)))
% 52.58/52.37 => ( 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)))
% 52.58/52.37 => hBOOL(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))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
% 52.58/52.37 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 52.58/52.37 ( hBOOL(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)))
% 52.58/52.37 => ( 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))
% 52.58/52.37 => hBOOL(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))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_trancl__into__trancl2,axiom,
% 52.58/52.37 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 52.58/52.37 ( hBOOL(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))
% 52.58/52.37 => ( 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)))
% 52.58/52.37 => hBOOL(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))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_r__r__into__trancl,axiom,
% 52.58/52.37 ! [V_c_2,V_R_2,V_b_2,V_a_2,T_b] :
% 52.58/52.37 ( hBOOL(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))
% 52.58/52.37 => ( 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))
% 52.58/52.37 => hBOOL(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))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_trancl__mono,axiom,
% 52.58/52.37 ! [V_s_2,V_r_2,V_p_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 52.58/52.37 => ( 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))
% 52.58/52.37 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_s_2))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_trancl__unfold,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_trancl__subset__Sigma,axiom,
% 52.58/52.37 ! [V_A_2,V_r_2,T_b] :
% 52.58/52.37 ( 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))))
% 52.58/52.37 => 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)))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_trancl__Int__subset,axiom,
% 52.58/52.37 ! [V_s_2,V_r_2,T_b] :
% 52.58/52.37 ( 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))
% 52.58/52.37 => ( 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))
% 52.58/52.37 => 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)) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_trancl__insert,axiom,
% 52.58/52.37 ! [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)))))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_reflcl__set__eq,axiom,
% 52.58/52.37 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 52.58/52.37 ( 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))
% 52.58/52.37 <=> hBOOL(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)))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_r__into__rtrancl,axiom,
% 52.58/52.37 ! [V_r_2,V_p_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 52.58/52.37 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rtrancl_Ortrancl__refl,axiom,
% 52.58/52.37 ! [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))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_IdI,axiom,
% 52.58/52.37 ! [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))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_trancl__into__rtrancl,axiom,
% 52.58/52.37 ! [V_r_2,V_b_2,V_a_2,T_b] :
% 52.58/52.37 ( hBOOL(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)))
% 52.58/52.37 => hBOOL(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))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_trancl__unfold__left,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_trancl__unfold__right,axiom,
% 52.58/52.37 ! [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) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_trancl__reflcl,axiom,
% 52.58/52.37 ! [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) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_reflcl__trancl,axiom,
% 52.58/52.37 ! [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) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rtrancl__trancl__absorb,axiom,
% 52.58/52.37 ! [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) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_trancl__rtrancl__absorb,axiom,
% 52.58/52.37 ! [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) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rtrancl__trans,axiom,
% 52.58/52.37 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 52.58/52.37 ( hBOOL(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)))
% 52.58/52.37 => ( 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)))
% 52.58/52.37 => hBOOL(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))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
% 52.58/52.37 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 52.58/52.37 ( hBOOL(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)))
% 52.58/52.37 => ( 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))
% 52.58/52.37 => hBOOL(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))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_converse__rtrancl__into__rtrancl,axiom,
% 52.58/52.37 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 52.58/52.37 ( hBOOL(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))
% 52.58/52.37 => ( 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)))
% 52.58/52.37 => hBOOL(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))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rtrancl__idemp,axiom,
% 52.58/52.37 ! [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) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_refl__rtrancl,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rtrancl__r__diff__Id,axiom,
% 52.58/52.37 ! [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) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rtrancl__mono,axiom,
% 52.58/52.37 ! [V_s_2,V_r_2,T_b] :
% 52.58/52.37 ( 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))
% 52.58/52.37 => 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))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rtrancl__subset,axiom,
% 52.58/52.37 ! [V_S_2,V_R_2,T_b] :
% 52.58/52.37 ( 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))
% 52.58/52.37 => ( 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)))
% 52.58/52.37 => c_Transitive__Closure_Ortrancl(T_b,V_S_2) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rtrancl__subset__rtrancl,axiom,
% 52.58/52.37 ! [V_s_2,V_r_2,T_b] :
% 52.58/52.37 ( 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)))
% 52.58/52.37 => 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))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rtrancl__reflcl__absorb,axiom,
% 52.58/52.37 ! [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) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rtrancl__Un__rtrancl,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rtrancl__reflcl,axiom,
% 52.58/52.37 ! [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) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rtrancl__Un__subset,axiom,
% 52.58/52.37 ! [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)))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Image__closed__trancl,axiom,
% 52.58/52.37 ! [V_X_2,V_r_2,T_b] :
% 52.58/52.37 ( 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))
% 52.58/52.37 => hAPP(c_Relation_OImage(T_b,T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_X_2) = V_X_2 ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_in__rtrancl__UnI,axiom,
% 52.58/52.37 ! [V_S_2,V_R_2,V_x_2,T_b] :
% 52.58/52.37 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 52.58/52.37 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) )
% 52.58/52.37 => 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)))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rtrancl__unfold,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rtrancl__idemp__self__comp,axiom,
% 52.58/52.37 ! [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) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_r__comp__rtrancl__eq,axiom,
% 52.58/52.37 ! [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) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rtrancl__Int__subset,axiom,
% 52.58/52.37 ! [V_r_2,V_s_2,T_b] :
% 52.58/52.37 ( 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))
% 52.58/52.37 => ( 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))
% 52.58/52.37 => 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)) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rtrancl__empty,axiom,
% 52.58/52.37 ! [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) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Range__rtrancl,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Domain__rtrancl,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_R__O__Id,axiom,
% 52.58/52.37 ! [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 ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Id__O__R,axiom,
% 52.58/52.37 ! [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 ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Image__Id,axiom,
% 52.58/52.37 ! [V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId(T_b)),V_A_2) = V_A_2 ).
% 52.58/52.37
% 52.58/52.37 fof(fact_pair__in__Id__conv,axiom,
% 52.58/52.37 ! [V_b_2,V_a_2,T_b] :
% 52.58/52.37 ( hBOOL(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)))
% 52.58/52.37 <=> V_a_2 = V_b_2 ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rtrancl__trancl__trancl,axiom,
% 52.58/52.37 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
% 52.58/52.37 ( hBOOL(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)))
% 52.58/52.37 => ( 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)))
% 52.58/52.37 => hBOOL(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))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_trancl__rtrancl__trancl,axiom,
% 52.58/52.37 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 52.58/52.37 ( hBOOL(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)))
% 52.58/52.37 => ( 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)))
% 52.58/52.37 => hBOOL(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))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rtrancl__into__trancl1,axiom,
% 52.58/52.37 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 52.58/52.37 ( hBOOL(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)))
% 52.58/52.37 => ( 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))
% 52.58/52.37 => hBOOL(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))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rtranclD,axiom,
% 52.58/52.37 ! [V_R_2,V_b_2,V_a_2,T_b] :
% 52.58/52.37 ( hBOOL(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)))
% 52.58/52.37 => ( V_a_2 = V_b_2
% 52.58/52.37 | ( V_a_2 != V_b_2
% 52.58/52.37 & hBOOL(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))) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rtrancl__into__trancl2,axiom,
% 52.58/52.37 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 52.58/52.37 ( hBOOL(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))
% 52.58/52.37 => ( 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)))
% 52.58/52.37 => hBOOL(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))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rtrancl__eq__or__trancl,axiom,
% 52.58/52.37 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 52.58/52.37 ( hBOOL(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)))
% 52.58/52.37 <=> ( V_x_2 = V_y_2
% 52.58/52.37 | ( V_x_2 != V_y_2
% 52.58/52.37 & hBOOL(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))) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Domain__Id,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Range__Id,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_refl__Id,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_pair__leq__def,axiom,
% 52.58/52.37 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))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Not__Domain__rtrancl,axiom,
% 52.58/52.37 ! [V_y_2,V_R_2,V_x_2,T_b] :
% 52.58/52.37 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_b),V_R_2)))
% 52.58/52.37 => ( hBOOL(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)))
% 52.58/52.37 <=> V_x_2 = V_y_2 ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_acc__downwards__aux,axiom,
% 52.58/52.37 ! [V_r_2,V_a_2,V_b_2,T_b] :
% 52.58/52.37 ( 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)))
% 52.58/52.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 52.58/52.37 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_acc__downwards,axiom,
% 52.58/52.37 ! [V_b_2,V_r_2,V_a_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 52.58/52.37 => ( 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)))
% 52.58/52.37 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__insert,axiom,
% 52.58/52.37 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 52.58/52.37 ( 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))
% 52.58/52.37 <=> ( c_Wellfounded_Owf(T_b,V_r_2)
% 52.58/52.37 & ~ hBOOL(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))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_acyclic__insert,axiom,
% 52.58/52.37 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 52.58/52.37 ( 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))
% 52.58/52.37 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 52.58/52.37 & ~ hBOOL(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))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_refl__reflcl,axiom,
% 52.58/52.37 ! [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))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Id__def,axiom,
% 52.58/52.37 ! [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))))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_irrefl__diff__Id,axiom,
% 52.58/52.37 ! [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))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_pred__nat__trancl__eq__le,axiom,
% 52.58/52.37 ! [V_n_2,V_m_2] :
% 52.58/52.37 ( 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)))
% 52.58/52.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_trancl__subset__Sigma__aux,axiom,
% 52.58/52.37 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_b] :
% 52.58/52.37 ( hBOOL(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)))
% 52.58/52.37 => ( 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))))
% 52.58/52.37 => ( V_a_2 = V_b_2
% 52.58/52.37 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_irrefl__tranclI,axiom,
% 52.58/52.37 ! [V_x_2,V_r_2,T_b] :
% 52.58/52.37 ( 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))
% 52.58/52.37 => ~ hBOOL(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))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_sequence__trans,axiom,
% 52.58/52.37 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_b] :
% 52.58/52.37 ( ! [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)))
% 52.58/52.37 => 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))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rtrancl__converse,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_converse__Id,axiom,
% 52.58/52.37 ! [T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId(T_b)) = c_Relation_OId(T_b) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_equiv__comp__eq,axiom,
% 52.58/52.37 ! [V_r_2,V_A_2,T_b] :
% 52.58/52.37 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 52.58/52.37 => 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 ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_converse__UNION,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_converseD,axiom,
% 52.58/52.37 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 52.58/52.37 ( 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)))
% 52.58/52.37 => 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)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_converseI,axiom,
% 52.58/52.37 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 52.58/52.37 ( 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))
% 52.58/52.37 => 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))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_converse__iff,axiom,
% 52.58/52.37 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 52.58/52.37 ( 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)))
% 52.58/52.37 <=> 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)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_converse__inv__image,axiom,
% 52.58/52.37 ! [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) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_converse__Id__on,axiom,
% 52.58/52.37 ! [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) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Field__converse,axiom,
% 52.58/52.37 ! [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) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_converse__converse,axiom,
% 52.58/52.37 ! [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 ).
% 52.58/52.37
% 52.58/52.37 fof(fact_converse__Int,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_refl__on__converse,axiom,
% 52.58/52.37 ! [V_r_2,V_A_2,T_b] :
% 52.58/52.37 ( c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 52.58/52.37 <=> c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_finite__converse,axiom,
% 52.58/52.37 ! [V_r_2,T_c,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 52.58/52.37 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2)) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_converse__Un,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_converse__rel__comp,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_acyclic__converse,axiom,
% 52.58/52.37 ! [V_r_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 52.58/52.37 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Range__converse,axiom,
% 52.58/52.37 ! [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) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Domain__converse,axiom,
% 52.58/52.37 ! [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) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Range__def,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__converse__trancl,axiom,
% 52.58/52.37 ! [V_r_2,T_b] :
% 52.58/52.37 ( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 52.58/52.37 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_trancl__converse,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rtrancl__converseI,axiom,
% 52.58/52.37 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 52.58/52.37 ( 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)))
% 52.58/52.37 => hBOOL(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)))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rtrancl__converseD,axiom,
% 52.58/52.37 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 52.58/52.37 ( hBOOL(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))))
% 52.58/52.37 => 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))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_trancl__converseI,axiom,
% 52.58/52.37 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 52.58/52.37 ( hBOOL(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))))
% 52.58/52.37 => hBOOL(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)))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_trancl__converseD,axiom,
% 52.58/52.37 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 52.58/52.37 ( hBOOL(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))))
% 52.58/52.37 => hBOOL(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)))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_Image__subset__eq,axiom,
% 52.58/52.37 ! [V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 52.58/52.37 ( 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))
% 52.58/52.37 <=> 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))))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_refl__on__comp__subset,axiom,
% 52.58/52.37 ! [V_r_2,V_A_2,T_b] :
% 52.58/52.37 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 52.58/52.37 => 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))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_comp__equivI,axiom,
% 52.58/52.37 ! [V_A_2,V_r_2,T_b] :
% 52.58/52.37 ( 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
% 52.58/52.37 => ( hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) = V_A_2
% 52.58/52.37 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_finite__acyclic__wf__converse,axiom,
% 52.58/52.37 ! [V_r_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 52.58/52.37 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 52.58/52.37 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_converse__def,axiom,
% 52.58/52.37 ! [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))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_total__on__diff__Id,axiom,
% 52.58/52.37 ! [V_r_2,V_A_2,T_b] :
% 52.58/52.37 ( 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)))
% 52.58/52.37 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rtrancl__imp__UN__rel__pow,axiom,
% 52.58/52.37 ! [V_R_2,V_p_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 52.58/52.37 => 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)))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rtrancl__power,axiom,
% 52.58/52.37 ! [V_R_2,V_p_2,T_b] :
% 52.58/52.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 52.58/52.37 <=> ? [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))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rel__pow__imp__rtrancl,axiom,
% 52.58/52.37 ! [V_R_2,V_n_2,V_p_2,T_b] :
% 52.58/52.37 ( 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)))
% 52.58/52.37 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_relpow_Osimps_I1_J,axiom,
% 52.58/52.37 ! [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) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rel__pow__1,axiom,
% 52.58/52.37 ! [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 ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rel__pow__add,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_relpow_Osimps_I2_J,axiom,
% 52.58/52.37 ! [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) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rel__pow__commute,axiom,
% 52.58/52.37 ! [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) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_funpow__swap1,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_funpow__mult,axiom,
% 52.58/52.37 ! [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) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_wf__exp,axiom,
% 52.58/52.37 ! [V_R_2,V_n_2,T_b] :
% 52.58/52.37 ( 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))
% 52.58/52.37 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_comp__funpow,axiom,
% 52.58/52.37 ! [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)) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_total__on__empty,axiom,
% 52.58/52.37 ! [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) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_total__on__converse,axiom,
% 52.58/52.37 ! [V_r_2,V_A_2,T_b] :
% 52.58/52.37 ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 52.58/52.37 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rel__pow__0__I,axiom,
% 52.58/52.37 ! [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))) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rel__pow__0__E,axiom,
% 52.58/52.37 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 52.58/52.37 ( hBOOL(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)))
% 52.58/52.37 => V_x_2 = V_y_2 ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rel__pow__Suc__I,axiom,
% 52.58/52.37 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_b] :
% 52.58/52.37 ( hBOOL(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)))
% 52.58/52.37 => ( 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))
% 52.58/52.37 => hBOOL(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))) ) ) ).
% 52.58/52.37
% 52.58/52.37 fof(fact_rel__pow__Suc__I2,axiom,
% 52.58/52.37 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_b] :
% 52.58/52.37 ( hBOOL(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))
% 52.58/52.38 => ( 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)))
% 52.58/52.38 => hBOOL(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))) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_funpow_Osimps_I2_J,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_funpow__add,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_funpow_Osimps_I1_J,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_trancl__power,axiom,
% 52.58/52.38 ! [V_R_2,V_p_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
% 52.58/52.38 <=> ? [B_n] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 52.58/52.38 & 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))) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_total__on__def,axiom,
% 52.58/52.38 ! [V_r_2,V_A_2,T_b] :
% 52.58/52.38 ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2)
% 52.58/52.38 <=> ! [B_x] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.58/52.38 => ! [B_xa] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 52.58/52.38 => ( B_x != B_xa
% 52.58/52.38 => ( 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))
% 52.58/52.38 | 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)) ) ) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_rtrancl__is__UN__rel__pow,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_funpow__code__def,axiom,
% 52.58/52.38 ! [T_b] : c_Nat_Ofunpow(T_b) = c_Nat_Ocompow(T_b,T_b) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_rel__pow__E,axiom,
% 52.58/52.38 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 52.58/52.38 ( hBOOL(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)))
% 52.58/52.38 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.58/52.38 => V_x_2 != V_z_2 )
% 52.58/52.38 => ~ ! [B_y,B_m] :
% 52.58/52.38 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 52.58/52.38 => ( 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)))
% 52.58/52.38 => ~ 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)) ) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_rel__pow__E2,axiom,
% 52.58/52.38 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 52.58/52.38 ( hBOOL(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)))
% 52.58/52.38 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.58/52.38 => V_x_2 != V_z_2 )
% 52.58/52.38 => ~ ! [B_y,B_m] :
% 52.58/52.38 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 52.58/52.38 => ( 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))
% 52.58/52.38 => ~ 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))) ) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_acyclicI,axiom,
% 52.58/52.38 ! [V_r_2,T_b] :
% 52.58/52.38 ( ! [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)))
% 52.58/52.38 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Image__Int__eq,axiom,
% 52.58/52.38 ! [V_B_2,V_A_2,V_R_2,T_c,T_b] :
% 52.58/52.38 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_R_2))
% 52.58/52.38 => 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)) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_rtrancl__Un__separator__converseE,axiom,
% 52.58/52.38 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_b] :
% 52.58/52.38 ( hBOOL(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))))
% 52.58/52.38 => ( ! [B_x] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => ! [B_y] :
% 52.58/52.38 ( 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))
% 52.58/52.38 => B_y = B_x ) )
% 52.58/52.38 => hBOOL(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))) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_single__valued__Id__on,axiom,
% 52.58/52.38 ! [V_A_2,T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_single__valued__subset,axiom,
% 52.58/52.38 ! [V_s_2,V_r_2,T_c,T_b] :
% 52.58/52.38 ( 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))
% 52.58/52.38 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2)
% 52.58/52.38 => c_Relation_Osingle__valued(T_b,T_c,V_r_2) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_single__valued__rel__comp,axiom,
% 52.58/52.38 ! [V_s_2,T_d,V_r_2,T_c,T_b] :
% 52.58/52.38 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 52.58/52.38 => ( c_Relation_Osingle__valued(T_c,T_d,V_s_2)
% 52.58/52.38 => 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)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_single__valued__Id,axiom,
% 52.58/52.38 ! [T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId(T_b)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_single__valued__rel__pow,axiom,
% 52.58/52.38 ! [V_n_2,V_R_2,T_b] :
% 52.58/52.38 ( c_Relation_Osingle__valued(T_b,T_b,V_R_2)
% 52.58/52.38 => 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)) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_single__valued__def,axiom,
% 52.58/52.38 ! [V_r_2,T_c,T_b] :
% 52.58/52.38 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 52.58/52.38 <=> ! [B_x,B_y] :
% 52.58/52.38 ( 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))
% 52.58/52.38 => ! [B_z] :
% 52.58/52.38 ( 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))
% 52.58/52.38 => B_y = B_z ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_single__valuedD,axiom,
% 52.58/52.38 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_c,T_b] :
% 52.58/52.38 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 52.58/52.38 => ( 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))
% 52.58/52.38 => ( 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))
% 52.58/52.38 => V_y_2 = V_z_2 ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_single__valued__confluent,axiom,
% 52.58/52.38 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
% 52.58/52.38 ( c_Relation_Osingle__valued(T_b,T_b,V_r_2)
% 52.58/52.38 => ( hBOOL(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)))
% 52.58/52.38 => ( hBOOL(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)))
% 52.58/52.38 => ( 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)))
% 52.58/52.38 | 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))) ) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_rtrancl__Un__separatorE,axiom,
% 52.58/52.38 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_b] :
% 52.58/52.38 ( hBOOL(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))))
% 52.58/52.38 => ( ! [B_x] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => ! [B_y] :
% 52.58/52.38 ( 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))
% 52.58/52.38 => B_x = B_y ) )
% 52.58/52.38 => hBOOL(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))) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_rel__pow__Suc__E,axiom,
% 52.58/52.38 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 52.58/52.38 ( hBOOL(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)))
% 52.58/52.38 => ~ ! [B_y] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => ~ 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)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_rel__pow__Suc__D2,axiom,
% 52.58/52.38 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 52.58/52.38 ( hBOOL(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)))
% 52.58/52.38 => ? [B_y] :
% 52.58/52.38 ( 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))
% 52.58/52.38 & 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))) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_rel__pow__Suc__E2,axiom,
% 52.58/52.38 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 52.58/52.38 ( hBOOL(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)))
% 52.58/52.38 => ~ ! [B_y] :
% 52.58/52.38 ( 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))
% 52.58/52.38 => ~ 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))) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_tranclD2,axiom,
% 52.58/52.38 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 52.58/52.38 ( hBOOL(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)))
% 52.58/52.38 => ? [B_z] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 & 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)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_tranclD,axiom,
% 52.58/52.38 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 52.58/52.38 ( hBOOL(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)))
% 52.58/52.38 => ? [B_z] :
% 52.58/52.38 ( 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))
% 52.58/52.38 & 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))) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_IdE,axiom,
% 52.58/52.38 ! [V_p_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Relation_OId(T_b)))
% 52.58/52.38 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom,
% 52.58/52.38 ! [V_x_2,V_A_2,T_b] :
% 52.58/52.38 ( class_Orderings_Olinorder(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.58/52.38 => 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) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_folding_Oeq__fold,axiom,
% 52.58/52.38 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 52.58/52.38 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => 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) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_fold__image__def,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_fold__empty,axiom,
% 52.58/52.38 ! [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 ).
% 52.58/52.38
% 52.58/52.38 fof(fact_fold__def,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_union__fold__insert,axiom,
% 52.58/52.38 ! [V_B_2,V_A_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => 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) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_fold__sup__insert,axiom,
% 52.58/52.38 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 52.58/52.38 ( class_Lattices_Osemilattice__sup(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => 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)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_fold__inf__insert,axiom,
% 52.58/52.38 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 52.58/52.38 ( class_Lattices_Osemilattice__inf(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => 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)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_min__max_Ofold__inf__insert,axiom,
% 52.58/52.38 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 52.58/52.38 ( class_Orderings_Olinorder(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => 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)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_min__max_Ofold__sup__insert,axiom,
% 52.58/52.38 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 52.58/52.38 ( class_Orderings_Olinorder(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => 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)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom,
% 52.58/52.38 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.38 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => 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) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom,
% 52.58/52.38 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.38 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => 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)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_sup__SUPR__fold__sup,axiom,
% 52.58/52.38 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 52.58/52.38 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => 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) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom,
% 52.58/52.38 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_b] :
% 52.58/52.38 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => 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) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_sup__le__fold__sup,axiom,
% 52.58/52.38 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 52.58/52.38 ( class_Lattices_Osemilattice__sup(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.58/52.38 => 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))) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_fold__inf__le__inf,axiom,
% 52.58/52.38 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 52.58/52.38 ( class_Lattices_Osemilattice__inf(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.58/52.38 => 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))) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_min__max_Ofold__inf__le__inf,axiom,
% 52.58/52.38 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 52.58/52.38 ( class_Orderings_Olinorder(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.58/52.38 => 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))) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_min__max_Osup__le__fold__sup,axiom,
% 52.58/52.38 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 52.58/52.38 ( class_Orderings_Olinorder(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.58/52.38 => 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))) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_fold1__eq__fold__idem,axiom,
% 52.58/52.38 ! [V_a_2,V_A_2,T_b] :
% 52.58/52.38 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => 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) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom,
% 52.58/52.38 ! [V_a_2,V_A_2,T_b] :
% 52.58/52.38 ( class_Lattices_Olattice(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => 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) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom,
% 52.58/52.38 ! [V_a_2,V_A_2,T_b] :
% 52.58/52.38 ( class_Lattices_Olattice(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => 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) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Min_Oeq__fold__idem_H,axiom,
% 52.58/52.38 ! [V_a_2,V_A_2,T_b] :
% 52.58/52.38 ( class_Orderings_Olinorder(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => 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) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Max_Oeq__fold__idem_H,axiom,
% 52.58/52.38 ! [V_a_2,V_A_2,T_b] :
% 52.58/52.38 ( class_Orderings_Olinorder(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => 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) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom,
% 52.58/52.38 ! [V_a_2,V_A_2,T_b] :
% 52.58/52.38 ( class_Orderings_Olinorder(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => 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) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom,
% 52.58/52.38 ! [V_a_2,V_A_2,T_b] :
% 52.58/52.38 ( class_Orderings_Olinorder(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => 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) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_minus__fold__remove,axiom,
% 52.58/52.38 ! [V_B_2,V_A_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => 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) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_folding__one_Oeq__fold_H,axiom,
% 52.58/52.38 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 52.58/52.38 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.58/52.38 => 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) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_SUPR__fold__sup,axiom,
% 52.58/52.38 ! [V_f_2,V_A_2,T_b,T_c] :
% 52.58/52.38 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => 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) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_fold1__eq__fold,axiom,
% 52.58/52.38 ! [V_a_2,V_A_2,T_b] :
% 52.58/52.38 ( class_Groups_Oab__semigroup__mult(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.58/52.38 => 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) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Sup__fin_Oeq__fold_H,axiom,
% 52.58/52.38 ! [V_x_2,V_A_2,T_b] :
% 52.58/52.38 ( class_Lattices_Olattice(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.58/52.38 => 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) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Inf__fin_Oeq__fold_H,axiom,
% 52.58/52.38 ! [V_x_2,V_A_2,T_b] :
% 52.58/52.38 ( class_Lattices_Olattice(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.58/52.38 => 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) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Min_Oeq__fold_H,axiom,
% 52.58/52.38 ! [V_x_2,V_A_2,T_b] :
% 52.58/52.38 ( class_Orderings_Olinorder(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.58/52.38 => 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) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Max_Oeq__fold_H,axiom,
% 52.58/52.38 ! [V_x_2,V_A_2,T_b] :
% 52.58/52.38 ( class_Orderings_Olinorder(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.58/52.38 => 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) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom,
% 52.58/52.38 ! [V_x_2,V_A_2,T_b] :
% 52.58/52.38 ( class_Orderings_Olinorder(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.58/52.38 => 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) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_fun__left__comm_Ofold__rec,axiom,
% 52.58/52.38 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.38 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.58/52.38 => 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)))))) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_fun__left__comm_Ofold__insert__remove,axiom,
% 52.58/52.38 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.38 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => 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)))))) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_fun__left__comm,axiom,
% 52.58/52.38 ! [T_b] :
% 52.58/52.38 ( class_Groups_Oab__semigroup__mult(T_b)
% 52.58/52.38 => c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_fun__left__comm_Ofun__left__comm,axiom,
% 52.58/52.38 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 52.58/52.38 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 52.58/52.38 => 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)) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom,
% 52.58/52.38 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 52.58/52.38 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 52.58/52.38 => 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)) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_fun__left__comm_Ofold__graph__determ,axiom,
% 52.58/52.38 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 52.58/52.38 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 52.58/52.38 => V_y_2 = V_x_2 ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_fun__left__comm_Ofun__comp__comm,axiom,
% 52.58/52.38 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 52.58/52.38 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 52.58/52.38 => 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)) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_fun__left__comm_Ofold__fun__comm,axiom,
% 52.58/52.38 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.38 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => 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) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_fun__left__comm_Ofold__equality,axiom,
% 52.58/52.38 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 52.58/52.38 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 52.58/52.38 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_fun__left__comm_Ofold__graph__fold,axiom,
% 52.58/52.38 ! [V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.38 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => 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))) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_fun__left__comm_Ofold__insert,axiom,
% 52.58/52.38 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.38 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.58/52.38 => 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)) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_fun__left__comm_Ofold__insert2,axiom,
% 52.58/52.38 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.38 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.58/52.38 => 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) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom,
% 52.58/52.38 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 52.58/52.38 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 52.58/52.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.58/52.38 => ? [B_y_H] :
% 52.58/52.38 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H)
% 52.58/52.38 & 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)) ) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INFI__fold__inf,axiom,
% 52.58/52.38 ! [V_f_2,V_A_2,T_b,T_c] :
% 52.58/52.38 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => 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) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INF2__E,axiom,
% 52.58/52.38 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 52.58/52.38 ( 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))
% 52.58/52.38 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
% 52.58/52.38 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INF2__D,axiom,
% 52.58/52.38 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 52.58/52.38 ( 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))
% 52.58/52.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.58/52.38 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INF1__D,axiom,
% 52.58/52.38 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 52.58/52.38 ( 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))
% 52.58/52.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.58/52.38 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INF1__E,axiom,
% 52.58/52.38 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 52.58/52.38 ( 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))
% 52.58/52.38 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 52.58/52.38 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INT__D,axiom,
% 52.58/52.38 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
% 52.58/52.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INT__E,axiom,
% 52.58/52.38 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
% 52.58/52.38 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_finite__INT,axiom,
% 52.58/52.38 ! [V_A_2,T_c,V_I_2,T_b] :
% 52.58/52.38 ( ? [B_x] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 52.58/52.38 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) )
% 52.58/52.38 => 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))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_UN__extend__simps_I7_J,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_UN__simps_I7_J,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INT__extend__simps_I9_J,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INT__simps_I9_J,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Compl__UN,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Compl__INT,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Collect__ball__eq,axiom,
% 52.58/52.38 ! [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))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INF__less__iff,axiom,
% 52.58/52.38 ! [V_a_2,V_f_2,V_A_2,T_c,T_b] :
% 52.58/52.38 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 52.58/52.38 & class_Orderings_Olinorder(T_b) )
% 52.58/52.38 => ( 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))
% 52.58/52.38 <=> ? [B_x] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 52.58/52.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INF__INT__eq2,axiom,
% 52.58/52.38 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 52.58/52.38 ( 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))
% 52.58/52.38 <=> 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))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INT__iff,axiom,
% 52.58/52.38 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 <=> ! [B_x] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 52.58/52.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INFI__bool__eq,axiom,
% 52.58/52.38 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_HOL_Obool) = c_Set_OBall(T_b) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INF__commute,axiom,
% 52.58/52.38 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 52.58/52.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 52.58/52.38 => 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))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INFI__apply,axiom,
% 52.58/52.38 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 52.58/52.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 52.58/52.38 => 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)) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Pow__INT__eq,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INTER__UNIV__conv_I1_J,axiom,
% 52.58/52.38 ! [V_B_2,V_A_2,T_c,T_b] :
% 52.58/52.38 ( 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)
% 52.58/52.38 <=> ! [B_x] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 52.58/52.38 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INTER__UNIV__conv_I2_J,axiom,
% 52.58/52.38 ! [V_B_2,V_A_2,T_b,T_c] :
% 52.58/52.38 ( 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))
% 52.58/52.38 <=> ! [B_x] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 52.58/52.38 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INT__Int__distrib,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INT__absorb,axiom,
% 52.58/52.38 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 52.58/52.38 => 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) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INF__INT__eq,axiom,
% 52.58/52.38 ! [V_x_2,V_r_2,T_c,T_b] :
% 52.58/52.38 ( 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))
% 52.58/52.38 <=> 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))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_vimage__INT,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INT__simps_I10_J,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INT__extend__simps_I10_J,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Image__INT__subset,axiom,
% 52.58/52.38 ! [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)))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INT__lower,axiom,
% 52.58/52.38 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 52.58/52.38 => 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))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_le__INF__iff,axiom,
% 52.58/52.38 ! [V_M_2,V_A_2,T_c,V_u_2,T_b] :
% 52.58/52.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 52.58/52.38 => ( 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)))
% 52.58/52.38 <=> ! [B_x] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 52.58/52.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INT__subset__iff,axiom,
% 52.58/52.38 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 <=> ! [B_x] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 52.58/52.38 => 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))) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INT__extend__simps_I5_J,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INT__simps_I5_J,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INT__insert__distrib,axiom,
% 52.58/52.38 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 52.58/52.38 => 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)) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INT__insert,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INF__const,axiom,
% 52.58/52.38 ! [V_M_2,T_b,V_A_2,T_c] :
% 52.58/52.38 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 52.58/52.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.38 => 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 ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INT__extend__simps_I1_J,axiom,
% 52.58/52.38 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 52.58/52.38 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.38 => 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 )
% 52.58/52.38 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.38 => 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)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INT__extend__simps_I2_J,axiom,
% 52.58/52.38 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 52.58/52.38 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.38 => 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 )
% 52.58/52.38 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.38 => 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)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INT__empty,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INT__constant,axiom,
% 52.58/52.38 ! [V_c_2,T_c,T_b,V_A_2] :
% 52.58/52.38 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.38 => 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)) )
% 52.58/52.38 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.38 => 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 ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Un__INT__distrib2,axiom,
% 52.58/52.38 ! [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))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INT__extend__simps_I6_J,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Un__INT__distrib,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INT__extend__simps_I7_J,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INT__simps_I6_J,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INT__simps_I7_J,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INT__Un,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_converse__INTER,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INF__subset,axiom,
% 52.58/52.38 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 52.58/52.38 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 52.58/52.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.58/52.38 => 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))) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INTER__def,axiom,
% 52.58/52.38 ! [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)))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INT__simps_I2_J,axiom,
% 52.58/52.38 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 52.58/52.38 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.38 => 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)) )
% 52.58/52.38 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.38 => 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)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INT__simps_I1_J,axiom,
% 52.58/52.38 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 52.58/52.38 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.38 => 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)) )
% 52.58/52.38 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.38 => 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) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INT__simps_I3_J,axiom,
% 52.58/52.38 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 52.58/52.38 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.38 => 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)) )
% 52.58/52.38 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.38 => 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) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INT__extend__simps_I3_J,axiom,
% 52.58/52.38 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 52.58/52.38 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.38 => 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) )
% 52.58/52.38 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.38 => 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)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INT__extend__simps_I4_J,axiom,
% 52.58/52.38 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 52.58/52.38 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.38 => 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 )
% 52.58/52.38 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.38 => 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)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INF__leI,axiom,
% 52.58/52.38 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 52.58/52.38 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 52.58/52.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 52.58/52.38 => 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))) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INT__greaterThan__UNIV,axiom,
% 52.58/52.38 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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INT__simps_I4_J,axiom,
% 52.58/52.38 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 52.58/52.38 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.38 => 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)) )
% 52.58/52.38 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.38 => 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)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Image__INT__eq,axiom,
% 52.58/52.38 ! [V_B_2,T_d,V_A_2,V_r_2,T_c,T_b] :
% 52.58/52.38 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))
% 52.58/52.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
% 52.58/52.38 => 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)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_inf__INFI__fold__inf,axiom,
% 52.58/52.38 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 52.58/52.38 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => 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) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Inf__fold__inf,axiom,
% 52.58/52.38 ! [V_A_2,T_b] :
% 52.58/52.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => 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) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Sup__fold__sup,axiom,
% 52.58/52.38 ! [V_A_2,T_b] :
% 52.58/52.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => 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) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_finite__Inter,axiom,
% 52.58/52.38 ! [V_M_2,T_b] :
% 52.58/52.38 ( ? [B_x] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2))
% 52.58/52.38 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) )
% 52.58/52.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_UnionI,axiom,
% 52.58/52.38 ! [V_A_2,V_C_2,V_X_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 52.58/52.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
% 52.58/52.38 => 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))) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_InterD,axiom,
% 52.58/52.38 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 52.58/52.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_InterE,axiom,
% 52.58/52.38 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 52.58/52.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INF1__iff,axiom,
% 52.58/52.38 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 52.58/52.38 ( 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))
% 52.58/52.38 <=> ! [B_x] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.58/52.38 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INF2__iff,axiom,
% 52.58/52.38 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 52.58/52.38 ( 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))
% 52.58/52.38 <=> ! [B_x] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.58/52.38 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INT__extend__simps_I8_J,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INT__simps_I8_J,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_INTER__eq__Inter__image,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Inter__image__eq,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Un__Inter,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Inter__eq,axiom,
% 52.58/52.38 ! [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)))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Inter__anti__mono,axiom,
% 52.58/52.38 ! [V_A_2,V_B_2,T_b] :
% 52.58/52.38 ( 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))
% 52.58/52.38 => 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))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Inter__empty,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Union__insert,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_subset__Pow__Union,axiom,
% 52.58/52.38 ! [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)))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Union__empty,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Union__disjoint,axiom,
% 52.58/52.38 ! [V_A_2,V_C_2,T_b] :
% 52.58/52.38 ( 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))
% 52.58/52.38 <=> ! [B_x] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2))
% 52.58/52.38 => 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)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Union__upper,axiom,
% 52.58/52.38 ! [V_A_2,V_B_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 52.58/52.38 => 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))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_le__Inf__iff,axiom,
% 52.58/52.38 ! [V_A_2,V_b_2,T_b] :
% 52.58/52.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 52.58/52.38 => ( 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)))
% 52.58/52.38 <=> ! [B_x] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.58/52.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Sup__le__iff,axiom,
% 52.58/52.38 ! [V_b_2,V_A_2,T_b] :
% 52.58/52.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 52.58/52.38 => ( 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))
% 52.58/52.38 <=> ! [B_x] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.58/52.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Inter__lower,axiom,
% 52.58/52.38 ! [V_A_2,V_B_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 52.58/52.38 => 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)) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Union__mono,axiom,
% 52.58/52.38 ! [V_B_2,V_A_2,T_b] :
% 52.58/52.38 ( 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))
% 52.58/52.38 => 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))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Field__Union,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Union__Pow__eq,axiom,
% 52.58/52.38 ! [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 ).
% 52.58/52.38
% 52.58/52.38 fof(fact_less__Sup__iff,axiom,
% 52.58/52.38 ! [V_S_2,V_a_2,T_b] :
% 52.58/52.38 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 52.58/52.38 & class_Orderings_Olinorder(T_b) )
% 52.58/52.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2)))
% 52.58/52.38 <=> ? [B_x] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 52.58/52.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x)) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Inf__less__iff,axiom,
% 52.58/52.38 ! [V_a_2,V_S_2,T_b] :
% 52.58/52.38 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 52.58/52.38 & class_Orderings_Olinorder(T_b) )
% 52.58/52.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2))
% 52.58/52.38 <=> ? [B_x] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 52.58/52.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2)) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Union__quotient,axiom,
% 52.58/52.38 ! [V_r_2,V_A_2,T_b] :
% 52.58/52.38 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 52.58/52.38 => 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 ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Inf__Sup,axiom,
% 52.58/52.38 ! [V_A_2,T_b] :
% 52.58/52.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 52.58/52.38 => 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))))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Sup__Inf,axiom,
% 52.58/52.38 ! [V_A_2,T_b] :
% 52.58/52.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 52.58/52.38 => 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)))))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_finite__UnionD,axiom,
% 52.58/52.38 ! [V_A_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))
% 52.58/52.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_image__Union,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Sigma__Union,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_vimage__Union,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_UN__simps_I8_J,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_UN__extend__simps_I8_J,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Int__Union,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Int__Union2,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Range__Union,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Domain__Union,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Inter__insert,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Union__Un__distrib,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Union__UNIV,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_UNION__eq__Union__image,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Union__image__eq,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Sup__upper,axiom,
% 52.58/52.38 ! [V_A_2,V_x_2,T_b] :
% 52.58/52.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.58/52.38 => 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))) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Inter__UNIV,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Inf__lower,axiom,
% 52.58/52.38 ! [V_A_2,V_x_2,T_b] :
% 52.58/52.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.58/52.38 => 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)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Inter__Un__distrib,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Sup__empty,axiom,
% 52.58/52.38 ! [T_b] :
% 52.58/52.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 52.58/52.38 => 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) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Sup__singleton,axiom,
% 52.58/52.38 ! [V_a_2,T_b] :
% 52.58/52.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 52.58/52.38 => 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 ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Sup__insert,axiom,
% 52.58/52.38 ! [V_A_2,V_a_2,T_b] :
% 52.58/52.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 52.58/52.38 => 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)) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Int__Inter__image,axiom,
% 52.58/52.38 ! [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))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Inf__singleton,axiom,
% 52.58/52.38 ! [V_a_2,T_b] :
% 52.58/52.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 52.58/52.38 => 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 ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Sup__UNIV,axiom,
% 52.58/52.38 ! [T_b] :
% 52.58/52.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 52.58/52.38 => 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) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Inf__empty,axiom,
% 52.58/52.38 ! [T_b] :
% 52.58/52.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 52.58/52.38 => 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) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Inf__UNIV,axiom,
% 52.58/52.38 ! [T_b] :
% 52.58/52.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 52.58/52.38 => 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) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Inf__insert,axiom,
% 52.58/52.38 ! [V_A_2,V_a_2,T_b] :
% 52.58/52.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 52.58/52.38 => 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)) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Un__eq__Union,axiom,
% 52.58/52.38 ! [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))))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Un__Union__image,axiom,
% 52.58/52.38 ! [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))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Union__Int__subset,axiom,
% 52.58/52.38 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),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)))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Int__eq__Inter,axiom,
% 52.58/52.38 ! [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))))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Inter__Un__subset,axiom,
% 52.58/52.38 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_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)))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Sup__binary,axiom,
% 52.58/52.38 ! [V_b_2,V_a_2,T_b] :
% 52.58/52.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 52.58/52.38 => 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) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Inf__binary,axiom,
% 52.58/52.38 ! [V_b_2,V_a_2,T_b] :
% 52.58/52.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 52.58/52.38 => 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) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_sup__Sup__fold__sup,axiom,
% 52.58/52.38 ! [V_B_2,V_A_2,T_b] :
% 52.58/52.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => 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) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Sup__fin__Sup,axiom,
% 52.58/52.38 ! [V_A_2,T_b] :
% 52.58/52.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.38 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_inf__Inf__fold__inf,axiom,
% 52.58/52.38 ! [V_B_2,V_A_2,T_b] :
% 52.58/52.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => 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) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Inf__fin__Inf,axiom,
% 52.58/52.38 ! [V_A_2,T_b] :
% 52.58/52.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.38 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_image__INT,axiom,
% 52.58/52.38 ! [V_j_2,V_B_2,V_A_2,T_d,V_C_2,V_f_2,T_c,T_b] :
% 52.58/52.38 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 52.58/52.38 => ( ! [B_x] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2))
% 52.58/52.38 => 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)) )
% 52.58/52.38 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_j_2),V_A_2))
% 52.58/52.38 => 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)) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_card__partition,axiom,
% 52.58/52.38 ! [V_k_2,V_C_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_C_2))
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
% 52.58/52.38 => ( ! [B_c] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c),V_C_2))
% 52.58/52.38 => hAPP(c_Finite__Set_Ocard(T_b),B_c) = V_k_2 )
% 52.58/52.38 => ( ! [B_c1] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c1),V_C_2))
% 52.58/52.38 => ! [B_c2] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c2),V_C_2))
% 52.58/52.38 => ( B_c1 != B_c2
% 52.58/52.38 => 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)) ) ) )
% 52.58/52.38 => 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)) ) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Inter__def,axiom,
% 52.58/52.38 ! [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))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Union__def,axiom,
% 52.58/52.38 ! [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))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_finite__Union,axiom,
% 52.58/52.38 ! [V_A_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2))
% 52.58/52.38 => ( ! [B_M] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2))
% 52.58/52.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M)) )
% 52.58/52.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_insert__partition,axiom,
% 52.58/52.38 ! [V_F_2,V_x_2,T_b] :
% 52.58/52.38 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))
% 52.58/52.38 => ( ! [B_x] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => ! [B_xa] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => ( B_x != B_xa
% 52.58/52.38 => 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)) ) ) )
% 52.58/52.38 => 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)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_inj__on__Inter,axiom,
% 52.58/52.38 ! [V_f_2,T_c,T_b,V_S_2] :
% 52.58/52.38 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 52.58/52.38 => ( ! [B_A] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_A),V_S_2))
% 52.58/52.38 => c_Fun_Oinj__on(T_b,T_c,V_f_2,B_A) )
% 52.58/52.38 => 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)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Inter__subset,axiom,
% 52.58/52.38 ! [V_B_2,V_A_2,T_b] :
% 52.58/52.38 ( ! [B_X] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2))
% 52.58/52.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_B_2)) )
% 52.58/52.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 52.58/52.38 => 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)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_inj__on__INTER,axiom,
% 52.58/52.38 ! [V_A_2,V_f_2,T_d,T_c,T_b,V_I_2] :
% 52.58/52.38 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.38 => ( ! [B_i] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_I_2))
% 52.58/52.38 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(V_A_2,B_i)) )
% 52.58/52.38 => 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)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom,
% 52.58/52.38 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 52.58/52.38 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 52.58/52.38 => ( 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))
% 52.58/52.38 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.58/52.38 => ~ ! [B_y] :
% 52.58/52.38 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y)
% 52.58/52.38 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_min__max_Ofold__sup__le__sup,axiom,
% 52.58/52.38 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 52.58/52.38 ( class_Orderings_Olinorder(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => ( ! [B_x] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.58/52.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
% 52.58/52.38 => 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))) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_min__max_Oinf__le__fold__inf,axiom,
% 52.58/52.38 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 52.58/52.38 ( class_Orderings_Olinorder(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => ( ! [B_x] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.58/52.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
% 52.58/52.38 => 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))) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_InterI,axiom,
% 52.58/52.38 ! [V_A_2,V_C_2,T_b] :
% 52.58/52.38 ( ! [B_X] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2))
% 52.58/52.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) )
% 52.58/52.38 => 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))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_inf__le__fold__inf,axiom,
% 52.58/52.38 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 52.58/52.38 ( class_Lattices_Osemilattice__inf(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => ( ! [B_x] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.58/52.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
% 52.58/52.38 => 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))) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_fold__sup__le__sup,axiom,
% 52.58/52.38 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 52.58/52.38 ( class_Lattices_Osemilattice__sup(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => ( ! [B_x] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.58/52.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
% 52.58/52.38 => 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))) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_wf__eq__minimal,axiom,
% 52.58/52.38 ! [V_r_2,T_b] :
% 52.58/52.38 ( c_Wellfounded_Owf(T_b,V_r_2)
% 52.58/52.38 <=> ! [B_Q] :
% 52.58/52.38 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 52.58/52.38 => ? [B_x] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 52.58/52.38 & ! [B_y] :
% 52.58/52.38 ( 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))
% 52.58/52.38 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q)) ) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_folding__image__simple__idem_Ounion__idem,axiom,
% 52.58/52.38 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 52.58/52.38 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 52.58/52.38 => 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)) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_transfer__nat__int__set__cong,axiom,
% 52.58/52.38 ! [V_P_H_2,V_P_2] :
% 52.58/52.38 ( ! [B_x] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 52.58/52.38 => ( hBOOL(hAPP(V_P_2,B_x))
% 52.58/52.38 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) )
% 52.58/52.38 => 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)) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_folding__image__simple__idem_Oidem,axiom,
% 52.58/52.38 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 52.58/52.38 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 52.58/52.38 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_folding__image__simple__idem_Oin__idem,axiom,
% 52.58/52.38 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 52.58/52.38 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 52.58/52.38 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 52.58/52.38 => 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) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
% 52.58/52.38 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 52.58/52.38 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 52.58/52.38 => 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)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
% 52.58/52.38 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 52.58/52.38 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 52.58/52.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
% 52.58/52.38 => 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) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Int__Collect__mono,axiom,
% 52.58/52.38 ! [V_Q_2,V_P_2,V_B_2,V_A_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.58/52.38 => ( ! [B_x] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 52.58/52.38 => ( hBOOL(hAPP(V_P_2,B_x))
% 52.58/52.38 => hBOOL(hAPP(V_Q_2,B_x)) ) )
% 52.58/52.38 => 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)))) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_UnionE,axiom,
% 52.58/52.38 ! [V_C_2,V_A_2,T_b] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => ~ ! [B_X] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X))
% 52.58/52.38 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__add__upd__left,axiom,
% 52.58/52.38 ! [V_u1_2,V_e1_2,V_e2_2,T_c,V_m_2,T_b] :
% 52.58/52.38 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_e2_2)))
% 52.58/52.38 => 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)) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_converseE,axiom,
% 52.58/52.38 ! [V_r_2,V_yx_2,T_c,T_b] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => ~ ! [B_x,B_y] :
% 52.58/52.38 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_y),B_x)
% 52.58/52.38 => ~ 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)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__add__def,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_empty__map__add,axiom,
% 52.58/52.38 ! [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 ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__add__empty,axiom,
% 52.58/52.38 ! [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 ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__add__assoc,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__add__find__right,axiom,
% 52.58/52.38 ! [V_m_2,T_c,V_xx_2,T_b,V_k_2,V_n_2] :
% 52.58/52.38 ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_xx_2)
% 52.58/52.38 => 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) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__add__None,axiom,
% 52.58/52.38 ! [V_k_2,V_n_2,V_m_2,T_b,T_c] :
% 52.58/52.38 ( hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = c_Option_Ooption_ONone(T_b)
% 52.58/52.38 <=> ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 52.58/52.38 & hAPP(V_m_2,V_k_2) = c_Option_Ooption_ONone(T_b) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__add__dom__app__simps_I1_J,axiom,
% 52.58/52.38 ! [V_l1_2,V_l2_2,T_c,V_m_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l2_2)))
% 52.58/52.38 => 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) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__add__dom__app__simps_I3_J,axiom,
% 52.58/52.38 ! [V_l1_2,V_l2_2,T_c,V_m_2,T_b] :
% 52.58/52.38 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l2_2)))
% 52.58/52.38 => 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) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__add__dom__app__simps_I2_J,axiom,
% 52.58/52.38 ! [V_l2_2,V_l1_2,T_c,V_m_2,T_b] :
% 52.58/52.38 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l1_2)))
% 52.58/52.38 => 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) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_dom__map__add,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__add__Some__iff,axiom,
% 52.58/52.38 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_b,T_c] :
% 52.58/52.38 ( 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)
% 52.58/52.38 <=> ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
% 52.58/52.38 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 52.58/52.38 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__add__SomeD,axiom,
% 52.58/52.38 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_b,T_c] :
% 52.58/52.38 ( 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)
% 52.58/52.38 => ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
% 52.58/52.38 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 52.58/52.38 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__add__upd,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_inj__on__map__add__dom,axiom,
% 52.58/52.38 ! [V_m_H_2,V_m_2,T_c,T_b] :
% 52.58/52.38 ( 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))
% 52.58/52.38 <=> 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)) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__add__comm,axiom,
% 52.58/52.38 ! [V_m2_2,V_m1_2,T_c,T_b] :
% 52.58/52.38 ( 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))
% 52.58/52.38 => 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) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_finite__range__map__of__map__add,axiom,
% 52.58/52.38 ! [V_l_2,V_f_2,T_c,T_b] :
% 52.58/52.38 ( 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)))))
% 52.58/52.38 => 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))))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_rel__compE,axiom,
% 52.58/52.38 ! [V_s_2,V_r_2,T_d,V_xz_2,T_c,T_b] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => ~ ! [B_x,B_y,B_z] :
% 52.58/52.38 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)
% 52.58/52.38 => ( 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))
% 52.58/52.38 => ~ 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)) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_finite__dom__map__of,axiom,
% 52.58/52.38 ! [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)))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_finite__range__map__of,axiom,
% 52.58/52.38 ! [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))))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__add__map__of__foldr,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_full__small__int__def,axiom,
% 52.58/52.38 ! [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))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_small_H_Osimps,axiom,
% 52.58/52.38 ! [V_f_2,V_i_2,V_d_2] :
% 52.58/52.38 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 52.58/52.38 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
% 52.58/52.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 52.58/52.38 => 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)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_small_H_Opsimps,axiom,
% 52.58/52.38 ! [V_i_2,V_d_2,V_f_2] :
% 52.58/52.38 ( 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))))
% 52.58/52.38 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 52.58/52.38 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
% 52.58/52.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 52.58/52.38 => 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)) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_small__int__def,axiom,
% 52.58/52.38 ! [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))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_small__prod__def,axiom,
% 52.58/52.38 ! [V_d_2,V_f_2,T_b,T_c] :
% 52.58/52.38 ( ( class_Smallcheck_Osmall(T_c)
% 52.58/52.38 & class_Smallcheck_Osmall(T_b) )
% 52.58/52.38 => 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) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_small_H_Opinduct,axiom,
% 52.58/52.38 ! [V_P_2,V_a2_2,V_a1_2,V_a0_2] :
% 52.58/52.38 ( 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))))
% 52.58/52.38 => ( ! [B_f,B_d,B_i] :
% 52.58/52.38 ( 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))))
% 52.58/52.38 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i))
% 52.58/52.38 => ( hAPP(B_f,B_i) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
% 52.58/52.38 => 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)))) ) )
% 52.58/52.38 => hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),B_i)) ) )
% 52.58/52.38 => hBOOL(hAPP(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2),V_a2_2)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_body__def,axiom,
% 52.58/52.38 c_Com_Obody = c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom,c_Com_Obodies) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__of__mapk__SomeI,axiom,
% 52.58/52.38 ! [V_x_2,V_k_2,V_t_2,T_d,V_f_2,T_c,T_b] :
% 52.58/52.38 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 52.58/52.38 => ( 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)
% 52.58/52.38 => 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) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__comp__def,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_inj__mapI,axiom,
% 52.58/52.38 ! [V_f_2,T_c,T_b] :
% 52.58/52.38 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 52.58/52.38 => 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))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__comp__simps_I2_J,axiom,
% 52.58/52.38 ! [V_m1_2,T_c,T_d,V_k_H_2,T_b,V_k_2,V_m2_2] :
% 52.58/52.38 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_k_H_2)
% 52.58/52.38 => 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) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__comp__Some__iff,axiom,
% 52.58/52.38 ! [V_v_2,V_k_2,V_m2_2,V_m1_2,T_d,T_b,T_c] :
% 52.58/52.38 ( 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)
% 52.58/52.38 <=> ? [B_k_H] :
% 52.58/52.38 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_k_H)
% 52.58/52.38 & hAPP(V_m1_2,B_k_H) = hAPP(c_Option_Ooption_OSome(T_b),V_v_2) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__comp__simps_I1_J,axiom,
% 52.58/52.38 ! [V_m1_2,T_c,T_d,T_b,V_k_2,V_m2_2] :
% 52.58/52.38 ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 52.58/52.38 => 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) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__injective,axiom,
% 52.58/52.38 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 52.58/52.38 ( 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)
% 52.58/52.38 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 52.58/52.38 => V_xs_2 = V_ys_2 ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_inj__mapD,axiom,
% 52.58/52.38 ! [V_f_2,T_c,T_b] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_inj__map__eq__map,axiom,
% 52.58/52.38 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 52.58/52.38 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 52.58/52.38 => ( 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)
% 52.58/52.38 <=> V_xs_2 = V_ys_2 ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_inj__map,axiom,
% 52.58/52.38 ! [V_f_2,T_c,T_b] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 <=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__ident,axiom,
% 52.58/52.38 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)),V_xs_2) = V_xs_2 ).
% 52.58/52.38
% 52.58/52.38 fof(fact_List_Omap_Oid,axiom,
% 52.58/52.38 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_List_Omap_Oidentity,axiom,
% 52.58/52.38 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_List_Omap_Ocomp,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__comp__map,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_List_Omap_Ocompositionality,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__map,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_foldr__map,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__comp__empty_I2_J,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__comp__empty_I1_J,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__comp__None__iff,axiom,
% 52.58/52.38 ! [V_k_2,V_m2_2,V_m1_2,T_d,T_b,T_c] :
% 52.58/52.38 ( 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)
% 52.58/52.38 <=> ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_c)
% 52.58/52.38 | ? [B_k_H] :
% 52.58/52.38 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_k_H)
% 52.58/52.38 & hAPP(V_m1_2,B_k_H) = c_Option_Ooption_ONone(T_b) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__of__map,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__of__map__keys,axiom,
% 52.58/52.38 ! [V_m_2,T_c,V_xs_2,T_b] :
% 52.58/52.38 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Map_Odom(T_b,T_c,V_m_2)
% 52.58/52.38 => 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 ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_finite__set,axiom,
% 52.58/52.38 ! [V_xs_2,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_set__map,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__eq__conv,axiom,
% 52.58/52.38 ! [V_g_2,V_xs_2,V_f_2,T_b,T_c] :
% 52.58/52.38 ( 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)
% 52.58/52.38 <=> ! [B_x] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
% 52.58/52.38 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_option__map__o__sum__case,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_option__map__comp,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Option_Omap_Ocompositionality,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Option_Omap_Ocomp,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Option_Omap_Oid,axiom,
% 52.58/52.38 ! [T_b] : hAPP(c_Option_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_Option_Ooption(T_b)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Option_Omap_Oidentity,axiom,
% 52.58/52.38 ! [T_b] : hAPP(c_Option_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_Option_Ooption(T_b)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_infinite__UNIV__listI,axiom,
% 52.58/52.38 ! [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)))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_dom__option__map,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_option__map__eq__Some,axiom,
% 52.58/52.38 ! [V_y_2,V_xo_2,V_f_2,T_b,T_c] :
% 52.58/52.38 ( 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)
% 52.58/52.38 <=> ? [B_z] :
% 52.58/52.38 ( V_xo_2 = hAPP(c_Option_Ooption_OSome(T_c),B_z)
% 52.58/52.38 & hAPP(V_f_2,B_z) = V_y_2 ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_option__map__Some,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_option__map__is__None,axiom,
% 52.58/52.38 ! [V_opt_2,V_f_2,T_b,T_c] :
% 52.58/52.38 ( hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),V_opt_2) = c_Option_Ooption_ONone(T_b)
% 52.58/52.38 <=> V_opt_2 = c_Option_Ooption_ONone(T_c) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_option__map__None,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_option__map__o__empty,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_option__map__o__map__upd,axiom,
% 52.58/52.38 ! [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))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__inj__on,axiom,
% 52.58/52.38 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 52.58/52.38 ( 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)
% 52.58/52.38 => ( 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)))
% 52.58/52.38 => V_xs_2 = V_ys_2 ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_inj__on__map__eq__map,axiom,
% 52.58/52.38 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => ( 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)
% 52.58/52.38 <=> V_xs_2 = V_ys_2 ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__fun__upd,axiom,
% 52.58/52.38 ! [V_v_2,V_f_2,T_c,V_xs_2,V_y_2,T_b] :
% 52.58/52.38 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.58/52.38 => 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) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_inj__on__mapI,axiom,
% 52.58/52.38 ! [V_A_2,V_f_2,T_c,T_b] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => 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) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__of__eq__dom,axiom,
% 52.58/52.38 ! [V_ys_2,V_xs_2,T_c,T_b] :
% 52.58/52.38 ( c_Map_Omap__of(T_b,T_c,V_xs_2) = c_Map_Omap__of(T_b,T_c,V_ys_2)
% 52.58/52.38 => 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)) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__of__SomeD,axiom,
% 52.58/52.38 ! [V_y_2,V_k_2,V_xs_2,T_b,T_c] :
% 52.58/52.38 ( 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)
% 52.58/52.38 => 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))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__of__is__SomeD,axiom,
% 52.58/52.38 ! [V_y_2,V_x_2,V_xys_2,T_b,T_c] :
% 52.58/52.38 ( 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)
% 52.58/52.38 => 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))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_dom__map__of__conv__image__fst,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__of__eq__None__iff,axiom,
% 52.58/52.38 ! [V_x_2,V_xys_2,T_b,T_c] :
% 52.58/52.38 ( hAPP(c_Map_Omap__of(T_c,T_b,V_xys_2),V_x_2) = c_Option_Ooption_ONone(T_b)
% 52.58/52.38 <=> ~ 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)))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Option_Omap__def,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_WT__bodies__def,axiom,
% 52.58/52.38 ( c_Com_OWT__bodies
% 52.58/52.38 <=> ! [B_x] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => 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)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__of__map__restrict,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_ran__distinct,axiom,
% 52.58/52.38 ! [V_al_2,T_c,T_b] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => 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)) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_set__map__of__compr,axiom,
% 52.58/52.38 ! [V_xs_2,T_c,T_b] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => 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)))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_distinct__map,axiom,
% 52.58/52.38 ! [V_xs_2,V_f_2,T_c,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
% 52.58/52.38 <=> ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
% 52.58/52.38 & c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__of__inject__set,axiom,
% 52.58/52.38 ! [V_ys_2,V_xs_2,T_c,T_b] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => ( 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)))
% 52.58/52.38 => ( c_Map_Omap__of(T_b,T_c,V_xs_2) = c_Map_Omap__of(T_b,T_c,V_ys_2)
% 52.58/52.38 <=> 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) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__of__is__SomeI,axiom,
% 52.58/52.38 ! [V_y_2,V_x_2,V_xys_2,T_c,T_b] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => ( 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)))
% 52.58/52.38 => 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) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__of__eq__Some__iff,axiom,
% 52.58/52.38 ! [V_y_2,V_x_2,V_xys_2,T_c,T_b] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => ( 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)
% 52.58/52.38 <=> 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))) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Some__eq__map__of__iff,axiom,
% 52.58/52.38 ! [V_x_2,V_y_2,V_xys_2,T_c,T_b] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => ( 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)
% 52.58/52.38 <=> 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))) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_greaterThanLessThan__upto,axiom,
% 52.58/52.38 ! [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)))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_weak__map__of__SomeI,axiom,
% 52.58/52.38 ! [V_l_2,V_x_2,V_k_2,T_c,T_b] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => ? [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) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_set__upto,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_atLeastAtMost__upto,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_distinct__upto,axiom,
% 52.58/52.38 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_atLeastLessThan__upto,axiom,
% 52.58/52.38 ! [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)))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_greaterThanAtMost__upto,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_nat__list__def,axiom,
% 52.58/52.38 ! [V_l_2] :
% 52.58/52.38 ( c_List_Onat__list(V_l_2)
% 52.58/52.38 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_set__remove1__eq,axiom,
% 52.58/52.38 ! [V_x_2,V_xs_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 52.58/52.38 => 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)))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_remove1__idem,axiom,
% 52.58/52.38 ! [V_xs_2,V_x_2,T_b] :
% 52.58/52.38 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.58/52.38 => c_List_Oremove1(T_b,V_x_2,V_xs_2) = V_xs_2 ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_notin__set__remove1,axiom,
% 52.58/52.38 ! [V_y_2,V_xs_2,V_x_2,T_b] :
% 52.58/52.38 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.58/52.38 => ~ 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)))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_in__set__remove1,axiom,
% 52.58/52.38 ! [V_xs_2,T_b,V_b_2,V_a_2] :
% 52.58/52.38 ( V_a_2 != V_b_2
% 52.58/52.38 => ( 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))))
% 52.58/52.38 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_set__remove1__subset,axiom,
% 52.58/52.38 ! [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))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_remove1__commute,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_distinct__remove1,axiom,
% 52.58/52.38 ! [V_x,V_xs,T_a] :
% 52.58/52.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 52.58/52.38 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_sorted__list__of__set__remove,axiom,
% 52.58/52.38 ! [V_x_2,V_A_2,T_b] :
% 52.58/52.38 ( class_Orderings_Olinorder(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => 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)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__of__zip__map,axiom,
% 52.58/52.38 ! [V_f_2,T_c,V_xs_2,V_x_2,T_b] :
% 52.58/52.38 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.58/52.38 => 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)) )
% 52.58/52.38 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.58/52.38 => 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) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_distinct__zipI1,axiom,
% 52.58/52.38 ! [V_ys,T_b,V_xs,T_a] :
% 52.58/52.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 52.58/52.38 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_distinct__zipI2,axiom,
% 52.58/52.38 ! [V_xs,T_b,V_ys,T_a] :
% 52.58/52.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys))
% 52.58/52.38 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_zip__same__conv__map,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_zip__map__fst__snd,axiom,
% 52.58/52.38 ! [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 ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__zip__map2,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__zip__map,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_in__set__zipE,axiom,
% 52.58/52.38 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 52.58/52.38 ( 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))))
% 52.58/52.38 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.58/52.38 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_set__zip__rightD,axiom,
% 52.58/52.38 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 52.58/52.38 ( 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))))
% 52.58/52.38 => hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_set__zip__leftD,axiom,
% 52.58/52.38 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 52.58/52.38 ( 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))))
% 52.58/52.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_zip__same,axiom,
% 52.58/52.38 ! [V_xs_2,V_b_2,V_a_2,T_b] :
% 52.58/52.38 ( hBOOL(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))))
% 52.58/52.38 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.58/52.38 & V_a_2 = V_b_2 ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_zip__map2,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_zip__map1,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_zip__map__map,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_sorted__list__of__set__insert,axiom,
% 52.58/52.38 ! [V_x_2,V_A_2,T_b] :
% 52.58/52.38 ( class_Orderings_Olinorder(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => 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)))))) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__of__zip__upd,axiom,
% 52.58/52.38 ! [V_z_2,V_y_2,V_x_2,V_zs_2,V_xs_2,T_c,V_ys_2,T_b] :
% 52.58/52.38 ( 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)
% 52.58/52.38 => ( 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)
% 52.58/52.38 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
% 52.58/52.38 => ( 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))
% 52.58/52.38 => 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)) ) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_length__zip,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_set__insort,axiom,
% 52.58/52.38 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 52.58/52.38 ( class_Orderings_Olinorder(T_c)
% 52.58/52.38 => 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)) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_length__insort,axiom,
% 52.58/52.38 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 52.58/52.38 ( class_Orderings_Olinorder(T_c)
% 52.58/52.38 => 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)) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_neq__if__length__neq,axiom,
% 52.58/52.38 ! [V_ys,V_xs,T_a] :
% 52.58/52.38 ( 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)
% 52.58/52.38 => V_xs != V_ys ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_insort__key__left__comm,axiom,
% 52.58/52.38 ! [V_xs_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 52.58/52.38 ( class_Orderings_Olinorder(T_b)
% 52.58/52.38 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
% 52.58/52.38 => 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)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_insort__left__comm,axiom,
% 52.58/52.38 ! [V_xs_2,V_y_2,V_x_2,T_b] :
% 52.58/52.38 ( class_Orderings_Olinorder(T_b)
% 52.58/52.38 => 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)) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_fun__left__comm__insort,axiom,
% 52.58/52.38 ! [T_b] :
% 52.58/52.38 ( class_Orderings_Olinorder(T_b)
% 52.58/52.38 => 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))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_lexn__length,axiom,
% 52.58/52.38 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 52.58/52.38 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_n_2
% 52.58/52.38 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_length__map,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__eq__imp__length__eq,axiom,
% 52.58/52.38 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_b,T_c] :
% 52.58/52.38 ( 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)
% 52.58/52.38 => 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) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_remove1__insort,axiom,
% 52.58/52.38 ! [V_xs_2,V_x_2,T_b] :
% 52.58/52.38 ( class_Orderings_Olinorder(T_b)
% 52.58/52.38 => 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 ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_card__length,axiom,
% 52.58/52.38 ! [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))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_distinct__card,axiom,
% 52.58/52.38 ! [V_xs_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 52.58/52.38 => 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) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_card__distinct,axiom,
% 52.58/52.38 ! [V_xs_2,T_b] :
% 52.58/52.38 ( 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)
% 52.58/52.38 => hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__of__zip__inject,axiom,
% 52.58/52.38 ! [V_zs_2,V_xs_2,T_c,V_ys_2,T_b] :
% 52.58/52.38 ( 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)
% 52.58/52.38 => ( 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)
% 52.58/52.38 => ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
% 52.58/52.38 => ( 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))
% 52.58/52.38 => V_ys_2 = V_zs_2 ) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__fst__zip,axiom,
% 52.58/52.38 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 52.58/52.38 ( 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)
% 52.58/52.38 => 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 ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__snd__zip,axiom,
% 52.58/52.38 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 52.58/52.38 ( 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)
% 52.58/52.38 => 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 ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_distinct__insort,axiom,
% 52.58/52.38 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 52.58/52.38 ( class_Orderings_Olinorder(T_c)
% 52.58/52.38 => ( 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)))
% 52.58/52.38 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.58/52.38 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_length__pos__if__in__set,axiom,
% 52.58/52.38 ! [V_xs_2,V_x_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.58/52.38 => 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))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_zip__eq__conv,axiom,
% 52.58/52.38 ! [V_zs_2,V_ys_2,T_c,V_xs_2,T_b] :
% 52.58/52.38 ( 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)
% 52.58/52.38 => ( hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) = V_zs_2
% 52.58/52.38 <=> ( 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
% 52.58/52.38 & 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 ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_lenlex__conv,axiom,
% 52.58/52.38 ! [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)))))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_lenlex__def,axiom,
% 52.58/52.38 ! [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)))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_finite__lists__length__eq,axiom,
% 52.58/52.38 ! [V_n_2,V_A_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => 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))))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_list__eq__iff__zip__eq,axiom,
% 52.58/52.38 ! [T_b,V_ys_2,V_xs_2] :
% 52.58/52.38 ( V_xs_2 = V_ys_2
% 52.58/52.38 <=> ( 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)
% 52.58/52.38 & ! [B_x] :
% 52.58/52.38 ( 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))))
% 52.58/52.38 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__of__zip__is__None,axiom,
% 52.58/52.38 ! [V_x_2,V_ys_2,T_c,V_xs_2,T_b] :
% 52.58/52.38 ( 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)
% 52.58/52.38 => ( 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)
% 52.58/52.38 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__of__zip__is__Some,axiom,
% 52.58/52.38 ! [V_x_2,V_ys_2,T_c,V_xs_2,T_b] :
% 52.58/52.38 ( 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)
% 52.58/52.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.58/52.38 <=> ? [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) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_length__remove1,axiom,
% 52.58/52.38 ! [V_xs_2,V_x_2,T_b] :
% 52.58/52.38 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.58/52.38 => 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)) )
% 52.58/52.38 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.58/52.38 => 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) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_dom__map__of__zip,axiom,
% 52.58/52.38 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 52.58/52.38 ( 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)
% 52.58/52.38 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 52.58/52.38 => 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) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_finite__lists__length__le,axiom,
% 52.58/52.38 ! [V_n_2,V_A_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => 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))))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Nitpick_Ocard_H__def,axiom,
% 52.58/52.38 ! [V_A_2,T_b] :
% 52.58/52.38 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => 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)))) )
% 52.58/52.38 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => c_Nitpick_Ocard_H(T_b,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_listrel__iff__zip,axiom,
% 52.58/52.38 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 52.58/52.38 <=> ( 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)
% 52.58/52.38 & ! [B_x] :
% 52.58/52.38 ( 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))))
% 52.58/52.38 => 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)) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_listrel__rtrancl__refl,axiom,
% 52.58/52.38 ! [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)))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_listrel__eq__len,axiom,
% 52.58/52.38 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 52.58/52.38 => 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) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_listrel__rtrancl__trans,axiom,
% 52.58/52.38 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 52.58/52.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 52.58/52.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_listrel__mono,axiom,
% 52.58/52.38 ! [V_s_2,V_r_2,T_b] :
% 52.58/52.38 ( 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))
% 52.58/52.38 => 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))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_listrelp__listrel__eq,axiom,
% 52.58/52.38 ! [V_xa_2,V_x_2,V_r_2,T_b] :
% 52.58/52.38 ( 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)
% 52.58/52.38 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_lexn_Osimps_I2_J,axiom,
% 52.58/52.38 ! [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)))))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_impossible__Cons,axiom,
% 52.58/52.38 ! [V_x,V_ys,V_xs,T_a] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_set__ConsD,axiom,
% 52.58/52.38 ! [V_xs_2,V_x_2,V_y_2,T_b] :
% 52.58/52.38 ( 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))))
% 52.58/52.38 => ( V_y_2 = V_x_2
% 52.58/52.38 | hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_zip__Cons__Cons,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_set__subset__Cons,axiom,
% 52.58/52.38 ! [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)))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_List_Oset_Osimps_I2_J,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_foldr_Osimps_I2_J,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_listrelp_OCons,axiom,
% 52.58/52.38 ! [V_ys_2,V_xs_2,T_b,V_y_2,V_x_2,V_r_2] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 52.58/52.38 => ( c_List_Olistrelp(T_b,V_r_2,V_xs_2,V_ys_2)
% 52.58/52.38 => 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)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_listrelp_Oequations_I2_J,axiom,
% 52.58/52.38 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_b] :
% 52.58/52.38 ( 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))
% 52.58/52.38 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2))
% 52.58/52.38 & c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_list_Oinject,axiom,
% 52.58/52.38 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_b] :
% 52.58/52.38 ( 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)
% 52.58/52.38 <=> ( V_a_2 = V_a_H_2
% 52.58/52.38 & V_list_2 = V_list_H_2 ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_not__Cons__self2,axiom,
% 52.58/52.38 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ).
% 52.58/52.38
% 52.58/52.38 fof(fact_not__Cons__self,axiom,
% 52.58/52.38 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map_Osimps_I2_J,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_remove1_Osimps_I2_J,axiom,
% 52.58/52.38 ! [V_xs,T_a,V_y,V_x] :
% 52.58/52.38 ( ( V_x = V_y
% 52.58/52.38 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs )
% 52.58/52.38 & ( V_x != V_y
% 52.58/52.38 => 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)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_insort__key_Osimps_I2_J,axiom,
% 52.58/52.38 ! [V_ys_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 52.58/52.38 ( class_Orderings_Olinorder(T_b)
% 52.58/52.38 => ( ( 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)))
% 52.58/52.38 => 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)) )
% 52.58/52.38 & ( ~ 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)))
% 52.58/52.38 => 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)) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_distinct_Osimps_I2_J,axiom,
% 52.58/52.38 ! [V_xs_2,V_x_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))
% 52.58/52.38 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.58/52.38 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__of__Cons__code_I2_J,axiom,
% 52.58/52.38 ! [V_ps,V_v,T_c,T_b,V_k,V_l] :
% 52.58/52.38 ( ( V_l = V_k
% 52.58/52.38 => 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) )
% 52.58/52.38 & ( V_l != V_k
% 52.58/52.38 => 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) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_list_Osize_I4_J,axiom,
% 52.58/52.38 ! [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))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_listrel_OCons,axiom,
% 52.58/52.38 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 52.58/52.38 ( hBOOL(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))
% 52.58/52.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 52.58/52.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__of_Osimps_I2_J,axiom,
% 52.58/52.38 ! [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))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Cons__in__lex,axiom,
% 52.58/52.38 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 52.58/52.38 <=> ( ( hBOOL(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))
% 52.58/52.38 & 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) )
% 52.58/52.38 | ( V_x_2 = V_y_2
% 52.58/52.38 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_listrel__Cons,axiom,
% 52.58/52.38 ! [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))))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_set__Cons__def,axiom,
% 52.58/52.38 ! [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)))))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_listrel__Cons1,axiom,
% 52.58/52.38 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 52.58/52.38 => ~ ! [B_y,B_ys] :
% 52.58/52.38 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys)
% 52.58/52.38 => ( 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))
% 52.58/52.38 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_listrel__Cons2,axiom,
% 52.58/52.38 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 52.58/52.38 => ~ ! [B_x,B_xs] :
% 52.58/52.38 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
% 52.58/52.38 => ( 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))
% 52.58/52.38 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_length__sublist,axiom,
% 52.58/52.38 ! [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)))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_pick_Osimps,axiom,
% 52.58/52.38 ! [V_xs,V_x,T_a,V_i] :
% 52.58/52.38 ( ( 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)))
% 52.58/52.38 => 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) )
% 52.58/52.38 & ( ~ 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)))
% 52.58/52.38 => 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))) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_distinct__sublistI,axiom,
% 52.58/52.38 ! [V_I_2,V_xs_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 52.58/52.38 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_in__set__sublistD,axiom,
% 52.58/52.38 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 52.58/52.38 ( 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))))
% 52.58/52.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_notin__set__sublistI,axiom,
% 52.58/52.38 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 52.58/52.38 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.58/52.38 => ~ 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)))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_set__sublist__subset,axiom,
% 52.58/52.38 ! [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))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_select__weight__cons__zero,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_pick__member,axiom,
% 52.58/52.38 ! [V_xs_2,T_b,V_i_2] :
% 52.58/52.38 ( 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))))
% 52.58/52.38 => 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)))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_listsum__simps_I2_J,axiom,
% 52.58/52.38 ! [V_xs,V_x,T_a] :
% 52.58/52.38 ( class_Groups_Omonoid__add(T_a)
% 52.58/52.38 => 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)) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_listsum__subtractf,axiom,
% 52.58/52.38 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 52.58/52.38 ( class_Groups_Oab__group__add(T_b)
% 52.58/52.38 => 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))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_listsum__mult__const,axiom,
% 52.58/52.38 ! [V_xs_2,V_c_2,V_f_2,T_c,T_b] :
% 52.58/52.38 ( class_Rings_Osemiring__0(T_b)
% 52.58/52.38 => 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) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_listsum__const__mult,axiom,
% 52.58/52.38 ! [V_xs_2,V_f_2,V_c_2,T_c,T_b] :
% 52.58/52.38 ( class_Rings_Osemiring__0(T_b)
% 52.58/52.38 => 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))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_listsum__addf,axiom,
% 52.58/52.38 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 52.58/52.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 52.58/52.38 => 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))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_listsum__0,axiom,
% 52.58/52.38 ! [V_xs_2,T_c,T_b] :
% 52.58/52.38 ( class_Groups_Omonoid__add(T_b)
% 52.58/52.38 => 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) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_listsum__abs,axiom,
% 52.58/52.38 ! [V_xs_2,T_b] :
% 52.58/52.38 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 52.58/52.38 => 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)))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_uminus__listsum__map,axiom,
% 52.58/52.38 ! [V_xs_2,V_f_2,T_c,T_b] :
% 52.58/52.38 ( class_Groups_Oab__group__add(T_b)
% 52.58/52.38 => 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)) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_distinct__listsum__conv__Setsum,axiom,
% 52.58/52.38 ! [V_xs_2,T_b] :
% 52.58/52.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 52.58/52.38 => 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)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_select__weight__def,axiom,
% 52.58/52.38 ! [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))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_listsum__distinct__conv__setsum__set,axiom,
% 52.58/52.38 ! [V_f_2,V_xs_2,T_b,T_c] :
% 52.58/52.38 ( class_Groups_Ocomm__monoid__add(T_c)
% 52.58/52.38 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 52.58/52.38 => 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)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_setsum__set__upto__conv__listsum__int,axiom,
% 52.58/52.38 ! [V_j_2,V_i_2,V_f_2,T_b] :
% 52.58/52.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 52.58/52.38 => 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))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_interv__listsum__conv__setsum__set__int,axiom,
% 52.58/52.38 ! [V_l_2,V_k_2,V_f_2,T_b] :
% 52.58/52.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 52.58/52.38 => 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))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_listsum__triv,axiom,
% 52.58/52.38 ! [V_xs_2,V_r_2,T_c,T_b] :
% 52.58/52.38 ( class_Rings_Osemiring__1(T_b)
% 52.58/52.38 => 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) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_listsum__map__remove1,axiom,
% 52.58/52.38 ! [V_f_2,V_xs_2,V_x_2,T_b,T_c] :
% 52.58/52.38 ( class_Groups_Ocomm__monoid__add(T_c)
% 52.58/52.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.58/52.38 => 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)))) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_select__weight__member,axiom,
% 52.58/52.38 ! [V_s_2,V_xs_2,T_b] :
% 52.58/52.38 ( 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))))
% 52.58/52.38 => 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)))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Nitpick_Osetsum_H__def,axiom,
% 52.58/52.38 ! [V_f_2,V_A_2,T_b,T_c] :
% 52.58/52.38 ( class_Groups_Ocomm__monoid__add(T_c)
% 52.58/52.38 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => 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))))) )
% 52.58/52.38 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.38 => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_upto_Opsimps,axiom,
% 52.58/52.38 ! [V_j_2,V_i_2] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 52.58/52.38 => 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)) )
% 52.58/52.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 52.58/52.38 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_listrel__Nil2,axiom,
% 52.58/52.38 ! [V_r_2,V_xs_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 52.58/52.38 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_listrel__Nil1,axiom,
% 52.58/52.38 ! [V_r_2,V_xs_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 52.58/52.38 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_listsum__eq__0__nat__iff__nat,axiom,
% 52.58/52.38 ! [V_ns_2] :
% 52.58/52.38 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.58/52.38 <=> ! [B_x] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 52.58/52.38 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_listsum__simps_I1_J,axiom,
% 52.58/52.38 ! [T_a] :
% 52.58/52.38 ( class_Groups_Omonoid__add(T_a)
% 52.58/52.38 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Nil__is__map__conv,axiom,
% 52.58/52.38 ! [V_xs_2,V_f_2,T_c,T_b] :
% 52.58/52.38 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)
% 52.58/52.38 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map_Osimps_I1_J,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__is__Nil__conv,axiom,
% 52.58/52.38 ! [V_xs_2,V_f_2,T_b,T_c] :
% 52.58/52.38 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 52.58/52.38 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_listrelp_ONil,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_listrelp_Oequations_I1_J,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_insort__not__Nil,axiom,
% 52.58/52.38 ! [V_xs_2,V_a_2,V_f_2,T_b,T_c] :
% 52.58/52.38 ( class_Orderings_Olinorder(T_c)
% 52.58/52.38 => 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) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_distinct_Osimps_I1_J,axiom,
% 52.58/52.38 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_remove1_Osimps_I1_J,axiom,
% 52.58/52.38 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_foldr_Osimps_I1_J,axiom,
% 52.58/52.38 ! [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 ).
% 52.58/52.38
% 52.58/52.38 fof(fact_upto__empty,axiom,
% 52.58/52.38 ! [V_i,V_j] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i))
% 52.58/52.38 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_zip_Osimps_I1_J,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_zip__Nil,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_length__0__conv,axiom,
% 52.58/52.38 ! [V_xs_2,T_b] :
% 52.58/52.38 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.58/52.38 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_list_Osize_I3_J,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_sorted__list__of__set__empty,axiom,
% 52.58/52.38 ! [T_b] :
% 52.58/52.38 ( class_Orderings_Olinorder(T_b)
% 52.58/52.38 => 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) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_List_Oset_Osimps_I1_J,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_set__empty2,axiom,
% 52.58/52.38 ! [V_xs_2,T_b] :
% 52.58/52.38 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),V_xs_2)
% 52.58/52.38 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_set__empty,axiom,
% 52.58/52.38 ! [V_xs_2,T_b] :
% 52.58/52.38 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 52.58/52.38 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_list_Osimps_I3_J,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_list_Osimps_I2_J,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_insort__key_Osimps_I1_J,axiom,
% 52.58/52.38 ! [V_x_2,V_f_2,T_b,T_c] :
% 52.58/52.38 ( class_Orderings_Olinorder(T_c)
% 52.58/52.38 => 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)) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_sublist__empty,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_sublist__nil,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_length__greater__0__conv,axiom,
% 52.58/52.38 ! [V_xs_2,T_b] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 <=> V_xs_2 != c_List_Olist_ONil(T_b) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_listrel_ONil,axiom,
% 52.58/52.38 ! [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))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Nil__notin__lex,axiom,
% 52.58/52.38 ! [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))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Nil2__notin__lex,axiom,
% 52.58/52.38 ! [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))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_upto_Osimps,axiom,
% 52.58/52.38 ! [V_j,V_i] :
% 52.58/52.38 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 52.58/52.38 => 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)) )
% 52.58/52.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 52.58/52.38 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_sublist__singleton,axiom,
% 52.58/52.38 ! [V_x_2,T_b,V_A_2] :
% 52.58/52.38 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 52.58/52.38 => 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)) )
% 52.58/52.38 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 52.58/52.38 => 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) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_upto__rec__number__of,axiom,
% 52.58/52.38 ! [V_n,V_m] :
% 52.58/52.38 ( ( 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)))
% 52.58/52.38 => 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))) )
% 52.58/52.38 & ( ~ 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)))
% 52.58/52.38 => 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) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_listrel__Nil,axiom,
% 52.58/52.38 ! [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))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_set__Cons__sing__Nil,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_select__weigth__select,axiom,
% 52.58/52.38 ! [T_b,V_xs_2] :
% 52.58/52.38 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 52.58/52.38 => 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) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_select,axiom,
% 52.58/52.38 ! [V_s_2,T_b,V_xs_2] :
% 52.58/52.38 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 52.58/52.38 => 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))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__of__Cons__code_I1_J,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__of_Osimps_I1_J,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_anamorph_Osimps,axiom,
% 52.58/52.38 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 52.58/52.38 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 52.58/52.38 => 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) )
% 52.58/52.38 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 52.58/52.38 => 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)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_listset_Osimps_I1_J,axiom,
% 52.58/52.38 ! [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))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_listset_Osimps_I2_J,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_zip__Cons1,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_zip__Cons,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_list_Osimps_I5_J,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_list_Osimps_I4_J,axiom,
% 52.58/52.38 ! [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 ).
% 52.58/52.38
% 52.58/52.38 fof(fact_select__def,axiom,
% 52.58/52.38 ! [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))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_pick__same,axiom,
% 52.58/52.38 ! [V_xs_2,T_b,V_l_2] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => 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) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_nth__Cons__Suc,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_nth__Cons__0,axiom,
% 52.58/52.38 ! [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 ).
% 52.58/52.38
% 52.58/52.38 fof(fact_nth_Osimps,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_nth__map,axiom,
% 52.58/52.38 ! [V_f_2,T_c,V_xs_2,T_b,V_n_2] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => 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)) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_all__set__conv__all__nth,axiom,
% 52.58/52.38 ! [V_P_2,V_xs_2,T_b] :
% 52.58/52.38 ( ! [B_x] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.58/52.38 => hBOOL(hAPP(V_P_2,B_x)) )
% 52.58/52.38 <=> ! [B_i] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_nth__eq__iff__index__eq,axiom,
% 52.58/52.38 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 52.58/52.38 => ( 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)))
% 52.58/52.38 => ( 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)))
% 52.58/52.38 => ( 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)
% 52.58/52.38 <=> V_i_2 = V_j_2 ) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_distinct__conv__nth,axiom,
% 52.58/52.38 ! [V_xs_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 52.58/52.38 <=> ! [B_i] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => ! [B_j] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => ( B_i != B_j
% 52.58/52.38 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j) ) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_list__eq__iff__nth__eq,axiom,
% 52.58/52.38 ! [T_b,V_ys_2,V_xs_2] :
% 52.58/52.38 ( V_xs_2 = V_ys_2
% 52.58/52.38 <=> ( 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)
% 52.58/52.38 & ! [B_i] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_nth__zip,axiom,
% 52.58/52.38 ! [V_ys,T_b,V_xs,T_a,V_i] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => ( 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)))
% 52.58/52.38 => 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)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_elem__le__listsum__nat,axiom,
% 52.58/52.38 ! [V_ns,V_k] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => 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))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_nth__mem,axiom,
% 52.58/52.38 ! [V_xs_2,T_b,V_n_2] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => 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))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_in__set__conv__nth,axiom,
% 52.58/52.38 ! [V_xs_2,V_x_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.58/52.38 <=> ? [B_i] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 & hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = V_x_2 ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_nth__Cons_H,axiom,
% 52.58/52.38 ! [V_xs,V_x,T_a,V_n] :
% 52.58/52.38 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.58/52.38 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x )
% 52.58/52.38 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.58/52.38 => 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))) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_set__conv__nth,axiom,
% 52.58/52.38 ! [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))))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_nth__Cons__number__of,axiom,
% 52.58/52.38 ! [V_xs,V_x,T_a,V_v] :
% 52.58/52.38 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.58/52.38 => 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 )
% 52.58/52.38 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.58/52.38 => 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))) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_listsum__setsum__nth,axiom,
% 52.58/52.38 ! [V_xs_2,T_b] :
% 52.58/52.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 52.58/52.38 => 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))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_set__sublist,axiom,
% 52.58/52.38 ! [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))))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_listrel__iff__nth,axiom,
% 52.58/52.38 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 52.58/52.38 <=> ( 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)
% 52.58/52.38 & ! [B_n] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => 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)) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_set__zip,axiom,
% 52.58/52.38 ! [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)))))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_insort__insert__insort__key,axiom,
% 52.58/52.38 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 52.58/52.38 ( class_Orderings_Olinorder(T_b)
% 52.58/52.38 => ( ~ 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))))
% 52.58/52.38 => 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) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_distinct__list__update,axiom,
% 52.58/52.38 ! [V_i_2,V_a_2,V_xs_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 52.58/52.38 => ( ~ 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))))))
% 52.58/52.38 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_a_2))) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_list__update__id,axiom,
% 52.58/52.38 ! [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 ).
% 52.58/52.38
% 52.58/52.38 fof(fact_nth__list__update__neq,axiom,
% 52.58/52.38 ! [V_x,V_xs,T_a,V_j,V_i] :
% 52.58/52.38 ( V_i != V_j
% 52.58/52.38 => 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) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_list__update__nonempty,axiom,
% 52.58/52.38 ! [V_x_2,V_k_2,V_xs_2,T_b] :
% 52.58/52.38 ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_b)
% 52.58/52.38 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_list__update_Osimps_I1_J,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_list__update__code_I1_J,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_zip__update,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_update__zip,axiom,
% 52.58/52.38 ! [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))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_length__list__update,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_list__update__swap,axiom,
% 52.58/52.38 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] :
% 52.58/52.38 ( V_i != V_i_H
% 52.58/52.38 => 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) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_list__update__overwrite,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_distinct__insort__insert,axiom,
% 52.58/52.38 ! [V_x_2,V_f_2,V_xs_2,T_b,T_c] :
% 52.58/52.38 ( class_Orderings_Olinorder(T_c)
% 52.58/52.38 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 52.58/52.38 => 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))) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_list__update__beyond,axiom,
% 52.58/52.38 ! [V_x,V_i,V_xs,T_a] :
% 52.58/52.38 ( 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))
% 52.58/52.38 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__update,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_list__update_Osimps_I2_J,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_list__update__code_I2_J,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_list__update__code_I3_J,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_set__update__subsetI,axiom,
% 52.58/52.38 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_b] :
% 52.58/52.38 ( 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))
% 52.58/52.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.58/52.38 => 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)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_set__update__subset__insert,axiom,
% 52.58/52.38 ! [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)))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_nth__list__update__eq,axiom,
% 52.58/52.38 ! [V_x,V_xs,T_a,V_i] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => 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 ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_list__update__same__conv,axiom,
% 52.58/52.38 ! [V_x_2,V_xs_2,T_b,V_i_2] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) = V_xs_2
% 52.58/52.38 <=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = V_x_2 ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_nth__list__update,axiom,
% 52.58/52.38 ! [V_x,V_j,V_xs,T_a,V_i] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => ( ( V_i = V_j
% 52.58/52.38 => 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 )
% 52.58/52.38 & ( V_i != V_j
% 52.58/52.38 => 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) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_set__update__memI,axiom,
% 52.58/52.38 ! [V_x_2,V_xs_2,T_b,V_n_2] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => 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)))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_insort__insert__triv,axiom,
% 52.58/52.38 ! [V_xs_2,V_x_2,T_b] :
% 52.58/52.38 ( class_Orderings_Olinorder(T_b)
% 52.58/52.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.58/52.38 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_set__insort__insert,axiom,
% 52.58/52.38 ! [V_xs_2,V_x_2,T_b] :
% 52.58/52.38 ( class_Orderings_Olinorder(T_b)
% 52.58/52.38 => 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)) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_listsum__update__nat,axiom,
% 52.58/52.38 ! [V_n,V_ns,V_k] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => 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)) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_insort__insert__key__triv,axiom,
% 52.58/52.38 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 52.58/52.38 ( class_Orderings_Olinorder(T_b)
% 52.58/52.38 => ( 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))))
% 52.58/52.38 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_insort__insert__insort,axiom,
% 52.58/52.38 ! [V_xs_2,V_x_2,T_b] :
% 52.58/52.38 ( class_Orderings_Olinorder(T_b)
% 52.58/52.38 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.58/52.38 => 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) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_sublist__Cons,axiom,
% 52.58/52.38 ! [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)))) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_lexord__cons__cons,axiom,
% 52.58/52.38 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_b] :
% 52.58/52.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 52.58/52.38 <=> ( hBOOL(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))
% 52.58/52.38 | ( V_a_2 = V_b_2
% 52.58/52.38 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_nth__append__length,axiom,
% 52.58/52.38 ! [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 ).
% 52.58/52.38
% 52.58/52.38 fof(fact_nth__append__length__plus,axiom,
% 52.58/52.38 ! [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) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_zip__append,axiom,
% 52.58/52.38 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] :
% 52.58/52.38 ( 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)
% 52.58/52.38 => ( 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)
% 52.58/52.38 => 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)) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_list__update__append1,axiom,
% 52.58/52.38 ! [V_x,V_ys,V_xs,T_a,V_i] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 => 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) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_length__append,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_list__update__length,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_append1__eq__conv,axiom,
% 52.58/52.38 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 52.58/52.38 ( 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)))
% 52.58/52.38 <=> ( V_xs_2 = V_ys_2
% 52.58/52.38 & V_x_2 = V_y_2 ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Cons__eq__append__conv,axiom,
% 52.58/52.38 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_b] :
% 52.58/52.38 ( 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)
% 52.58/52.38 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 52.58/52.38 & hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = V_zs_2 )
% 52.58/52.38 | ? [B_ys_H] :
% 52.58/52.38 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) = V_ys_2
% 52.58/52.38 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_append__eq__Cons__conv,axiom,
% 52.58/52.38 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_b] :
% 52.58/52.38 ( 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)
% 52.58/52.38 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 52.58/52.38 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) )
% 52.58/52.38 | ? [B_ys_H] :
% 52.58/52.38 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H)
% 52.58/52.38 & hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_lexord__append__left__rightI,axiom,
% 52.58/52.38 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_b] :
% 52.58/52.38 ( hBOOL(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))
% 52.58/52.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_Cons__eq__appendI,axiom,
% 52.58/52.38 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] :
% 52.58/52.38 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys
% 52.58/52.38 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs)
% 52.58/52.38 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_append__Cons,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_listsum__append,axiom,
% 52.58/52.38 ! [V_ys,V_xs,T_a] :
% 52.58/52.38 ( class_Groups_Omonoid__add(T_a)
% 52.58/52.38 => 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)) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_map__append,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_set__append,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_append__assoc,axiom,
% 52.58/52.38 ! [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)) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_append__eq__append__conv2,axiom,
% 52.58/52.38 ! [V_tsa_2,V_zs_2,V_ys_2,V_xs_2,T_b] :
% 52.58/52.38 ( 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)
% 52.58/52.38 <=> ? [B_us] :
% 52.58/52.38 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us)
% 52.58/52.38 & hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) = V_tsa_2 )
% 52.58/52.38 | ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) = V_zs_2
% 52.58/52.38 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_tsa_2) ) ) ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_same__append__eq,axiom,
% 52.58/52.38 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 52.58/52.38 ( 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)
% 52.58/52.38 <=> V_ys_2 = V_zs_2 ) ).
% 52.58/52.38
% 52.58/52.38 fof(fact_append__same__eq,axiom,
% 52.58/52.38 ! [V_zs_2,V_xs_2,V_ys_2,T_b] :
% 52.58/52.38 ( 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)
% 52.58/52.38 <=> V_ys_2 = V_zs_2 ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_append__eq__appendI,axiom,
% 52.58/52.39 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] :
% 52.58/52.39 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs
% 52.58/52.39 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us)
% 52.58/52.39 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_map__of__append,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_foldr__append,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_lexord__append__leftI,axiom,
% 52.58/52.39 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_b] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 52.58/52.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_eq__Nil__appendI,axiom,
% 52.58/52.39 ! [T_a,V_ys,V_xs] :
% 52.58/52.39 ( V_xs = V_ys
% 52.58/52.39 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_append__self__conv2,axiom,
% 52.58/52.39 ! [V_ys_2,V_xs_2,T_b] :
% 52.58/52.39 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_ys_2
% 52.58/52.39 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_append__self__conv,axiom,
% 52.58/52.39 ! [V_ys_2,V_xs_2,T_b] :
% 52.58/52.39 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_xs_2
% 52.58/52.39 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_append__is__Nil__conv,axiom,
% 52.58/52.39 ! [V_ys_2,V_xs_2,T_b] :
% 52.58/52.39 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_b)
% 52.58/52.39 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 52.58/52.39 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_self__append__conv2,axiom,
% 52.58/52.39 ! [V_xs_2,T_b,V_ys_2] :
% 52.58/52.39 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 52.58/52.39 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_self__append__conv,axiom,
% 52.58/52.39 ! [V_ys_2,T_b,V_xs_2] :
% 52.58/52.39 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 52.58/52.39 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_append__Nil2,axiom,
% 52.58/52.39 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ).
% 52.58/52.39
% 52.58/52.39 fof(fact_Nil__is__append__conv,axiom,
% 52.58/52.39 ! [V_ys_2,V_xs_2,T_b] :
% 52.58/52.39 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 52.58/52.39 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 52.58/52.39 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_append__Nil,axiom,
% 52.58/52.39 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ).
% 52.58/52.39
% 52.58/52.39 fof(fact_remove1__append,axiom,
% 52.58/52.39 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 52.58/52.39 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.58/52.39 => 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) )
% 52.58/52.39 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.58/52.39 => 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)) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_distinct__append,axiom,
% 52.58/52.39 ! [V_ys_2,V_xs_2,T_b] :
% 52.58/52.39 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
% 52.58/52.39 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 52.58/52.39 & hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 52.58/52.39 & 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)) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_nth__append,axiom,
% 52.58/52.39 ! [V_ys,V_xs,T_a,V_n] :
% 52.58/52.39 ( ( 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)))
% 52.58/52.39 => 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) )
% 52.58/52.39 & ( ~ 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)))
% 52.58/52.39 => 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))) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_list__update__append,axiom,
% 52.58/52.39 ! [V_x,V_ys,V_xs,T_a,V_n] :
% 52.58/52.39 ( ( 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)))
% 52.58/52.39 => 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) )
% 52.58/52.39 & ( ~ 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)))
% 52.58/52.39 => 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)) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_lexord__Nil__right,axiom,
% 52.58/52.39 ! [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))) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_sublist__append,axiom,
% 52.58/52.39 ! [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)))) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_lexord__lex,axiom,
% 52.58/52.39 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 52.58/52.39 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 52.58/52.39 & 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) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_map__upds__append1,axiom,
% 52.58/52.39 ! [V_x_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] :
% 52.58/52.39 ( 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)))
% 52.58/52.39 => 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)))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_lexord__take__index__conv,axiom,
% 52.58/52.39 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 52.58/52.39 <=> ( ( 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)))
% 52.58/52.39 & 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 )
% 52.58/52.39 | ? [B_i] :
% 52.58/52.39 ( 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))))
% 52.58/52.39 & hAPP(hAPP(c_List_Otake(T_b),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_b),B_i),V_y_2)
% 52.58/52.39 & 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)) ) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_take__append,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_fun__upds__append__drop,axiom,
% 52.58/52.39 ! [V_zs_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] :
% 52.58/52.39 ( 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)
% 52.58/52.39 => 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) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_fun__upds__append2__drop,axiom,
% 52.58/52.39 ! [V_zs_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] :
% 52.58/52.39 ( 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)
% 52.58/52.39 => 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) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_take__0,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_take__eq__Nil,axiom,
% 52.58/52.39 ! [V_xs_2,V_n_2,T_b] :
% 52.58/52.39 ( hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 52.58/52.39 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.58/52.39 | V_xs_2 = c_List_Olist_ONil(T_b) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_take__Nil,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_map__upds__Nil1,axiom,
% 52.58/52.39 ! [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 ).
% 52.58/52.39
% 52.58/52.39 fof(fact_map__upds__Nil2,axiom,
% 52.58/52.39 ! [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 ).
% 52.58/52.39
% 52.58/52.39 fof(fact_sublist__upt__eq__take,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_take__zip,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_take__take,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_map__add__upds,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_distinct__take,axiom,
% 52.58/52.39 ! [V_i,V_xs,T_a] :
% 52.58/52.39 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 52.58/52.39 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_set__take__subset,axiom,
% 52.58/52.39 ! [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))) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_set__take__subset__set__take,axiom,
% 52.58/52.39 ! [V_xs_2,T_b,V_n_2,V_m_2] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 52.58/52.39 => 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)))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_map__upds__apply__nontin,axiom,
% 52.58/52.39 ! [V_ys_2,V_f_2,T_c,V_xs_2,V_x_2,T_b] :
% 52.58/52.39 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.58/52.39 => 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) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_in__set__takeD,axiom,
% 52.58/52.39 ! [V_xs_2,V_n_2,V_x_2,T_b] :
% 52.58/52.39 ( 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))))
% 52.58/52.39 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_take__map,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_take__Suc__Cons,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_take__1__Cons,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_map__upd__upds__conv__if,axiom,
% 52.58/52.39 ! [V_y_2,V_f_2,V_xs_2,V_ys_2,T_c,V_x_2,T_b] :
% 52.58/52.39 ( ( 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))))
% 52.58/52.39 => 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) )
% 52.58/52.39 & ( ~ 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))))
% 52.58/52.39 => 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)) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_dom__map__upds,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_take__all,axiom,
% 52.58/52.39 ! [V_n,V_xs,T_a] :
% 52.58/52.39 ( 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))
% 52.58/52.39 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_length__take,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_nth__take,axiom,
% 52.58/52.39 ! [V_xs,T_a,V_n,V_i] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 52.58/52.39 => 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) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_map__upds__Cons,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_take__Cons,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_take__Cons_H,axiom,
% 52.58/52.39 ! [V_xs,V_x,T_a,V_n] :
% 52.58/52.39 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.58/52.39 => 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) )
% 52.58/52.39 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.58/52.39 => 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)) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_map__upds__list__update2__drop,axiom,
% 52.58/52.39 ! [V_y_2,V_m_2,V_ys_2,T_c,V_i_2,V_xs_2,T_b] :
% 52.58/52.39 ( 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))
% 52.58/52.39 => ( 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)))
% 52.58/52.39 => 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) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_map__upds__twist,axiom,
% 52.58/52.39 ! [V_bs_2,V_b_2,V_m_2,T_c,V_as_2,V_a_2,T_b] :
% 52.58/52.39 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_as_2)))
% 52.58/52.39 => 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)) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_take__Cons__number__of,axiom,
% 52.58/52.39 ! [V_xs,V_x,T_a,V_v] :
% 52.58/52.39 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.58/52.39 => 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) )
% 52.58/52.39 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.58/52.39 => 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)) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_restrict__map__upds,axiom,
% 52.58/52.39 ! [V_m_2,V_D_2,V_ys_2,T_c,V_xs_2,T_b] :
% 52.58/52.39 ( 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)
% 52.58/52.39 => ( 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))
% 52.58/52.39 => 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) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_take__Suc__conv__app__nth,axiom,
% 52.58/52.39 ! [V_xs,T_a,V_i] :
% 52.58/52.39 ( 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)))
% 52.58/52.39 => 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))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_snoc__listrel1__snoc__iff,axiom,
% 52.58/52.39 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 52.58/52.39 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 52.58/52.39 & V_x_2 = V_y_2 )
% 52.58/52.39 | ( V_xs_2 = V_ys_2
% 52.58/52.39 & hBOOL(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)) ) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_lexord__append__leftD,axiom,
% 52.58/52.39 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_b] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 52.58/52.39 => ( ! [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))
% 52.58/52.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_Cons__acc__listrel1I,axiom,
% 52.58/52.39 ! [V_xs_2,V_r_2,V_x_2,T_b] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 52.58/52.39 => ( 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))))
% 52.58/52.39 => 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)))) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_listrel1__mono,axiom,
% 52.58/52.39 ! [V_s_2,V_r_2,T_b] :
% 52.58/52.39 ( 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))
% 52.58/52.39 => 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))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
% 52.58/52.39 ! [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)))) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_listrel1__converse,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_listrel__subset__rtrancl__listrel1,axiom,
% 52.58/52.39 ! [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)))) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_listrel1I2,axiom,
% 52.58/52.39 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 52.58/52.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_rtrancl__listrel1__ConsI1,axiom,
% 52.58/52.39 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 52.58/52.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_listrel1__eq__len,axiom,
% 52.58/52.39 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 52.58/52.39 => 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) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_rtrancl__listrel1__eq__len,axiom,
% 52.58/52.39 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 52.58/52.39 => 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) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_not__Nil__listrel1,axiom,
% 52.58/52.39 ! [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))) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_not__listrel1__Nil,axiom,
% 52.58/52.39 ! [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))) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_append__listrel1I,axiom,
% 52.58/52.39 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 52.58/52.39 ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 52.58/52.39 & V_us_2 = V_vs_2 )
% 52.58/52.39 | ( V_xs_2 = V_ys_2
% 52.58/52.39 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) )
% 52.58/52.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_in__listrel1__converse,axiom,
% 52.58/52.39 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 52.58/52.39 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_rtrancl__listrel1__if__listrel,axiom,
% 52.58/52.39 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 52.58/52.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_listrel__reflcl__if__listrel1,axiom,
% 52.58/52.39 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 52.58/52.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_Cons__listrel1__Cons,axiom,
% 52.58/52.39 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 52.58/52.39 <=> ( ( hBOOL(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))
% 52.58/52.39 & V_xs_2 = V_ys_2 )
% 52.58/52.39 | ( V_x_2 = V_y_2
% 52.58/52.39 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_listrel1I1,axiom,
% 52.58/52.39 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 52.58/52.39 ( hBOOL(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))
% 52.58/52.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_listrel1__subset__listrel,axiom,
% 52.58/52.39 ! [V_r_H_2,V_r_2,T_b] :
% 52.58/52.39 ( 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))
% 52.58/52.39 => ( c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_r_H_2)
% 52.58/52.39 => 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))) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_listrel1I,axiom,
% 52.58/52.39 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 52.58/52.39 ( hBOOL(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))
% 52.58/52.39 => ( 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))
% 52.58/52.39 => ( 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))
% 52.58/52.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_rtrancl__listrel1__ConsI2,axiom,
% 52.58/52.39 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 52.58/52.39 ( hBOOL(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)))
% 52.58/52.39 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 52.58/52.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_listrel1__iff__update,axiom,
% 52.58/52.39 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 52.58/52.39 <=> ? [B_y,B_n] :
% 52.58/52.39 ( 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))
% 52.58/52.39 & 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)))
% 52.58/52.39 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_listrel1E,axiom,
% 52.58/52.39 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 52.58/52.39 => ~ ! [B_x,B_y] :
% 52.58/52.39 ( 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))
% 52.58/52.39 => ! [B_us,B_vs] :
% 52.58/52.39 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_vs))
% 52.58/52.39 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_vs)) ) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_rotate1__def,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_upd__conv__take__nth__drop,axiom,
% 52.58/52.39 ! [V_a,V_xs,T_a,V_i] :
% 52.58/52.39 ( 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)))
% 52.58/52.39 => 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))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_set__drop__subset__set__drop,axiom,
% 52.58/52.39 ! [V_xs_2,T_b,V_m_2,V_n_2] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2))
% 52.58/52.39 => 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)))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_drop__eq__Nil,axiom,
% 52.58/52.39 ! [V_xs_2,V_n_2,T_b] :
% 52.58/52.39 ( hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 52.58/52.39 <=> 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)) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_drop__all,axiom,
% 52.58/52.39 ! [V_n,V_xs,T_a] :
% 52.58/52.39 ( 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))
% 52.58/52.39 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_nth__via__drop,axiom,
% 52.58/52.39 ! [V_ys,V_y,V_xs,V_n,T_a] :
% 52.58/52.39 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)
% 52.58/52.39 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_length__drop,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_length__rotate1,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_drop__Suc__Cons,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_drop__1__Cons,axiom,
% 52.58/52.39 ! [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 ).
% 52.58/52.39
% 52.58/52.39 fof(fact_drop__map,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_in__set__dropD,axiom,
% 52.58/52.39 ! [V_xs_2,V_n_2,V_x_2,T_b] :
% 52.58/52.39 ( 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))))
% 52.58/52.39 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_set__rotate1,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_set__drop__subset,axiom,
% 52.58/52.39 ! [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))) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_distinct__drop,axiom,
% 52.58/52.39 ! [V_i,V_xs,T_a] :
% 52.58/52.39 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 52.58/52.39 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_distinct1__rotate,axiom,
% 52.58/52.39 ! [V_xs_2,T_b] :
% 52.58/52.39 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)))
% 52.58/52.39 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_drop__0,axiom,
% 52.58/52.39 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ).
% 52.58/52.39
% 52.58/52.39 fof(fact_drop__drop,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_drop__zip,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_rotate1__is__Nil__conv,axiom,
% 52.58/52.39 ! [V_xs_2,T_b] :
% 52.58/52.39 ( hAPP(c_List_Orotate1(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 52.58/52.39 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_drop__Nil,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_drop__append,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_take__drop,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_drop__take,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_append__take__drop__id,axiom,
% 52.58/52.39 ! [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 ).
% 52.58/52.39
% 52.58/52.39 fof(fact_append__eq__conv__conj,axiom,
% 52.58/52.39 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 52.58/52.39 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_zs_2
% 52.58/52.39 <=> ( 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)
% 52.58/52.39 & 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) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_drop__Cons,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_drop__Cons_H,axiom,
% 52.58/52.39 ! [V_xs,V_x,T_a,V_n] :
% 52.58/52.39 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.58/52.39 => 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) )
% 52.58/52.39 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.58/52.39 => 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) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_nth__drop,axiom,
% 52.58/52.39 ! [V_xs,T_a,V_i,V_n] :
% 52.58/52.39 ( 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)))
% 52.58/52.39 => 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)) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_append__eq__append__conv__if,axiom,
% 52.58/52.39 ! [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] :
% 52.58/52.39 ( 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)
% 52.58/52.39 <=> ( ( 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)))
% 52.58/52.39 => ( 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)
% 52.58/52.39 & 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) ) )
% 52.58/52.39 & ( ~ 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)))
% 52.58/52.39 => ( 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
% 52.58/52.39 & 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 ) ) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_nth__drop_H,axiom,
% 52.58/52.39 ! [V_xs,T_a,V_i] :
% 52.58/52.39 ( 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)))
% 52.58/52.39 => 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) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_rotate__simps,axiom,
% 52.58/52.39 ! [V_xs,V_x,T_b,T_a] :
% 52.58/52.39 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a)
% 52.58/52.39 & 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))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_drop__Cons__number__of,axiom,
% 52.58/52.39 ! [V_xs,V_x,T_a,V_v] :
% 52.58/52.39 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.58/52.39 => 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) )
% 52.58/52.39 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.58/52.39 => 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) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_take__add,axiom,
% 52.58/52.39 ! [V_xs,T_a,V_j,V_i] :
% 52.58/52.39 ( 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)))
% 52.58/52.39 => 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))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_rotate1__length01,axiom,
% 52.58/52.39 ! [V_xs,T_a] :
% 52.58/52.39 ( 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)))
% 52.58/52.39 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_zip__append1,axiom,
% 52.58/52.39 ! [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))) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_zip__append2,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_id__take__nth__drop,axiom,
% 52.58/52.39 ! [V_xs,T_a,V_i] :
% 52.58/52.39 ( 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)))
% 52.58/52.39 => 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))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_take__hd__drop,axiom,
% 52.58/52.39 ! [V_xs,T_a,V_n] :
% 52.58/52.39 ( 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)))
% 52.58/52.39 => 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) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_hd__drop__conv__nth,axiom,
% 52.58/52.39 ! [V_n,T_a,V_xs] :
% 52.58/52.39 ( V_xs != c_List_Olist_ONil(T_a)
% 52.58/52.39 => ( 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)))
% 52.58/52.39 => 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) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_hd__map,axiom,
% 52.58/52.39 ! [V_f_2,T_c,T_b,V_xs_2] :
% 52.58/52.39 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 52.58/52.39 => 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)) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_hd_Osimps,axiom,
% 52.58/52.39 ! [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 ).
% 52.58/52.39
% 52.58/52.39 fof(fact_hd__append,axiom,
% 52.58/52.39 ! [V_ys,T_a,V_xs] :
% 52.58/52.39 ( ( V_xs = c_List_Olist_ONil(T_a)
% 52.58/52.39 => 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) )
% 52.58/52.39 & ( V_xs != c_List_Olist_ONil(T_a)
% 52.58/52.39 => 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) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_hd__append2,axiom,
% 52.58/52.39 ! [V_ys,T_a,V_xs] :
% 52.58/52.39 ( V_xs != c_List_Olist_ONil(T_a)
% 52.58/52.39 => 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) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_hd__in__set,axiom,
% 52.58/52.39 ! [T_b,V_xs_2] :
% 52.58/52.39 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 52.58/52.39 => 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))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_hd__conv__nth,axiom,
% 52.58/52.39 ! [T_a,V_xs] :
% 52.58/52.39 ( V_xs != c_List_Olist_ONil(T_a)
% 52.58/52.39 => 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)) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_rotate1__hd__tl,axiom,
% 52.58/52.39 ! [T_a,V_xs] :
% 52.58/52.39 ( V_xs != c_List_Olist_ONil(T_a)
% 52.58/52.39 => hAPP(c_List_Orotate1(T_a),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Otl(T_a),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),V_xs)),c_List_Olist_ONil(T_a))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_hd__rotate__conv__nth,axiom,
% 52.58/52.39 ! [V_n,T_a,V_xs] :
% 52.58/52.39 ( V_xs != c_List_Olist_ONil(T_a)
% 52.58/52.39 => 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))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_tl__drop,axiom,
% 52.58/52.39 ! [V_xs,V_n,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_drop__tl,axiom,
% 52.58/52.39 ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_drop__Suc,axiom,
% 52.58/52.39 ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_tl__append2,axiom,
% 52.58/52.39 ! [V_ys,T_a,V_xs] :
% 52.58/52.39 ( V_xs != c_List_Olist_ONil(T_a)
% 52.58/52.39 => hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Otl(T_a),V_xs)),V_ys) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_rotate__conv__mod,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_length__rotate,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_tl_Osimps_I2_J,axiom,
% 52.58/52.39 ! [V_xs,V_x,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_xs ).
% 52.58/52.39
% 52.58/52.39 fof(fact_map__tl,axiom,
% 52.58/52.39 ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Otl(T_c),V_xs_2)) = hAPP(c_List_Otl(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_rotate__map,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_set__rotate,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_distinct__tl,axiom,
% 52.58/52.39 ! [V_xs,T_a] :
% 52.58/52.39 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 52.58/52.39 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_distinct__rotate,axiom,
% 52.58/52.39 ! [V_xs_2,V_n_2,T_b] :
% 52.58/52.39 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)))
% 52.58/52.39 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_rotate__rotate,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_rotate__is__Nil__conv,axiom,
% 52.58/52.39 ! [V_xs_2,V_n_2,T_b] :
% 52.58/52.39 ( hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 52.58/52.39 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_tl_Osimps_I1_J,axiom,
% 52.58/52.39 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_take__tl,axiom,
% 52.58/52.39 ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_rotate__def,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_rotate__Suc,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_rotate1__rotate__swap,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_tl__append,axiom,
% 52.58/52.39 ! [V_ys_2,V_xs_2,T_b] : hAPP(c_List_Otl(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,hAPP(c_List_Otl(T_b),V_ys_2),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Oappend(T_b)),V_ys_2))),V_xs_2) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_rotate0,axiom,
% 52.58/52.39 ! [T_b] : c_List_Orotate(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_rotate__add,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_rotate__id,axiom,
% 52.58/52.39 ! [V_xs,T_a,V_n] :
% 52.58/52.39 ( 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)
% 52.58/52.39 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_rotate__length01,axiom,
% 52.58/52.39 ! [V_n,V_xs,T_a] :
% 52.58/52.39 ( 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)))
% 52.58/52.39 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_length__tl,axiom,
% 52.58/52.39 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_tl__take,axiom,
% 52.58/52.39 ! [V_xs,V_n,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(T_a),V_xs)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_take__Suc,axiom,
% 52.58/52.39 ! [V_n,T_a,V_xs] :
% 52.58/52.39 ( V_xs != c_List_Olist_ONil(T_a)
% 52.58/52.39 => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),V_xs)),hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_rotate__drop__take,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_fold1__set,axiom,
% 52.58/52.39 ! [V_xs_2,T_b] :
% 52.58/52.39 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 52.58/52.39 => ( V_xs_2 != c_List_Olist_ONil(T_b)
% 52.58/52.39 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Ohd(T_b),V_xs_2)),hAPP(c_List_Otl(T_b),V_xs_2)) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_list_Osize_I2_J,axiom,
% 52.58/52.39 ! [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))) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_foldl__Nil,axiom,
% 52.58/52.39 ! [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 ).
% 52.58/52.39
% 52.58/52.39 fof(fact_foldr__conv__foldl,axiom,
% 52.58/52.39 ! [V_a_2,V_xs_2,T_b] :
% 52.58/52.39 ( class_Groups_Oab__semigroup__add(T_b)
% 52.58/52.39 => 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) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_foldl__absorb0,axiom,
% 52.58/52.39 ! [V_zs_2,V_x_2,T_b] :
% 52.58/52.39 ( class_Groups_Omonoid__add(T_b)
% 52.58/52.39 => 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) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_foldl__assoc,axiom,
% 52.58/52.39 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 52.58/52.39 ( class_Groups_Osemigroup__add(T_b)
% 52.58/52.39 => 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)) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_start__le__sum,axiom,
% 52.58/52.39 ! [V_ns_2,V_n_2,V_m_2] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 52.58/52.39 => 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))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_foldl__map,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_list__size__map,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_foldl__Cons,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_foldl__append,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_listsum__foldl,axiom,
% 52.58/52.39 ! [T_b] :
% 52.58/52.39 ( class_Groups_Omonoid__add(T_b)
% 52.58/52.39 => 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)) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_foldl__foldr1__lemma,axiom,
% 52.58/52.39 ! [V_xs_2,V_a_2,T_b] :
% 52.58/52.39 ( class_Groups_Omonoid__add(T_b)
% 52.58/52.39 => 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))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_foldl__foldr1,axiom,
% 52.58/52.39 ! [V_xs_2,T_b] :
% 52.58/52.39 ( class_Groups_Omonoid__add(T_b)
% 52.58/52.39 => 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)) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_sum__eq__0__conv,axiom,
% 52.58/52.39 ! [V_ns_2,V_m_2] :
% 52.58/52.39 ( 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)
% 52.58/52.39 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.58/52.39 & ! [B_x] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 52.58/52.39 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_list_Osize_I1_J,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_fun__left__comm__idem_Ofold__set,axiom,
% 52.58/52.39 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
% 52.58/52.39 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 52.58/52.39 => 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) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_Sup__set__fold,axiom,
% 52.58/52.39 ! [V_xs_2,T_b] :
% 52.58/52.39 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 52.58/52.39 => 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) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_Inf__set__fold,axiom,
% 52.58/52.39 ! [V_xs_2,T_b] :
% 52.58/52.39 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 52.58/52.39 => 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) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_Sup__fin__set__fold,axiom,
% 52.58/52.39 ! [V_xs_2,V_x_2,T_b] :
% 52.58/52.39 ( class_Lattices_Olattice(T_b)
% 52.58/52.39 => 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) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_Inf__fin__set__fold,axiom,
% 52.58/52.39 ! [V_xs_2,V_x_2,T_b] :
% 52.58/52.39 ( class_Lattices_Olattice(T_b)
% 52.58/52.39 => 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) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_Min__fin__set__fold,axiom,
% 52.58/52.39 ! [V_xs_2,V_x_2,T_b] :
% 52.58/52.39 ( class_Orderings_Olinorder(T_b)
% 52.58/52.39 => 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) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_Max__fin__set__fold,axiom,
% 52.58/52.39 ! [V_xs_2,V_x_2,T_b] :
% 52.58/52.39 ( class_Orderings_Olinorder(T_b)
% 52.58/52.39 => 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) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_min__max_OInf__fin__set__fold,axiom,
% 52.58/52.39 ! [V_xs_2,V_x_2,T_b] :
% 52.58/52.39 ( class_Orderings_Olinorder(T_b)
% 52.58/52.39 => 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) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_min__max_OSup__fin__set__fold,axiom,
% 52.58/52.39 ! [V_xs_2,V_x_2,T_b] :
% 52.58/52.39 ( class_Orderings_Olinorder(T_b)
% 52.58/52.39 => 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) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_SUPR__set__fold,axiom,
% 52.58/52.39 ! [V_f_2,V_xs_2,T_c,T_b] :
% 52.58/52.39 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 52.58/52.39 => 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) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_INFI__set__fold,axiom,
% 52.58/52.39 ! [V_f_2,V_xs_2,T_c,T_b] :
% 52.58/52.39 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 52.58/52.39 => 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) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_list__size__estimation,axiom,
% 52.58/52.39 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.58/52.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 52.58/52.39 => 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))) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_list__size__estimation_H,axiom,
% 52.58/52.39 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.58/52.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 52.58/52.39 => 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))) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_map__upds__fold__map__upd,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_elem__le__sum,axiom,
% 52.58/52.39 ! [V_ns_2,V_n_2] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 52.58/52.39 => 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))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_list__size__conv__listsum,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_listrel__subset,axiom,
% 52.58/52.39 ! [V_A_2,V_r_2,T_b] :
% 52.58/52.39 ( 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))))
% 52.58/52.39 => 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))))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_lists__accI,axiom,
% 52.58/52.39 ! [V_r_2,V_xs_2,T_b] :
% 52.58/52.39 ( 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))))
% 52.58/52.39 => 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)))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_lists_ONil,axiom,
% 52.58/52.39 ! [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))) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_equiv__listrel,axiom,
% 52.58/52.39 ! [V_r_2,V_A_2,T_b] :
% 52.58/52.39 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 52.58/52.39 => 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)) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_listrel__refl__on,axiom,
% 52.58/52.39 ! [V_r_2,V_A_2,T_b] :
% 52.58/52.39 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 52.58/52.39 => 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)) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_append__in__lists__conv,axiom,
% 52.58/52.39 ! [V_A_2,V_ys_2,V_xs_2,T_b] :
% 52.58/52.39 ( 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)))
% 52.58/52.39 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 52.58/52.39 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_lists__mono,axiom,
% 52.58/52.39 ! [V_B_2,V_A_2,T_b] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 52.58/52.39 => 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))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_lists__UNIV,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_Cons__in__lists__iff,axiom,
% 52.58/52.39 ! [V_A_2,V_xs_2,V_x_2,T_b] :
% 52.58/52.39 ( 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)))
% 52.58/52.39 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 52.58/52.39 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_in__lists__conv__set,axiom,
% 52.58/52.39 ! [V_A_2,V_xs_2,T_b] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 52.58/52.39 <=> ! [B_x] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.58/52.39 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_lists__eq__set,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_lists__empty,axiom,
% 52.58/52.39 ! [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))) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_lists__accD,axiom,
% 52.58/52.39 ! [V_r_2,V_xs_2,T_b] :
% 52.58/52.39 ( 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))))
% 52.58/52.39 => 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)))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_lexord__append__rightI,axiom,
% 52.58/52.39 ! [V_r_2,V_x_2,T_b,V_y_2] :
% 52.58/52.39 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_b),B_z)
% 52.58/52.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_lexord__Nil__left,axiom,
% 52.58/52.39 ! [V_r_2,V_y_2,T_b] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 52.58/52.39 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_last__list__update,axiom,
% 52.58/52.39 ! [V_x,V_k,T_a,V_xs] :
% 52.58/52.39 ( V_xs != c_List_Olist_ONil(T_a)
% 52.58/52.39 => ( ( 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))
% 52.58/52.39 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x )
% 52.58/52.39 & ( 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))
% 52.58/52.39 => 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) ) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_listsum__mono,axiom,
% 52.58/52.39 ! [V_g_2,V_f_2,V_xs_2,T_b,T_c] :
% 52.58/52.39 ( ( class_Groups_Omonoid__add(T_c)
% 52.58/52.39 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 52.58/52.39 => ( ! [B_x] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.58/52.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 52.58/52.39 => 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)))) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_last__appendL,axiom,
% 52.58/52.39 ! [V_xs,T_a,V_ys] :
% 52.58/52.39 ( V_ys = c_List_Olist_ONil(T_a)
% 52.58/52.39 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_last__appendR,axiom,
% 52.58/52.39 ! [V_xs,T_a,V_ys] :
% 52.58/52.39 ( V_ys != c_List_Olist_ONil(T_a)
% 52.58/52.39 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_last__append,axiom,
% 52.58/52.39 ! [V_xs,T_a,V_ys] :
% 52.58/52.39 ( ( V_ys = c_List_Olist_ONil(T_a)
% 52.58/52.39 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) )
% 52.58/52.39 & ( V_ys != c_List_Olist_ONil(T_a)
% 52.58/52.39 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_last__ConsL,axiom,
% 52.58/52.39 ! [V_x,T_a,V_xs] :
% 52.58/52.39 ( V_xs = c_List_Olist_ONil(T_a)
% 52.58/52.39 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_last__ConsR,axiom,
% 52.58/52.39 ! [V_x,T_a,V_xs] :
% 52.58/52.39 ( V_xs != c_List_Olist_ONil(T_a)
% 52.58/52.39 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_last_Osimps,axiom,
% 52.58/52.39 ! [V_x,T_a,V_xs] :
% 52.58/52.39 ( ( V_xs = c_List_Olist_ONil(T_a)
% 52.58/52.39 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x )
% 52.58/52.39 & ( V_xs != c_List_Olist_ONil(T_a)
% 52.58/52.39 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_last__map,axiom,
% 52.58/52.39 ! [V_f_2,T_c,T_b,V_xs_2] :
% 52.58/52.39 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 52.58/52.39 => 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)) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_last__in__set,axiom,
% 52.58/52.39 ! [T_b,V_as_2] :
% 52.58/52.39 ( V_as_2 != c_List_Olist_ONil(T_b)
% 52.58/52.39 => hBOOL(hAPP(hAPP(c_member(T_b),c_List_Olast(T_b,V_as_2)),hAPP(c_List_Oset(T_b),V_as_2))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_last__snoc,axiom,
% 52.58/52.39 ! [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 ).
% 52.58/52.39
% 52.58/52.39 fof(fact_last__drop,axiom,
% 52.58/52.39 ! [V_xs,T_a,V_n] :
% 52.58/52.39 ( 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)))
% 52.58/52.39 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_last__conv__nth,axiom,
% 52.58/52.39 ! [T_a,V_xs] :
% 52.58/52.39 ( V_xs != c_List_Olist_ONil(T_a)
% 52.58/52.39 => 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))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_lexord__linear,axiom,
% 52.58/52.39 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 52.58/52.39 ( ! [B_a,B_b] :
% 52.58/52.39 ( 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))
% 52.58/52.39 | B_a = B_b
% 52.58/52.39 | 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)) )
% 52.58/52.39 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 52.58/52.39 | V_x_2 = V_y_2
% 52.58/52.39 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_lexord__irreflexive,axiom,
% 52.58/52.39 ! [V_y_2,V_r_2,T_b] :
% 52.58/52.39 ( ! [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))
% 52.58/52.39 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_lists_Osimps,axiom,
% 52.58/52.39 ! [V_A_2,V_a_2,T_b] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2)))
% 52.58/52.39 <=> ( V_a_2 = c_List_Olist_ONil(T_b)
% 52.58/52.39 | ? [B_a,B_l] :
% 52.58/52.39 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l)
% 52.58/52.39 & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 52.58/52.39 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2))) ) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_list__size__pointwise,axiom,
% 52.58/52.39 ! [V_g_2,V_f_2,V_xs_2,T_b] :
% 52.58/52.39 ( ! [B_x] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.58/52.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 52.58/52.39 => 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))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_butlast__take,axiom,
% 52.58/52.39 ! [V_xs,T_a,V_n] :
% 52.58/52.39 ( 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)))
% 52.58/52.39 => 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) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_nth__take__lemma,axiom,
% 52.58/52.39 ! [V_ys,V_xs,T_a,V_k] :
% 52.58/52.39 ( 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)))
% 52.58/52.39 => ( 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)))
% 52.58/52.39 => ( ! [B_i] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k))
% 52.58/52.39 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) )
% 52.58/52.39 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_map__butlast,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_distinct__butlast,axiom,
% 52.58/52.39 ! [T_a,V_xs] :
% 52.58/52.39 ( V_xs != c_List_Olist_ONil(T_a)
% 52.58/52.39 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 52.58/52.39 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_butlast_Osimps_I1_J,axiom,
% 52.58/52.39 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_in__set__butlastD,axiom,
% 52.58/52.39 ! [V_xs_2,V_x_2,T_b] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 52.58/52.39 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_butlast_Osimps_I2_J,axiom,
% 52.58/52.39 ! [V_x,T_a,V_xs] :
% 52.58/52.39 ( ( V_xs = c_List_Olist_ONil(T_a)
% 52.58/52.39 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) )
% 52.58/52.39 & ( V_xs != c_List_Olist_ONil(T_a)
% 52.58/52.39 => 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)) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_butlast__append,axiom,
% 52.58/52.39 ! [V_xs,T_a,V_ys] :
% 52.58/52.39 ( ( V_ys = c_List_Olist_ONil(T_a)
% 52.58/52.39 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) )
% 52.58/52.39 & ( V_ys != c_List_Olist_ONil(T_a)
% 52.58/52.39 => 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)) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_drop__butlast,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_butlast__drop,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_in__set__butlast__appendI,axiom,
% 52.58/52.39 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 52.58/52.39 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 52.58/52.39 | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_ys_2)))) )
% 52.58/52.39 => 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))))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_butlast__snoc,axiom,
% 52.58/52.39 ! [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 ).
% 52.58/52.39
% 52.58/52.39 fof(fact_take__butlast,axiom,
% 52.58/52.39 ! [V_xs,T_a,V_n] :
% 52.58/52.39 ( 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)))
% 52.58/52.39 => 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) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_length__butlast,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_butlast__conv__take,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_butlast__list__update,axiom,
% 52.58/52.39 ! [V_x,V_xs,T_a,V_k] :
% 52.58/52.39 ( ( 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))
% 52.58/52.39 => 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) )
% 52.58/52.39 & ( 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))
% 52.58/52.39 => 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) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_snoc__eq__iff__butlast,axiom,
% 52.58/52.39 ! [V_ys_2,V_x_2,V_xs_2,T_b] :
% 52.58/52.39 ( 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
% 52.58/52.39 <=> ( V_ys_2 != c_List_Olist_ONil(T_b)
% 52.58/52.39 & c_List_Obutlast(T_b,V_ys_2) = V_xs_2
% 52.58/52.39 & c_List_Olast(T_b,V_ys_2) = V_x_2 ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_append__butlast__last__id,axiom,
% 52.58/52.39 ! [T_a,V_xs] :
% 52.58/52.39 ( V_xs != c_List_Olist_ONil(T_a)
% 52.58/52.39 => 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 ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_transpose__aux__max,axiom,
% 52.58/52.39 ! [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)))) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_partition__set,axiom,
% 52.58/52.39 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_b] :
% 52.58/52.39 ( 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)
% 52.58/52.39 => 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) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_length__filter__map,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_filter__is__subset,axiom,
% 52.58/52.39 ! [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))) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_length__filter__le,axiom,
% 52.58/52.39 ! [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))) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_set__filter,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_filter__append,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_sum__length__filter__compl,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_filter_Osimps_I2_J,axiom,
% 52.58/52.39 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 52.58/52.39 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 52.58/52.39 => 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)) )
% 52.58/52.39 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 52.58/52.39 => 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) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_filter__id__conv,axiom,
% 52.58/52.39 ! [V_xs_2,V_P_2,T_b] :
% 52.58/52.39 ( hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) = V_xs_2
% 52.58/52.39 <=> ! [B_x] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.58/52.39 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_filter__insort__triv,axiom,
% 52.58/52.39 ! [V_xs_2,V_f_2,T_b,V_x_2,V_P_2,T_c] :
% 52.58/52.39 ( class_Orderings_Olinorder(T_c)
% 52.58/52.39 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 52.58/52.39 => 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) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_distinct__filter,axiom,
% 52.58/52.39 ! [V_P_2,V_xs_2,T_b] :
% 52.58/52.39 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 52.58/52.39 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_remove1__filter__not,axiom,
% 52.58/52.39 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 52.58/52.39 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 52.58/52.39 => 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) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_filter__remove1,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_filter__filter,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_partition__filter1,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_filter__empty__conv,axiom,
% 52.58/52.39 ! [V_xs_2,V_P_2,T_b] :
% 52.58/52.39 ( hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 52.58/52.39 <=> ! [B_x] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.58/52.39 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_filter_Osimps_I1_J,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_partition__filter__conv,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_partition__filter2,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_filter__map,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_length__filter__less,axiom,
% 52.58/52.39 ! [V_P_2,V_xs_2,V_x_2,T_b] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.58/52.39 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 52.58/52.39 => 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))) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_set__minus__filter__out,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_partition__P,axiom,
% 52.58/52.39 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_b] :
% 52.58/52.39 ( 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)
% 52.58/52.39 => ( ! [B_x] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_yes_2)))
% 52.58/52.39 => hBOOL(hAPP(V_P_2,B_x)) )
% 52.58/52.39 & ! [B_x] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_no_2)))
% 52.58/52.39 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_partition_Osimps_I1_J,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_filter__in__sublist,axiom,
% 52.58/52.39 ! [V_s_2,V_xs_2,T_b] :
% 52.58/52.39 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 52.58/52.39 => 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) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_partition_Osimps_I2_J,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_length__filter__conv__card,axiom,
% 52.58/52.39 ! [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))))) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_map__filter__def,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_transpose__max__length,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_map__of__filter__in,axiom,
% 52.58/52.39 ! [V_P_2,V_z_2,V_k_2,V_xs_2,T_b,T_c] :
% 52.58/52.39 ( 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)
% 52.58/52.39 => ( hBOOL(hAPP(hAPP(V_P_2,V_k_2),V_z_2))
% 52.58/52.39 => 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) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_transpose__map__map,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_map__filter__simps_I1_J,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_transpose_Osimps_I1_J,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_map__filter__simps_I2_J,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_transpose__empty,axiom,
% 52.58/52.39 ! [V_xs_2,T_b] :
% 52.58/52.39 ( c_List_Otranspose(T_b,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_b))
% 52.58/52.39 <=> ! [B_x] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 52.58/52.39 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_transpose_Osimps_I2_J,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_sublist__shift__lemma__Suc,axiom,
% 52.58/52.39 ! [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)))) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_select__weigth__drop__zero,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_pick__drop__zero,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_nth__transpose,axiom,
% 52.58/52.39 ! [V_xs_2,T_b,V_i_2] :
% 52.58/52.39 ( 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))))
% 52.58/52.39 => 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)) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_length__transpose,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_map__filter__map__filter,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_insort__key__remove1,axiom,
% 52.58/52.39 ! [V_f_2,V_xs_2,V_a_2,T_b,T_c] :
% 52.58/52.39 ( class_Orderings_Olinorder(T_c)
% 52.58/52.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.58/52.39 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 52.58/52.39 => ( 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
% 52.58/52.39 => 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 ) ) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_sublist__def,axiom,
% 52.58/52.39 ! [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))))) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_sorted_ONil,axiom,
% 52.58/52.39 ! [T_a] :
% 52.58/52.39 ( class_Orderings_Olinorder(T_a)
% 52.58/52.39 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_sorted__single,axiom,
% 52.58/52.39 ! [V_x,T_a] :
% 52.58/52.39 ( class_Orderings_Olinorder(T_a)
% 52.58/52.39 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_sorted__same,axiom,
% 52.58/52.39 ! [V_xs_2,V_g_2,T_b] :
% 52.58/52.39 ( class_Orderings_Olinorder(T_b)
% 52.58/52.39 => 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)) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_sorted__filter,axiom,
% 52.58/52.39 ! [V_P_2,V_xs_2,V_f_2,T_c,T_b] :
% 52.58/52.39 ( class_Orderings_Olinorder(T_b)
% 52.58/52.39 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 52.58/52.39 => 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))) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_sorted__map__same,axiom,
% 52.58/52.39 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 52.58/52.39 ( class_Orderings_Olinorder(T_b)
% 52.58/52.39 => 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))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_length__upt,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_last__upt,axiom,
% 52.58/52.39 ! [V_j,V_i] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 52.58/52.39 => 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)) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_sorted__butlast,axiom,
% 52.58/52.39 ! [V_xs,T_a] :
% 52.58/52.39 ( class_Orderings_Olinorder(T_a)
% 52.58/52.39 => ( V_xs != c_List_Olist_ONil(T_a)
% 52.58/52.39 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 52.58/52.39 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_take__upt,axiom,
% 52.58/52.39 ! [V_n,V_m,V_i] :
% 52.58/52.39 ( 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))
% 52.58/52.39 => 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)) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_upt__eq__Nil__conv,axiom,
% 52.58/52.39 ! [V_j_2,V_i_2] :
% 52.58/52.39 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat)
% 52.58/52.39 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 52.58/52.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_upt__conv__Nil,axiom,
% 52.58/52.39 ! [V_i,V_j] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 52.58/52.39 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_sorted__many,axiom,
% 52.58/52.39 ! [V_zs,V_y,V_x,T_a] :
% 52.58/52.39 ( class_Orderings_Olinorder(T_a)
% 52.58/52.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 52.58/52.39 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))
% 52.58/52.39 => 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))) ) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_sorted__many__eq,axiom,
% 52.58/52.39 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 52.58/52.39 ( class_Orderings_Olinorder(T_b)
% 52.58/52.39 => ( 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)))
% 52.58/52.39 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 52.58/52.39 & c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)) ) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_upt__add__eq__append,axiom,
% 52.58/52.39 ! [V_k,V_j,V_i] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 52.58/52.39 => 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))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_upt__Suc,axiom,
% 52.58/52.39 ! [V_j,V_i] :
% 52.58/52.39 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 52.58/52.39 => 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))) )
% 52.58/52.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 52.58/52.39 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_upt__Suc__append,axiom,
% 52.58/52.39 ! [V_j,V_i] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 52.58/52.39 => 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))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_sorted__Cons,axiom,
% 52.58/52.39 ! [V_xs_2,V_x_2,T_b] :
% 52.58/52.39 ( class_Orderings_Olinorder(T_b)
% 52.58/52.39 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 52.58/52.39 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 52.58/52.39 & ! [B_x] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.58/52.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_sorted__append,axiom,
% 52.58/52.39 ! [V_ys_2,V_xs_2,T_b] :
% 52.58/52.39 ( class_Orderings_Olinorder(T_b)
% 52.58/52.39 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 52.58/52.39 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 52.58/52.39 & c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 52.58/52.39 & ! [B_x] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.58/52.39 => ! [B_xa] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2)))
% 52.58/52.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) ) ) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_sorted__drop,axiom,
% 52.58/52.39 ! [V_n,V_xs,T_a] :
% 52.58/52.39 ( class_Orderings_Olinorder(T_a)
% 52.58/52.39 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 52.58/52.39 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_drop__upt,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_hd__upt,axiom,
% 52.58/52.39 ! [V_j,V_i] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 52.58/52.39 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_sorted__insort__insert,axiom,
% 52.58/52.39 ! [V_x_2,V_xs_2,T_b] :
% 52.58/52.39 ( class_Orderings_Olinorder(T_b)
% 52.58/52.39 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 52.58/52.39 => 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)) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_upt__rec,axiom,
% 52.58/52.39 ! [V_j,V_i] :
% 52.58/52.39 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 52.58/52.39 => 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)) )
% 52.58/52.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 52.58/52.39 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_upt__conv__Cons,axiom,
% 52.58/52.39 ! [V_j,V_i] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 52.58/52.39 => 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)) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_set__upt,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_atLeastLessThan__upt,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_sorted__distinct__set__unique,axiom,
% 52.58/52.39 ! [V_ys_2,V_xs_2,T_b] :
% 52.58/52.39 ( class_Orderings_Olinorder(T_b)
% 52.58/52.39 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 52.58/52.39 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 52.58/52.39 => ( c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 52.58/52.39 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 52.58/52.39 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 52.58/52.39 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_sorted__insort,axiom,
% 52.58/52.39 ! [V_xs_2,V_x_2,T_b] :
% 52.58/52.39 ( class_Orderings_Olinorder(T_b)
% 52.58/52.39 => ( 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))
% 52.58/52.39 <=> c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_distinct__upt,axiom,
% 52.58/52.39 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_sorted__remove1,axiom,
% 52.58/52.39 ! [V_a,V_xs,T_a] :
% 52.58/52.39 ( class_Orderings_Olinorder(T_a)
% 52.58/52.39 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 52.58/52.39 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_sorted__upt,axiom,
% 52.58/52.39 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_sorted__upto,axiom,
% 52.58/52.39 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_sorted__list__of__set__range,axiom,
% 52.58/52.39 ! [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) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_sorted_Oequations_I1_J,axiom,
% 52.58/52.39 ! [T_a] :
% 52.58/52.39 ( class_Orderings_Olinorder(T_a)
% 52.58/52.39 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_upt__0,axiom,
% 52.58/52.39 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_sorted__take,axiom,
% 52.58/52.39 ! [V_n,V_xs,T_a] :
% 52.58/52.39 ( class_Orderings_Olinorder(T_a)
% 52.58/52.39 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 52.58/52.39 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_sorted__tl,axiom,
% 52.58/52.39 ! [V_xs,T_a] :
% 52.58/52.39 ( class_Orderings_Olinorder(T_a)
% 52.58/52.39 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 52.58/52.39 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_upt__rec__number__of,axiom,
% 52.58/52.39 ! [V_n,V_m] :
% 52.58/52.39 ( ( 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)))
% 52.58/52.39 => 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))) )
% 52.58/52.39 & ( ~ 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)))
% 52.58/52.39 => 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) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_sorted__insort__key,axiom,
% 52.58/52.39 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 52.58/52.39 ( class_Orderings_Olinorder(T_b)
% 52.58/52.39 => ( 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)))
% 52.58/52.39 <=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_sorted__map__remove1,axiom,
% 52.58/52.39 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 52.58/52.39 ( class_Orderings_Olinorder(T_b)
% 52.58/52.39 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 52.58/52.39 => 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))) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_map__Suc__upt,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_sorted__insort__insert__key,axiom,
% 52.58/52.39 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 52.58/52.39 ( class_Orderings_Olinorder(T_b)
% 52.58/52.39 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 52.58/52.39 => 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))) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_upt__eq__Cons__conv,axiom,
% 52.58/52.39 ! [V_xs_2,V_x_2,V_j_2,V_i_2] :
% 52.58/52.39 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2)
% 52.58/52.39 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2))
% 52.58/52.39 & V_i_2 = V_x_2
% 52.58/52.39 & 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 ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_filter__insort,axiom,
% 52.58/52.39 ! [V_x_2,V_P_2,V_xs_2,V_f_2,T_c,T_b] :
% 52.58/52.39 ( class_Orderings_Olinorder(T_b)
% 52.58/52.39 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 52.58/52.39 => ( hBOOL(hAPP(V_P_2,V_x_2))
% 52.58/52.39 => 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)) ) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_map__nth,axiom,
% 52.58/52.39 ! [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 ).
% 52.58/52.39
% 52.58/52.39 fof(fact_atLeastAtMost__upt,axiom,
% 52.58/52.39 ! [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))) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_atLeast__upt,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
% 52.58/52.39 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 52.58/52.39 ( class_Groups_Ocomm__monoid__add(T_b)
% 52.58/52.39 => 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))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
% 52.58/52.39 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 52.58/52.39 ( class_Groups_Ocomm__monoid__add(T_b)
% 52.58/52.39 => 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))) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_nth__upt,axiom,
% 52.58/52.39 ! [V_j,V_k,V_i] :
% 52.58/52.39 ( 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))
% 52.58/52.39 => 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) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_greaterThanAtMost__upt,axiom,
% 52.58/52.39 ! [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))) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_sorted_Oequations_I2_J,axiom,
% 52.58/52.39 ! [V_a1_2,V_a2_2,T_b] :
% 52.58/52.39 ( class_Orderings_Olinorder(T_b)
% 52.58/52.39 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2))
% 52.58/52.39 <=> ( ! [B_x] :
% 52.58/52.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2)))
% 52.58/52.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x)) )
% 52.58/52.39 & c_List_Olinorder__class_Osorted(T_b,V_a1_2) ) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_greaterThanLessThan__upt,axiom,
% 52.58/52.39 ! [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)) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_nth__map__upt,axiom,
% 52.58/52.39 ! [V_f_2,T_b,V_m_2,V_n_2,V_i_2] :
% 52.58/52.39 ( 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)))
% 52.58/52.39 => 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)) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_sorted__list__of__set,axiom,
% 52.58/52.39 ! [V_A_2,T_b] :
% 52.58/52.39 ( class_Orderings_Olinorder(T_b)
% 52.58/52.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 52.58/52.39 => ( hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) = V_A_2
% 52.58/52.39 & c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))
% 52.58/52.39 & hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))) ) ) ) ).
% 52.58/52.39
% 52.58/52.39 fof(fact_atMost__upto,axiom,
% 52.62/52.39 ! [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))) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_insort__remove1,axiom,
% 52.62/52.39 ! [V_xs_2,V_a_2,T_b] :
% 52.62/52.39 ( class_Orderings_Olinorder(T_b)
% 52.62/52.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.62/52.39 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 52.62/52.39 => 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 ) ) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_sorted__equals__nth__mono,axiom,
% 52.62/52.39 ! [V_xs_2,T_b] :
% 52.62/52.39 ( class_Orderings_Olinorder(T_b)
% 52.62/52.39 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 52.62/52.39 <=> ! [B_j] :
% 52.62/52.39 ( 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)))
% 52.62/52.39 => ! [B_i] :
% 52.62/52.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 52.62/52.39 => 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))) ) ) ) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_sorted__nth__mono,axiom,
% 52.62/52.39 ! [V_j,V_i,V_xs,T_a] :
% 52.62/52.39 ( class_Orderings_Olinorder(T_a)
% 52.62/52.39 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 52.62/52.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 52.62/52.39 => ( 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)))
% 52.62/52.39 => 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))) ) ) ) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_map__sorted__distinct__set__unique,axiom,
% 52.62/52.39 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 52.62/52.39 ( class_Orderings_Olinorder(T_c)
% 52.62/52.39 => ( 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)))
% 52.62/52.39 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 52.62/52.39 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)))
% 52.62/52.39 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2))
% 52.62/52.39 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)))
% 52.62/52.39 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 52.62/52.39 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_sublist__shift__lemma,axiom,
% 52.62/52.39 ! [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))))) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_transpose__rectangle,axiom,
% 52.62/52.39 ! [V_n_2,T_b,V_xs_2] :
% 52.62/52.39 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 52.62/52.39 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 52.62/52.39 => ( ! [B_i] :
% 52.62/52.39 ( 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)))
% 52.62/52.39 => 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 )
% 52.62/52.39 => 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)) ) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_transpose_Opsimps_I2_J,axiom,
% 52.62/52.39 ! [V_xss_2,T_b] :
% 52.62/52.39 ( 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)))
% 52.62/52.39 => 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) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_transpose_Opsimps_I1_J,axiom,
% 52.62/52.39 ! [T_b] :
% 52.62/52.39 ( 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))))
% 52.62/52.39 => c_List_Otranspose(T_b,c_List_Olist_ONil(tc_List_Olist(T_b))) = c_List_Olist_ONil(tc_List_Olist(T_b)) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_transpose__column,axiom,
% 52.62/52.39 ! [V_i_2,V_xs_2,T_b] :
% 52.62/52.39 ( 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)))
% 52.62/52.39 => ( 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)))
% 52.62/52.39 => 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) ) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_transpose__aux__filter__head,axiom,
% 52.62/52.39 ! [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)) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_inj__on__rev,axiom,
% 52.62/52.39 ! [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) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_filter__concat,axiom,
% 52.62/52.39 ! [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)) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_length__concat,axiom,
% 52.62/52.39 ! [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)) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_rev_Osimps_I2_J,axiom,
% 52.62/52.39 ! [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))) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_rev__eq__Cons__iff,axiom,
% 52.62/52.39 ! [V_ys_2,V_y_2,V_xs_2,T_b] :
% 52.62/52.39 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
% 52.62/52.39 <=> 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))) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_concat_Osimps_I2_J,axiom,
% 52.62/52.39 ! [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)) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_singleton__rev__conv,axiom,
% 52.62/52.39 ! [V_xs_2,V_x_2,T_b] :
% 52.62/52.39 ( 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)
% 52.62/52.39 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_rev__singleton__conv,axiom,
% 52.62/52.39 ! [V_x_2,V_xs_2,T_b] :
% 52.62/52.39 ( 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))
% 52.62/52.39 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_Nil__eq__concat__conv,axiom,
% 52.62/52.39 ! [V_xss_2,T_b] :
% 52.62/52.39 ( c_List_Olist_ONil(T_b) = c_List_Oconcat(T_b,V_xss_2)
% 52.62/52.39 <=> ! [B_x] :
% 52.62/52.39 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 52.62/52.39 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_concat__eq__Nil__conv,axiom,
% 52.62/52.39 ! [V_xss_2,T_b] :
% 52.62/52.39 ( c_List_Oconcat(T_b,V_xss_2) = c_List_Olist_ONil(T_b)
% 52.62/52.39 <=> ! [B_x] :
% 52.62/52.39 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 52.62/52.39 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_rev__is__Nil__conv,axiom,
% 52.62/52.39 ! [V_xs_2,T_b] :
% 52.62/52.39 ( hAPP(c_List_Orev(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 52.62/52.39 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_Nil__is__rev__conv,axiom,
% 52.62/52.39 ! [V_xs_2,T_b] :
% 52.62/52.39 ( c_List_Olist_ONil(T_b) = hAPP(c_List_Orev(T_b),V_xs_2)
% 52.62/52.39 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_concat_Osimps_I1_J,axiom,
% 52.62/52.39 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_rev_Osimps_I1_J,axiom,
% 52.62/52.39 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_map__concat,axiom,
% 52.62/52.39 ! [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)) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_rev__map,axiom,
% 52.62/52.39 ! [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)) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_rev__concat,axiom,
% 52.62/52.39 ! [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))) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_concat__conv__foldl,axiom,
% 52.62/52.39 ! [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) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_rev__foldl__cons,axiom,
% 52.62/52.39 ! [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) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_foldl__conv__concat,axiom,
% 52.62/52.39 ! [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)) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_distinct__rev,axiom,
% 52.62/52.39 ! [V_xs_2,T_b] :
% 52.62/52.39 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2)))
% 52.62/52.39 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_concat__append,axiom,
% 52.62/52.39 ! [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)) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_rev__append,axiom,
% 52.62/52.39 ! [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)) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_set__concat,axiom,
% 52.62/52.39 ! [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)) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_length__rev,axiom,
% 52.62/52.39 ! [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) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_listsum__rev,axiom,
% 52.62/52.39 ! [V_xs,T_a] :
% 52.62/52.39 ( class_Groups_Ocomm__monoid__add(T_a)
% 52.62/52.39 => 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) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_rev__rev__ident,axiom,
% 52.62/52.39 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ).
% 52.62/52.39
% 52.62/52.39 fof(fact_rev__swap,axiom,
% 52.62/52.39 ! [V_ys_2,V_xs_2,T_b] :
% 52.62/52.39 ( hAPP(c_List_Orev(T_b),V_xs_2) = V_ys_2
% 52.62/52.39 <=> V_xs_2 = hAPP(c_List_Orev(T_b),V_ys_2) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_rev__is__rev__conv,axiom,
% 52.62/52.39 ! [V_ys_2,V_xs_2,T_b] :
% 52.62/52.39 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Orev(T_b),V_ys_2)
% 52.62/52.39 <=> V_xs_2 = V_ys_2 ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_foldl__foldr,axiom,
% 52.62/52.39 ! [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) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_foldr__foldl,axiom,
% 52.62/52.39 ! [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)) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_set__rev,axiom,
% 52.62/52.39 ! [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) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_zip__rev,axiom,
% 52.62/52.39 ! [V_ys,T_b,V_xs,T_a] :
% 52.62/52.39 ( 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)
% 52.62/52.39 => 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)) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_rev__filter,axiom,
% 52.62/52.39 ! [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)) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_hd__rev,axiom,
% 52.62/52.39 ! [T_a,V_xs] :
% 52.62/52.39 ( V_xs != c_List_Olist_ONil(T_a)
% 52.62/52.39 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_last__rev,axiom,
% 52.62/52.39 ! [T_a,V_xs] :
% 52.62/52.39 ( V_xs != c_List_Olist_ONil(T_a)
% 52.62/52.39 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_sorted__transpose,axiom,
% 52.62/52.39 ! [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)))) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_rev__take,axiom,
% 52.62/52.39 ! [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)) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_rev__drop,axiom,
% 52.62/52.39 ! [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)) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_rotate__rev,axiom,
% 52.62/52.39 ! [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)) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_transpose_Osimps_I3_J,axiom,
% 52.62/52.39 ! [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))))) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_rev__nth,axiom,
% 52.62/52.39 ! [V_xs,T_a,V_n] :
% 52.62/52.39 ( 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)))
% 52.62/52.39 => 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))) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_concat__injective,axiom,
% 52.62/52.39 ! [V_ys_2,V_xs_2,T_b] :
% 52.62/52.39 ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 52.62/52.39 => ( 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)
% 52.62/52.39 => ( ! [B_x] :
% 52.62/52.39 ( 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))))
% 52.62/52.39 => 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)) )
% 52.62/52.39 => V_xs_2 = V_ys_2 ) ) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_concat__eq__concat__iff,axiom,
% 52.62/52.39 ! [V_ys_2,V_xs_2,T_b] :
% 52.62/52.39 ( ! [B_x] :
% 52.62/52.39 ( 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))))
% 52.62/52.39 => 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)) )
% 52.62/52.39 => ( 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)
% 52.62/52.39 => ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 52.62/52.39 <=> V_xs_2 = V_ys_2 ) ) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_rev__update,axiom,
% 52.62/52.39 ! [V_y,V_xs,T_a,V_k] :
% 52.62/52.39 ( 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)))
% 52.62/52.39 => 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) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_concat__map__singleton,axiom,
% 52.62/52.39 ! [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) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_sorted__rev__nth__mono,axiom,
% 52.62/52.39 ! [V_j,V_i,V_xs,T_a] :
% 52.62/52.39 ( class_Orderings_Olinorder(T_a)
% 52.62/52.39 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs))
% 52.62/52.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 52.62/52.39 => ( 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)))
% 52.62/52.39 => 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))) ) ) ) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_foldr__max__sorted,axiom,
% 52.62/52.39 ! [V_y_2,V_xs_2,T_b] :
% 52.62/52.39 ( class_Orderings_Olinorder(T_b)
% 52.62/52.39 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),V_xs_2))
% 52.62/52.39 => ( ( V_xs_2 = c_List_Olist_ONil(T_b)
% 52.62/52.39 => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = V_y_2 )
% 52.62/52.39 & ( V_xs_2 != c_List_Olist_ONil(T_b)
% 52.62/52.39 => 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) ) ) ) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_transpose_Opsimps_I3_J,axiom,
% 52.62/52.39 ! [V_xss_2,V_xs_2,V_x_2,T_b] :
% 52.62/52.39 ( 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)))
% 52.62/52.39 => 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))))) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_length__transpose__sorted,axiom,
% 52.62/52.39 ! [V_xs_2,T_b] :
% 52.62/52.39 ( 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)))
% 52.62/52.39 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 52.62/52.39 => 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) )
% 52.62/52.39 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_b))
% 52.62/52.39 => 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))) ) ) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_transpose__column__length,axiom,
% 52.62/52.39 ! [V_i_2,V_xs_2,T_b] :
% 52.62/52.39 ( 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)))
% 52.62/52.39 => ( 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)))
% 52.62/52.39 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2)) ) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_transpose__aux__filter__tail,axiom,
% 52.62/52.39 ! [V_xss_2,T_b] : c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Otl(T_b)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xss_2)) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_nth__nth__transpose__sorted,axiom,
% 52.62/52.39 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 52.62/52.39 ( 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)))
% 52.62/52.39 => ( 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))))
% 52.62/52.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_xs_2))))
% 52.62/52.39 => hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),c_List_Otranspose(T_b,V_xs_2)),V_i_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_j_2)),V_i_2) ) ) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_transpose__transpose,axiom,
% 52.62/52.39 ! [V_xs_2,T_b] :
% 52.62/52.39 ( 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)))
% 52.62/52.39 => c_List_Otranspose(T_b,c_List_Otranspose(T_b,V_xs_2)) = c_List_OtakeWhile(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b))),V_xs_2) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_transfer__nat__int__list__functions_I2_J,axiom,
% 52.62/52.39 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_takeWhile__map,axiom,
% 52.62/52.39 ! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OtakeWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2),V_xs_2)) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_return__list__def,axiom,
% 52.62/52.39 ! [V_l_2] : c_List_Oreturn__list(V_l_2) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),V_l_2) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_zip__takeWhile__snd,axiom,
% 52.62/52.39 ! [V_ys_2,V_P_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),c_List_OtakeWhile(T_c,V_P_2,V_ys_2)) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_c,tc_HOL_Obool,tc_prod(T_b,T_c),V_P_2),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_zip__takeWhile__fst,axiom,
% 52.62/52.39 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),V_ys_2) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,tc_prod(T_b,T_c),V_P_2),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_set__takeWhileD,axiom,
% 52.62/52.39 ! [V_xs_2,V_P_2,V_x_2,T_b] :
% 52.62/52.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))))
% 52.62/52.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.62/52.39 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_takeWhile__eq__all__conv,axiom,
% 52.62/52.39 ! [V_xs_2,V_P_2,T_b] :
% 52.62/52.39 ( c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = V_xs_2
% 52.62/52.39 <=> ! [B_x] :
% 52.62/52.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.62/52.39 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_length__takeWhile__le,axiom,
% 52.62/52.39 ! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_takeWhile__eq__take,axiom,
% 52.62/52.39 ! [V_xs_2,V_P_2,T_b] : c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))),V_xs_2) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_distinct__takeWhile,axiom,
% 52.62/52.39 ! [V_P_2,V_xs_2,T_b] :
% 52.62/52.39 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 52.62/52.39 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_takeWhile_Osimps_I1_J,axiom,
% 52.62/52.39 ! [V_P_2,T_b] : c_List_OtakeWhile(T_b,V_P_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_sorted__takeWhile,axiom,
% 52.62/52.39 ! [V_P_2,V_xs_2,T_b] :
% 52.62/52.39 ( class_Orderings_Olinorder(T_b)
% 52.62/52.39 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 52.62/52.39 => c_List_Olinorder__class_Osorted(T_b,c_List_OtakeWhile(T_b,V_P_2,V_xs_2)) ) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_takeWhile_Osimps_I2_J,axiom,
% 52.62/52.39 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 52.62/52.39 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 52.62/52.39 => c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)) )
% 52.62/52.39 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 52.62/52.39 => c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_b) ) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_takeWhile__tail,axiom,
% 52.62/52.39 ! [V_l_2,V_xs_2,T_b,V_x_2,V_P_2] :
% 52.62/52.39 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 52.62/52.39 => c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2))) = c_List_OtakeWhile(T_b,V_P_2,V_xs_2) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_takeWhile__append1,axiom,
% 52.62/52.39 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_b] :
% 52.62/52.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 52.62/52.39 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 52.62/52.39 => c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_b,V_P_2,V_xs_2) ) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_takeWhile__nth,axiom,
% 52.62/52.39 ! [V_xs_2,V_P_2,T_b,V_j_2] :
% 52.62/52.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))))
% 52.62/52.39 => hAPP(hAPP(c_List_Onth(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_nth__length__takeWhile,axiom,
% 52.62/52.39 ! [V_xs_2,V_P_2,T_b] :
% 52.62/52.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 52.62/52.39 => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))))) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_map__upds__def,axiom,
% 52.62/52.39 ! [V_ys_2,V_xs_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2) = c_Map_Omap__add(T_b,T_c,V_m_2,c_Map_Omap__of(T_b,T_c,hAPP(c_List_Orev(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)))) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_takeWhile__not__last,axiom,
% 52.62/52.39 ! [T_b,V_xs_2] :
% 52.62/52.39 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 52.62/52.39 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 52.62/52.39 => c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),c_List_Olast(T_b,V_xs_2))),V_xs_2) = c_List_Obutlast(T_b,V_xs_2) ) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_filter__equals__takeWhile__sorted__rev,axiom,
% 52.62/52.39 ! [V_t_2,V_xs_2,V_f_2,T_c,T_b] :
% 52.62/52.39 ( class_Orderings_Olinorder(T_b)
% 52.62/52.39 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
% 52.62/52.39 => hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2)),V_xs_2) = c_List_OtakeWhile(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2),V_xs_2) ) ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_transfer__nat__int__list__return__embed,axiom,
% 52.62/52.39 ! [V_l] :
% 52.62/52.39 ( c_List_Onat__list(V_l)
% 52.62/52.39 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ).
% 52.62/52.39
% 52.62/52.39 fof(fact_length__remdups__concat,axiom,
% 52.62/52.39 ! [V_xss_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,c_List_Oconcat(T_b,V_xss_2))) = hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)),c_List_Oset(T_b))) ).
% 52.62/52.39
% 52.62/52.39 %----Arity declarations (201)
% 52.62/52.39 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom,
% 52.62/52.39 class_Lattices_Obounded__lattice(tc_HOL_Obool) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_fun__Lattices_Obounded__lattice,axiom,
% 52.62/52.39 ! [T_2,T_1] :
% 52.62/52.39 ( class_Lattices_Obounded__lattice(T_1)
% 52.62/52.39 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
% 52.62/52.39 ! [T_2,T_1] :
% 52.62/52.39 ( class_Complete__Lattice_Ocomplete__lattice(T_1)
% 52.62/52.39 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_fun__Lattices_Obounded__lattice__top,axiom,
% 52.62/52.39 ! [T_2,T_1] :
% 52.62/52.39 ( class_Lattices_Obounded__lattice(T_1)
% 52.62/52.39 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
% 52.62/52.39 ! [T_2,T_1] :
% 52.62/52.39 ( class_Lattices_Obounded__lattice(T_1)
% 52.62/52.39 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_fun__Lattices_Osemilattice__sup,axiom,
% 52.62/52.39 ! [T_2,T_1] :
% 52.62/52.39 ( class_Lattices_Olattice(T_1)
% 52.62/52.39 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_fun__Lattices_Osemilattice__inf,axiom,
% 52.62/52.39 ! [T_2,T_1] :
% 52.62/52.39 ( class_Lattices_Olattice(T_1)
% 52.62/52.39 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_fun__Lattices_Odistrib__lattice,axiom,
% 52.62/52.39 ! [T_2,T_1] :
% 52.62/52.39 ( class_Lattices_Odistrib__lattice(T_1)
% 52.62/52.39 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_fun__Lattices_Oboolean__algebra,axiom,
% 52.62/52.39 ! [T_2,T_1] :
% 52.62/52.39 ( class_Lattices_Oboolean__algebra(T_1)
% 52.62/52.39 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_fun__Orderings_Opreorder,axiom,
% 52.62/52.39 ! [T_2,T_1] :
% 52.62/52.39 ( class_Orderings_Opreorder(T_1)
% 52.62/52.39 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_fun__Finite__Set_Ofinite,axiom,
% 52.62/52.39 ! [T_1,T_2] :
% 52.62/52.39 ( ( class_Finite__Set_Ofinite(T_2)
% 52.62/52.39 & class_Finite__Set_Ofinite(T_1) )
% 52.62/52.39 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_fun__Lattices_Olattice,axiom,
% 52.62/52.39 ! [T_2,T_1] :
% 52.62/52.39 ( class_Lattices_Olattice(T_1)
% 52.62/52.39 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_fun__Orderings_Oorder,axiom,
% 52.62/52.39 ! [T_2,T_1] :
% 52.62/52.39 ( class_Orderings_Oorder(T_1)
% 52.62/52.39 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_fun__Orderings_Otop,axiom,
% 52.62/52.39 ! [T_2,T_1] :
% 52.62/52.39 ( class_Orderings_Otop(T_1)
% 52.62/52.39 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_fun__Orderings_Oord,axiom,
% 52.62/52.39 ! [T_2,T_1] :
% 52.62/52.39 ( class_Orderings_Oord(T_1)
% 52.62/52.39 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_fun__Orderings_Obot,axiom,
% 52.62/52.39 ! [T_2,T_1] :
% 52.62/52.39 ( class_Orderings_Obot(T_1)
% 52.62/52.39 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_fun__Groups_Ouminus,axiom,
% 52.62/52.39 ! [T_2,T_1] :
% 52.62/52.39 ( class_Groups_Ouminus(T_1)
% 52.62/52.39 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_fun__Groups_Ominus,axiom,
% 52.62/52.39 ! [T_2,T_1] :
% 52.62/52.39 ( class_Groups_Ominus(T_1)
% 52.62/52.39 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 52.62/52.39 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 52.62/52.39 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 52.62/52.39 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 52.62/52.39 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 52.62/52.39 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom,
% 52.62/52.39 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 52.62/52.39 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 52.62/52.39 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 52.62/52.39 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 52.62/52.39 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 52.62/52.39 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 52.62/52.39 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 52.62/52.39 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 52.62/52.39 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 52.62/52.39 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 52.62/52.39 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 52.62/52.39 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 52.62/52.39 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 52.62/52.39 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 52.62/52.39 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 52.62/52.39 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 52.62/52.39 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom,
% 52.62/52.39 class_Lattices_Osemilattice__sup(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom,
% 52.62/52.39 class_Lattices_Osemilattice__inf(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom,
% 52.62/52.39 class_Lattices_Odistrib__lattice(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 52.62/52.39 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 52.62/52.39 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 52.62/52.39 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 52.62/52.39 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
% 52.62/52.39 class_Rings_Oordered__ring__abs(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 52.62/52.39 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 52.62/52.39 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 52.62/52.39 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 52.62/52.39 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 52.62/52.39 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom,
% 52.62/52.39 class_Groups_Osemigroup__add(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
% 52.62/52.39 class_Divides_Osemiring__div(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 52.62/52.39 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom,
% 52.62/52.39 class_Nat_Osemiring__char__0(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 52.62/52.39 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 52.62/52.39 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 52.62/52.39 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 52.62/52.39 class_Orderings_Opreorder(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 52.62/52.39 class_Orderings_Olinorder(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 52.62/52.39 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 52.62/52.39 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 52.62/52.39 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Smallcheck_Osmall,axiom,
% 52.62/52.39 class_Smallcheck_Osmall(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
% 52.62/52.39 class_Rings_Osemiring__1(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 52.62/52.39 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Lattices_Olattice,axiom,
% 52.62/52.39 class_Lattices_Olattice(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 52.62/52.39 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Divides_Oring__div,axiom,
% 52.62/52.39 class_Divides_Oring__div(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 52.62/52.39 class_Rings_Omult__zero(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
% 52.62/52.39 class_Rings_Ocomm__ring(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 52.62/52.39 class_Orderings_Oorder(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 52.62/52.39 class_Int_Oring__char__0(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Int_Onumber__ring,axiom,
% 52.62/52.39 class_Int_Onumber__ring(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 52.62/52.39 class_Rings_Osemiring(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 52.62/52.39 class_Orderings_Oord(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Groups_Ouminus,axiom,
% 52.62/52.39 class_Groups_Ouminus(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Groups_Osgn__if,axiom,
% 52.62/52.39 class_Groups_Osgn__if(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Groups_Oabs__if,axiom,
% 52.62/52.39 class_Groups_Oabs__if(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 52.62/52.39 class_Rings_Oring__1(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Groups_Ominus,axiom,
% 52.62/52.39 class_Groups_Ominus(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Power_Opower,axiom,
% 52.62/52.39 class_Power_Opower(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 52.62/52.39 class_Groups_Ozero(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Rings_Oring,axiom,
% 52.62/52.39 class_Rings_Oring(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 52.62/52.39 class_Rings_Oidom(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Int_Onumber,axiom,
% 52.62/52.39 class_Int_Onumber(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Groups_Oone,axiom,
% 52.62/52.39 class_Groups_Oone(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Int__Oint__Rings_Odvd,axiom,
% 52.62/52.39 class_Rings_Odvd(tc_Int_Oint) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 52.62/52.39 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 52.62/52.39 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 52.62/52.39 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 52.62/52.39 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom,
% 52.62/52.39 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 52.62/52.39 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 52.62/52.39 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 52.62/52.39 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 52.62/52.39 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 52.62/52.39 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 52.62/52.39 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 52.62/52.39 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 52.62/52.39 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 52.62/52.39 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom,
% 52.62/52.39 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom,
% 52.62/52.39 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom,
% 52.62/52.39 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 52.62/52.39 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 52.62/52.39 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 52.62/52.39 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 52.62/52.39 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 52.62/52.39 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 52.62/52.39 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 52.62/52.39 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom,
% 52.62/52.39 class_Groups_Osemigroup__add(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
% 52.62/52.39 class_Divides_Osemiring__div(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 52.62/52.39 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Orderings_Owellorder,axiom,
% 52.62/52.39 class_Orderings_Owellorder(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom,
% 52.62/52.39 class_Nat_Osemiring__char__0(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 52.62/52.39 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 52.62/52.39 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 52.62/52.39 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 52.62/52.39 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 52.62/52.39 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
% 52.62/52.39 class_Rings_Osemiring__1(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 52.62/52.39 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Lattices_Olattice,axiom,
% 52.62/52.39 class_Lattices_Olattice(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 52.62/52.39 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 52.62/52.39 class_Orderings_Oorder(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 52.62/52.39 class_Rings_Osemiring(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 52.62/52.39 class_Orderings_Oord(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Orderings_Obot,axiom,
% 52.62/52.39 class_Orderings_Obot(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Groups_Ominus,axiom,
% 52.62/52.39 class_Groups_Ominus(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Power_Opower,axiom,
% 52.62/52.39 class_Power_Opower(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 52.62/52.39 class_Groups_Ozero(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Int_Onumber,axiom,
% 52.62/52.39 class_Int_Onumber(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 52.62/52.39 class_Groups_Oone(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Nat__Onat__Rings_Odvd,axiom,
% 52.62/52.39 class_Rings_Odvd(tc_Nat_Onat) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom,
% 52.62/52.39 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom,
% 52.62/52.39 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom,
% 52.62/52.39 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom,
% 52.62/52.39 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom,
% 52.62/52.39 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom,
% 52.62/52.39 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
% 52.62/52.39 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 52.62/52.39 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
% 52.62/52.39 class_Finite__Set_Ofinite(tc_HOL_Obool) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_HOL__Obool__Lattices_Olattice,axiom,
% 52.62/52.39 class_Lattices_Olattice(tc_HOL_Obool) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 52.62/52.39 class_Orderings_Oorder(tc_HOL_Obool) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_HOL__Obool__Orderings_Otop,axiom,
% 52.62/52.39 class_Orderings_Otop(tc_HOL_Obool) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 52.62/52.39 class_Orderings_Oord(tc_HOL_Obool) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_HOL__Obool__Orderings_Obot,axiom,
% 52.62/52.39 class_Orderings_Obot(tc_HOL_Obool) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_HOL__Obool__Groups_Ouminus,axiom,
% 52.62/52.39 class_Groups_Ouminus(tc_HOL_Obool) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_HOL__Obool__Groups_Ominus,axiom,
% 52.62/52.39 class_Groups_Ominus(tc_HOL_Obool) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_sum__Finite__Set_Ofinite,axiom,
% 52.62/52.39 ! [T_1,T_2] :
% 52.62/52.39 ( ( class_Finite__Set_Ofinite(T_2)
% 52.62/52.39 & class_Finite__Set_Ofinite(T_1) )
% 52.62/52.39 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
% 52.62/52.39 ! [T_1] :
% 52.62/52.39 ( class_Finite__Set_Ofinite(T_1)
% 52.62/52.39 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_prod__Finite__Set_Ofinite,axiom,
% 52.62/52.39 ! [T_1,T_2] :
% 52.62/52.39 ( ( class_Finite__Set_Ofinite(T_2)
% 52.62/52.39 & class_Finite__Set_Ofinite(T_1) )
% 52.62/52.39 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_prod__Smallcheck_Osmall,axiom,
% 52.62/52.39 ! [T_1,T_2] :
% 52.62/52.39 ( ( class_Smallcheck_Osmall(T_2)
% 52.62/52.39 & class_Smallcheck_Osmall(T_1) )
% 52.62/52.39 => class_Smallcheck_Osmall(tc_prod(T_2,T_1)) ) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
% 52.62/52.39 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Product____Type__Ounit__Smallcheck_Osmall,axiom,
% 52.62/52.39 class_Smallcheck_Osmall(tc_Product__Type_Ounit) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 52.62/52.39 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 52.62/52.39 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom,
% 52.62/52.39 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom,
% 52.62/52.39 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom,
% 52.62/52.39 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom,
% 52.62/52.39 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom,
% 52.62/52.39 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom,
% 52.62/52.39 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom,
% 52.62/52.39 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom,
% 52.62/52.39 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom,
% 52.62/52.39 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom,
% 52.62/52.39 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom,
% 52.62/52.39 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom,
% 52.62/52.39 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom,
% 52.62/52.39 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom,
% 52.62/52.39 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom,
% 52.62/52.39 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom,
% 52.62/52.39 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom,
% 52.62/52.39 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom,
% 52.62/52.39 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom,
% 52.62/52.39 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom,
% 52.62/52.39 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom,
% 52.62/52.39 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom,
% 52.62/52.39 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom,
% 52.62/52.39 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom,
% 52.62/52.39 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom,
% 52.62/52.39 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom,
% 52.62/52.39 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom,
% 52.62/52.39 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom,
% 52.62/52.39 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom,
% 52.62/52.39 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom,
% 52.62/52.39 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom,
% 52.62/52.39 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom,
% 52.62/52.39 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom,
% 52.62/52.39 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom,
% 52.62/52.39 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom,
% 52.62/52.39 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom,
% 52.62/52.39 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom,
% 52.62/52.39 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom,
% 52.62/52.39 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Odvd,axiom,
% 52.62/52.39 class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral) ).
% 52.62/52.39
% 52.62/52.39 %----Helper facts (20)
% 52.62/52.39 fof(help_c__COMBI__1,axiom,
% 52.62/52.39 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ).
% 52.62/52.39
% 52.62/52.39 fof(help_c__COMBK__1,axiom,
% 52.62/52.39 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ).
% 52.62/52.39
% 52.62/52.39 fof(help_c__COMBB__1,axiom,
% 52.62/52.39 ! [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)) ).
% 52.62/52.39
% 52.62/52.39 fof(help_c__COMBC__1,axiom,
% 52.62/52.39 ! [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) ).
% 52.62/52.39
% 52.62/52.39 fof(help_c__COMBS__1,axiom,
% 52.62/52.39 ! [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)) ).
% 52.62/52.39
% 52.62/52.39 fof(help_c__fequal__1,axiom,
% 52.62/52.39 ! [V_y_2,V_x_2] :
% 52.62/52.39 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
% 52.62/52.39 | V_x_2 = V_y_2 ) ).
% 52.62/52.39
% 52.62/52.39 fof(help_c__fequal__2,axiom,
% 52.62/52.39 ! [V_y_2,V_x_2] :
% 52.62/52.39 ( V_x_2 != V_y_2
% 52.62/52.39 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ).
% 52.62/52.39
% 52.62/52.39 fof(help_c__fFalse__1,axiom,
% 52.62/52.39 ~ hBOOL(c_fFalse) ).
% 52.62/52.39
% 52.62/52.39 fof(help_c__fTrue__1,axiom,
% 52.62/52.39 hBOOL(c_fTrue) ).
% 52.62/52.39
% 52.62/52.39 fof(help_c__fNot__1,axiom,
% 52.62/52.39 ! [V_P_2] :
% 52.62/52.39 ( ~ hBOOL(hAPP(c_fNot,V_P_2))
% 52.62/52.39 | ~ hBOOL(V_P_2) ) ).
% 52.62/52.39
% 52.62/52.39 fof(help_c__fNot__2,axiom,
% 52.62/52.39 ! [V_P_2] :
% 52.62/52.39 ( ~ ~ hBOOL(V_P_2)
% 52.62/52.39 | hBOOL(hAPP(c_fNot,V_P_2)) ) ).
% 52.62/52.39
% 52.62/52.39 fof(help_c__fconj__1,axiom,
% 52.62/52.39 ! [V_Q_2,V_P_2] :
% 52.62/52.39 ( ~ hBOOL(V_P_2)
% 52.62/52.39 | ~ hBOOL(V_Q_2)
% 52.62/52.39 | hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ) ).
% 52.62/52.39
% 52.62/52.39 fof(help_c__fconj__2,axiom,
% 52.62/52.39 ! [V_Q_2,V_P_2] :
% 52.62/52.39 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
% 52.62/52.39 | hBOOL(V_P_2) ) ).
% 52.62/52.39
% 52.62/52.39 fof(help_c__fconj__3,axiom,
% 52.62/52.39 ! [V_Q_2,V_P_2] :
% 52.62/52.39 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
% 52.62/52.39 | hBOOL(V_Q_2) ) ).
% 52.62/52.39
% 52.62/52.39 fof(help_c__fdisj__1,axiom,
% 52.62/52.39 ! [V_Q_2,V_P_2] :
% 52.62/52.39 ( ~ hBOOL(V_P_2)
% 52.62/52.39 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ).
% 52.62/52.39
% 52.62/52.39 fof(help_c__fdisj__2,axiom,
% 52.62/52.39 ! [V_P_2,V_Q_2] :
% 52.62/52.39 ( ~ hBOOL(V_Q_2)
% 52.62/52.39 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ).
% 52.62/52.39
% 52.62/52.39 fof(help_c__fdisj__3,axiom,
% 52.62/52.39 ! [V_Q_2,V_P_2] :
% 52.62/52.39 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2))
% 52.62/52.39 | hBOOL(V_P_2)
% 52.62/52.39 | hBOOL(V_Q_2) ) ).
% 52.62/52.39
% 52.62/52.39 fof(help_c__fimplies__1,axiom,
% 52.62/52.39 ! [V_Q_2,V_P_2] :
% 52.62/52.39 ( hBOOL(V_P_2)
% 52.62/52.39 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ).
% 52.62/52.39
% 52.62/52.39 fof(help_c__fimplies__2,axiom,
% 52.62/52.39 ! [V_P_2,V_Q_2] :
% 52.62/52.39 ( ~ hBOOL(V_Q_2)
% 52.62/52.39 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ).
% 52.62/52.39
% 52.62/52.39 fof(help_c__fimplies__3,axiom,
% 52.62/52.39 ! [V_Q_2,V_P_2] :
% 52.62/52.39 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2))
% 52.62/52.39 | ~ hBOOL(V_P_2)
% 52.62/52.39 | hBOOL(V_Q_2) ) ).
% 52.62/52.39
% 52.62/52.39 %----Conjectures (7)
% 52.62/52.39 fof(conj_0,hypothesis,
% 52.62/52.39 ! [B_x] :
% 52.62/52.39 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G))
% 52.62/52.39 => c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,B_x) ) ).
% 52.62/52.39
% 52.62/52.39 fof(conj_1,hypothesis,
% 52.62/52.39 ! [B_Z,B_s] :
% 52.62/52.39 ( v_P(B_Z,B_s)
% 52.62/52.39 => ! [B_s_H] :
% 52.62/52.39 ( c_Natural_Oevaln(v_c,B_s,v_n,B_s_H)
% 52.62/52.39 => v_Q(B_Z,B_s_H) ) ) ).
% 52.62/52.39
% 52.62/52.39 fof(conj_2,hypothesis,
% 52.62/52.39 ! [B_Z,B_s] :
% 52.62/52.39 ( v_Q(B_Z,B_s)
% 52.62/52.39 => ! [B_s_H] :
% 52.62/52.39 ( c_Natural_Oevaln(v_d,B_s,v_n,B_s_H)
% 52.62/52.39 => v_R(B_Z,B_s_H) ) ) ).
% 52.62/52.39
% 52.62/52.39 fof(conj_3,hypothesis,
% 52.62/52.39 v_P(v_Z,v_s) ).
% 52.62/52.39
% 52.62/52.39 fof(conj_4,hypothesis,
% 52.62/52.39 c_Natural_Oevaln(v_c,v_s,v_n,v_s1) ).
% 52.62/52.39
% 52.62/52.39 fof(conj_5,hypothesis,
% 52.62/52.39 c_Natural_Oevaln(v_d,v_s1,v_n,v_s_H) ).
% 52.62/52.39
% 52.62/52.39 fof(conj_6,conjecture,
% 52.62/52.39 v_R(v_Z,v_s_H) ).
% 52.62/52.39
% 52.62/52.39 %------------------------------------------------------------------------------
% 52.62/52.39 %-------------------------------------------
% 52.62/52.39 % Proof found
% 52.62/52.39 % SZS status Theorem for theBenchmark
% 52.62/52.39 % SZS output start Proof
% 52.62/52.40 %ClaNum:10040(EqnAxiom:2806)
% 52.62/52.40 %VarNum:77833(SingletonVarNum:23509)
% 52.62/52.40 %MaxLitNum:8
% 52.62/52.40 %MaxfuncDepth:13
% 52.62/52.40 %SharedTerms:1046
% 52.62/52.40 %goalClause: 4362
% 52.62/52.40 %singleGoalClaCount:1
% 52.62/52.40 [2810]P1(a177)
% 52.62/52.40 [2811]P2(a845)
% 52.62/52.40 [2812]P2(a1)
% 52.62/52.40 [2813]P2(a101)
% 52.62/52.40 [2814]P3(a845)
% 52.62/52.40 [2815]P3(a1)
% 52.62/52.40 [2816]P3(a101)
% 52.62/52.40 [2817]P73(a845)
% 52.62/52.40 [2818]P73(a1)
% 52.62/52.40 [2819]P73(a101)
% 52.62/52.40 [2820]P4(a845)
% 52.62/52.40 [2821]P4(a1)
% 52.62/52.40 [2822]P4(a101)
% 52.62/52.40 [2823]P68(a1)
% 52.62/52.40 [2824]P137(a845)
% 52.62/52.40 [2825]P137(a1)
% 52.62/52.40 [2826]P74(a845)
% 52.62/52.40 [2827]P74(a1)
% 52.62/52.40 [2828]P74(a101)
% 52.62/52.40 [2829]P5(a845)
% 52.62/52.40 [2830]P5(a1)
% 52.62/52.40 [2831]P5(a101)
% 52.62/52.40 [2832]P6(a845)
% 52.62/52.40 [2833]P6(a1)
% 52.62/52.40 [2834]P6(a101)
% 52.62/52.40 [2835]P7(a845)
% 52.62/52.40 [2836]P7(a1)
% 52.62/52.40 [2837]P7(a101)
% 52.62/52.40 [2838]P75(a845)
% 52.62/52.40 [2839]P75(a1)
% 52.62/52.40 [2840]P75(a101)
% 52.62/52.40 [2841]P81(a845)
% 52.62/52.40 [2842]P81(a1)
% 52.62/52.40 [2843]P81(a101)
% 52.62/52.40 [2844]P82(a845)
% 52.62/52.40 [2845]P82(a1)
% 52.62/52.40 [2846]P82(a101)
% 52.62/52.40 [2847]P110(a1)
% 52.62/52.40 [2848]P117(a845)
% 52.62/52.40 [2849]P117(a1)
% 52.62/52.40 [2850]P117(a101)
% 52.62/52.40 [2851]P86(a845)
% 52.62/52.40 [2852]P86(a1)
% 52.62/52.40 [2853]P86(a101)
% 52.62/52.40 [2854]P99(a845)
% 52.62/52.40 [2855]P99(a839)
% 52.62/52.40 [2856]P99(a1)
% 52.62/52.40 [2857]P99(a101)
% 52.62/52.40 [2858]P103(a845)
% 52.62/52.40 [2859]P103(a839)
% 52.62/52.40 [2860]P103(a1)
% 52.62/52.40 [2861]P103(a101)
% 52.62/52.40 [2862]P100(a845)
% 52.62/52.40 [2863]P100(a1)
% 52.62/52.40 [2864]P100(a101)
% 52.62/52.40 [2865]P102(a845)
% 52.62/52.40 [2866]P102(a839)
% 52.62/52.40 [2867]P102(a1)
% 52.62/52.40 [2868]P102(a101)
% 52.62/52.40 [2869]P111(a1)
% 52.62/52.40 [2870]P120(a1)
% 52.62/52.40 [2871]P121(a1)
% 52.62/52.40 [2872]P66(a845)
% 52.62/52.40 [2873]P66(a1)
% 52.62/52.40 [2874]P66(a101)
% 52.62/52.40 [2875]P69(a1)
% 52.62/52.40 [2876]P87(a1)
% 52.62/52.40 [2877]P70(a845)
% 52.62/52.40 [2878]P70(a1)
% 52.62/52.40 [2879]P70(a101)
% 52.62/52.40 [2880]P76(a845)
% 52.62/52.40 [2881]P76(a1)
% 52.62/52.40 [2882]P76(a101)
% 52.62/52.40 [2883]P77(a845)
% 52.62/52.40 [2884]P77(a1)
% 52.62/52.40 [2885]P77(a101)
% 52.62/52.40 [2886]P133(a1)
% 52.62/52.40 [2887]P104(a1)
% 52.62/52.40 [2888]P78(a1)
% 52.62/52.40 [2889]P8(a1)
% 52.62/52.40 [2890]P122(a845)
% 52.62/52.40 [2891]P122(a1)
% 52.62/52.40 [2892]P122(a101)
% 52.62/52.40 [2893]P134(a1)
% 52.62/52.40 [2894]P127(a845)
% 52.62/52.40 [2895]P127(a1)
% 52.62/52.40 [2896]P127(a101)
% 52.62/52.40 [2897]P138(a845)
% 52.62/52.40 [2898]P138(a1)
% 52.62/52.40 [2899]P138(a101)
% 52.62/52.40 [2900]P109(a845)
% 52.62/52.40 [2901]P109(a1)
% 52.62/52.40 [2902]P109(a101)
% 52.62/52.40 [2903]P135(a845)
% 52.62/52.40 [2904]P135(a1)
% 52.62/52.40 [2905]P135(a101)
% 52.62/52.40 [2906]P118(a1)
% 52.62/52.40 [2907]P119(a1)
% 52.62/52.40 [2908]P123(a845)
% 52.62/52.40 [2909]P123(a1)
% 52.62/52.40 [2910]P123(a101)
% 52.62/52.40 [2911]P115(a845)
% 52.62/52.40 [2912]P115(a1)
% 52.62/52.40 [2913]P115(a101)
% 52.62/52.40 [2914]P83(a1)
% 52.62/52.40 [2915]P124(a1)
% 52.62/52.40 [2916]P79(a845)
% 52.62/52.40 [2917]P79(a1)
% 52.62/52.40 [2918]P79(a101)
% 52.62/52.40 [2919]P128(a845)
% 52.62/52.40 [2920]P128(a1)
% 52.62/52.40 [2921]P128(a101)
% 52.62/52.40 [2922]P129(a1)
% 52.62/52.40 [2923]P131(a845)
% 52.62/52.40 [2924]P131(a1)
% 52.62/52.40 [2925]P131(a101)
% 52.62/52.40 [2926]P130(a845)
% 52.62/52.40 [2927]P130(a1)
% 52.62/52.40 [2928]P130(a101)
% 52.62/52.40 [2929]P125(a845)
% 52.62/52.40 [2930]P125(a1)
% 52.62/52.40 [2931]P125(a101)
% 52.62/52.40 [2932]P126(a1)
% 52.62/52.40 [2933]P90(a839)
% 52.62/52.40 [2934]P9(a845)
% 52.62/52.40 [2935]P9(a1)
% 52.62/52.40 [2936]P9(a101)
% 52.62/52.40 [2937]P10(a1)
% 52.62/52.40 [2938]P85(a839)
% 52.62/52.40 [2939]P85(a1)
% 52.62/52.40 [2940]P71(a845)
% 52.62/52.40 [2941]P71(a839)
% 52.62/52.40 [2942]P71(a1)
% 52.62/52.40 [2943]P71(a101)
% 52.62/52.40 [2944]P88(a1)
% 52.62/52.40 [2945]P89(a845)
% 52.62/52.40 [2946]P89(a1)
% 52.62/52.40 [2947]P89(a101)
% 52.62/52.40 [2948]P80(a1)
% 52.62/52.40 [2949]P132(a1)
% 52.62/52.40 [2950]P67(a1)
% 52.62/52.40 [2951]P105(a845)
% 52.62/52.40 [2952]P105(a1)
% 52.62/52.40 [2953]P105(a101)
% 52.62/52.40 [2954]P136(a845)
% 52.62/52.40 [2955]P136(a1)
% 52.62/52.40 [2956]P136(a101)
% 52.62/52.40 [2957]P112(a845)
% 52.62/52.40 [2958]P112(a1)
% 52.62/52.40 [2959]P112(a101)
% 52.62/52.40 [2960]P108(a1)
% 52.62/52.40 [2961]P92(a845)
% 52.62/52.40 [2962]P92(a839)
% 52.62/52.40 [2963]P92(a1)
% 52.62/52.40 [2964]P93(a845)
% 52.62/52.40 [2965]P93(a839)
% 52.62/52.40 [2966]P93(a1)
% 52.62/52.40 [2967]P11(a839)
% 52.62/52.40 [2968]P106(a839)
% 52.62/52.40 [2969]P94(a839)
% 52.62/52.40 [2970]P101(a845)
% 52.62/52.40 [2971]P101(a839)
% 52.62/52.40 [2972]P95(a839)
% 52.62/52.40 [2973]P61(a839)
% 52.62/52.40 [2974]P61(a848)
% 52.62/52.40 [2975]P97(a845)
% 52.62/52.40 [2976]P97(a839)
% 52.62/52.40 [2977]P97(a1)
% 52.62/52.40 [2978]P98(a845)
% 52.62/52.40 [2979]P98(a839)
% 52.62/52.40 [2980]P98(a1)
% 52.62/52.40 [2981]P72(a845)
% 52.62/52.40 [2982]P72(a1)
% 52.62/52.40 [2983]P72(a101)
% 52.62/52.40 [2984]P107(a845)
% 52.62/52.40 [2985]P139(a1)
% 52.62/52.40 [2986]P139(a848)
% 52.62/52.40 [2987]P84(a845)
% 52.62/52.40 [2988]P84(a1)
% 52.62/52.40 [2989]P84(a101)
% 52.62/52.40 [2990]P96(a839)
% 52.62/52.40 [3002]P38(a845,a237)
% 52.62/52.40 [3003]P38(a845,a323)
% 52.62/52.40 [3004]P142(a851,a856)
% 52.62/52.40 [3392]P41(a857,a856,a858,a860)
% 52.62/52.40 [3393]P41(a859,a860,a858,a861)
% 52.62/52.40 [4358]~E(a99,a85)
% 52.62/52.40 [4359]~E(a99,a85)
% 52.62/52.40 [4360]~P1(a178)
% 52.62/52.40 [4362]~P143(a851,a861)
% 52.62/52.40 [2807]E(f2(a1),a85)
% 52.62/52.40 [2808]E(f3(a101),a4)
% 52.62/52.40 [2809]E(f102(a101),a5)
% 52.62/52.40 [2991]E(f34(a25),f2(a845))
% 52.62/52.40 [2992]E(f86(a178),f2(a845))
% 52.62/52.40 [2993]E(f86(a177),f2(a845))
% 52.62/52.40 [2994]E(f179(a845),f103(a845))
% 52.62/52.40 [2995]E(f180(a845),f2(a845))
% 52.62/52.40 [2996]E(f236(a845),f104(a845))
% 52.62/52.40 [2997]E(f105(a1),f39(a1))
% 52.62/52.40 [2998]P12(f2(a1))
% 52.62/52.40 [2999]P12(f80(a1))
% 52.62/52.40 [3041]P1(f332(a26,a25))
% 52.62/52.40 [3042]P1(f332(a26,a25))
% 52.62/52.40 [3051]P38(f852(a845,a845),a40)
% 52.62/52.40 [3080]E(f166(a841,a840,a29),a30)
% 52.62/52.40 [3391]E(f326(a845,a845,a237,a237),a40)
% 52.62/52.40 [4361]~E(f80(a1),f2(a1))
% 52.62/52.40 [3000]E(f113(f2(a845)),f2(a845))
% 52.62/52.40 [3001]E(f6(f2(a101)),f2(a845))
% 52.62/52.40 [3006]E(f332(f81(a1),a85),a85)
% 52.62/52.40 [3009]E(f332(a107,f2(a1)),f2(a845))
% 52.62/52.40 [3010]E(f332(a5,f2(a845)),f2(a101))
% 52.62/52.40 [3011]E(f332(a114,f2(a845)),f80(a845))
% 52.62/52.40 [3012]E(f332(a107,f80(a1)),f80(a845))
% 52.62/52.40 [3013]E(f332(a5,f80(a845)),f80(a101))
% 52.62/52.40 [3014]E(f332(f106(a845),a85),f2(a845))
% 52.62/52.40 [3015]E(f332(f106(a1),a85),f2(a1))
% 52.62/52.40 [3016]E(f332(f106(a101),a85),f2(a101))
% 52.62/52.40 [3017]E(f332(a107,f2(a1)),f2(a845))
% 52.62/52.40 [3018]E(f332(f181(a840),a25),f2(a845))
% 52.62/52.40 [3019]E(f332(f181(a839),a178),f2(a845))
% 52.62/52.40 [3020]E(f332(f181(a839),a177),f2(a845))
% 52.62/52.40 [3021]E(f332(f106(a845),a85),f2(a845))
% 52.62/52.40 [3027]E(f332(f81(a1),f80(a1)),a99)
% 52.62/52.40 [3032]E(f332(f102(a1),f2(a845)),f2(a1))
% 52.62/52.40 [3033]E(f332(f102(a1),f80(a845)),f80(a1))
% 52.62/52.40 [3034]E(f332(f181(a845),f2(a845)),f2(a845))
% 52.62/52.40 [3035]E(f332(f181(a101),f2(a101)),f2(a845))
% 52.62/52.40 [3036]E(f332(f102(a1),f2(a845)),f2(a1))
% 52.62/52.40 [3037]E(f332(f102(a1),f80(a845)),f80(a1))
% 52.62/52.40 [3038]E(f332(f81(a1),f2(a1)),f2(a1))
% 52.62/52.40 [3047]E(f332(a107,f80(a1)),f332(a114,f2(a845)))
% 52.62/52.40 [3049]E(f324(f852(a845,a845),a40),a41)
% 52.62/52.40 [3050]E(f325(f852(a845,a845),a40),a42)
% 52.62/52.40 [3071]E(f332(f257(a845),f2(a845)),f180(f853(a845,a839)))
% 52.62/52.40 [3072]E(f332(f258(a845),f2(a845)),f239(f853(a845,a839)))
% 52.62/52.40 [3082]P40(f180(f853(a1,a839)))
% 52.62/52.40 [3117]E(f332(f332(f3(a101),f2(a101)),f80(a101)),f2(a101))
% 52.62/52.40 [3158]E(f332(f332(f143(a1,a845),a107),f115(a1)),f115(a845))
% 52.62/52.40 [3188]P1(f332(f332(f233(a1),a99),f2(a1)))
% 52.62/52.40 [3213]P1(f332(f332(f233(a1),f2(a1)),f80(a1)))
% 52.62/52.40 [3214]P1(f332(f332(f232(a1),f2(a1)),f2(a1)))
% 52.62/52.40 [3215]P1(f332(f332(f232(a1),f2(a1)),f80(a1)))
% 52.62/52.40 [3382]P1(f332(f64(a841),f169(a841,a840,a30)))
% 52.62/52.40 [3426]E(f332(f332(f281(a845,a845,a845),a323),f300(a845,a323)),a237)
% 52.62/52.40 [3463]P42(a1,a845,a107,f332(f232(a1),f2(a1)))
% 52.62/52.40 [3466]E(f332(f332(f47(a845,f853(a845,a839)),f239(f853(a845,a839))),f257(a845)),f239(f853(a845,a839)))
% 52.62/52.40 [3467]E(f332(f332(f47(a845,f853(a845,a839)),f239(f853(a845,a839))),f293(a845)),f239(f853(a845,a839)))
% 52.62/52.40 [3468]E(f332(f332(f47(a845,f853(a845,a839)),f239(f853(a845,a839))),f258(a845)),f239(f853(a845,a839)))
% 52.62/52.40 [3469]E(f332(f332(f48(a845,f853(a845,a839)),f239(f853(a845,a839))),f296(a845)),f180(f853(a845,a839)))
% 52.62/52.40 [3485]P31(a845,a1,f102(a1),f239(f853(a845,a839)))
% 52.62/52.40 [3498]P42(a845,a1,f102(a1),f332(f18(a839,a845),a177))
% 52.62/52.40 [3629]E(f332(f75(a845,a101,a1,a5),a107),f106(a101))
% 52.62/52.40 [3846]P57(a101,a845,a22,a5,f239(f853(a845,a839)))
% 52.62/52.40 [3854]P57(a1,f853(f852(a845,a845),a839),a110,a91,a100)
% 52.62/52.40 [4123]E(f252(a1,a1,a1,a1,f39(a1),f81(a1)),a59)
% 52.62/52.40 [4393]~E(f332(f106(a1),a99),f332(f106(a1),a85))
% 52.62/52.40 [4394]~P1(f332(a186,f2(a1)))
% 52.62/52.40 [4395]~P1(f332(a186,f80(a1)))
% 52.62/52.40 [4451]~P1(f332(f332(f233(a1),a85),f2(a1)))
% 52.62/52.40 [3063]E(f332(f332(f82(a1),a85),a99),a99)
% 52.62/52.40 [3064]E(f332(f332(f82(a1),a85),a85),a85)
% 52.62/52.40 [3065]E(f332(f332(f3(a1),a99),a99),a85)
% 52.62/52.40 [3079]E(f332(f102(a1),f332(a114,f2(a845))),f80(a1))
% 52.62/52.40 [3141]E(f332(f43(a848),f239(f853(a848,a839))),f80(a845))
% 52.62/52.40 [3163]P1(f332(a186,f332(f106(a1),a99)))
% 52.62/52.40 [3164]P1(f332(f332(f233(a1),a99),a85))
% 52.62/52.40 [3165]P1(f332(f332(f232(a1),a99),a99))
% 52.62/52.40 [3166]P1(f332(f332(f232(a1),a99),a85))
% 52.62/52.40 [3167]P1(f332(f332(f232(a1),a85),a85))
% 52.62/52.40 [3224]E(f332(f332(f302(a845),f2(a845)),f180(f853(a845,a839))),f332(f293(a845),f2(a845)))
% 52.62/52.40 [3280]P1(f332(f332(f232(a1),f2(a1)),f332(f106(a1),a85)))
% 52.62/52.40 [3291]E(f332(f303(a845,a845,a114),f239(f853(a845,a839))),f332(f296(a845),f2(a845)))
% 52.62/52.40 [3296]E(f332(f303(a1,a845,a107),f180(f853(a1,a839))),f180(f853(a845,a839)))
% 52.62/52.40 [3305]E(f332(f303(a845,a1,f102(a1)),f180(f853(a845,a839))),f180(f853(a1,a839)))
% 52.62/52.40 [3329]P14(f852(a845,a845),f239(f853(f852(a845,a845),a839)),a111)
% 52.62/52.40 [3636]E(f332(f75(a845,a1,a101,f102(a1)),a22),a23)
% 52.62/52.40 [3696]P38(a845,f332(f256(f852(a845,a845)),f332(f251(a845,a845,a839),f233(a845))))
% 52.62/52.40 [4442]~P1(f332(a186,f332(f106(a1),a85)))
% 52.62/52.40 [4443]~P1(f332(f332(f233(a1),a99),a99))
% 52.62/52.40 [4444]~P1(f332(f332(f233(a1),a85),a99))
% 52.62/52.40 [4445]~P1(f332(f332(f233(a1),a85),a85))
% 52.62/52.40 [4446]~P1(f332(f332(f232(a1),a85),a99))
% 52.62/52.40 [4461]~P1(f332(f64(a845),f239(f853(a845,a839))))
% 52.62/52.40 [4462]~P1(f332(f64(a1),f239(f853(a1,a839))))
% 52.62/52.40 [4288]E(f332(f251(a1,a1,a839),f332(f332(f10(f853(a1,a839),f853(a1,a839),a1),f332(f20(a1,a839,a839),f332(f332(f10(a839,f853(a839,a839),a1),a330),f332(f233(a1),f2(a1))))),f332(f332(f9(a1,a1,f853(a1,a839)),f332(f332(f10(f853(a1,f853(a1,a839)),f853(a1,f853(a1,a839)),a1),f9(a1,a1,a839)),f332(f332(f10(f853(a1,a1),f853(a1,f853(a1,a839)),a1),f332(f10(a1,f853(a1,a839),a1),a329)),a212))),f80(a1)))),a208)
% 52.62/52.40 [3332]E(f332(f332(f3(a1),f332(f332(f82(a1),a99),a99)),a99),a99)
% 52.62/52.40 [3364]E(f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99),f332(f81(a1),a99))
% 52.62/52.40 [3408]E(f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99),f332(f332(f3(a1),a85),a99))
% 52.62/52.40 [3561]E(f332(f332(f62(f852(a845,a845)),f239(f853(f852(a845,a845),a839))),a111),a100)
% 52.62/52.40 [3590]E(f332(f106(a845),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f80(a845))
% 52.62/52.40 [3591]E(f332(f106(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f80(a1))
% 52.62/52.40 [3592]E(f332(f106(a101),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f80(a101))
% 52.62/52.40 [3593]E(f332(f106(a845),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f80(a845))
% 52.62/52.40 [3596]E(f332(f106(a845),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(a114,f2(a845)))
% 52.62/52.40 [3984]E(f332(f332(f103(f853(f852(f852(a845,a845),f852(a845,a845)),a839)),a40),f300(f852(a845,a845),f180(f853(f852(f852(a845,a845),f852(a845,a845)),a839)))),a72)
% 52.62/52.40 [4055]E(f332(a91,f332(f277(f852(a845,a845),f852(a845,a845),a111),f332(f332(f302(f852(a845,a845)),f332(f332(f241(a845,a845),f2(a845)),f2(a845))),f180(f853(f852(a845,a845),a839))))),f2(a1))
% 52.62/52.40 [4056]E(f332(a91,f332(f277(f852(a845,a845),f852(a845,a845),a111),f332(f332(f302(f852(a845,a845)),f332(f332(f241(a845,a845),f80(a845)),f2(a845))),f180(f853(f852(a845,a845),a839))))),f80(a1))
% 52.62/52.40 [4070]E(f332(f256(f852(a845,a845)),f332(f251(a845,a845,a839),f332(f332(f10(a845,f853(a845,a839),a845),f332(f9(a845,a845,a839),a329)),a114))),a323)
% 52.62/52.40 [4038]E(f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))),f332(a114,f332(a114,f2(a845))))
% 52.62/52.40 [4039]E(f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))),f332(a114,f332(a114,f2(a845))))
% 52.62/52.40 [4042]E(f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))),f332(f332(f82(a845),f80(a845)),f80(a845)))
% 52.62/52.40 [4043]E(f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))),f332(f43(a839),f239(f853(a839,a839))))
% 52.62/52.40 [4108]P12(f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))
% 52.62/52.40 [4182]P32(f853(f852(a845,a845),a839),f332(f332(f241(f853(f852(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839)),a839),f853(f852(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839)),a839)),a41),a73))
% 52.62/52.40 [4183]P32(f853(f852(a845,a845),a839),f332(f332(f241(f853(f852(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839)),a839),f853(f852(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839)),a839)),a42),a71))
% 52.62/52.40 [4220]E(f332(f332(f103(f853(f852(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839)),a839)),f325(f852(a845,a845),a72)),f332(f332(f302(f852(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839))),f332(f332(f241(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839)),f180(f853(f852(a845,a845),a839))),f180(f853(f852(a845,a845),a839)))),f180(f853(f852(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839)),a839)))),a71)
% 52.62/52.40 [4221]E(f332(f332(f103(f853(f852(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839)),a839)),f324(f852(a845,a845),a72)),f332(f332(f302(f852(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839))),f332(f332(f241(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839)),f180(f853(f852(a845,a845),a839))),f180(f853(f852(a845,a845),a839)))),f180(f853(f852(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839)),a839)))),a73)
% 52.62/52.40 [4110]E(f332(a107,f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f332(a114,f332(a114,f2(a845))))
% 52.62/52.40 [4158]E(f332(a107,f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))
% 52.62/52.40 [4159]E(f332(f102(a1),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))
% 52.62/52.40 [4192]P1(f332(f332(f232(a1),f2(a1)),f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))))
% 52.62/52.40 [4193]E(f332(f106(a845),f332(f332(f3(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))),a99)),f332(a114,f332(a114,f332(a114,f2(a845)))))
% 52.62/52.40 [4233]P12(f332(f106(a1),f332(f332(f3(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))),a99)))
% 52.62/52.40 [4259]E(f332(a107,f332(f106(a1),f332(f332(f3(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))),a99))),f332(f106(a845),f332(f332(f3(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))),a99)))
% 52.62/52.40 [4260]E(f332(f102(a1),f332(f106(a845),f332(f332(f3(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))),a99))),f332(f106(a1),f332(f332(f3(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))),a99)))
% 52.62/52.40 [4274]P1(f332(f332(f232(a1),f2(a1)),f332(f106(a1),f332(f332(f3(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))),a99))))
% 52.62/52.40 [3005]P13(x30051,a329)
% 52.62/52.40 [3394]P31(a845,a845,a114,x33941)
% 52.62/52.40 [3022]P38(a1,f108(x30221))
% 52.62/52.40 [3023]P38(a1,f109(x30231))
% 52.62/52.40 [3026]P39(x30261,f183(x30261))
% 52.62/52.40 [3068]P38(f853(x30681,a839),f299(x30681))
% 52.62/52.40 [3108]E(f53(a1,x31081,x31081),f2(a1))
% 52.62/52.40 [3160]P21(x31601,f853(x31601,a839),f302(x31601))
% 52.62/52.40 [4363]~E(f332(a27,x43631),a25)
% 52.62/52.40 [4364]~E(f332(a27,x43641),a25)
% 52.62/52.40 [4365]~E(f332(a114,x43651),x43651)
% 52.62/52.40 [4366]~E(f332(a114,x43661),x43661)
% 52.62/52.40 [4373]~E(f332(a114,x43731),f2(a845))
% 52.62/52.40 [4374]~E(f332(a114,x43741),f2(a845))
% 52.62/52.40 [4375]~E(f332(a114,x43751),f2(a845))
% 52.62/52.40 [4376]~E(f332(a114,x43761),f2(a845))
% 52.62/52.40 [4377]~E(f332(a114,x43771),f2(a845))
% 52.62/52.40 [4378]~E(f332(a114,x43781),f2(a845))
% 52.62/52.40 [3007]E(f332(f181(a845),x30071),x30071)
% 52.62/52.40 [3008]E(f332(f106(a1),x30081),x30081)
% 52.62/52.40 [3024]E(f332(a91,f333(x30241)),x30241)
% 52.62/52.40 [3025]E(f238(x30251,f2(a101)),f2(a101))
% 52.62/52.40 [3039]E(f116(x30391,f115(x30391)),f115(x30391))
% 52.62/52.40 [3043]E(f34(f332(a27,x30431)),f2(a845))
% 52.62/52.40 [3044]E(f332(f141(x30441),f115(x30441)),f115(x30441))
% 52.62/52.40 [3045]E(f332(f157(x30451),f115(x30451)),f115(x30451))
% 52.62/52.40 [3046]E(f332(f142(x30461),f115(x30461)),f115(x30461))
% 52.62/52.40 [3052]E(f332(f106(a1),x30521),f332(f105(a1),x30521))
% 52.62/52.40 [3053]E(f332(a5,f332(a22,x30531)),x30531)
% 52.62/52.40 [3054]E(f332(a5,f332(a22,x30541)),x30541)
% 52.62/52.40 [3055]E(f332(a22,f332(a5,x30551)),x30551)
% 52.62/52.40 [3056]E(f332(a91,f332(a110,x30561)),x30561)
% 52.62/52.40 [3057]P12(f332(f102(a1),x30571))
% 52.62/52.40 [3061]E(f332(f181(f849(x30611)),f183(x30611)),f2(a845))
% 52.62/52.40 [3062]E(f332(f181(f846(x30621)),f115(x30621)),f2(a845))
% 52.62/52.40 [3067]E(f332(f181(a840),f332(a27,x30671)),f2(a845))
% 52.62/52.40 [3077]E(f226(x30771,f183(x30771)),f180(f853(x30771,a839)))
% 52.62/52.40 [3085]E(f332(f332(f82(a845),x30851),f2(a845)),x30851)
% 52.62/52.40 [3086]E(f332(f332(f82(a1),x30861),f2(a1)),x30861)
% 52.62/52.40 [3087]E(f332(f332(f83(a845),x30871),f80(a845)),x30871)
% 52.62/52.40 [3088]E(f332(f332(f83(a1),x30881),f80(a1)),x30881)
% 52.62/52.40 [3089]E(f332(f332(f3(a845),x30891),f2(a845)),x30891)
% 52.62/52.40 [3090]E(f332(f332(f179(a845),x30901),f2(a845)),x30901)
% 52.62/52.40 [3091]E(f332(f332(f83(a845),x30911),f2(a845)),f2(a845))
% 52.62/52.40 [3092]E(f332(f332(f44(a1),x30921),f2(a1)),f2(a1))
% 52.62/52.40 [3093]E(f332(f332(f236(a845),x30931),f2(a845)),f2(a845))
% 52.62/52.40 [3099]E(f332(f158(x30991),f115(x30991)),f180(f853(x30991,a839)))
% 52.62/52.40 [3103]P1(f332(f127(x31031),f115(x31031)))
% 52.62/52.40 [3109]E(f332(f143(x31091,x31091),f7(x31091)),f39(f846(x31091)))
% 52.62/52.40 [3110]E(f332(f143(x31101,x31101),f39(x31101)),f39(f846(x31101)))
% 52.62/52.40 [3111]E(f332(f196(x31111,x31111),f7(x31111)),f39(f849(x31111)))
% 52.62/52.40 [3112]E(f332(f196(x31121,x31121),f39(x31121)),f39(f849(x31121)))
% 52.62/52.40 [3113]E(f53(a1,x31131,f2(a1)),x31131)
% 52.62/52.40 [3114]E(f332(f232(a845),f332(a114,x31141)),f332(f233(a845),x31141))
% 52.62/52.40 [3115]E(f332(f257(a845),f332(a114,x31151)),f332(f293(a845),x31151))
% 52.62/52.40 [3116]E(f332(f258(a845),f332(a114,x31161)),f332(f296(a845),x31161))
% 52.62/52.40 [3118]E(f53(a1,f2(a1),x31181),f2(a1))
% 52.62/52.40 [3125]E(f332(f332(f82(a845),x31251),f80(a845)),f332(a114,x31251))
% 52.62/52.40 [3135]E(f332(f294(a845,x31351),f2(a845)),f180(f853(a845,a839)))
% 52.62/52.40 [3146]E(f295(a845,f2(a845),x31461),f332(f293(a845),x31461))
% 52.62/52.40 [3191]E(f332(f332(f3(a845),f332(a114,x31911)),f80(a845)),x31911)
% 52.62/52.40 [3204]E(f55(f2(a1),x32041),f332(f332(f241(a1,a1),f2(a1)),f2(a1)))
% 52.62/52.40 [3208]E(f332(f332(f82(a845),f332(a22,x32081)),f2(a845)),f332(a22,x32081))
% 52.62/52.40 [3254]P1(f332(f332(f233(a845),x32541),f332(a114,x32541)))
% 52.62/52.40 [3268]P1(f332(f332(f233(a845),f2(a845)),f332(a114,x32681)))
% 52.62/52.40 [3278]E(f332(f332(f173(f846(x32781),f846(x32781)),f2(a845)),f141(x32781)),f39(f846(x32781)))
% 52.62/52.40 [3548]E(f332(f332(f3(a101),f332(a5,f332(a114,f332(a22,x35481)))),f80(a101)),x35481)
% 52.62/52.40 [3618]P1(f332(f332(f232(a1),f332(f81(a1),f332(f102(a1),x36181))),f2(a1)))
% 52.62/52.40 [3770]P1(f332(f332(f233(a1),f332(f81(a1),f332(f102(a1),f332(a114,x37701)))),f2(a1)))
% 52.62/52.40 [4401]~E(f239(f853(x44011,a839)),f180(f853(x44011,a839)))
% 52.62/52.40 [4452]~P1(f332(f332(f233(a845),x44521),f2(a845)))
% 52.62/52.40 [4453]~P1(f332(f332(f233(a845),x44531),f2(a845)))
% 52.62/52.40 [4454]~P1(f332(f332(f233(a845),x44541),f2(a845)))
% 52.62/52.40 [4470]~P1(f332(f332(f233(a1),f332(f102(a1),x44701)),f2(a1)))
% 52.62/52.40 [3066]E(f164(x30661,f115(f846(x30661))),f115(f846(x30661)))
% 52.62/52.40 [3069]E(f332(f332(f83(a1),a85),x30691),a85)
% 52.62/52.40 [3070]E(f332(f332(f82(a1),a85),x30701),x30701)
% 52.62/52.40 [3073]E(f332(a107,f332(f102(a1),x30731)),x30731)
% 52.62/52.40 [3074]E(f332(f332(f82(a1),x30741),a85),x30741)
% 52.62/52.40 [3075]E(f332(f332(f3(a1),x30751),a85),x30751)
% 52.62/52.40 [3078]E(f332(f332(f3(a845),x30781),x30781),f2(a845))
% 52.62/52.40 [3083]E(f332(f81(a1),f332(f81(a1),x30831)),x30831)
% 52.62/52.40 [3084]E(f332(f43(a845),f332(f257(a845),x30841)),x30841)
% 52.62/52.40 [3094]E(f332(f332(f82(a845),f2(a845)),x30941),x30941)
% 52.62/52.40 [3095]E(f332(f332(f82(a1),f2(a1)),x30951),x30951)
% 52.62/52.40 [3096]E(f332(f332(f83(a845),f80(a845)),x30961),x30961)
% 52.62/52.40 [3097]E(f332(f332(f83(a1),f80(a1)),x30971),x30971)
% 52.62/52.40 [3098]E(f332(f332(f179(a845),f2(a845)),x30981),x30981)
% 52.62/52.40 [3104]E(f332(f332(f83(a845),f2(a845)),x31041),f2(a845))
% 52.62/52.40 [3105]E(f332(f332(f44(a1),f2(a1)),x31051),f2(a1))
% 52.62/52.40 [3106]E(f332(f332(f3(a845),f2(a845)),x31061),f2(a845))
% 52.62/52.40 [3107]E(f332(f332(f236(a845),f2(a845)),x31071),f2(a845))
% 52.62/52.40 [3123]E(f332(f294(a845,f2(a845)),x31231),f332(f257(a845),x31231))
% 52.62/52.40 [3124]E(f332(f332(f83(a1),a99),x31241),f332(f81(a1),x31241))
% 52.62/52.40 [3126]E(f332(a107,f332(f106(a1),x31261)),f332(f106(a845),x31261))
% 52.62/52.40 [3127]E(f332(a107,f332(f106(a1),x31271)),f332(f106(a845),x31271))
% 52.62/52.40 [3128]E(f332(a22,f332(f106(a101),x31281)),f332(f106(a845),x31281))
% 52.62/52.40 [3129]E(f332(f43(a845),f332(f293(a845),x31291)),f332(a114,x31291))
% 52.62/52.40 [3139]E(f332(f332(f82(a845),f80(a845)),x31391),f332(a114,x31391))
% 52.62/52.40 [3142]E(f332(f105(a1),f332(f102(a1),x31421)),f332(f102(a1),x31421))
% 52.62/52.40 [3143]E(f332(f77(a1),f332(f102(a1),x31431)),f332(f102(a1),x31431))
% 52.62/52.40 [3148]E(f332(f43(x31481),f180(f853(x31481,a839))),f2(a845))
% 52.62/52.40 [3150]E(f332(f332(f44(a845),x31501),f332(a114,f2(a845))),x31501)
% 52.62/52.40 [3161]E(f53(a845,x31611,f332(a114,f2(a845))),f2(a845))
% 52.62/52.40 [3162]E(f53(a1,x31621,f332(f106(a1),a99)),f2(a1))
% 52.62/52.40 [3169]E(f332(f332(f82(a1),a99),x31691),f332(f332(f82(a1),x31691),a99))
% 52.62/52.40 [3176]E(f332(f332(f44(a1),x31761),f332(f106(a1),a99)),f332(f81(a1),x31761))
% 52.62/52.40 [3180]E(f130(a845,f332(f294(a845,x31801),f2(a845))),f115(a845))
% 52.62/52.40 [3181]E(f332(f332(f3(a1),x31811),f80(a1)),f332(f332(f82(a1),x31811),a99))
% 52.62/52.40 [3182]E(f332(f332(f82(a1),x31821),f80(a1)),f332(f332(f3(a1),x31821),a99))
% 52.62/52.40 [3183]P1(f332(f332(f187(a25),x31831),x31831))
% 52.62/52.40 [3184]P1(f332(f332(f187(a25),x31841),x31841))
% 52.62/52.40 [3185]P1(f332(f332(f232(a845),x31851),x31851))
% 52.62/52.40 [3186]P1(f332(f332(f232(a1),x31861),x31861))
% 52.62/52.40 [3187]P1(f332(f332(f279(a845),x31871),x31871))
% 52.62/52.40 [3192]E(f332(f81(a1),f332(f106(a1),x31921)),f332(f106(a1),f332(f81(a1),x31921)))
% 52.62/52.40 [3193]P1(f332(f64(a845),f332(f257(a845),x31931)))
% 52.62/52.40 [3194]P1(f332(f64(a845),f332(f293(a845),x31941)))
% 52.62/52.40 [3202]E(f149(x32021,f239(f853(x32021,a839))),f239(f853(f846(x32021),a839)))
% 52.62/52.40 [3206]P1(f332(f332(f232(a845),f2(a845)),x32061))
% 52.62/52.40 [3207]P1(f332(f332(f232(a845),f2(a845)),x32071))
% 52.62/52.40 [3218]E(f332(f332(f82(a845),f113(x32181)),f332(a114,f2(a845))),f113(f332(a114,x32181)))
% 52.62/52.40 [3219]E(f332(f256(x32191),f332(f18(a839,x32191),a177)),f239(f853(x32191,a839)))
% 52.62/52.40 [3220]E(f332(f256(x32201),f332(f18(a839,x32201),a178)),f180(f853(x32201,a839)))
% 52.62/52.40 [3223]E(f332(f332(f302(a845),x32231),f332(f257(a845),x32231)),f332(f257(a845),f332(a114,x32231)))
% 52.62/52.40 [3234]E(f332(f332(f82(a1),f80(a1)),f332(f102(a1),x32341)),f332(f102(a1),f332(a114,x32341)))
% 52.62/52.40 [3257]E(f180(f853(f852(x32571,x32571),a839)),f260(x32571,f180(f853(x32571,a839))))
% 52.62/52.40 [3258]E(f332(f301(x32581),f239(f853(x32581,a839))),f239(f853(f853(x32581,a839),a839)))
% 52.62/52.40 [3259]E(f332(f81(f853(x32591,a839)),f239(f853(x32591,a839))),f180(f853(x32591,a839)))
% 52.62/52.40 [3260]E(f332(f81(f853(x32601,a839)),f180(f853(x32601,a839))),f239(f853(x32601,a839)))
% 52.62/52.40 [3261]P1(f332(f64(x32611),f180(f853(x32611,a839))))
% 52.62/52.40 [3262]P1(f332(f64(x32621),f180(f853(x32621,a839))))
% 52.62/52.40 [3264]E(f332(f294(a845,x32641),f332(a114,x32641)),f332(f332(f302(a845),x32641),f180(f853(a845,a839))))
% 52.62/52.40 [3265]E(f87(f852(a845,a845),f56(x32651,f2(a845))),f332(f332(f241(a845,a845),f2(a845)),x32651))
% 52.62/52.40 [3279]E(f332(f332(f302(a845),f332(a114,x32791)),f332(f293(a845),x32791)),f332(f293(a845),f332(a114,x32791)))
% 52.62/52.40 [3282]P38(x32821,f180(f853(f852(x32821,x32821),a839)))
% 52.62/52.40 [3284]P1(f332(f332(f232(a1),f2(a1)),f332(f102(a1),x32841)))
% 52.62/52.40 [3285]P1(f332(f332(f232(a1),f2(a1)),f332(f102(a1),x32851)))
% 52.62/52.40 [3293]E(f332(f332(f82(a845),f332(f181(a845),x32931)),f332(a114,f2(a845))),f332(f181(a845),f332(a114,x32931)))
% 52.62/52.40 [3344]E(f332(f303(x33441,x33441,f39(x33441)),f239(f853(x33441,a839))),f239(f853(x33441,a839)))
% 52.62/52.40 [3401]P40(f332(f303(a845,a1,f102(a1)),x34011))
% 52.62/52.40 [3441]P49(x34411,f180(f853(x34411,a839)),f180(f853(f852(x34411,x34411),a839)))
% 52.62/52.40 [3460]E(f332(f332(f241(a1,a1),f332(f106(a1),a99)),f332(f332(f3(a1),x34601),f80(a1))),f58(f332(f106(a1),a99),x34601))
% 52.62/52.40 [3461]P1(f332(f332(f334(a845),f332(a22,x34611)),f239(f853(a845,a839))))
% 52.62/52.40 [3510]P60(x35101,f332(f18(f853(x35101,a839),x35101),f332(f18(a839,x35101),a178)))
% 52.62/52.40 [3519]E(f282(a845,f279(a845),x35191,x35191),f332(f332(f302(a845),x35191),f180(f853(a845,a839))))
% 52.62/52.40 [3690]E(f332(f132(f846(x36901),f846(x36901),f125(x36901),f115(x36901)),f115(f846(x36901))),f115(x36901))
% 52.62/52.40 [3710]P1(f332(f332(f334(f853(f852(a845,a845),a839)),f333(x37101)),a100))
% 52.62/52.40 [3734]P1(f332(f332(f334(f853(f852(a845,a845),a839)),f332(a110,x37341)),a100))
% 52.62/52.40 [3864]P31(x38641,f853(x38641,a839),f332(f332(f9(x38641,f853(x38641,a839),f853(x38641,a839)),f302(x38641)),f180(f853(x38641,a839))),f239(f853(x38641,a839)))
% 52.62/52.40 [4396]~E(f332(f332(f82(a1),x43961),x43961),a99)
% 52.62/52.40 [4397]~E(f332(f332(f82(a1),x43971),x43971),a99)
% 52.62/52.40 [4440]~E(f332(a5,f332(a114,f332(a22,x44401))),f2(a101))
% 52.62/52.40 [4441]~E(f332(a5,f332(a114,f332(a22,x44411))),f2(a101))
% 52.62/52.40 [4447]~P1(f332(a186,f332(f102(a1),x44471)))
% 52.62/52.40 [4449]~P1(f332(f332(f233(a845),x44491),x44491))
% 52.62/52.40 [4450]~P1(f332(f332(f233(a845),x44501),x44501))
% 52.62/52.40 [4463]~P1(f332(f332(f232(a845),f332(a114,x44631)),x44631))
% 52.62/52.40 [3209]E(f332(a107,f332(f81(a1),f332(f102(a1),x32091))),f2(a845))
% 52.62/52.40 [3212]E(f332(f332(f82(a1),f332(f81(a1),x32121)),x32121),f2(a1))
% 52.62/52.40 [3217]E(f332(f43(a1),f332(f294(a1,f2(a1)),x32171)),f332(a107,x32171))
% 52.62/52.40 [3227]E(f332(f332(f242(a845),f332(a114,f2(a845))),x32271),f332(a114,f2(a845)))
% 52.62/52.40 [3326]E(f332(f276(x33261),f180(f853(f852(x33261,x33261),a839))),f180(f853(x33261,a839)))
% 52.62/52.40 [3328]P1(f332(f64(a1),f332(f294(a1,f2(a1)),x33281)))
% 52.62/52.40 [3334]E(f46(f853(x33341,a839),f239(f853(f853(x33341,a839),a839))),f180(f853(x33341,a839)))
% 52.62/52.40 [3335]E(f46(f853(x33351,a839),f180(f853(f853(x33351,a839),a839))),f239(f853(x33351,a839)))
% 52.62/52.40 [3336]E(f45(f853(x33361,a839),f239(f853(f853(x33361,a839),a839))),f239(f853(x33361,a839)))
% 52.62/52.40 [3337]E(f45(f853(x33371,a839),f180(f853(f853(x33371,a839),a839))),f180(f853(x33371,a839)))
% 52.62/52.40 [3342]P1(f332(f332(f279(a845),f332(a114,f2(a845))),x33421))
% 52.62/52.40 [3380]E(f332(f332(f302(f846(x33801)),f115(x33801)),f180(f853(f846(x33801),a839))),f150(x33801,f115(f853(x33801,a839))))
% 52.62/52.40 [3381]E(f332(f332(f302(f846(x33811)),f115(x33811)),f180(f853(f846(x33811),a839))),f149(x33811,f180(f853(x33811,a839))))
% 52.62/52.40 [3414]E(f332(f332(f82(a1),f332(f81(a1),x34141)),f332(f81(a1),x34141)),f332(f81(a1),f332(f332(f82(a1),x34141),x34141)))
% 52.62/52.40 [3425]E(f332(f332(f82(a845),f6(x34251)),f332(a114,f2(a845))),f6(f332(a5,f332(a114,f332(a22,x34251)))))
% 52.62/52.40 [3452]E(f332(f43(a1),f332(f303(a845,a1,f102(a1)),x34521)),f332(f43(a845),x34521))
% 52.62/52.40 [3455]P1(f332(f332(f232(a845),x34551),f332(f332(f83(a845),x34551),x34551)))
% 52.62/52.40 [3491]E(f332(f303(a1,a845,a107),f295(a1,f2(a1),f332(f102(a1),x34911))),f332(f293(a845),x34911))
% 52.62/52.40 [3505]E(f332(f332(f44(a845),f332(a114,f2(a845))),f332(f106(a845),x35051)),f332(a107,f332(f332(f44(a1),f80(a1)),f332(f106(a1),x35051))))
% 52.62/52.40 [3507]E(f332(f158(a845),f130(a845,f332(f294(a845,f2(a845)),f332(a114,x35071)))),f332(f293(a845),x35071))
% 52.62/52.40 [3508]E(f332(f332(f82(a845),f332(f181(a101),x35081)),f332(a114,f2(a845))),f332(f181(a101),f332(a5,f332(a114,f332(a22,x35081)))))
% 52.62/52.40 [3524]E(f332(f303(a1,a845,a107),f332(f303(a845,a1,f102(a1)),x35241)),x35241)
% 52.62/52.40 [3553]E(f332(f332(f302(a845),f2(a845)),f332(f303(a845,a845,a114),f332(f257(a845),x35531))),f332(f257(a845),f332(a114,x35531)))
% 52.62/52.40 [3560]P55(x35601,x35601,f300(x35601,f180(f853(f852(x35601,x35601),a839))))
% 52.62/52.40 [3566]P1(f332(a186,f332(f81(a1),f332(f102(a1),f332(a114,x35661)))))
% 52.62/52.40 [3577]E(f332(f332(f3(f853(a845,a839)),f332(f258(a845),x35771)),f332(f332(f302(a845),x35771),f180(f853(a845,a839)))),f332(f258(a845),f332(a114,x35771)))
% 52.62/52.40 [3594]E(f332(f332(f82(a1),f332(f332(f3(a1),a85),x35941)),f332(f332(f3(a1),a85),x35941)),f332(f332(f3(a1),a85),f332(f332(f82(a1),x35941),x35941)))
% 52.62/52.40 [3597]P49(x35971,f239(f853(x35971,a839)),f300(x35971,f180(f853(f852(x35971,x35971),a839))))
% 52.62/52.40 [3608]E(f332(f332(f302(f853(x36081,a839)),f180(f853(x36081,a839))),f180(f853(f853(x36081,a839),a839))),f332(f301(x36081),f180(f853(x36081,a839))))
% 52.62/52.40 [3637]E(f332(f332(f3(f853(a845,a839)),f332(f296(a845),x36371)),f332(f332(f302(a845),f332(a114,x36371)),f180(f853(a845,a839)))),f332(f296(a845),f332(a114,x36371)))
% 52.62/52.40 [3646]E(f332(f332(f302(f849(x36461)),f183(x36461)),f332(f303(x36461,f849(x36461),f227(x36461)),f239(f853(x36461,a839)))),f239(f853(f849(x36461),a839)))
% 52.62/52.40 [3746]E(f332(f106(a845),f332(f332(f82(a1),x37461),x37461)),f332(f332(f88(a845,a845),f332(f106(a845),x37461)),f332(f332(f20(a845,a845,a845),f82(a845)),f7(a845))))
% 52.62/52.40 [4134]P21(x41341,f853(x41341,a839),f332(f332(f10(f853(x41341,a839),f853(f853(x41341,a839),f853(x41341,a839)),x41341),f332(f9(f853(x41341,a839),f853(x41341,a839),f853(x41341,a839)),f3(f853(x41341,a839)))),f332(f332(f9(x41341,f853(x41341,a839),f853(x41341,a839)),f302(x41341)),f180(f853(x41341,a839)))))
% 52.62/52.40 [4219]E(f332(f256(f852(a1,a1)),f332(f251(a1,a1,a839),f332(f332(f10(f853(a1,a839),f853(a1,a839),a1),f332(f20(a1,a839,a839),f332(f332(f10(a839,f853(a839,a839),a1),a330),f332(f232(a1),x42191)))),f233(a1)))),f108(x42191))
% 52.62/52.40 [4251]E(f332(f256(f852(a1,a1)),f332(f251(a1,a1,a839),f332(f332(f20(a1,f853(a1,a839),f853(a1,a839)),f332(f332(f10(f853(a839,a839),f853(f853(a1,a839),f853(a1,a839)),a1),f10(a839,a839,a1)),f332(f332(f10(a839,f853(a839,a839),a1),a330),f332(f232(a1),x42511)))),f233(a1)))),f109(x42511))
% 52.62/52.40 [4303]E(f332(f256(f852(f853(x43031,a839),f853(x43031,a839))),f332(f251(f853(x43031,a839),f853(x43031,a839),a839),f332(f332(f9(f853(x43031,a839),f853(f853(x43031,a839),a839),f853(f853(x43031,a839),a839)),f332(f332(f10(f853(f853(x43031,a839),f853(a839,a839)),f853(f853(f853(x43031,a839),a839),f853(f853(x43031,a839),a839)),f853(x43031,a839)),f20(f853(x43031,a839),a839,a839)),f332(f332(f10(f853(f853(x43031,a839),a839),f853(f853(x43031,a839),f853(a839,a839)),f853(x43031,a839)),f332(f10(a839,f853(a839,a839),f853(x43031,a839)),a330)),f233(f853(x43031,a839))))),f64(x43031)))),f299(x43031))
% 52.62/52.40 [4467]~P1(f332(f64(f846(x44671)),f239(f853(f846(x44671),a839))))
% 52.62/52.40 [4480]~P1(f332(f332(f232(a1),f2(a1)),f332(f81(a1),f332(f102(a1),f332(a114,x44801)))))
% 52.62/52.40 [3358]E(f332(f332(f3(a1),f332(f332(f82(a1),x33581),a99)),a99),x33581)
% 52.62/52.40 [3374]E(f332(f158(a845),f130(a845,f332(f294(a845,f2(a845)),x33741))),f332(f257(a845),x33741))
% 52.62/52.40 [3568]E(f332(f259(x35681,x35681),f300(x35681,f180(f853(f852(x35681,x35681),a839)))),f239(f853(x35681,a839)))
% 52.62/52.40 [3569]E(f332(f261(x35691,x35691),f300(x35691,f180(f853(f852(x35691,x35691),a839)))),f239(f853(x35691,a839)))
% 52.62/52.40 [3614]E(f332(f332(f82(a1),f332(f332(f82(a1),f80(a1)),x36141)),x36141),f332(f332(f3(a1),f332(f332(f82(a1),x36141),x36141)),a99))
% 52.62/52.40 [3664]E(f332(f278(x36641,x36641),f300(x36641,f180(f853(f852(x36641,x36641),a839)))),f300(x36641,f180(f853(f852(x36641,x36641),a839))))
% 52.62/52.40 [3713]P1(f332(f332(f232(a845),x37131),f332(f332(f83(a845),x37131),f332(f332(f83(a845),x37131),x37131))))
% 52.62/52.40 [3800]E(f332(f332(f281(x38001,x38001,x38001),f180(f853(f852(x38001,x38001),a839))),f300(x38001,f180(f853(f852(x38001,x38001),a839)))),f180(f853(f852(x38001,x38001),a839)))
% 52.62/52.40 [3988]P1(f332(f64(a845),f332(f256(a845),f332(f332(f9(a845,a845,a839),f233(a845)),x39881))))
% 52.62/52.40 [3989]P1(f332(f64(a845),f332(f256(a845),f332(f332(f9(a845,a845,a839),f232(a845)),x39891))))
% 52.62/52.40 [4270]E(f332(f256(f852(x42701,x42701)),f332(f332(f10(f853(x42701,a839),a839,f852(x42701,x42701)),f89(x42701)),f332(f332(f9(f852(x42701,x42701),f853(x42701,f852(x42701,x42701)),f853(x42701,a839)),f332(f332(f10(f853(f852(x42701,x42701),a839),f853(f853(x42701,f852(x42701,x42701)),f853(x42701,a839)),f852(x42701,x42701)),f10(f852(x42701,x42701),a839,x42701)),a329)),f332(f332(f20(x42701,x42701,f852(x42701,x42701)),f241(x42701,x42701)),f7(x42701))))),f300(x42701,f180(f853(f852(x42701,x42701),a839))))
% 52.62/52.40 [4468]~E(f332(f332(f3(a1),f332(f332(f82(a1),x44681),x44681)),a99),a85)
% 52.62/52.40 [4469]~E(f332(f332(f3(a1),f332(f332(f82(a1),x44691),x44691)),a99),a85)
% 52.62/52.40 [4471]~E(f332(f332(f82(a1),f332(f332(f82(a1),f80(a1)),x44711)),x44711),f2(a1))
% 52.62/52.40 [3758]E(f332(f332(f82(a1),f332(f332(f3(a1),a99),x37581)),f332(f332(f3(a1),a99),x37581)),f332(f332(f3(a1),a99),f332(f332(f3(a1),f332(f332(f82(a1),x37581),x37581)),a99)))
% 52.62/52.40 [3872]E(f332(f332(f3(a1),f332(f332(f82(a1),f332(f332(f3(a1),a99),x38721)),f332(f332(f3(a1),a99),x38721))),a99),f332(f332(f3(a1),a99),f332(f332(f82(a1),x38721),x38721)))
% 52.62/52.40 [3908]E(f332(f332(f3(a1),f332(f332(f82(a1),f332(f332(f82(a1),x39081),a99)),f332(f332(f82(a1),x39081),a99))),a99),f332(f332(f82(a1),f332(f332(f82(a1),x39081),x39081)),a99))
% 52.62/52.40 [3947]E(f332(f332(f3(a1),f332(f332(f82(a1),f332(f332(f3(a1),a99),x39471)),f332(f332(f3(a1),a99),x39471))),a99),f332(f332(f3(a1),a85),f332(f332(f3(a1),f332(f332(f82(a1),x39471),x39471)),a99)))
% 52.62/52.40 [4051]E(f332(a91,f332(f277(f852(a845,a845),f852(a845,a845),a111),f332(f332(f302(f852(a845,a845)),f332(f332(f241(a845,a845),x40511),f2(a845))),f180(f853(f852(a845,a845),a839))))),f332(f102(a1),x40511))
% 52.62/52.40 [4061]E(f332(a91,f332(f277(f852(a845,a845),f852(a845,a845),a111),f332(f332(f302(f852(a845,a845)),f332(f332(f241(a845,a845),f337(x40611)),f490(x40611))),f180(f853(f852(a845,a845),a839))))),x40611)
% 52.62/52.40 [4091]E(f332(f256(a1),f332(f332(f20(a1,a839,a839),f332(f332(f10(a839,f853(a839,a839),a1),a330),f332(f232(a1),f2(a1)))),x40911)),f332(f303(a845,a1,f102(a1)),f332(f256(a845),f332(f332(f10(a1,a839,a845),x40911),f102(a1)))))
% 52.62/52.40 [4142]P40(f332(f256(a1),f332(f332(f20(a1,a839,a839),f332(f332(f10(a839,f853(a839,a839),a1),a330),f332(f232(a1),f2(a1)))),x41421)))
% 52.62/52.40 [4162]P1(f332(f332(f334(f852(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839))),f332(f332(f241(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839)),x41621),f180(f853(f852(a845,a845),a839)))),a73))
% 52.62/52.40 [4168]E(f332(f303(a1,a845,a107),f332(f256(a1),f332(f332(f20(a1,a839,a839),f332(f332(f10(a839,f853(a839,a839),a1),a330),f332(f232(a1),f2(a1)))),f332(f332(f10(a845,a839,a1),x41681),a107)))),f332(f256(a845),x41681))
% 52.62/52.40 [4317]E(f306(a845,f332(f332(f47(f852(a845,a845),f853(a845,a839)),f332(a110,x43171)),f332(f251(a845,a845,f853(a845,a839)),f332(f332(f9(a845,f853(a845,a839),f853(a845,f853(a845,a839))),f332(f332(f10(f853(a845,f853(f853(a845,a839),f853(a845,a839))),f853(f853(a845,a839),f853(a845,f853(a845,a839))),a845),f9(a845,f853(a845,a839),f853(a845,a839))),f332(f332(f10(f853(a845,a845),f853(a845,f853(f853(a845,a839),f853(a845,a839))),a845),f332(f10(a845,f853(f853(a845,a839),f853(a845,a839)),a845),f302(a845))),f3(a845)))),f180(f853(a845,a839)))))),f332(a107,x43171))
% 52.62/52.40 [3801]E(f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),x38011),x38011)),a99)),a99),f332(f332(f82(a1),x38011),x38011))
% 52.62/52.40 [3847]E(f332(f332(f3(a1),f332(f332(f3(a1),f332(f332(f82(a1),x38471),x38471)),a99)),a99),f332(f332(f82(a1),f332(f332(f3(a1),x38471),a99)),f332(f332(f3(a1),x38471),a99)))
% 52.62/52.40 [4068]E(f332(f332(f3(a1),f332(f332(f82(a1),f332(f332(f82(a1),f332(f81(a1),x40681)),a99)),f332(f332(f82(a1),f332(f81(a1),x40681)),a99))),a99),f332(f81(a1),f332(f332(f3(a1),f332(f332(f82(a1),x40681),x40681)),a99)))
% 52.62/52.40 [4111]E(f332(f332(f82(a845),x41111),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f332(a114,f332(a114,x41111)))
% 52.62/52.40 [4112]E(f332(f332(f83(a845),x41121),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f332(f332(f82(a845),x41121),x41121))
% 52.62/52.40 [4113]E(f332(f332(f44(a845),f332(f332(f82(a845),x41131),x41131)),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),x41131)
% 52.62/52.40 [4195]E(f53(a845,f332(a114,f332(a114,x41951)),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f53(a845,x41951,f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))))
% 52.62/52.40 [4334]E(f332(a91,f332(f332(f47(f852(a845,a845),f853(f852(a845,a845),a839)),f332(a110,x43341)),f332(f251(a845,a845,f853(f852(a845,a845),a839)),f332(f332(f10(f853(a845,f853(f852(a845,a845),a839)),f853(a845,f853(f852(a845,a845),a839)),a845),f332(f10(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839),a845),f277(f852(a845,a845),f852(a845,a845),a111))),f332(f332(f9(a845,f853(f852(a845,a845),a839),f853(a845,f853(f852(a845,a845),a839))),f332(f332(f10(f853(a845,f853(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839))),f853(f853(f852(a845,a845),a839),f853(a845,f853(f852(a845,a845),a839))),a845),f9(a845,f853(f852(a845,a845),a839),f853(f852(a845,a845),a839))),f332(f332(f10(f853(a845,f852(a845,a845)),f853(a845,f853(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839))),a845),f332(f10(f852(a845,a845),f853(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839)),a845),f302(f852(a845,a845)))),f332(f9(a845,a845,f852(a845,a845)),f241(a845,a845))))),f180(f853(f852(a845,a845),a839))))))),f332(f81(a1),x43341))
% 52.62/52.40 [4190]E(f332(f332(f82(a845),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),x41901),f332(a114,f332(a114,x41901)))
% 52.62/52.40 [4191]E(f332(f332(f83(a845),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),x41911),f332(f332(f82(a845),x41911),x41911))
% 52.62/52.40 [4224]E(f332(f332(f44(a845),f332(a114,f332(a114,x42241))),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f332(a114,f332(f332(f44(a845),x42241),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))))
% 52.62/52.40 [4275]E(f332(f332(f82(a845),f332(f106(a845),f332(f332(f3(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))),a99))),x42751),f332(a114,f332(a114,f332(a114,x42751))))
% 52.62/52.40 [4355]E(f332(f251(a1,a1,f852(a1,a1)),f332(f332(f20(a1,f853(a1,f852(a1,a1)),f853(a1,f852(a1,a1))),f332(f332(f10(f853(a1,f853(f852(a1,a1),f852(a1,a1))),f853(f853(a1,f852(a1,a1)),f853(a1,f852(a1,a1))),a1),f20(a1,f852(a1,a1),f852(a1,a1))),f332(f332(f10(f853(a1,f852(a1,a1)),f853(a1,f853(f852(a1,a1),f852(a1,a1))),a1),f332(f20(a1,f852(a1,a1),f853(f852(a1,a1),f852(a1,a1))),f332(f332(f10(a839,f853(f852(a1,a1),f853(f852(a1,a1),f852(a1,a1))),a1),f98(f852(a1,a1))),f332(f332(f10(a1,a839,a1),f332(f232(a1),f2(a1))),f332(f332(f9(a1,a1,a1),f3(a1)),x43551))))),f332(f332(f9(a1,f853(a1,a1),f853(a1,f852(a1,a1))),f332(f332(f10(f853(a1,f852(a1,a1)),f853(f853(a1,a1),f853(a1,f852(a1,a1))),a1),f10(a1,f852(a1,a1),a1)),f332(f332(f10(a1,f853(a1,f852(a1,a1)),a1),f241(a1,a1)),f332(f332(f9(a1,a1,a1),f332(f332(f10(a1,f853(a1,a1),a1),f82(a1)),f332(f83(a1),f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))))),f80(a1))))),f332(f332(f9(a1,a1,a1),f3(a1)),x43551))))),f332(f332(f10(a1,f853(a1,f852(a1,a1)),a1),f241(a1,a1)),f332(f83(a1),f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))))),f51(x43551))
% 52.62/52.40 [3403]P41(a25,x34031,x34032,x34031)
% 52.62/52.40 [3404]P41(a25,x34041,x34042,x34041)
% 52.62/52.40 [3060]P20(a1,f163(x30601,x30602))
% 52.62/52.40 [3156]P49(x31561,x31562,f260(x31561,x31562))
% 52.62/52.40 [3157]P55(x31571,x31571,f260(x31571,x31572))
% 52.62/52.40 [3428]P31(x34281,x34281,f7(x34281),x34282)
% 52.62/52.40 [3429]P31(x34291,x34291,f39(x34291),x34292)
% 52.62/52.40 [3435]P36(x34351,x34352,f115(x34351),f115(x34351))
% 52.62/52.40 [3436]P36(x34361,x34362,f115(x34361),f115(x34361))
% 52.62/52.40 [3437]P31(x34371,f849(x34371),f227(x34371),x34372)
% 52.62/52.40 [3446]P31(f846(x34461),f846(x34461),f142(x34461),x34462)
% 52.62/52.40 [4367]~E(f36(x43671,x43672),a25)
% 52.62/52.40 [4368]~E(f35(x43681,x43682),a25)
% 52.62/52.40 [4369]~E(f28(x43691,x43692),a25)
% 52.62/52.40 [4370]~E(f36(x43701,x43702),a25)
% 52.62/52.40 [4371]~E(f35(x43711,x43712),a25)
% 52.62/52.40 [4372]~E(f28(x43721,x43722),a25)
% 52.62/52.40 [3028]E(f332(f7(x30281),x30282),x30282)
% 52.62/52.40 [3029]E(f332(f256(x30291),x30292),x30292)
% 52.62/52.40 [3030]E(f332(f39(x30301),x30302),x30302)
% 52.62/52.40 [3031]E(f332(f39(x30311),x30312),x30312)
% 52.62/52.40 [3040]E(f332(f184(x30401),x30402),f117(x30401))
% 52.62/52.40 [3048]E(f34(f28(x30481,x30482)),f2(a845))
% 52.62/52.40 [3058]E(f87(x30581,f332(a329,x30582)),x30582)
% 52.62/52.40 [3059]E(f92(x30591,f332(a329,x30592)),x30592)
% 52.62/52.40 [3076]E(f332(f181(a840),f28(x30761,x30762)),f2(a845))
% 52.62/52.40 [3081]E(f332(f126(x30811,x30812),f115(x30811)),f115(x30811))
% 52.62/52.40 [3100]E(f300(x31001,f300(x31001,x31002)),f300(x31001,x31002))
% 52.62/52.40 [3121]E(f332(f332(f125(x31211),x31212),f115(x31211)),x31212)
% 52.62/52.40 [3130]E(f332(f332(f159(x31301),x31302),f115(x31301)),f115(x31301))
% 52.62/52.40 [3131]E(f332(f332(f128(x31311),x31312),f115(x31311)),f115(x31311))
% 52.62/52.40 [3133]E(f228(x31331,x31332,f183(x31331)),f2(a845))
% 52.62/52.40 [3134]E(f144(x31341,x31342,f115(x31341)),f2(a845))
% 52.62/52.40 [3136]E(f151(x31361,x31362,f115(x31361)),f115(x31361))
% 52.62/52.40 [3137]E(f162(x31371,x31372,f115(x31371)),f115(x31371))
% 52.62/52.40 [3138]E(f160(x31381,f115(x31381),x31382),f115(x31381))
% 52.62/52.40 [3144]E(f332(f259(x31441,x31441),f260(x31441,x31442)),x31442)
% 52.62/52.40 [3145]E(f332(f261(x31451,x31451),f260(x31451,x31452)),x31452)
% 52.62/52.40 [3153]P1(f332(a26,f28(x31531,x31532)))
% 52.62/52.40 [3154]P1(f332(a26,f28(x31541,x31542)))
% 52.62/52.40 [3155]E(f332(f278(x31551,x31551),f260(x31551,x31552)),f260(x31551,x31552))
% 52.62/52.40 [3168]E(f300(f846(x31681),f146(x31681,x31682)),f147(x31681,f300(x31681,x31682)))
% 52.62/52.40 [3170]P1(f332(f127(a1),f163(x31701,x31702)))
% 52.62/52.40 [3178]E(f332(f259(x31781,x31781),f300(x31781,x31782)),f239(f853(x31781,a839)))
% 52.62/52.40 [3179]E(f332(f261(x31791,x31791),f300(x31791,x31792)),f239(f853(x31791,a839)))
% 52.62/52.40 [3189]E(f332(f158(a1),f163(x31891,x31892)),f295(a1,x31891,x31892))
% 52.62/52.40 [3190]E(f332(f158(a1),f163(x31901,x31902)),f295(a1,x31901,x31902))
% 52.62/52.40 [3205]P56(x32051,f180(f853(x32051,a839)),x32052)
% 52.62/52.40 [3210]E(f332(f250(a1,a1),f54(x32101,x32102)),f53(a1,x32101,x32102))
% 52.62/52.40 [3211]E(f332(f294(a845,x32111),f332(a114,x32112)),f295(a845,x32111,x32112))
% 52.62/52.40 [3238]E(f295(a845,f332(a114,x32381),x32382),f297(a845,x32381,x32382))
% 52.62/52.40 [3241]P49(x32411,f239(f853(x32411,a839)),f300(x32411,x32412))
% 52.62/52.40 [3304]E(f332(f332(f3(a845),x33041),f332(a114,x33042)),f332(f43(a845),f298(a845,x33042,x33041)))
% 52.62/52.40 [3359]E(f155(x33591,x33592,f115(x33591)),f332(f332(f241(f846(x33591),f846(x33591)),f115(x33591)),f115(x33591)))
% 52.62/52.40 [3378]E(f332(f251(x33781,x33782,f852(x33781,x33782)),f241(x33781,x33782)),f39(f852(x33781,x33782)))
% 52.62/52.40 [3383]P1(f332(f332(f334(f846(x33831)),f115(x33831)),f149(x33831,x33832)))
% 52.62/52.40 [3384]E(f332(f181(f846(x33841)),f116(x33841,x33842)),f332(f332(f3(a845),f332(f181(f846(x33841)),x33842)),f80(a845)))
% 52.62/52.40 [3395]P1(f332(f64(a845),f295(a845,x33951,x33952)))
% 52.62/52.40 [3396]P1(f332(f64(a845),f297(a845,x33961,x33962)))
% 52.62/52.40 [3397]P1(f332(f64(a845),f298(a845,x33971,x33972)))
% 52.62/52.40 [3398]P1(f332(f64(a1),f295(a1,x33981,x33982)))
% 52.62/52.40 [3399]P1(f332(f64(a1),f297(a1,x33991,x33992)))
% 52.62/52.40 [3400]P1(f332(f64(a1),f298(a1,x34001,x34002)))
% 52.62/52.40 [3504]E(f332(f303(a845,a845,a114),f295(a845,x35041,x35042)),f295(a845,f332(a114,x35041),f332(a114,x35042)))
% 52.62/52.40 [3521]E(f332(f332(f281(x35211,x35211,x35211),f300(x35211,x35212)),f300(x35211,x35212)),f300(x35211,x35212))
% 52.62/52.40 [3551]E(f332(f332(f241(a1,a1),f332(f332(f44(a1),x35511),x35512)),f53(a1,x35511,x35512)),f54(x35511,x35512))
% 52.62/52.40 [3552]E(f332(f332(f241(a101,a101),f332(f332(f44(a101),x35521),x35522)),f53(a101,x35521,x35522)),f24(x35521,x35522))
% 52.62/52.40 [3581]E(f332(f332(f241(a845,a845),f332(f332(f44(a845),x35811),x35812)),f53(a845,x35811,x35812)),f87(f852(a845,a845),f56(x35811,x35812)))
% 52.62/52.40 [3633]P1(f332(f332(f233(a845),f332(f332(f3(a845),x36331),x36332)),f332(a114,x36331)))
% 52.62/52.40 [3733]E(f332(f332(f82(a1),f332(f332(f83(a1),x37331),f332(f332(f44(a1),x37332),x37331))),f53(a1,x37332,x37331)),x37332)
% 52.62/52.40 [3737]E(f332(f332(f47(a845,f853(f852(f846(x37371),f846(x37371)),a839)),f239(f853(a845,a839))),f133(x37371,x37372)),f135(x37371,x37372))
% 52.62/52.40 [3962]P1(f332(f332(f334(f852(f846(x39621),f846(x39621))),f332(f332(f241(f846(x39621),f846(x39621)),f115(x39621)),f115(x39621))),f147(x39621,x39622)))
% 52.62/52.40 [4124]E(f252(x41241,x41241,x41242,x41242,f39(x41241),f39(x41242)),f39(f852(x41241,x41242)))
% 52.62/52.40 [4125]E(f252(x41251,x41251,x41252,x41252,f7(x41251),f7(x41252)),f39(f852(x41251,x41252)))
% 52.62/52.40 [4126]E(f252(x41261,x41261,x41262,x41262,f39(x41261),f39(x41262)),f39(f852(x41261,x41262)))
% 52.62/52.40 [4127]E(f252(x41271,x41271,x41272,x41272,f39(x41271),f39(x41272)),f39(f852(x41271,x41272)))
% 52.62/52.40 [4379]~E(f332(f227(x43791),x43792),f183(x43791))
% 52.62/52.40 [4380]~E(f332(f227(x43801),x43802),f183(x43801))
% 52.62/52.40 [4398]~P39(x43981,f332(f227(x43981),x43982))
% 52.62/52.40 [3119]E(f332(f231(x31191),f332(f227(x31191),x31192)),x31192)
% 52.62/52.40 [3120]E(f332(f142(x31201),f332(f142(x31201),x31202)),x31202)
% 52.62/52.40 [3122]E(f332(f332(f128(x31221),f2(a845)),x31222),x31222)
% 52.62/52.40 [3132]E(f332(f332(f159(x31321),f2(a845)),x31322),f115(x31321))
% 52.62/52.40 [3140]E(f332(f332(f125(x31401),f115(x31401)),x31402),x31402)
% 52.62/52.40 [3147]E(f332(f181(f849(x31471)),f332(f227(x31471),x31472)),f2(a845))
% 52.62/52.40 [3149]E(f45(f853(x31491,a839),f332(f301(x31491),x31492)),x31492)
% 52.62/52.40 [3151]E(f332(f158(x31511),f332(f141(x31511),x31512)),f332(f158(x31511),x31512))
% 52.62/52.40 [3152]E(f332(f158(x31521),f332(f142(x31521),x31522)),f332(f158(x31521),x31522))
% 52.62/52.40 [3159]E(f332(f332(f3(a101),x31591),x31592),f332(f332(a4,x31591),x31592))
% 52.62/52.40 [3172]E(f332(f332(f82(a845),x31721),x31722),f332(f332(f82(a845),x31722),x31721))
% 52.62/52.40 [3173]E(f332(f332(f82(a1),x31731),x31732),f332(f332(f82(a1),x31732),x31731))
% 52.62/52.40 [3174]E(f332(f332(f83(a845),x31741),x31742),f332(f332(f83(a845),x31742),x31741))
% 52.62/52.40 [3175]E(f332(f332(f83(a1),x31751),x31752),f332(f332(f83(a1),x31752),x31751))
% 52.62/52.40 [3197]E(f332(f332(f173(x31971,x31971),f2(a845)),x31972),f39(x31971))
% 52.62/52.40 [3198]E(f332(f181(f846(x31981)),f332(f141(x31981),x31982)),f332(f181(f846(x31981)),x31982))
% 52.62/52.40 [3199]E(f332(f181(f846(x31991)),f332(f142(x31991),x31992)),f332(f181(f846(x31991)),x31992))
% 52.62/52.40 [3200]E(f160(x32001,x32002,f180(f853(a845,a839))),f115(x32001))
% 52.62/52.40 [3201]E(f332(f332(f143(x32011,x32011),f7(x32011)),x32012),x32012)
% 52.62/52.40 [3203]E(f332(f240(a1,a1),f54(x32031,x32032)),f332(f332(f44(a1),x32031),x32032))
% 52.62/52.40 [3221]E(f34(f35(x32211,x32212)),f332(f332(f82(a845),f34(x32212)),f332(a114,f2(a845))))
% 52.62/52.40 [3222]E(f332(f276(x32221),f332(f278(x32221,x32221),x32222)),f332(f276(x32221),x32222))
% 52.62/52.40 [3226]P1(f332(f64(x32261),f332(f158(x32261),x32262)))
% 52.62/52.40 [3232]E(f332(f332(f82(a1),x32321),f332(f81(a1),x32322)),f332(f332(f3(a1),x32321),x32322))
% 52.62/52.40 [3233]E(f332(f332(f82(a1),x32331),f332(f81(a1),x32332)),f332(f332(f3(a1),x32331),x32332))
% 52.62/52.40 [3239]P30(x32391,x32392,f180(f853(f844(x32391),a839)))
% 52.62/52.40 [3240]P30(x32401,x32402,f180(f853(f844(x32401),a839)))
% 52.62/52.40 [3244]E(f332(f303(x32441,x32441,f7(x32441)),x32442),x32442)
% 52.62/52.40 [3245]E(f332(f303(x32451,x32451,f39(x32451)),x32452),x32452)
% 52.62/52.40 [3246]E(f332(f305(x32461,x32461,f7(x32461)),x32462),x32462)
% 52.62/52.40 [3247]E(f332(f305(x32471,x32471,f39(x32471)),x32472),x32472)
% 52.62/52.40 [3248]P1(f332(f239(f853(x32481,a839)),x32482))
% 52.62/52.40 [3250]E(f332(f43(a845),f332(f294(a845,x32501),x32502)),f332(f332(f3(a845),x32502),x32501))
% 52.62/52.40 [3251]E(f332(f294(a845,f332(a114,x32511)),x32512),f298(a845,x32511,x32512))
% 52.62/52.40 [3263]E(f332(f332(f302(x32631),x32632),f180(f853(x32631,a839))),f332(f256(x32631),f332(a329,x32632)))
% 52.62/52.40 [3269]E(f332(f332(f302(x32691),x32692),f180(f853(x32691,a839))),f226(x32691,f332(f227(x32691),x32692)))
% 52.62/52.40 [3271]E(f300(x32711,f332(f278(x32711,x32711),x32712)),f332(f278(x32711,x32711),f300(x32711,x32712)))
% 52.62/52.40 [3275]E(f332(f332(f82(a845),f332(a114,x32751)),x32752),f332(f332(f82(a845),x32751),f332(a114,x32752)))
% 52.62/52.40 [3276]E(f332(f332(f3(a845),f332(a114,x32761)),f332(a114,x32762)),f332(f332(f3(a845),x32761),x32762))
% 52.62/52.40 [3281]E(f332(f43(a845),f297(a845,x32811,x32812)),f332(f332(f3(a845),x32812),x32811))
% 52.62/52.40 [3290]P38(x32901,f332(f332(f280(a845,x32901),a237),x32902))
% 52.62/52.40 [3292]P20(a845,f130(a845,f332(f294(a845,x32921),x32922)))
% 52.62/52.40 [3294]P1(f332(f64(a845),f332(f294(a845,x32941),x32942)))
% 52.62/52.40 [3295]P1(f332(f64(a1),f332(f294(a1,x32951),x32952)))
% 52.62/52.40 [3297]E(f332(f278(f846(x32971),f846(x32971)),f146(x32971,x32972)),f146(x32971,f332(f278(x32971,x32971),x32972)))
% 52.62/52.40 [3298]E(f332(f181(a840),f35(x32981,x32982)),f332(f332(f82(a845),f332(f181(a840),x32982)),f332(a114,f2(a845))))
% 52.62/52.40 [3300]E(f332(f294(a1,x33001),f332(f332(f82(a1),x33002),f80(a1))),f295(a1,x33001,x33002))
% 52.62/52.40 [3303]E(f332(f332(f44(a1),f332(f81(a1),x33031)),f332(f81(a1),x33032)),f332(f332(f44(a1),x33031),x33032))
% 52.62/52.40 [3311]E(f171(x33111,x33112,f332(f18(f849(x33112),x33111),f183(x33112))),f180(f853(x33112,a839)))
% 52.62/52.40 [3312]E(f169(x33121,x33122,f332(f18(f849(x33122),x33121),f183(x33122))),f180(f853(x33121,a839)))
% 52.62/52.40 [3313]E(f332(f332(f173(f852(x33131,x33131),a839),f80(a845)),x33132),x33132)
% 52.62/52.40 [3315]E(f332(f332(f3(f853(x33151,a839)),x33152),f180(f853(x33151,a839))),x33152)
% 52.62/52.40 [3316]E(f332(f332(f103(f853(x33161,a839)),x33162),f180(f853(x33161,a839))),x33162)
% 52.62/52.40 [3317]E(f332(f332(f104(f853(x33171,a839)),x33172),f239(f853(x33171,a839))),x33172)
% 52.62/52.40 [3318]E(f332(f240(a845,a845),f87(f852(a845,a845),f56(x33181,x33182))),f332(f332(f44(a845),x33181),x33182))
% 52.62/52.40 [3324]E(f307(x33241,f332(a23,x33242),f332(f81(a1),f332(a23,x33242))),f332(f332(f310(a1),x33241),x33242))
% 52.62/52.40 [3325]E(f295(a1,f332(f332(f82(a1),x33251),f80(a1)),x33252),f297(a1,x33251,x33252))
% 52.62/52.40 [3330]E(f332(f250(a845,a845),f87(f852(a845,a845),f56(x33301,x33302))),f53(a845,x33301,x33302))
% 52.62/52.40 [3338]E(f308(x33381,f332(a23,x33382),f332(f81(a1),f332(a23,x33382))),f309(a1,x33381,x33382))
% 52.62/52.40 [3340]P1(f332(f332(f334(x33401),x33402),f239(f853(x33401,a839))))
% 52.62/52.40 [3341]P1(f332(f332(f334(x33411),x33412),f239(f853(x33411,a839))))
% 52.62/52.40 [3345]E(f332(f332(f3(a845),f332(a114,x33451)),x33452),f332(f43(a845),f295(a845,x33452,x33451)))
% 52.62/52.40 [3370]E(f332(f332(f3(f853(x33701,a839)),x33702),f239(f853(x33701,a839))),f180(f853(x33701,a839)))
% 52.62/52.40 [3371]E(f332(f332(f103(f853(x33711,a839)),x33712),f239(f853(x33711,a839))),f239(f853(x33711,a839)))
% 52.62/52.40 [3372]E(f332(f332(f104(f853(x33721,a839)),x33722),f180(f853(x33721,a839))),f180(f853(x33721,a839)))
% 52.62/52.40 [3385]E(f53(a1,f332(f102(a1),x33851),f332(f102(a1),x33852)),f332(f102(a1),f53(a845,x33851,x33852)))
% 52.62/52.40 [3386]E(f53(a1,f332(f102(a1),x33861),f332(f102(a1),x33862)),f332(f102(a1),f53(a845,x33861,x33862)))
% 52.62/52.40 [3387]E(f53(a1,f332(f81(a1),x33871),f332(f81(a1),x33872)),f332(f81(a1),f53(a1,x33871,x33872)))
% 52.62/52.40 [3402]E(f332(f181(f846(x34021)),f332(f157(x34021),x34022)),f332(f332(f3(a845),f332(f181(f846(x34021)),x34022)),f80(a845)))
% 52.62/52.40 [3430]E(f332(f332(f44(a1),f53(a1,x34301,x34302)),x34302),f2(a1))
% 52.62/52.40 [3439]E(f332(a5,f53(a845,f332(a22,x34391),f332(a22,x34392))),f53(a101,x34391,x34392))
% 52.62/52.40 [3471]E(f332(a5,f332(f332(f82(a845),f332(a22,x34711)),f332(a22,x34712))),f332(f332(f82(a101),x34711),x34712))
% 52.62/52.40 [3472]E(f332(a5,f332(f332(f83(a845),f332(a22,x34721)),f332(a22,x34722))),f332(f332(f83(a101),x34721),x34722))
% 52.62/52.40 [3473]E(f332(a5,f332(f332(f44(a845),f332(a22,x34731)),f332(a22,x34732))),f332(f332(f44(a101),x34731),x34732))
% 52.62/52.40 [3474]E(f332(a5,f332(f332(f3(a845),f332(a22,x34741)),f332(a22,x34742))),f332(f332(f3(a101),x34741),x34742))
% 52.62/52.40 [3483]E(f332(f303(a845,a845,a114),f332(f294(a845,x34831),x34832)),f332(f294(a845,f332(a114,x34831)),f332(a114,x34832)))
% 52.62/52.40 [3509]P1(f332(f56(x35091,x35092),f87(f852(a845,a845),f56(x35091,x35092))))
% 52.62/52.40 [3526]E(f332(f332(f82(a845),f332(f332(f82(a845),f34(x35261)),f34(x35262))),f332(a114,f2(a845))),f34(f36(x35261,x35262)))
% 52.62/52.40 [3527]E(f53(a845,f332(a114,f53(a845,x35271,x35272)),x35272),f53(a845,f332(a114,x35271),x35272))
% 52.62/52.40 [3541]E(f332(f332(f48(f853(x35411,a839),f853(x35411,a839)),x35412),f7(f853(x35411,a839))),f46(f853(x35411,a839),x35412))
% 52.62/52.40 [3542]E(f332(f332(f47(f853(x35421,a839),f853(x35421,a839)),x35422),f7(f853(x35421,a839))),f45(f853(x35421,a839),x35422))
% 52.62/52.40 [3545]P1(f332(f332(f334(f853(x35451,a839)),x35452),f332(f301(x35451),x35452)))
% 52.62/52.40 [3550]E(f53(a1,f332(f81(a1),f53(a1,x35501,x35502)),x35502),f53(a1,f332(f81(a1),x35501),x35502))
% 52.62/52.40 [3562]P1(f332(f332(f232(f853(x35621,a839)),x35622),f239(f853(x35621,a839))))
% 52.62/52.40 [3564]E(f332(f332(f281(x35641,x35641,x35641),f300(x35641,x35642)),f300(x35641,f300(x35641,x35642))),f300(x35641,x35642))
% 52.62/52.40 [3565]E(f332(f332(f103(f853(x35651,a839)),f332(f261(x35651,x35651),x35652)),f332(f259(x35651,x35651),x35652)),f332(f276(x35651),x35652))
% 52.62/52.40 [3587]E(f314(x35871,x35872,f239(f853(x35871,a839)),f239(f853(x35872,a839))),f239(f853(f854(x35871,x35872),a839)))
% 52.62/52.40 [3638]P1(f332(f332(f232(a845),f53(a845,x36381,x36382)),x36381))
% 52.62/52.40 [3662]P1(f332(f332(f232(a1),f332(f81(a1),f332(f102(a1),x36621))),f332(f102(a1),x36622)))
% 52.62/52.40 [3687]P1(f332(f332(f334(f853(x36871,a839)),f180(f853(x36871,a839))),f332(f301(x36871),x36872)))
% 52.62/52.40 [3692]E(f300(x36921,f332(f332(f281(x36921,x36921,x36921),x36922),f300(x36921,x36922))),f300(x36921,x36922))
% 52.62/52.40 [3694]E(f332(f332(f281(x36941,x36941,x36941),f300(x36941,x36942)),x36942),f332(f332(f281(x36941,x36941,x36941),x36942),f300(x36941,x36942)))
% 52.62/52.40 [3695]E(f332(f332(f281(x36951,x36951,x36951),f300(x36951,x36952)),x36952),f332(f332(f281(x36951,x36951,x36951),x36952),f300(x36951,x36952)))
% 52.62/52.40 [3697]E(f332(a107,f332(f332(f82(a1),f332(f332(f3(a1),x36971),x36972)),f80(a1))),f332(f43(a1),f295(a1,x36972,x36971)))
% 52.62/52.40 [3714]E(f332(f259(x37141,x37141),f332(f332(f281(x37141,x37141,x37141),x37142),f300(x37141,x37142))),f332(f259(x37141,x37141),x37142))
% 52.62/52.40 [3715]E(f332(f261(x37151,x37151),f332(f332(f281(x37151,x37151,x37151),x37152),f300(x37151,x37152))),f332(f261(x37151,x37151),x37152))
% 52.62/52.40 [3729]E(f332(f332(f82(a845),f332(f332(f82(a845),f332(f181(a840),x37291)),f332(f181(a840),x37292))),f332(a114,f2(a845))),f332(f181(a840),f36(x37291,x37292)))
% 52.62/52.40 [3741]P31(a845,a845,f332(f332(f9(a845,a845,a845),f82(a845)),x37411),x37412)
% 52.62/52.40 [3743]P20(a845,f332(f142(a845),f332(f332(f143(f846(x37431),a845),f181(f846(x37431))),f164(x37431,x37432))))
% 52.62/52.40 [3790]P1(f332(f332(f233(a1),f332(f81(a1),f332(f102(a1),f332(a114,x37901)))),f332(f102(a1),x37902)))
% 52.62/52.40 [3830]E(f332(f132(f846(x38301),x38301,f332(f9(x38301,f846(x38301),f846(x38301)),f140(x38301)),f115(x38301)),x38302),f332(f142(x38301),x38302))
% 52.62/52.40 [3879]P1(f332(f332(f232(f853(f852(f846(x38791),f846(x38791)),a839)),f147(x38791,x38792)),f300(f846(x38791),f146(x38791,x38792))))
% 52.62/52.40 [3912]P1(f332(f56(x39121,x39122),f332(f332(f241(a845,a845),f332(f332(f44(a845),x39121),x39122)),f53(a845,x39121,x39122))))
% 52.62/52.40 [3923]P1(f332(f332(f232(f853(f852(f846(x39231),f846(x39231)),a839)),f146(x39231,f300(x39231,x39232))),f300(f846(x39231),f146(x39231,x39232))))
% 52.62/52.40 [4154]E(f332(f332(f253(f852(a101,a101),a101,f852(a101,a101),f852(x41541,f852(a101,a101))),f264(f332(f154(a101),f332(f332(f143(f852(a101,x41541),a101),f240(a101,x41541)),x41542)))),f332(f332(f10(x41541,f853(f852(a101,a101),f852(x41541,f852(a101,a101))),a101),f241(x41541,f852(a101,a101))),f265(x41541,x41542))),f263(x41541,x41542))
% 52.62/52.40 [4299]E(f53(a845,f332(f332(f82(a845),f332(f106(a845),f332(f332(f3(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))),a99))),x42991),f332(f106(a845),x42992)),f53(a845,f332(a114,f332(a114,f332(a114,x42991))),f332(f106(a845),x42992)))
% 52.62/52.40 [4313]E(f332(f332(f44(a845),f332(f332(f82(a845),f332(f106(a845),f332(f332(f3(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))),a99))),x43131)),f332(f106(a845),x43132)),f332(f332(f44(a845),f332(a114,f332(a114,f332(a114,x43131)))),f332(f106(a845),x43132)))
% 52.62/52.40 [4333]E(f332(f251(f853(f852(x43331,x43331),a839),f853(f852(x43331,x43331),a839),f853(f853(x43332,x43331),f852(f853(f852(x43332,x43332),a839),f853(f852(x43332,x43332),a839)))),f332(f332(f9(f853(f852(x43331,x43331),a839),f853(f853(f852(x43331,x43331),a839),f853(f853(x43332,x43331),f853(f852(x43332,x43332),a839))),f853(f853(f852(x43331,x43331),a839),f853(f853(x43332,x43331),f852(f853(f852(x43332,x43332),a839),f853(f852(x43332,x43332),a839))))),f332(f332(f10(f853(f853(f853(x43332,x43331),f853(f852(x43332,x43332),a839)),f853(f853(x43332,x43331),f852(f853(f852(x43332,x43332),a839),f853(f852(x43332,x43332),a839)))),f853(f853(f853(f852(x43331,x43331),a839),f853(f853(x43332,x43331),f853(f852(x43332,x43332),a839))),f853(f853(f852(x43331,x43331),a839),f853(f853(x43332,x43331),f852(f853(f852(x43332,x43332),a839),f853(f852(x43332,x43332),a839))))),f853(f852(x43331,x43331),a839)),f10(f853(f853(x43332,x43331),f853(f852(x43332,x43332),a839)),f853(f853(x43332,x43331),f852(f853(f852(x43332,x43332),a839),f853(f852(x43332,x43332),a839))),f853(f852(x43331,x43331),a839))),f332(f332(f10(f853(f853(x43332,x43331),f853(f853(f852(x43332,x43332),a839),f852(f853(f852(x43332,x43332),a839),f853(f852(x43332,x43332),a839)))),f853(f853(f853(x43332,x43331),f853(f852(x43332,x43332),a839)),f853(f853(x43332,x43331),f852(f853(f852(x43332,x43332),a839),f853(f852(x43332,x43332),a839)))),f853(f852(x43331,x43331),a839)),f20(f853(x43332,x43331),f853(f852(x43332,x43332),a839),f852(f853(f852(x43332,x43332),a839),f853(f852(x43332,x43332),a839)))),f332(f332(f10(f853(f853(x43332,x43331),f853(f852(x43332,x43332),a839)),f853(f853(x43332,x43331),f853(f853(f852(x43332,x43332),a839),f852(f853(f852(x43332,x43332),a839),f853(f852(x43332,x43332),a839)))),f853(f852(x43331,x43331),a839)),f332(f10(f853(f852(x43332,x43332),a839),f853(f853(f852(x43332,x43332),a839),f852(f853(f852(x43332,x43332),a839),f853(f852(x43332,x43332),a839))),f853(x43332,x43331)),f241(f853(f852(x43332,x43332),a839),f853(f852(x43332,x43332),a839)))),f280(x43331,x43332))))),f280(x43331,x43332))),f76(x43331,x43332))
% 52.62/52.40 [4448]~E(f332(f301(x44481),x44482),f180(f853(f853(x44481,a839),a839)))
% 52.62/52.40 [4465]~P1(f332(f332(f334(x44651),x44652),f180(f853(x44651,a839))))
% 52.62/52.40 [4466]~P1(f332(f332(f334(x44661),x44662),f180(f853(x44661,a839))))
% 52.62/52.40 [4475]~P1(f332(f332(f233(f853(x44751,a839)),x44752),f180(f853(x44751,a839))))
% 52.62/52.40 [3253]E(f332(f332(f3(a845),x32531),f332(f332(f82(a845),x32531),x32532)),f2(a845))
% 52.62/52.40 [3255]E(f332(f332(f103(f853(x32551,a839)),x32552),x32552),x32552)
% 52.62/52.40 [3256]E(f332(f332(f104(f853(x32561,a839)),x32562),x32562),x32562)
% 52.62/52.40 [3283]E(f332(f332(f3(f853(x32831,a839)),x32832),x32832),f180(f853(x32831,a839)))
% 52.62/52.40 [3286]E(f332(f133(x32861,x32862),f2(a845)),f180(f853(f852(f846(x32861),f846(x32861)),a839)))
% 52.62/52.40 [3287]E(f332(f332(f82(a845),x32871),f332(a114,x32872)),f332(a114,f332(f332(f82(a845),x32871),x32872)))
% 52.62/52.40 [3299]E(f188(f332(f102(a1),x32991),f332(f102(a1),x32992)),f332(f102(a1),f332(f332(f3(a845),x32991),x32992)))
% 52.62/52.40 [3302]E(f332(f332(f44(a1),f332(f81(a1),x33021)),x33022),f332(f332(f44(a1),x33021),f332(f81(a1),x33022)))
% 52.62/52.40 [3306]E(f332(f43(a1),f332(f294(a1,x33061),x33062)),f332(a107,f332(f332(f3(a1),x33062),x33061)))
% 52.62/52.40 [3309]E(f332(f332(f82(a845),f332(a114,x33091)),x33092),f332(a114,f332(f332(f82(a845),x33091),x33092)))
% 52.62/52.40 [3314]E(f332(f81(f853(x33141,a839)),f332(f81(f853(x33141,a839)),x33142)),x33142)
% 52.62/52.40 [3327]E(f164(x33271,f332(f332(f140(f846(x33271)),f115(x33271)),x33272)),f164(x33271,x33272))
% 52.62/52.40 [3331]E(f332(f332(f82(a845),x33311),f332(f332(f83(a845),x33311),x33312)),f332(f332(f83(a845),x33311),f332(a114,x33312)))
% 52.62/52.40 [3339]E(f332(f332(a4,f332(a5,x33391)),f332(a5,x33392)),f332(a5,f332(f332(f3(a845),x33391),x33392)))
% 52.62/52.40 [3349]E(f332(f332(f242(a1),f332(f102(a1),x33491)),x33492),f332(f102(a1),f332(f332(f242(a845),x33491),x33492)))
% 52.62/52.40 [3350]E(f332(f332(f83(a1),f332(f81(a1),x33501)),x33502),f332(f81(a1),f332(f332(f83(a1),x33501),x33502)))
% 52.62/52.40 [3351]E(f332(f332(f242(a1),f332(f102(a1),x33511)),x33512),f332(f102(a1),f332(f332(f242(a845),x33511),x33512)))
% 52.62/52.40 [3352]E(f332(f332(f242(a1),f332(f102(a1),x33521)),x33522),f332(f102(a1),f332(f332(f242(a845),x33521),x33522)))
% 52.62/52.40 [3353]E(f332(f332(f82(a101),f332(a5,x33531)),f332(a5,x33532)),f332(a5,f332(f332(f82(a845),x33531),x33532)))
% 52.62/52.40 [3354]E(f332(f332(f83(a101),f332(a5,x33541)),f332(a5,x33542)),f332(a5,f332(f332(f83(a845),x33541),x33542)))
% 52.62/52.40 [3355]E(f332(f332(f236(a845),f332(a114,x33551)),f332(a114,x33552)),f332(a114,f332(f332(f236(a845),x33551),x33552)))
% 52.62/52.40 [3356]E(f332(f332(f179(a845),f332(a114,x33561)),f332(a114,x33562)),f332(a114,f332(f332(f179(a845),x33561),x33562)))
% 52.62/52.40 [3361]E(f332(f158(a845),f130(a845,f332(f294(a845,x33611),x33612))),f332(f294(a845,x33611),x33612))
% 52.62/52.40 [3362]E(f332(f158(a845),f130(a845,f332(f294(a845,x33621),x33622))),f332(f294(a845,x33621),x33622))
% 52.62/52.40 [3363]E(f306(x33631,f332(f332(f302(x33631),x33632),f180(f853(x33631,a839)))),x33632)
% 52.62/52.40 [3368]E(f332(f259(x33681,x33682),f180(f853(f852(x33681,x33682),a839))),f180(f853(x33682,a839)))
% 52.62/52.40 [3369]E(f332(f261(x33691,x33692),f180(f853(f852(x33691,x33692),a839))),f180(f853(x33691,a839)))
% 52.62/52.40 [3373]E(f332(a107,f332(f332(f3(a1),x33731),x33732)),f332(f43(a1),f297(a1,x33732,x33731)))
% 52.62/52.40 [3377]E(f332(f332(f82(a845),x33771),f332(f332(f83(a845),x33772),x33771)),f332(f332(f83(a845),f332(a114,x33772)),x33771))
% 52.62/52.40 [3379]E(f332(f332(f62(x33791),f180(f853(x33791,a839))),x33792),f180(f853(f853(x33791,a839),a839)))
% 52.62/52.40 [3388]E(f332(f181(f846(a845)),f130(a845,f332(f294(a845,x33881),x33882))),f332(f332(f3(a845),x33882),x33881))
% 52.62/52.40 [3409]E(f332(f332(f103(f853(x34091,a839)),f180(f853(x34091,a839))),x34092),x34092)
% 52.62/52.40 [3410]E(f332(f332(f104(f853(x34101,a839)),f239(f853(x34101,a839))),x34102),x34102)
% 52.62/52.40 [3411]E(f332(f332(f83(a1),f332(f102(a1),x34111)),f332(f102(a1),x34112)),f332(f102(a1),f332(f332(f83(a845),x34111),x34112)))
% 52.62/52.40 [3412]E(f332(f332(f44(a1),f332(f102(a1),x34121)),f332(f102(a1),x34122)),f332(f102(a1),f332(f332(f44(a845),x34121),x34122)))
% 52.62/52.40 [3413]E(f332(f332(f82(a1),f332(f81(a1),x34131)),f332(f81(a1),x34132)),f332(f81(a1),f332(f332(f82(a1),x34131),x34132)))
% 52.62/52.40 [3415]E(f332(f332(f82(a1),f332(f102(a1),x34151)),f332(f102(a1),x34152)),f332(f102(a1),f332(f332(f82(a845),x34151),x34152)))
% 52.62/52.40 [3416]E(f332(f332(f82(a1),f332(f102(a1),x34161)),f332(f102(a1),x34162)),f332(f102(a1),f332(f332(f82(a845),x34161),x34162)))
% 52.62/52.40 [3417]E(f332(f332(f82(a1),f332(f106(a1),x34171)),f332(f106(a1),x34172)),f332(f106(a1),f332(f332(f82(a1),x34171),x34172)))
% 52.62/52.40 [3418]E(f332(f332(f83(a1),f332(f102(a1),x34181)),f332(f102(a1),x34182)),f332(f102(a1),f332(f332(f83(a845),x34181),x34182)))
% 52.62/52.40 [3419]E(f332(f332(f83(a1),f332(f102(a1),x34191)),f332(f102(a1),x34192)),f332(f102(a1),f332(f332(f83(a845),x34191),x34192)))
% 52.62/52.40 [3420]E(f332(f332(f83(a1),f332(f106(a1),x34201)),f332(f106(a1),x34202)),f332(f106(a1),f332(f332(f83(a1),x34201),x34202)))
% 52.62/52.40 [3421]E(f332(f332(f44(a1),f332(f102(a1),x34211)),f332(f102(a1),x34212)),f332(f102(a1),f332(f332(f44(a845),x34211),x34212)))
% 52.62/52.40 [3440]E(f332(f332(f8(x34401,a845),f332(f18(a845,x34401),f80(a845))),x34402),f332(f43(x34401),x34402))
% 52.62/52.40 [3447]E(f332(f81(a1),f53(a1,f332(f81(a1),x34471),x34472)),f53(a1,x34471,f332(f81(a1),x34472)))
% 52.62/52.40 [3449]E(f332(f158(a1),f163(x34491,f332(f332(f3(a1),x34492),f80(a1)))),f332(f294(a1,x34491),x34492))
% 52.62/52.40 [3453]P1(f332(f332(f232(a845),x34531),f332(f332(f82(a845),x34532),x34531)))
% 52.62/52.40 [3454]P1(f332(f332(f232(a845),x34541),f332(f332(f82(a845),x34541),x34542)))
% 52.62/52.40 [3457]E(f332(f332(f3(f853(x34571,a839)),f180(f853(x34571,a839))),x34572),f180(f853(x34571,a839)))
% 52.62/52.40 [3458]E(f332(f332(f103(f853(x34581,a839)),f239(f853(x34581,a839))),x34582),f239(f853(x34581,a839)))
% 52.62/52.40 [3459]E(f332(f332(f104(f853(x34591,a839)),f180(f853(x34591,a839))),x34592),f180(f853(x34591,a839)))
% 52.62/52.40 [3464]E(f332(f332(f241(a1,a1),x34641),f332(f81(a1),x34642)),f332(a59,f332(f332(f241(a1,a1),x34641),x34642)))
% 52.62/52.40 [3465]E(f332(f294(a1,f332(f332(f82(a1),x34651),f80(a1))),x34652),f298(a1,x34651,x34652))
% 52.62/52.40 [3475]E(f332(f332(f83(a845),x34751),f332(f332(f44(a845),x34752),x34751)),f332(f332(f3(a845),x34752),f53(a845,x34752,x34751)))
% 52.62/52.40 [3476]E(f332(f332(f83(a1),x34761),f332(f332(f44(a1),x34762),x34761)),f332(f332(f3(a1),x34762),f53(a1,x34762,x34761)))
% 52.62/52.40 [3480]E(f332(f158(a1),f163(f332(f332(f82(a1),x34801),f80(a1)),x34802)),f297(a1,x34801,x34802))
% 52.62/52.40 [3484]P1(f332(f332(f232(f853(x34841,a839)),x34842),x34842))
% 52.62/52.40 [3489]E(f332(f332(f103(f853(x34891,a839)),x34892),f332(f81(f853(x34891,a839)),x34892)),f239(f853(x34891,a839)))
% 52.62/52.40 [3490]E(f332(f332(f104(f853(x34901,a839)),x34902),f332(f81(f853(x34901,a839)),x34902)),f180(f853(x34901,a839)))
% 52.62/52.40 [3496]E(f332(f332(f3(a845),f332(f332(f3(a845),x34961),f80(a845))),x34962),f332(f332(f3(a845),x34961),f332(a114,x34962)))
% 52.62/52.40 [3501]E(f332(f332(f3(f853(x35011,a839)),f239(f853(x35011,a839))),x35012),f332(f81(f853(x35011,a839)),x35012))
% 52.62/52.40 [3502]E(f332(f332(f3(a1),f332(f106(a1),x35021)),f332(f106(a1),x35022)),f332(f106(a1),f332(f332(f82(a1),x35021),f332(f81(a1),x35022))))
% 52.62/52.40 [3514]E(f332(f158(a845),f130(a845,f332(f294(a845,x35141),f332(a114,x35142)))),f295(a845,x35141,x35142))
% 52.62/52.40 [3543]E(f332(f332(f173(f852(x35431,x35431),a839),f2(a845)),x35432),f300(x35431,f180(f853(f852(x35431,x35431),a839))))
% 52.62/52.40 [3547]P1(f332(f127(a845),f130(a845,f332(f294(a845,x35471),x35472))))
% 52.62/52.40 [3563]E(f332(f303(a1,a845,a107),f295(a1,f332(f102(a1),x35631),f332(f102(a1),x35632))),f295(a845,x35631,x35632))
% 52.62/52.40 [3573]E(f175(a845,f2(a845),f7(a845),f332(f332(f3(a845),x35731),x35732)),f332(f332(f3(a845),x35731),f332(a114,x35732)))
% 52.62/52.40 [3574]E(f332(a107,f332(f332(f3(a1),x35741),f332(f332(f82(a1),x35742),f80(a1)))),f332(f43(a1),f298(a1,x35742,x35741)))
% 52.62/52.40 [3609]E(f332(f332(f143(a845,a845),a114),f130(a845,f332(f294(a845,x36091),x36092))),f130(a845,f332(f294(a845,f332(a114,x36091)),f332(a114,x36092))))
% 52.62/52.40 [3616]E(f332(f158(a1),f163(f332(f332(f82(a1),x36161),f80(a1)),f332(f332(f3(a1),x36162),f80(a1)))),f298(a1,x36161,x36162))
% 52.62/52.40 [3630]P1(f332(f332(f232(f853(x36301,a839)),f180(f853(x36301,a839))),x36302))
% 52.62/52.40 [3634]E(f87(x36341,f332(f332(f9(x36341,x36341,a839),a329),x36342)),x36342)
% 52.62/52.40 [3635]E(f92(x36351,f332(f332(f9(x36351,x36351,a839),a329),x36352)),x36352)
% 52.62/52.40 [3639]E(f332(f158(a845),f130(a845,f332(f294(a845,f332(a114,x36391)),f332(a114,x36392)))),f297(a845,x36391,x36392))
% 52.62/52.40 [3665]E(f332(f332(f248(x36651,x36652),f239(f853(x36651,a839))),f332(f18(f853(x36652,a839),x36651),f239(f853(x36652,a839)))),f239(f853(f852(x36651,x36652),a839)))
% 52.62/52.40 [3701]E(f332(f256(x37011),f332(f332(f10(a839,a839,x37011),a328),x37012)),f332(f81(f853(x37011,a839)),f332(f256(x37011),x37012)))
% 52.62/52.40 [3704]E(f332(f256(x37041),f332(f332(f9(x37041,x37041,a839),a329),x37042)),f332(f332(f302(x37041),x37042),f180(f853(x37041,a839))))
% 52.62/52.40 [3711]E(f332(f332(f82(a1),f332(f332(f82(a1),x37111),x37111)),f332(f332(f82(a1),x37112),x37112)),f332(f332(f82(a1),f332(f332(f82(a1),x37111),x37112)),f332(f332(f82(a1),x37111),x37112)))
% 52.62/52.40 [3712]E(f332(f332(f3(a1),f332(f332(f82(a1),x37121),x37121)),f332(f332(f82(a1),x37122),x37122)),f332(f332(f82(a1),f332(f332(f3(a1),x37121),x37122)),f332(f332(f3(a1),x37121),x37122)))
% 52.62/52.40 [3727]P1(f332(f332(f232(a845),f332(f43(x37271),f332(f158(x37271),x37272))),f332(f181(f846(x37271)),x37272)))
% 52.62/52.40 [3738]E(f332(f256(x37381),f332(f332(f9(x37381,f853(x37381,a839),a839),f334(x37381)),x37382)),x37382)
% 52.62/52.40 [3754]E(f332(f332(f159(x37541),f332(f332(f3(a845),f332(f181(f846(x37541)),x37542)),f80(a845))),x37542),f116(x37541,x37542))
% 52.62/52.40 [3777]E(f175(a845,f2(a845),f332(f332(f10(a845,a845,a845),a114),f332(f236(a845),x37771)),x37772),f332(f332(f236(a845),f332(a114,x37771)),x37772))
% 52.62/52.40 [3781]E(f45(f853(x37811,a839),f332(f303(f853(f852(x37811,x37811),a839),f853(x37811,a839),f276(x37811)),x37812)),f332(f276(x37811),f45(f853(f852(x37811,x37811),a839),x37812)))
% 52.62/52.40 [3782]E(f175(a845,f332(a114,x37821),f332(f332(f10(a845,a845,a845),a114),f332(f179(a845),x37821)),x37822),f332(f332(f179(a845),f332(a114,x37821)),x37822))
% 52.62/52.40 [3784]E(f332(f332(f241(a1,a1),f332(f332(f44(a1),f332(f77(a1),x37841)),f332(f77(a1),x37842))),f53(a1,f332(f77(a1),x37841),f332(f77(a1),x37842))),f61(x37841,x37842))
% 52.62/52.40 [3804]P1(f332(f332(f232(f853(f853(x38041,a839),a839)),x38042),f332(f301(x38041),f45(f853(x38041,a839),x38042))))
% 52.62/52.40 [3835]E(f332(f332(f47(x38351,f853(x38351,a839)),x38352),f332(f332(f9(x38351,f853(x38351,a839),f853(x38351,a839)),f302(x38351)),f180(f853(x38351,a839)))),x38352)
% 52.62/52.40 [3836]E(f332(f332(f281(x38361,x38361,x38361),f332(f278(x38361,x38361),x38362)),f300(x38361,f332(f278(x38361,x38361),x38362))),f332(f278(x38361,x38361),f332(f332(f281(x38361,x38361,x38361),x38362),f300(x38361,x38362))))
% 52.62/52.40 [3904]E(f332(f158(x39041),f332(f132(f846(x39041),f846(x39041),f125(x39041),f115(x39041)),x39042)),f332(f332(f47(f846(x39041),f853(x39041,a839)),f332(f158(f846(x39041)),x39042)),f158(x39041)))
% 52.62/52.40 [3935]E(f332(f332(f103(f853(f852(x39351,x39351),a839)),f300(x39351,f180(f853(f852(x39351,x39351),a839)))),f332(f332(f281(x39351,x39351,x39351),f300(x39351,x39352)),x39352)),f300(x39351,x39352))
% 52.62/52.40 [3973]E(f332(f332(f167(x39731,x39731),x39732),x39732),f332(f332(f143(x39731,f852(x39731,x39731)),f332(f332(f20(x39731,x39731,f852(x39731,x39731)),f241(x39731,x39731)),f7(x39731))),x39732))
% 52.62/52.40 [4087]E(f332(f132(a845,f846(x40871),f332(f9(f846(x40871),a845,a845),f332(f332(f10(a845,f853(a845,a845),f846(x40871)),f179(a845)),f181(f846(x40871)))),f2(a845)),f332(f142(f846(x40871)),x40872)),f332(f181(f846(f846(x40871))),f164(x40871,x40872)))
% 52.62/52.40 [4167]E(f332(f332(f280(f852(a845,f846(x41671)),f846(x41671)),f326(a845,f846(x41671),a237,f135(x41671,x41672))),f332(f332(f20(f846(x41671),f846(x41671),f852(a845,f846(x41671))),f332(f332(f10(a845,f853(f846(x41671),f852(a845,f846(x41671))),f846(x41671)),f241(a845,f846(x41671))),f181(f846(x41671)))),f7(f846(x41671)))),f136(x41671,x41672))
% 52.62/52.40 [4290]E(f332(f256(x42901),f332(f332(f10(f853(f853(x42901,a839),a839),a839,x42901),f90(f853(x42901,a839))),f332(f332(f10(f853(f853(x42901,a839),a839),f853(f853(x42901,a839),a839),x42901),f332(f20(f853(x42901,a839),a839,a839),f332(f332(f10(a839,f853(a839,a839),f853(x42901,a839)),a335),f332(f332(f9(f853(x42901,a839),f853(f853(x42901,a839),a839),a839),f334(f853(x42901,a839))),x42902)))),f334(x42901)))),f46(f853(x42901,a839),x42902))
% 52.62/52.40 [4476]~P1(f332(f332(f233(a1),f332(f102(a1),x44761)),f332(f81(a1),f332(f102(a1),x44762))))
% 52.62/52.40 [3375]E(f332(f332(f3(a845),f332(f332(f82(a845),x33751),x33752)),x33752),x33751)
% 52.62/52.40 [3376]E(f332(f332(f3(a845),f332(f332(f82(a845),x33761),x33762)),x33761),x33762)
% 52.62/52.40 [3448]E(f332(f332(f82(a845),f332(f332(f3(a845),x34481),x34482)),x34482),f332(f332(f179(a845),x34481),x34482))
% 52.62/52.40 [3549]E(f332(f332(f83(a845),f332(f332(f44(a845),x35491),x35492)),x35492),f332(f332(f3(a845),x35491),f53(a845,x35491,x35492)))
% 52.62/52.40 [3578]E(f332(f158(a845),f130(a845,f332(f294(a845,f332(a114,x35781)),x35782))),f298(a845,x35781,x35782))
% 52.62/52.40 [3586]E(f332(f102(a1),f211(f332(a107,f332(f77(a1),x35861)),f332(a107,f332(f77(a1),x35862)))),f332(f332(a212,x35861),x35862))
% 52.62/52.40 [3588]E(f332(f332(f103(f853(x35881,a839)),f332(f81(f853(x35881,a839)),x35882)),x35882),f239(f853(x35881,a839)))
% 52.62/52.40 [3589]E(f332(f332(f104(f853(x35891,a839)),f332(f81(f853(x35891,a839)),x35892)),x35892),f180(f853(x35891,a839)))
% 52.62/52.40 [3605]P1(f332(f332(f232(a845),f332(f332(f44(a845),x36051),x36052)),x36051))
% 52.62/52.40 [3606]P1(f332(f332(f232(a845),f332(f332(f3(a845),x36061),x36062)),x36061))
% 52.62/52.40 [3631]P1(f332(f332(f233(a845),x36311),f332(a114,f332(f332(f82(a845),x36312),x36311))))
% 52.62/52.40 [3632]P1(f332(f332(f233(a845),x36321),f332(a114,f332(f332(f82(a845),x36321),x36322))))
% 52.62/52.40 [3651]E(f332(f332(f83(a845),f332(a107,f332(f77(a1),x36511))),f332(a107,f332(f77(a1),x36512))),f332(a107,f332(f77(a1),f332(f332(f83(a1),x36511),x36512))))
% 52.62/52.40 [3658]E(f332(f332(f82(a1),f332(f332(f83(a1),x36581),x36582)),f332(f332(f83(a1),x36581),x36582)),f332(f332(f83(a1),f332(f332(f82(a1),x36581),x36581)),x36582))
% 52.62/52.40 [3661]P1(f332(f332(f232(a1),f2(a1)),f332(f332(f242(a1),f332(f77(a1),x36611)),x36612)))
% 52.62/52.40 [3732]E(f332(f277(f846(x37321),f846(x37321),f147(x37321,x37322)),f332(f332(f302(f846(x37321)),f115(x37321)),f180(f853(f846(x37321),a839)))),f332(f332(f302(f846(x37321)),f115(x37321)),f180(f853(f846(x37321),a839))))
% 52.62/52.40 [3750]E(f332(f332(f103(f853(f852(x37501,x37501),a839)),f300(x37501,x37502)),f300(x37501,f180(f853(f852(x37501,x37501),a839)))),f300(x37501,x37502))
% 52.62/52.40 [3766]E(f332(f332(f44(a1),f332(f106(a1),f332(f332(f82(a1),x37661),x37661))),f332(f106(a1),f332(f332(f82(a1),x37662),x37662))),f332(f332(f44(a1),f332(f106(a1),x37661)),f332(f106(a1),x37662)))
% 52.62/52.40 [3825]E(f332(f332(f242(a1),x38251),f332(f106(a845),f332(f332(f82(a1),x38252),x38252))),f332(f332(f88(a1,a1),f332(f332(f242(a1),x38251),f332(f106(a845),x38252))),f332(f332(f20(a1,a1,a1),f83(a1)),f7(a1))))
% 52.62/52.40 [3831]E(f332(f256(f853(x38311,a839)),f332(f332(f9(f853(x38311,a839),f853(x38311,a839),a839),f232(f853(x38311,a839))),x38312)),f332(f301(x38311),x38312))
% 52.62/52.40 [3878]E(f332(f303(a1,a1,f332(f332(f9(a1,a1,a1),f82(a1)),x38781)),f332(f294(a1,f2(a1)),f332(f332(f3(a1),x38782),x38781))),f332(f294(a1,x38781),x38782))
% 52.62/52.40 [3881]P50(x38811,f332(f332(f3(f853(f852(x38811,x38811),a839)),x38812),f300(x38811,f180(f853(f852(x38811,x38811),a839)))))
% 52.62/52.40 [3901]E(f332(f181(f846(x39011)),f332(f132(f846(x39011),f846(x39011),f125(x39011),f115(x39011)),x39012)),f332(f154(a845),f332(f332(f143(f846(x39011),a845),f181(f846(x39011))),x39012)))
% 52.62/52.40 [3906]P49(x39061,f239(f853(x39061,a839)),f332(f332(f103(f853(f852(x39061,x39061),a839)),x39062),f300(x39061,f180(f853(f852(x39061,x39061),a839)))))
% 52.62/52.40 [3946]P1(f332(f332(f334(f852(x39461,x39461)),f332(f332(f241(x39461,x39461),x39462),x39462)),f300(x39461,f180(f853(f852(x39461,x39461),a839)))))
% 52.62/52.40 [3952]E(f175(a845,f2(a845),f332(f332(f10(a845,a845,a845),a114),f332(f332(f9(a845,a845,a845),f236(a845)),x39521)),x39522),f332(f332(f236(a845),x39522),f332(a114,x39521)))
% 52.62/52.40 [3955]E(f175(a845,f332(a114,x39551),f332(f332(f10(a845,a845,a845),a114),f332(f332(f9(a845,a845,a845),f179(a845)),x39551)),x39552),f332(f332(f179(a845),x39552),f332(a114,x39551)))
% 52.62/52.40 [3958]E(f332(f303(x39581,f846(x39581),f332(f332(f9(x39581,f846(x39581),f846(x39581)),f140(x39581)),f115(x39581))),x39582),f161(x39581,x39582,f332(f332(f302(f846(x39581)),f115(x39581)),f180(f853(f846(x39581),a839)))))
% 52.62/52.40 [3959]E(f332(f332(f103(f853(f852(x39591,x39591),a839)),f332(f332(f281(x39591,x39591,x39591),x39592),f300(x39591,x39592))),f300(x39591,f180(f853(f852(x39591,x39591),a839)))),f300(x39591,x39592))
% 52.62/52.40 [3967]P1(f332(f332(f232(f853(f852(x39671,x39671),a839)),f260(x39671,x39672)),f332(f332(f248(x39671,x39671),x39672),f332(f18(f853(x39671,a839),x39671),x39672))))
% 52.62/52.40 [3971]E(f332(f303(a1,a845,a107),f332(f332(f103(f853(a1,a839)),f332(f303(a845,a1,f102(a1)),x39711)),f332(f303(a845,a1,f102(a1)),x39712))),f332(f332(f103(f853(a845,a839)),x39711),x39712))
% 52.62/52.40 [3972]E(f332(f303(a1,a845,a107),f332(f332(f104(f853(a1,a839)),f332(f303(a845,a1,f102(a1)),x39721)),f332(f303(a845,a1,f102(a1)),x39722))),f332(f332(f104(f853(a845,a839)),x39721),x39722))
% 52.62/52.40 [3976]E(f332(f256(x39761),f332(f332(f10(a839,a839,x39761),a328),f332(f332(f9(x39761,f853(x39761,a839),a839),f334(x39761)),x39762))),f332(f81(f853(x39761,a839)),x39762))
% 52.62/52.40 [4003]E(f332(f132(f846(x40031),f846(x40031),f125(x40031),f115(x40031)),f332(f332(f143(f846(x40031),f846(x40031)),f142(x40031)),f332(f142(f846(x40031)),x40032))),f332(f142(x40031),f332(f132(f846(x40031),f846(x40031),f125(x40031),f115(x40031)),x40032)))
% 52.62/52.40 [4030]E(f332(f332(f47(a845,f853(f852(x40301,x40301),a839)),f239(f853(a845,a839))),f332(f332(f9(a845,f853(f852(x40301,x40301),a839),f853(f852(x40301,x40301),a839)),f173(f852(x40301,x40301),a839)),x40302)),f300(x40301,x40302))
% 52.62/52.40 [4052]E(f87(x40521,f332(f332(f10(f853(x40521,a839),a839,x40521),f332(a329,x40522)),f332(f332(f9(x40521,f853(x40521,a839),f853(x40521,a839)),f302(x40521)),f180(f853(x40521,a839))))),f306(x40521,x40522))
% 52.62/52.40 [4060]E(f332(f181(f846(x40601)),f156(x40601,f332(f132(f846(x40601),f846(x40601),f125(x40601),f115(x40601)),x40602))),f332(f43(x40601),f332(f332(f47(f846(x40601),f853(x40601,a839)),f332(f158(f846(x40601)),x40602)),f158(x40601))))
% 52.62/52.40 [4075]E(f332(f332(f103(f853(f852(x40751,x40751),a839)),x40752),f332(f332(f281(x40751,x40751,x40751),f332(f332(f281(x40751,x40751,x40751),x40752),f300(x40751,x40752))),x40752)),f332(f332(f281(x40751,x40751,x40751),x40752),f300(x40751,x40752)))
% 52.62/52.40 [4096]P1(f332(f332(f232(f853(f852(x40961,x40961),a839)),f332(f332(f281(x40961,x40961,x40961),x40962),f300(x40961,x40962))),f332(f332(f248(x40961,x40961),f332(f276(x40961),x40962)),f332(f18(f853(x40961,a839),x40961),f332(f276(x40961),x40962)))))
% 52.62/52.40 [4143]E(f332(f256(f846(x41431)),f332(f332(f9(f846(x41431),f853(x41431,a839),a839),f332(f332(f10(f853(x41431,a839),f853(f853(x41431,a839),a839),f846(x41431)),f232(f853(x41431,a839))),f158(x41431))),x41432)),f149(x41431,x41432))
% 52.62/52.40 [4155]E(f332(f145(f846(x41551),x41551,f115(x41551),f332(f332(f10(f846(x41551),f853(f846(x41551),f846(x41551)),x41551),f332(f9(f846(x41551),f846(x41551),f846(x41551)),f125(x41551))),f332(f332(f9(x41551,f846(x41551),f846(x41551)),f140(x41551)),f115(x41551)))),x41552),f332(f141(x41551),x41552))
% 52.62/52.40 [4194]P31(f853(x41941,x41942),f853(f852(x41941,x41942),a839),f332(f332(f10(f853(f852(x41941,x41942),a839),f853(f852(x41941,x41942),a839),f853(x41941,x41942)),f256(f852(x41941,x41942))),f332(f332(f10(f853(x41941,f853(x41942,a839)),f853(f852(x41941,x41942),a839),f853(x41941,x41942)),f251(x41941,x41942,a839)),f332(f10(x41942,f853(x41942,a839),x41941),f332(f9(x41942,x41942,a839),a329)))),f239(f853(f853(x41941,x41942),a839)))
% 52.62/52.40 [4199]E(f53(a1,f332(f106(a1),f332(f332(f82(a1),x41991),x41991)),f332(f106(a1),f332(f332(f82(a1),x41992),x41992))),f332(f332(f83(a1),f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f53(a1,f332(f106(a1),x41991),f332(f106(a1),x41992))))
% 52.62/52.40 [4240]E(f332(f332(f47(x42401,f853(f852(x42401,x42401),a839)),x42402),f332(f332(f9(x42401,f853(f852(x42401,x42401),a839),f853(f852(x42401,x42401),a839)),f332(f332(f10(f852(x42401,x42401),f853(f853(f852(x42401,x42401),a839),f853(f852(x42401,x42401),a839)),x42401),f302(f852(x42401,x42401))),f332(f332(f20(x42401,x42401,f852(x42401,x42401)),f241(x42401,x42401)),f7(x42401)))),f180(f853(f852(x42401,x42401),a839)))),f260(x42401,x42402))
% 52.62/52.40 [4248]E(f198(x42481,f332(f332(f241(a1,a1),f332(f81(a1),f332(f332(f75(f852(a1,a1),a1,x42481,f240(a1,a1)),f207(x42481)),x42482))),f332(f332(f75(f852(a1,a1),a1,x42481,f250(a1,a1)),f207(x42481)),x42482))),f221(x42481,x42482))
% 52.62/52.40 [4328]E(f332(f256(f853(x43281,a839)),f332(f332(f10(f853(f853(x43281,a839),a839),a839,f853(x43281,a839)),f89(f853(x43281,a839))),f332(f332(f9(f853(x43281,a839),f853(f853(x43281,a839),a839),f853(f853(x43281,a839),a839)),f332(f332(f10(f853(f853(x43281,a839),f853(a839,a839)),f853(f853(f853(x43281,a839),a839),f853(f853(x43281,a839),a839)),f853(x43281,a839)),f20(f853(x43281,a839),a839,a839)),f332(f332(f10(f853(f853(x43281,a839),a839),f853(f853(x43281,a839),f853(a839,a839)),f853(x43281,a839)),f332(f10(a839,f853(a839,a839),f853(x43281,a839)),a330)),f332(f332(f9(f853(x43281,a839),f853(f853(x43281,a839),f853(x43281,a839)),f853(f853(x43281,a839),a839)),f332(f332(f10(f853(f853(x43281,a839),a839),f853(f853(f853(x43281,a839),f853(x43281,a839)),f853(f853(x43281,a839),a839)),f853(x43281,a839)),f10(f853(x43281,a839),a839,f853(x43281,a839))),a329)),f81(f853(x43281,a839)))))),f332(f332(f10(f853(f853(x43281,a839),a839),a839,f853(x43281,a839)),f332(f334(f853(x43281,a839)),x43282)),f301(x43281))))),f332(f301(x43281),f332(f81(f853(x43281,a839)),x43282)))
% 52.62/52.40 [4472]~E(f332(f332(f82(a1),x44721),x44721),f332(f332(f3(a1),f332(f332(f82(a1),x44722),x44722)),a99))
% 52.62/52.40 [4473]~E(f332(f332(f82(a1),x44731),x44731),f332(f332(f3(a1),f332(f332(f82(a1),x44732),x44732)),a99))
% 52.62/52.40 [4478]~P1(f332(f332(f233(a845),f332(f332(f82(a845),x44781),x44782)),x44782))
% 52.62/52.40 [4479]~P1(f332(f332(f233(a845),f332(f332(f82(a845),x44791),x44792)),x44791))
% 52.62/52.40 [3666]E(f332(f332(f3(a845),x36661),f332(f332(f83(a845),f332(f332(f44(a845),x36661),x36662)),x36662)),f53(a845,x36661,x36662))
% 52.62/52.40 [3667]E(f332(f332(f3(a1),x36671),f332(f332(f83(a1),f332(f332(f44(a1),x36671),x36672)),x36672)),f53(a1,x36671,x36672))
% 52.62/52.40 [3702]E(f332(f332(f143(a845,x37021),f332(f152(x37021),x37022)),f130(a845,f332(f294(a845,f2(a845)),f332(f181(f846(x37021)),x37022)))),x37022)
% 52.62/52.40 [3762]E(f332(f277(x37621,x37621,f300(x37621,f180(f853(f852(x37621,x37621),a839)))),x37622),x37622)
% 52.62/52.40 [3882]E(f300(x38821,f332(f332(f3(f853(f852(x38821,x38821),a839)),x38822),f300(x38821,f180(f853(f852(x38821,x38821),a839))))),f300(x38821,x38822))
% 52.62/52.40 [3883]E(f300(x38831,f332(f332(f103(f853(f852(x38831,x38831),a839)),x38832),f300(x38831,f180(f853(f852(x38831,x38831),a839))))),f300(x38831,x38832))
% 52.62/52.40 [3939]E(f332(f332(f3(a1),f332(f332(f3(a1),f332(f332(f82(a1),x39391),x39391)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),x39392),x39392)),a99)),f332(f332(f82(a1),f332(f332(f3(a1),x39391),x39392)),f332(f332(f3(a1),x39391),x39392)))
% 52.62/52.40 [3981]E(f332(f332(f3(a1),f332(f332(f82(a1),f332(f332(f82(a1),x39811),x39812)),f332(f332(f82(a1),x39811),x39812))),a99),f332(f332(f82(a1),f332(f332(f82(a1),x39811),x39811)),f332(f332(f3(a1),f332(f332(f82(a1),x39812),x39812)),a99)))
% 52.62/52.40 [4007]E(f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),x40071),x40071)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),x40072),x40072)),a99)),f332(f332(f82(a1),f332(f332(f82(a1),x40071),f332(f332(f3(a1),x40072),a99))),f332(f332(f82(a1),x40071),f332(f332(f3(a1),x40072),a99))))
% 52.62/52.40 [4018]E(f332(f332(f3(a1),f332(f332(f82(a1),f332(f332(f82(a1),x40181),x40182)),f332(f332(f82(a1),x40181),x40182))),a99),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),x40181),x40181)),a99)),f332(f332(f82(a1),x40182),x40182)))
% 52.62/52.40 [4019]E(f332(f332(f3(a1),f332(f332(f82(a1),f332(f332(f3(a1),x40191),x40192)),f332(f332(f3(a1),x40191),x40192))),a99),f332(f332(f3(a1),f332(f332(f3(a1),f332(f332(f82(a1),x40191),x40191)),a99)),f332(f332(f82(a1),x40192),x40192)))
% 52.62/52.40 [4072]E(f332(f102(a1),f332(f332(f44(a845),f332(f332(f83(a845),f332(a107,f332(f77(a1),x40721))),f332(a107,f332(f77(a1),x40722)))),f211(f332(a107,f332(f77(a1),x40721)),f332(a107,f332(f77(a1),x40722))))),f213(x40721,x40722))
% 52.62/52.40 [4117]E(f332(f332(f253(f852(a101,a101),a101,f852(a101,a101),f852(x41171,f852(a101,a101))),f264(f332(a5,f332(f181(f846(x41171)),x41172)))),f332(f332(f10(x41171,f853(f852(a101,a101),f852(x41171,f852(a101,a101))),a101),f241(x41171,f852(a101,a101))),f332(f332(f10(a845,x41171,a101),f332(f152(x41171),x41172)),a22))),f270(x41171,x41172))
% 52.62/52.40 [4200]E(f332(f132(a845,f846(x42001),f332(f9(f846(x42001),a845,a845),f332(f332(f10(a845,f853(a845,a845),f846(x42001)),f179(a845)),f181(f846(x42001)))),f2(a845)),f332(f142(f846(x42001)),f164(x42001,x42002))),f332(f181(f846(f846(x42001))),f332(f126(f846(x42001),f332(f332(f10(a839,a839,f846(x42001)),a328),f332(f332(f9(f846(x42001),f846(x42001),a839),a329),f115(x42001)))),x42002)))
% 52.62/52.40 [4206]E(f332(f332(f47(a845,f853(x42061,a839)),f239(f853(a845,a839))),f332(f332(f9(a845,f853(a845,f853(x42061,a839)),f853(x42061,a839)),f332(f332(f10(f853(a845,a839),f853(f853(a845,f853(x42061,a839)),f853(x42061,a839)),a845),f47(a845,f853(x42061,a839))),f294(a845,f2(a845)))),x42062)),f332(f332(f47(a845,f853(x42061,a839)),f239(f853(a845,a839))),x42062))
% 52.62/52.40 [4225]P1(f332(f64(a845),f332(f256(a845),f332(f332(f20(a845,a839,a839),f332(f332(f10(a839,f853(a839,a839),a845),a330),x42251)),f332(f332(f9(a845,a845,a839),f233(a845)),x42252)))))
% 52.62/52.40 [4338]E(f332(f256(f852(f846(x43381),f846(x43381))),f332(f251(f846(x43381),f846(x43381),a839),f332(f332(f20(f846(x43381),f853(f846(x43381),a839),f853(f846(x43381),a839)),f332(f332(f10(f853(f846(x43381),f853(a839,a839)),f853(f853(f846(x43381),a839),f853(f846(x43381),a839)),f846(x43381)),f20(f846(x43381),a839,a839)),f332(f332(f10(f853(f846(x43381),a839),f853(f846(x43381),f853(a839,a839)),f846(x43381)),f332(f10(a839,f853(a839,a839),f846(x43381)),a331)),f332(f332(f9(f846(x43381),f853(f846(x43381),a845),f853(f846(x43381),a839)),f332(f332(f10(f853(a845,a839),f853(f853(f846(x43381),a845),f853(f846(x43381),a839)),f846(x43381)),f10(a845,a839,f846(x43381))),f332(f332(f10(a845,f853(a845,a839),f846(x43381)),f233(a845)),f181(f846(x43381))))),f181(f846(x43381)))))),f332(f332(f20(f846(x43381),f853(f846(x43381),a839),f853(f846(x43381),a839)),f332(f332(f10(f853(f846(x43381),f853(a839,a839)),f853(f853(f846(x43381),a839),f853(f846(x43381),a839)),f846(x43381)),f20(f846(x43381),a839,a839)),f332(f332(f10(f853(f846(x43381),a839),f853(f846(x43381),f853(a839,a839)),f846(x43381)),f332(f10(a839,f853(a839,a839),f846(x43381)),a330)),f332(f332(f9(f846(x43381),f853(f846(x43381),a845),f853(f846(x43381),a839)),f332(f332(f10(f853(a845,a839),f853(f853(f846(x43381),a845),f853(f846(x43381),a839)),f846(x43381)),f10(a845,a839,f846(x43381))),f332(f332(f10(a845,f853(a845,a839),f846(x43381)),a329),f181(f846(x43381))))),f181(f846(x43381)))))),f332(f332(f9(f846(x43381),f853(f852(f846(x43381),f846(x43381)),a839),f853(f846(x43381),a839)),f332(f332(f10(f853(f846(x43381),f853(f853(f852(f846(x43381),f846(x43381)),a839),a839)),f853(f853(f852(f846(x43381),f846(x43381)),a839),f853(f846(x43381),a839)),f846(x43381)),f9(f846(x43381),f853(f852(f846(x43381),f846(x43381)),a839),a839)),f332(f332(f10(f853(f846(x43381),f852(f846(x43381),f846(x43381))),f853(f846(x43381),f853(f853(f852(f846(x43381),f846(x43381)),a839),a839)),f846(x43381)),f332(f10(f852(f846(x43381),f846(x43381)),f853(f853(f852(f846(x43381),f846(x43381)),a839),a839),f846(x43381)),f334(f852(f846(x43381),f846(x43381))))),f241(f846(x43381),f846(x43381))))),f135(x43381,x43382)))))),f136(x43381,x43382))
% 52.62/52.40 [4010]E(f332(f332(f82(a1),f332(f332(f82(a1),f332(f332(f83(a1),x40101),x40102)),f332(f332(f83(a1),x40101),x40102))),x40102),f332(f332(f83(a1),f332(f332(f3(a1),f332(f332(f82(a1),x40101),x40101)),a99)),x40102))
% 52.62/52.40 [4115]E(f332(a107,f332(a91,f332(f277(f852(a845,a845),f852(a845,a845),a111),f332(f332(f302(f852(a845,a845)),f332(f332(f241(a845,a845),x41151),x41152)),f180(f853(f852(a845,a845),a839)))))),f332(f332(f3(a845),x41151),x41152))
% 52.62/52.40 [4121]E(f332(f332(f281(x41211,x41211,x41211),f332(f332(f103(f853(f852(x41211,x41211),a839)),x41212),f300(x41211,f180(f853(f852(x41211,x41211),a839))))),f300(x41211,f332(f332(f103(f853(f852(x41211,x41211),a839)),x41212),f300(x41211,f180(f853(f852(x41211,x41211),a839)))))),f300(x41211,x41212))
% 52.62/52.40 [4160]E(f265(x41601,f332(f126(f852(a101,x41601),f332(f251(a101,x41601,a839),f332(f332(f10(a839,f853(x41601,a839),a101),f18(a839,x41601)),f332(f233(a101),f2(a101))))),x41602)),f265(x41601,x41602))
% 52.62/52.40 [4161]E(f263(x41611,f332(f126(f852(a101,x41611),f332(f251(a101,x41611,a839),f332(f332(f10(a839,f853(x41611,a839),a101),f18(a839,x41611)),f332(f233(a101),f2(a101))))),x41612)),f263(x41611,x41612))
% 52.62/52.40 [4163]E(f332(f81(a1),f332(a91,f332(f277(f852(a845,a845),f852(a845,a845),a111),f332(f332(f302(f852(a845,a845)),f332(f332(f241(a845,a845),x41631),x41632)),f180(f853(f852(a845,a845),a839)))))),f332(a91,f332(f277(f852(a845,a845),f852(a845,a845),a111),f332(f332(f302(f852(a845,a845)),f332(f332(f241(a845,a845),x41632),x41631)),f180(f853(f852(a845,a845),a839))))))
% 52.62/52.40 [4237]E(f332(f332(f88(a1,a845),f332(f106(a1),f332(f332(f82(a1),x42371),a99))),f332(f332(f20(a1,a845,a845),f332(f332(f9(a1,a845,f853(a845,a845)),f332(f332(f10(a839,f853(a845,f853(a845,a845)),a1),f98(a845)),a186)),f2(a845))),f332(f332(f10(a845,a845,a1),a114),f332(f332(f10(a845,a845,a1),f332(f236(a845),x42372)),a107)))),f332(f332(f236(a845),f332(a114,x42372)),f332(f106(a845),x42371)))
% 52.62/52.40 [4238]E(f332(f332(f88(a1,a845),f332(f106(a1),f332(f332(f82(a1),x42381),a99))),f332(f332(f20(a1,a845,a845),f332(f332(f9(a1,a845,f853(a845,a845)),f332(f332(f10(a839,f853(a845,f853(a845,a845)),a1),f98(a845)),a186)),f332(a114,x42382))),f332(f332(f10(a845,a845,a1),a114),f332(f332(f10(a845,a845,a1),f332(f179(a845),x42382)),a107)))),f332(f332(f179(a845),f332(a114,x42382)),f332(f106(a845),x42381)))
% 52.62/52.40 [4258]E(f332(f132(f846(x42581),f846(x42581),f125(x42581),f115(x42581)),f332(f332(f143(f846(x42581),f846(x42581)),f145(f846(x42581),x42581,f115(x42581),f332(f332(f10(f846(x42581),f853(f846(x42581),f846(x42581)),x42581),f18(f846(x42581),f846(x42581))),f332(f332(f9(x42581,f846(x42581),f846(x42581)),f140(x42581)),f115(x42581))))),x42582)),f332(f332(f143(f846(x42581),x42581),f131(x42581)),f332(f126(f846(x42581),f332(f332(f10(a839,a839,f846(x42581)),a328),f332(f332(f9(f846(x42581),f846(x42581),a839),a329),f115(x42581)))),x42582)))
% 52.62/52.40 [4318]E(f332(f251(a1,a1,a839),f332(f332(f9(a1,f853(a1,a839),f853(a1,a839)),f332(f332(f10(f853(a1,f853(a839,a839)),f853(f853(a1,a839),f853(a1,a839)),a1),f20(a1,a839,a839)),f332(f332(f10(f853(a1,a839),f853(a1,f853(a839,a839)),a1),f332(f10(a839,f853(a839,a839),a1),a330)),f332(f332(f10(f853(a1,a1),f853(a1,a839),a1),f332(f10(a1,a839,a1),f332(a329,x43181))),f332(f332(f10(a1,f853(a1,a1),a1),f82(a1)),f332(f83(a1),x43182)))))),f332(f332(f20(a1,a839,a839),f332(f332(f10(a839,f853(a839,a839),a1),a330),f332(f332(f10(a839,a839,a1),f332(a335,f332(f332(f233(a1),f2(a1)),x43182))),f332(f332(f20(a1,a839,a839),f332(f332(f10(a839,f853(a839,a839),a1),a330),f332(f232(a1),f2(a1)))),f332(f332(f9(a1,a1,a839),f233(a1)),x43182))))),f332(f332(f10(a839,a839,a1),f332(a335,f332(a328,f332(f332(f233(a1),f2(a1)),x43182)))),f332(f332(f20(a1,a839,a839),f332(f332(f10(a839,f853(a839,a839),a1),a330),f332(f233(a1),x43182))),f332(f332(f9(a1,a1,a839),f232(a1)),f2(a1))))))),f57(x43181,x43182))
% 52.62/52.40 [4320]E(f332(f256(x43201),f332(f332(f10(f853(a845,a839),a839,x43201),f89(a845)),f332(f332(f9(x43201,f853(a845,a839),f853(a845,a839)),f332(f332(f10(f853(a845,f853(a839,a839)),f853(f853(a845,a839),f853(a845,a839)),x43201),f20(a845,a839,a839)),f332(f332(f10(f853(a845,a839),f853(a845,f853(a839,a839)),x43201),f332(f10(a839,f853(a839,a839),a845),a330)),f332(f332(f9(x43201,f853(a845,x43201),f853(a845,a839)),f332(f332(f10(f853(x43201,a839),f853(f853(a845,x43201),f853(a845,a839)),x43201),f10(x43201,a839,a845)),a329)),f332(f152(x43201),x43202))))),f332(f332(f9(a845,a845,a839),f233(a845)),f332(f181(f846(x43201)),x43202))))),f332(f158(x43201),x43202))
% 52.62/52.40 [4133]E(f332(f332(f3(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),x41331),a99)),x41332)),f332(f332(f3(a1),f332(f332(f82(a1),x41331),a99)),x41332))),a99),f332(f332(f3(a1),f332(f332(f82(a1),x41331),x41331)),f332(f332(f3(a1),f332(f332(f82(a1),x41332),x41332)),a99)))
% 52.62/52.40 [4253]E(f332(f132(f846(f846(x42531)),f846(f846(x42531)),f125(f846(x42531)),f115(f846(x42531))),f332(f332(f143(f846(x42531),f846(f846(x42531))),f145(f846(f846(x42531)),x42531,f115(f846(x42531)),f332(f18(f853(f846(x42531),f846(f846(x42531))),x42531),f332(f332(f9(f846(x42531),f846(f846(x42531)),f846(f846(x42531))),f140(f846(x42531))),f115(f846(x42531)))))),x42532)),f332(f332(f143(f846(x42531),f846(x42531)),f157(x42531)),f332(f126(f846(x42531),f332(f332(f10(a839,a839,f846(x42531)),a328),f332(f332(f9(f846(x42531),f846(x42531),a839),a329),f115(x42531)))),x42532)))
% 52.62/52.40 [4263]E(f332(f332(f88(a1,a845),f332(f106(a1),f332(f332(f82(a1),x42631),a99))),f332(f332(f20(a1,a845,a845),f332(f332(f9(a1,a845,f853(a845,a845)),f332(f332(f10(a839,f853(a845,f853(a845,a845)),a1),f98(a845)),a186)),f2(a845))),f332(f332(f10(a845,a845,a1),a114),f332(f332(f9(a1,a845,a845),f332(f332(f10(a845,f853(a845,a845),a1),f236(a845)),a107)),x42632)))),f332(f332(f236(a845),f332(f106(a845),x42631)),f332(a114,x42632)))
% 52.62/52.40 [4264]E(f332(f332(f88(a1,a845),f332(f106(a1),f332(f332(f82(a1),x42641),a99))),f332(f332(f20(a1,a845,a845),f332(f332(f9(a1,a845,f853(a845,a845)),f332(f332(f10(a839,f853(a845,f853(a845,a845)),a1),f98(a845)),a186)),f332(a114,x42642))),f332(f332(f10(a845,a845,a1),a114),f332(f332(f9(a1,a845,a845),f332(f332(f10(a845,f853(a845,a845),a1),f179(a845)),a107)),x42642)))),f332(f332(f179(a845),f332(f106(a845),x42641)),f332(a114,x42642)))
% 52.62/52.40 [4252]E(f332(f251(x42521,x42521,a839),f332(f332(f20(x42521,a839,f853(x42521,a839)),f332(f332(f10(f853(x42521,f853(a839,a839)),f853(a839,f853(x42521,a839)),x42521),f9(x42521,a839,a839)),f332(f332(f10(f853(x42521,a839),f853(x42521,f853(a839,a839)),x42521),f332(f10(a839,f853(a839,a839),x42521),a330)),a329))),x42522)),f260(x42521,x42522))
% 52.62/52.40 [4296]E(f332(f332(f44(a845),x42961),f332(f332(f82(a845),f332(f106(a845),f332(f332(f3(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))),a99))),x42962)),f332(f332(f44(a845),x42961),f332(a114,f332(a114,f332(a114,x42962)))))
% 52.62/52.40 [4297]E(f53(a845,x42971,f332(f332(f82(a845),f332(f106(a845),f332(f332(f3(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))),a99))),x42972)),f53(a845,x42971,f332(a114,f332(a114,f332(a114,x42972)))))
% 52.62/52.40 [4298]E(f53(a845,f332(f332(f82(a845),f332(f106(a845),f332(f332(f3(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))),a99))),x42981),x42982),f53(a845,f332(a114,f332(a114,f332(a114,x42981))),x42982))
% 52.62/52.40 [4311]E(f122(f332(x43111,f332(f332(f83(a101),f332(f106(a101),f332(f332(f3(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))),a99))),x43112))),f332(f195(x43111),x43112))
% 52.62/52.40 [4312]E(f332(f332(f44(a845),f332(f332(f82(a845),f332(f106(a845),f332(f332(f3(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))),a99))),x43121)),x43122),f332(f332(f44(a845),f332(a114,f332(a114,f332(a114,x43121)))),x43122))
% 52.62/52.40 [3487]P31(x34871,f854(x34872,x34871),f313(x34871,x34872),x34873)
% 52.62/52.40 [3488]P31(x34881,f854(x34881,x34882),f304(x34881,x34882),x34883)
% 52.62/52.40 [4381]~E(f36(x43811,x43812),f332(a27,x43813))
% 52.62/52.40 [4382]~E(f35(x43821,x43822),f332(a27,x43823))
% 52.62/52.40 [4383]~E(f28(x43831,x43832),f332(a27,x43833))
% 52.62/52.40 [4384]~E(f332(a27,x43841),f36(x43842,x43843))
% 52.62/52.40 [4385]~E(f332(a27,x43851),f35(x43852,x43853))
% 52.62/52.40 [4386]~E(f332(a27,x43861),f28(x43862,x43863))
% 52.62/52.40 [4402]~E(f33(x44021,x44022,x44023),a25)
% 52.62/52.40 [4403]~E(f32(x44031,x44032,x44033),a25)
% 52.62/52.40 [4404]~E(f31(x44041,x44042,x44043),a25)
% 52.62/52.40 [4405]~E(f33(x44051,x44052,x44053),a25)
% 52.62/52.40 [4406]~E(f32(x44061,x44062,x44063),a25)
% 52.62/52.40 [4407]~E(f31(x44071,x44072,x44073),a25)
% 52.62/52.40 [3101]E(f332(f185(x31011,x31012),x31013),f120(x31011,x31012))
% 52.62/52.40 [3102]E(f332(f194(x31021,x31022),x31023),f123(x31021,x31022))
% 52.62/52.40 [3195]E(f332(f332(f143(x31951,x31952),x31953),f115(x31951)),f115(x31952))
% 52.62/52.40 [3196]E(f332(f332(f196(x31961,x31962),x31963),f183(x31961)),f183(x31962))
% 52.62/52.40 [3216]E(f34(f31(x32161,x32162,x32163)),f2(a845))
% 52.62/52.40 [3235]E(f332(f174(x32351,x32352,x32353),f2(a845)),x32352)
% 52.62/52.40 [3236]E(f332(f181(a840),f31(x32361,x32362,x32363)),f2(a845))
% 52.62/52.40 [3237]E(f332(f332(f167(x32371,x32372),x32373),f115(x32372)),f115(f852(x32371,x32372)))
% 52.62/52.40 [3274]E(f87(x32741,f65(x32741,x32742,x32743)),f332(f66(x32741,x32742),x32743))
% 52.62/52.40 [3343]E(f332(f240(f846(x33431),f846(x33431)),f155(x33431,x33432,x33433)),f332(f126(x33431,x33432),x33433))
% 52.62/52.40 [3422]E(f175(x34221,x34222,x34223,f2(a845)),x34222)
% 52.62/52.40 [3423]E(f19(x34231,x34232,x34233,f2(a101)),x34232)
% 52.62/52.40 [3424]E(f21(x34241,x34242,x34243,f2(a101)),x34242)
% 52.62/52.40 [3431]E(f153(x34311,x34312,x34313,f115(x34311)),f115(x34312))
% 52.62/52.40 [3438]E(f332(f332(f152(x34381),f332(f332(f140(x34381),x34382),x34383)),f2(a845)),x34382)
% 52.62/52.40 [3486]P31(x34861,x34862,x34863,f180(f853(x34861,a839)))
% 52.62/52.40 [3582]E(f262(x35821,x35822,x35823),f332(f241(f853(a101,f853(a839,f849(f847(x35821)))),f852(a101,a101)),f49(x35821)))
% 52.62/52.40 [3641]E(f332(f75(x36411,x36412,x36411,x36413),f39(x36411)),x36413)
% 52.62/52.40 [3816]P1(f332(f332(f334(f852(x38161,x38161)),f332(f332(f241(x38161,x38161),x38162),x38162)),f300(x38161,x38163)))
% 52.62/52.40 [4482]~P1(f332(f332(f334(f852(f846(x44821),f846(x44821))),f332(f332(f241(f846(x44821),f846(x44821)),x44822),f115(x44821))),f135(x44821,x44823)))
% 52.62/52.40 [4483]~P1(f332(f332(f334(f852(f846(x44831),f846(x44831))),f332(f332(f241(f846(x44831),f846(x44831)),x44832),f115(x44831))),f137(x44831,x44833)))
% 52.62/52.40 [4484]~P1(f332(f332(f334(f852(f846(x44841),f846(x44841))),f332(f332(f241(f846(x44841),f846(x44841)),x44842),f115(x44841))),f146(x44841,x44843)))
% 52.62/52.40 [4485]~P1(f332(f332(f334(f852(f846(x44851),f846(x44851))),f332(f332(f241(f846(x44851),f846(x44851)),f115(x44851)),x44852)),f135(x44851,x44853)))
% 52.62/52.40 [4486]~P1(f332(f332(f334(f852(f846(x44861),f846(x44861))),f332(f332(f241(f846(x44861),f846(x44861)),f115(x44861)),x44862)),f146(x44861,x44863)))
% 52.62/52.40 [3171]E(f332(f332(f197(x31711),x31712),x31713),f198(x31711,f210(x31712,x31713)))
% 52.62/52.40 [3225]E(f332(f278(x32251,x32252),f332(f278(x32252,x32251),x32253)),x32253)
% 52.62/52.40 [3242]E(f312(x32421,x32422,f332(f304(x32421,x32422),x32423)),x32423)
% 52.62/52.40 [3243]E(f315(x32431,x32432,f332(f313(x32432,x32431),x32433)),x32433)
% 52.62/52.40 [3249]E(f332(f332(f167(x32491,x32492),f115(x32491)),x32493),f115(f852(x32491,x32492)))
% 52.62/52.40 [3252]E(f160(x32521,x32522,f332(f257(a845),x32523)),f332(f332(f159(x32521),x32523),x32522))
% 52.62/52.40 [3266]E(f332(f181(f854(x32661,x32662)),f332(f304(x32661,x32662),x32663)),f2(a845))
% 52.62/52.40 [3267]E(f332(f181(f854(x32671,x32672)),f332(f313(x32672,x32671),x32673)),f2(a845))
% 52.62/52.40 [3270]E(f332(f261(x32701,x32702),f332(f278(x32702,x32701),x32703)),f332(f259(x32702,x32701),x32703))
% 52.62/52.40 [3272]E(f332(f259(x32721,x32722),f332(f278(x32722,x32721),x32723)),f332(f261(x32722,x32721),x32723))
% 52.62/52.40 [3273]E(f332(f261(x32731,x32732),f332(f278(x32732,x32731),x32733)),f332(f259(x32732,x32731),x32733))
% 52.62/52.40 [3288]E(f332(f126(x32881,x32882),f332(f142(x32881),x32883)),f332(f142(x32881),f332(f126(x32881,x32882),x32883)))
% 52.62/52.40 [3301]E(f332(f332(f128(x33011),x33012),f332(f157(x33011),x33013)),f332(f332(f128(x33011),f332(a114,x33012)),x33013))
% 52.62/52.40 [3319]E(f34(f32(x33191,x33192,x33193)),f332(f332(f82(a845),f34(x33193)),f332(a114,f2(a845))))
% 52.62/52.40 [3320]E(f332(f303(x33201,x33202,x33203),f180(f853(x33201,a839))),f180(f853(x33202,a839)))
% 52.62/52.40 [3321]E(f332(f277(x33211,x33212,x33213),f180(f853(x33211,a839))),f180(f853(x33212,a839)))
% 52.62/52.40 [3322]E(f332(f305(x33221,x33222,x33223),f239(f853(x33222,a839))),f239(f853(x33221,a839)))
% 52.62/52.40 [3323]E(f332(f305(x33231,x33232,x33233),f180(f853(x33232,a839))),f180(f853(x33231,a839)))
% 52.62/52.40 [3360]E(f228(x33601,x33602,f332(f227(x33601),x33603)),f332(f332(f82(a845),f332(x33602,x33603)),f332(a114,f2(a845))))
% 52.62/52.40 [3442]E(f332(f181(a840),f32(x34421,x34422,x34423)),f332(f332(f82(a845),f332(f181(a840),x34423)),f332(a114,f2(a845))))
% 52.62/52.40 [3443]E(f332(f303(f852(x34431,x34432),x34432,f250(x34431,x34432)),x34433),f332(f259(x34431,x34432),x34433))
% 52.62/52.40 [3444]E(f332(f303(f852(x34441,x34442),x34441,f240(x34441,x34442)),x34443),f332(f261(x34441,x34442),x34443))
% 52.62/52.40 [3512]E(f332(f332(f241(x35121,x35122),f332(f240(x35121,x35122),x35123)),f332(f250(x35121,x35122),x35123)),x35123)
% 52.62/52.40 [3513]E(f332(f332(f241(x35131,x35132),f332(f240(x35131,x35132),x35133)),f332(f250(x35131,x35132),x35133)),x35133)
% 52.62/52.40 [3520]E(f332(f332(f251(x35201,x35202,x35201),f18(x35201,x35202)),x35203),f332(f240(x35201,x35202),x35203))
% 52.62/52.40 [3539]E(f170(x35391,x35392,x35393,f332(f18(f849(x35392),x35391),f183(x35392))),x35393)
% 52.62/52.40 [3540]E(f170(x35401,x35402,f332(f18(f849(x35402),x35401),f183(x35402)),x35403),x35403)
% 52.62/52.40 [3595]E(f34(f33(x35951,x35952,x35953)),f332(f332(f82(a845),f332(f332(f82(a845),f34(x35952)),f34(x35953))),f332(a114,f2(a845))))
% 52.62/52.40 [3645]E(f332(f75(x36451,x36451,x36452,f39(x36451)),x36453),x36453)
% 52.62/52.40 [3730]P1(f332(f64(x37301),f169(x37301,x37302,f166(x37301,x37302,x37303))))
% 52.62/52.40 [3752]P1(f332(f332(f187(f28(x37521,x37522)),x37523),f332(f332(f332(a189,x37523),x37521),f332(x37522,x37523))))
% 52.62/52.40 [3753]P1(f332(f332(f187(f28(x37531,x37532)),x37533),f332(f332(f332(a189,x37533),x37531),f332(x37532,x37533))))
% 52.62/52.40 [3755]E(f332(f181(a840),f33(x37551,x37552,x37553)),f332(f332(f82(a845),f332(f332(f82(a845),f332(f181(a840),x37552)),f332(f181(a840),x37553))),f332(a114,f2(a845))))
% 52.62/52.40 [3826]P1(f332(f332(f232(f853(x38261,a839)),f332(f158(x38261),f332(f126(x38261,x38262),x38263))),f332(f158(x38261),x38263)))
% 52.62/52.40 [3869]P1(f332(f332(f232(f853(x38691,a839)),f332(f158(x38691),f332(f332(f159(x38691),x38692),x38693))),f332(f158(x38691),x38693)))
% 52.62/52.40 [3870]P1(f332(f332(f232(f853(x38701,a839)),f332(f158(x38701),f332(f332(f128(x38701),x38702),x38703))),f332(f158(x38701),x38703)))
% 52.62/52.40 [3874]P1(f332(f332(f232(f853(x38741,a839)),f332(f158(x38741),f151(x38741,x38742,x38743))),f332(f158(x38741),x38743)))
% 52.62/52.40 [3875]P1(f332(f332(f232(f853(x38751,a839)),f332(f158(x38751),f160(x38751,x38752,x38753))),f332(f158(x38751),x38752)))
% 52.62/52.40 [3899]P31(f852(x38991,x38992),f852(x38992,x38991),f332(f251(x38991,x38992,f852(x38992,x38991)),f332(f9(x38992,x38991,f852(x38992,x38991)),f241(x38992,x38991))),x38993)
% 52.62/52.40 [3911]E(f332(f332(f332(f173(f846(x39111),f846(x39111)),f53(a845,x39112,f332(f181(f846(x39111)),x39113))),f141(x39111)),x39113),f332(f332(f332(f173(f846(x39111),f846(x39111)),x39112),f141(x39111)),x39113))
% 52.62/52.40 [3953]E(f332(f75(f846(x39531),f846(x39531),f846(x39531),f332(f332(f173(f846(x39531),f846(x39531)),x39532),f141(x39531))),f332(f332(f173(f846(x39531),f846(x39531)),x39533),f141(x39531))),f332(f332(f173(f846(x39531),f846(x39531)),f332(f332(f82(a845),x39532),x39533)),f141(x39531)))
% 52.62/52.40 [3956]P1(f332(f332(f334(f852(f846(x39561),f846(x39561))),f332(f332(f241(f846(x39561),f846(x39561)),x39562),x39562)),f147(x39561,f300(x39561,x39563))))
% 52.62/52.40 [4100]E(f87(f852(x41001,x41002),f332(f332(f20(f852(x41001,x41002),x41002,a839),f332(f332(f10(x41001,f853(x41002,a839),f852(x41001,x41002)),x41003),f240(x41001,x41002))),f250(x41001,x41002))),f87(f852(x41001,x41002),f332(f251(x41001,x41002,a839),x41003)))
% 52.62/52.40 [4101]E(f92(f852(x41011,x41012),f332(f332(f20(f852(x41011,x41012),x41012,a839),f332(f332(f10(x41011,f853(x41012,a839),f852(x41011,x41012)),x41013),f240(x41011,x41012))),f250(x41011,x41012))),f92(f852(x41011,x41012),f332(f251(x41011,x41012,a839),x41013)))
% 52.62/52.40 [4140]E(f332(f332(f280(f852(a845,x41401),x41401),f326(a845,x41401,a237,x41402)),f332(f332(f20(x41401,x41401,f852(a845,x41401)),f332(f332(f10(a845,f853(x41401,f852(a845,x41401)),x41401),f241(a845,x41401)),x41403)),f7(x41401))),f327(x41401,x41403,x41402))
% 52.62/52.40 [4202]E(f332(f252(x42021,x42021,x42022,x42022,f7(x42021),f7(x42022)),x42023),x42023)
% 52.62/52.40 [4337]E(f332(f332(f88(a1,x43371),f213(f332(f332(f75(f852(a1,a1),a1,x43371,f250(a1,a1)),f207(x43371)),x43372),f332(f332(f75(f852(a1,a1),a1,x43371,f250(a1,a1)),f207(x43371)),x43373))),f332(f332(f20(a1,a1,x43371),f332(f332(f10(a1,f853(a1,x43371),a1),f197(x43371)),f332(f332(f20(a1,a1,a1),f332(f332(f10(a1,f853(a1,a1),a1),f82(a1)),f332(f332(f10(a1,a1,a1),f332(f83(a1),f332(f332(f75(f852(a1,a1),a1,x43371,f240(a1,a1)),f207(x43371)),x43372))),f332(f332(f9(a1,a1,a1),f44(a1)),f332(f332(f75(f852(a1,a1),a1,x43371,f250(a1,a1)),f207(x43371)),x43372))))),f332(f332(f10(a1,a1,a1),f332(f83(a1),f332(f332(f75(f852(a1,a1),a1,x43371,f240(a1,a1)),f207(x43371)),x43373))),f332(f332(f9(a1,a1,a1),f44(a1)),f332(f332(f75(f852(a1,a1),a1,x43371,f250(a1,a1)),f207(x43371)),x43373)))))),f7(a1))),f224(x43371,x43372,x43373))
% 52.62/52.40 [4399]~E(f332(f332(f140(x43991),x43992),x43993),x43993)
% 52.62/52.40 [4400]~E(f332(f332(f140(x44001),x44002),x44003),x44003)
% 52.62/52.40 [4408]~E(f332(f332(f140(x44081),x44082),x44083),f115(x44081))
% 52.62/52.40 [4409]~E(f332(f332(f140(x44091),x44092),x44093),f115(x44091))
% 52.62/52.40 [4434]~E(f332(f332(f302(x44341),x44342),x44343),f180(f853(x44341,a839)))
% 52.62/52.40 [4435]~E(f332(f332(f302(x44351),x44352),x44353),f180(f853(x44351,a839)))
% 52.62/52.40 [4464]~E(f332(f303(x44641,f853(x44641,a839),x44642),x44643),f332(f301(x44641),x44643))
% 52.62/52.40 [3228]E(f332(f332(f148(x32281,f115(x32281)),x32282),x32283),f115(x32281))
% 52.62/52.40 [3229]E(f332(f332(f148(x32291,f115(x32291)),x32292),x32293),f115(x32291))
% 52.62/52.40 [3230]E(f332(f131(x32301),f332(f332(f140(x32301),x32302),x32303)),x32302)
% 52.62/52.40 [3231]E(f332(f157(x32311),f332(f332(f140(x32311),x32312),x32313)),x32313)
% 52.62/52.40 [3277]E(f332(f332(f128(x32771),f80(a845)),f332(f332(f140(x32771),x32772),x32773)),x32773)
% 52.62/52.40 [3307]E(f116(x33071,f332(f332(f128(x33071),x33072),x33073)),f332(f332(f128(x33071),x33072),f116(x33071,x33073)))
% 52.62/52.40 [3308]E(f116(x33081,f332(f332(f128(x33081),x33082),x33083)),f332(f332(f128(x33081),x33082),f116(x33081,x33083)))
% 52.62/52.40 [3310]E(f332(f332(f148(x33101,x33102),x33103),f332(f332(f152(x33101),x33102),x33103)),x33102)
% 52.62/52.40 [3333]E(f332(f332(f302(x33331),x33332),f332(f332(f302(x33331),x33332),x33333)),f332(f332(f302(x33331),x33332),x33333))
% 52.62/52.40 [3346]E(f332(f332(f302(x33461),x33462),f332(f158(x33461),x33463)),f332(f158(x33461),f332(f332(f140(x33461),x33462),x33463)))
% 52.62/52.40 [3347]E(f332(f332(f128(x33471),x33472),f332(f157(x33471),x33473)),f332(f157(x33471),f332(f332(f128(x33471),x33472),x33473)))
% 52.62/52.40 [3348]E(f332(f332(f128(x33481),x33482),f332(f157(x33481),x33483)),f332(f157(x33481),f332(f332(f128(x33481),x33482),x33483)))
% 52.62/52.40 [3357]E(f332(f332(f159(x33571),f80(a845)),f332(f332(f140(x33571),x33572),x33573)),f332(f332(f140(x33571),x33572),f115(x33571)))
% 52.62/52.40 [3389]E(f332(f166(x33891,x33892,f115(f852(x33891,x33892))),x33893),f183(x33892))
% 52.62/52.40 [3390]E(f332(f166(x33901,x33902,f115(f852(x33901,x33902))),x33903),f183(x33902))
% 52.62/52.40 [3407]E(f332(f66(x34071,x34072),f332(f332(f302(x34071),x34073),f180(f853(x34071,a839)))),x34073)
% 52.62/52.40 [3450]E(f332(f332(f82(a845),x34501),f332(f332(f82(a845),x34502),x34503)),f332(f332(f82(a845),x34502),f332(f332(f82(a845),x34501),x34503)))
% 52.62/52.40 [3451]E(f332(f332(f82(a1),x34511),f332(f332(f82(a1),x34512),x34513)),f332(f332(f82(a1),x34512),f332(f332(f82(a1),x34511),x34513)))
% 52.62/52.40 [3456]E(f332(f332(f248(x34561,x34562),f180(f853(x34561,a839))),x34563),f180(f853(f852(x34561,x34562),a839)))
% 52.62/52.40 [3478]E(f332(f332(f103(f853(x34781,a839)),x34782),x34783),f332(f332(f103(f853(x34781,a839)),x34783),x34782))
% 52.62/52.40 [3479]E(f332(f332(f104(f853(x34791,a839)),x34792),x34793),f332(f332(f104(f853(x34791,a839)),x34793),x34792))
% 52.62/52.40 [3481]E(f332(f332(f125(x34811),x34812),f332(f332(f140(x34811),x34813),f115(x34811))),f332(f141(x34811),f332(f332(f140(x34811),x34813),x34812)))
% 52.62/52.40 [3482]E(f332(f332(f125(x34821),f332(f142(x34821),x34822)),f332(f142(x34821),x34823)),f332(f142(x34821),f332(f332(f125(x34821),x34823),x34822)))
% 52.62/52.40 [3492]E(f332(f157(x34921),f332(f332(f159(x34921),f332(a114,x34922)),x34923)),f332(f332(f159(x34921),x34922),f332(f157(x34921),x34923)))
% 52.62/52.40 [3499]P1(f332(f332(f334(x34991),x34992),f332(f332(f302(x34991),x34992),x34993)))
% 52.62/52.40 [3503]E(f332(f332(f48(x35031,f853(x35032,a839)),f180(f853(x35031,a839))),x35033),f239(f853(x35032,a839)))
% 52.62/52.40 [3506]E(f332(f277(x35061,x35061,f260(x35061,x35062)),x35063),f332(f332(f104(f853(x35061,a839)),x35062),x35063))
% 52.62/52.40 [3518]E(f332(f181(f846(x35181)),f332(f332(f140(x35181),x35182),x35183)),f332(f332(f82(a845),f332(f181(f846(x35181)),x35183)),f332(a114,f2(a845))))
% 52.62/52.40 [3522]E(f134(x35221,f332(f332(f125(x35221),x35222),f332(f332(f140(x35221),x35223),f115(x35221)))),x35223)
% 52.62/52.40 [3523]E(f116(x35231,f332(f332(f125(x35231),x35232),f332(f332(f140(x35231),x35233),f115(x35231)))),x35232)
% 52.62/52.40 [3528]E(f332(f332(f125(x35281),f332(f332(f159(x35281),x35282),x35283)),f332(f332(f128(x35281),x35282),x35283)),x35283)
% 52.62/52.40 [3537]E(f332(f332(f3(a845),f332(f332(f82(a845),x35371),x35372)),f332(f332(f82(a845),x35373),x35372)),f332(f332(f3(a845),x35371),x35373))
% 52.62/52.40 [3538]E(f332(f332(f3(a845),f332(f332(f82(a845),x35381),x35382)),f332(f332(f82(a845),x35381),x35383)),f332(f332(f3(a845),x35382),x35383))
% 52.62/52.40 [3544]E(f332(f332(f125(x35441),f332(f142(x35441),x35442)),f332(f332(f140(x35441),x35443),f115(x35441))),f332(f142(x35441),f332(f332(f140(x35441),x35443),x35442)))
% 52.62/52.40 [3546]E(f332(f332(f82(a845),f332(f181(f846(x35461)),x35462)),f332(f181(f846(x35461)),x35463)),f332(f181(f846(x35461)),f332(f332(f125(x35461),x35462),x35463)))
% 52.62/52.40 [3556]E(f332(f332(f103(f853(x35561,a839)),f332(f158(x35561),x35562)),f332(f158(x35561),x35563)),f332(f158(x35561),f332(f332(f125(x35561),x35562),x35563)))
% 52.62/52.40 [3557]E(f53(a845,f332(f332(f83(a845),x35571),x35572),f332(f332(f83(a845),x35571),x35573)),f332(f332(f83(a845),x35571),f53(a845,x35572,x35573)))
% 52.62/52.40 [3570]E(f332(f332(f159(x35701),f332(f332(f3(a845),x35702),f80(a845))),f332(f157(x35701),x35703)),f332(f157(x35701),f332(f332(f159(x35701),x35702),x35703)))
% 52.62/52.40 [3575]E(f332(f332(f104(f853(x35751,a839)),x35752),f332(f81(f853(x35751,a839)),x35753)),f332(f332(f3(f853(x35751,a839)),x35752),x35753))
% 52.62/52.40 [3576]E(f332(f332(f3(f853(x35761,a839)),x35762),f332(f81(f853(x35761,a839)),x35763)),f332(f332(f104(f853(x35761,a839)),x35762),x35763))
% 52.62/52.40 [3598]E(f332(f332(f248(x35981,x35982),x35983),f332(f18(f853(x35982,a839),x35981),f180(f853(x35982,a839)))),f180(f853(f852(x35981,x35982),a839)))
% 52.62/52.40 [3600]E(f332(f332(f82(a845),f332(f332(f83(a845),x36001),x36002)),f332(f332(f83(a845),x36001),x36003)),f332(f332(f83(a845),x36001),f332(f332(f82(a845),x36002),x36003)))
% 52.62/52.40 [3601]E(f332(f332(f3(a845),f332(f332(f83(a845),x36011),x36012)),f332(f332(f83(a845),x36011),x36013)),f332(f332(f83(a845),x36011),f332(f332(f3(a845),x36012),x36013)))
% 52.62/52.40 [3602]E(f332(f332(f82(a1),f332(f332(f83(a1),x36021),x36022)),f332(f332(f83(a1),x36021),x36023)),f332(f332(f83(a1),x36021),f332(f332(f82(a1),x36022),x36023)))
% 52.62/52.40 [3603]E(f332(f332(f3(a1),f332(f332(f83(a1),x36031),x36032)),f332(f332(f83(a1),x36031),x36033)),f332(f332(f83(a1),x36031),f332(f332(f3(a1),x36032),x36033)))
% 52.62/52.40 [3604]E(f332(f332(f83(a1),f332(f332(f242(a1),x36041),x36042)),f332(f332(f242(a1),x36041),x36043)),f332(f332(f242(a1),x36041),f332(f332(f82(a845),x36042),x36043)))
% 52.62/52.40 [3617]E(f332(f332(f47(x36171,f853(x36172,a839)),x36173),f332(f18(f853(x36172,a839),x36171),f180(f853(x36172,a839)))),f180(f853(x36172,a839)))
% 52.62/52.40 [3619]E(f53(a845,f332(f332(f83(a845),x36191),x36192),f332(f332(f83(a845),x36193),x36192)),f332(f332(f83(a845),f53(a845,x36191,x36193)),x36192))
% 52.62/52.40 [3623]E(f53(a1,f332(f332(f83(a1),x36231),f53(a1,x36232,x36233)),x36233),f53(a1,f332(f332(f83(a1),x36231),x36232),x36233))
% 52.62/52.40 [3624]E(f53(a1,f332(f332(f83(a1),x36241),f53(a1,x36242,x36243)),x36243),f53(a1,f332(f332(f83(a1),x36241),x36242),x36243))
% 52.62/52.40 [3625]E(f53(a1,f332(f332(f3(a1),x36251),f53(a1,x36252,x36253)),x36253),f53(a1,f332(f332(f3(a1),x36251),x36252),x36253))
% 52.62/52.40 [3626]P1(f332(f332(f232(f853(x36261,a839)),x36262),f332(f332(f302(x36261),x36263),x36262)))
% 52.62/52.40 [3650]E(f332(f303(f852(x36501,x36502),x36501,f240(x36501,x36502)),f332(f158(f852(x36501,x36502)),x36503)),f169(x36501,x36502,f166(x36501,x36502,x36503)))
% 52.62/52.40 [3707]E(f332(f332(f48(f853(x37071,a839),f853(x37071,a839)),x37072),f332(f103(f853(x37071,a839)),x37073)),f332(f332(f103(f853(x37071,a839)),x37073),f46(f853(x37071,a839),x37072)))
% 52.62/52.40 [3708]E(f332(f332(f47(f853(x37081,a839),f853(x37081,a839)),x37082),f332(f104(f853(x37081,a839)),x37083)),f332(f332(f104(f853(x37081,a839)),x37083),f45(f853(x37081,a839),x37082)))
% 52.62/52.40 [3718]E(f332(f158(x37181),f332(f332(f332(f173(f846(x37181),f846(x37181)),x37182),f141(x37181)),x37183)),f332(f158(x37181),x37183))
% 52.62/52.40 [3722]E(f332(f332(f159(x37221),f332(f181(f846(x37221)),f162(x37221,x37222,x37223))),x37223),f162(x37221,x37222,x37223))
% 52.62/52.40 [3723]E(f169(x37231,x37232,f332(f332(f10(x37232,f849(x37232),x37231),f227(x37232)),x37233)),f239(f853(x37231,a839)))
% 52.62/52.40 [3726]E(f332(f181(f846(x37261)),f332(f332(f332(f173(f846(x37261),f846(x37261)),x37262),f141(x37261)),x37263)),f332(f181(f846(x37261)),x37263))
% 52.62/52.40 [3728]E(f332(f332(f251(x37281,x37282,x37282),f332(f18(f853(x37282,x37282),x37281),f7(x37282))),x37283),f332(f250(x37281,x37282),x37283))
% 52.62/52.40 [3735]E(f53(a1,f332(f332(f3(a1),f53(a1,x37351,x37352)),x37353),x37352),f53(a1,f332(f332(f3(a1),x37351),x37353),x37352))
% 52.62/52.40 [3736]E(f53(a1,f332(f332(f242(a1),f53(a1,x37361,x37362)),x37363),x37362),f53(a1,f332(f332(f242(a1),x37361),x37363),x37362))
% 52.62/52.40 [3739]E(f332(f332(f47(f853(f852(x37391,x37392),a839),f853(x37392,a839)),x37393),f259(x37391,x37392)),f332(f259(x37391,x37392),f45(f853(f852(x37391,x37392),a839),x37393)))
% 52.62/52.40 [3740]E(f332(f332(f47(f853(f852(x37401,x37402),a839),f853(x37401,a839)),x37403),f261(x37401,x37402)),f332(f261(x37401,x37402),f45(f853(f852(x37401,x37402),a839),x37403)))
% 52.62/52.40 [3768]E(f332(f75(x37681,x37681,x37681,x37682),f332(f332(f173(x37681,x37681),x37683),x37682)),f332(f332(f173(x37681,x37681),f332(a114,x37683)),x37682))
% 52.62/52.40 [3778]E(f229(f849(x37781),x37782,f183(x37781),f332(f332(f10(x37781,f849(x37781),x37782),f227(x37781)),x37783)),f332(f196(x37782,x37781),x37783))
% 52.62/52.40 [3785]E(f332(f332(f128(x37851),f332(f332(f3(a845),f332(f181(f846(x37851)),x37852)),x37853)),f332(f142(x37851),x37852)),f332(f142(x37851),f332(f332(f159(x37851),x37853),x37852)))
% 52.62/52.40 [3786]E(f332(f332(f159(x37861),f332(f332(f3(a845),f332(f181(f846(x37861)),x37862)),x37863)),f332(f142(x37861),x37862)),f332(f142(x37861),f332(f332(f128(x37861),x37863),x37862)))
% 52.62/52.40 [3789]E(f332(f332(f82(a845),f332(f154(a845),f332(f332(f143(x37891,a845),x37892),x37893))),f332(f181(f846(x37891)),x37893)),f144(x37891,x37892,x37893))
% 52.62/52.40 [3798]E(f332(f332(f332(f173(f846(x37981),f846(x37981)),x37982),f141(x37981)),f332(f141(x37981),x37983)),f332(f141(x37981),f332(f332(f332(f173(f846(x37981),f846(x37981)),x37982),f141(x37981)),x37983)))
% 52.62/52.40 [3805]E(f332(f141(x38051),f332(f332(f332(f173(f846(x38051),f846(x38051)),x38052),f141(x38051)),x38053)),f332(f332(f332(f173(f846(x38051),f846(x38051)),f332(a114,x38052)),f141(x38051)),x38053))
% 52.62/52.40 [3817]P1(f332(f332(f232(a845),f332(f181(f846(x38171)),f332(f126(x38171,x38172),x38173))),f332(f181(f846(x38171)),x38173)))
% 52.62/52.40 [3834]E(f332(f332(f103(f853(f853(x38341,a839),a839)),f332(f301(x38341),x38342)),f332(f303(f853(x38341,a839),f853(x38341,a839),f332(f302(x38341),x38343)),f332(f301(x38341),x38342))),f332(f301(x38341),f332(f332(f302(x38341),x38343),x38342)))
% 52.62/52.40 [3849]P30(x38491,x38492,f332(f332(f302(f844(x38491)),f332(f332(f332(f93(x38491),x38493),a25),x38493)),f180(f853(f844(x38491),a839))))
% 52.62/52.40 [3850]P30(x38501,x38502,f332(f332(f302(f844(x38501)),f332(f332(f332(f93(x38501),x38503),a25),x38503)),f180(f853(f844(x38501),a839))))
% 52.62/52.40 [3866]P1(f332(f332(f232(a845),f332(f181(f846(x38661)),f162(x38661,x38662,x38663))),f332(f181(f846(x38661)),x38663)))
% 52.62/52.40 [3873]E(f332(f261(x38731,x38732),f332(f256(f852(x38731,x38732)),f332(f251(x38731,x38732,a839),x38733))),f332(f256(x38731),f332(f332(f10(f853(x38732,a839),a839,x38731),f89(x38732)),x38733)))
% 52.62/52.40 [3886]E(f332(f303(a845,a845,f332(f332(f9(a845,a845,a845),f82(a845)),x38861)),f295(a845,x38862,x38863)),f295(a845,f332(f332(f82(a845),x38862),x38861),f332(f332(f82(a845),x38863),x38861)))
% 52.62/52.40 [3902]E(f332(f303(a845,a845,f332(f332(f9(a845,a845,a845),f82(a845)),x39021)),f332(f294(a845,x39022),x39023)),f332(f294(a845,f332(f332(f82(a845),x39022),x39021)),f332(f332(f82(a845),x39023),x39021)))
% 52.62/52.40 [3920]E(f332(f332(f167(x39201,x39202),f332(f332(f143(f852(x39201,x39202),x39201),f240(x39201,x39202)),x39203)),f332(f332(f143(f852(x39201,x39202),x39202),f250(x39201,x39202)),x39203)),x39203)
% 52.62/52.40 [3925]E(f332(f332(f82(a845),f332(f332(f83(a845),x39251),f53(a845,f332(f332(f44(a845),x39252),x39251),x39253))),f53(a845,x39252,x39251)),f53(a845,x39252,f332(f332(f83(a845),x39251),x39253)))
% 52.62/52.40 [3936]P1(f332(f64(f849(x39361)),f332(f303(x39362,f849(x39361),f166(x39362,x39361,x39363)),f239(f853(x39362,a839)))))
% 52.62/52.40 [3940]E(f332(f332(f125(x39401),x39402),f332(f132(f846(x39401),f846(x39401),f125(x39401),f115(x39401)),x39403)),f332(f132(f846(x39401),f846(x39401),f125(x39401),x39402),x39403))
% 52.62/52.40 [3960]P1(f332(f332(f334(f852(x39601,x39601)),f332(f332(f241(x39601,x39601),x39602),x39602)),f332(f332(f173(f852(x39601,x39601),a839),f2(a845)),x39603)))
% 52.62/52.40 [3966]E(f332(f256(x39661),f332(f332(f10(f853(x39662,a839),a839,x39661),f89(x39662)),f332(f9(x39662,x39661,a839),x39663))),f332(f259(x39662,x39661),f332(f256(f852(x39662,x39661)),f332(f251(x39662,x39661,a839),x39663))))
% 52.62/52.40 [3985]E(f332(f332(f103(f853(x39851,a839)),f332(f332(f47(a845,f853(x39851,a839)),f295(a845,f80(a845),x39852)),x39853)),f332(x39853,f2(a845))),f332(f332(f47(a845,f853(x39851,a839)),f332(f293(a845),x39852)),x39853))
% 52.62/52.40 [4000]E(f332(f132(f846(x40001),f846(x40001),f125(x40001),f115(x40001)),f332(f332(f143(f846(x40001),f846(x40001)),f126(x40001,x40002)),x40003)),f332(f126(x40001,x40002),f332(f132(f846(x40001),f846(x40001),f125(x40001),f115(x40001)),x40003)))
% 52.62/52.40 [4005]E(f332(f250(f846(x40051),f846(x40051)),f155(x40051,x40052,x40053)),f332(f126(x40051,f332(f75(a839,a839,x40051,a328),x40052)),x40053))
% 52.62/52.40 [4054]E(f332(f332(f82(a1),f332(f332(f82(a1),f332(f332(f83(a1),x40541),f332(f332(f44(a1),x40542),x40541))),f53(a1,x40542,x40541))),x40543),f332(f332(f82(a1),x40542),x40543))
% 52.62/52.40 [4088]E(f332(f332(f82(a1),f332(f332(f82(a1),f332(f332(f83(a1),f332(f332(f44(a1),x40881),x40882)),x40882)),f53(a1,x40881,x40882))),x40883),f332(f332(f82(a1),x40881),x40883))
% 52.62/52.40 [4118]E(f87(f852(x41181,x41182),f332(f251(x41181,x41182,a839),f332(f332(f10(f853(x41182,f852(x41181,x41182)),f853(x41182,a839),x41181),f332(f10(f852(x41181,x41182),a839,x41182),x41183)),f241(x41181,x41182)))),f87(f852(x41181,x41182),x41183))
% 52.62/52.40 [4119]E(f92(f852(x41191,x41192),f332(f251(x41191,x41192,a839),f332(f332(f10(f853(x41192,f852(x41191,x41192)),f853(x41192,a839),x41191),f332(f10(f852(x41191,x41192),a839,x41192),x41193)),f241(x41191,x41192)))),f92(f852(x41191,x41192),x41193))
% 52.62/52.40 [4151]P1(f332(f332(f232(f853(x41511,a839)),f45(f853(x41511,a839),f332(f332(f104(f853(f853(x41511,a839),a839)),x41512),x41513))),f332(f332(f104(f853(x41511,a839)),f45(f853(x41511,a839),x41512)),f45(f853(x41511,a839),x41513))))
% 52.62/52.40 [4152]E(f332(f142(x41521),f332(f332(f332(f173(f846(x41521),f846(x41521)),f332(f332(f3(a845),f332(f181(f846(x41521)),x41522)),f53(a845,x41523,f332(f181(f846(x41521)),x41522)))),f141(x41521)),x41522)),f332(f332(f332(f173(f846(x41521),f846(x41521)),x41523),f141(x41521)),f332(f142(x41521),x41522)))
% 52.62/52.40 [4164]E(f332(f256(x41641),f332(f332(f10(a839,a839,x41641),a328),f332(f332(f9(x41641,f849(x41642),a839),f332(f332(f10(f849(x41642),f853(f849(x41642),a839),x41641),a329),x41643)),f183(x41642)))),f169(x41641,x41642,x41643))
% 52.62/52.40 [4227]E(f332(f256(x42271),f332(f332(f10(f853(x42272,a839),a839,x42271),f89(x42272)),f332(f332(f10(f849(x42271),f853(x42272,a839),x42271),f332(f9(x42272,f849(x42271),a839),f332(f332(f10(f849(x42271),f853(f849(x42271),a839),x42272),a329),x42273))),f227(x42271)))),f171(x42272,x42271,x42273))
% 52.62/52.40 [4477]~P1(f332(f65(x44771,x44772,f180(f853(x44771,a839))),x44773))
% 52.62/52.40 [3493]E(f332(f181(f846(x34931)),f332(f332(f159(x34931),x34932),x34933)),f332(f332(f236(a845),f332(f181(f846(x34931)),x34933)),x34932))
% 52.62/52.40 [3494]E(f332(f181(f846(x34941)),f332(f332(f128(x34941),x34942),x34943)),f332(f332(f3(a845),f332(f181(f846(x34941)),x34943)),x34942))
% 52.62/52.40 [3530]E(f332(f332(f44(a845),f332(f332(f44(a845),x35301),x35302)),x35303),f332(f332(f44(a845),x35301),f332(f332(f83(a845),x35302),x35303)))
% 52.62/52.40 [3531]E(f332(f332(f82(a845),f332(f332(f82(a845),x35311),x35312)),x35313),f332(f332(f82(a845),x35311),f332(f332(f82(a845),x35312),x35313)))
% 52.62/52.40 [3532]E(f332(f332(f82(a1),f332(f332(f82(a1),x35321),x35322)),x35323),f332(f332(f82(a1),x35321),f332(f332(f82(a1),x35322),x35323)))
% 52.62/52.40 [3533]E(f332(f332(f83(a845),f332(f332(f83(a845),x35331),x35332)),x35333),f332(f332(f83(a845),x35331),f332(f332(f83(a845),x35332),x35333)))
% 52.62/52.40 [3534]E(f332(f332(f83(a1),f332(f332(f83(a1),x35341),x35342)),x35343),f332(f332(f83(a1),x35341),f332(f332(f83(a1),x35342),x35343)))
% 52.62/52.40 [3535]E(f332(f332(f3(a845),f332(f332(f3(a845),x35351),x35352)),x35353),f332(f332(f3(a845),x35351),f332(f332(f82(a845),x35352),x35353)))
% 52.62/52.40 [3536]E(f332(f332(f242(a1),f332(f332(f242(a1),x35361),x35362)),x35363),f332(f332(f242(a1),x35361),f332(f332(f83(a845),x35362),x35363)))
% 52.62/52.40 [3554]E(f150(x35541,f332(f332(f140(f853(x35541,a839)),x35542),x35543)),f161(x35541,x35542,f150(x35541,x35543)))
% 52.62/52.40 [3599]E(f332(f332(f3(a845),f332(f332(f3(a845),x35991),x35992)),x35993),f332(f332(f3(a845),f332(f332(f3(a845),x35991),x35993)),x35992))
% 52.62/52.40 [3607]E(f332(f332(f104(f853(x36071,a839)),x36072),f332(f332(f3(f853(x36071,a839)),x36073),x36072)),f180(f853(x36071,a839)))
% 52.62/52.40 [3652]E(f46(f853(x36521,a839),f332(f332(f302(f853(x36521,a839)),x36522),x36523)),f332(f332(f104(f853(x36521,a839)),x36522),f46(f853(x36521,a839),x36523)))
% 52.62/52.40 [3653]E(f45(f853(x36531,a839),f332(f332(f302(f853(x36531,a839)),x36532),x36533)),f332(f332(f103(f853(x36531,a839)),x36532),f45(f853(x36531,a839),x36533)))
% 52.62/52.40 [3655]E(f332(f332(f82(a845),f332(f332(f83(a845),x36551),x36552)),f332(f332(f83(a845),x36553),x36552)),f332(f332(f83(a845),f332(f332(f82(a845),x36551),x36553)),x36552))
% 52.62/52.40 [3656]E(f332(f332(f3(a845),f332(f332(f83(a845),x36561),x36562)),f332(f332(f83(a845),x36563),x36562)),f332(f332(f83(a845),f332(f332(f3(a845),x36561),x36563)),x36562))
% 52.62/52.40 [3657]E(f332(f332(f82(a1),f332(f332(f83(a1),x36571),x36572)),f332(f332(f83(a1),x36573),x36572)),f332(f332(f83(a1),f332(f332(f82(a1),x36571),x36573)),x36572))
% 52.62/52.40 [3659]E(f332(f332(f3(a1),f332(f332(f83(a1),x36591),x36592)),f332(f332(f83(a1),x36593),x36592)),f332(f332(f83(a1),f332(f332(f3(a1),x36591),x36593)),x36592))
% 52.62/52.40 [3660]E(f332(f332(f236(a845),f332(f332(f3(a845),x36601),x36602)),f332(f332(f3(a845),x36603),x36602)),f332(f332(f3(a845),f332(f332(f236(a845),x36601),x36603)),x36602))
% 52.62/52.40 [3684]E(f332(f332(f103(f853(x36841,a839)),x36842),f332(f332(f3(f853(x36841,a839)),x36843),x36842)),f332(f332(f103(f853(x36841,a839)),x36842),x36843))
% 52.62/52.40 [3685]E(f332(f332(f103(f853(x36851,a839)),x36852),f332(f332(f103(f853(x36851,a839)),x36852),x36853)),f332(f332(f103(f853(x36851,a839)),x36852),x36853))
% 52.62/52.40 [3686]E(f332(f332(f104(f853(x36861,a839)),x36862),f332(f332(f104(f853(x36861,a839)),x36862),x36863)),f332(f332(f104(f853(x36861,a839)),x36862),x36863))
% 52.62/52.40 [3698]E(f332(f332(f281(x36981,x36982,x36982),x36983),f300(x36982,f180(f853(f852(x36982,x36982),a839)))),x36983)
% 52.62/52.40 [3703]E(f332(f332(f103(f853(x37031,a839)),f332(f332(f302(x37031),x37032),f180(f853(x37031,a839)))),x37033),f332(f332(f302(x37031),x37032),x37033))
% 52.62/52.40 [3721]E(f332(f332(f3(a845),f332(f332(f3(a845),f332(a114,x37211)),x37212)),f332(a114,x37213)),f332(f332(f3(a845),f332(f332(f3(a845),x37211),x37212)),x37213))
% 52.62/52.40 [3748]E(f332(f332(f104(f853(f853(x37481,a839),a839)),f332(f301(x37481),x37482)),f332(f301(x37481),x37483)),f332(f301(x37481),f332(f332(f104(f853(x37481,a839)),x37482),x37483)))
% 52.62/52.40 [3751]E(f332(f332(f103(f853(x37511,a839)),f332(f81(f853(x37511,a839)),x37512)),x37513),f332(f81(f853(x37511,a839)),f332(f332(f3(f853(x37511,a839)),x37512),x37513)))
% 52.62/52.40 [3764]E(f332(f332(f302(x37641),x37642),f332(f332(f3(f853(x37641,a839)),x37643),f332(f332(f302(x37641),x37642),f180(f853(x37641,a839))))),f332(f332(f302(x37641),x37642),x37643))
% 52.62/52.40 [3775]P1(f332(f332(f232(f853(x37751,a839)),x37752),f332(f332(f103(f853(x37751,a839)),x37753),x37752)))
% 52.62/52.40 [3776]P1(f332(f332(f232(f853(x37761,a839)),x37762),f332(f332(f103(f853(x37761,a839)),x37762),x37763)))
% 52.62/52.40 [3779]E(f332(f332(f104(f853(x37791,a839)),f332(f81(f853(x37791,a839)),x37792)),f332(f81(f853(x37791,a839)),x37793)),f332(f81(f853(x37791,a839)),f332(f332(f103(f853(x37791,a839)),x37792),x37793)))
% 52.62/52.40 [3780]E(f332(f332(f103(f853(x37801,a839)),f332(f81(f853(x37801,a839)),x37802)),f332(f81(f853(x37801,a839)),x37803)),f332(f81(f853(x37801,a839)),f332(f332(f104(f853(x37801,a839)),x37802),x37803)))
% 52.62/52.40 [3793]P1(f332(f332(f232(f853(x37931,a839)),f332(f158(x37931),x37932)),f332(f158(x37931),f332(f332(f140(x37931),x37933),x37932))))
% 52.62/52.40 [3802]E(f332(f332(f103(f853(x38021,a839)),f332(f332(f3(f853(x38021,a839)),x38022),x38023)),f332(f332(f104(f853(x38021,a839)),x38022),x38023)),x38022)
% 52.62/52.40 [3852]E(f332(f332(f8(x38521,a1),f332(f332(f10(a845,a1,x38521),f102(a1)),x38522)),x38523),f332(f102(a1),f332(f332(f8(x38521,a845),x38522),x38523)))
% 52.62/52.40 [3853]E(f332(f332(f11(x38531,a1),f332(f332(f10(a845,a1,x38531),f102(a1)),x38532)),x38533),f332(f102(a1),f332(f332(f11(x38531,a845),x38532),x38533)))
% 52.62/52.40 [3909]E(f332(f81(f853(f852(x39091,x39092),a839)),f332(f332(f248(x39091,x39092),x39093),f332(f18(f853(x39092,a839),x39091),f239(f853(x39092,a839))))),f332(f332(f248(x39091,x39092),f332(f81(f853(x39091,a839)),x39093)),f332(f18(f853(x39092,a839),x39091),f239(f853(x39092,a839)))))
% 52.62/52.40 [3910]E(f332(f81(f853(f852(x39101,x39102),a839)),f332(f332(f248(x39101,x39102),f239(f853(x39101,a839))),f332(f18(f853(x39102,a839),x39101),x39103))),f332(f332(f248(x39101,x39102),f239(f853(x39101,a839))),f332(f18(f853(x39102,a839),x39101),f332(f81(f853(x39102,a839)),x39103))))
% 52.62/52.40 [3961]E(f332(f332(f47(f853(x39611,a839),f853(x39611,a839)),x39612),f332(f332(f9(f853(x39611,a839),f853(x39611,a839),f853(x39611,a839)),f104(f853(x39611,a839))),x39613)),f332(f332(f104(f853(x39611,a839)),f45(f853(x39611,a839),x39612)),x39613))
% 52.62/52.40 [3968]E(f332(f132(f846(x39681),f846(x39681),f125(x39681),f115(x39681)),f332(f332(f140(f846(x39681)),x39682),x39683)),f332(f332(f125(x39681),x39682),f332(f132(f846(x39681),f846(x39681),f125(x39681),f115(x39681)),x39683)))
% 52.62/52.40 [3991]E(f332(f332(f302(f853(x39911,a839)),f332(f277(x39911,x39911,x39912),f332(f332(f302(x39911),x39913),f180(f853(x39911,a839))))),f180(f853(f853(x39911,a839),a839))),f332(f332(f62(x39911),f332(f332(f302(x39911),x39913),f180(f853(x39911,a839)))),x39912))
% 52.62/52.40 [4001]E(f332(f332(f82(a845),f332(f332(f83(a845),x40011),f332(f332(f44(a845),x40012),x40013))),f332(f332(f44(a845),f332(f332(f83(a845),x40011),f53(a845,x40012,x40013))),x40013)),f332(f332(f44(a845),f332(f332(f83(a845),x40011),x40012)),x40013))
% 52.62/52.40 [4002]E(f332(f332(f82(a1),f332(f332(f83(a1),x40021),f332(f332(f44(a1),x40022),x40023))),f332(f332(f44(a1),f332(f332(f83(a1),x40021),f53(a1,x40022,x40023))),x40023)),f332(f332(f44(a1),f332(f332(f83(a1),x40021),x40022)),x40023))
% 52.62/52.40 [4086]E(f332(f332(f125(x40861),f332(f132(f846(x40861),f846(x40861),f125(x40861),f115(x40861)),x40862)),f332(f132(f846(x40861),f846(x40861),f125(x40861),f115(x40861)),x40863)),f332(f132(f846(x40861),f846(x40861),f125(x40861),f115(x40861)),f332(f332(f125(f846(x40861)),x40862),x40863)))
% 52.62/52.40 [4089]E(f332(f332(f241(f846(x40891),f846(x40891)),f332(f126(x40891,x40892),x40893)),f332(f126(x40891,f332(f75(a839,a839,x40891,a328),x40892)),x40893)),f155(x40891,x40892,x40893))
% 52.62/52.40 [4092]E(f332(f332(f82(a845),f332(f332(f82(a845),f332(f332(f44(a845),x40921),x40922)),f332(f332(f44(a845),x40923),x40922))),f332(f332(f44(a845),f332(f332(f82(a845),f53(a845,x40921,x40922)),f53(a845,x40923,x40922))),x40922)),f332(f332(f44(a845),f332(f332(f82(a845),x40921),x40923)),x40922))
% 52.62/52.40 [4093]E(f332(f332(f82(a1),f332(f332(f82(a1),f332(f332(f44(a1),x40931),x40932)),f332(f332(f44(a1),x40933),x40932))),f332(f332(f44(a1),f332(f332(f82(a1),f53(a1,x40931,x40932)),f53(a1,x40933,x40932))),x40932)),f332(f332(f44(a1),f332(f332(f82(a1),x40931),x40933)),x40932))
% 52.62/52.40 [4165]E(f332(f256(x41651),f332(f332(f20(x41651,a839,a839),f332(f332(f10(a839,f853(a839,a839),x41651),a331),f332(f332(f9(x41651,x41651,a839),a329),x41652))),f332(f332(f9(x41651,f853(x41651,a839),a839),f334(x41651)),x41653))),f332(f332(f302(x41651),x41652),x41653))
% 52.62/52.40 [4166]E(f332(f256(x41661),f332(f332(f20(x41661,a839,a839),f332(f332(f10(a839,f853(a839,a839),x41661),a331),f332(f332(f9(x41661,x41661,a839),a329),x41662))),f332(f332(f9(x41661,f853(x41661,a839),a839),f334(x41661)),x41663))),f332(f332(f302(x41661),x41662),x41663))
% 52.62/52.40 [4188]E(f332(f256(x41881),f332(f332(f20(x41881,a839,a839),f332(f332(f10(a839,f853(a839,a839),x41881),a331),f332(f332(f9(x41881,f853(x41881,a839),a839),f334(x41881)),x41882))),f332(f332(f9(x41881,f853(x41881,a839),a839),f334(x41881)),x41883))),f332(f332(f103(f853(x41881,a839)),x41882),x41883))
% 52.62/52.40 [4189]E(f332(f256(x41891),f332(f332(f20(x41891,a839,a839),f332(f332(f10(a839,f853(a839,a839),x41891),a330),f332(f332(f9(x41891,f853(x41891,a839),a839),f334(x41891)),x41892))),f332(f332(f9(x41891,f853(x41891,a839),a839),f334(x41891)),x41893))),f332(f332(f104(f853(x41891,a839)),x41892),x41893))
% 52.62/52.40 [4276]E(f332(f332(f47(x42761,f853(f853(x42761,a839),a839)),x42762),f332(f332(f9(x42761,f853(f853(x42761,a839),a839),f853(f853(x42761,a839),a839)),f332(f332(f10(f853(x42761,a839),f853(f853(f853(x42761,a839),a839),f853(f853(x42761,a839),a839)),x42761),f302(f853(x42761,a839))),f332(f332(f10(f853(x42761,a839),f853(x42761,a839),x42761),f277(x42761,x42761,x42763)),f332(f332(f9(x42761,f853(x42761,a839),f853(x42761,a839)),f302(x42761)),f180(f853(x42761,a839)))))),f180(f853(f853(x42761,a839),a839)))),f332(f332(f62(x42761),x42762),x42763))
% 52.62/52.40 [4278]E(f332(f332(f197(x42781),f332(f332(f83(a1),f332(f332(f75(f852(a1,a1),a1,x42781,f240(a1,a1)),f207(x42781)),x42782)),f332(f332(f75(f852(a1,a1),a1,x42781,f240(a1,a1)),f207(x42781)),x42783))),f332(f332(f83(a1),f332(f332(f75(f852(a1,a1),a1,x42781,f250(a1,a1)),f207(x42781)),x42782)),f332(f332(f75(f852(a1,a1),a1,x42781,f250(a1,a1)),f207(x42781)),x42783))),f222(x42781,x42782,x42783))
% 52.62/52.40 [3673]E(f53(a845,f332(f332(f82(a845),f332(f332(f83(a845),x36731),x36732)),x36733),x36732),f53(a845,x36733,x36732))
% 52.62/52.40 [3720]E(f130(a845,f332(f294(a845,f332(f332(f82(a845),x37201),x37202)),x37203)),f332(f332(f128(a845),x37202),f130(a845,f332(f294(a845,x37201),x37203))))
% 52.62/52.40 [3763]E(f332(f332(f82(a1),f332(f102(a1),x37631)),f332(f332(f82(a1),f332(f102(a1),x37632)),x37633)),f332(f332(f82(a1),f332(f102(a1),f332(f332(f82(a845),x37631),x37632))),x37633))
% 52.62/52.40 [3771]E(f332(f332(f3(f853(x37711,a839)),f332(f332(f3(f853(x37711,a839)),x37712),x37713)),x37713),f332(f332(f3(f853(x37711,a839)),x37712),x37713))
% 52.62/52.40 [3772]E(f332(f332(f103(f853(x37721,a839)),f332(f332(f3(f853(x37721,a839)),x37722),x37723)),x37723),f332(f332(f103(f853(x37721,a839)),x37722),x37723))
% 52.62/52.40 [3794]E(f332(f332(f281(x37941,x37941,x37942),f300(x37941,f180(f853(f852(x37941,x37941),a839)))),x37943),x37943)
% 52.62/52.40 [3799]E(f332(f332(f103(f853(x37991,a839)),f332(f276(x37991),x37992)),f332(f276(x37991),x37993)),f332(f276(x37991),f332(f332(f103(f853(f852(x37991,x37991),a839)),x37992),x37993)))
% 52.62/52.40 [3808]E(f263(x38081,f332(f332(f140(f852(a101,x38081)),f332(f332(f241(a101,x38081),f2(a101)),x38082)),x38083)),f263(x38081,x38083))
% 52.62/52.40 [3811]E(f332(f332(f104(f853(x38111,a839)),f46(f853(x38111,a839),x38112)),f46(f853(x38111,a839),x38113)),f46(f853(x38111,a839),f332(f332(f103(f853(f853(x38111,a839),a839)),x38112),x38113)))
% 52.62/52.40 [3812]E(f332(f332(f103(f853(x38121,a839)),f45(f853(x38121,a839),x38122)),f45(f853(x38121,a839),x38123)),f45(f853(x38121,a839),f332(f332(f103(f853(f853(x38121,a839),a839)),x38122),x38123)))
% 52.62/52.40 [3845]E(f332(f332(f281(x38451,x38451,x38451),f332(f332(f173(f852(x38451,x38451),a839),x38452),x38453)),x38453),f332(f332(f173(f852(x38451,x38451),a839),f332(a114,x38452)),x38453))
% 52.62/52.40 [3895]P1(f332(f332(f232(f853(x38951,a839)),f332(f332(f3(f853(x38951,a839)),x38952),x38953)),x38952))
% 52.62/52.40 [3896]P1(f332(f332(f232(f853(x38961,a839)),f332(f332(f104(f853(x38961,a839)),x38962),x38963)),x38963))
% 52.62/52.40 [3897]P1(f332(f332(f232(f853(x38971,a839)),f332(f332(f104(f853(x38971,a839)),x38972),x38973)),x38972))
% 52.62/52.40 [3922]E(f300(x39221,f332(f332(f103(f853(f852(x39221,x39221),a839)),f300(x39221,x39222)),f300(x39221,x39223))),f300(x39221,f332(f332(f103(f853(f852(x39221,x39221),a839)),x39222),x39223)))
% 52.62/52.40 [3926]E(f45(f853(x39261,a839),f332(f332(f302(f853(x39261,a839)),x39262),f332(f332(f302(f853(x39261,a839)),x39263),f180(f853(f853(x39261,a839),a839))))),f332(f332(f103(f853(x39261,a839)),x39262),x39263))
% 52.62/52.40 [3927]E(f46(f853(x39271,a839),f332(f332(f302(f853(x39271,a839)),x39272),f332(f332(f302(f853(x39271,a839)),x39273),f180(f853(f853(x39271,a839),a839))))),f332(f332(f104(f853(x39271,a839)),x39272),x39273))
% 52.62/52.40 [3933]E(f332(f332(f281(x39331,x39331,x39331),f332(f332(f173(f852(x39331,x39331),a839),x39332),x39333)),x39333),f332(f332(f281(x39331,x39331,x39331),x39333),f332(f332(f173(f852(x39331,x39331),a839),x39332),x39333)))
% 52.62/52.40 [4006]E(f332(f332(f103(f853(x40061,a839)),f332(f256(x40061),f332(f332(f9(x40061,x40061,a839),a329),x40062))),x40063),f332(f332(f302(x40061),x40062),x40063))
% 52.62/52.40 [4008]E(f332(a107,f332(f332(f8(x40081,a1),f332(f332(f10(a845,a1,x40081),f102(a1)),x40082)),x40083)),f332(f332(f8(x40081,a845),x40082),x40083))
% 52.62/52.40 [4009]E(f332(a107,f332(f332(f11(x40091,a1),f332(f332(f10(a845,a1,x40091),f102(a1)),x40092)),x40093)),f332(f332(f11(x40091,a845),x40092),x40093))
% 52.62/52.40 [4083]E(f332(f145(f846(x40831),x40831,f332(f157(x40831),x40832),f332(f18(f853(f846(x40831),f846(x40831)),x40831),f332(f332(f9(f846(x40831),f846(x40831),f846(x40831)),f125(x40831)),x40832))),x40833),f332(f157(x40831),f332(f332(f125(x40831),x40833),x40832)))
% 52.62/52.40 [4114]P1(f332(f332(f232(f853(f853(x41141,a839),a839)),f332(f332(f103(f853(f853(x41141,a839),a839)),f332(f301(x41141),x41142)),f332(f301(x41141),x41143))),f332(f301(x41141),f332(f332(f103(f853(x41141,a839)),x41142),x41143))))
% 52.62/52.40 [4207]E(f332(f256(x42071),f332(f332(f20(x42071,a839,a839),f332(f332(f10(a839,f853(a839,a839),x42071),a330),f332(f332(f9(x42071,f853(x42071,a839),a839),f334(x42071)),x42072))),f332(f332(f10(a839,a839,x42071),a328),f332(f332(f9(x42071,f853(x42071,a839),a839),f334(x42071)),x42073)))),f332(f332(f3(f853(x42071,a839)),x42072),x42073))
% 52.62/52.40 [4228]E(f332(f43(a845),f332(f256(a845),f332(f332(f20(a845,a839,a839),f332(f332(f10(a839,f853(a839,a839),a845),a330),f332(f332(f9(a845,a845,a839),f233(a845)),f332(f181(f846(x42281)),x42282)))),f332(f332(f10(x42281,a839,a845),x42283),f332(f152(x42281),x42282))))),f332(f181(f846(x42281)),f332(f126(x42281,x42283),x42282)))
% 52.62/52.40 [4230]E(f332(f181(f846(x42301)),f160(x42301,x42302,x42303)),f332(f43(a845),f332(f256(a845),f332(f332(f20(a845,a839,a839),f332(f332(f10(a839,f853(a839,a839),a845),a330),f332(f332(f9(a845,a845,a839),f233(a845)),f332(f181(f846(x42301)),x42302)))),f332(f332(f9(a845,f853(a845,a839),a839),f334(a845)),x42303)))))
% 52.62/52.40 [4323]E(f332(f332(f104(f853(f852(f846(x43231),f846(x43231)),a839)),f332(f303(f852(f852(x43231,f846(x43231)),f852(x43231,f846(x43231))),f852(f846(x43231),f846(x43231)),f252(f852(x43231,f846(x43231)),f846(x43231),f852(x43231,f846(x43231)),f846(x43231),f332(f251(x43231,f846(x43231),f846(x43231)),f140(x43231)),f332(f251(x43231,f846(x43231),f846(x43231)),f140(x43231)))),f326(x43231,f846(x43231),x43232,f332(f133(x43231,x43232),x43233)))),f332(f256(f852(f846(x43231),f846(x43231))),f332(f251(f846(x43231),f846(x43231),a839),f332(f332(f9(f846(x43231),f853(f846(x43231),a839),f853(f846(x43231),a839)),f332(f332(f10(f853(a839,a839),f853(f853(f846(x43231),a839),f853(f846(x43231),a839)),f846(x43231)),f10(a839,a839,f846(x43231))),f332(f332(f10(a839,f853(a839,a839),f846(x43231)),a330),f332(f332(f9(f846(x43231),a845,a839),f332(f332(f10(a845,f853(a845,a839),f846(x43231)),a329),f181(f846(x43231)))),f332(a114,x43233))))),f332(f332(f9(f846(x43231),a845,a839),f332(f332(f10(a845,f853(a845,a839),f846(x43231)),a329),f181(f846(x43231)))),f332(a114,x43233)))))),f332(f133(x43231,x43232),f332(a114,x43233)))
% 52.62/52.40 [3813]E(f53(a845,f332(a114,f332(f332(f82(a845),f332(f332(f83(a845),x38131),x38132)),x38133)),x38132),f53(a845,f332(a114,x38133),x38132))
% 52.62/52.40 [4073]E(f332(f256(x40731),f332(f332(f20(x40731,a839,a839),f332(f332(f10(a839,f853(a839,a839),x40731),a330),x40732)),x40733)),f332(f332(f104(f853(x40731,a839)),f332(f256(x40731),x40732)),f332(f256(x40731),x40733)))
% 52.62/52.40 [4074]E(f332(f256(x40741),f332(f332(f20(x40741,a839,a839),f332(f332(f10(a839,f853(a839,a839),x40741),a331),x40742)),x40743)),f332(f332(f103(f853(x40741,a839)),f332(f256(x40741),x40742)),f332(f256(x40741),x40743)))
% 52.62/52.40 [4076]E(f332(f332(f125(x40761),f332(f332(f128(x40761),f53(a845,x40762,f332(f181(f846(x40761)),x40763))),x40763)),f332(f332(f159(x40761),f53(a845,x40762,f332(f181(f846(x40761)),x40763))),x40763)),f332(f332(f332(f173(f846(x40761),f846(x40761)),x40762),f141(x40761)),x40763))
% 52.62/52.40 [4081]E(f332(f256(x40811),f332(f332(f20(x40811,a839,a839),f332(f332(f10(a839,f853(a839,a839),x40811),a335),x40812)),x40813)),f332(f332(f103(f853(x40811,a839)),f332(f81(f853(x40811,a839)),f332(f256(x40811),x40812))),f332(f256(x40811),x40813)))
% 52.62/52.40 [4095]E(f332(f332(f82(a845),f332(f181(f846(x40951)),f332(f126(x40951,x40952),x40953))),f332(f181(f846(x40951)),f332(f126(x40951,f332(f332(f10(a839,a839,x40951),a328),x40952)),x40953))),f332(f181(f846(x40951)),x40953))
% 52.62/52.40 [4122]P1(f332(f332(f232(f853(x41221,a839)),f332(f332(f103(f853(x41221,a839)),f46(f853(x41221,a839),x41222)),f46(f853(x41221,a839),x41223))),f46(f853(x41221,a839),f332(f332(f104(f853(f853(x41221,a839),a839)),x41222),x41223))))
% 52.62/52.40 [4138]E(f332(f158(x41381),f332(f126(x41381,f332(f332(f10(a839,a839,x41381),a328),f332(f332(f9(x41381,x41381,a839),a329),x41382))),x41383)),f332(f332(f3(f853(x41381,a839)),f332(f158(x41381),x41383)),f332(f332(f302(x41381),x41382),f180(f853(x41381,a839)))))
% 52.62/52.40 [4147]P1(f332(f332(f232(f853(f852(x41471,x41471),a839)),f332(f332(f103(f853(f852(x41471,x41471),a839)),f300(x41471,x41472)),f300(x41471,x41473))),f300(x41471,f332(f332(f103(f853(f852(x41471,x41471),a839)),x41472),x41473))))
% 52.62/52.40 [4171]E(f332(f332(f83(a845),f332(a114,f332(a114,f2(a845)))),f332(f332(f8(a845,a845),f332(f332(f10(a845,a845,a845),f332(f82(a845),x41711)),f332(f332(f9(a845,a845,a845),f83(a845)),x41712))),f332(f257(a845),x41713))),f332(f332(f83(a845),x41713),f332(f332(f82(a845),x41711),f332(f332(f82(a845),x41711),f332(f332(f83(a845),f332(f332(f3(a845),x41713),f80(a845))),x41712)))))
% 52.62/52.40 [4181]E(f332(f256(x41811),f332(f332(f20(x41811,a839,a839),f332(f332(f10(a839,f853(a839,a839),x41811),a330),f332(f332(f9(x41811,f853(x41811,a839),a839),f334(x41811)),f332(f158(x41811),x41812)))),x41813)),f332(f158(x41811),f332(f126(x41811,x41813),x41812)))
% 52.62/52.40 [4322]E(f332(f256(x43221),f332(f332(f10(f853(a845,a839),a839,x43221),f89(a845)),f332(f332(f9(x43221,f853(a845,a839),f853(a845,a839)),f332(f332(f10(f853(a845,f853(a839,a839)),f853(f853(a845,a839),f853(a845,a839)),x43221),f20(a845,a839,a839)),f332(f332(f10(f853(a845,a839),f853(a845,f853(a839,a839)),x43221),f332(f10(a839,f853(a839,a839),a845),a330)),f332(f332(f9(x43221,f853(a845,x43221),f853(a845,a839)),f332(f332(f10(f853(x43221,a839),f853(f853(a845,x43221),f853(a845,a839)),x43221),f10(x43221,a839,a845)),a329)),f332(f152(x43221),x43222))))),f332(f332(f20(a845,a839,a839),f332(f332(f10(a839,f853(a839,a839),a845),a330),f332(f332(f9(a845,a845,a839),f233(a845)),f332(f181(f846(x43221)),x43222)))),f332(f332(f9(a845,f853(a845,a839),a839),f334(a845)),x43223))))),f332(f158(x43221),f160(x43221,x43222,x43223)))
% 52.62/52.40 [4218]E(f332(f256(x42181),f332(f332(f20(x42181,a839,a839),f332(f332(f10(a839,f853(a839,a839),x42181),a335),f332(f332(f10(a839,a839,x42181),a328),f332(f332(f9(x42181,x42181,a839),a329),x42182)))),x42183)),f332(f332(f302(x42181),x42182),f332(f256(x42181),x42183)))
% 52.62/52.40 [4249]E(f332(f332(f143(f852(x42491,a845),x42491),f240(x42491,a845)),f332(f126(f852(x42491,a845),f332(f332(f9(f852(x42491,a845),f853(a845,a839),a839),f332(f332(f10(a845,f853(f853(a845,a839),a839),f852(x42491,a845)),f334(a845)),f250(x42491,a845))),x42492)),f332(f332(f167(x42491,a845),x42493),f130(a845,f332(f294(a845,f2(a845)),f332(f181(f846(x42491)),x42493)))))),f160(x42491,x42493,x42492))
% 52.62/52.40 [4277]E(f332(f332(f83(a1),f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f332(f332(f8(a845,a1),f332(f332(f10(a1,a1,a845),f332(f82(a1),x42771)),f332(f332(f9(a845,a1,a1),f332(f332(f10(a1,f853(a1,a1),a845),f83(a1)),f102(a1))),x42772))),f332(f257(a845),x42773))),f332(f332(f83(a1),f332(f102(a1),x42773)),f332(f332(f82(a1),x42771),f332(f332(f82(a1),x42771),f332(f332(f83(a1),f332(f102(a1),f332(f332(f3(a845),x42773),f80(a845)))),x42772)))))
% 52.62/52.40 [4316]E(f332(f256(f852(x43161,x43162)),f332(f251(x43161,x43162,a839),f332(f332(f9(x43161,f853(f852(x43162,x43161),a839),f853(x43162,a839)),f332(f332(f10(f853(x43162,f853(f853(f852(x43162,x43161),a839),a839)),f853(f853(f852(x43162,x43161),a839),f853(x43162,a839)),x43161),f9(x43162,f853(f852(x43162,x43161),a839),a839)),f332(f332(f10(f853(x43162,f852(x43162,x43161)),f853(x43162,f853(f853(f852(x43162,x43161),a839),a839)),x43161),f332(f10(f852(x43162,x43161),f853(f853(f852(x43162,x43161),a839),a839),x43162),f334(f852(x43162,x43161)))),f332(f9(x43162,x43161,f852(x43162,x43161)),f241(x43162,x43161))))),x43163))),f332(f278(x43162,x43161),x43163))
% 52.62/52.40 [4351]E(f332(f256(f846(x43511)),f332(f332(f10(f853(x43511,a839),a839,f846(x43511)),f89(x43511)),f332(f332(f10(f853(x43511,f853(f846(x43511),a839)),f853(x43511,a839),f846(x43511)),f332(f10(f853(f846(x43511),a839),a839,x43511),f89(f846(x43511)))),f332(f332(f9(f846(x43511),f853(x43511,f853(f846(x43511),a839)),f853(x43511,f853(f846(x43511),a839))),f332(f332(f10(f853(x43511,f853(f853(f846(x43511),a839),f853(f846(x43511),a839))),f853(f853(x43511,f853(f846(x43511),a839)),f853(x43511,f853(f846(x43511),a839))),f846(x43511)),f20(x43511,f853(f846(x43511),a839),f853(f846(x43511),a839))),f332(f332(f10(f853(x43511,f853(f846(x43511),f853(a839,a839))),f853(x43511,f853(f853(f846(x43511),a839),f853(f846(x43511),a839))),f846(x43511)),f332(f10(f853(f846(x43511),f853(a839,a839)),f853(f853(f846(x43511),a839),f853(f846(x43511),a839)),x43511),f20(f846(x43511),a839,a839))),f332(f332(f10(f853(x43511,f853(f846(x43511),a839)),f853(x43511,f853(f846(x43511),f853(a839,a839))),f846(x43511)),f332(f10(f853(f846(x43511),a839),f853(f846(x43511),f853(a839,a839)),x43511),f332(f10(a839,f853(a839,a839),f846(x43511)),a330))),f332(f332(f9(f846(x43511),f853(x43511,f853(f846(x43511),f846(x43511))),f853(x43511,f853(f846(x43511),a839))),f332(f332(f10(f853(f853(f846(x43511),f846(x43511)),f853(f846(x43511),a839)),f853(f853(x43511,f853(f846(x43511),f846(x43511))),f853(x43511,f853(f846(x43511),a839))),f846(x43511)),f10(f853(f846(x43511),f846(x43511)),f853(f846(x43511),a839),x43511)),f332(f332(f10(f853(f846(x43511),a839),f853(f853(f846(x43511),f846(x43511)),f853(f846(x43511),a839)),f846(x43511)),f10(f846(x43511),a839,f846(x43511))),a329))),f140(x43511)))))),f332(f332(f9(x43511,f853(f846(x43511),a839),f853(f846(x43511),a839)),f332(f332(f10(f853(a839,a839),f853(f853(f846(x43511),a839),f853(f846(x43511),a839)),x43511),f10(a839,a839,f846(x43511))),f332(f332(f10(a839,f853(a839,a839),x43511),a330),f332(f332(f9(x43511,f853(x43511,a839),a839),f334(x43511)),x43512)))),f332(f332(f9(f846(x43511),f853(f846(x43511),a839),a839),f334(f846(x43511))),x43513)))))),f161(x43511,x43512,x43513))
% 52.62/52.40 [4336]E(f332(f332(f88(a1,f852(a1,a1)),f332(f332(f3(a1),x43361),x43362)),f332(f332(f9(a1,f852(a1,a1),f852(a1,a1)),f332(f332(f20(a1,f852(a1,a1),f853(f852(a1,a1),f852(a1,a1))),f332(f332(f10(a839,f853(f852(a1,a1),f853(f852(a1,a1),f852(a1,a1))),a1),f98(f852(a1,a1))),f332(f232(a1),f2(a1)))),f332(f241(a1,a1),f332(f332(f82(a1),f332(f332(f83(a1),f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),x43363)),f80(a1))))),f332(f332(f241(a1,a1),f332(f332(f83(a1),f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),x43363)),x43361))),f332(f51(x43362),f332(f332(f241(a1,a1),x43363),x43361)))
% 52.62/52.40 [4387]~E(f35(x43871,x43872),f36(x43873,x43874))
% 52.62/52.40 [4388]~E(f35(x43881,x43882),f36(x43883,x43884))
% 52.62/52.40 [4389]~E(f28(x43891,x43892),f36(x43893,x43894))
% 52.62/52.40 [4390]~E(f28(x43901,x43902),f35(x43903,x43904))
% 52.62/52.40 [4391]~E(f28(x43911,x43912),f36(x43913,x43914))
% 52.62/52.40 [4392]~E(f28(x43921,x43922),f35(x43923,x43924))
% 52.62/52.40 [4410]~E(f332(a27,x44101),f33(x44102,x44103,x44104))
% 52.62/52.40 [4411]~E(f332(a27,x44111),f32(x44112,x44113,x44114))
% 52.62/52.40 [4412]~E(f332(a27,x44121),f31(x44122,x44123,x44124))
% 52.62/52.40 [4413]~E(f33(x44131,x44132,x44133),f332(a27,x44134))
% 52.62/52.40 [4414]~E(f32(x44141,x44142,x44143),f332(a27,x44144))
% 52.62/52.40 [4415]~E(f31(x44151,x44152,x44153),f332(a27,x44154))
% 52.62/52.40 [3367]E(f332(f332(f332(f74(x33671,x33672),x33673),x33674),f332(x33673,x33674)),x33673)
% 52.62/52.40 [3432]E(f332(f332(f243(x34321,x34322,x34323),x34324),f2(a845)),x34322)
% 52.62/52.40 [3470]E(f175(x34701,x34702,x34703,f332(a114,x34704)),f332(x34703,x34704))
% 52.62/52.40 [3511]E(f151(x35111,x35112,f151(x35111,x35113,x35114)),f151(x35111,x35113,f151(x35111,x35112,x35114)))
% 52.62/52.40 [3627]P41(f28(x36271,x36272),x36273,x36274,f332(f332(f332(a189,x36273),x36271),f332(x36272,x36273)))
% 52.62/52.40 [3628]P41(f28(x36281,x36282),x36283,x36284,f332(f332(f332(a189,x36283),x36281),f332(x36282,x36283)))
% 52.62/52.40 [3640]E(f332(f229(x36401,x36402,x36403,x36404),f183(x36402)),x36403)
% 52.62/52.40 [3642]E(f332(f145(x36421,x36422,x36423,x36424),f115(x36422)),x36423)
% 52.62/52.40 [3643]E(f332(f132(x36431,x36432,x36433,x36434),f115(x36432)),x36434)
% 52.62/52.40 [3680]E(f332(f181(f850(x36801,x36802)),f215(x36801,x36802,x36803,x36804)),f2(a845))
% 52.62/52.40 [3705]E(f332(f251(x37051,x37052,x37053),f249(x37051,x37052,x37053,x37054)),x37054)
% 52.62/52.40 [3760]E(f332(f229(f849(x37601),x37602,f183(x37601),f332(f18(f849(x37601),x37602),f183(x37601))),f332(x37603,x37604)),f183(x37601))
% 52.62/52.40 [3803]E(f332(f332(f103(f853(x38031,a839)),f169(x38031,x38032,x38033)),f169(x38031,x38032,x38034)),f169(x38031,x38032,f170(x38031,x38032,x38034,x38033)))
% 52.62/52.40 [3832]E(f332(f332(f253(x38321,x38322,x38323,f852(x38322,x38323)),x38324),f241(x38322,x38323)),x38324)
% 52.62/52.40 [3841]E(f230(x38411,x38412,x38413,x38414,f183(x38412)),x38413)
% 52.62/52.40 [4128]P43(x41281,x41282,x41283,x41284,f180(f853(x41281,a839)),x41284)
% 52.62/52.40 [4129]P43(x41291,x41292,x41293,x41294,f180(f853(x41291,a839)),x41294)
% 52.62/52.40 [4436]~E(f332(f313(x44361,x44362),x44363),f332(f304(x44362,x44361),x44364))
% 52.62/52.40 [4437]~E(f332(f313(x44371,x44372),x44373),f332(f304(x44372,x44371),x44374))
% 52.62/52.40 [4438]~E(f332(f313(x44381,x44382),x44383),f332(f304(x44382,x44381),x44384))
% 52.62/52.40 [4439]~E(f332(f313(x44391,x44392),x44393),f332(f304(x44392,x44391),x44394))
% 52.62/52.40 [3177]E(f332(f332(f18(x31771,x31772),x31773),x31774),x31773)
% 52.62/52.40 [3289]E(f332(f332(f196(x32891,x32892),x32893),f332(f227(x32891),x32894)),f332(f227(x32892),f332(x32893,x32894)))
% 52.62/52.40 [3462]E(f151(x34621,x34622,f332(f126(x34621,x34623),x34624)),f332(f126(x34621,x34623),f151(x34621,x34622,x34624)))
% 52.62/52.40 [3495]E(f332(f332(f67(x34951,x34952,x34953),x34954),f180(f853(x34951,a839))),x34954)
% 52.62/52.40 [3517]E(f332(f332(f152(x35171),f332(f332(f140(x35171),x35172),x35173)),f332(a114,x35174)),f332(f332(f152(x35171),x35173),x35174))
% 52.62/52.40 [3555]P33(x35551,f2(a845),f332(f332(f332(f93(x35551),x35552),f332(a27,x35553)),x35554))
% 52.62/52.40 [3580]E(f332(f332(x35801,x35802),f332(f174(x35803,x35804,x35801),x35802)),f332(f174(x35803,x35804,x35801),f332(a114,x35802)))
% 52.62/52.40 [3620]E(f249(x36201,x36202,x36203,f332(f251(x36201,x36202,x36203),x36204)),x36204)
% 52.62/52.40 [3678]E(f332(f332(f148(x36781,f332(f332(f140(x36781),x36782),x36783)),f2(a845)),x36784),f332(f332(f140(x36781),x36784),x36783))
% 52.62/52.40 [3688]E(f332(f332(f47(f853(x36881,a839),f853(x36882,a839)),x36883),f303(x36881,x36882,x36884)),f332(f303(x36881,x36882,x36884),f45(f853(x36881,a839),x36883)))
% 52.62/52.40 [3689]E(f332(f332(f47(f853(x36891,a839),f853(x36892,a839)),x36893),f305(x36892,x36891,x36894)),f332(f305(x36892,x36891,x36894),f45(f853(x36891,a839),x36893)))
% 52.62/52.40 [3788]E(f169(x37881,x37882,f172(x37881,x37882,x37883,x37884)),f332(f332(f104(f853(x37881,a839)),f169(x37881,x37882,x37883)),x37884))
% 52.62/52.40 [3807]E(f332(f132(x38071,x38072,f332(f9(x38072,x38071,x38071),x38073),x38074),f332(f142(x38072),f115(x38072))),x38074)
% 52.62/52.40 [3851]E(f78(x38511,x38512,x38513,x38514,f180(f853(x38511,a839))),x38513)
% 52.62/52.40 [3898]E(f332(f332(f332(f332(f74(x38981,f849(x38982)),f332(f18(f849(x38982),x38981),f183(x38982))),x38983),f183(x38982)),x38984),f183(x38982))
% 52.62/52.40 [4047]E(f319(x40471,x40472,x40473,f332(f332(f10(f854(x40471,x40473),x40472,x40471),x40474),f304(x40471,x40473)),f332(f332(f10(f854(x40471,x40473),x40472,x40473),x40474),f313(x40473,x40471))),x40474)
% 52.62/52.40 [4057]E(f332(f251(x40571,x40572,x40573),f332(f332(f10(f853(x40572,f852(x40571,x40572)),f853(x40572,x40573),x40571),f332(f10(f852(x40571,x40572),x40573,x40572),x40574)),f241(x40571,x40572))),x40574)
% 52.62/52.40 [3365]E(f332(f250(x33651,x33652),f332(f332(f241(x33651,x33652),x33653),x33654)),x33654)
% 52.62/52.40 [3366]E(f332(f240(x33661,x33662),f332(f332(f241(x33661,x33662),x33663),x33664)),x33663)
% 52.62/52.40 [3405]E(f332(f181(f846(x34051)),f332(f332(f143(x34052,x34051),x34053),x34054)),f332(f181(f846(x34052)),x34054))
% 52.62/52.40 [3406]E(f332(f181(f846(x34061)),f332(f332(f148(x34061,x34062),x34063),x34064)),f332(f181(f846(x34061)),x34062))
% 52.62/52.40 [3427]E(f332(f332(f128(x34271),f332(a114,x34272)),f332(f332(f140(x34271),x34273),x34274)),f332(f332(f128(x34271),x34272),x34274))
% 52.62/52.40 [3497]E(f332(f332(f302(x34971),x34972),f332(f332(f302(x34971),x34973),x34974)),f332(f332(f302(x34971),x34973),f332(f332(f302(x34971),x34972),x34974)))
% 52.62/52.40 [3500]E(f332(f332(f143(x35001,x35002),x35003),f116(x35001,x35004)),f116(x35002,f332(f332(f143(x35001,x35002),x35003),x35004)))
% 52.62/52.40 [3515]E(f332(f142(x35151),f332(f332(f143(x35152,x35151),x35153),x35154)),f332(f332(f143(x35152,x35151),x35153),f332(f142(x35152),x35154)))
% 52.62/52.40 [3516]E(f332(f332(f143(x35161,x35162),x35163),f332(f157(x35161),x35164)),f332(f157(x35162),f332(f332(f143(x35161,x35162),x35163),x35164)))
% 52.62/52.40 [3525]E(f332(f332(f159(x35251),f332(a114,x35252)),f332(f332(f140(x35251),x35253),x35254)),f332(f332(f140(x35251),x35253),f332(f332(f159(x35251),x35252),x35254)))
% 52.62/52.40 [3529]E(f332(f158(x35291),f332(f332(f143(x35292,x35291),x35293),x35294)),f332(f303(x35292,x35291,x35293),f332(f158(x35292),x35294)))
% 52.62/52.40 [3579]E(f19(x35791,x35792,x35793,f332(a5,f332(a114,f332(a22,x35794)))),f332(x35793,x35794))
% 52.62/52.40 [3583]E(f332(f332(f125(x35831),f332(f126(x35831,x35832),x35833)),f332(f126(x35831,x35832),x35834)),f332(f126(x35831,x35832),f332(f332(f125(x35831),x35833),x35834)))
% 52.62/52.40 [3610]E(f332(f278(x36101,x36101),f332(f332(f280(x36102,x36101),x36103),x36104)),f332(f332(f280(x36102,x36101),f332(f278(x36102,x36102),x36103)),x36104))
% 52.62/52.40 [3621]E(f332(f332(f281(x36211,x36212,x36213),x36214),f180(f853(f852(x36212,x36213),a839))),f180(f853(f852(x36211,x36213),a839)))
% 52.62/52.40 [3622]E(f332(f332(f159(x36221),f332(f332(f3(a845),x36222),x36223)),f332(f332(f128(x36221),x36223),x36224)),f332(f332(f128(x36221),x36223),f332(f332(f159(x36221),x36222),x36224)))
% 52.62/52.40 [3644]E(f332(f332(f332(f273(x36441),x36442),x36443),x36444),f332(f241(f853(a101,f853(a839,f849(f847(x36441)))),f852(a101,a101)),f332(f50(x36441),x36442)))
% 52.62/52.40 [3668]E(f45(f853(x36681,a839),f332(f303(x36682,f853(x36681,a839),x36683),x36684)),f332(f332(f47(x36682,f853(x36681,a839)),x36684),x36683))
% 52.62/52.40 [3669]E(f46(f853(x36691,a839),f332(f303(x36692,f853(x36691,a839),x36693),x36694)),f332(f332(f48(x36692,f853(x36691,a839)),x36694),x36693))
% 52.62/52.40 [3670]E(f46(f853(x36701,a839),f332(f303(x36702,f853(x36701,a839),x36703),x36704)),f332(f332(f48(x36702,f853(x36701,a839)),x36704),x36703))
% 52.62/52.40 [3671]E(f45(f853(x36711,a839),f332(f303(x36712,f853(x36711,a839),x36713),x36714)),f332(f332(f47(x36712,f853(x36711,a839)),x36714),x36713))
% 52.62/52.40 [3672]E(f332(f181(f846(f852(x36721,x36722))),f332(f332(f167(x36721,x36722),x36723),x36724)),f332(f332(f236(a845),f332(f181(f846(x36721)),x36723)),f332(f181(f846(x36722)),x36724)))
% 52.62/52.40 [3674]E(f332(f305(x36741,x36742,x36743),f332(f81(f853(x36742,a839)),x36744)),f332(f81(f853(x36741,a839)),f332(f305(x36741,x36742,x36743),x36744)))
% 52.62/52.40 [3706]E(f332(f172(x37061,x37062,x37063,f180(f853(x37061,a839))),x37064),f183(x37062))
% 52.62/52.40 [3725]E(f332(f305(x37251,x37252,x37253),f332(f256(x37252),x37254)),f332(f256(x37251),f332(f332(f10(x37252,a839,x37251),x37254),x37253)))
% 52.62/52.40 [3742]E(f332(f332(f152(x37421),f332(f332(f125(x37421),x37422),f332(f332(f140(x37421),x37423),x37424))),f332(f181(f846(x37421)),x37422)),x37423)
% 52.62/52.40 [3747]E(f332(f172(x37471,x37472,f332(f18(f849(x37472),x37471),f183(x37472)),x37473),x37474),f183(x37472))
% 52.62/52.40 [3769]E(f332(f303(x37691,x37692,x37693),f332(f305(x37691,x37692,x37693),x37694)),f332(f332(f104(f853(x37692,a839)),x37694),f332(f303(x37691,x37692,x37693),f239(f853(x37691,a839)))))
% 52.62/52.40 [3787]P1(f332(f332(f334(x37871),f332(x37872,x37873)),f332(f303(x37874,x37871,x37872),f239(f853(x37874,a839)))))
% 52.62/52.40 [3795]E(f21(x37951,x37952,x37953,f332(a5,f332(a114,f332(a22,x37954)))),f332(f332(x37953,x37954),f21(x37951,x37952,x37953,x37954)))
% 52.62/52.40 [3810]E(f144(x38101,x38102,f332(f332(f140(x38101),x38103),x38104)),f332(f332(f82(a845),f332(f332(f82(a845),f332(x38102,x38103)),f144(x38101,x38102,x38104))),f332(a114,f2(a845))))
% 52.62/52.40 [3823]E(f175(f846(x38231),f332(f332(f140(x38231),x38232),x38233),f332(f332(f9(a845,f846(x38231),f846(x38231)),f128(x38231)),x38233),x38234),f332(f332(f128(x38231),x38234),f332(f332(f140(x38231),x38232),x38233)))
% 52.62/52.40 [3824]P31(x38241,f852(x38242,x38241),f336(x38243,x38244,x38242,x38241),f332(f332(f47(x38242,f853(x38241,a839)),x38244),x38243))
% 52.62/52.40 [3833]E(f332(f332(f3(f853(x38331,a839)),f332(f332(f3(f853(x38331,a839)),x38332),x38333)),f332(f332(f302(x38331),x38334),f180(f853(x38331,a839)))),f332(f332(f3(f853(x38331,a839)),x38332),f332(f332(f302(x38331),x38334),x38333)))
% 52.62/52.40 [3844]E(f332(f332(f173(f853(x38441,x38442),f853(x38441,x38442)),x38443),f75(x38442,x38442,x38441,x38444)),f75(x38442,x38442,x38441,f332(f332(f173(x38442,x38442),x38443),x38444)))
% 52.62/52.40 [3921]E(f332(f332(f332(f173(f846(x39211),f846(x39211)),x39212),f141(x39211)),f332(f332(f332(f173(f846(x39211),f846(x39211)),x39213),f141(x39211)),x39214)),f332(f332(f332(f173(f846(x39211),f846(x39211)),f332(f332(f82(a845),x39212),x39213)),f141(x39211)),x39214))
% 52.62/52.40 [3970]E(f332(f332(f103(f853(f854(x39701,x39702),a839)),f332(f303(x39701,f854(x39701,x39702),f304(x39701,x39702)),x39703)),f332(f303(x39702,f854(x39701,x39702),f313(x39702,x39701)),x39704)),f314(x39701,x39702,x39703,x39704))
% 52.62/52.40 [4011]P1(f332(f332(f232(f853(x40111,a839)),f332(f158(x40111),f332(f332(f148(x40111,x40112),x40113),x40114))),f332(f332(f302(x40111),x40114),f332(f158(x40111),x40112))))
% 52.62/52.40 [4045]E(f332(f332(f47(f853(x40451,a839),f853(f852(x40451,x40452),a839)),x40453),f332(f332(f9(f853(x40451,a839),f853(x40451,f853(x40452,a839)),f853(f852(x40451,x40452),a839)),f248(x40451,x40452)),x40454)),f332(f332(f248(x40451,x40452),f45(f853(x40451,a839),x40453)),x40454))
% 52.62/52.40 [4082]E(f204(x40821,x40822,x40823,f332(f75(x40822,f853(a101,f853(a101,f853(f852(a101,a101),f853(a101,f847(x40822))))),x40821,f203(x40822)),x40824)),f205(x40821,x40822,x40824,x40823))
% 52.62/52.40 [4098]E(f200(x40981,x40982,x40983,f332(f75(x40982,f853(a101,f853(a101,f853(f852(a101,a101),f853(a101,f847(f849(x40982)))))),x40981,f199(x40982)),x40984)),f201(x40981,x40982,x40984,x40983))
% 52.62/52.40 [4102]P1(f332(f69(x41021,x41022,x41023,x41024,f180(f853(x41021,a839))),x41024))
% 52.62/52.40 [4103]P1(f332(f69(x41031,x41032,x41033,x41034,f180(f853(x41031,a839))),x41034))
% 52.62/52.40 [4150]E(f332(f332(f47(x41501,f853(x41502,a839)),x41503),f332(f332(f9(x41501,f853(x41502,a839),f853(x41502,a839)),f332(f332(f10(x41502,f853(f853(x41502,a839),f853(x41502,a839)),x41501),f302(x41502)),x41504)),f180(f853(x41502,a839)))),f332(f303(x41501,x41502,x41504),x41503))
% 52.62/52.40 [4156]P1(f332(f332(f232(f853(x41561,a839)),f332(f259(x41562,x41561),f332(f332(f104(f853(f852(x41562,x41561),a839)),x41563),x41564))),f332(f332(f104(f853(x41561,a839)),f332(f259(x41562,x41561),x41563)),f332(f259(x41562,x41561),x41564))))
% 52.62/52.40 [4157]P1(f332(f332(f232(f853(x41571,a839)),f332(f261(x41571,x41572),f332(f332(f104(f853(f852(x41571,x41572),a839)),x41573),x41574))),f332(f332(f104(f853(x41571,a839)),f332(f261(x41571,x41572),x41573)),f332(f261(x41571,x41572),x41574))))
% 52.62/52.40 [4216]P1(f332(f332(f232(f853(f852(x42161,x42162),a839)),f332(f303(x42162,f852(x42161,x42162),f336(x42163,x42164,x42161,x42162)),f332(f332(f47(x42161,f853(x42162,a839)),x42164),x42163))),f332(f332(f248(x42161,x42162),x42164),x42163)))
% 52.62/52.40 [4217]E(f271(x42171,x42172,x42173,f332(f75(x42172,f853(a101,f853(a101,f853(f852(a101,a101),f852(f853(a101,f853(a839,f849(f847(x42172)))),f852(a101,a101))))),x42171,f273(x42172)),x42174)),f274(x42171,x42172,x42174,x42173))
% 52.62/52.40 [4255]E(f87(f852(x42551,x42552),f332(f251(x42551,x42552,a839),f332(f332(f9(x42551,f853(x42552,a839),f853(x42552,a839)),f332(f332(f10(f853(a839,a839),f853(f853(x42552,a839),f853(x42552,a839)),x42551),f10(a839,a839,x42552)),f332(f332(f10(a839,f853(a839,a839),x42551),a330),f332(a329,x42553)))),f332(a329,x42554)))),f332(f332(f241(x42551,x42552),x42553),x42554))
% 52.62/52.40 [4256]E(f92(f852(x42561,x42562),f332(f251(x42561,x42562,a839),f332(f332(f9(x42561,f853(x42562,a839),f853(x42562,a839)),f332(f332(f10(f853(a839,a839),f853(f853(x42562,a839),f853(x42562,a839)),x42561),f10(a839,a839,x42562)),f332(f332(f10(a839,f853(a839,a839),x42561),a330),f332(a329,x42563)))),f332(a329,x42564)))),f332(f332(f241(x42561,x42562),x42563),x42564))
% 52.62/52.40 [4326]E(f332(f332(f251(f846(x43261),f846(x43261),f852(f846(x43261),f846(x43261))),f332(f332(f20(f846(x43261),f853(f846(x43261),f852(f846(x43261),f846(x43261))),f853(f846(x43261),f852(f846(x43261),f846(x43261)))),f332(f332(f10(f853(f846(x43261),f853(f852(f846(x43261),f846(x43261)),f852(f846(x43261),f846(x43261)))),f853(f853(f846(x43261),f852(f846(x43261),f846(x43261))),f853(f846(x43261),f852(f846(x43261),f846(x43261)))),f846(x43261)),f20(f846(x43261),f852(f846(x43261),f846(x43261)),f852(f846(x43261),f846(x43261)))),f332(f332(f10(f853(f846(x43261),f852(f846(x43261),f846(x43261))),f853(f846(x43261),f853(f852(f846(x43261),f846(x43261)),f852(f846(x43261),f846(x43261)))),f846(x43261)),f332(f10(f852(f846(x43261),f846(x43261)),f853(f852(f846(x43261),f846(x43261)),f852(f846(x43261),f846(x43261))),f846(x43261)),f332(f98(f852(f846(x43261),f846(x43261))),f332(x43262,x43263)))),f332(f332(f10(f846(x43261),f853(f846(x43261),f852(f846(x43261),f846(x43261))),f846(x43261)),f241(f846(x43261),f846(x43261))),f332(f140(x43261),x43263))))),f332(f332(f9(f846(x43261),f853(f846(x43261),f846(x43261)),f853(f846(x43261),f852(f846(x43261),f846(x43261)))),f332(f332(f10(f853(f846(x43261),f852(f846(x43261),f846(x43261))),f853(f853(f846(x43261),f846(x43261)),f853(f846(x43261),f852(f846(x43261),f846(x43261)))),f846(x43261)),f10(f846(x43261),f852(f846(x43261),f846(x43261)),f846(x43261))),f241(f846(x43261),f846(x43261)))),f332(f140(x43261),x43263)))),f155(x43261,x43262,x43264)),f155(x43261,x43262,f332(f332(f140(x43261),x43263),x43264)))
% 52.62/52.40 [4332]E(f332(f132(f853(x43321,f849(x43322)),f852(x43321,x43322),f332(f9(f852(x43321,x43322),f853(x43321,f849(x43322)),f853(x43321,f849(x43322))),f332(f251(x43321,x43322,f853(f853(x43321,f849(x43322)),f853(x43321,f849(x43322)))),f332(f332(f9(x43321,f853(x43322,f849(x43322)),f853(x43322,f853(f853(x43321,f849(x43322)),f853(x43321,f849(x43322))))),f332(f332(f10(f853(f849(x43322),f853(f853(x43321,f849(x43322)),f853(x43321,f849(x43322)))),f853(f853(x43322,f849(x43322)),f853(x43322,f853(f853(x43321,f849(x43322)),f853(x43321,f849(x43322))))),x43321),f10(f849(x43322),f853(f853(x43321,f849(x43322)),f853(x43321,f849(x43322))),x43322)),f332(f332(f10(f853(f853(x43321,f849(x43322)),f853(f849(x43322),f853(x43321,f849(x43322)))),f853(f849(x43322),f853(f853(x43321,f849(x43322)),f853(x43321,f849(x43322)))),x43321),f9(f853(x43321,f849(x43322)),f849(x43322),f853(x43321,f849(x43322)))),f332(f9(f853(x43321,f849(x43322)),x43321,f853(f849(x43322),f853(x43321,f849(x43322)))),f74(x43321,f849(x43322)))))),f227(x43322)))),x43323),f332(f142(f852(x43321,x43322)),x43324)),f170(x43321,x43322,x43323,f166(x43321,x43322,x43324)))
% 52.62/52.40 [3445]E(f332(f181(f844(x34451)),f332(f332(f332(f93(x34451),x34452),x34453),x34454)),f2(a845))
% 52.62/52.40 [3558]E(f332(f332(f159(x35581),x35582),f332(f332(f159(x35581),x35583),x35584)),f332(f332(f159(x35581),f332(f332(f236(a845),x35582),x35583)),x35584))
% 52.62/52.40 [3559]E(f332(f332(f128(x35591),x35592),f332(f332(f128(x35591),x35593),x35594)),f332(f332(f128(x35591),f332(f332(f82(a845),x35592),x35593)),x35594))
% 52.62/52.40 [3571]E(f332(f332(f125(x35711),f332(f332(f140(x35711),x35712),x35713)),x35714),f332(f332(f140(x35711),x35712),f332(f332(f125(x35711),x35713),x35714)))
% 52.62/52.40 [3572]E(f332(f332(f125(x35721),f332(f332(f125(x35721),x35722),x35723)),x35724),f332(f332(f125(x35721),x35722),f332(f332(f125(x35721),x35723),x35724)))
% 52.62/52.40 [3654]E(f332(f332(f152(x36541),f332(f332(f140(x36541),x36542),x36543)),x36544),f175(x36541,x36542,f332(f152(x36541),x36543),x36544))
% 52.62/52.40 [3663]E(f332(f332(f173(x36631,x36631),x36632),f332(f332(f173(x36631,x36631),x36633),x36634)),f332(f332(f173(x36631,x36631),f332(f332(f83(a845),x36633),x36632)),x36634))
% 52.62/52.40 [3691]E(f332(f332(f103(f853(x36911,a839)),x36912),f332(f332(f302(x36911),x36913),x36914)),f332(f332(f302(x36911),x36913),f332(f332(f103(f853(x36911,a839)),x36912),x36914)))
% 52.62/52.40 [3709]E(f332(f332(f332(f173(x37091,x37091),x37092),x37093),f332(x37093,x37094)),f332(x37093,f332(f332(f332(f173(x37091,x37091),x37092),x37093),x37094)))
% 52.62/52.40 [3716]E(f332(f332(f281(x37161,x37162,x37163),f180(f853(f852(x37161,x37162),a839))),x37164),f180(f853(f852(x37161,x37163),a839)))
% 52.62/52.40 [3731]E(f332(f332(f103(f853(x37311,a839)),f332(f332(f302(x37311),x37312),x37313)),x37314),f332(f332(f302(x37311),x37312),f332(f332(f103(f853(x37311,a839)),x37313),x37314)))
% 52.62/52.40 [3749]E(f332(f43(f852(x37491,x37492)),f332(f332(f248(x37491,x37492),x37493),f332(f18(f853(x37492,a839),x37491),x37494))),f332(f332(f83(a845),f332(f43(x37491),x37493)),f332(f43(x37492),x37494)))
% 52.62/52.40 [3757]E(f332(f332(f104(f853(x37571,a839)),f332(f332(f302(x37571),x37572),x37573)),f332(f332(f302(x37571),x37572),x37574)),f332(f332(f302(x37571),x37572),f332(f332(f104(f853(x37571,a839)),x37573),x37574)))
% 52.62/52.40 [3767]E(f170(x37671,x37672,f166(x37671,x37672,x37673),f166(x37671,x37672,x37674)),f166(x37671,x37672,f332(f332(f125(f852(x37671,x37672)),x37674),x37673)))
% 52.62/52.40 [3773]E(f332(f332(f103(f853(x37731,a839)),x37732),f332(f332(f103(f853(x37731,a839)),x37733),x37734)),f332(f332(f103(f853(x37731,a839)),x37733),f332(f332(f103(f853(x37731,a839)),x37732),x37734)))
% 52.62/52.40 [3774]E(f332(f332(f104(f853(x37741,a839)),x37742),f332(f332(f104(f853(x37741,a839)),x37743),x37744)),f332(f332(f104(f853(x37741,a839)),x37743),f332(f332(f104(f853(x37741,a839)),x37742),x37744)))
% 52.62/52.40 [3783]E(f67(x37831,x37832,f332(f332(f10(x37832,f853(x37832,x37832),x37831),x37833),x37834)),f332(f68(x37832,x37831,x37833),x37834))
% 52.62/52.40 [3792]E(f164(x37921,f332(f332(f143(f846(x37922),f846(x37921)),f332(f143(x37922,x37921),x37923)),x37924)),f332(f332(f143(f846(x37922),f846(x37921)),f332(f143(x37922,x37921),x37923)),f164(x37922,x37924)))
% 52.62/52.40 [3809]E(f172(x38091,x38092,x38093,f332(f81(f853(x38091,a839)),f332(f332(f302(x38091),x38094),f180(f853(x38091,a839))))),f332(f332(f332(f74(x38091,f849(x38092)),x38093),x38094),f183(x38092)))
% 52.62/52.40 [3865]E(f332(f75(x38651,x38651,x38651,f332(f332(f173(x38651,x38651),x38652),x38653)),f332(f332(f173(x38651,x38651),x38654),x38653)),f332(f332(f173(x38651,x38651),f332(f332(f82(a845),x38652),x38654)),x38653))
% 52.62/52.40 [3880]E(f332(f332(f332(f74(x38801,f849(x38802)),f166(x38801,x38802,x38803)),f332(f240(x38801,x38802),x38804)),f332(f227(x38802),f332(f250(x38801,x38802),x38804))),f166(x38801,x38802,f332(f332(f140(f852(x38801,x38802)),x38804),x38803)))
% 52.62/52.40 [3887]E(f170(x38871,x38872,x38873,f166(x38871,x38872,f332(f142(f852(x38871,x38872)),f332(f332(f167(x38871,x38872),x38874),f115(x38872))))),x38873)
% 52.62/52.40 [3890]E(f332(f332(f104(f853(x38901,a839)),f332(f332(f3(f853(x38901,a839)),x38902),x38903)),f332(f332(f3(f853(x38901,a839)),x38902),x38904)),f332(f332(f3(f853(x38901,a839)),x38902),f332(f332(f103(f853(x38901,a839)),x38903),x38904)))
% 52.62/52.40 [3891]E(f332(f332(f103(f853(x38911,a839)),f332(f332(f3(f853(x38911,a839)),x38912),x38913)),f332(f332(f3(f853(x38911,a839)),x38912),x38914)),f332(f332(f3(f853(x38911,a839)),x38912),f332(f332(f104(f853(x38911,a839)),x38913),x38914)))
% 52.62/52.40 [3892]E(f332(f332(f104(f853(x38921,a839)),f332(f332(f103(f853(x38921,a839)),x38922),x38923)),f332(f332(f103(f853(x38921,a839)),x38922),x38924)),f332(f332(f103(f853(x38921,a839)),x38922),f332(f332(f104(f853(x38921,a839)),x38923),x38924)))
% 52.62/52.40 [3893]E(f332(f332(f3(f853(x38931,a839)),f332(f332(f104(f853(x38931,a839)),x38932),x38933)),f332(f332(f104(f853(x38931,a839)),x38932),x38934)),f332(f332(f104(f853(x38931,a839)),x38932),f332(f332(f3(f853(x38931,a839)),x38933),x38934)))
% 52.62/52.40 [3894]E(f332(f332(f103(f853(x38941,a839)),f332(f332(f104(f853(x38941,a839)),x38942),x38943)),f332(f332(f104(f853(x38941,a839)),x38942),x38944)),f332(f332(f104(f853(x38941,a839)),x38942),f332(f332(f103(f853(x38941,a839)),x38943),x38944)))
% 52.62/52.40 [3900]E(f332(f43(f852(x39001,x39002)),f332(f332(f248(x39001,x39002),f332(f332(f302(x39001),x39003),f180(f853(x39001,a839)))),f332(f18(f853(x39002,a839),x39001),x39004))),f332(f43(x39002),x39004))
% 52.62/52.40 [3937]E(f332(f332(f48(x39371,f853(x39372,a839)),x39373),f332(f332(f10(f853(x39372,a839),f853(x39372,a839),x39371),f81(f853(x39372,a839))),x39374)),f332(f81(f853(x39372,a839)),f332(f332(f47(x39371,f853(x39372,a839)),x39373),x39374)))
% 52.62/52.40 [3938]E(f332(f332(f47(x39381,f853(x39382,a839)),x39383),f332(f332(f10(f853(x39382,a839),f853(x39382,a839),x39381),f81(f853(x39382,a839))),x39384)),f332(f81(f853(x39382,a839)),f332(f332(f48(x39381,f853(x39382,a839)),x39383),x39384)))
% 52.62/52.40 [3954]E(f332(f332(f281(x39541,x39541,x39541),f332(f332(f173(f852(x39541,x39541),a839),x39542),x39543)),f332(f332(f173(f852(x39541,x39541),a839),x39544),x39543)),f332(f332(f173(f852(x39541,x39541),a839),f332(f332(f82(a845),x39542),x39544)),x39543))
% 52.62/52.40 [3986]E(f332(f332(f48(x39861,f853(f853(x39862,a839),a839)),x39863),f332(f332(f10(f853(x39862,a839),f853(f853(x39862,a839),a839),x39861),f301(x39862)),x39864)),f332(f301(x39862),f332(f332(f48(x39861,f853(x39862,a839)),x39863),x39864)))
% 52.62/52.40 [4014]E(f332(f332(f47(f853(x40141,a839),f853(x40142,a839)),x40143),f332(f332(f9(f853(x40141,a839),f853(x40141,f853(x40142,a839)),f853(x40142,a839)),f47(x40141,f853(x40142,a839))),x40144)),f332(f332(f47(x40141,f853(x40142,a839)),f45(f853(x40141,a839),x40143)),x40144))
% 52.62/52.40 [4015]E(f332(f332(f48(f853(x40151,a839),f853(x40152,a839)),x40153),f332(f332(f9(f853(x40151,a839),f853(x40151,f853(x40152,a839)),f853(x40152,a839)),f48(x40151,f853(x40152,a839))),x40154)),f332(f332(f48(x40151,f853(x40152,a839)),f45(f853(x40151,a839),x40153)),x40154))
% 52.62/52.40 [4016]E(f332(f332(f47(f853(x40161,a839),f853(x40162,a839)),x40163),f332(f332(f9(f853(x40161,a839),f853(x40161,f853(x40162,a839)),f853(x40162,a839)),f47(x40161,f853(x40162,a839))),x40164)),f332(f332(f47(x40161,f853(x40162,a839)),f45(f853(x40161,a839),x40163)),x40164))
% 52.62/52.40 [4017]E(f332(f332(f48(f853(x40171,a839),f853(x40172,a839)),x40173),f332(f332(f9(f853(x40171,a839),f853(x40171,f853(x40172,a839)),f853(x40172,a839)),f48(x40171,f853(x40172,a839))),x40174)),f332(f332(f48(x40171,f853(x40172,a839)),f45(f853(x40171,a839),x40173)),x40174))
% 52.62/52.40 [4022]E(f332(f332(f143(x40221,x40222),x40223),f332(f132(f846(x40221),f846(x40221),f125(x40221),f115(x40221)),x40224)),f332(f132(f846(x40222),f846(x40222),f125(x40222),f115(x40222)),f332(f332(f143(f846(x40221),f846(x40222)),f332(f143(x40221,x40222),x40223)),x40224)))
% 52.62/52.40 [4024]E(f175(f846(x40241),f115(x40241),f332(f332(f10(f846(x40241),f846(x40241),a845),f332(f140(x40241),x40242)),f332(f332(f9(a845,f846(x40241),f846(x40241)),f159(x40241)),x40243)),x40244),f332(f332(f159(x40241),x40244),f332(f332(f140(x40241),x40242),x40243)))
% 52.62/52.40 [4067]P1(f332(f332(f232(f853(x40671,a839)),f332(f303(x40672,x40671,x40673),f332(f305(x40672,x40671,x40673),x40674))),x40674))
% 52.62/52.40 [4069]E(f332(f303(f852(x40691,x40692),f852(x40692,x40691),f332(f251(x40691,x40692,f852(x40692,x40691)),f332(f9(x40692,x40691,f852(x40692,x40691)),f241(x40692,x40691)))),f332(f332(f248(x40691,x40692),x40693),f332(f18(f853(x40692,a839),x40691),x40694))),f332(f332(f248(x40692,x40691),x40694),f332(f18(f853(x40691,a839),x40692),x40693)))
% 52.62/52.40 [4078]E(f332(f332(f47(x40781,f853(x40782,a839)),x40783),f332(f332(f10(f853(x40781,a839),f853(x40782,a839),x40781),f277(x40781,x40782,x40784)),f332(f332(f9(x40781,f853(x40781,a839),f853(x40781,a839)),f302(x40781)),f180(f853(x40781,a839))))),f332(f277(x40781,x40782,x40784),x40783))
% 52.62/52.40 [4079]E(f332(f332(f47(x40791,f853(x40792,a839)),x40793),f332(f332(f10(f853(x40791,a839),f853(x40792,a839),x40791),f305(x40792,x40791,x40794)),f332(f332(f9(x40791,f853(x40791,a839),f853(x40791,a839)),f302(x40791)),f180(f853(x40791,a839))))),f332(f305(x40792,x40791,x40794),x40793))
% 52.62/52.40 [4170]E(f332(f332(f104(f853(x41701,a839)),f332(f332(f104(f853(x41701,a839)),f332(f332(f103(f853(x41701,a839)),x41702),x41703)),f332(f332(f103(f853(x41701,a839)),x41703),x41704))),f332(f332(f103(f853(x41701,a839)),x41704),x41702)),f332(f332(f103(f853(x41701,a839)),f332(f332(f103(f853(x41701,a839)),f332(f332(f104(f853(x41701,a839)),x41702),x41703)),f332(f332(f104(f853(x41701,a839)),x41703),x41704))),f332(f332(f104(f853(x41701,a839)),x41704),x41702)))
% 52.62/52.40 [4229]E(f332(f132(f846(x42291),f846(x42291),f125(x42291),f115(x42291)),f332(f332(f143(x42292,f846(x42291)),f332(f332(f9(x42292,f846(x42291),f846(x42291)),f332(f332(f10(x42291,f853(f846(x42291),f846(x42291)),x42292),f140(x42291)),x42293)),f115(x42291))),x42294)),f332(f332(f143(x42292,x42291),x42293),x42294))
% 52.62/52.40 [4239]E(f332(f332(f88(a1,x42391),f332(f106(a1),f332(f332(f82(a1),x42392),a99))),f332(f332(f20(a1,x42391,x42391),f332(f332(f9(a1,x42391,f853(x42391,x42391)),f332(f332(f10(a839,f853(x42391,f853(x42391,x42391)),a1),f98(x42391)),a186)),x42393)),f332(f332(f10(a845,x42391,a1),x42394),a107))),f175(x42391,x42393,x42394,f332(f106(a845),x42392)))
% 52.62/52.40 [4481]~P1(f332(f332(f180(f853(x44811,f853(x44812,a839))),x44813),x44814))
% 52.62/52.40 [3719]E(f332(f332(f152(x37191),f332(f332(f125(x37191),x37192),x37193)),f332(f332(f82(a845),f332(f181(f846(x37191)),x37192)),x37194)),f332(f332(f152(x37191),x37193),x37194))
% 52.62/52.40 [3724]E(f332(f332(f128(x37241),x37242),f332(f332(f159(x37241),f332(f332(f82(a845),x37243),x37242)),x37244)),f332(f332(f159(x37241),x37243),f332(f332(f128(x37241),x37242),x37244)))
% 52.62/52.40 [3821]E(f332(f332(f103(f853(x38211,a839)),f332(f259(x38212,x38211),x38213)),f332(f259(x38212,x38211),x38214)),f332(f259(x38212,x38211),f332(f332(f103(f853(f852(x38212,x38211),a839)),x38213),x38214)))
% 52.62/52.40 [3822]E(f332(f332(f103(f853(x38221,a839)),f332(f261(x38221,x38222),x38223)),f332(f261(x38221,x38222),x38224)),f332(f261(x38221,x38222),f332(f332(f103(f853(f852(x38221,x38222),a839)),x38223),x38224)))
% 52.62/52.40 [3827]E(f332(f332(f3(f853(x38271,a839)),f332(f332(f104(f853(x38271,a839)),x38272),x38273)),x38274),f332(f332(f104(f853(x38271,a839)),x38272),f332(f332(f3(f853(x38271,a839)),x38273),x38274)))
% 52.62/52.40 [3828]E(f332(f332(f103(f853(x38281,a839)),f332(f332(f103(f853(x38281,a839)),x38282),x38283)),x38284),f332(f332(f103(f853(x38281,a839)),x38282),f332(f332(f103(f853(x38281,a839)),x38283),x38284)))
% 52.62/52.40 [3829]E(f332(f332(f104(f853(x38291,a839)),f332(f332(f104(f853(x38291,a839)),x38292),x38293)),x38294),f332(f332(f104(f853(x38291,a839)),x38292),f332(f332(f104(f853(x38291,a839)),x38293),x38294)))
% 52.62/52.40 [3867]E(f332(f332(f103(f853(f852(x38671,x38672),a839)),f332(f278(x38672,x38671),x38673)),f332(f278(x38672,x38671),x38674)),f332(f278(x38672,x38671),f332(f332(f103(f853(f852(x38672,x38671),a839)),x38673),x38674)))
% 52.62/52.40 [3868]E(f332(f332(f104(f853(f852(x38681,x38682),a839)),f332(f278(x38682,x38681),x38683)),f332(f278(x38682,x38681),x38684)),f332(f278(x38682,x38681),f332(f332(f104(f853(f852(x38682,x38681),a839)),x38683),x38684)))
% 52.62/52.40 [3903]E(f170(x39031,x39032,x39033,f166(x39031,x39032,f332(f142(f852(x39031,x39032)),f332(f332(f167(x39031,x39032),f115(x39031)),x39034)))),x39033)
% 52.62/52.40 [3941]E(f332(f332(f103(f853(x39411,a839)),f332(f332(f3(f853(x39411,a839)),x39412),x39413)),f332(f332(f3(f853(x39411,a839)),x39414),x39413)),f332(f332(f3(f853(x39411,a839)),f332(f332(f103(f853(x39411,a839)),x39412),x39414)),x39413))
% 52.62/52.40 [3942]E(f332(f332(f104(f853(x39421,a839)),f332(f332(f103(f853(x39421,a839)),x39422),x39423)),f332(f332(f103(f853(x39421,a839)),x39424),x39423)),f332(f332(f103(f853(x39421,a839)),f332(f332(f104(f853(x39421,a839)),x39422),x39424)),x39423))
% 52.62/52.40 [3943]E(f332(f332(f3(f853(x39431,a839)),f332(f332(f104(f853(x39431,a839)),x39432),x39433)),f332(f332(f104(f853(x39431,a839)),x39434),x39433)),f332(f332(f104(f853(x39431,a839)),f332(f332(f3(f853(x39431,a839)),x39432),x39434)),x39433))
% 52.62/52.40 [3944]E(f332(f332(f103(f853(x39441,a839)),f332(f332(f104(f853(x39441,a839)),x39442),x39443)),f332(f332(f104(f853(x39441,a839)),x39444),x39443)),f332(f332(f104(f853(x39441,a839)),f332(f332(f103(f853(x39441,a839)),x39442),x39444)),x39443))
% 52.62/52.40 [3945]E(f332(f332(f3(f853(x39451,a839)),f332(f332(f104(f853(x39451,a839)),x39452),x39453)),f332(f332(f104(f853(x39451,a839)),x39454),x39453)),f332(f332(f3(f853(x39451,a839)),f332(f332(f104(f853(x39451,a839)),x39452),x39453)),x39454))
% 52.62/52.40 [3957]E(f332(f332(f3(f853(x39571,a839)),f332(f332(f3(f853(x39571,a839)),x39572),f332(f332(f302(x39571),x39573),f180(f853(x39571,a839))))),x39574),f332(f332(f3(f853(x39571,a839)),x39572),f332(f332(f302(x39571),x39573),x39574)))
% 52.62/52.40 [4013]E(f332(f332(f103(f853(x40131,a839)),f332(f332(f302(x40131),x40132),f332(f332(f302(x40131),x40133),f180(f853(x40131,a839))))),f332(f276(x40131),x40134)),f332(f276(x40131),f332(f332(f302(f852(x40131,x40131)),f332(f332(f241(x40131,x40131),x40132),x40133)),x40134)))
% 52.62/52.40 [4040]E(f332(f332(f47(a845,f853(x40401,a839)),f332(f293(a845),x40402)),f332(f332(f10(a845,f853(x40401,a839),a845),x40403),f332(f332(f9(a845,a845,a845),f82(a845)),x40404))),f332(f332(f47(a845,f853(x40401,a839)),f295(a845,x40404,f332(f332(f82(a845),x40402),x40404))),x40403))
% 52.62/52.40 [4041]E(f161(x40411,f332(f277(x40411,x40411,x40412),f332(f332(f302(x40411),x40413),f180(f853(x40411,a839)))),f332(f277(f846(x40411),f846(x40411),f147(x40411,x40412)),f332(f332(f302(f846(x40411)),x40414),f180(f853(f846(x40411),a839))))),f332(f277(f846(x40411),f846(x40411),f147(x40411,x40412)),f332(f332(f302(f846(x40411)),f332(f332(f140(x40411),x40413),x40414)),f180(f853(f846(x40411),a839)))))
% 52.62/52.40 [4104]E(f166(x41041,x41042,f332(f332(f143(x41041,f852(x41041,x41042)),f332(f332(f20(x41041,x41042,f852(x41041,x41042)),f241(x41041,x41042)),x41043)),x41044)),f172(x41041,x41042,f332(f75(x41042,f849(x41042),x41041,f227(x41042)),x41043),f332(f158(x41041),x41044)))
% 52.62/52.40 [4107]E(f332(f256(x41071),f332(f332(f9(x41071,f853(x41072,a839),a839),f332(f332(f10(x41072,f853(f853(x41072,a839),a839),x41071),f334(x41072)),x41073)),x41074)),f332(f305(x41071,x41072,x41073),x41074))
% 52.62/52.40 [4201]E(f332(f256(x42011),f332(f332(f9(x42011,f853(f852(x42012,x42011),a839),a839),f332(f332(f10(f852(x42012,x42011),f853(f853(f852(x42012,x42011),a839),a839),x42011),f334(f852(x42012,x42011))),f332(f241(x42012,x42011),x42013))),x42014)),f332(f277(x42012,x42011,x42014),f332(f332(f302(x42012),x42013),f180(f853(x42012,a839)))))
% 52.62/52.40 [4215]E(f332(f332(f143(f852(x42151,a845),x42151),f240(x42151,a845)),f332(f126(f852(x42151,a845),f332(f332(f10(a845,a839,f852(x42151,a845)),x42152),f332(f332(f10(a845,a845,f852(x42151,a845)),a114),f250(x42151,a845)))),f332(f332(f167(x42151,a845),x42153),x42154))),f332(f332(f143(f852(x42151,a845),x42151),f240(x42151,a845)),f332(f126(f852(x42151,a845),f332(f332(f10(a845,a839,f852(x42151,a845)),x42152),f250(x42151,a845))),f332(f332(f167(x42151,a845),x42153),f332(f332(f143(a845,a845),a114),x42154)))))
% 52.62/52.40 [4222]P1(f332(f332(f232(f853(f853(x42221,a839),a839)),f332(f332(f47(x42222,f853(f853(x42221,a839),a839)),x42223),f332(f332(f10(f853(x42221,a839),f853(f853(x42221,a839),a839),x42222),f301(x42221)),x42224))),f332(f301(x42221),f332(f332(f47(x42222,f853(x42221,a839)),x42223),x42224))))
% 52.62/52.40 [4262]E(f332(f332(f88(a1,x42621),f332(f106(a1),f332(f332(f82(a1),x42622),a99))),f332(f332(f20(a1,x42621,x42621),f332(f332(f9(a1,x42621,f853(x42621,x42621)),f332(f332(f10(a839,f853(x42621,f853(x42621,x42621)),a1),f98(x42621)),a186)),x42623)),f332(f332(f20(a1,x42621,x42621),f332(f332(f10(a845,f853(x42621,x42621),a1),x42624),a107)),f332(f332(f10(a845,x42621,a1),f174(x42621,x42623,x42624)),a107)))),f332(f174(x42621,x42623,x42624),f332(f106(a845),x42622)))
% 52.62/52.40 [4265]E(f332(f332(f143(x42651,x42652),f332(f75(f849(x42652),x42652,x42651,f231(x42652)),x42653)),f332(f126(x42651,f332(f332(f10(a839,a839,x42651),a328),f332(f332(f9(x42651,f849(x42652),a839),f332(f332(f10(f849(x42652),f853(f849(x42652),a839),x42651),a329),x42653)),f183(x42652)))),x42654)),f153(x42651,x42652,x42653,x42654))
% 52.62/52.40 [4286]E(f332(f256(f852(x42861,x42862)),f332(f251(x42861,x42862,a839),f332(f332(f9(x42861,f853(x42862,a839),f853(x42862,a839)),f332(f332(f10(f853(a839,a839),f853(f853(x42862,a839),f853(x42862,a839)),x42861),f10(a839,a839,x42862)),f332(f332(f10(a839,f853(a839,a839),x42861),a330),f332(f332(f9(x42861,f853(x42861,a839),a839),f334(x42861)),x42863)))),f332(f332(f9(x42862,f853(x42862,a839),a839),f334(x42862)),x42864)))),f223(x42861,x42862,x42863,x42864))
% 52.62/52.40 [4319]E(f332(f332(f47(x43191,f853(f852(x43191,x43192),a839)),x43193),f332(f332(f20(x43191,f853(x43192,f853(f852(x43191,x43192),a839)),f853(f852(x43191,x43192),a839)),f332(f332(f10(f853(x43192,a839),f853(f853(x43192,f853(f852(x43191,x43192),a839)),f853(f852(x43191,x43192),a839)),x43191),f47(x43192,f853(f852(x43191,x43192),a839))),x43194)),f332(f332(f9(x43191,f853(f852(x43191,x43192),a839),f853(x43192,f853(f852(x43191,x43192),a839))),f332(f332(f10(f853(x43192,f853(f853(f852(x43191,x43192),a839),f853(f852(x43191,x43192),a839))),f853(f853(f852(x43191,x43192),a839),f853(x43192,f853(f852(x43191,x43192),a839))),x43191),f9(x43192,f853(f852(x43191,x43192),a839),f853(f852(x43191,x43192),a839))),f332(f332(f10(f853(x43192,f852(x43191,x43192)),f853(x43192,f853(f853(f852(x43191,x43192),a839),f853(f852(x43191,x43192),a839))),x43191),f332(f10(f852(x43191,x43192),f853(f853(f852(x43191,x43192),a839),f853(f852(x43191,x43192),a839)),x43192),f302(f852(x43191,x43192)))),f241(x43191,x43192)))),f180(f853(f852(x43191,x43192),a839))))),f332(f332(f248(x43191,x43192),x43193),x43194))
% 52.62/52.40 [3876]E(f332(f332(f125(x38761),f332(f332(f159(x38761),x38762),x38763)),f332(f332(f159(x38761),f332(f332(f3(a845),x38762),f332(f181(f846(x38761)),x38763))),x38764)),f332(f332(f159(x38761),x38762),f332(f332(f125(x38761),x38763),x38764)))
% 52.62/52.40 [3877]E(f332(f332(f125(x38771),f332(f332(f128(x38771),x38772),x38773)),f332(f332(f128(x38771),f332(f332(f3(a845),x38772),f332(f181(f846(x38771)),x38773))),x38774)),f332(f332(f128(x38771),x38772),f332(f332(f125(x38771),x38773),x38774)))
% 52.62/52.40 [3930]E(f332(f332(f82(a845),f332(f332(f83(a845),x39301),x39302)),f332(f332(f82(a845),f332(f332(f83(a845),x39303),x39302)),x39304)),f332(f332(f82(a845),f332(f332(f83(a845),f332(f332(f82(a845),x39301),x39303)),x39302)),x39304))
% 52.62/52.40 [4135]P1(f332(f332(f232(f853(x41351,a839)),f332(f332(f3(f853(x41351,a839)),f332(f259(x41352,x41351),x41353)),f332(f259(x41352,x41351),x41354))),f332(f259(x41352,x41351),f332(f332(f3(f853(f852(x41352,x41351),a839)),x41353),x41354))))
% 52.62/52.40 [4136]P1(f332(f332(f232(f853(x41361,a839)),f332(f332(f3(f853(x41361,a839)),f332(f261(x41361,x41362),x41363)),f332(f261(x41361,x41362),x41364))),f332(f261(x41361,x41362),f332(f332(f3(f853(f852(x41361,x41362),a839)),x41363),x41364))))
% 52.62/52.40 [4241]E(f332(f332(f82(a1),f332(a91,f332(f277(f852(a845,a845),f852(a845,a845),a111),f332(f332(f302(f852(a845,a845)),f332(f332(f241(a845,a845),x42411),x42412)),f180(f853(f852(a845,a845),a839)))))),f332(a91,f332(f277(f852(a845,a845),f852(a845,a845),a111),f332(f332(f302(f852(a845,a845)),f332(f332(f241(a845,a845),x42413),x42414)),f180(f853(f852(a845,a845),a839)))))),f332(a91,f332(f277(f852(a845,a845),f852(a845,a845),a111),f332(f332(f302(f852(a845,a845)),f332(f332(f241(a845,a845),f332(f332(f82(a845),x42411),x42413)),f332(f332(f82(a845),x42412),x42414))),f180(f853(f852(a845,a845),a839))))))
% 52.62/52.40 [4281]E(f332(f332(f83(a1),f332(a91,f332(f277(f852(a845,a845),f852(a845,a845),a111),f332(f332(f302(f852(a845,a845)),f332(f332(f241(a845,a845),x42811),x42812)),f180(f853(f852(a845,a845),a839)))))),f332(a91,f332(f277(f852(a845,a845),f852(a845,a845),a111),f332(f332(f302(f852(a845,a845)),f332(f332(f241(a845,a845),x42813),x42814)),f180(f853(f852(a845,a845),a839)))))),f332(a91,f332(f277(f852(a845,a845),f852(a845,a845),a111),f332(f332(f302(f852(a845,a845)),f332(f332(f241(a845,a845),f332(f332(f82(a845),f332(f332(f83(a845),x42811),x42813)),f332(f332(f83(a845),x42812),x42814))),f332(f332(f82(a845),f332(f332(f83(a845),x42811),x42814)),f332(f332(f83(a845),x42812),x42813)))),f180(f853(f852(a845,a845),a839))))))
% 52.62/52.40 [4301]E(f332(f256(x43011),f332(f332(f10(f853(x43012,a839),a839,x43011),f90(x43012)),f332(f332(f10(f853(x43012,a839),f853(x43012,a839),x43011),f332(f20(x43012,a839,a839),f332(f332(f10(a839,f853(a839,a839),x43012),a335),f332(f332(f9(x43012,f853(x43012,a839),a839),f334(x43012)),x43013)))),f332(f332(f9(x43011,f853(x43012,f853(x43011,a839)),f853(x43012,a839)),f332(f332(f10(f853(f853(x43011,a839),a839),f853(f853(x43012,f853(x43011,a839)),f853(x43012,a839)),x43011),f10(f853(x43011,a839),a839,x43012)),f334(x43011))),x43014)))),f332(f332(f48(x43012,f853(x43011,a839)),x43013),x43014))
% 52.62/52.40 [4335]E(f332(f332(f281(x43351,x43351,x43351),f332(f332(f302(f852(x43351,x43351)),f332(f332(f241(x43351,x43351),x43352),x43353)),x43354)),f300(x43351,f332(f332(f302(f852(x43351,x43351)),f332(f332(f241(x43351,x43351),x43352),x43353)),x43354))),f332(f332(f103(f853(f852(x43351,x43351),a839)),f332(f332(f281(x43351,x43351,x43351),x43354),f300(x43351,x43354))),f332(f256(f852(x43351,x43351)),f332(f251(x43351,x43351,a839),f332(f332(f9(x43351,f853(x43351,a839),f853(x43351,a839)),f332(f332(f10(f853(a839,a839),f853(f853(x43351,a839),f853(x43351,a839)),x43351),f10(a839,a839,x43351)),f332(f332(f10(a839,f853(a839,a839),x43351),a330),f332(f332(f9(x43351,f853(f852(x43351,x43351),a839),a839),f332(f332(f10(f852(x43351,x43351),f853(f853(f852(x43351,x43351),a839),a839),x43351),f334(f852(x43351,x43351))),f332(f332(f9(x43351,x43351,f852(x43351,x43351)),f241(x43351,x43351)),x43352))),f300(x43351,x43354))))),f332(f332(f9(x43351,f853(f852(x43351,x43351),a839),a839),f332(f332(f10(f852(x43351,x43351),f853(f853(f852(x43351,x43351),a839),a839),x43351),f334(f852(x43351,x43351))),f332(f241(x43351,x43351),x43353))),f300(x43351,x43354)))))))
% 52.62/52.40 [4137]E(f332(f126(x41371,f332(f332(f20(x41371,a839,a839),f332(f332(f10(a839,f853(a839,a839),x41371),a330),x41372)),x41373)),x41374),f332(f126(x41371,x41373),f332(f126(x41371,x41372),x41374)))
% 52.62/52.40 [4235]E(f332(f332(f125(x42351),f332(f332(f332(f98(f846(x42351)),f332(f332(f334(a845),f2(a845)),x42352)),f332(f332(f140(x42351),x42353),f115(x42351))),f115(x42351))),f160(x42351,x42354,f332(f256(a845),f332(f332(f9(a845,f853(a845,a839),a839),f332(f332(f10(a845,f853(f853(a845,a839),a839),a845),f334(a845)),a114)),x42352)))),f160(x42351,f332(f332(f140(x42351),x42353),x42354),x42352))
% 52.62/52.40 [4330]E(f332(f256(f852(x43301,x43302)),f332(f332(f10(f853(a845,a839),a839,f852(x43301,x43302)),f89(a845)),f332(f332(f9(f852(x43301,x43302),f853(a845,a839),f853(a845,a839)),f332(f332(f10(f853(a845,f853(a839,a839)),f853(f853(a845,a839),f853(a845,a839)),f852(x43301,x43302)),f20(a845,a839,a839)),f332(f332(f10(f853(a845,a839),f853(a845,f853(a839,a839)),f852(x43301,x43302)),f332(f10(a839,f853(a839,a839),a845),a330)),f332(f332(f9(f852(x43301,x43302),f853(a845,f852(x43301,x43302)),f853(a845,a839)),f332(f332(f10(f853(f852(x43301,x43302),a839),f853(f853(a845,f852(x43301,x43302)),f853(a845,a839)),f852(x43301,x43302)),f10(f852(x43301,x43302),a839,a845)),a329)),f332(f332(f20(a845,x43302,f852(x43301,x43302)),f332(f332(f10(x43301,f853(x43302,f852(x43301,x43302)),a845),f241(x43301,x43302)),f332(f152(x43301),x43303))),f332(f152(x43302),x43304)))))),f332(f332(f9(a845,a845,a839),f233(a845)),f332(f332(f236(a845),f332(f181(f846(x43301)),x43303)),f332(f181(f846(x43302)),x43304)))))),f332(f158(f852(x43301,x43302)),f332(f332(f167(x43301,x43302),x43303),x43304)))
% 52.62/52.40 [4254]E(f332(f256(f852(x42541,x42542)),f332(f251(x42541,x42542,a839),f332(f332(f9(x42541,f853(x42542,a839),f853(x42542,a839)),f332(f332(f10(f853(a839,a839),f853(f853(x42542,a839),f853(x42542,a839)),x42541),f10(a839,a839,x42542)),f332(f332(f10(a839,f853(a839,a839),x42541),a330),x42543))),x42544))),f332(f332(f248(x42541,x42542),f332(f256(x42541),x42543)),f332(f18(f853(x42542,a839),x42541),f332(f256(x42542),x42544))))
% 52.62/52.40 [4257]E(f332(f256(f852(x42571,x42572)),f332(f251(x42571,x42572,a839),f332(f332(f20(x42571,f853(x42572,a839),f853(x42572,a839)),f332(f332(f10(f853(a839,a839),f853(f853(x42572,a839),f853(x42572,a839)),x42571),f10(a839,a839,x42572)),f332(f332(f10(a839,f853(a839,a839),x42571),a330),x42573))),x42574))),f332(f332(f248(x42571,x42572),f332(f256(x42571),x42573)),f332(f332(f10(f853(x42572,a839),f853(x42572,a839),x42571),f256(x42572)),x42574)))
% 52.62/52.40 [4272]E(f332(f256(x42721),f332(f332(f10(f853(x42722,a839),a839,x42721),f90(x42722)),f332(f332(f10(f853(x42722,a839),f853(x42722,a839),x42721),f332(f20(x42722,a839,a839),f332(f332(f10(a839,f853(a839,a839),x42722),a335),f332(f332(f9(x42722,f853(x42722,a839),a839),f334(x42722)),x42723)))),x42724))),f332(f332(f48(x42722,f853(x42721,a839)),x42723),f332(f332(f10(f853(x42721,a839),f853(x42721,a839),x42722),f256(x42721)),f332(f9(x42721,x42722,a839),x42724))))
% 52.62/52.40 [4314]E(f332(f332(f143(f852(x43141,a845),x43141),f240(x43141,a845)),f332(f126(f852(x43141,a845),f332(f332(f9(f852(x43141,a845),f853(a845,a839),a839),f332(f332(f10(a845,f853(f853(a845,a839),a839),f852(x43141,a845)),f334(a845)),f250(x43141,a845))),x43142)),f332(f332(f167(x43141,a845),x43143),f130(a845,f332(f294(a845,x43144),f332(f332(f82(a845),x43144),f332(f181(f846(x43141)),x43143))))))),f332(f332(f143(f852(x43141,a845),x43141),f240(x43141,a845)),f332(f126(f852(x43141,a845),f332(f332(f9(f852(x43141,a845),f853(a845,a839),a839),f332(f332(f10(a845,f853(f853(a845,a839),a839),f852(x43141,a845)),f334(a845)),f332(f332(f9(f852(x43141,a845),a845,a845),f332(f332(f10(a845,f853(a845,a845),f852(x43141,a845)),f82(a845)),f250(x43141,a845))),x43144))),x43142)),f332(f332(f167(x43141,a845),x43143),f130(a845,f332(f294(a845,f2(a845)),f332(f181(f846(x43141)),x43143)))))))
% 52.62/52.40 [4315]E(f332(a114,f332(f332(f179(a845),f332(f181(f846(x43151)),x43152)),f332(f132(a845,f846(x43153),f332(f9(f846(x43153),a845,a845),f332(f332(f10(a845,f853(a845,a845),f846(x43153)),f179(a845)),f332(f332(f9(f846(x43153),a845,a845),f332(f332(f10(a845,f853(a845,a845),f846(x43153)),f3(a845)),f181(f846(x43153)))),f332(a114,f2(a845))))),f2(a845)),f332(f142(f846(x43153)),f332(f126(f846(x43153),f332(f332(f10(a839,a839,f846(x43153)),a328),f332(f332(f9(f846(x43153),f846(x43153),a839),a329),f115(x43153)))),x43154))))),f332(f332(f179(a845),f332(a114,f332(f181(f846(x43151)),x43152))),f332(f132(a845,f846(x43153),f332(f9(f846(x43153),a845,a845),f332(f332(f10(a845,f853(a845,a845),f846(x43153)),f179(a845)),f181(f846(x43153)))),f2(a845)),f332(f142(f846(x43153)),x43154))))
% 52.62/52.40 [4271]E(f332(f332(f125(x42711),f160(x42711,x42712,x42713)),f160(x42711,x42714,f332(f256(a845),f332(f332(f9(a845,f853(a845,a839),a839),f332(f332(f10(a845,f853(f853(a845,a839),a839),a845),f334(a845)),f332(f332(f9(a845,a845,a845),f82(a845)),f332(f181(f846(x42711)),x42712)))),x42713)))),f160(x42711,f332(f332(f125(x42711),x42712),x42714),x42713))
% 52.62/52.40 [4321]E(f332(f332(f140(f846(x43211)),f332(f332(f140(x43211),x43212),f332(f132(f846(x43211),f846(x43211),f125(x43211),f115(x43211)),f332(f332(f143(f846(x43211),f846(x43211)),f145(f846(x43211),x43211,f115(x43211),f332(f332(f10(f846(x43211),f853(f846(x43211),f846(x43211)),x43211),f18(f846(x43211),f846(x43211))),f332(f332(f9(x43211,f846(x43211),f846(x43211)),f140(x43211)),f115(x43211))))),x43213)))),f164(x43211,f332(f332(f140(f846(x43211)),x43214),f332(f132(f846(f846(x43211)),f846(f846(x43211)),f125(f846(x43211)),f115(f846(x43211))),f332(f332(f143(f846(x43211),f846(f846(x43211))),f145(f846(f846(x43211)),x43211,f115(f846(x43211)),f332(f18(f853(f846(x43211),f846(f846(x43211))),x43211),f332(f332(f9(f846(x43211),f846(f846(x43211)),f846(f846(x43211))),f140(f846(x43211))),f115(f846(x43211)))))),x43213))))),f164(x43211,f332(f332(f140(f846(x43211)),f332(f332(f140(x43211),x43212),x43214)),x43213)))
% 52.62/52.40 [4331]E(f332(f256(f852(x43311,x43311)),f332(f251(x43311,x43311,a839),f332(f332(f9(x43311,f853(f852(x43312,x43312),a839),f853(x43311,a839)),f332(f332(f10(f853(x43311,f853(f853(f852(x43312,x43312),a839),a839)),f853(f853(f852(x43312,x43312),a839),f853(x43311,a839)),x43311),f9(x43311,f853(f852(x43312,x43312),a839),a839)),f332(f332(f10(f853(x43311,f852(x43312,x43312)),f853(x43311,f853(f853(f852(x43312,x43312),a839),a839)),x43311),f332(f10(f852(x43312,x43312),f853(f853(f852(x43312,x43312),a839),a839),x43311),f334(f852(x43312,x43312)))),f332(f332(f9(x43311,f853(x43311,x43312),f853(x43311,f852(x43312,x43312))),f332(f332(f10(f853(x43312,f852(x43312,x43312)),f853(f853(x43311,x43312),f853(x43311,f852(x43312,x43312))),x43311),f10(x43312,f852(x43312,x43312),x43311)),f332(f332(f10(x43312,f853(x43312,f852(x43312,x43312)),x43311),f241(x43312,x43312)),x43313))),x43313)))),x43314))),f332(f332(f280(x43312,x43311),x43314),x43313))
% 52.62/52.40 [4416]~E(f36(x44161,x44162),f33(x44163,x44164,x44165))
% 52.62/52.40 [4417]~E(f36(x44171,x44172),f32(x44173,x44174,x44175))
% 52.62/52.40 [4418]~E(f36(x44181,x44182),f31(x44183,x44184,x44185))
% 52.62/52.40 [4419]~E(f35(x44191,x44192),f33(x44193,x44194,x44195))
% 52.62/52.40 [4420]~E(f35(x44201,x44202),f32(x44203,x44204,x44205))
% 52.62/52.40 [4421]~E(f35(x44211,x44212),f31(x44213,x44214,x44215))
% 52.62/52.40 [4422]~E(f28(x44221,x44222),f33(x44223,x44224,x44225))
% 52.62/52.40 [4423]~E(f28(x44231,x44232),f32(x44233,x44234,x44235))
% 52.62/52.40 [4424]~E(f28(x44241,x44242),f31(x44243,x44244,x44245))
% 52.62/52.40 [4425]~E(f33(x44251,x44252,x44253),f36(x44254,x44255))
% 52.62/52.40 [4426]~E(f33(x44261,x44262,x44263),f35(x44264,x44265))
% 52.62/52.40 [4427]~E(f33(x44271,x44272,x44273),f28(x44274,x44275))
% 52.62/52.40 [4428]~E(f32(x44281,x44282,x44283),f36(x44284,x44285))
% 52.62/52.40 [4429]~E(f32(x44291,x44292,x44293),f35(x44294,x44295))
% 52.62/52.40 [4430]~E(f32(x44301,x44302,x44303),f28(x44304,x44305))
% 52.62/52.40 [4431]~E(f31(x44311,x44312,x44313),f36(x44314,x44315))
% 52.62/52.40 [4432]~E(f31(x44321,x44322,x44323),f35(x44324,x44325))
% 52.62/52.40 [4433]~E(f31(x44331,x44332,x44333),f28(x44334,x44335))
% 52.62/52.40 [3819]E(f332(f170(x38191,x38192,x38193,x38194),x38195),f332(f229(f849(x38192),x38192,f332(x38193,x38195),f227(x38192)),f332(x38194,x38195)))
% 52.62/52.40 [3905]E(f170(x39051,x39052,f170(x39051,x39052,x39053,x39054),x39055),f170(x39051,x39052,x39053,f170(x39051,x39052,x39054,x39055)))
% 52.62/52.40 [3647]E(f332(f332(f251(x36471,x36472,x36473),x36474),x36475),f332(f332(x36474,f332(f240(x36471,x36472),x36475)),f332(f250(x36471,x36472),x36475)))
% 52.62/52.40 [3648]E(f332(f332(f251(x36481,x36482,x36483),x36484),x36485),f332(f332(x36484,f332(f240(x36481,x36482),x36485)),f332(f250(x36481,x36482),x36485)))
% 52.62/52.40 [3649]E(f332(f332(f251(x36491,x36492,x36493),x36494),x36495),f332(f332(x36494,f332(f240(x36491,x36492),x36495)),f332(f250(x36491,x36492),x36495)))
% 52.62/52.40 [3675]E(f332(f229(x36751,x36752,x36753,x36754),f332(f227(x36752),x36755)),f332(x36754,x36755))
% 52.62/52.40 [3683]E(f332(f332(f332(f68(x36831,x36832,x36833),x36834),x36835),f180(f853(x36832,a839))),x36835)
% 52.62/52.40 [3699]E(f332(f316(x36991,x36992,x36993,x36994),f332(f304(x36991,x36993),x36995)),f332(x36994,x36995))
% 52.62/52.40 [3700]E(f332(f317(x37001,x37002,x37003,x37004),f332(f313(x37001,x37003),x37005)),f332(x37004,x37005))
% 52.62/52.40 [3848]E(f230(x38481,x38482,x38483,x38484,f332(f227(x38482),x38485)),f332(x38484,x38485))
% 52.62/52.40 [3884]E(f318(x38841,x38842,x38843,x38844,f332(f304(x38841,x38842),x38845)),f332(f332(f82(a845),f332(x38843,x38845)),f332(a114,f2(a845))))
% 52.62/52.40 [3885]E(f318(x38851,x38852,x38853,x38854,f332(f313(x38852,x38851),x38855)),f332(f332(f82(a845),f332(x38854,x38855)),f332(a114,f2(a845))))
% 52.62/52.40 [3963]E(f332(f75(f849(x39631),f849(x39632),f849(x39633),f332(f196(x39631,x39632),x39634)),f332(f196(x39633,x39631),x39635)),f332(f196(x39633,x39632),f332(f75(x39631,x39632,x39633,x39634),x39635)))
% 52.62/52.40 [3964]E(f332(f75(f846(x39641),f846(x39642),f846(x39643),f332(f143(x39641,x39642),x39644)),f332(f143(x39643,x39641),x39645)),f332(f143(x39643,x39642),f332(f75(x39641,x39642,x39643,x39644),x39645)))
% 52.62/52.40 [3965]E(f332(f75(f846(x39651),f846(x39652),f846(x39653),f332(f143(x39651,x39652),x39654)),f332(f143(x39653,x39651),x39655)),f332(f143(x39653,x39652),f332(f75(x39651,x39652,x39653,x39654),x39655)))
% 52.62/52.40 [4044]E(f87(x40441,f69(x40442,x40441,x40443,x40444,x40445)),f332(f332(f67(x40442,x40441,x40443),x40444),x40445))
% 52.62/52.40 [4080]E(f332(f332(f82(a845),f332(f332(f82(a845),f332(x40801,f332(f240(x40802,x40803),x40804))),f332(x40805,f332(f250(x40802,x40803),x40804)))),f332(a114,f2(a845))),f255(x40802,x40803,x40801,x40805,x40804))
% 52.62/52.40 [4267]E(f153(x42671,x42672,f332(f332(f9(x42671,f849(x42672),f849(x42672)),f332(f332(f20(x42671,f849(x42672),f853(f849(x42672),f849(x42672))),f332(f332(f10(a839,f853(f849(x42672),f853(f849(x42672),f849(x42672))),x42671),f98(f849(x42672))),x42673)),f332(f332(f10(x42672,f849(x42672),x42671),f227(x42672)),x42674))),f183(x42672)),x42675),f332(f332(f143(x42671,x42672),x42674),f332(f126(x42671,x42673),x42675)))
% 52.62/52.40 [4474]~E(f332(f332(f332(f74(x44741,f849(x44742)),x44743),x44744),f332(f227(x44742),x44745)),f332(f18(f849(x44742),x44741),f183(x44742)))
% 52.62/52.40 [3584]E(f332(f332(f159(x35841),x35842),f332(f332(f143(x35843,x35841),x35844),x35845)),f332(f332(f143(x35843,x35841),x35844),f332(f332(f159(x35843),x35842),x35845)))
% 52.62/52.40 [3585]E(f332(f332(f128(x35851),x35852),f332(f332(f143(x35853,x35851),x35854),x35855)),f332(f332(f143(x35853,x35851),x35854),f332(f332(f128(x35853),x35852),x35855)))
% 52.62/52.40 [3615]E(f332(f332(f143(x36151,x36152),x36153),f332(f332(f140(x36151),x36154),x36155)),f332(f332(f140(x36152),f332(x36153,x36154)),f332(f332(f143(x36151,x36152),x36153),x36155)))
% 52.62/52.40 [3679]E(f332(f303(x36791,x36792,x36793),f332(f332(f302(x36791),x36794),x36795)),f332(f332(f302(x36792),f332(x36793,x36794)),f332(f303(x36791,x36792,x36793),x36795)))
% 52.62/52.40 [3744]E(f332(f332(f167(x37441,x37442),f332(f332(f159(x37441),x37443),x37444)),f332(f332(f159(x37442),x37443),x37445)),f332(f332(f159(f852(x37441,x37442)),x37443),f332(f332(f167(x37441,x37442),x37444),x37445)))
% 52.62/52.40 [3745]E(f332(f332(f167(x37451,x37452),f332(f332(f128(x37451),x37453),x37454)),f332(f332(f128(x37452),x37453),x37455)),f332(f332(f128(f852(x37451,x37452)),x37453),f332(f332(f167(x37451,x37452),x37454),x37455)))
% 52.62/52.40 [3756]E(f332(f332(f148(x37561,f332(f332(f140(x37561),x37562),x37563)),f332(a114,x37564)),x37565),f332(f332(f140(x37561),x37562),f332(f332(f148(x37561,x37563),x37564),x37565)))
% 52.62/52.40 [3759]E(f332(f229(f849(x37591),x37592,f183(x37591),x37593),f332(f332(f18(f849(x37592),x37594),f183(x37592)),x37595)),f183(x37591))
% 52.62/52.40 [3761]E(f332(f332(f125(x37611),f332(f332(f143(x37612,x37611),x37613),x37614)),f332(f332(f143(x37612,x37611),x37613),x37615)),f332(f332(f143(x37612,x37611),x37613),f332(f332(f125(x37612),x37614),x37615)))
% 52.62/52.40 [3765]E(f332(f332(x37651,x37652),f332(f332(f243(x37653,x37654,x37651),x37652),x37655)),f332(f332(f243(x37653,x37654,x37651),x37652),f332(a114,x37655)))
% 52.62/52.40 [3806]E(f332(f332(f281(x38061,x38062,x38063),f332(f278(x38062,x38061),x38064)),f332(f278(x38063,x38062),x38065)),f332(f278(x38063,x38061),f332(f332(f281(x38063,x38062,x38061),x38065),x38064)))
% 52.62/52.40 [3837]E(f332(f332(f332(f173(f846(x38371),f846(x38371)),x38372),f141(x38371)),f332(f332(f143(x38373,x38371),x38374),x38375)),f332(f332(f143(x38373,x38371),x38374),f332(f332(f332(f173(f846(x38373),f846(x38373)),x38372),f141(x38373)),x38375)))
% 52.62/52.40 [3838]E(f332(f332(f253(x38381,x38382,x38381,x38383),f332(f241(x38382,x38381),x38384)),x38385),f332(x38385,x38384))
% 52.62/52.40 [3862]E(f144(x38621,x38622,f332(f332(f143(x38623,x38621),x38624),x38625)),f144(x38623,f332(f75(x38621,a845,x38623,x38622),x38624),x38625))
% 52.62/52.40 [3928]E(f332(f332(f75(f849(x39281),f849(x39282),x39283,f332(f196(x39281,x39282),x39284)),f332(f18(f849(x39281),x39283),f183(x39281))),x39285),f183(x39282))
% 52.62/52.40 [3929]E(f162(f852(x39291,x39292),f332(f75(x39292,a839,f852(x39291,x39292),x39293),f250(x39291,x39292)),f332(f332(f167(x39291,x39292),x39294),x39295)),f332(f332(f167(x39291,x39292),x39294),f162(x39292,x39293,x39295)))
% 52.62/52.40 [3934]E(f332(f303(x39341,x39342,f332(f332(f10(x39343,x39342,x39341),x39344),x39345)),f239(f853(x39341,a839))),f332(f303(x39343,x39342,x39344),f332(f303(x39341,x39343,x39345),f239(f853(x39341,a839)))))
% 52.62/52.40 [3948]E(f162(f852(x39481,x39482),f332(f75(x39481,a839,f852(x39481,x39482),x39483),f240(x39481,x39482)),f332(f332(f167(x39481,x39482),x39484),x39485)),f332(f332(f167(x39481,x39482),f162(x39481,x39483,x39484)),x39485))
% 52.62/52.40 [3969]E(f332(f332(f103(f853(x39691,a839)),f332(f305(x39691,x39692,x39693),f332(f332(f302(x39692),x39694),f180(f853(x39692,a839))))),f332(f305(x39691,x39692,x39693),x39695)),f332(f305(x39691,x39692,x39693),f332(f332(f302(x39692),x39694),x39695)))
% 52.62/52.40 [4029]E(f332(f332(f143(x40291,x40292),x40293),f162(x40291,f332(f75(x40292,a839,x40291,x40294),x40293),x40295)),f162(x40292,x40294,f332(f332(f143(x40291,x40292),x40293),x40295)))
% 52.62/52.40 [4036]E(f332(f132(x40361,x40362,f332(f9(x40362,x40361,x40361),f332(f9(x40361,x40362,x40361),x40363)),x40364),f332(f142(x40362),f332(f142(x40362),x40365))),f332(f132(x40361,x40362,x40363,x40364),x40365))
% 52.62/52.40 [4037]E(f332(f332(f332(f74(x40371,f849(x40372)),f172(x40371,x40372,x40373,x40374)),x40375),f332(x40373,x40375)),f172(x40371,x40372,x40373,f332(f332(f302(x40371),x40375),x40374)))
% 52.62/52.40 [4046]E(f332(f319(x40461,x40462,x40463,f332(f18(x40462,x40461),x40464),f332(f18(x40462,x40463),x40464)),x40465),x40464)
% 52.62/52.40 [4105]E(f332(f229(f846(x41051),x41051,f153(x41052,x41051,x41053,x41054),f332(f332(f9(x41051,f846(x41051),f846(x41051)),f140(x41051)),f153(x41052,x41051,x41053,x41054))),f332(x41053,x41055)),f153(x41052,x41051,x41053,f332(f332(f140(x41052),x41055),x41054)))
% 52.62/52.40 [4145]P1(f332(f332(f232(f853(x41451,a839)),f332(f303(x41452,x41451,x41453),f332(f332(f104(f853(x41452,a839)),x41454),x41455))),f332(f332(f104(f853(x41451,a839)),f332(f303(x41452,x41451,x41453),x41454)),f332(f303(x41452,x41451,x41453),x41455))))
% 52.62/52.40 [4146]P1(f332(f332(f232(f853(x41461,a839)),f332(f277(x41462,x41461,x41463),f332(f332(f104(f853(x41462,a839)),x41464),x41465))),f332(f332(f104(f853(x41461,a839)),f332(f277(x41462,x41461,x41463),x41464)),f332(f277(x41462,x41461,x41463),x41465))))
% 52.62/52.40 [4242]E(f332(f250(x42421,x42422),f332(f252(x42423,x42421,x42422,x42422,x42424,f39(x42422)),x42425)),f332(f250(x42423,x42422),x42425))
% 52.62/52.40 [4243]E(f332(f240(x42431,x42432),f332(f252(x42431,x42431,x42433,x42432,f39(x42431),x42434),x42435)),f332(f240(x42431,x42433),x42435))
% 52.62/52.40 [4246]E(f332(f240(x42461,x42462),f332(f252(x42463,x42461,x42462,x42462,x42464,f39(x42462)),x42465)),f332(x42464,f332(f240(x42463,x42462),x42465)))
% 52.62/52.40 [4247]E(f332(f250(x42471,x42472),f332(f252(x42471,x42471,x42473,x42472,f39(x42471),x42474),x42475)),f332(x42474,f332(f250(x42471,x42473),x42475)))
% 52.62/52.40 [4324]P30(x43241,x43242,f332(f332(f302(f844(x43241)),f332(f332(f332(f93(x43241),f332(f332(f9(x43241,f853(a842,a842),f853(a842,a839)),f332(f332(f10(f853(a842,a839),f853(f853(a842,a842),f853(a842,a839)),x43241),f10(a842,a839,a842)),x43243)),f332(f332(f20(a842,a845,a842),f332(f332(f9(a842,a843,f853(a845,a842)),a189),x43244)),x43245))),f28(x43244,x43245)),x43243)),f180(f853(f844(x43241),a839))))
% 52.62/52.40 [4325]P30(x43251,x43252,f332(f332(f302(f844(x43251)),f332(f332(f332(f93(x43251),f332(f332(f9(x43251,f853(a842,a842),f853(a842,a839)),f332(f332(f10(f853(a842,a839),f853(f853(a842,a842),f853(a842,a839)),x43251),f10(a842,a839,a842)),x43253)),f332(f332(f20(a842,a845,a842),f332(f332(f9(a842,a843,f853(a845,a842)),a189),x43254)),x43255))),f28(x43254,x43255)),x43253)),f180(f853(f844(x43251),a839))))
% 52.62/52.40 [4329]P30(x43291,x43292,f332(f332(f302(f844(x43291)),f332(f332(f332(f93(x43291),f332(f332(f9(x43291,f853(a842,a839),f853(a842,a839)),f332(f332(f10(f853(a842,f853(a839,a839)),f853(f853(a842,a839),f853(a842,a839)),x43291),f20(a842,a839,a839)),f332(f332(f10(f853(a842,a839),f853(a842,f853(a839,a839)),x43291),f332(f10(a839,f853(a839,a839),a842),a330)),x43293))),f332(f332(f10(a839,a839,a842),a328),x43294))),f35(x43294,x43295)),x43293)),f180(f853(f844(x43291),a839))))
% 52.62/52.40 [3433]E(f332(f332(f332(f332(f199(x34331),x34332),x34333),x34334),x34335),f185(x34331,x34332))
% 52.62/52.40 [3434]E(f332(f332(f332(f332(f203(x34341),x34342),x34343),x34344),x34345),f194(x34341,x34342))
% 52.62/52.40 [3477]E(f95(x34771,x34772,f332(f332(f332(f93(x34771),x34773),x34774),x34775)),f2(a845))
% 52.62/52.40 [3567]E(f332(f332(f332(f332(f74(x35671,x35672),x35673),x35674),x35675),x35674),x35675)
% 52.62/52.40 [3796]E(f332(f332(f47(x37961,f853(x37962,a839)),f332(f332(f302(x37961),x37963),x37964)),x37965),f332(f332(f103(f853(x37962,a839)),f332(x37965,x37963)),f332(f332(f47(x37961,f853(x37962,a839)),x37964),x37965)))
% 52.62/52.40 [3797]E(f332(f332(f48(x37971,f853(x37972,a839)),f332(f332(f302(x37971),x37973),x37974)),x37975),f332(f332(f104(f853(x37972,a839)),f332(x37975,x37973)),f332(f332(f48(x37971,f853(x37972,a839)),x37974),x37975)))
% 52.62/52.40 [3855]E(f332(f332(f103(f853(x38551,a839)),f332(f303(x38552,x38551,x38553),x38554)),f332(f303(x38552,x38551,x38553),x38555)),f332(f303(x38552,x38551,x38553),f332(f332(f103(f853(x38552,a839)),x38554),x38555)))
% 52.62/52.40 [3856]E(f332(f332(f103(f853(x38561,a839)),f332(f277(x38562,x38561,x38563),x38564)),f332(f277(x38562,x38561,x38563),x38565)),f332(f277(x38562,x38561,x38563),f332(f332(f103(f853(x38562,a839)),x38564),x38565)))
% 52.62/52.40 [3857]E(f332(f332(f3(f853(x38571,a839)),f332(f305(x38571,x38572,x38573),x38574)),f332(f305(x38571,x38572,x38573),x38575)),f332(f305(x38571,x38572,x38573),f332(f332(f3(f853(x38572,a839)),x38574),x38575)))
% 52.62/52.40 [3858]E(f332(f332(f103(f853(x38581,a839)),f332(f305(x38581,x38582,x38583),x38584)),f332(f305(x38581,x38582,x38583),x38585)),f332(f305(x38581,x38582,x38583),f332(f332(f103(f853(x38582,a839)),x38584),x38585)))
% 52.62/52.40 [3859]E(f332(f332(f104(f853(x38591,a839)),f332(f305(x38591,x38592,x38593),x38594)),f332(f305(x38591,x38592,x38593),x38595)),f332(f305(x38591,x38592,x38593),f332(f332(f104(f853(x38592,a839)),x38594),x38595)))
% 52.62/52.40 [3861]E(f172(x38611,x38612,f172(x38611,x38612,x38613,x38614),x38615),f172(x38611,x38612,x38613,f332(f332(f104(f853(x38611,a839)),x38614),x38615)))
% 52.62/52.40 [3863]E(f118(x38631,x38632,f332(x38633,x38634),f332(f332(f9(x38631,a101,f847(x38632)),x38635),x38634)),f332(f192(x38631,x38632,x38633,x38635),x38634))
% 52.62/52.40 [3924]E(f332(f332(f148(x39241,f332(f332(f125(x39241),x39242),f332(f332(f140(x39241),x39243),x39244))),f332(f181(f846(x39241)),x39242)),x39245),f332(f332(f125(x39241),x39242),f332(f332(f140(x39241),x39245),x39244)))
% 52.62/52.40 [3931]E(f332(f332(f48(x39311,f853(x39312,a839)),x39313),f332(f332(f10(f853(x39312,a839),f853(x39312,a839),x39311),f332(f302(x39312),x39314)),x39315)),f332(f332(f302(x39312),x39314),f332(f332(f48(x39311,f853(x39312,a839)),x39313),x39315)))
% 52.62/52.40 [3932]E(f332(f332(f48(x39321,f853(x39322,a839)),x39323),f332(f332(f10(f853(x39322,a839),f853(x39322,a839),x39321),f332(f302(x39322),x39324)),x39325)),f332(f332(f302(x39322),x39324),f332(f332(f48(x39321,f853(x39322,a839)),x39323),x39325)))
% 52.62/52.40 [4004]E(f172(x40041,x40042,f332(f332(f332(f74(x40041,f849(x40042)),x40043),x40044),f332(f227(x40042),x40045)),f332(f81(f853(x40041,a839)),f332(f332(f302(x40041),x40044),f180(f853(x40041,a839))))),f172(x40041,x40042,x40043,f332(f81(f853(x40041,a839)),f332(f332(f302(x40041),x40044),f180(f853(x40041,a839))))))
% 52.62/52.40 [4048]E(f332(f332(f3(f853(f852(x40481,x40482),a839)),f332(f332(f248(x40481,x40482),x40483),f332(f18(f853(x40482,a839),x40481),x40484))),f332(f332(f248(x40481,x40482),x40485),f332(f18(f853(x40482,a839),x40481),x40484))),f332(f332(f248(x40481,x40482),f332(f332(f3(f853(x40481,a839)),x40483),x40485)),f332(f18(f853(x40482,a839),x40481),x40484)))
% 52.62/52.40 [4049]E(f332(f332(f103(f853(f852(x40491,x40492),a839)),f332(f332(f248(x40491,x40492),x40493),f332(f18(f853(x40492,a839),x40491),x40494))),f332(f332(f248(x40491,x40492),x40495),f332(f18(f853(x40492,a839),x40491),x40494))),f332(f332(f248(x40491,x40492),f332(f332(f103(f853(x40491,a839)),x40493),x40495)),f332(f18(f853(x40492,a839),x40491),x40494)))
% 52.62/52.40 [4050]E(f332(f332(f104(f853(f852(x40501,x40502),a839)),f332(f332(f248(x40501,x40502),x40503),f332(f18(f853(x40502,a839),x40501),x40504))),f332(f332(f248(x40501,x40502),x40505),f332(f18(f853(x40502,a839),x40501),x40504))),f332(f332(f248(x40501,x40502),f332(f332(f104(f853(x40501,a839)),x40503),x40505)),f332(f18(f853(x40502,a839),x40501),x40504)))
% 52.62/52.40 [4090]E(f332(f332(f143(x40901,x40902),x40903),f332(f126(x40901,f332(f75(x40902,a839,x40901,x40904),x40903)),x40905)),f332(f126(x40902,x40904),f332(f332(f143(x40901,x40902),x40903),x40905)))
% 52.62/52.40 [4097]E(f332(f181(f846(x40971)),f332(f126(x40971,x40972),f332(f332(f143(x40973,x40971),x40974),x40975))),f332(f181(f846(x40973)),f332(f126(x40973,f332(f75(x40971,a839,x40973,x40972),x40974)),x40975)))
% 52.62/52.40 [4234]E(f332(f332(f103(f853(x42341,a839)),f332(f332(f3(f853(x42341,a839)),f169(x42341,x42342,x42343)),f332(f256(x42341),f332(f332(f9(x42341,f853(x42341,a839),a839),f334(x42341)),f332(f332(f3(f853(x42341,a839)),x42344),f169(x42341,x42342,x42345)))))),f332(f256(x42341),f332(f332(f9(x42341,f853(x42341,a839),a839),f334(x42341)),f332(f332(f104(f853(x42341,a839)),x42344),f169(x42341,x42342,x42345))))),f169(x42341,x42342,f78(x42341,f849(x42342),x42343,x42345,x42344)))
% 52.62/52.40 [4306]E(f332(f145(f846(f852(x43061,x43062)),x43062,f115(f852(x43061,x43062)),f332(f332(f9(x43062,f853(f846(x43062),f846(f852(x43061,x43062))),f853(f846(x43062),f846(f852(x43061,x43062)))),f332(f332(f10(f853(f846(f852(x43061,x43062)),f846(f852(x43061,x43062))),f853(f853(f846(x43062),f846(f852(x43061,x43062))),f853(f846(x43062),f846(f852(x43061,x43062)))),x43062),f10(f846(f852(x43061,x43062)),f846(f852(x43061,x43062)),f846(x43062))),f332(f332(f10(f852(x43061,x43062),f853(f846(f852(x43061,x43062)),f846(f852(x43061,x43062))),x43062),f140(f852(x43061,x43062))),f332(f241(x43061,x43062),x43063)))),f332(f167(x43061,x43062),x43064))),x43065),f332(f332(f167(x43061,x43062),f332(f332(f140(x43061),x43063),x43064)),x43065))
% 52.62/52.40 [3791]E(f332(f332(f148(x37911,f332(f332(f148(x37911,x37912),x37913),x37914)),x37913),x37915),f332(f332(f148(x37911,x37912),x37913),x37915))
% 52.62/52.40 [3839]E(f332(f259(x38391,x38392),f332(f332(f302(f852(x38391,x38392)),f332(f332(f241(x38391,x38392),x38393),x38394)),x38395)),f332(f332(f302(x38392),x38394),f332(f259(x38391,x38392),x38395)))
% 52.62/52.40 [3840]E(f332(f261(x38401,x38402),f332(f332(f302(f852(x38401,x38402)),f332(f332(f241(x38401,x38402),x38403),x38404)),x38405)),f332(f332(f302(x38401),x38403),f332(f261(x38401,x38402),x38405)))
% 52.62/52.40 [3888]E(f121(x38881,x38882,f332(x38883,x38884),f332(f332(f9(x38881,a101,f847(f849(x38882))),x38885),x38884)),f332(f190(x38881,x38882,x38883,x38885),x38884))
% 52.62/52.40 [3917]E(f332(f332(f3(f853(f852(x39171,x39172),a839)),f332(f332(f248(x39171,x39172),x39173),x39174)),f332(f332(f248(x39171,x39172),x39175),x39174)),f332(f332(f248(x39171,x39172),f332(f332(f3(f853(x39171,a839)),x39173),x39175)),x39174))
% 52.62/52.40 [3918]E(f332(f332(f103(f853(f852(x39181,x39182),a839)),f332(f332(f248(x39181,x39182),x39183),x39184)),f332(f332(f248(x39181,x39182),x39185),x39184)),f332(f332(f248(x39181,x39182),f332(f332(f103(f853(x39181,a839)),x39183),x39185)),x39184))
% 52.62/52.40 [3919]E(f332(f332(f104(f853(f852(x39191,x39192),a839)),f332(f332(f248(x39191,x39192),x39193),x39194)),f332(f332(f248(x39191,x39192),x39195),x39194)),f332(f332(f248(x39191,x39192),f332(f332(f104(f853(x39191,a839)),x39193),x39195)),x39194))
% 52.62/52.40 [3982]E(f332(f332(f103(f853(x39821,a839)),f332(f332(f47(x39822,f853(x39821,a839)),x39823),x39824)),f332(f332(f47(x39822,f853(x39821,a839)),x39825),x39824)),f332(f332(f47(x39822,f853(x39821,a839)),f332(f332(f103(f853(x39822,a839)),x39823),x39825)),x39824))
% 52.62/52.40 [3983]E(f332(f332(f104(f853(x39831,a839)),f332(f332(f48(x39832,f853(x39831,a839)),x39833),x39834)),f332(f332(f48(x39832,f853(x39831,a839)),x39835),x39834)),f332(f332(f48(x39832,f853(x39831,a839)),f332(f332(f103(f853(x39832,a839)),x39833),x39835)),x39834))
% 52.62/52.40 [3992]E(f332(f332(f47(x39921,f853(x39922,a839)),x39923),f332(f332(f10(f853(x39922,a839),f853(x39922,a839),x39921),f332(f3(f853(x39922,a839)),x39924)),x39925)),f332(f332(f3(f853(x39922,a839)),x39924),f332(f332(f48(x39921,f853(x39922,a839)),x39923),x39925)))
% 52.62/52.40 [3993]E(f332(f332(f48(x39931,f853(x39932,a839)),x39933),f332(f332(f10(f853(x39932,a839),f853(x39932,a839),x39931),f332(f103(f853(x39932,a839)),x39934)),x39935)),f332(f332(f103(f853(x39932,a839)),x39934),f332(f332(f48(x39931,f853(x39932,a839)),x39933),x39935)))
% 52.62/52.40 [3994]E(f332(f332(f48(x39941,f853(x39942,a839)),x39943),f332(f332(f10(f853(x39942,a839),f853(x39942,a839),x39941),f332(f103(f853(x39942,a839)),x39944)),x39945)),f332(f332(f103(f853(x39942,a839)),x39944),f332(f332(f48(x39941,f853(x39942,a839)),x39943),x39945)))
% 52.62/52.40 [3995]E(f332(f332(f47(x39951,f853(x39952,a839)),x39953),f332(f332(f10(f853(x39952,a839),f853(x39952,a839),x39951),f332(f104(f853(x39952,a839)),x39954)),x39955)),f332(f332(f104(f853(x39952,a839)),x39954),f332(f332(f47(x39951,f853(x39952,a839)),x39953),x39955)))
% 52.62/52.40 [3996]E(f332(f332(f47(x39961,f853(x39962,a839)),x39963),f332(f332(f10(f853(x39962,a839),f853(x39962,a839),x39961),f332(f104(f853(x39962,a839)),x39964)),x39965)),f332(f332(f104(f853(x39962,a839)),x39964),f332(f332(f47(x39961,f853(x39962,a839)),x39963),x39965)))
% 52.62/52.40 [3997]E(f332(f332(f47(x39971,f853(x39972,a839)),x39973),f332(f332(f10(f853(x39972,a839),f853(x39972,a839),x39971),f332(f3(f853(x39972,a839)),x39974)),x39975)),f332(f332(f3(f853(x39972,a839)),x39974),f332(f332(f48(x39971,f853(x39972,a839)),x39973),x39975)))
% 52.62/52.40 [3998]E(f332(f332(f47(x39981,f853(x39982,a839)),x39983),f332(f332(f10(f853(x39982,a839),f853(x39982,a839),x39981),f332(f104(f853(x39982,a839)),x39984)),x39985)),f332(f332(f104(f853(x39982,a839)),x39984),f332(f332(f47(x39981,f853(x39982,a839)),x39983),x39985)))
% 52.62/52.40 [3999]E(f332(f332(f48(x39991,f853(x39992,a839)),x39993),f332(f332(f10(f853(x39992,a839),f853(x39992,a839),x39991),f332(f103(f853(x39992,a839)),x39994)),x39995)),f332(f332(f103(f853(x39992,a839)),x39994),f332(f332(f48(x39991,f853(x39992,a839)),x39993),x39995)))
% 52.62/52.40 [4058]E(f175(f846(x40581),f332(f332(f140(x40581),x40582),x40583),f332(f332(f10(f846(x40581),f846(x40581),a845),f332(f140(x40581),x40584)),f332(f332(f9(a845,x40581,f846(x40581)),f148(x40581,x40583)),x40582)),x40585),f332(f332(f148(x40581,f332(f332(f140(x40581),x40584),x40583)),x40585),x40582))
% 52.62/52.40 [4062]E(f332(f332(f47(x40621,f853(f852(x40622,x40623),a839)),x40624),f332(f332(f10(f853(f852(x40623,x40622),a839),f853(f852(x40622,x40623),a839),x40621),f278(x40623,x40622)),x40625)),f332(f278(x40623,x40622),f332(f332(f47(x40621,f853(f852(x40623,x40622),a839)),x40624),x40625)))
% 52.62/52.40 [4063]E(f332(f332(f48(x40631,f853(f852(x40632,x40633),a839)),x40634),f332(f332(f10(f853(f852(x40633,x40632),a839),f853(f852(x40632,x40633),a839),x40631),f278(x40633,x40632)),x40635)),f332(f278(x40633,x40632),f332(f332(f48(x40631,f853(f852(x40633,x40632),a839)),x40634),x40635)))
% 52.62/52.40 [4116]E(f169(x41161,x41162,f332(f332(f20(x41161,f849(x41163),f849(x41162)),f332(f332(f10(f853(x41163,x41162),f853(f849(x41163),f849(x41162)),x41161),f196(x41163,x41162)),x41164)),x41165)),f169(x41161,x41163,x41165))
% 52.62/52.40 [4169]P1(f332(f332(f232(f853(x41691,a839)),f332(f332(f3(f853(x41691,a839)),f332(f303(x41692,x41691,x41693),x41694)),f332(f303(x41692,x41691,x41693),x41695))),f332(f303(x41692,x41691,x41693),f332(f332(f3(f853(x41692,a839)),x41694),x41695))))
% 52.62/52.40 [4310]E(f332(f145(f846(f852(x43101,x43102)),x43101,f115(f852(x43101,x43102)),f332(f332(f9(x43101,f853(f846(x43101),f846(f852(x43101,x43102))),f853(f846(x43101),f846(f852(x43101,x43102)))),f332(f332(f10(f853(f846(f852(x43101,x43102)),f846(f852(x43101,x43102))),f853(f853(f846(x43101),f846(f852(x43101,x43102))),f853(f846(x43101),f846(f852(x43101,x43102)))),x43101),f10(f846(f852(x43101,x43102)),f846(f852(x43101,x43102)),f846(x43101))),f332(f332(f10(f852(x43101,x43102),f853(f846(f852(x43101,x43102)),f846(f852(x43101,x43102))),x43101),f140(f852(x43101,x43102))),f332(f332(f9(x43101,x43102,f852(x43101,x43102)),f241(x43101,x43102)),x43103)))),f332(f332(f9(f846(x43101),f846(x43102),f846(f852(x43101,x43102))),f167(x43101,x43102)),x43104))),x43105),f332(f332(f167(x43101,x43102),x43105),f332(f332(f140(x43102),x43103),x43104)))
% 52.62/52.40 [4327]E(f332(f132(f853(x43271,f849(x43272)),f852(x43271,x43272),f332(f332(f10(f853(x43271,f853(x43272,f853(x43271,f849(x43272)))),f853(f852(x43271,x43272),f853(x43271,f849(x43272))),f853(x43271,f849(x43272))),f251(x43271,x43272,f853(x43271,f849(x43272)))),f332(f332(f9(f853(x43271,f849(x43272)),f853(x43272,f849(x43272)),f853(x43271,f853(x43272,f853(x43271,f849(x43272))))),f332(f332(f10(f853(x43271,f853(f853(x43272,f849(x43272)),f853(x43272,f853(x43271,f849(x43272))))),f853(f853(x43272,f849(x43272)),f853(x43271,f853(x43272,f853(x43271,f849(x43272))))),f853(x43271,f849(x43272))),f9(x43271,f853(x43272,f849(x43272)),f853(x43272,f853(x43271,f849(x43272))))),f332(f332(f10(f853(x43271,f853(f849(x43272),f853(x43271,f849(x43272)))),f853(x43271,f853(f853(x43272,f849(x43272)),f853(x43272,f853(x43271,f849(x43272))))),f853(x43271,f849(x43272))),f332(f10(f853(f849(x43272),f853(x43271,f849(x43272))),f853(f853(x43272,f849(x43272)),f853(x43272,f853(x43271,f849(x43272)))),x43271),f10(f849(x43272),f853(x43271,f849(x43272)),x43272))),f74(x43271,f849(x43272))))),f227(x43272))),x43273),f332(f332(f167(x43271,x43272),x43274),x43275)),f170(x43271,x43272,x43273,f166(x43271,x43272,f332(f142(f852(x43271,x43272)),f332(f332(f167(x43271,x43272),x43274),x43275)))))
% 52.62/52.40 [4023]E(f332(f332(f103(f853(x40231,a839)),f332(f277(x40232,x40231,x40233),x40234)),f332(f277(x40232,x40231,x40235),x40234)),f332(f277(x40232,x40231,f332(f332(f103(f853(f852(x40232,x40231),a839)),x40233),x40235)),x40234))
% 52.62/52.40 [4065]E(f332(f332(f125(f852(x40651,x40652)),f332(f332(f167(x40651,x40652),x40653),f332(f332(f159(x40652),f332(f181(f846(x40651)),x40653)),x40654))),f332(f332(f167(x40651,x40652),x40655),f332(f332(f128(x40652),f332(f181(f846(x40651)),x40653)),x40654))),f332(f332(f167(x40651,x40652),f332(f332(f125(x40651),x40653),x40655)),x40654))
% 52.62/52.40 [4094]E(f169(x40941,x40942,f170(x40941,x40942,x40943,f166(x40941,x40942,f332(f142(f852(x40941,x40942)),f332(f332(f167(x40941,x40942),x40944),x40945))))),f332(f332(f103(f853(x40941,a839)),f332(f158(x40941),f332(f332(f159(x40941),f332(f181(f846(x40942)),x40945)),x40944))),f169(x40941,x40942,x40943)))
% 52.62/52.40 [4172]E(f332(f332(f248(x41721,x41722),x41723),f332(f332(f20(x41721,f853(x41722,a839),f853(x41722,a839)),f332(f332(f10(f853(x41722,a839),f853(f853(x41722,a839),f853(x41722,a839)),x41721),f3(f853(x41722,a839))),x41724)),x41725)),f332(f332(f3(f853(f852(x41721,x41722),a839)),f332(f332(f248(x41721,x41722),x41723),x41724)),f332(f332(f248(x41721,x41722),x41723),x41725)))
% 52.62/52.40 [4173]E(f332(f332(f248(x41731,x41732),x41733),f332(f332(f20(x41731,f853(x41732,a839),f853(x41732,a839)),f332(f332(f10(f853(x41732,a839),f853(f853(x41732,a839),f853(x41732,a839)),x41731),f103(f853(x41732,a839))),x41734)),x41735)),f332(f332(f103(f853(f852(x41731,x41732),a839)),f332(f332(f248(x41731,x41732),x41733),x41734)),f332(f332(f248(x41731,x41732),x41733),x41735)))
% 52.62/52.40 [4174]E(f332(f332(f248(x41741,x41742),x41743),f332(f332(f20(x41741,f853(x41742,a839),f853(x41742,a839)),f332(f332(f10(f853(x41742,a839),f853(f853(x41742,a839),f853(x41742,a839)),x41741),f104(f853(x41742,a839))),x41744)),x41745)),f332(f332(f104(f853(f852(x41741,x41742),a839)),f332(f332(f248(x41741,x41742),x41743),x41744)),f332(f332(f248(x41741,x41742),x41743),x41745)))
% 52.62/52.40 [4175]E(f332(f332(f47(x41751,f853(x41752,a839)),x41753),f332(f332(f9(x41751,f853(x41752,a839),f853(x41752,a839)),f332(f332(f10(f853(x41752,a839),f853(f853(x41752,a839),f853(x41752,a839)),x41751),f3(f853(x41752,a839))),x41754)),x41755)),f332(f332(f3(f853(x41752,a839)),f332(f332(f47(x41751,f853(x41752,a839)),x41753),x41754)),x41755))
% 52.62/52.40 [4176]E(f332(f332(f48(x41761,f853(x41762,a839)),x41763),f332(f332(f9(x41761,f853(x41762,a839),f853(x41762,a839)),f332(f332(f10(f853(x41762,a839),f853(f853(x41762,a839),f853(x41762,a839)),x41761),f103(f853(x41762,a839))),x41764)),x41765)),f332(f332(f103(f853(x41762,a839)),f332(f332(f48(x41761,f853(x41762,a839)),x41763),x41764)),x41765))
% 52.62/52.40 [4177]E(f332(f332(f47(x41771,f853(x41772,a839)),x41773),f332(f332(f9(x41771,f853(x41772,a839),f853(x41772,a839)),f332(f332(f10(f853(x41772,a839),f853(f853(x41772,a839),f853(x41772,a839)),x41771),f104(f853(x41772,a839))),x41774)),x41775)),f332(f332(f104(f853(x41772,a839)),f332(f332(f47(x41771,f853(x41772,a839)),x41773),x41774)),x41775))
% 52.62/52.40 [4178]E(f332(f332(f47(x41781,f853(x41782,a839)),x41783),f332(f332(f9(x41781,f853(x41782,a839),f853(x41782,a839)),f332(f332(f10(f853(x41782,a839),f853(f853(x41782,a839),f853(x41782,a839)),x41781),f3(f853(x41782,a839))),x41784)),x41785)),f332(f332(f3(f853(x41782,a839)),f332(f332(f47(x41781,f853(x41782,a839)),x41783),x41784)),x41785))
% 52.62/52.40 [4179]E(f332(f332(f47(x41791,f853(x41792,a839)),x41793),f332(f332(f9(x41791,f853(x41792,a839),f853(x41792,a839)),f332(f332(f10(f853(x41792,a839),f853(f853(x41792,a839),f853(x41792,a839)),x41791),f104(f853(x41792,a839))),x41794)),x41795)),f332(f332(f104(f853(x41792,a839)),f332(f332(f47(x41791,f853(x41792,a839)),x41793),x41794)),x41795))
% 52.62/52.40 [4180]E(f332(f332(f48(x41801,f853(x41802,a839)),x41803),f332(f332(f9(x41801,f853(x41802,a839),f853(x41802,a839)),f332(f332(f10(f853(x41802,a839),f853(f853(x41802,a839),f853(x41802,a839)),x41801),f103(f853(x41802,a839))),x41804)),x41805)),f332(f332(f103(f853(x41802,a839)),f332(f332(f48(x41801,f853(x41802,a839)),x41803),x41804)),x41805))
% 52.62/52.40 [4184]E(f332(f332(f47(x41841,f853(x41842,a839)),x41843),f332(f332(f20(x41841,f853(x41842,a839),f853(x41842,a839)),f332(f332(f10(f853(x41842,a839),f853(f853(x41842,a839),f853(x41842,a839)),x41841),f103(f853(x41842,a839))),x41844)),x41845)),f332(f332(f103(f853(x41842,a839)),f332(f332(f47(x41841,f853(x41842,a839)),x41843),x41844)),f332(f332(f47(x41841,f853(x41842,a839)),x41843),x41845)))
% 52.62/52.40 [4185]E(f332(f332(f48(x41851,f853(x41852,a839)),x41853),f332(f332(f20(x41851,f853(x41852,a839),f853(x41852,a839)),f332(f332(f10(f853(x41852,a839),f853(f853(x41852,a839),f853(x41852,a839)),x41851),f104(f853(x41852,a839))),x41854)),x41855)),f332(f332(f104(f853(x41852,a839)),f332(f332(f48(x41851,f853(x41852,a839)),x41853),x41854)),f332(f332(f48(x41851,f853(x41852,a839)),x41853),x41855)))
% 52.62/52.40 [4197]E(f332(f332(f47(x41971,f853(x41972,a839)),x41973),f332(f332(f20(x41971,f853(x41972,a839),f853(x41972,a839)),f332(f332(f10(f853(x41972,a839),f853(f853(x41972,a839),f853(x41972,a839)),x41971),f103(f853(x41972,a839))),x41974)),x41975)),f332(f332(f103(f853(x41972,a839)),f45(f853(x41972,a839),f332(f303(x41971,f853(x41972,a839),x41974),x41973))),f45(f853(x41972,a839),f332(f303(x41971,f853(x41972,a839),x41975),x41973))))
% 52.62/52.40 [4198]E(f332(f332(f48(x41981,f853(x41982,a839)),x41983),f332(f332(f20(x41981,f853(x41982,a839),f853(x41982,a839)),f332(f332(f10(f853(x41982,a839),f853(f853(x41982,a839),f853(x41982,a839)),x41981),f104(f853(x41982,a839))),x41984)),x41985)),f332(f332(f104(f853(x41982,a839)),f46(f853(x41982,a839),f332(f303(x41981,f853(x41982,a839),x41984),x41983))),f46(f853(x41982,a839),f332(f303(x41981,f853(x41982,a839),x41985),x41983))))
% 52.62/52.40 [4106]E(f332(f332(f125(f852(x41061,x41062)),f332(f332(f167(x41061,x41062),f332(f332(f159(x41061),f332(f181(f846(x41062)),x41063)),x41064)),x41063)),f332(f332(f167(x41061,x41062),f332(f332(f128(x41061),f332(f181(f846(x41062)),x41063)),x41064)),x41065)),f332(f332(f167(x41061,x41062),x41064),f332(f332(f125(x41062),x41063),x41065)))
% 52.62/52.40 [4223]E(f87(x42231,f332(f332(f20(x42231,a839,a839),f332(f332(f10(a839,f853(a839,a839),x42231),a330),f332(f332(f9(x42231,f853(x42231,a839),a839),f334(x42231)),x42232))),f332(f332(f9(x42231,x42233,a839),f332(f332(f10(x42233,f853(x42233,a839),x42231),a329),x42234)),x42235))),f332(f79(x42231,x42233,x42232,x42234),x42235))
% 52.62/52.40 [4273]E(f332(f332(f88(a1,x42731),f332(f106(a1),f332(f332(f82(a1),x42732),a99))),f332(f332(f20(a1,x42731,x42731),f332(f332(f9(a1,x42731,f853(x42731,x42731)),f332(f332(f10(a839,f853(x42731,f853(x42731,x42731)),a1),f98(x42731)),a186)),f175(x42731,x42733,x42734,x42735))),f332(f332(f10(a845,x42731,a1),x42734),f332(f332(f9(a1,a845,a845),f332(f332(f10(a845,f853(a845,a845),a1),f82(a845)),a107)),x42735)))),f175(x42731,x42733,x42734,f332(f332(f82(a845),f332(f106(a845),x42732)),x42735)))
% 52.62/52.40 [4307]E(f166(x43071,x43072,f332(f332(f143(f852(x43071,x43073),f852(x43071,x43072)),f332(f251(x43071,x43073,f852(x43071,x43072)),f332(f332(f9(x43071,f853(x43073,x43072),f853(x43073,f852(x43071,x43072))),f332(f332(f10(f853(x43072,f852(x43071,x43072)),f853(f853(x43073,x43072),f853(x43073,f852(x43071,x43072))),x43071),f10(x43072,f852(x43071,x43072),x43073)),f241(x43071,x43072))),x43074))),x43075)),f332(f75(f849(x43073),f849(x43072),x43071,f332(f196(x43073,x43072),x43074)),f166(x43071,x43073,x43075)))
% 52.62/52.40 [4266]E(f169(x42661,x42662,f332(f332(f20(x42661,f849(x42662),f849(x42662)),f332(f332(f20(x42661,f849(x42662),f853(f849(x42662),f849(x42662))),f332(f332(f10(a839,f853(f849(x42662),f853(f849(x42662),f849(x42662))),x42661),f98(f849(x42662))),x42663)),x42664)),x42665)),f332(f332(f103(f853(x42661,a839)),f332(f332(f104(f853(x42661,a839)),f169(x42661,x42662,x42664)),f332(f256(x42661),x42663))),f332(f332(f104(f853(x42661,a839)),f169(x42661,x42662,x42665)),f332(f256(x42661),f332(f332(f10(a839,a839,x42661),a328),x42663)))))
% 52.62/52.40 [4305]E(f332(f332(f88(a1,x43051),f332(f106(a1),f332(f332(f82(a1),x43052),a99))),f332(f332(f20(a1,x43051,x43051),f332(f332(f9(a1,x43051,f853(x43051,x43051)),f332(f332(f10(a839,f853(x43051,f853(x43051,x43051)),a1),f98(x43051)),a186)),f332(f174(x43051,x43053,x43054),x43055))),f332(f332(f20(a1,x43051,x43051),f332(f332(f10(a845,f853(x43051,x43051),a1),x43054),f332(f332(f9(a1,a845,a845),f332(f332(f10(a845,f853(a845,a845),a1),f82(a845)),a107)),x43055))),f332(f332(f10(a845,x43051,a1),f174(x43051,x43053,x43054)),f332(f332(f9(a1,a845,a845),f332(f332(f10(a845,f853(a845,a845),a1),f82(a845)),a107)),x43055))))),f332(f174(x43051,x43053,x43054),f332(f332(f82(a845),f332(f106(a845),x43052)),x43055)))
% 52.62/52.40 [4354]E(f332(f256(f852(x43541,x43542)),f332(f251(x43541,x43542,a839),f332(f332(f10(f853(x43542,f853(x43543,a839)),f853(x43542,a839),x43541),f332(f10(f853(x43543,a839),a839,x43542),f89(x43543))),f332(f332(f9(x43541,f853(x43542,f853(x43543,a839)),f853(x43542,f853(x43543,a839))),f332(f332(f10(f853(f853(x43543,a839),f853(x43543,a839)),f853(f853(x43542,f853(x43543,a839)),f853(x43542,f853(x43543,a839))),x43541),f10(f853(x43543,a839),f853(x43543,a839),x43542)),f332(f332(f10(f853(x43543,f853(a839,a839)),f853(f853(x43543,a839),f853(x43543,a839)),x43541),f20(x43543,a839,a839)),f332(f332(f10(f853(x43543,a839),f853(x43543,f853(a839,a839)),x43541),f332(f10(a839,f853(a839,a839),x43543),a330)),f332(f332(f9(x43541,f853(f852(x43541,x43543),a839),f853(x43543,a839)),f332(f332(f10(f853(x43543,f853(f853(f852(x43541,x43543),a839),a839)),f853(f853(f852(x43541,x43543),a839),f853(x43543,a839)),x43541),f9(x43543,f853(f852(x43541,x43543),a839),a839)),f332(f332(f10(f853(x43543,f852(x43541,x43543)),f853(x43543,f853(f853(f852(x43541,x43543),a839),a839)),x43541),f332(f10(f852(x43541,x43543),f853(f853(f852(x43541,x43543),a839),a839),x43543),f334(f852(x43541,x43543)))),f241(x43541,x43543)))),x43544))))),f332(f332(f9(x43542,f853(f852(x43543,x43542),a839),f853(x43543,a839)),f332(f332(f10(f853(x43543,f853(f853(f852(x43543,x43542),a839),a839)),f853(f853(f852(x43543,x43542),a839),f853(x43543,a839)),x43542),f9(x43543,f853(f852(x43543,x43542),a839),a839)),f332(f332(f10(f853(x43543,f852(x43543,x43542)),f853(x43543,f853(f853(f852(x43543,x43542),a839),a839)),x43542),f332(f10(f852(x43543,x43542),f853(f853(f852(x43543,x43542),a839),a839),x43543),f334(f852(x43543,x43542)))),f332(f9(x43543,x43542,f852(x43543,x43542)),f241(x43543,x43542))))),x43545))))),f332(f332(f281(x43541,x43543,x43542),x43544),x43545))
% 52.62/52.40 [4455]~E(f32(x44551,x44552,x44553),f33(x44554,x44555,x44556))
% 52.62/52.40 [4456]~E(f32(x44561,x44562,x44563),f33(x44564,x44565,x44566))
% 52.62/52.40 [4457]~E(f31(x44571,x44572,x44573),f33(x44574,x44575,x44576))
% 52.62/52.40 [4458]~E(f31(x44581,x44582,x44583),f32(x44584,x44585,x44586))
% 52.62/52.40 [4459]~E(f31(x44591,x44592,x44593),f33(x44594,x44595,x44596))
% 52.62/52.40 [4460]~E(f31(x44601,x44602,x44603),f32(x44604,x44605,x44606))
% 52.62/52.40 [3949]E(f218(x39491,x39492,x39493,x39494,f215(x39491,x39492,x39495,x39496)),f332(f332(x39494,x39495),x39496))
% 52.62/52.40 [3950]E(f219(x39501,x39502,x39503,x39504,f215(x39501,x39502,x39505,x39506)),f332(f332(x39504,x39505),x39506))
% 52.62/52.40 [4213]E(f332(f75(f852(x42131,x42132),x42132,f852(x42133,x42134),f250(x42131,x42132)),f252(x42133,x42131,x42134,x42132,x42135,x42136)),f332(f75(x42134,x42132,f852(x42133,x42134),x42136),f250(x42133,x42134)))
% 52.62/52.40 [4214]E(f332(f75(f852(x42141,x42142),x42141,f852(x42143,x42144),f240(x42141,x42142)),f252(x42143,x42141,x42144,x42142,x42145,x42146)),f332(f75(x42143,x42141,f852(x42143,x42144),x42145),f240(x42143,x42144)))
% 52.62/52.40 [3814]E(f332(f332(f75(x38141,x38142,x38143,x38144),x38145),x38146),f332(x38144,f332(x38145,x38146)))
% 52.62/52.40 [3815]E(f332(f332(f75(x38151,x38152,x38153,x38154),x38155),x38156),f332(x38154,f332(x38155,x38156)))
% 52.62/52.40 [4012]E(f220(x40121,x40122,x40123,x40124,f215(x40121,x40122,x40125,x40126)),f332(f332(f82(a845),f332(f332(f82(a845),f332(x40123,x40125)),f332(x40124,x40126))),f332(a114,f2(a845))))
% 52.62/52.40 [4034]E(f332(f319(x40341,x40342,x40343,x40344,x40345),f332(f304(x40341,x40343),x40346)),f332(x40344,x40346))
% 52.62/52.40 [4035]E(f332(f319(x40351,x40352,x40353,x40354,x40355),f332(f313(x40353,x40351),x40356)),f332(x40355,x40356))
% 52.62/52.40 [4130]E(f320(x41301,x41302,x41303,x41304,x41305,f332(f304(x41301,x41303),x41306)),f332(x41304,x41306))
% 52.62/52.40 [4131]E(f320(x41311,x41312,x41313,x41314,x41315,f332(f313(x41313,x41311),x41316)),f332(x41315,x41316))
% 52.62/52.40 [3611]E(f332(f332(f251(x36111,x36112,x36113),x36114),f332(f332(f241(x36111,x36112),x36115),x36116)),f332(f332(x36114,x36115),x36116))
% 52.62/52.40 [3612]E(f332(f332(f251(x36121,x36122,x36123),x36124),f332(f332(f241(x36121,x36122),x36125),x36126)),f332(f332(x36124,x36125),x36126))
% 52.62/52.40 [3613]E(f332(f332(f251(x36131,x36132,x36133),x36134),f332(f332(f241(x36131,x36132),x36135),x36136)),f332(f332(x36134,x36135),x36136))
% 52.62/52.40 [3676]E(f332(f332(f332(f10(x36761,x36762,x36763),x36764),x36765),x36766),f332(x36764,f332(x36765,x36766)))
% 52.62/52.40 [3677]E(f332(f332(f332(f9(x36771,x36772,x36773),x36774),x36775),x36776),f332(f332(x36774,x36776),x36775))
% 52.62/52.40 [3693]E(f332(f332(f332(f20(x36931,x36932,x36933),x36934),x36935),x36936),f332(f332(x36934,x36936),f332(x36935,x36936)))
% 52.62/52.40 [3717]E(f332(f145(x37171,x37172,x37173,x37174),f332(f332(f140(x37172),x37175),x37176)),f332(f332(x37174,x37175),x37176))
% 52.62/52.40 [3818]E(f332(f332(f140(f852(x38181,x38182)),f332(f332(f241(x38181,x38182),x38183),x38184)),f332(f332(f167(x38181,x38182),x38185),x38186)),f332(f332(f167(x38181,x38182),f332(f332(f140(x38181),x38183),x38185)),f332(f332(f140(x38182),x38184),x38186)))
% 52.62/52.40 [3820]E(f332(f332(f143(x38201,x38202),x38203),f332(f332(f148(x38201,x38204),x38205),x38206)),f332(f332(f148(x38202,f332(f332(f143(x38201,x38202),x38203),x38204)),x38205),f332(x38203,x38206)))
% 52.62/52.40 [3842]E(f332(f332(f249(x38421,x38422,x38423,x38424),x38425),x38426),f332(x38424,f332(f332(f241(x38421,x38422),x38425),x38426)))
% 52.62/52.40 [3843]E(f332(f332(f249(x38431,x38432,x38433,x38434),x38435),x38436),f332(x38434,f332(f332(f241(x38431,x38432),x38435),x38436)))
% 52.62/52.40 [3860]E(f332(f132(x38601,x38602,x38603,x38604),f332(f332(f140(x38602),x38605),x38606)),f332(f132(x38601,x38602,x38603,f332(f332(x38603,x38604),x38605)),x38606))
% 52.62/52.40 [3889]E(f254(x38891,x38892,x38893,x38894,f332(f332(f241(x38891,x38892),x38895),x38896)),f332(f332(x38894,x38895),x38896))
% 52.62/52.40 [3975]E(f332(f332(f47(x39751,f853(x39752,a839)),x39753),f332(f75(x39754,f853(x39752,a839),x39751,x39755),x39756)),f332(f332(f47(x39754,f853(x39752,a839)),f332(f303(x39751,x39754,x39756),x39753)),x39755))
% 52.62/52.40 [4025]E(f332(f332(f143(x40251,x40252),x40253),f332(f332(f143(x40254,x40251),x40255),x40256)),f332(f332(f143(x40254,x40252),f332(f75(x40251,x40252,x40254,x40253),x40255)),x40256))
% 52.62/52.40 [4026]E(f332(f332(f143(x40261,x40262),x40263),f332(f332(f143(x40264,x40261),x40265),x40266)),f332(f332(f143(x40264,x40262),f332(f75(x40261,x40262,x40264,x40263),x40265)),x40266))
% 52.62/52.40 [4027]E(f332(f332(f196(x40271,x40272),x40273),f332(f332(f196(x40274,x40271),x40275),x40276)),f332(f332(f196(x40274,x40272),f332(f75(x40271,x40272,x40274,x40273),x40275)),x40276))
% 52.62/52.40 [4028]E(f332(f332(f196(x40281,x40282),x40283),f332(f332(f196(x40284,x40281),x40285),x40286)),f332(f332(f196(x40284,x40282),f332(f75(x40281,x40282,x40284,x40283),x40285)),x40286))
% 52.62/52.40 [4032]E(f332(f303(x40321,x40322,f332(f75(x40323,x40322,x40321,x40324),x40325)),x40326),f332(f303(x40323,x40322,x40324),f332(f303(x40321,x40323,x40325),x40326)))
% 52.62/52.40 [4033]E(f332(f305(x40331,x40332,f332(f75(x40333,x40332,x40331,x40334),x40335)),x40336),f332(f305(x40331,x40333,x40335),f332(f305(x40333,x40332,x40334),x40336)))
% 52.62/52.40 [4064]E(f170(x40641,x40642,x40643,f332(f332(f332(f74(x40641,f849(x40642)),x40644),x40645),f332(f227(x40642),x40646))),f332(f332(f332(f74(x40641,f849(x40642)),f170(x40641,x40642,x40643,x40644)),x40645),f332(f227(x40642),x40646)))
% 52.62/52.40 [4066]E(f332(f132(x40661,x40662,x40663,f332(f132(x40661,x40662,x40663,x40664),x40665)),x40666),f332(f132(x40661,x40662,x40663,x40664),f332(f332(f125(x40662),x40665),x40666)))
% 52.62/52.40 [4203]E(f332(f252(x42031,x42031,x42032,x42033,f39(x42031),x42034),f332(f332(f241(x42031,x42032),x42035),x42036)),f332(f332(f241(x42031,x42033),x42035),f332(x42034,x42036)))
% 52.62/52.40 [4204]E(f332(f252(x42041,x42042,x42043,x42043,x42044,f39(x42043)),f332(f332(f241(x42041,x42043),x42045),x42046)),f332(f332(f241(x42042,x42043),f332(x42044,x42045)),x42046))
% 52.62/52.40 [4289]E(f332(f332(f143(f852(x42891,x42892),f852(x42891,x42893)),f332(f251(x42891,x42892,f852(x42891,x42893)),f332(f332(f9(x42891,f853(x42892,x42893),f853(x42892,f852(x42891,x42893))),f332(f332(f10(f853(x42893,f852(x42891,x42893)),f853(f853(x42892,x42893),f853(x42892,f852(x42891,x42893))),x42891),f10(x42893,f852(x42891,x42893),x42892)),f241(x42891,x42893))),x42894))),f332(f332(f167(x42891,x42892),x42895),x42896)),f332(f332(f167(x42891,x42893),x42895),f332(f332(f143(x42892,x42893),x42894),x42896)))
% 52.62/52.40 [3681]E(f96(x36811,x36812,x36813,f332(f332(f332(f93(x36811),x36814),x36815),x36816)),f332(f332(f332(x36813,x36814),x36815),x36816))
% 52.62/52.40 [3682]E(f97(x36821,x36822,x36823,f332(f332(f332(f93(x36821),x36824),x36825),x36826)),f332(f332(f332(x36823,x36824),x36825),x36826))
% 52.62/52.40 [3871]E(f332(f332(f75(x38711,x38712,x38713,f332(f18(x38712,x38711),x38714)),x38715),x38716),x38714)
% 52.62/52.40 [3907]E(f332(f303(x39071,x39072,x39073),f332(f303(x39074,x39071,x39075),x39076)),f332(f303(x39074,x39072,f332(f332(f10(x39071,x39072,x39074),x39073),x39075)),x39076))
% 52.62/52.40 [3913]E(f332(f332(f47(x39131,f853(x39132,a839)),f332(f303(x39133,x39131,x39134),x39135)),x39136),f332(f332(f47(x39133,f853(x39132,a839)),x39135),f332(f332(f10(x39131,f853(x39132,a839),x39133),x39136),x39134)))
% 52.62/52.40 [3914]E(f332(f332(f48(x39141,f853(x39142,a839)),f332(f303(x39143,x39141,x39144),x39145)),x39146),f332(f332(f48(x39143,f853(x39142,a839)),x39145),f332(f332(f10(x39141,f853(x39142,a839),x39143),x39146),x39144)))
% 52.62/52.40 [3915]E(f332(f332(f47(x39151,f853(x39152,a839)),x39153),f332(f332(f10(x39154,f853(x39152,a839),x39151),x39155),x39156)),f332(f332(f47(x39154,f853(x39152,a839)),f332(f303(x39151,x39154,x39156),x39153)),x39155))
% 52.62/52.40 [3916]E(f332(f332(f48(x39161,f853(x39162,a839)),x39163),f332(f332(f10(x39164,f853(x39162,a839),x39161),x39165),x39166)),f332(f332(f48(x39164,f853(x39162,a839)),f332(f303(x39161,x39164,x39166),x39163)),x39165))
% 52.62/52.40 [3977]E(f332(f332(f47(x39771,f853(x39772,a839)),x39773),f332(f332(f10(f853(x39774,a839),f853(x39772,a839),x39771),f303(x39774,x39772,x39775)),x39776)),f332(f303(x39774,x39772,x39775),f332(f332(f47(x39771,f853(x39774,a839)),x39773),x39776)))
% 52.62/52.40 [3978]E(f332(f332(f47(x39781,f853(x39782,a839)),x39783),f332(f332(f10(f853(x39784,a839),f853(x39782,a839),x39781),f277(x39784,x39782,x39785)),x39786)),f332(f277(x39784,x39782,x39785),f332(f332(f47(x39781,f853(x39784,a839)),x39783),x39786)))
% 52.62/52.40 [3979]E(f332(f332(f47(x39791,f853(x39792,a839)),x39793),f332(f332(f10(f853(x39794,a839),f853(x39792,a839),x39791),f305(x39792,x39794,x39795)),x39796)),f332(f305(x39792,x39794,x39795),f332(f332(f47(x39791,f853(x39794,a839)),x39793),x39796)))
% 52.62/52.40 [3980]E(f332(f332(f48(x39801,f853(x39802,a839)),x39803),f332(f332(f10(f853(x39804,a839),f853(x39802,a839),x39801),f305(x39802,x39804,x39805)),x39806)),f332(f305(x39802,x39804,x39805),f332(f332(f48(x39801,f853(x39804,a839)),x39803),x39806)))
% 52.62/52.40 [4071]E(f332(f132(x40711,x40712,f332(f9(x40712,x40711,x40711),x40713),x40714),f332(f142(x40712),f332(f332(f140(x40712),x40715),x40716))),f332(f332(x40713,x40715),f332(f132(x40711,x40712,f332(f9(x40712,x40711,x40711),x40713),x40714),f332(f142(x40712),x40716))))
% 52.62/52.40 [4132]E(f332(f332(f20(f852(x41321,x41322),x41322,x41323),f332(f332(f10(x41324,f853(x41322,x41323),f852(x41321,x41322)),x41325),f332(f332(f10(x41321,x41324,f852(x41321,x41322)),x41326),f240(x41321,x41322)))),f250(x41321,x41322)),f332(f251(x41321,x41322,x41323),f332(f332(f10(x41324,f853(x41322,x41323),x41321),x41325),x41326)))
% 52.62/52.40 [4139]E(f332(f132(x41391,x41392,f332(f9(x41392,x41391,x41391),x41393),f332(f132(x41391,x41392,f332(f9(x41392,x41391,x41391),x41393),x41394),f332(f142(x41392),x41395))),f332(f142(x41392),x41396)),f332(f132(x41391,x41392,f332(f9(x41392,x41391,x41391),x41393),x41394),f332(f142(x41392),f332(f332(f125(x41392),x41396),x41395))))
% 52.62/52.40 [4141]E(f332(f332(f143(f852(x41411,x41412),f852(x41413,x41412)),f332(f251(x41411,x41412,f852(x41413,x41412)),f332(f332(f10(x41413,f853(x41412,f852(x41413,x41412)),x41411),f241(x41413,x41412)),x41414))),f332(f332(f167(x41411,x41412),x41415),x41416)),f332(f332(f167(x41413,x41412),f332(f332(f143(x41411,x41413),x41414),x41415)),x41416))
% 52.62/52.40 [4187]P1(f332(f332(f232(f853(x41871,a839)),f332(f277(x41872,x41871,x41873),f332(f332(f48(x41874,f853(x41872,a839)),x41875),x41876))),f332(f332(f48(x41874,f853(x41871,a839)),x41875),f332(f332(f10(f853(x41872,a839),f853(x41871,a839),x41874),f277(x41872,x41871,x41873)),x41876))))
% 52.62/52.40 [3990]E(f332(f332(f167(x39901,x39902),f332(f332(f148(x39901,x39903),x39904),f332(f240(x39901,x39902),x39905))),f332(f332(f148(x39902,x39906),x39904),f332(f250(x39901,x39902),x39905))),f332(f332(f148(f852(x39901,x39902),f332(f332(f167(x39901,x39902),x39903),x39906)),x39904),x39905))
% 52.62/52.40 [4053]E(f332(f332(f103(f853(f852(x40531,x40532),a839)),f332(f332(f281(x40531,x40533,x40532),x40534),x40535)),f332(f332(f281(x40531,x40533,x40532),x40534),x40536)),f332(f332(f281(x40531,x40533,x40532),x40534),f332(f332(f103(f853(f852(x40533,x40532),a839)),x40535),x40536)))
% 52.62/52.40 [4153]E(f332(f332(f302(f852(x41531,x41532)),f332(f332(f241(x41531,x41532),x41533),x41534)),f332(f332(f103(f853(f852(x41531,x41532),a839)),f332(f332(f248(x41531,x41532),x41535),f332(f18(f853(x41532,a839),x41531),f332(f332(f302(x41532),x41534),x41536)))),f332(f332(f248(x41531,x41532),f332(f332(f302(x41531),x41533),x41535)),f332(f18(f853(x41532,a839),x41531),x41536)))),f332(f332(f248(x41531,x41532),f332(f332(f302(x41531),x41533),x41535)),f332(f18(f853(x41532,a839),x41531),f332(f332(f302(x41532),x41534),x41536))))
% 52.62/52.40 [4226]E(f332(f332(f104(f853(x42261,a839)),f332(f305(x42261,x42262,f332(f75(f852(x42262,x42263),x42262,x42261,f240(x42262,x42263)),x42264)),x42265)),f332(f305(x42261,x42263,f332(f75(f852(x42262,x42263),x42263,x42261,f250(x42262,x42263)),x42264)),x42266)),f332(f305(x42261,f852(x42262,x42263),x42264),f332(f332(f248(x42262,x42263),x42265),f332(f18(f853(x42263,a839),x42262),x42266))))
% 52.62/52.40 [3974]E(f332(f332(f332(f74(x39741,x39742),f332(f332(f332(f74(x39741,x39742),x39743),x39744),x39745)),x39744),x39746),f332(f332(f332(f74(x39741,x39742),x39743),x39744),x39746))
% 52.62/52.40 [4077]E(f332(f332(f103(f853(f852(x40771,x40772),a839)),f332(f332(f281(x40771,x40773,x40772),x40774),x40775)),f332(f332(f281(x40771,x40773,x40772),x40776),x40775)),f332(f332(f281(x40771,x40773,x40772),f332(f332(f103(f853(f852(x40771,x40773),a839)),x40774),x40776)),x40775))
% 52.62/52.40 [4099]E(f170(x40991,x40992,f170(x40991,x40992,x40993,x40994),f166(x40991,x40992,f332(f142(f852(x40991,x40992)),f332(f332(f167(x40991,x40992),x40995),x40996)))),f170(x40991,x40992,x40993,f170(x40991,x40992,x40994,f166(x40991,x40992,f332(f142(f852(x40991,x40992)),f332(f332(f167(x40991,x40992),x40995),x40996))))))
% 52.62/52.40 [4208]E(f332(f332(f47(x42081,f853(x42082,a839)),x42083),f332(f332(f9(x42081,f853(x42084,f853(x42082,a839)),f853(x42082,a839)),f332(f332(f10(f853(x42084,a839),f853(f853(x42084,f853(x42082,a839)),f853(x42082,a839)),x42081),f47(x42084,f853(x42082,a839))),x42085)),x42086)),f332(f332(f47(x42084,f853(x42082,a839)),f332(f332(f47(x42081,f853(x42084,a839)),x42083),x42085)),x42086))
% 52.62/52.40 [4209]E(f332(f332(f47(x42091,f853(x42092,a839)),x42093),f332(f332(f9(x42091,f853(x42094,f853(x42092,a839)),f853(x42092,a839)),f332(f332(f10(f853(x42094,a839),f853(f853(x42094,f853(x42092,a839)),f853(x42092,a839)),x42091),f47(x42094,f853(x42092,a839))),x42095)),x42096)),f332(f332(f47(x42094,f853(x42092,a839)),f332(f332(f47(x42091,f853(x42094,a839)),x42093),x42095)),x42096))
% 52.62/52.40 [4210]E(f332(f332(f48(x42101,f853(x42102,a839)),x42103),f332(f332(f9(x42101,f853(x42104,f853(x42102,a839)),f853(x42102,a839)),f332(f332(f10(f853(x42104,a839),f853(f853(x42104,f853(x42102,a839)),f853(x42102,a839)),x42101),f48(x42104,f853(x42102,a839))),x42105)),x42106)),f332(f332(f48(x42104,f853(x42102,a839)),f332(f332(f47(x42101,f853(x42104,a839)),x42103),x42105)),x42106))
% 52.62/52.40 [4211]E(f332(f332(f47(x42111,f853(x42112,a839)),x42113),f332(f332(f9(x42111,f853(x42114,f853(x42112,a839)),f853(x42112,a839)),f332(f332(f10(f853(x42114,a839),f853(f853(x42114,f853(x42112,a839)),f853(x42112,a839)),x42111),f47(x42114,f853(x42112,a839))),x42115)),x42116)),f332(f332(f47(x42114,f853(x42112,a839)),f332(f332(f47(x42111,f853(x42114,a839)),x42113),x42115)),x42116))
% 52.62/52.40 [4212]E(f332(f332(f48(x42121,f853(x42122,a839)),x42123),f332(f332(f9(x42121,f853(x42124,f853(x42122,a839)),f853(x42122,a839)),f332(f332(f10(f853(x42124,a839),f853(f853(x42124,f853(x42122,a839)),f853(x42122,a839)),x42121),f48(x42124,f853(x42122,a839))),x42125)),x42126)),f332(f332(f48(x42124,f853(x42122,a839)),f332(f332(f47(x42121,f853(x42124,a839)),x42123),x42125)),x42126))
% 52.62/52.40 [4261]E(f332(f251(x42611,x42612,f852(x42613,x42614)),f332(f332(f9(x42611,f853(x42612,x42614),f853(x42612,f852(x42613,x42614))),f332(f332(f10(f853(x42614,f852(x42613,x42614)),f853(f853(x42612,x42614),f853(x42612,f852(x42613,x42614))),x42611),f10(x42614,f852(x42613,x42614),x42612)),f332(f332(f10(x42613,f853(x42614,f852(x42613,x42614)),x42611),f241(x42613,x42614)),x42615))),x42616)),f252(x42611,x42613,x42612,x42614,x42615,x42616))
% 52.62/52.40 [4186]E(f332(f332(f332(f74(x41861,f849(x41862)),f172(x41861,x41862,x41863,f332(f332(f3(f853(x41861,a839)),x41864),f332(f332(f302(x41861),x41865),f180(f853(x41861,a839)))))),x41865),x41866),f332(f332(f332(f74(x41861,f849(x41862)),f172(x41861,x41862,x41863,x41864)),x41865),x41866))
% 52.62/52.40 [4284]E(f332(f303(x42841,x42842,f332(f332(f20(x42841,x42842,x42842),f332(f332(f20(x42841,x42842,f853(x42842,x42842)),f332(f332(f10(a839,f853(x42842,f853(x42842,x42842)),x42841),f98(x42842)),x42843)),x42844)),x42845)),x42846),f332(f332(f103(f853(x42842,a839)),f332(f303(x42841,x42842,x42844),f332(f332(f104(f853(x42841,a839)),x42846),f332(f256(x42841),x42843)))),f332(f303(x42841,x42842,x42845),f332(f332(f104(f853(x42841,a839)),x42846),f332(f256(x42841),f332(f332(f10(a839,a839,x42841),a328),x42843))))))
% 52.62/52.40 [4295]E(f332(f303(x42951,f852(x42952,x42953),f332(f332(f20(x42951,x42953,f852(x42952,x42953)),f332(f332(f10(x42952,f853(x42953,f852(x42952,x42953)),x42951),f241(x42952,x42953)),x42954)),x42955)),x42956),f332(f332(f248(x42952,x42953),f332(f303(x42951,x42952,x42954),x42956)),f332(f332(f10(f853(x42951,a839),f853(x42953,a839),x42952),f303(x42951,x42953,x42955)),f332(f332(f9(x42952,f853(x42951,a839),f853(x42951,a839)),f332(f332(f10(f853(x42951,a839),f853(f853(x42951,a839),f853(x42951,a839)),x42952),f104(f853(x42951,a839))),f332(f332(f10(f853(x42952,a839),f853(x42951,a839),x42952),f305(x42951,x42952,x42954)),f332(f332(f9(x42952,f853(x42952,a839),f853(x42952,a839)),f302(x42952)),f180(f853(x42952,a839)))))),x42956))))
% 52.62/52.40 [4244]E(f332(f250(x42441,x42442),f332(f252(x42443,x42441,x42444,x42442,x42445,x42446),x42447)),f332(x42446,f332(f250(x42443,x42444),x42447)))
% 52.62/52.40 [4245]E(f332(f240(x42451,x42452),f332(f252(x42453,x42451,x42454,x42452,x42455,x42456),x42457)),f332(x42455,f332(f240(x42453,x42454),x42457)))
% 52.62/52.40 [3951]E(f332(f332(f167(x39511,x39512),f332(f332(f148(x39511,x39513),x39514),x39515)),f332(f332(f148(x39512,x39516),x39514),x39517)),f332(f332(f148(f852(x39511,x39512),f332(f332(f167(x39511,x39512),x39513),x39516)),x39514),f332(f332(f241(x39511,x39512),x39515),x39517)))
% 52.62/52.40 [4020]E(f332(f332(f332(f253(x40201,x40202,x40203,x40204),x40205),x40206),x40207),f332(f332(f251(x40202,x40203,x40204),x40206),f332(x40205,x40207)))
% 52.62/52.40 [4021]E(f332(f332(f332(f253(x40211,x40212,x40213,x40214),x40215),x40216),x40217),f332(f332(f251(x40212,x40213,x40214),x40216),f332(x40215,x40217)))
% 52.62/52.40 [4031]E(f332(f332(f332(f253(x40311,x40312,x40313,x40314),x40315),x40316),x40317),f332(f332(x40316,f332(f240(x40312,x40313),f332(x40315,x40317))),f332(f250(x40312,x40313),f332(x40315,x40317))))
% 52.62/52.40 [4084]E(f332(f75(x40841,x40842,x40843,x40844),f332(f75(x40845,x40841,x40843,x40846),x40847)),f332(f75(x40845,x40842,x40843,f332(f75(x40841,x40842,x40845,x40844),x40846)),x40847))
% 52.62/52.40 [4148]E(f332(f75(f849(x41481),f849(x41482),x41483,f332(f196(x41481,x41482),x41484)),f332(f332(f332(f74(x41483,f849(x41481)),x41485),x41486),f332(f227(x41481),x41487))),f332(f332(f332(f74(x41483,f849(x41482)),f332(f75(f849(x41481),f849(x41482),x41483,f332(f196(x41481,x41482),x41484)),x41485)),x41486),f332(f227(x41482),f332(x41484,x41487))))
% 52.62/52.40 [4268]E(f332(f252(x42681,x42682,x42683,x42683,x42684,f39(x42683)),f332(f252(x42681,x42681,x42685,x42683,f39(x42681),x42686),x42687)),f332(f332(f241(x42682,x42683),f332(x42684,f332(f240(x42681,x42685),x42687))),f332(x42686,f332(f250(x42681,x42685),x42687))))
% 52.62/52.40 [4269]E(f332(f252(x42691,x42691,x42692,x42693,f39(x42691),x42694),f332(f252(x42695,x42691,x42692,x42692,x42696,f39(x42692)),x42697)),f332(f332(f241(x42691,x42693),f332(x42696,f332(f240(x42695,x42692),x42697))),f332(x42694,f332(f250(x42695,x42692),x42697))))
% 52.62/52.40 [4282]E(f332(f252(x42821,x42822,x42823,x42823,x42824,f39(x42823)),f332(f252(x42825,x42821,x42823,x42823,x42826,f39(x42823)),x42827)),f332(f252(x42825,x42822,x42823,x42823,f332(f75(x42821,x42822,x42825,x42824),x42826),f39(x42823)),x42827))
% 52.62/52.40 [4283]E(f332(f252(x42831,x42831,x42832,x42833,f39(x42831),x42834),f332(f252(x42831,x42831,x42835,x42832,f39(x42831),x42836),x42837)),f332(f252(x42831,x42831,x42835,x42833,f39(x42831),f332(f75(x42832,x42833,x42835,x42834),x42836)),x42837))
% 52.62/52.40 [4292]E(f332(f252(x42921,x42922,x42923,x42923,x42924,f39(x42923)),f332(f252(x42921,x42921,x42925,x42923,f39(x42921),x42926),x42927)),f332(f252(x42922,x42922,x42925,x42923,f39(x42922),x42926),f332(f252(x42921,x42922,x42925,x42925,x42924,f39(x42925)),x42927)))
% 52.62/52.40 [3987]E(f332(f332(f281(x39871,x39872,x39873),f332(f332(f281(x39871,x39874,x39872),x39875),x39876)),x39877),f332(f332(f281(x39871,x39874,x39873),x39875),f332(f332(f281(x39874,x39872,x39873),x39876),x39877)))
% 52.62/52.40 [4059]E(f332(f332(f251(x40591,x40592,x40593),f332(f75(x40594,f853(x40592,x40593),x40591,x40595),x40596)),x40597),f332(f332(x40595,f332(x40596,f332(f240(x40591,x40592),x40597))),f332(f250(x40591,x40592),x40597)))
% 52.62/52.40 [4109]E(f332(f75(x41091,x41092,x41093,x41094),f332(f332(f332(f74(x41093,x41091),x41095),x41096),x41097)),f332(f332(f332(f74(x41093,x41092),f332(f75(x41091,x41092,x41093,x41094),x41095)),x41096),f332(x41094,x41097)))
% 52.62/52.40 [4144]E(f332(f132(x41441,x41442,f332(f9(x41442,x41441,x41441),x41443),x41444),f332(f142(x41442),f332(f332(f143(x41445,x41442),x41446),x41447))),f332(f132(x41441,x41445,f332(f9(x41445,x41441,x41441),f332(f75(x41442,f853(x41441,x41441),x41445,x41443),x41446)),x41444),f332(f142(x41445),x41447)))
% 52.62/52.40 [4149]E(f319(x41491,f849(x41492),x41493,f332(f75(f849(x41494),f849(x41492),x41491,f332(f196(x41494,x41492),x41495)),x41496),f332(f75(f849(x41494),f849(x41492),x41493,f332(f196(x41494,x41492),x41495)),x41497)),f332(f75(f849(x41494),f849(x41492),f854(x41491,x41493),f332(f196(x41494,x41492),x41495)),f319(x41491,f849(x41494),x41493,x41496,x41497)))
% 52.62/52.40 [4085]E(f332(f332(f47(x40851,f853(f852(x40852,x40853),a839)),x40854),f332(f332(f10(f853(f852(x40855,x40853),a839),f853(f852(x40852,x40853),a839),x40851),f332(f281(x40852,x40855,x40853),x40856)),x40857)),f332(f332(f281(x40852,x40855,x40853),x40856),f332(f332(f47(x40851,f853(f852(x40855,x40853),a839)),x40854),x40857)))
% 52.62/52.40 [4120]E(f170(x41201,x41202,f332(f332(f332(f74(x41201,f849(x41202)),x41203),x41204),f332(f227(x41202),x41205)),f166(x41201,x41202,f332(f142(f852(x41201,x41202)),f332(f332(f167(x41201,x41202),x41206),x41207)))),f170(x41201,x41202,x41203,f166(x41201,x41202,f332(f142(f852(x41201,x41202)),f332(f332(f167(x41201,x41202),f332(f332(f140(x41201),x41204),x41206)),f332(f332(f140(x41202),x41205),x41207))))))
% 52.62/52.40 [4231]E(f332(f332(f47(x42311,f853(f852(x42312,x42313),a839)),x42314),f332(f332(f9(x42311,f853(f852(x42315,x42313),a839),f853(f852(x42312,x42313),a839)),f332(f332(f10(f853(f852(x42312,x42315),a839),f853(f853(f852(x42315,x42313),a839),f853(f852(x42312,x42313),a839)),x42311),f281(x42312,x42315,x42313)),x42316)),x42317)),f332(f332(f281(x42312,x42315,x42313),f332(f332(f47(x42311,f853(f852(x42312,x42315),a839)),x42314),x42316)),x42317))
% 52.62/52.40 [4232]E(f332(f132(x42321,x42322,f332(f332(f9(x42321,f853(x42322,x42323),f853(x42322,x42321)),f332(f332(f10(f853(x42323,x42321),f853(f853(x42322,x42323),f853(x42322,x42321)),x42321),f10(x42323,x42321,x42322)),x42324)),x42325),x42326),x42327),f332(f132(x42321,x42323,x42324,x42326),f332(f332(f143(x42322,x42323),x42325),x42327)))
% 52.62/52.40 [4293]E(f332(f332(f48(x42931,f853(x42932,a839)),x42933),f332(f332(f10(f853(x42934,f853(x42932,a839)),f853(x42932,a839),x42931),f332(f48(x42934,f853(x42932,a839)),x42935)),f332(f332(f9(x42931,f853(x42934,f853(x42932,a839)),f853(x42934,f853(x42932,a839))),f332(f332(f10(f853(f853(x42932,a839),f853(x42932,a839)),f853(f853(x42934,f853(x42932,a839)),f853(x42934,f853(x42932,a839))),x42931),f10(f853(x42932,a839),f853(x42932,a839),x42934)),f332(f332(f10(f853(x42932,a839),f853(f853(x42932,a839),f853(x42932,a839)),x42931),f103(f853(x42932,a839))),x42936))),x42937))),f332(f332(f103(f853(x42932,a839)),f332(f332(f48(x42931,f853(x42932,a839)),x42933),x42936)),f332(f332(f48(x42934,f853(x42932,a839)),x42935),x42937)))
% 52.62/52.40 [4294]E(f332(f332(f47(x42941,f853(x42942,a839)),x42943),f332(f332(f10(f853(x42944,f853(x42942,a839)),f853(x42942,a839),x42941),f332(f47(x42944,f853(x42942,a839)),x42945)),f332(f332(f9(x42941,f853(x42944,f853(x42942,a839)),f853(x42944,f853(x42942,a839))),f332(f332(f10(f853(f853(x42942,a839),f853(x42942,a839)),f853(f853(x42944,f853(x42942,a839)),f853(x42944,f853(x42942,a839))),x42941),f10(f853(x42942,a839),f853(x42942,a839),x42944)),f332(f332(f10(f853(x42942,a839),f853(f853(x42942,a839),f853(x42942,a839)),x42941),f104(f853(x42942,a839))),x42946))),x42947))),f332(f332(f104(f853(x42942,a839)),f332(f332(f47(x42941,f853(x42942,a839)),x42943),x42946)),f332(f332(f47(x42944,f853(x42942,a839)),x42945),x42947)))
% 52.62/52.40 [4287]E(f192(x42871,x42872,f332(f332(f332(x42873,x42874),x42875),x42876),f332(f332(f9(x42871,f852(a101,a101),f853(a101,f847(x42872))),f332(f332(f9(x42871,a101,f853(f852(a101,a101),f853(a101,f847(x42872)))),f332(f332(f9(x42871,a101,f853(a101,f853(f852(a101,a101),f853(a101,f847(x42872))))),x42877),x42874)),x42875)),x42876)),f332(f332(f332(f204(x42871,x42872,x42873,x42877),x42874),x42875),x42876))
% 52.62/52.40 [4300]E(f193(x43001,x43002,f332(f332(f332(x43003,x43004),x43005),x43006),f332(f332(f9(x43001,f852(a101,a101),f853(a101,f847(x43002))),f332(f332(f9(x43001,a101,f853(f852(a101,a101),f853(a101,f847(x43002)))),f332(f332(f9(x43001,a101,f853(a101,f853(f852(a101,a101),f853(a101,f847(x43002))))),x43007),x43004)),x43005)),x43006)),f206(x43001,x43002,x43003,x43007,x43004,x43005,x43006))
% 52.62/52.40 [4291]E(f190(x42911,x42912,f332(f332(f332(x42913,x42914),x42915),x42916),f332(f332(f9(x42911,f852(a101,a101),f853(a101,f847(f849(x42912)))),f332(f332(f9(x42911,a101,f853(f852(a101,a101),f853(a101,f847(f849(x42912))))),f332(f332(f9(x42911,a101,f853(a101,f853(f852(a101,a101),f853(a101,f847(f849(x42912)))))),x42917),x42914)),x42915)),x42916)),f332(f332(f332(f200(x42911,x42912,x42913,x42917),x42914),x42915),x42916))
% 52.62/52.40 [4302]E(f191(x43021,x43022,f332(f332(f332(x43023,x43024),x43025),x43026),f332(f332(f9(x43021,f852(a101,a101),f853(a101,f847(f849(x43022)))),f332(f332(f9(x43021,a101,f853(f852(a101,a101),f853(a101,f847(f849(x43022))))),f332(f332(f9(x43021,a101,f853(a101,f853(f852(a101,a101),f853(a101,f847(f849(x43022)))))),x43027),x43024)),x43025)),x43026)),f202(x43021,x43022,x43023,x43027,x43024,x43025,x43026))
% 52.62/52.40 [4205]E(f332(f252(x42051,x42052,x42053,x42054,x42055,x42056),f332(f332(f241(x42051,x42053),x42057),x42058)),f332(f332(f241(x42052,x42054),f332(x42055,x42057)),f332(x42056,x42058)))
% 52.62/52.40 [4304]E(f332(f332(f143(f852(x43041,x43042),f852(x43043,x43044)),f332(f251(x43041,x43042,f852(x43043,x43044)),f332(f332(f9(x43041,f853(x43042,x43044),f853(x43042,f852(x43043,x43044))),f332(f332(f10(f853(x43044,f852(x43043,x43044)),f853(f853(x43042,x43044),f853(x43042,f852(x43043,x43044))),x43041),f10(x43044,f852(x43043,x43044),x43042)),f332(f332(f10(x43043,f853(x43044,f852(x43043,x43044)),x43041),f241(x43043,x43044)),x43045))),x43046))),f332(f332(f167(x43041,x43042),x43047),x43048)),f332(f332(f167(x43043,x43044),f332(f332(f143(x43041,x43043),x43045),x43047)),f332(f332(f143(x43042,x43044),x43046),x43048)))
% 52.62/52.40 [4308]E(f332(f332(f143(f852(x43081,x43082),x43083),f332(f251(x43081,x43082,x43083),f332(f332(f10(f853(x43082,f852(x43081,x43084)),f853(x43082,x43083),x43081),f332(f10(f852(x43081,x43084),x43083,x43082),x43085)),f332(f332(f9(x43081,f853(x43082,x43084),f853(x43082,f852(x43081,x43084))),f332(f332(f10(f853(x43084,f852(x43081,x43084)),f853(f853(x43082,x43084),f853(x43082,f852(x43081,x43084))),x43081),f10(x43084,f852(x43081,x43084),x43082)),f241(x43081,x43084))),x43086)))),f332(f332(f167(x43081,x43082),x43087),x43088)),f332(f332(f143(f852(x43081,x43084),x43083),x43085),f332(f332(f167(x43081,x43084),x43087),f332(f332(f143(x43082,x43084),x43086),x43088))))
% 52.62/52.40 [4236]E(f332(f332(f143(f852(x42361,x42362),x42363),f332(f251(x42361,x42362,x42363),f332(f332(f10(f853(x42362,f852(x42364,x42362)),f853(x42362,x42363),x42361),f332(f10(f852(x42364,x42362),x42363,x42362),x42365)),f332(f332(f10(x42364,f853(x42362,f852(x42364,x42362)),x42361),f241(x42364,x42362)),x42366)))),f332(f332(f167(x42361,x42362),x42367),x42368)),f332(f332(f143(f852(x42364,x42362),x42363),x42365),f332(f332(f167(x42364,x42362),f332(f332(f143(x42361,x42364),x42366),x42367)),x42368)))
% 52.62/52.40 [4196]E(f332(f332(f251(x41961,x41962,x41963),f332(f332(f10(f853(x41962,f852(x41964,x41965)),f853(x41962,x41963),x41961),f332(f10(f852(x41964,x41965),x41963,x41962),f332(f251(x41964,x41965,x41963),x41966))),x41967)),x41968),f332(f332(f251(x41964,x41965,x41963),x41966),f332(f332(f251(x41961,x41962,f852(x41964,x41965)),x41967),x41968)))
% 52.62/52.40 [4309]E(f332(f332(f47(f852(x43091,x43092),f853(f852(x43093,x43094),a839)),f332(f332(f248(x43091,x43092),x43095),f332(f18(f853(x43092,a839),x43091),x43096))),f332(f251(x43091,x43092,f853(f852(x43093,x43094),a839)),f332(f332(f9(x43091,f853(x43092,f853(x43093,f853(x43094,a839))),f853(x43092,f853(f852(x43093,x43094),a839))),f332(f332(f10(f853(f853(x43093,f853(x43094,a839)),f853(f852(x43093,x43094),a839)),f853(f853(x43092,f853(x43093,f853(x43094,a839))),f853(x43092,f853(f852(x43093,x43094),a839))),x43091),f10(f853(x43093,f853(x43094,a839)),f853(f852(x43093,x43094),a839),x43092)),f332(f332(f10(f853(x43093,a839),f853(f853(x43093,f853(x43094,a839)),f853(f852(x43093,x43094),a839)),x43091),f248(x43093,x43094)),x43097))),f332(f332(f10(f853(x43094,a839),f853(x43093,f853(x43094,a839)),x43092),f18(f853(x43094,a839),x43093)),x43098)))),f332(f332(f248(x43093,x43094),f332(f332(f47(x43091,f853(x43093,a839)),x43095),x43097)),f332(f18(f853(x43094,a839),x43093),f332(f332(f47(x43092,f853(x43094,a839)),x43096),x43098))))
% 52.62/52.40 [4339]E(f37(x43391,x43392,x43393,x43394,x43395,x43396,x43397,x43398,x43399,a25),x43392)
% 52.62/52.40 [4340]E(f38(x43401,x43402,x43403,x43404,x43405,x43406,x43407,x43408,x43409,a25),x43402)
% 52.62/52.40 [4250]E(f332(f332(f253(x42501,x42502,x42503,x42504),f332(f332(f253(x42501,x42505,x42506,f852(x42502,x42503)),x42507),x42508)),x42509),f332(f332(f253(x42501,x42505,x42506,x42504),x42507),f332(f332(f9(x42505,f853(x42502,f853(x42503,x42504)),f853(x42506,x42504)),f332(f332(f10(f853(x42506,f852(x42502,x42503)),f853(f853(x42502,f853(x42503,x42504)),f853(x42506,x42504)),x42505),f253(x42506,x42502,x42503,x42504)),x42508)),x42509)))
% 52.62/52.40 [4341]E(f37(x43411,x43412,x43413,x43414,x43415,x43416,x43417,x43418,x43419,f332(a27,x434110)),f332(x43418,x434110))
% 52.62/52.40 [4342]E(f38(x43421,x43422,x43423,x43424,x43425,x43426,x43427,x43428,x43429,f332(a27,x434210)),f332(x43428,x434210))
% 52.62/52.40 [4279]E(f332(f75(f852(x42791,x42792),f852(x42793,x42794),f852(x42795,x42796),f252(x42791,x42793,x42792,x42794,x42797,x42798)),f252(x42795,x42791,x42796,x42792,x42799,x427910)),f252(x42795,x42793,x42796,x42794,f332(f75(x42791,x42793,x42795,x42797),x42799),f332(f75(x42792,x42794,x42796,x42798),x427910)))
% 52.62/52.40 [4280]E(f332(f75(f852(x42801,x42802),f852(x42803,x42804),f852(x42805,x42806),f252(x42801,x42803,x42802,x42804,x42807,x42808)),f252(x42805,x42801,x42806,x42802,x42809,x428010)),f252(x42805,x42803,x42806,x42804,f332(f75(x42801,x42803,x42805,x42807),x42809),f332(f75(x42802,x42804,x42806,x42808),x428010)))
% 52.62/52.40 [4343]E(f37(x43431,x43432,x43433,x43434,x43435,x43436,x43437,x43438,x43439,f36(x434310,x434311)),f332(f332(x43435,x434310),x434311))
% 52.62/52.40 [4344]E(f37(x43441,x43442,x43443,x43444,x43445,x43446,x43447,x43448,x43449,f35(x434410,x434411)),f332(f332(x43447,x434410),x434411))
% 52.62/52.40 [4345]E(f37(x43451,x43452,x43453,x43454,x43455,x43456,x43457,x43458,x43459,f28(x434510,x434511)),f332(f332(x43453,x434510),x434511))
% 52.62/52.40 [4346]E(f38(x43461,x43462,x43463,x43464,x43465,x43466,x43467,x43468,x43469,f28(x434610,x434611)),f332(f332(x43463,x434610),x434611))
% 52.62/52.40 [4352]E(f332(f332(f332(x43521,x43522),x43523),f38(x43524,x43525,x43526,x43527,x43528,x43529,x43521,x435210,x435211,x43523)),f38(x43524,x43525,x43526,x43527,x43528,x43529,x43521,x435210,x435211,f35(x43522,x43523)))
% 52.62/52.40 [4356]E(f332(f332(f332(f332(x43561,x43562),x43563),f38(x43564,x43565,x43566,x43567,x43561,x43568,x43569,x435610,x435611,x43562)),f38(x43564,x43565,x43566,x43567,x43561,x43568,x43569,x435610,x435611,x43563)),f38(x43564,x43565,x43566,x43567,x43561,x43568,x43569,x435610,x435611,f36(x43562,x43563)))
% 52.62/52.40 [4285]E(f332(f252(x42851,x42852,x42853,x42854,x42855,x42856),f332(f252(x42857,x42851,x42858,x42853,x42859,x428510),x428511)),f332(f252(x42857,x42852,x42858,x42854,f332(f75(x42851,x42852,x42857,x42855),x42859),f332(f75(x42853,x42854,x42858,x42856),x428510)),x428511))
% 52.62/52.40 [4353]E(f332(f332(f332(f332(x43531,x43532),x43533),x43534),f38(x43535,x43536,x43537,x43531,x43538,x43539,x435310,x435311,x435312,x43534)),f38(x43535,x43536,x43537,x43531,x43538,x43539,x435310,x435311,x435312,f32(x43532,x43533,x43534)))
% 52.62/52.40 [4357]E(f332(f332(f332(f332(f332(x43571,x43572),x43573),x43574),f38(x43575,x43576,x43577,x43578,x43579,x43571,x435710,x435711,x435712,x43573)),f38(x43575,x43576,x43577,x43578,x43579,x43571,x435710,x435711,x435712,x43574)),f38(x43575,x43576,x43577,x43578,x43579,x43571,x435710,x435711,x435712,f33(x43572,x43573,x43574)))
% 52.62/52.40 [4347]E(f37(x43471,x43472,x43473,x43474,x43475,x43476,x43477,x43478,x43479,f33(x434710,x434711,x434712)),f332(f332(f332(x43476,x434710),x434711),x434712))
% 52.62/52.40 [4348]E(f37(x43481,x43482,x43483,x43484,x43485,x43486,x43487,x43488,x43489,f32(x434810,x434811,x434812)),f332(f332(f332(x43484,x434810),x434811),x434812))
% 52.62/52.40 [4349]E(f37(x43491,x43492,x43493,x43494,x43495,x43496,x43497,x43498,x43499,f31(x434910,x434911,x434912)),f332(f332(f332(x43499,x434910),x434911),x434912))
% 52.62/52.40 [4350]E(f38(x43501,x43502,x43503,x43504,x43505,x43506,x43507,x43508,x43509,f31(x435010,x435011,x435012)),f332(f332(f332(x43509,x435010),x435011),x435012))
% 52.62/52.40 [6361]P15(a500)+P1(f332(f332(f334(f852(a841,a840)),a695),f332(f158(f852(a841,a840)),a29)))
% 52.62/52.40 [8402]P15(a500)+~P1(f332(f332(f251(a841,a840,a839),f332(f18(f853(a840,a839),a841),a26)),a695))
% 52.62/52.40 [4487]~P61(x44871)+P61(f849(x44871))
% 52.62/52.40 [4489]~P138(x44891)+~E(f80(x44891),f2(x44891))
% 52.62/52.40 [4490]~P138(x44901)+~E(f80(x44901),f2(x44901))
% 52.62/52.40 [4492]~E(x44921,f2(a101))+E(f332(a23,x44921),f2(a1))
% 52.62/52.40 [4493]~E(x44931,f2(a1))+E(f84(a1,x44931),f2(a1))
% 52.62/52.40 [4499]~P2(x44991)+P35(x44991,f2(x44991))
% 52.62/52.40 [4500]~P100(x45001)+P20(x45001,f115(x45001))
% 52.62/52.40 [4501]~P100(x45011)+P20(x45011,f115(x45011))
% 52.62/52.40 [4510]P1(x45101)+P1(f332(a328,x45101))
% 52.62/52.40 [4551]~P2(x45511)+~P35(x45511,f80(x45511))
% 52.62/52.40 [4595]~P1(x45951)+~P1(f332(a328,x45951))
% 52.62/52.40 [4618]E(f332(a107,x46181),f2(a845))+~P1(f332(a186,x46181))
% 52.62/52.40 [4678]~P91(x46781)+P21(x46781,x46781,f83(x46781))
% 52.62/52.40 [4679]~P100(x46791)+P21(x46791,x46791,f236(x46791))
% 52.62/52.40 [4680]~P100(x46801)+P21(x46801,x46801,f179(x46801))
% 52.62/52.40 [4681]~P92(x46811)+P21(x46811,x46811,f103(x46811))
% 52.62/52.40 [4682]~P98(x46821)+P21(x46821,x46821,f104(x46821))
% 52.62/52.40 [4683]~P66(x46831)+P22(x46831,x46831,f83(x46831))
% 52.62/52.40 [4497]E(x44971,f2(a845))+E(f332(a114,f491(x44971)),x44971)
% 52.62/52.40 [4498]~E(x44981,f2(a845))+E(f332(f102(a1),x44981),f2(a1))
% 52.62/52.40 [4503]~P88(x45031)+E(f332(f106(x45031),a85),f2(x45031))
% 52.62/52.40 [4504]~P88(x45041)+E(f332(f106(x45041),a85),f2(x45041))
% 52.62/52.40 [4506]~E(f600(x45061),f2(a845))+E(f332(f154(a845),x45061),f2(a845))
% 52.62/52.40 [4507]~P102(x45071)+E(f234(x45071,f232(x45071)),f236(x45071))
% 52.62/52.40 [4508]~P102(x45081)+E(f235(x45081,f232(x45081)),f179(x45081))
% 52.62/52.40 [4509]~P83(x45091)+E(f84(x45091,f2(x45091)),f2(x45091))
% 52.62/52.40 [4516]~P2(x45161)+E(f332(f102(x45161),f2(a845)),f2(x45161))
% 52.62/52.40 [4517]~P2(x45171)+E(f332(f102(x45171),f80(a845)),f80(x45171))
% 52.62/52.40 [4518]~P133(x45181)+E(f332(f105(x45181),f2(a1)),f2(x45181))
% 52.62/52.40 [4519]~P133(x45191)+E(f332(f105(x45191),f80(a1)),f80(x45191))
% 52.62/52.40 [4520]E(x45201,f2(a845))+~E(f332(f102(a1),x45201),f2(a1))
% 52.62/52.40 [4545]~P69(x45451)+E(f332(f81(x45451),f2(x45451)),f2(x45451))
% 52.62/52.40 [4546]~P90(x45461)+E(f332(f81(x45461),f239(x45461)),f180(x45461))
% 52.62/52.40 [4547]~P90(x45471)+E(f332(f81(x45471),f180(x45471)),f239(x45471))
% 52.62/52.40 [4548]~P80(x45481)+E(f332(f77(x45481),f2(x45481)),f2(x45481))
% 52.62/52.40 [4549]~P110(x45491)+E(f332(f77(x45491),f80(x45491)),f80(x45491))
% 52.62/52.40 [4550]~P3(x45501)+E(f332(f154(x45501),f115(x45501)),f2(x45501))
% 52.62/52.40 [4571]~P37(x45711)+P40(f332(f158(a1),x45711))
% 52.62/52.40 [4599]~P88(x45991)+E(f332(f81(x45991),f80(x45991)),f332(f106(x45991),a99))
% 52.62/52.40 [4600]~P88(x46001)+E(f332(f81(x46001),f80(x46001)),f332(f106(x46001),a99))
% 52.62/52.40 [4617]~P88(x46171)+P35(x46171,f332(f106(x46171),a85))
% 52.62/52.40 [4642]P37(x46421)+~P40(f332(f158(a1),x46421))
% 52.62/52.40 [4684]E(f332(f102(a1),f332(a107,x46841)),x46841)+P1(f332(a186,x46841))
% 52.62/52.40 [4750]~P105(x47501)+E(f243(x47501,f80(x47501),f83(x47501)),f242(x47501))
% 52.62/52.40 [4778]~P88(x47781)+~P35(x47781,f332(f106(x47781),a99))
% 52.62/52.40 [4788]E(f332(a30,x47881),f183(a840))+P1(f332(a26,f332(a27,x47881)))
% 52.62/52.40 [4865]~E(x48651,f2(a845))+P1(f332(f332(f232(a845),x48651),f2(a845)))
% 52.62/52.40 [4866]~E(x48661,f80(a845))+P1(f332(f332(f279(a845),x48661),f80(a845)))
% 52.62/52.40 [4918]E(f332(f77(a1),x49181),x49181)+P1(f332(f332(f233(a1),x49181),f2(a1)))
% 52.62/52.40 [4938]~E(f332(a107,x49381),f2(a845))+P1(f332(f332(f232(a1),x49381),f2(a1)))
% 52.62/52.40 [4973]~E(f332(f77(a1),x49731),f80(a1))+P1(f332(f332(f279(a1),x49731),f80(a1)))
% 52.62/52.40 [5003]~P1(f332(a186,x50031))+P1(f332(f332(f233(a1),x50031),f2(a1)))
% 52.62/52.40 [5043]~P2(x50431)+P1(f332(f332(f334(x50431),f2(x50431)),f176(x50431)))
% 52.62/52.40 [5044]~P133(x50441)+P1(f332(f332(f334(x50441),f2(x50441)),f112(x50441)))
% 52.62/52.40 [5045]~P2(x50451)+P1(f332(f332(f334(x50451),f80(x50451)),f176(x50451)))
% 52.62/52.40 [5046]~P133(x50461)+P1(f332(f332(f334(x50461),f80(x50461)),f112(x50461)))
% 52.62/52.40 [5047]~P117(x50471)+P1(f332(f332(f233(x50471),f2(x50471)),f80(x50471)))
% 52.62/52.40 [5048]~P117(x50481)+P1(f332(f332(f232(x50481),f2(x50481)),f80(x50481)))
% 52.62/52.40 [5051]E(f332(f227(a840),f492(x50511)),f332(a30,x50511))+~P1(f332(a26,f332(a27,x50511)))
% 52.62/52.40 [5052]E(f332(f227(a840),f556(x50521)),f332(a30,x50521))+~P1(f332(a26,f332(a27,x50521)))
% 52.62/52.40 [5102]E(x51021,f2(a845))+~P1(f332(f332(f232(a845),x51021),f2(a845)))
% 52.62/52.40 [5103]E(x51031,f80(a845))+~P1(f332(f332(f279(a845),x51031),f80(a845)))
% 52.62/52.40 [5145]E(f332(a107,x51451),f2(a845))+~P1(f332(f332(f232(a1),x51451),f2(a1)))
% 52.62/52.40 [5146]E(f332(a107,x51461),f2(a845))+~P1(f332(f332(f232(a1),x51461),f2(a1)))
% 52.62/52.40 [5174]E(f332(f77(a1),x51741),f80(a1))+~P1(f332(f332(f279(a1),x51741),f80(a1)))
% 52.62/52.40 [5201]P1(f332(a186,x52011))+~P1(f332(f332(f233(a1),x52011),f2(a1)))
% 52.62/52.40 [5206]~P100(x52061)+P22(x52061,f846(x52061),f138(x52061,x52061,f7(x52061)))
% 52.62/52.40 [5224]P40(x52241)+~P1(f332(f332(f232(a1),f2(a1)),f338(x52241)))
% 52.62/52.40 [5230]E(f332(f77(a1),x52301),f332(f81(a1),x52301))+~P1(f332(f332(f233(a1),x52301),f2(a1)))
% 52.62/52.40 [5399]~P117(x53991)+~P1(f332(f332(f233(x53991),f80(x53991)),f2(x53991)))
% 52.62/52.40 [5400]~P117(x54001)+~P1(f332(f332(f232(x54001),f80(x54001)),f2(x54001)))
% 52.62/52.40 [5412]~E(x54121,f2(a1))+P1(f332(f332(f233(a1),f332(f77(a1),x54121)),f80(a1)))
% 52.62/52.40 [5413]~E(x54131,f2(a845))+P1(f332(f332(f232(a1),f332(f102(a1),x54131)),f2(a1)))
% 52.62/52.40 [5527]~P3(x55271)+E(f132(x55271,x55271,f82(x55271),f2(x55271)),f154(x55271))
% 52.62/52.40 [5702]~P86(x57021)+P31(a845,x57021,f102(x57021),f239(f853(a845,a839)))
% 52.62/52.40 [5899]E(x58991,f2(a845))+~P1(f332(f332(f232(a1),f332(f102(a1),x58991)),f2(a1)))
% 52.62/52.40 [5900]E(x59001,f2(a1))+~P1(f332(f332(f233(a1),f332(f77(a1),x59001)),f80(a1)))
% 52.62/52.40 [6733]~P1(f332(f332(f233(a1),x67331),f2(a1)))+P1(f332(f332(f233(a1),f332(f332(f82(a1),x67331),x67331)),f2(a1)))
% 52.62/52.40 [7307]P1(f332(f332(f233(a1),x73071),f2(a1)))+~P1(f332(f332(f233(a1),f332(f332(f82(a1),x73071),x73071)),f2(a1)))
% 52.62/52.40 [7872]E(x78721,f332(a5,f2(a845)))+P1(f332(f332(f233(a845),f332(f332(f3(a845),f332(a22,x78721)),f332(a114,f2(a845)))),f332(a22,x78721)))
% 52.62/52.40 [8614]~P1(f332(f332(f233(a1),x86141),f2(a1)))+P1(f332(f332(f233(a1),f332(f332(f3(a1),f332(f332(f82(a1),x86141),x86141)),a99)),f2(a1)))
% 52.62/52.40 [8698]~P1(f332(f332(f233(a1),x86981),f2(a1)))+P1(f332(f332(f233(a1),f332(f332(f82(a1),f332(f332(f82(a1),f80(a1)),x86981)),x86981)),f2(a1)))
% 52.62/52.40 [8982]P1(f332(f332(f233(a1),x89821),f2(a1)))+~P1(f332(f332(f233(a1),f332(f332(f3(a1),f332(f332(f82(a1),x89821),x89821)),a99)),f2(a1)))
% 52.62/52.40 [9046]P1(f332(f332(f233(a1),x90461),f2(a1)))+~P1(f332(f332(f233(a1),f332(f332(f82(a1),f332(f332(f82(a1),f80(a1)),x90461)),x90461)),f2(a1)))
% 52.62/52.40 [4588]~E(a85,x45881)+E(f332(f332(f82(a1),x45881),x45881),a85)
% 52.62/52.40 [4589]~E(x45891,a85)+E(f332(f332(f82(a1),x45891),x45891),a85)
% 52.62/52.40 [4603]E(x46031,f2(a1))+E(f332(f332(f44(a1),x46031),x46031),f80(a1))
% 52.62/52.40 [4728]E(x47281,a85)+~E(f332(f332(f82(a1),x47281),x47281),a85)
% 52.62/52.40 [4729]E(a85,x47291)+~E(f332(f332(f82(a1),x47291),x47291),a85)
% 52.62/52.40 [4730]~P88(x47301)+E(f332(f105(x47301),f332(f106(a1),a99)),f332(f106(x47301),a99))
% 52.62/52.40 [4740]~P11(x47401)+E(f46(x47401,f239(f853(x47401,a839))),f180(x47401))
% 52.62/52.40 [4741]~P11(x47411)+E(f46(x47411,f180(f853(x47411,a839))),f239(x47411))
% 52.62/52.40 [4742]~P11(x47421)+E(f45(x47421,f239(f853(x47421,a839))),f239(x47421))
% 52.62/52.40 [4743]~P11(x47431)+E(f45(x47431,f180(f853(x47431,a839))),f180(x47431))
% 52.62/52.40 [4744]~P100(x47441)+E(f130(x47441,f180(f853(x47441,a839))),f115(x47441))
% 52.62/52.40 [4877]E(x48771,f2(a845))+P1(f332(f332(f233(a845),f2(a845)),x48771))
% 52.62/52.40 [4878]E(x48781,f2(a845))+P1(f332(f332(f233(a845),f2(a845)),x48781))
% 52.62/52.40 [4898]~P12(x48981)+P1(f332(f332(f232(a1),f2(a1)),x48981))
% 52.62/52.40 [4928]~E(f332(f106(a845),x49281),f2(a845))+P1(f332(f332(f232(a1),x49281),a85))
% 52.62/52.40 [4929]~E(f332(f106(a845),x49291),f2(a845))+P1(f332(f332(f232(a1),x49291),a85))
% 52.62/52.40 [4934]P40(x49341)+P1(f332(f332(f334(a1),f338(x49341)),x49341))
% 52.62/52.40 [4935]E(x49351,f332(a5,f2(a845)))+P1(f332(f332(f232(a101),f80(a101)),x49351))
% 52.62/52.40 [4978]P1(f332(a186,x49781))+P1(f332(f332(f232(a1),f2(a1)),x49781))
% 52.62/52.40 [5025]E(f332(f102(a1),f332(a107,x50251)),f2(a1))+P1(f332(f332(f232(a1),f2(a1)),x50251))
% 52.62/52.40 [5077]~P61(x50771)+P1(f332(f64(x50771),f239(f853(x50771,a839))))
% 52.62/52.40 [5090]E(f332(f102(a1),f332(f106(a845),x50901)),f332(f106(a1),x50901))+P1(f332(a186,f332(f106(a1),x50901)))
% 52.62/52.40 [5092]~E(x50921,f2(a845))+P1(f332(f332(f233(a845),x50921),f332(a114,f2(a845))))
% 52.62/52.40 [5109]E(f332(f106(a845),x51091),f2(a845))+~P1(f332(f332(f232(a1),x51091),a85))
% 52.62/52.40 [5110]E(f332(f106(a845),x51101),f2(a845))+~P1(f332(a186,f332(f106(a1),x51101)))
% 52.62/52.40 [5111]E(f332(f106(a845),x51111),f2(a845))+~P1(f332(f332(f232(a1),x51111),a85))
% 52.62/52.40 [5143]P12(x51431)+~P1(f332(f332(f232(a1),f2(a1)),x51431))
% 52.62/52.40 [5161]~E(x51611,f2(a845))+~P1(f332(f332(f233(a845),f2(a845)),x51611))
% 52.62/52.40 [5184]~E(x51841,f332(a114,f2(a845)))+P1(f332(f332(f279(a845),x51841),f332(a114,f2(a845))))
% 52.62/52.40 [5209]E(f332(a114,f525(x52091)),x52091)+~P1(f332(f332(f233(a845),f2(a845)),x52091))
% 52.62/52.40 [5210]E(f332(a114,f617(x52101)),x52101)+~P1(f332(f332(f233(a845),f2(a845)),x52101))
% 52.62/52.40 [5218]E(f332(a114,f332(f106(a845),x52181)),f80(a845))+~P1(f332(a186,f332(f106(a1),x52181)))
% 52.62/52.40 [5226]E(f332(f102(a1),f636(x52261)),x52261)+~P1(f332(f332(f233(a1),f2(a1)),x52261))
% 52.62/52.40 [5233]~E(x52331,f332(a5,f2(a845)))+~P1(f332(f332(f232(a101),f80(a101)),x52331))
% 52.62/52.40 [5240]E(f332(f102(a1),f332(f106(a845),x52401)),f2(a1))+~P1(f332(a186,f332(f106(a1),x52401)))
% 52.62/52.40 [5264]E(f332(f154(a845),x52641),f2(a845))+P1(f332(f332(f334(a845),f600(x52641)),f332(f158(a845),x52641)))
% 52.62/52.40 [5283]E(f332(f102(a1),f332(a107,x52831)),x52831)+~P1(f332(f332(f232(a1),f2(a1)),x52831))
% 52.62/52.40 [5284]E(f332(f102(a1),f332(a107,x52841)),x52841)+~P1(f332(f332(f232(a1),f2(a1)),x52841))
% 52.62/52.40 [5293]~P1(f332(a186,x52931))+~P1(f332(f332(f232(a1),f2(a1)),x52931))
% 52.62/52.40 [5392]E(f332(f332(f82(a845),f80(a845)),f332(f106(a845),x53921)),f80(a845))+~P1(f332(f332(f233(a1),x53921),a85))
% 52.62/52.40 [5449]E(x54491,f2(a845))+~P1(f332(f332(f233(a845),x54491),f332(a114,f2(a845))))
% 52.62/52.40 [5470]E(x54701,f332(a114,f2(a845)))+~P1(f332(f332(f279(a845),x54701),f332(a114,f2(a845))))
% 52.62/52.40 [5488]E(f332(f332(f82(a845),f332(f106(a845),x54881)),f80(a845)),f80(a845))+~P1(f332(f332(f233(a1),x54881),a85))
% 52.62/52.40 [5489]E(f332(f332(f3(a845),f332(f106(a845),x54891)),f80(a845)),f2(a845))+~P1(f332(f332(f232(a1),x54891),a85))
% 52.62/52.40 [5499]~P40(x54991)+E(f332(f43(a845),f332(f303(a1,a845,a107),x54991)),f332(f43(a1),x54991))
% 52.62/52.40 [5528]~P100(x55281)+E(f234(x55281,f332(f9(x55281,x55281,a839),f232(x55281))),f179(x55281))
% 52.62/52.40 [5529]~P100(x55291)+E(f235(x55291,f332(f9(x55291,x55291,a839),f232(x55291))),f236(x55291))
% 52.62/52.40 [5538]E(f53(a845,f332(a114,f2(a845)),f332(f106(a845),x55381)),f332(a114,f2(a845)))+~P1(f332(a186,f332(f106(a1),x55381)))
% 52.62/52.40 [5546]P1(f332(f332(f233(a1),f2(a1)),x55461))+~P1(f332(f332(f232(a1),f80(a1)),x55461))
% 52.62/52.40 [5547]~P1(f332(f332(f233(a1),f2(a1)),x55471))+P1(f332(f332(f232(a1),f80(a1)),x55471))
% 52.62/52.40 [5556]E(f332(a114,f332(f332(f3(a845),x55561),f80(a845))),x55561)+~P1(f332(f332(f233(a845),f2(a845)),x55561))
% 52.62/52.40 [5557]E(f332(a114,f332(f332(f3(a845),x55571),f80(a845))),x55571)+~P1(f332(f332(f233(a845),f2(a845)),x55571))
% 52.62/52.40 [5615]P1(f332(f332(f233(a845),f2(a845)),f636(x56151)))+~P1(f332(f332(f233(a1),f2(a1)),x56151))
% 52.62/52.40 [5672]E(f53(a1,f332(f106(a1),a99),x56721),f332(f332(f3(a1),x56721),f80(a1)))+~P1(f332(f332(f233(a1),f2(a1)),x56721))
% 52.62/52.40 [5717]~P1(f332(f332(f233(a1),a85),x57171))+P1(f332(f332(f233(a845),f2(a845)),f332(f106(a845),x57171)))
% 52.62/52.40 [5771]P1(f332(f332(f233(a845),f2(a845)),f332(a107,x57711)))+~P1(f332(f332(f233(a1),f2(a1)),x57711))
% 52.62/52.40 [5793]E(f332(a22,f332(a5,x57931)),x57931)+~P1(f332(f332(f334(a845),x57931),f239(f853(a845,a839))))
% 52.62/52.40 [5818]~P1(f332(f332(f233(a845),f2(a845)),x58181))+P1(f332(f332(f233(a1),f2(a1)),f332(f102(a1),x58181)))
% 52.62/52.40 [5853]~P1(f332(f332(f233(a845),f2(a845)),f332(a107,x58531)))+P1(f332(f332(f233(a1),f2(a1)),x58531))
% 52.62/52.40 [5868]~P40(x58681)+E(f332(f303(a845,a1,f102(a1)),f332(f303(a1,a845,a107),x58681)),x58681)
% 52.62/52.40 [5879]P1(f332(f332(f233(a1),a85),x58791))+~P1(f332(f332(f233(a845),f2(a845)),f332(f106(a845),x58791)))
% 52.62/52.40 [5942]P1(f332(f332(f233(a845),f2(a845)),x59421))+~P1(f332(f332(f233(a1),f2(a1)),f332(f102(a1),x59421)))
% 52.62/52.40 [5974]E(f164(x59741,f115(f846(x59741))),f115(f846(x59741)))+~P1(f332(f321(f846(f846(x59741)),f165(x59741)),f115(f846(x59741))))
% 52.62/52.40 [6058]E(f332(f303(a845,a1,f102(a1)),f332(f257(a845),f332(a107,x60581))),f332(f294(a1,f2(a1)),x60581))+~P1(f332(f332(f232(a1),f2(a1)),x60581))
% 52.62/52.40 [6074]~P117(x60741)+P1(f332(f332(f233(x60741),f2(x60741)),f332(f332(f82(x60741),f80(x60741)),f80(x60741))))
% 52.62/52.40 [6127]P1(f332(f332(f233(a845),f332(a114,f2(a845))),f332(a107,x61271)))+~P1(f332(f332(f233(a1),f80(a1)),x61271))
% 52.62/52.40 [6224]E(x62241,f2(a1))+P1(f332(f57(f2(a1),x62241),f332(f332(f241(a1,a1),f2(a1)),f2(a1))))
% 52.62/52.40 [6404]~P1(f332(f332(f233(a845),f332(a114,f2(a845))),f332(a107,x64041)))+P1(f332(f332(f233(a1),f80(a1)),x64041))
% 52.62/52.40 [6455]E(f332(a114,f332(f332(f3(a845),f332(f106(a845),x64551)),f80(a845))),f332(f106(a845),x64551))+~P1(f332(f332(f233(a845),f2(a845)),f332(f106(a845),x64551)))
% 52.62/52.40 [6854]~P107(x68541)+P38(x68541,f332(f256(f852(x68541,x68541)),f332(f251(x68541,x68541,a839),f233(x68541))))
% 52.62/52.40 [5108]~P37(x51081)+E(f129(f332(f332(f143(a1,a845),a107),x51081)),x51081)
% 52.62/52.40 [5439]E(f332(f106(a845),f332(f332(f3(a1),x54391),a99)),f332(a114,f332(f106(a845),x54391)))+P1(f332(a186,f332(f106(a1),x54391)))
% 52.62/52.40 [5464]P33(a838,a858,x54641)+~P1(f332(f332(f334(f844(a838)),x54641),a855))
% 52.62/52.40 [5563]E(f332(f81(a1),f332(f102(a1),f332(a114,f683(x55631)))),x55631)+~P1(f332(f332(f233(a1),x55631),f2(a1)))
% 52.62/52.40 [5573]E(f332(f332(f82(a845),f80(a845)),f332(f106(a845),x55731)),f332(f106(a845),f332(f332(f3(a1),x55731),a99)))+P1(f332(f332(f233(a1),x55731),a85))
% 52.62/52.40 [5617]E(f332(f332(f44(a1),f332(f106(a1),a99)),x56171),f332(f106(a1),a99))+~P1(f332(f332(f233(a1),f2(a1)),x56171))
% 52.62/52.40 [5713]E(f332(f332(f82(a845),f332(f106(a845),x57131)),f80(a845)),f332(f106(a845),f332(f332(f3(a1),x57131),a99)))+P1(f332(f332(f233(a1),x57131),a85))
% 52.62/52.40 [5714]E(f332(f332(f3(a845),f332(f106(a845),x57141)),f80(a845)),f332(f106(a845),f332(f332(f82(a1),x57141),a99)))+P1(f332(f332(f232(a1),x57141),a85))
% 52.62/52.40 [5757]E(f332(a107,f332(f332(f82(a1),f80(a1)),x57571)),f332(a114,f332(a107,x57571)))+~P1(f332(f332(f232(a1),f2(a1)),x57571))
% 52.62/52.40 [5795]E(f332(a114,f332(f332(f3(a845),x57951),f332(a114,f2(a845)))),x57951)+~P1(f332(f332(f233(a845),f2(a845)),x57951))
% 52.62/52.40 [6003]E(f53(a845,f332(a114,f2(a845)),f332(f106(a845),x60031)),f332(a107,f53(a1,f80(a1),f332(f106(a1),x60031))))+P1(f332(a186,f332(f106(a1),x60031)))
% 52.62/52.40 [6049]~P1(f332(f332(f233(a1),a99),x60491))+P1(f332(f332(f233(a1),a99),f332(f332(f82(a1),x60491),x60491)))
% 52.62/52.40 [6050]~P1(f332(f332(f233(a1),a85),x60501))+P1(f332(f332(f233(a1),a85),f332(f332(f82(a1),x60501),x60501)))
% 52.62/52.40 [6051]~P1(f332(f332(f233(a1),a99),x60511))+P1(f332(f332(f232(a1),a99),f332(f332(f82(a1),x60511),x60511)))
% 52.62/52.40 [6052]~P1(f332(f332(f232(a1),a85),x60521))+P1(f332(f332(f232(a1),a85),f332(f332(f82(a1),x60521),x60521)))
% 52.62/52.40 [6238]~P1(f332(f64(x62381),f239(f853(x62381,a839))))+P1(f332(f64(f849(x62381)),f239(f853(f849(x62381),a839))))
% 52.62/52.40 [6329]~P1(f332(f332(f232(a1),f2(a1)),x63291))+P1(f332(f332(f233(a1),f2(a1)),f332(f332(f82(a1),f80(a1)),x63291)))
% 52.62/52.40 [6335]E(f332(f240(a1,a1),f55(f80(a1),f332(f106(a1),x63351))),f332(f332(f44(a1),f80(a1)),f332(f106(a1),x63351)))+~P1(f332(f332(f232(a1),f2(a1)),f332(f106(a1),x63351)))
% 52.62/52.40 [6360]E(f332(f250(a1,a1),f55(f80(a1),f332(f106(a1),x63601))),f53(a1,f80(a1),f332(f106(a1),x63601)))+~P1(f332(f332(f232(a1),f2(a1)),f332(f106(a1),x63601)))
% 52.62/52.40 [6373]P1(f332(f64(x63731),f239(f853(x63731,a839))))+~P1(f332(f64(f849(x63731)),f239(f853(f849(x63731),a839))))
% 52.62/52.40 [6405]P1(f332(f332(f233(a1),a99),x64051))+~P1(f332(f332(f233(a1),a99),f332(f332(f82(a1),x64051),x64051)))
% 52.62/52.40 [6406]P1(f332(f332(f233(a1),a99),x64061))+~P1(f332(f332(f232(a1),a99),f332(f332(f82(a1),x64061),x64061)))
% 52.62/52.40 [6407]P1(f332(f332(f233(a1),a85),x64071))+~P1(f332(f332(f233(a1),a85),f332(f332(f82(a1),x64071),x64071)))
% 52.62/52.40 [6408]P1(f332(f332(f232(a1),a85),x64081))+~P1(f332(f332(f232(a1),a85),f332(f332(f82(a1),x64081),x64081)))
% 52.62/52.40 [6603]~P1(f332(f64(a845),x66031))+P1(f332(f64(a1),f332(f303(a845,a1,f102(a1)),x66031)))
% 52.62/52.40 [6738]~P1(f332(f64(x67381),f239(f853(x67381,a839))))+P1(f332(f332(f233(a845),f2(a845)),f332(f43(x67381),f239(f853(x67381,a839)))))
% 52.62/52.40 [7352]P1(f332(f64(a845),x73521))+~P1(f332(f64(a1),f332(f303(a845,a1,f102(a1)),x73521)))
% 52.62/52.40 [5367]~E(a99,x53671)+E(f332(f332(f3(a1),f332(f332(f82(a1),x53671),x53671)),a99),a99)
% 52.62/52.40 [5368]~E(x53681,a99)+E(f332(f332(f3(a1),f332(f332(f82(a1),x53681),x53681)),a99),a99)
% 52.62/52.40 [5873]E(x58731,a99)+~E(f332(f332(f3(a1),f332(f332(f82(a1),x58731),x58731)),a99),a99)
% 52.62/52.40 [5874]E(a99,x58741)+~E(f332(f332(f3(a1),f332(f332(f82(a1),x58741),x58741)),a99),a99)
% 52.62/52.40 [6298]~E(f332(f106(a845),x62981),f2(a845))+P1(f332(a186,f332(f106(a1),f332(f332(f82(a1),x62981),a99))))
% 52.62/52.40 [6663]~P1(f332(a186,f332(f106(a1),x66631)))+P1(f332(a186,f332(f106(a1),f332(f332(f82(a1),x66631),x66631))))
% 52.62/52.40 [6664]~P1(f332(f332(f232(a1),x66641),a99))+P1(f332(f332(f233(a1),f332(f332(f82(a1),x66641),x66641)),a99))
% 52.62/52.40 [6665]~P1(f332(f332(f233(a1),x66651),a85))+P1(f332(f332(f233(a1),f332(f332(f82(a1),x66651),x66651)),a85))
% 52.62/52.40 [6666]~P1(f332(f332(f232(a1),x66661),a99))+P1(f332(f332(f232(a1),f332(f332(f82(a1),x66661),x66661)),a99))
% 52.62/52.40 [6667]~P1(f332(f332(f232(a1),x66671),a85))+P1(f332(f332(f232(a1),f332(f332(f82(a1),x66671),x66671)),a85))
% 52.62/52.40 [6996]E(f332(f106(a845),x69961),f2(a845))+~P1(f332(a186,f332(f106(a1),f332(f332(f82(a1),x69961),a99))))
% 52.62/52.40 [7255]~P1(f332(f332(f232(a1),f2(a1)),f332(f106(a1),x72551)))+P1(f332(f332(f232(a1),f2(a1)),f332(f106(a1),f332(f332(f82(a1),x72551),x72551))))
% 52.62/52.40 [7256]P1(f332(a186,f332(f106(a1),x72561)))+~P1(f332(a186,f332(f106(a1),f332(f332(f82(a1),x72561),x72561))))
% 52.62/52.40 [7257]P1(f332(f332(f233(a1),x72571),a85))+~P1(f332(f332(f233(a1),f332(f332(f82(a1),x72571),x72571)),a85))
% 52.62/52.40 [7258]P1(f332(f332(f232(a1),x72581),a99))+~P1(f332(f332(f233(a1),f332(f332(f82(a1),x72581),x72581)),a99))
% 52.62/52.40 [7259]P1(f332(f332(f232(a1),x72591),a99))+~P1(f332(f332(f232(a1),f332(f332(f82(a1),x72591),x72591)),a99))
% 52.62/52.40 [7260]P1(f332(f332(f232(a1),x72601),a85))+~P1(f332(f332(f232(a1),f332(f332(f82(a1),x72601),x72601)),a85))
% 52.62/52.40 [7639]E(f332(a110,f571(x76391)),x76391)+~P1(f332(f332(f334(f853(f852(a845,a845),a839)),x76391),a100))
% 52.62/52.40 [6210]~P88(x62101)+E(f332(f106(x62101),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f80(x62101))
% 52.62/52.40 [6211]~P88(x62111)+E(f332(f106(x62111),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f80(x62111))
% 52.62/52.40 [6717]~P1(f332(a186,f332(f106(a1),x67171)))+E(f332(f106(a845),f332(f332(f3(a1),f332(f332(f82(a1),x67171),x67171)),a99)),f2(a845))
% 52.62/52.40 [7818]~P1(f332(f332(f233(a1),f332(f106(a1),x78181)),f2(a1)))+E(f332(f240(a1,a1),f332(a59,f58(f332(f81(a1),f80(a1)),f332(f81(a1),f332(f106(a1),x78181))))),f332(f332(f44(a1),f80(a1)),f332(f106(a1),x78181)))
% 52.62/52.40 [7831]~P1(f332(f332(f233(a1),f332(f106(a1),x78311)),f2(a1)))+E(f332(f250(a1,a1),f332(a59,f58(f332(f81(a1),f80(a1)),f332(f81(a1),f332(f106(a1),x78311))))),f53(a1,f80(a1),f332(f106(a1),x78311)))
% 52.62/52.40 [7878]~P1(f332(f332(f233(a1),a99),x78781))+P1(f332(f332(f233(a1),a99),f332(f332(f3(a1),f332(f332(f82(a1),x78781),x78781)),a99)))
% 52.62/52.40 [7879]~P1(f332(f332(f232(a1),a85),x78791))+P1(f332(f332(f233(a1),a85),f332(f332(f3(a1),f332(f332(f82(a1),x78791),x78791)),a99)))
% 52.62/52.40 [7880]~P1(f332(f332(f232(a1),a99),x78801))+P1(f332(f332(f232(a1),a99),f332(f332(f3(a1),f332(f332(f82(a1),x78801),x78801)),a99)))
% 52.62/52.40 [7881]~P1(f332(f332(f232(a1),a85),x78811))+P1(f332(f332(f232(a1),a85),f332(f332(f3(a1),f332(f332(f82(a1),x78811),x78811)),a99)))
% 52.62/52.40 [8178]~P88(x81781)+~P35(x81781,f332(f106(x81781),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))
% 52.62/52.40 [8358]P1(f332(f332(f233(a1),a99),x83581))+~P1(f332(f332(f233(a1),a99),f332(f332(f3(a1),f332(f332(f82(a1),x83581),x83581)),a99)))
% 52.62/52.40 [8359]P1(f332(f332(f232(a1),a99),x83591))+~P1(f332(f332(f232(a1),a99),f332(f332(f3(a1),f332(f332(f82(a1),x83591),x83591)),a99)))
% 52.62/52.40 [8360]P1(f332(f332(f232(a1),a85),x83601))+~P1(f332(f332(f233(a1),a85),f332(f332(f3(a1),f332(f332(f82(a1),x83601),x83601)),a99)))
% 52.62/52.40 [8361]P1(f332(f332(f232(a1),a85),x83611))+~P1(f332(f332(f232(a1),a85),f332(f332(f3(a1),f332(f332(f82(a1),x83611),x83611)),a99)))
% 52.62/52.40 [8657]E(f332(f106(a845),f332(f332(f3(a1),f332(f332(f82(a1),x86571),x86571)),a99)),f332(f332(f88(a845,a845),f332(f106(a845),x86571)),f332(f332(f10(a845,a845,a845),a114),f332(f332(f20(a845,a845,a845),f82(a845)),f7(a845)))))+P1(f332(a186,f332(f106(a1),x86571)))
% 52.62/52.40 [9430]E(x94301,f180(f853(f852(a845,a845),a839)))+P1(f332(f332(f334(f852(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839))),f332(f332(f241(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839)),x94301),f180(f853(f852(a845,a845),a839)))),a41))
% 52.62/52.40 [8591]~P1(f332(a186,f332(f106(a1),x85911)))+P1(f332(a186,f332(f106(a1),f332(f332(f3(a1),f332(f332(f82(a1),x85911),x85911)),a99))))
% 52.62/52.40 [8592]~P1(f332(f332(f233(a1),x85921),a99))+P1(f332(f332(f233(a1),f332(f332(f3(a1),f332(f332(f82(a1),x85921),x85921)),a99)),a99))
% 52.62/52.40 [8593]~P1(f332(f332(f233(a1),x85931),a85))+P1(f332(f332(f233(a1),f332(f332(f3(a1),f332(f332(f82(a1),x85931),x85931)),a99)),a85))
% 52.62/52.40 [8594]~P1(f332(f332(f232(a1),x85941),a99))+P1(f332(f332(f232(a1),f332(f332(f3(a1),f332(f332(f82(a1),x85941),x85941)),a99)),a99))
% 52.62/52.40 [8595]~P1(f332(f332(f233(a1),x85951),a85))+P1(f332(f332(f232(a1),f332(f332(f3(a1),f332(f332(f82(a1),x85951),x85951)),a99)),a85))
% 52.62/52.40 [8691]~P1(f332(f332(f232(a1),f2(a1)),f332(f106(a1),x86911)))+P1(f332(f332(f232(a1),f2(a1)),f332(f106(a1),f332(f332(f3(a1),f332(f332(f82(a1),x86911),x86911)),a99))))
% 52.62/52.40 [8821]~P88(x88211)+E(f332(f332(f82(x88211),f80(x88211)),f80(x88211)),f332(f106(x88211),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))
% 52.62/52.40 [8968]P1(f332(a186,f332(f106(a1),x89681)))+~P1(f332(a186,f332(f106(a1),f332(f332(f3(a1),f332(f332(f82(a1),x89681),x89681)),a99))))
% 52.62/52.40 [8969]P1(f332(f332(f233(a1),x89691),a99))+~P1(f332(f332(f233(a1),f332(f332(f3(a1),f332(f332(f82(a1),x89691),x89691)),a99)),a99))
% 52.62/52.40 [8970]P1(f332(f332(f233(a1),x89701),a85))+~P1(f332(f332(f233(a1),f332(f332(f3(a1),f332(f332(f82(a1),x89701),x89701)),a99)),a85))
% 52.62/52.40 [8971]P1(f332(f332(f233(a1),x89711),a85))+~P1(f332(f332(f232(a1),f332(f332(f3(a1),f332(f332(f82(a1),x89711),x89711)),a99)),a85))
% 52.62/52.40 [8972]P1(f332(f332(f232(a1),x89721),a99))+~P1(f332(f332(f232(a1),f332(f332(f3(a1),f332(f332(f82(a1),x89721),x89721)),a99)),a99))
% 52.62/52.40 [9478]~P1(f332(f64(f852(a845,a845)),x94781))+P1(f332(f332(f334(f852(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839))),f332(f332(f241(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839)),f180(f853(f852(a845,a845),a839))),x94781)),a71))
% 52.62/52.40 [9264]~P2(x92641)+E(f332(f332(f242(x92641),f2(x92641)),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f2(x92641))
% 52.62/52.40 [9265]~P2(x92651)+E(f332(f332(f242(x92651),f80(x92651)),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f80(x92651))
% 52.62/52.40 [9675]~P1(f332(f332(f233(a845),f80(a845)),x96751))+P1(f332(f332(f233(a845),f2(a845)),f332(f332(f44(a845),x96751),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))))
% 52.62/52.40 [9681]~P1(f332(f332(f233(a845),f2(a845)),x96811))+P1(f332(f332(f233(a845),f2(a845)),f332(f332(f44(a845),f332(f332(f82(a845),x96811),f80(a845))),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))))
% 52.62/52.40 [9721]~E(f53(a845,x97211,f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f80(a845))+P1(f332(f332(f233(a845),f2(a845)),f53(a845,x97211,f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))))
% 52.62/52.40 [9756]E(f53(a845,x97561,f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f80(a845))+~P1(f332(f332(f233(a845),f2(a845)),f53(a845,x97561,f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))))
% 52.62/52.40 [4524]~P38(x45241,x45242)+P58(x45241,x45242)
% 52.62/52.40 [4525]~P44(x45251,x45252)+P58(x45251,x45252)
% 52.62/52.40 [4488]~E(x44881,x44882)+E(f266(x44881,x44882),f80(a101))
% 52.62/52.40 [4491]E(f211(x44911,x44912),x44911)+~E(x44912,f2(a845))
% 52.62/52.40 [4496]P39(x44961,x44962)+~E(x44962,f183(x44961))
% 52.62/52.40 [4502]~P39(x45022,x45021)+E(x45021,f183(x45022))
% 52.62/52.40 [4529]~P99(x45292)+P99(f853(x45291,x45292))
% 52.62/52.40 [4530]~P103(x45302)+P103(f853(x45301,x45302))
% 52.62/52.40 [4531]~P102(x45312)+P102(f853(x45311,x45312))
% 52.62/52.40 [4532]~P90(x45322)+P90(f853(x45321,x45322))
% 52.62/52.40 [4533]~P85(x45332)+P85(f853(x45331,x45332))
% 52.62/52.40 [4534]~P71(x45342)+P71(f853(x45341,x45342))
% 52.62/52.40 [4535]~P93(x45352)+P92(f853(x45351,x45352))
% 52.62/52.40 [4536]~P93(x45362)+P93(f853(x45361,x45362))
% 52.62/52.40 [4537]~P11(x45372)+P11(f853(x45371,x45372))
% 52.62/52.40 [4538]~P106(x45382)+P106(f853(x45381,x45382))
% 52.62/52.40 [4539]~P96(x45392)+P94(f853(x45391,x45392))
% 52.62/52.40 [4540]~P101(x45402)+P101(f853(x45401,x45402))
% 52.62/52.40 [4541]~P96(x45412)+P95(f853(x45411,x45412))
% 52.62/52.40 [4542]~P97(x45422)+P97(f853(x45421,x45422))
% 52.62/52.40 [4543]~P93(x45432)+P98(f853(x45431,x45432))
% 52.62/52.40 [4544]~P96(x45442)+P96(f853(x45441,x45442))
% 52.62/52.40 [4556]E(x45561,x45562)+~E(f332(a114,x45561),f332(a114,x45562))
% 52.62/52.40 [4557]E(x45571,x45572)+~E(f332(a114,x45571),f332(a114,x45572))
% 52.62/52.40 [4558]E(x45581,x45582)+~E(f332(a27,x45581),f332(a27,x45582))
% 52.62/52.40 [4559]E(x45591,x45592)+~E(f332(a5,x45591),f332(a5,x45592))
% 52.62/52.40 [4560]E(x45601,x45602)+~E(f332(a22,x45601),f332(a22,x45602))
% 52.62/52.40 [4561]E(x45611,x45612)+~E(f332(a22,x45611),f332(a22,x45612))
% 52.62/52.40 [4562]E(x45621,x45622)+~E(f332(a110,x45621),f332(a110,x45622))
% 52.62/52.40 [4658]~P9(x46581)+E(f53(x46581,x46582,x46582),f2(x46581))
% 52.62/52.40 [4691]~P38(x46911,x46912)+P38(f846(x46911),f136(x46911,x46912))
% 52.62/52.40 [4692]~P38(x46921,x46922)+P38(f846(x46921),f135(x46921,x46922))
% 52.62/52.40 [4783]~P38(x47831,x47832)+P38(f853(x47831,a839),f324(x47831,x47832))
% 52.62/52.40 [4784]~P38(x47841,x47842)+P38(f853(x47841,a839),f325(x47841,x47842))
% 52.62/52.40 [4903]~P12(x49031)+P40(f295(a1,x49031,x49032))
% 52.62/52.40 [5006]~P38(x50061,x50062)+P60(x50061,f70(x50061,x50061,x50062))
% 52.62/52.40 [5493]~P78(x54931)+P31(x54931,x54931,f81(x54931),x54932)
% 52.62/52.40 [4511]~E(x45112,f115(x45111))+E(f332(f142(x45111),x45112),f115(x45111))
% 52.62/52.40 [4512]~E(x45122,f115(x45121))+E(f332(f141(x45121),x45122),f115(x45121))
% 52.62/52.40 [4513]~E(x45132,f115(x45131))+E(f332(f142(x45131),x45132),f115(x45131))
% 52.62/52.40 [4566]E(x45661,f332(a107,x45662))+~E(f332(f102(a1),x45661),x45662)
% 52.62/52.40 [4568]E(x45681,f115(x45682))+~E(f332(f142(x45682),x45681),f115(x45682))
% 52.62/52.40 [4569]E(x45691,f115(x45692))+~E(f332(f141(x45692),x45691),f115(x45692))
% 52.62/52.40 [4570]E(x45701,f115(x45702))+~E(f332(f142(x45702),x45701),f115(x45702))
% 52.62/52.40 [4585]~P88(x45851)+E(f332(f106(x45851),x45852),f332(f105(x45851),x45852))
% 52.62/52.40 [4592]~E(x45922,f183(x45921))+E(f226(x45921,x45922),f180(f853(x45921,a839)))
% 52.62/52.40 [4593]~P61(x45931)+P1(f332(f64(x45931),x45932))
% 52.62/52.40 [4594]~P61(x45941)+P1(f332(f64(x45941),x45942))
% 52.62/52.40 [4601]E(x46011,f183(x46012))+E(f332(f227(x46012),f554(x46012,x46011)),x46011)
% 52.62/52.40 [4602]E(x46021,f183(x46022))+E(f332(f227(x46022),f580(x46022,x46021)),x46021)
% 52.62/52.40 [4604]~E(f721(x46042,x46041),f115(x46041))+E(f164(x46041,x46042),f115(f846(x46041)))
% 52.62/52.40 [4613]~E(x46132,f115(x46131))+E(f332(f158(x46131),x46132),f180(f853(x46131,a839)))
% 52.62/52.40 [4614]~E(x46142,f115(x46141))+E(f180(f853(x46141,a839)),f332(f158(x46141),x46142))
% 52.62/52.40 [4615]E(x46151,x46152)+~E(f332(f102(a1),x46151),f332(f102(a1),x46152))
% 52.62/52.40 [4616]E(x46161,x46162)+~E(f332(f102(a1),x46161),f332(f102(a1),x46162))
% 52.62/52.40 [4619]E(f209(x46191,x46192),f2(a845))+P1(f332(f64(x46191),x46192))
% 52.62/52.40 [4637]~P110(x46371)+E(f84(x46371,f84(x46371,x46372)),f84(x46371,x46372))
% 52.62/52.40 [4649]~P73(x46491)+E(f332(f332(f242(x46491),x46492),f80(a845)),x46492)
% 52.62/52.40 [4650]~P76(x46501)+E(f332(f332(f242(x46501),x46502),f80(a845)),x46502)
% 52.62/52.40 [4652]E(x46521,x46522)+E(f266(x46521,x46522),f332(f332(f82(a101),x46522),f80(a101)))
% 52.62/52.40 [4653]E(f332(f43(x46531),x46532),f2(a845))+P1(f332(f64(x46531),x46532))
% 52.62/52.40 [4654]E(f332(f43(x46541),x46542),f2(a845))+P1(f332(f64(x46541),x46542))
% 52.62/52.40 [4655]E(f332(f43(x46551),x46552),f2(a845))+P1(f332(f64(x46551),x46552))
% 52.62/52.40 [4661]~P3(x46611)+E(f332(f332(f82(x46611),x46612),f2(x46611)),x46612)
% 52.62/52.40 [4662]~P73(x46621)+E(f332(f332(f82(x46621),x46622),f2(x46621)),x46622)
% 52.62/52.40 [4663]~P4(x46631)+E(f332(f332(f82(x46631),x46632),f2(x46631)),x46632)
% 52.62/52.40 [4664]~P73(x46641)+E(f332(f332(f83(x46641),x46642),f80(x46641)),x46642)
% 52.62/52.40 [4665]~P70(x46651)+E(f332(f332(f83(x46651),x46652),f80(x46651)),x46652)
% 52.62/52.40 [4666]~P76(x46661)+E(f332(f332(f83(x46661),x46662),f80(x46661)),x46662)
% 52.62/52.40 [4667]~P9(x46671)+E(f332(f332(f44(x46671),x46672),f80(x46671)),x46672)
% 52.62/52.40 [4668]~P69(x46681)+E(f332(f332(f3(x46681),x46682),f2(x46681)),x46682)
% 52.62/52.40 [4669]~P113(x46691)+E(f332(f332(f283(x46691),x46692),f80(x46691)),x46692)
% 52.62/52.40 [4670]~P95(x46701)+E(f332(f332(f103(x46701),x46702),f180(x46701)),x46702)
% 52.62/52.40 [4671]~P94(x46711)+E(f332(f332(f104(x46711),x46712),f239(x46711)),x46712)
% 52.62/52.40 [4672]~P73(x46721)+E(f332(f332(f242(x46721),x46722),f2(a845)),f80(x46721))
% 52.62/52.40 [4673]~P105(x46731)+E(f332(f332(f242(x46731),x46732),f2(a845)),f80(x46731))
% 52.62/52.40 [4674]~E(x46742,f180(f853(x46741,a839)))+E(f332(f43(x46741),x46742),f2(a845))
% 52.62/52.40 [4685]~P9(x46851)+E(f53(x46851,x46852,f2(x46851)),x46852)
% 52.62/52.40 [4693]~P73(x46931)+E(f332(f332(f83(x46931),x46932),f2(x46931)),f2(x46931))
% 52.62/52.40 [4694]~P122(x46941)+E(f332(f332(f83(x46941),x46942),f2(x46941)),f2(x46941))
% 52.62/52.40 [4695]~P9(x46951)+E(f332(f332(f44(x46951),x46952),f2(x46951)),f2(x46951))
% 52.62/52.40 [4696]~P114(x46961)+E(f332(f332(f283(x46961),x46962),f2(x46961)),f2(x46961))
% 52.62/52.40 [4697]~P94(x46971)+E(f332(f332(f103(x46971),x46972),f239(x46971)),f239(x46971))
% 52.62/52.40 [4698]~P95(x46981)+E(f332(f332(f104(x46981),x46982),f180(x46981)),f180(x46981))
% 52.62/52.40 [4699]E(x46991,f183(x46992))+~E(f226(x46992,x46991),f180(f853(x46992,a839)))
% 52.62/52.40 [4700]~P9(x47001)+E(f53(x47001,x47002,f80(x47001)),f2(x47001))
% 52.62/52.40 [4701]~P9(x47011)+E(f53(x47011,f2(x47011),x47012),f2(x47011))
% 52.62/52.40 [4752]P38(x47521,x47522)+~E(f601(x47522,x47521),f180(f853(x47521,a839)))
% 52.62/52.40 [4753]E(x47531,f115(x47532))+~E(f332(f158(x47532),x47531),f180(f853(x47532,a839)))
% 52.62/52.40 [4754]E(x47541,f115(x47542))+~E(f180(f853(x47542,a839)),f332(f158(x47542),x47541))
% 52.62/52.40 [4757]~E(x47571,x47572)+P1(f332(f332(a329,x47571),x47572))
% 52.62/52.40 [4767]P1(x47671)+P1(f332(f332(a335,x47671),x47672))
% 52.62/52.40 [4768]E(x47681,f115(x47682))+E(f332(f332(f152(x47682),x47681),f2(a845)),f332(f131(x47682),x47681))
% 52.62/52.40 [4774]~P1(x47742)+P1(f332(f332(a335,x47741),x47742))
% 52.62/52.40 [4775]~P1(x47752)+P1(f332(f332(a331,x47751),x47752))
% 52.62/52.40 [4776]~P1(x47761)+P1(f332(f332(a331,x47761),x47762))
% 52.62/52.40 [4786]~E(f722(x47862,x47861),f726(x47862,x47861))+P1(f332(f127(x47861),x47862))
% 52.62/52.40 [4794]E(f332(f256(x47941),x47942),f180(f853(x47941,a839)))+P1(f332(x47942,f555(x47942)))
% 52.62/52.40 [4795]E(f180(f853(x47951,a839)),f332(f256(x47951),x47952))+P1(f332(x47952,f579(x47952)))
% 52.62/52.40 [4859]~P110(x48591)+E(f332(f332(f83(x48591),x48592),f84(x48591,x48592)),f332(f77(x48591),x48592))
% 52.62/52.40 [4870]~E(x48701,f2(a1))+E(f54(x48701,x48702),f332(f332(f241(a1,a1),f2(a1)),f2(a1)))
% 52.62/52.40 [4871]~E(x48711,f2(a1))+E(f54(x48711,x48712),f332(f332(f241(a1,a1),f2(a1)),f2(a1)))
% 52.62/52.40 [4902]~P58(x49021,x49022)+P58(x49021,f332(f278(x49021,x49021),x49022))
% 52.62/52.40 [4919]~E(f332(a30,x49191),f332(f227(a840),x49192))+P1(f332(a26,f332(a27,x49191)))
% 52.62/52.40 [4923]E(x49231,x49232)+~P1(f332(f332(a329,x49231),x49232))
% 52.62/52.40 [4926]~P1(f332(a26,x49262))+P1(f332(a26,f35(x49261,x49262)))
% 52.62/52.40 [4927]~P1(f332(a26,x49272))+P1(f332(a26,f35(x49271,x49272)))
% 52.62/52.40 [4936]P1(x49361)+~P1(f332(f332(a330,x49362),x49361))
% 52.62/52.40 [4937]P1(x49371)+~P1(f332(f332(a330,x49371),x49372))
% 52.62/52.40 [4941]~P106(x49411)+P1(f332(f332(f232(x49411),x49412),f239(x49411)))
% 52.62/52.40 [4942]~P73(x49421)+P1(f332(f332(f279(x49421),x49422),f2(x49421)))
% 52.62/52.40 [4946]E(x49461,x49462)+~E(f332(x49461,f379(x49462,x49461)),f332(x49462,f379(x49462,x49461)))
% 52.62/52.40 [4980]E(x49801,f2(a845))+E(f211(x49801,f53(a845,x49802,x49801)),f211(x49802,x49801))
% 52.62/52.40 [4985]~P100(x49851)+P20(x49851,f332(f332(f140(x49851),x49852),f115(x49851)))
% 52.62/52.40 [4987]E(x49871,f2(a1))+P1(f332(f57(x49872,x49871),f54(x49872,x49871)))
% 52.62/52.40 [5004]~E(x50041,x50042)+P1(f332(f332(f233(a845),x50041),f332(a114,x50042)))
% 52.62/52.40 [5014]~E(x50141,f2(a845))+P1(f332(f332(f233(a845),x50141),f332(a114,x50142)))
% 52.62/52.40 [5024]P1(f332(x50241,x50242))+P1(f332(f332(f232(a1),f2(a1)),f767(x50241)))
% 52.62/52.40 [5060]P1(f332(a26,x50601))+~P1(f332(a26,f35(x50602,x50601)))
% 52.62/52.40 [5061]P1(f332(a26,x50611))+~P1(f332(a26,f35(x50612,x50611)))
% 52.62/52.40 [5062]P1(f332(a26,x50621))+~P1(f332(a26,f36(x50622,x50621)))
% 52.62/52.40 [5063]P1(f332(a26,x50631))+~P1(f332(a26,f36(x50632,x50631)))
% 52.62/52.40 [5064]P1(f332(a26,x50641))+~P1(f332(a26,f36(x50641,x50642)))
% 52.62/52.40 [5065]P1(f332(a26,x50651))+~P1(f332(a26,f36(x50651,x50652)))
% 52.62/52.40 [5093]P58(x50931,x50932)+~P58(x50931,f332(f278(x50931,x50931),x50932))
% 52.62/52.40 [5095]~E(f53(a845,x50952,x50951),f2(a845))+E(f332(f332(f83(a845),x50951),f784(x50951,x50952)),x50952)
% 52.62/52.40 [5096]~E(f53(a1,x50962,x50961),f2(a1))+E(f332(f332(f83(a1),x50961),f785(x50961,x50962)),x50962)
% 52.62/52.40 [5101]~E(x51011,f332(a114,x51012))+P1(f332(f332(f232(a845),x51011),f332(a114,x51012)))
% 52.62/52.40 [5123]~P1(f332(x51231,x51232))+P1(f332(f332(f232(a1),f2(a1)),f759(x51231)))
% 52.62/52.40 [5135]E(f332(f332(f3(a845),f332(a107,x51351)),f332(a107,x51352)),f332(a107,x51351))+~P1(f332(a186,x51352))
% 52.62/52.40 [5163]E(f267(x51631,x51632),f80(a101))+~P1(f332(f332(f232(a101),x51631),f80(a101)))
% 52.62/52.40 [5252]E(f332(f332(f152(x52521),x52522),f722(x52522,x52521)),f332(f332(f152(x52521),x52522),f726(x52522,x52521)))+P1(f332(f127(x52521),x52522))
% 52.62/52.40 [5294]~P1(f332(x52941,f92(x52942,x52941)))+P1(f332(x52941,f602(x52942,x52941)))
% 52.62/52.40 [5357]P60(x53571,x53572)+~P1(f332(f321(x53571,x53572),f591(x53572,x53571)))
% 52.62/52.40 [5500]~E(f332(a114,f53(a845,x55001,x55002)),x55002)+E(f53(a845,f332(a114,x55001),x55002),f2(a845))
% 52.62/52.40 [5553]P38(x55531,x55532)+P1(f332(f332(f334(x55531),f681(x55532,x55531)),f682(x55532,x55531)))
% 52.62/52.40 [5559]~P2(x55591)+P1(f332(f332(f334(x55591),f332(f102(x55591),x55592)),f176(x55591)))
% 52.62/52.40 [5560]~P133(x55601)+P1(f332(f332(f334(x55601),f332(f102(x55601),x55602)),f112(x55601)))
% 52.62/52.40 [5561]~P133(x55611)+P1(f332(f332(f334(x55611),f332(f105(x55611),x55612)),f112(x55611)))
% 52.62/52.40 [5562]~P88(x55621)+P1(f332(f332(f334(x55621),f332(f106(x55621),x55622)),f112(x55621)))
% 52.62/52.40 [5716]E(f332(a114,f53(a845,x57161,x57162)),x57162)+E(f53(a845,f332(a114,x57161),x57162),f332(a114,f53(a845,x57161,x57162)))
% 52.62/52.40 [6140]P38(x61401,x61402)+~P1(f332(f332(f334(x61401),f581(x61402,x61401)),f322(x61401,x61402)))
% 52.62/52.40 [6174]~P117(x61741)+~P1(f332(f332(f233(x61741),f332(f102(x61741),x61742)),f2(x61741)))
% 52.62/52.40 [6175]~P80(x61751)+~P1(f332(f332(f233(x61751),f332(f77(x61751),x61752)),f2(x61751)))
% 52.62/52.40 [6266]P1(f332(f332(f233(a1),x62661),f53(a1,x62662,x62661)))+~P1(f332(f332(f233(a1),x62661),f2(a1)))
% 52.62/52.40 [6267]P1(f332(f332(f233(a1),x62671),f53(a1,x62672,x62671)))+~P1(f332(f332(f233(a1),x62671),f2(a1)))
% 52.62/52.40 [6375]E(f332(f332(f302(a845),f332(a114,x63751)),f295(a845,x63752,x63751)),f295(a845,x63752,f332(a114,x63751)))+~P1(f332(f332(f232(a845),x63752),f332(a114,x63751)))
% 52.62/52.40 [6601]E(f332(f141(x66011),x66012),x66012)+~P1(f332(f332(f232(a845),f332(f181(f846(x66011)),x66012)),f80(a845)))
% 52.62/52.40 [6624]~P80(x66241)+P1(f332(f332(f232(x66241),f332(f81(x66241),f332(f77(x66241),x66242))),f2(x66241)))
% 52.62/52.40 [6660]~P38(x66601,x66602)+P38(x66601,f332(f332(f281(x66601,x66601,x66601),x66602),f300(x66601,x66602)))
% 52.62/52.40 [6890]~P1(f332(f332(f233(a1),x68902),f2(a1)))+P1(f332(f332(f232(a1),f53(a1,x68901,x68902)),f2(a1)))
% 52.62/52.40 [6891]~P1(f332(f332(f233(a1),x68912),f2(a1)))+P1(f332(f332(f232(a1),f53(a1,x68911,x68912)),f2(a1)))
% 52.62/52.40 [7302]~P2(x73021)+E(f182(x73021,f332(f332(f9(x73021,x73021,x73021),f82(x73021)),f80(x73021)),x73022,f2(x73021)),f332(f102(x73021),x73022))
% 52.62/52.40 [7335]~P118(x73351)+~P1(f332(f332(f233(x73351),f332(f332(f83(x73351),x73352),x73352)),f2(x73351)))
% 52.62/52.40 [9851]~P110(x98511)+~P1(f332(f332(f233(x98511),f332(f332(f242(x98511),x98512),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))),f2(x98511)))
% 52.62/52.40 [4567]~E(x45672,f115(x45671))+E(f332(f181(f846(x45671)),x45672),f2(a845))
% 52.62/52.40 [4605]~E(x46051,f2(a845))+E(f332(f332(f82(a845),x46051),x46052),x46052)
% 52.62/52.40 [4606]~E(x46062,f2(a845))+E(f332(f332(f83(a845),x46061),x46062),f2(a845))
% 52.62/52.40 [4607]~E(x46071,f2(a845))+E(f332(f332(f83(a845),x46071),x46072),f2(a845))
% 52.62/52.40 [4608]~E(x46081,f2(a845))+E(f332(f332(f83(a845),x46081),x46082),f2(a845))
% 52.62/52.40 [4609]~E(x46092,f2(a1))+E(f332(f332(f44(a1),x46091),x46092),f2(a1))
% 52.62/52.40 [4610]~E(x46102,f2(a845))+E(f332(f332(f242(a845),x46101),x46102),f80(a845))
% 52.62/52.40 [4620]E(x46201,f115(x46202))+~E(f332(f181(f846(x46202)),x46201),f2(a845))
% 52.62/52.40 [4621]~P91(x46211)+E(f332(f332(f83(x46211),x46212),x46212),x46212)
% 52.62/52.40 [4622]~P91(x46221)+E(f332(f332(f83(x46221),x46222),x46222),x46222)
% 52.62/52.40 [4623]~P100(x46231)+E(f332(f332(f236(x46231),x46232),x46232),x46232)
% 52.62/52.40 [4624]~P100(x46241)+E(f332(f332(f236(x46241),x46242),x46242),x46242)
% 52.62/52.40 [4625]~P100(x46251)+E(f332(f332(f179(x46251),x46252),x46252),x46252)
% 52.62/52.40 [4626]~P100(x46261)+E(f332(f332(f179(x46261),x46262),x46262),x46262)
% 52.62/52.40 [4627]~P92(x46271)+E(f332(f332(f103(x46271),x46272),x46272),x46272)
% 52.62/52.40 [4628]~P92(x46281)+E(f332(f332(f103(x46281),x46282),x46282),x46282)
% 52.62/52.40 [4629]~P93(x46291)+E(f332(f332(f103(x46291),x46292),x46292),x46292)
% 52.62/52.40 [4630]~P93(x46301)+E(f332(f332(f104(x46301),x46302),x46302),x46302)
% 52.62/52.40 [4631]~P98(x46311)+E(f332(f332(f104(x46311),x46312),x46312),x46312)
% 52.62/52.40 [4632]~P98(x46321)+E(f332(f332(f104(x46321),x46322),x46322),x46322)
% 52.62/52.40 [4648]~P69(x46481)+E(f332(f332(f3(x46481),x46482),x46482),f2(x46481))
% 52.62/52.40 [4659]~P69(x46591)+E(f332(f81(x46591),f332(f81(x46591),x46592)),x46592)
% 52.62/52.40 [4660]~P90(x46601)+E(f332(f81(x46601),f332(f81(x46601),x46602)),x46602)
% 52.62/52.41 [4677]~E(x46772,f2(a845))+E(f332(f332(f242(a845),x46771),x46772),f332(a114,f2(a845)))
% 52.62/52.41 [4709]~P3(x47091)+E(f332(f332(f82(x47091),f2(x47091)),x47092),x47092)
% 52.62/52.41 [4710]~P73(x47101)+E(f332(f332(f82(x47101),f2(x47101)),x47102),x47102)
% 52.62/52.41 [4711]~P4(x47111)+E(f332(f332(f82(x47111),f2(x47111)),x47112),x47112)
% 52.62/52.41 [4712]~P73(x47121)+E(f332(f332(f83(x47121),f80(x47121)),x47122),x47122)
% 52.62/52.41 [4713]~P70(x47131)+E(f332(f332(f83(x47131),f80(x47131)),x47132),x47132)
% 52.62/52.41 [4714]~P76(x47141)+E(f332(f332(f83(x47141),f80(x47141)),x47142),x47142)
% 52.62/52.41 [4715]~P95(x47151)+E(f332(f332(f103(x47151),f180(x47151)),x47152),x47152)
% 52.62/52.41 [4716]~P94(x47161)+E(f332(f332(f104(x47161),f239(x47161)),x47162),x47162)
% 52.62/52.41 [4733]~P73(x47331)+E(f332(f332(f83(x47331),f2(x47331)),x47332),f2(x47331))
% 52.62/52.41 [4734]~P122(x47341)+E(f332(f332(f83(x47341),f2(x47341)),x47342),f2(x47341))
% 52.62/52.41 [4735]~P9(x47351)+E(f332(f332(f44(x47351),f2(x47351)),x47352),f2(x47351))
% 52.62/52.41 [4736]~P76(x47361)+E(f332(f332(f242(x47361),f80(x47361)),x47362),f80(x47361))
% 52.62/52.41 [4737]~P113(x47371)+E(f332(f332(f283(x47371),f2(x47371)),x47372),f2(x47371))
% 52.62/52.41 [4738]~P94(x47381)+E(f332(f332(f103(x47381),f239(x47381)),x47382),f239(x47381))
% 52.62/52.41 [4739]~P95(x47391)+E(f332(f332(f104(x47391),f180(x47391)),x47392),f180(x47391))
% 52.62/52.41 [4747]E(x47471,f115(x47472))+E(f134(x47472,f332(f142(x47472),x47471)),f332(f131(x47472),x47471))
% 52.62/52.41 [4748]E(x47481,f115(x47482))+E(f332(f131(x47482),f332(f142(x47482),x47481)),f134(x47482,x47481))
% 52.62/52.41 [4749]E(x47491,f2(a845))+~E(f332(f332(f82(a845),x47492),x47491),x47492)
% 52.62/52.41 [4755]~P133(x47551)+E(f332(f105(x47551),f332(f102(a1),x47552)),f332(f102(x47551),x47552))
% 52.62/52.41 [4756]~P88(x47561)+E(f332(f105(x47561),f332(f106(a1),x47562)),f332(f106(x47561),x47562))
% 52.62/52.41 [4761]E(x47611,f80(a845))+~E(f332(f332(f83(a845),x47612),x47611),f80(a845))
% 52.62/52.41 [4762]E(x47621,f80(a845))+~E(f332(f332(f83(a845),x47621),x47622),f80(a845))
% 52.62/52.41 [4763]E(x47631,f2(a845))+~E(f332(f332(f82(a845),x47632),x47631),f2(a845))
% 52.62/52.41 [4764]E(x47641,f2(a845))+~E(f332(f332(f82(a845),x47641),x47642),f2(a845))
% 52.62/52.41 [4765]E(x47651,f80(a845))+~E(f332(f332(f83(a845),x47652),x47651),f80(a845))
% 52.62/52.41 [4766]E(x47661,f80(a845))+~E(f332(f332(f83(a845),x47661),x47662),f80(a845))
% 52.62/52.41 [4779]~P110(x47791)+E(f332(f77(x47791),f332(f102(x47791),x47792)),f332(f102(x47791),x47792))
% 52.62/52.41 [4780]~P80(x47801)+E(f332(f77(x47801),f332(f81(x47801),x47802)),f332(f77(x47801),x47802))
% 52.62/52.41 [4781]~P80(x47811)+E(f332(f77(x47811),f332(f77(x47811),x47812)),f332(f77(x47811),x47812))
% 52.62/52.41 [4782]~P4(x47821)+E(f332(f154(x47821),f332(f142(x47821),x47822)),f332(f154(x47821),x47822))
% 52.62/52.41 [4787]~E(x47871,f332(a114,f2(a845)))+E(f332(f332(f242(a845),x47871),x47872),f332(a114,f2(a845)))
% 52.62/52.41 [4797]~P69(x47971)+E(f332(f332(f3(x47971),f2(x47971)),x47972),f332(f81(x47971),x47972))
% 52.62/52.41 [4798]~E(x47982,f2(a845))+E(f130(a845,f332(f294(a845,x47981),x47982)),f115(a845))
% 52.62/52.41 [4807]~P88(x48071)+E(f332(f332(f82(x48071),x48072),f332(f106(x48071),a85)),x48072)
% 52.62/52.41 [4808]E(x48081,f2(a1))+E(f55(f332(f77(a1),x48082),f332(f77(a1),x48081)),f61(x48082,x48081))
% 52.62/52.41 [4818]~E(x48181,x48182)+P1(f332(f332(f232(a845),x48181),x48182))
% 52.62/52.41 [4819]~E(x48191,x48192)+P1(f332(f332(f232(a845),x48191),x48192))
% 52.62/52.41 [4820]~E(x48201,x48202)+P1(f332(f332(f232(a845),x48201),x48202))
% 52.62/52.41 [4821]~E(x48211,x48212)+P1(f332(f332(f279(a845),x48211),x48212))
% 52.62/52.41 [4822]~E(x48221,x48222)+P1(f332(f332(f279(a845),x48221),x48222))
% 52.62/52.41 [4823]~E(x48231,x48232)+P1(f332(f332(f279(a845),x48231),x48232))
% 52.62/52.41 [4824]~E(x48241,x48242)+P1(f332(f332(f279(a845),x48241),x48242))
% 52.62/52.41 [4831]~E(x48311,f2(a101))+E(f332(f332(f82(a845),f332(a22,x48311)),x48312),x48312)
% 52.62/52.41 [4832]~E(f332(f106(a1),x48322),f332(f102(a1),x48321))+E(x48321,f332(a107,f332(f106(a1),x48322)))
% 52.62/52.41 [4841]~P12(x48411)+P12(f332(f332(f242(a1),x48411),x48412))
% 52.62/52.41 [4842]~P69(x48421)+E(f332(f332(f82(x48421),x48422),f332(f81(x48421),x48422)),f2(x48421))
% 52.62/52.41 [4843]~P90(x48431)+E(f332(f332(f103(x48431),x48432),f332(f81(x48431),x48432)),f239(x48431))
% 52.62/52.41 [4844]~P90(x48441)+E(f332(f332(f104(x48441),x48442),f332(f81(x48441),x48442)),f180(x48441))
% 52.62/52.41 [4868]E(x48681,f2(a845))+~E(f332(f81(a1),f332(f102(a1),x48682)),f332(f102(a1),x48681))
% 52.62/52.41 [4869]E(x48691,f2(a845))+~E(f332(f81(a1),f332(f102(a1),x48691)),f332(f102(a1),x48692))
% 52.62/52.41 [4879]E(f188(x48791,x48792),f2(a1))+P1(f332(f332(f232(a1),x48792),x48791))
% 52.62/52.41 [4880]E(f238(x48801,x48802),f2(a101))+P1(f332(f332(f233(a101),x48801),x48802))
% 52.62/52.41 [4881]E(f163(x48811,x48812),f115(a1))+P1(f332(f332(f232(a1),x48811),x48812))
% 52.62/52.41 [4894]E(x48941,f332(a114,f2(a845)))+~E(f332(f332(f83(a845),x48942),x48941),f332(a114,f2(a845)))
% 52.62/52.41 [4895]E(x48951,f332(a114,f2(a845)))+~E(f332(f332(f83(a845),x48951),x48952),f332(a114,f2(a845)))
% 52.62/52.41 [4896]~P103(x48961)+P1(f332(f332(f232(x48961),x48962),x48962))
% 52.62/52.41 [4897]~P73(x48971)+P1(f332(f332(f279(x48971),x48972),x48972))
% 52.62/52.41 [4900]~P88(x49001)+E(f332(f332(f83(x49001),x49002),f332(f106(x49001),a99)),f332(f81(x49001),x49002))
% 52.62/52.41 [4915]~P88(x49151)+E(f332(f81(x49151),f332(f106(x49151),x49152)),f332(f106(x49151),f332(f81(a1),x49152)))
% 52.62/52.41 [4916]~P133(x49161)+E(f332(f81(x49161),f332(f105(x49161),x49162)),f332(f105(x49161),f332(f81(a1),x49162)))
% 52.62/52.41 [4917]~P88(x49171)+E(f332(f81(x49171),f332(f106(x49171),x49172)),f332(f106(x49171),f332(f81(a1),x49172)))
% 52.62/52.41 [4951]~E(x49511,f332(a114,x49512))+P1(f332(f332(f233(a845),f2(a845)),x49511))
% 52.62/52.41 [4968]~P100(x49681)+E(f332(f81(f853(x49681,a839)),f332(f257(x49681),x49682)),f332(f258(x49681),x49682))
% 52.62/52.41 [4969]~P100(x49691)+E(f332(f81(f853(x49691,a839)),f332(f296(x49691),x49692)),f332(f293(x49691),x49692))
% 52.62/52.41 [4970]~P100(x49701)+E(f332(f81(f853(x49701,a839)),f332(f293(x49701),x49702)),f332(f296(x49701),x49702))
% 52.62/52.41 [4971]~P100(x49711)+E(f332(f81(f853(x49711,a839)),f332(f258(x49711),x49712)),f332(f257(x49711),x49712))
% 52.62/52.41 [4979]~E(f332(f102(a1),x49792),x49791)+P1(f332(f332(f232(a1),f2(a1)),x49791))
% 52.62/52.41 [4986]~E(x49862,f2(a1))+E(f61(x49861,x49862),f332(f332(f241(a1,a1),f2(a1)),f332(f77(a1),x49861)))
% 52.62/52.41 [4988]~P101(x49881)+P1(f332(f332(f232(x49881),f180(x49881)),x49882))
% 52.62/52.41 [4989]~P73(x49891)+P1(f332(f332(f279(x49891),f80(x49891)),x49892))
% 52.62/52.41 [5019]E(x50191,x50192)+~E(f332(f332(f82(a1),x50191),x50191),f332(f332(f82(a1),x50192),x50192))
% 52.62/52.41 [5023]~P1(f332(x50231,x50232))+P1(f332(x50231,f332(a107,f759(x50231))))
% 52.62/52.41 [5049]~P110(x50491)+E(f332(f332(f83(x50491),f84(x50491,x50492)),f332(f77(x50491),x50492)),x50492)
% 52.62/52.41 [5050]E(x50501,x50502)+~P1(f332(f332(f187(a25),x50501),x50502))
% 52.62/52.41 [5059]~E(x50592,f2(a845))+E(f87(f852(a845,a845),f56(x50591,x50592)),f332(f332(f241(a845,a845),f2(a845)),x50591))
% 52.62/52.41 [5066]~E(x50661,x50662)+~P1(f332(f332(f233(a845),x50661),x50662))
% 52.62/52.41 [5067]~E(x50671,x50672)+~P1(f332(f332(f233(a845),x50671),x50672))
% 52.62/52.41 [5068]~E(x50681,x50682)+~P1(f332(f332(f233(a845),x50681),x50682))
% 52.62/52.41 [5069]~E(x50691,x50692)+~P1(f332(f332(f233(a845),x50691),x50692))
% 52.62/52.41 [5070]~E(x50701,x50702)+~P1(f332(f332(f233(a845),x50701),x50702))
% 52.62/52.41 [5071]~E(x50711,x50712)+~P1(f332(f332(f233(a1),x50711),x50712))
% 52.62/52.41 [5074]~P2(x50741)+E(f332(f332(f82(x50741),f80(x50741)),f332(f102(x50741),x50742)),f332(f102(x50741),f332(a114,x50742)))
% 52.62/52.41 [5078]~E(x50781,f2(a845))+~P1(f332(f332(f233(a845),x50782),x50781))
% 52.62/52.41 [5091]E(f332(f43(x50911),f332(f158(x50911),x50912)),f332(f181(f846(x50911)),x50912))+~P1(f332(f127(x50911),x50912))
% 52.62/52.41 [5100]~P1(f332(x51001,f727(x51001)))+P1(f332(x51001,f332(f102(a1),x51002)))
% 52.62/52.41 [5112]E(f238(x51121,x51122),x51122)+~P1(f332(f332(f233(a101),x51121),x51122))
% 52.62/52.41 [5114]E(f267(x51141,x51142),f80(a101))+~P1(f332(f332(f233(a101),x51142),x51141))
% 52.62/52.41 [5115]E(f163(x51151,x51152),f115(a1))+~P1(f332(f332(f233(a1),x51152),x51151))
% 52.62/52.41 [5118]~P99(x51181)+E(f295(x51181,x51182,x51182),f332(f332(f302(x51181),x51182),f180(f853(x51181,a839))))
% 52.62/52.41 [5138]~E(f332(f332(f3(a845),x51381),x51382),f2(a845))+P1(f332(f332(f232(a845),x51381),x51382))
% 52.62/52.41 [5164]~P103(x51641)+~P1(f332(f332(f233(x51641),x51642),x51642))
% 52.62/52.41 [5166]~E(f53(a1,x51661,x51662),f2(a1))+E(f53(a1,x51661,f332(f81(a1),x51662)),f2(a1))
% 52.62/52.41 [5167]~E(f53(a1,x51671,x51672),f2(a1))+E(f53(a1,x51671,f332(f81(a1),x51672)),f2(a1))
% 52.62/52.41 [5168]~E(f53(a1,x51681,x51682),f2(a1))+E(f53(a1,f332(f81(a1),x51681),x51682),f2(a1))
% 52.62/52.41 [5169]~E(f53(a1,x51691,x51692),f2(a1))+E(f53(a1,f332(f81(a1),x51691),x51692),f2(a1))
% 52.62/52.41 [5176]E(f332(f294(a845,x51761),f332(a114,x51762)),f180(f853(a845,a839)))+P1(f332(f332(f232(a845),x51761),x51762))
% 52.62/52.41 [5193]E(f130(a845,f332(f294(a845,x51931),x51932)),f115(a845))+P1(f332(f332(f233(a845),x51931),x51932))
% 52.62/52.41 [5198]~E(f332(f43(x51981),f332(f158(x51981),x51982)),f332(f181(f846(x51981)),x51982))+P1(f332(f127(x51981),x51982))
% 52.62/52.41 [5202]~P1(f332(f127(x52021),x52022))+P1(f332(f127(x52021),f332(f141(x52021),x52022)))
% 52.62/52.41 [5203]~P1(f332(f127(x52031),x52032))+P1(f332(f127(x52031),f332(f157(x52031),x52032)))
% 52.62/52.41 [5204]~P1(f332(f127(x52041),x52042))+P1(f332(f127(x52041),f332(f142(x52041),x52042)))
% 52.62/52.41 [5212]P1(f332(x52121,x52122))+~P1(f332(x52121,f332(a107,f767(x52121))))
% 52.62/52.41 [5213]P1(f332(f332(f232(a845),x52132),x52131))+P1(f332(f332(f232(a845),x52131),x52132))
% 52.62/52.41 [5214]P1(f332(f332(f232(a1),x52142),x52141))+P1(f332(f332(f232(a1),x52141),x52142))
% 52.62/52.41 [5216]~P80(x52161)+P1(f332(f332(f232(x52161),x52162),f332(f77(x52161),x52162)))
% 52.62/52.41 [5219]P1(f332(x52191,f728(x52191)))+~P1(f332(x52191,f332(f102(a1),x52192)))
% 52.62/52.41 [5243]E(f332(f332(f44(a845),x52431),x52432),f2(a845))+~P1(f332(f332(f233(a845),x52431),x52432))
% 52.62/52.41 [5244]E(f332(f332(f3(a845),x52441),x52442),f2(a845))+~P1(f332(f332(f232(a845),x52441),x52442))
% 52.62/52.41 [5245]E(f332(f332(f3(a845),x52451),x52452),f2(a845))+~P1(f332(f332(f232(a845),x52451),x52452))
% 52.62/52.41 [5261]E(f53(a845,x52611,x52612),x52611)+~P1(f332(f332(f233(a845),x52611),x52612))
% 52.62/52.41 [5262]E(f53(a845,x52621,x52622),x52621)+~P1(f332(f332(f233(a845),x52621),x52622))
% 52.62/52.41 [5269]E(f53(a1,x52691,f332(f81(a1),x52692)),f284(x52691,x52692))+P1(f332(f332(f232(a1),f2(a1)),x52692))
% 52.62/52.41 [5281]E(f332(f332(f3(a1),x52811),x52812),f188(x52811,x52812))+~P1(f332(f332(f232(a1),x52812),x52811))
% 52.62/52.41 [5282]E(f332(f332(f3(a1),x52821),x52822),f188(x52821,x52822))+~P1(f332(f332(f232(a1),x52822),x52821))
% 52.62/52.41 [5300]P1(f332(f332(f232(a1),f2(a1)),f727(x53001)))+P1(f332(x53001,f332(f102(a1),x53002)))
% 52.62/52.41 [5312]~P117(x53121)+P1(f332(f332(f232(x53121),f2(x53121)),f332(f102(x53121),x53122)))
% 52.62/52.41 [5313]~P117(x53131)+P1(f332(f332(f232(x53131),f2(x53131)),f332(f102(x53131),x53132)))
% 52.62/52.41 [5314]~P80(x53141)+P1(f332(f332(f232(x53141),f2(x53141)),f332(f77(x53141),x53142)))
% 52.62/52.41 [5342]E(f332(f332(f82(a845),x53421),f680(x53422,x53421)),x53422)+~P1(f332(f332(f232(a845),x53421),x53422))
% 52.62/52.41 [5343]E(f332(f332(f82(a845),x53431),f618(x53432,x53431)),x53432)+~P1(f332(f332(f233(a845),x53431),x53432))
% 52.62/52.41 [5355]~E(f332(f106(a1),x53551),f332(f102(a1),x53552))+P1(f332(f332(f232(a1),f2(a1)),f332(f106(a1),x53551)))
% 52.62/52.41 [5358]E(f295(a1,x53581,x53582),f180(f853(a1,a839)))+~P1(f332(f332(f233(a1),x53582),x53581))
% 52.62/52.41 [5361]~P110(x53611)+E(f332(f332(f83(x53611),f332(f77(x53611),x53612)),f332(f77(x53611),x53612)),f332(f332(f83(x53611),x53612),x53612))
% 52.62/52.41 [5366]E(f130(a845,f332(f294(a845,x53661),f332(a114,x53662))),f115(a845))+P1(f332(f332(f232(a845),x53661),x53662))
% 52.62/52.41 [5370]E(f332(f332(f44(a1),x53701),x53702),f285(x53701,x53702))+~P1(f332(f332(f232(a1),f2(a1)),x53702))
% 52.62/52.41 [5390]P1(f332(f127(x53901),x53902))+~P1(f332(f127(x53901),f332(f141(x53901),x53902)))
% 52.62/52.41 [5391]P1(f332(f127(x53911),x53912))+~P1(f332(f127(x53911),f332(f142(x53911),x53912)))
% 52.62/52.41 [5414]P1(f332(f64(a845),x54141))+P1(f332(f332(f334(a845),f381(x54141,x54142)),x54141))
% 52.62/52.41 [5415]P1(f332(f64(a845),x54151))+P1(f332(f332(f334(a845),f410(x54151,x54152)),x54151))
% 52.62/52.41 [5416]P1(f332(f332(f233(a845),x54162),f332(a114,x54161)))+P1(f332(f332(f233(a845),x54161),x54162))
% 52.62/52.41 [5417]E(f53(a1,x54171,x54172),f284(x54171,x54172))+~P1(f332(f332(f232(a1),f2(a1)),x54172))
% 52.62/52.41 [5419]E(f130(a845,f332(f294(a845,x54191),x54192)),f115(a845))+~P1(f332(f332(f232(a845),x54192),x54191))
% 52.62/52.41 [5420]E(f130(a845,f332(f294(a845,x54201),x54202)),f115(a845))+~P1(f332(f332(f232(a845),x54202),x54201))
% 52.62/52.41 [5421]~P78(x54211)+E(f332(f303(x54211,x54211,f81(x54211)),f332(f257(x54211),x54212)),f332(f296(x54211),f332(f81(x54211),x54212)))
% 52.62/52.41 [5422]~P78(x54221)+E(f332(f303(x54221,x54221,f81(x54221)),f332(f296(x54221),x54222)),f332(f257(x54221),f332(f81(x54221),x54222)))
% 52.62/52.41 [5423]~P78(x54231)+E(f332(f303(x54231,x54231,f81(x54231)),f332(f293(x54231),x54232)),f332(f258(x54231),f332(f81(x54231),x54232)))
% 52.62/52.41 [5424]~P78(x54241)+E(f332(f303(x54241,x54241,f81(x54241)),f332(f258(x54241),x54242)),f332(f293(x54241),f332(f81(x54241),x54242)))
% 52.62/52.41 [5435]E(x54351,f180(f853(x54352,a839)))+P1(f332(f332(f334(x54352),f382(x54351,x54352)),x54351))
% 52.62/52.41 [5436]E(x54361,f180(f853(x54362,a839)))+P1(f332(f332(f334(x54362),f402(x54361,x54362)),x54361))
% 52.62/52.41 [5443]~P1(f332(f332(f233(a845),x54431),x54432))+P1(f332(f332(f232(a845),x54431),x54432))
% 52.62/52.41 [5444]~P1(f332(f332(f233(a845),x54441),x54442))+P1(f332(f332(f232(a845),x54441),x54442))
% 52.62/52.41 [5445]~P1(f332(f332(f233(a845),x54451),x54452))+P1(f332(f332(f232(a845),x54451),x54452))
% 52.62/52.41 [5446]~P1(f332(f332(f233(a845),x54461),x54462))+P1(f332(f332(f232(a845),x54461),x54462))
% 52.62/52.41 [5447]~P1(f332(f332(f233(a845),x54471),x54472))+P1(f332(f332(f232(a845),x54471),x54472))
% 52.62/52.41 [5448]~P1(f332(f332(f233(a1),x54481),x54482))+P1(f332(f332(f232(a1),x54481),x54482))
% 52.62/52.41 [5460]E(f55(x54601,x54602),f332(f332(f241(a1,a1),f2(a1)),x54601))+~P1(f332(f332(f233(a1),x54601),x54602))
% 52.62/52.41 [5461]E(f210(f332(f81(a1),x54611),f332(f81(a1),x54612)),f210(x54611,x54612))+~P1(f332(f332(f233(a1),x54612),f2(a1)))
% 52.62/52.41 [5474]E(x54741,x54742)+~E(f332(a5,f332(a114,f332(a22,x54741))),f332(a5,f332(a114,f332(a22,x54742))))
% 52.62/52.41 [5479]E(f55(x54791,x54792),f332(f332(f241(a1,a1),f2(a1)),x54791))+~P1(f332(f332(f232(a1),x54792),f2(a1)))
% 52.62/52.41 [5506]E(f53(a845,f332(f106(a845),x55061),f332(f106(a845),x55062)),f2(a845))+~P1(f332(a186,f332(f106(a1),x55061)))
% 52.62/52.41 [5520]P1(f332(f332(f232(a1),f2(a1)),f728(x55201)))+~P1(f332(x55201,f332(f102(a1),x55202)))
% 52.62/52.41 [5551]P40(f295(a1,x55511,x55512))+~P1(f332(f332(f232(a1),f2(a1)),x55511))
% 52.62/52.41 [5555]~P1(f332(f64(x55551),x55552))+P1(f332(f64(f853(x55551,a839)),f332(f301(x55551),x55552)))
% 52.62/52.41 [5568]E(f332(f332(f82(a1),x55681),f332(f102(a1),f786(x55682,x55681))),x55682)+~P1(f332(f332(f232(a1),x55681),x55682))
% 52.62/52.41 [5576]P1(f332(f332(f232(a845),x55761),x55762))+P1(f332(f332(f232(a845),f332(a114,x55762)),x55761))
% 52.62/52.41 [5621]E(f332(f332(f44(a845),f332(f106(a845),x56211)),f332(f106(a845),x56212)),f2(a845))+~P1(f332(a186,f332(f106(a1),x56211)))
% 52.62/52.41 [5622]E(f332(f332(f83(a845),f332(f106(a845),x56221)),f332(f106(a845),x56222)),f2(a845))+~P1(f332(f332(f233(a1),x56221),a85))
% 52.62/52.41 [5623]P1(f332(f332(f233(a845),x56231),f332(a114,x56232)))+~P1(f332(f332(f233(a845),x56231),x56232))
% 52.62/52.41 [5624]P1(f332(f332(f233(a845),x56241),f332(a114,x56242)))+~P1(f332(f332(f233(a845),x56241),x56242))
% 52.62/52.41 [5625]P1(f332(f332(f233(a845),x56251),f332(a114,x56252)))+~P1(f332(f332(f232(a845),x56251),x56252))
% 52.62/52.41 [5626]P1(f332(f332(f233(a845),x56261),f332(a114,x56262)))+~P1(f332(f332(f232(a845),x56261),x56262))
% 52.62/52.41 [5627]P1(f332(f332(f232(a845),x56271),f332(a114,x56272)))+~P1(f332(f332(f232(a845),x56271),x56272))
% 52.62/52.41 [5628]P1(f332(f332(f232(a845),x56281),f332(a114,x56282)))+~P1(f332(f332(f232(a845),x56281),x56282))
% 52.62/52.41 [5629]~E(x56291,x56292)+P1(f332(f332(f233(a1),x56291),f332(f332(f82(a1),x56292),f80(a1))))
% 52.62/52.41 [5632]E(f53(a1,x56321,x56322),f2(a1))+E(f332(f332(f3(a1),x56322),f53(a1,x56321,x56322)),f53(a1,f332(f81(a1),x56321),x56322))
% 52.62/52.41 [5640]E(x56401,f115(x56402))+P1(f332(f332(f334(x56402),f134(x56402,x56401)),f332(f158(x56402),x56401)))
% 52.62/52.41 [5651]E(f87(f852(a845,a845),f56(x56511,x56512)),f332(f332(f241(a845,a845),f2(a845)),x56511))+~P1(f332(f332(f233(a845),x56511),x56512))
% 52.62/52.41 [5652]E(f87(f852(a845,a845),f56(x56521,x56522)),f332(f332(f241(a845,a845),f2(a845)),x56521))+~P1(f332(f332(f233(a845),x56521),x56522))
% 52.62/52.41 [5692]E(f332(f332(f82(a845),f332(f106(a845),x56921)),f332(f106(a845),x56922)),f332(f106(a845),x56922))+~P1(f332(f332(f233(a1),x56921),a85))
% 52.62/52.41 [5693]E(f332(f332(f3(a845),f332(f106(a845),x56931)),f332(f106(a845),x56932)),f332(f106(a845),x56931))+~P1(f332(f332(f233(a1),x56932),a85))
% 52.62/52.41 [5698]E(f332(a114,f332(f332(f82(a845),x56981),f557(x56982,x56981))),x56982)+~P1(f332(f332(f233(a845),x56981),x56982))
% 52.62/52.41 [5699]E(f332(a114,f332(f332(f82(a845),x56991),f603(x56992,x56991))),x56992)+~P1(f332(f332(f233(a845),x56991),x56992))
% 52.62/52.41 [5706]~P1(f332(f332(f279(a1),x57061),x57062))+P1(f332(f332(f279(a1),x57061),f332(f81(a1),x57062)))
% 52.62/52.41 [5707]P1(f332(f332(f233(a845),f2(a845)),f618(x57071,x57072)))+~P1(f332(f332(f233(a845),x57072),x57071))
% 52.62/52.41 [5726]P1(f332(x57261,x57262))+~P1(f332(x57261,f332(a91,f604(x57262,x57261))))
% 52.62/52.41 [5734]~P1(f332(f332(f233(a845),x57341),f332(a114,x57342)))+P1(f332(f332(f232(a845),x57341),x57342))
% 52.62/52.41 [5783]E(f332(f332(f302(a845),x57831),f332(f294(a845,x57832),x57831)),f332(f294(a845,x57832),f332(a114,x57831)))+~P1(f332(f332(f232(a845),x57832),x57831))
% 52.62/52.41 [5788]E(x57881,f115(x57882))+E(f332(f332(f125(x57882),f116(x57882,x57881)),f332(f332(f140(x57882),f134(x57882,x57881)),f115(x57882))),x57881)
% 52.62/52.41 [5798]P1(f332(f64(x57981),x57982))+~P1(f332(f332(f233(a845),f2(a845)),f332(f43(x57981),x57982)))
% 52.62/52.41 [5799]P1(f332(f64(x57991),x57992))+~P1(f332(f332(f233(a845),f2(a845)),f332(f43(x57991),x57992)))
% 52.62/52.41 [5803]~E(x58031,f180(f853(x58032,a839)))+~P1(f332(f332(f233(a845),f2(a845)),f332(f43(x58032),x58031)))
% 52.62/52.41 [5811]~P1(f332(f332(f233(a845),x58111),x58112))+P1(f332(f332(f232(a845),f332(a114,x58111)),x58112))
% 52.62/52.41 [5812]~P1(f332(f332(f233(a845),x58121),x58122))+P1(f332(f332(f232(a845),f332(a114,x58121)),x58122))
% 52.62/52.41 [5813]~P1(f332(f332(f233(a845),x58131),x58132))+P1(f332(f332(f232(a845),f332(a114,x58131)),x58132))
% 52.62/52.41 [5821]E(x58211,f115(x58212))+P1(f332(f332(f334(x58212),f332(f131(x58212),x58211)),f332(f158(x58212),x58211)))
% 52.62/52.41 [5827]~P117(x58271)+P1(f332(f332(f233(x58271),x58272),f332(f332(f82(x58271),x58272),f80(x58271))))
% 52.62/52.41 [5829]~P80(x58291)+P1(f332(f332(f232(x58291),f332(f81(x58291),x58292)),f332(f77(x58291),x58292)))
% 52.62/52.41 [5841]P1(f332(f332(f279(a1),x58411),x58412))+~P1(f332(f332(f279(a1),x58411),f332(f81(a1),x58412)))
% 52.62/52.41 [5842]~E(x58421,x58422)+E(f282(a845,f279(a845),x58421,x58422),f332(f332(f302(a845),x58421),f180(f853(a845,a839))))
% 52.62/52.41 [5860]P1(f332(f64(a845),x58601))+~P1(f332(f332(f233(a845),f381(x58601,x58602)),x58602))
% 52.62/52.41 [5861]P1(f332(f64(a845),x58611))+~P1(f332(f332(f232(a845),f410(x58611,x58612)),x58612))
% 52.62/52.41 [5865]~P1(f332(f64(f852(x58651,x58651)),x58652))+P1(f332(f64(x58651),f332(f276(x58651),x58652)))
% 52.62/52.41 [5915]E(f282(a845,f279(a845),x59151,x59152),f180(f853(a845,a839)))+P1(f332(f332(f279(a845),x59151),x59152))
% 52.62/52.41 [5916]E(f282(a845,f279(a845),x59161,x59162),f180(f853(a845,a839)))+P1(f332(f332(f279(a845),x59161),x59162))
% 52.62/52.41 [5917]E(f163(f332(f106(a1),x59171),f332(f106(a1),x59172)),f115(a1))+P1(f332(f332(f232(a1),f332(f106(a1),x59171)),f332(f106(a1),x59172)))
% 52.62/52.41 [5922]~P1(f332(f332(f233(a845),x59222),f332(a114,x59221)))+~P1(f332(f332(f233(a845),x59221),x59222))
% 52.62/52.41 [5923]~P99(x59231)+E(f332(f332(f104(f853(x59231,a839)),f332(f293(x59231),x59232)),f332(f258(x59231),x59232)),f332(f332(f302(x59231),x59232),f180(f853(x59231,a839))))
% 52.62/52.41 [5925]E(f332(f332(f242(a845),f332(f106(a845),x59251)),f332(f106(a845),x59252)),f332(f332(f242(a845),f2(a845)),f332(f106(a845),x59252)))+~P1(f332(a186,f332(f106(a1),x59251)))
% 52.62/52.41 [5937]P1(f332(f64(x59371),x59372))+~P1(f332(f64(f853(x59371,a839)),f332(f301(x59371),x59372)))
% 52.62/52.41 [5960]P1(f332(f332(f233(a845),f332(a114,x59601)),f332(a114,x59602)))+~P1(f332(f332(f233(a845),x59601),x59602))
% 52.62/52.41 [5961]P1(f332(f332(f233(a845),f332(a114,x59611)),f332(a114,x59612)))+~P1(f332(f332(f233(a845),x59611),x59612))
% 52.62/52.41 [5962]P1(f332(f332(f233(a845),f332(a22,x59621)),f332(a22,x59622)))+~P1(f332(f332(f233(a101),x59621),x59622))
% 52.62/52.41 [5963]P1(f332(f332(f233(a101),f332(a5,x59631)),f332(a5,x59632)))+~P1(f332(f332(f233(a845),x59631),x59632))
% 52.62/52.41 [5964]P1(f332(f332(f232(a845),f332(a114,x59641)),f332(a114,x59642)))+~P1(f332(f332(f232(a845),x59641),x59642))
% 52.62/52.41 [5965]P1(f332(f332(f232(a845),f332(a22,x59651)),f332(a22,x59652)))+~P1(f332(f332(f232(a101),x59651),x59652))
% 52.62/52.41 [5966]P1(f332(f332(f232(a101),f332(a5,x59661)),f332(a5,x59662)))+~P1(f332(f332(f232(a845),x59661),x59662))
% 52.62/52.41 [5969]E(x59691,x59692)+~E(f332(f303(a845,a1,f102(a1)),x59691),f332(f303(a845,a1,f102(a1)),x59692))
% 52.62/52.41 [5985]P1(f332(f332(f233(a845),x59851),x59852))+~P1(f332(f332(f233(a845),f332(a114,x59851)),x59852))
% 52.62/52.41 [5986]P1(f332(f332(f233(a845),x59861),x59862))+~P1(f332(f332(f232(a845),f332(a114,x59861)),x59862))
% 52.62/52.41 [5987]P1(f332(f332(f233(a845),x59871),x59872))+~P1(f332(f332(f232(a845),f332(a114,x59871)),x59872))
% 52.62/52.41 [5988]P1(f332(f332(f233(a845),x59881),x59882))+~P1(f332(f332(f232(a845),f332(a114,x59881)),x59882))
% 52.62/52.41 [5989]P1(f332(f332(f232(a845),x59891),x59892))+~P1(f332(f332(f232(a845),f332(a114,x59891)),x59892))
% 52.62/52.41 [6006]E(f53(a1,x60061,x60062),f2(a1))+E(f332(f332(f3(a1),f53(a1,x60061,x60062)),x60062),f53(a1,x60061,f332(f81(a1),x60062)))
% 52.62/52.41 [6077]E(f332(f43(f853(x60771,a839)),f332(f301(x60771),x60772)),f332(f332(f242(a845),f332(a114,f332(a114,f2(a845)))),f332(f43(x60771),x60772)))+~P1(f332(f64(x60771),x60772))
% 52.62/52.41 [6080]E(x60801,f115(x60802))+E(f332(f332(f152(x60802),x60801),f332(f332(f3(a845),f332(f181(f846(x60802)),x60801)),f80(a845))),f134(x60802,x60801))
% 52.62/52.41 [6104]E(x61041,f115(x61042))+E(f332(f332(f125(x61042),f332(f157(x61042),x61041)),f332(f332(f140(x61042),f332(f131(x61042),x61041)),f115(x61042))),f332(f141(x61042),x61041))
% 52.62/52.41 [6105]~P1(f332(f180(f853(x61051,a839)),x61052))+P1(f332(f332(f334(x61051),x61052),f180(f853(x61051,a839))))
% 52.62/52.41 [6137]~P1(f332(f64(x61371),f45(f853(x61371,a839),x61372)))+P1(f332(f64(f853(x61371,a839)),x61372))
% 52.62/52.41 [6158]P1(f332(f332(f232(a845),f332(f106(a845),x61581)),f332(f106(a845),x61582)))+~P1(f332(f332(f232(a1),x61581),a85))
% 52.62/52.41 [6178]~P1(f332(f332(f233(a1),x61781),x61782))+P1(f332(f332(f233(a1),x61781),f332(f332(f82(a1),x61782),f80(a1))))
% 52.62/52.41 [6179]~P1(f332(f332(f232(a1),x61791),x61792))+P1(f332(f332(f233(a1),x61791),f332(f332(f82(a1),x61792),f80(a1))))
% 52.62/52.41 [6180]~P1(f332(f332(f233(a1),x61801),x61802))+P1(f332(f332(f232(a1),x61801),f332(f332(f3(a1),x61802),f80(a1))))
% 52.62/52.41 [6182]~P1(f332(f332(f233(a845),x61821),x61822))+P1(f332(f332(f233(a1),f332(f102(a1),x61821)),f332(f102(a1),x61822)))
% 52.62/52.41 [6183]~P1(f332(f332(f233(a845),x61831),x61832))+P1(f332(f332(f233(a1),f332(f102(a1),x61831)),f332(f102(a1),x61832)))
% 52.62/52.41 [6184]~P1(f332(f332(f233(a1),x61841),x61842))+P1(f332(f332(f233(a1),f332(f106(a1),x61841)),f332(f106(a1),x61842)))
% 52.62/52.41 [6185]~P1(f332(f332(f232(a1),x61851),x61852))+P1(f332(f332(f232(a845),f332(f106(a845),x61851)),f332(f106(a845),x61852)))
% 52.62/52.41 [6186]~P1(f332(f332(f232(a845),x61861),x61862))+P1(f332(f332(f232(a1),f332(f102(a1),x61861)),f332(f102(a1),x61862)))
% 52.62/52.41 [6187]~P1(f332(f332(f232(a845),x61871),x61872))+P1(f332(f332(f232(a1),f332(f102(a1),x61871)),f332(f102(a1),x61872)))
% 52.62/52.41 [6188]~P1(f332(f332(f232(a1),x61881),x61882))+P1(f332(f332(f232(a1),f332(f106(a1),x61881)),f332(f106(a1),x61882)))
% 52.62/52.41 [6189]~P1(f332(f332(f279(a845),x61891),x61892))+P1(f332(f332(f279(a1),f332(f102(a1),x61891)),f332(f102(a1),x61892)))
% 52.62/52.41 [6190]~P1(f332(f332(f279(a845),x61901),x61902))+P1(f332(f332(f279(a1),f332(f102(a1),x61901)),f332(f102(a1),x61902)))
% 52.62/52.41 [6197]~E(x61972,f180(f853(x61971,a839)))+P1(f332(f332(f232(f853(x61971,a839)),x61972),f180(f853(x61971,a839))))
% 52.62/52.41 [6206]~P1(f332(f332(f232(a845),x62061),x62062))+~P1(f332(f332(f232(a845),f332(a114,x62062)),x62061))
% 52.62/52.41 [6253]~P1(f332(f332(f233(a845),f332(a114,x62531)),f332(a114,x62532)))+P1(f332(f332(f233(a845),x62531),x62532))
% 52.62/52.41 [6254]~P1(f332(f332(f233(a845),f332(a114,x62541)),f332(a114,x62542)))+P1(f332(f332(f233(a845),x62541),x62542))
% 52.62/52.41 [6255]~P1(f332(f332(f233(a101),f332(a5,x62551)),f332(a5,x62552)))+P1(f332(f332(f233(a845),x62551),x62552))
% 52.62/52.41 [6256]~P1(f332(f332(f233(a845),f332(a107,x62561)),f332(a107,x62562)))+P1(f332(f332(f233(a1),x62561),x62562))
% 52.62/52.41 [6257]~P1(f332(f332(f233(a845),f332(a22,x62571)),f332(a22,x62572)))+P1(f332(f332(f233(a101),x62571),x62572))
% 52.62/52.41 [6258]~P1(f332(f332(f232(a845),f332(a114,x62581)),f332(a114,x62582)))+P1(f332(f332(f232(a845),x62581),x62582))
% 52.62/52.41 [6259]~P1(f332(f332(f232(a101),f332(a5,x62591)),f332(a5,x62592)))+P1(f332(f332(f232(a845),x62591),x62592))
% 52.62/52.41 [6260]~P1(f332(f332(f232(a845),f332(a22,x62601)),f332(a22,x62602)))+P1(f332(f332(f232(a101),x62601),x62602))
% 52.62/52.41 [6277]~P1(f332(f332(f279(a845),x62772),x62771))+P1(f332(f332(f334(a845),x62771),f286(a845,f279(a845),x62772)))
% 52.62/52.41 [6278]~P1(f332(f332(f279(a845),x62781),x62782))+P1(f332(f332(f334(a845),x62781),f288(a845,f279(a845),x62782)))
% 52.62/52.41 [6283]~P1(f332(f332(f334(x62831),x62832),f180(f853(x62831,a839))))+P1(f332(f180(f853(x62831,a839)),x62832))
% 52.62/52.41 [6304]~P1(f332(f332(f233(a845),f332(a107,x63042)),f332(a107,x63041)))+P1(f332(f332(f233(a1),f2(a1)),x63041))
% 52.62/52.41 [6315]~E(f53(a1,f332(f106(a1),x63152),f332(f106(a1),x63151)),f2(a1))+P1(f332(f332(f279(a1),f332(f106(a1),x63151)),f332(f106(a1),x63152)))
% 52.62/52.41 [6333]P1(f332(f332(f232(a1),f2(a1)),f53(a1,x63331,x63332)))+~P1(f332(f332(f233(a1),f2(a1)),x63332))
% 52.62/52.41 [6334]P1(f332(f332(f232(a1),f2(a1)),f53(a1,x63341,x63342)))+~P1(f332(f332(f233(a1),f2(a1)),x63342))
% 52.62/52.41 [6503]P38(x65031,x65032)+~E(f332(f332(f281(x65031,x65031,x65031),x65032),x65032),f180(f853(f852(x65031,x65031),a839)))
% 52.62/52.41 [6519]~P38(x65191,x65192)+P38(x65191,f332(f332(f281(x65191,x65191,x65191),x65192),x65192))
% 52.62/52.41 [6531]P1(f332(f332(f233(a1),x65311),x65312))+~P1(f332(f332(f232(a1),x65311),f332(f332(f3(a1),x65312),f80(a1))))
% 52.62/52.41 [6532]P1(f332(f332(f232(a1),x65321),x65322))+~P1(f332(f332(f233(a1),x65321),f332(f332(f82(a1),x65322),f80(a1))))
% 52.62/52.41 [6534]P1(f332(f332(f233(a845),x65341),x65342))+~P1(f332(f332(f233(a1),f332(f102(a1),x65341)),f332(f102(a1),x65342)))
% 52.62/52.41 [6535]P1(f332(f332(f233(a845),x65351),x65352))+~P1(f332(f332(f233(a1),f332(f102(a1),x65351)),f332(f102(a1),x65352)))
% 52.62/52.41 [6536]P1(f332(f332(f233(a1),x65361),x65362))+~P1(f332(f332(f233(a845),f332(f106(a845),x65361)),f332(f106(a845),x65362)))
% 52.62/52.41 [6537]P1(f332(f332(f233(a1),x65371),x65372))+~P1(f332(f332(f233(a1),f332(f106(a1),x65371)),f332(f106(a1),x65372)))
% 52.62/52.41 [6538]P1(f332(f332(f232(a845),x65381),x65382))+~P1(f332(f332(f232(a1),f332(f102(a1),x65381)),f332(f102(a1),x65382)))
% 52.62/52.41 [6539]P1(f332(f332(f232(a845),x65391),x65392))+~P1(f332(f332(f232(a1),f332(f102(a1),x65391)),f332(f102(a1),x65392)))
% 52.62/52.41 [6540]P1(f332(f332(f232(a1),x65401),x65402))+~P1(f332(f332(f232(a1),f332(f106(a1),x65401)),f332(f106(a1),x65402)))
% 52.62/52.41 [6541]P1(f332(f332(f279(a845),x65411),x65412))+~P1(f332(f332(f279(a1),f332(f102(a1),x65411)),f332(f102(a1),x65412)))
% 52.62/52.41 [6542]P1(f332(f332(f279(a845),x65421),x65422))+~P1(f332(f332(f279(a1),f332(f102(a1),x65421)),f332(f102(a1),x65422)))
% 52.62/52.41 [6597]E(f53(a1,f332(f106(a1),x65971),f332(f106(a1),x65972)),f2(a1))+~P1(f332(f332(f279(a1),f332(f106(a1),x65972)),f332(f106(a1),x65971)))
% 52.62/52.41 [6611]~E(f282(a845,f279(a845),x66111,x66112),f180(f853(a845,a839)))+~P1(f332(f332(f279(a845),x66111),x66112))
% 52.62/52.41 [6612]~E(f282(a845,f279(a845),x66121,x66122),f180(f853(a845,a839)))+~P1(f332(f332(f279(a845),x66121),x66122))
% 52.62/52.41 [6638]P1(f332(f332(f279(a845),x66381),x66382))+~P1(f332(f332(f334(a845),x66382),f286(a845,f279(a845),x66381)))
% 52.62/52.41 [6639]P1(f332(f332(f279(a845),x66391),x66392))+~P1(f332(f332(f334(a845),x66391),f288(a845,f279(a845),x66392)))
% 52.62/52.41 [6640]~E(f771(x66402,x66401),f115(x66401))+E(f332(f132(f846(x66401),f846(x66401),f125(x66401),f115(x66401)),x66402),f115(x66401))
% 52.62/52.41 [6641]~E(f772(x66412,x66411),f115(x66411))+E(f332(f132(f846(x66411),f846(x66411),f125(x66411),f115(x66411)),x66412),f115(x66411))
% 52.62/52.41 [6648]~P11(x66481)+E(f332(f132(x66481,x66481,f104(x66481),f239(x66481)),x66482),f46(x66481,f332(f158(x66481),x66482)))
% 52.62/52.41 [6649]~P11(x66491)+E(f332(f132(x66491,x66491,f103(x66491),f180(x66491)),x66492),f45(x66491,f332(f158(x66491),x66492)))
% 52.62/52.41 [6661]E(x66611,f2(a101))+E(f332(f332(f82(a845),f332(a22,f332(f332(f3(a101),x66611),f80(a101)))),f332(a114,x66612)),f332(f332(f82(a845),f332(a22,x66611)),x66612))
% 52.62/52.41 [6713]P1(f332(f332(f233(a1),f332(f332(f3(a1),x67131),x67132)),f2(a1)))+~P1(f332(f332(f233(a1),x67131),x67132))
% 52.62/52.41 [6740]~P100(x67401)+E(f332(f332(f103(f853(x67401,a839)),f332(f332(f302(x67401),x67402),f180(f853(x67401,a839)))),f332(f296(x67401),x67402)),f332(f258(x67401),x67402))
% 52.62/52.41 [6822]~P60(x68221,x68222)+P38(x68221,f332(f256(f852(x68221,x68221)),f332(f251(x68221,x68221,a839),x68222)))
% 52.62/52.41 [6823]~P60(x68231,x68232)+P58(x68231,f332(f256(f852(x68231,x68231)),f332(f251(x68231,x68231,a839),x68232)))
% 52.62/52.41 [6824]E(x68241,f180(f853(x68242,a839)))+~P1(f332(f332(f232(f853(x68242,a839)),x68241),f180(f853(x68242,a839))))
% 52.62/52.41 [6909]~P1(f332(f332(f233(a845),f2(a845)),x69092))+P1(f332(f332(f233(a845),f53(a845,x69091,x69092)),x69092))
% 52.62/52.41 [6910]~P1(f332(f332(f233(a1),f2(a1)),x69102))+P1(f332(f332(f233(a1),f53(a1,x69101,x69102)),x69102))
% 52.62/52.41 [6911]~P1(f332(f332(f233(a1),f2(a1)),x69112))+P1(f332(f332(f233(a1),f53(a1,x69111,x69112)),x69112))
% 52.62/52.41 [6912]~P1(f332(f332(f233(a845),f2(a845)),x69122))+P1(f332(f332(f232(a845),f53(a845,x69121,x69122)),x69122))
% 52.62/52.41 [6913]~P1(f332(f332(f232(a1),f2(a1)),x69131))+P1(f332(f332(f232(a1),f53(a1,x69131,x69132)),x69131))
% 52.62/52.41 [6985]~P99(x69851)+E(f332(f332(f3(f853(x69851,a839)),f332(f332(f302(x69851),x69852),f180(f853(x69851,a839)))),f332(f257(x69851),x69852)),f332(f332(f302(x69851),x69852),f180(f853(x69851,a839))))
% 52.62/52.41 [7063]~P51(x70631,x70632)+P49(x70631,f239(f853(x70631,a839)),f332(f256(f852(x70631,x70631)),f332(f251(x70631,x70631,a839),x70632)))
% 52.62/52.41 [7064]P1(f332(x70641,x70642))+P1(f332(f332(f334(f853(f852(a845,a845),a839)),f604(x70642,x70641)),a100))
% 52.62/52.41 [7106]E(f332(f332(f125(a845),f130(a845,f332(f294(a845,x71061),x71062))),f332(f332(f140(a845),x71062),f115(a845))),f130(a845,f332(f294(a845,x71061),f332(a114,x71062))))+~P1(f332(f332(f232(a845),x71061),x71062))
% 52.62/52.41 [7107]E(f332(f332(f125(a845),f130(a845,f332(f294(a845,x71071),x71072))),f332(f332(f140(a845),x71072),f115(a845))),f130(a845,f332(f294(a845,x71071),f332(a114,x71072))))+~P1(f332(f332(f232(a845),x71071),x71072))
% 52.62/52.41 [7264]E(x72641,f2(a845))+~E(f332(f132(a845,a845,f82(a845),x72641),x72642),f2(a845))
% 52.62/52.41 [7293]~P1(f332(f332(f233(a1),f332(f332(f3(a1),x72931),x72932)),f2(a1)))+P1(f332(f332(f233(a1),x72931),x72932))
% 52.62/52.41 [7323]P38(x73231,x73232)+~P38(x73231,f332(f332(f281(x73231,x73231,x73231),x73232),x73232))
% 52.62/52.41 [7355]~P1(f332(f332(f232(a845),f332(a114,x73551)),x73552))+P1(f175(a839,a178,f332(f232(a845),x73551),x73552))
% 52.62/52.41 [7515]P31(a845,a845,f332(f332(f9(a845,a845,a845),f3(a845)),x75151),x75152)+P1(f332(f332(f334(a845),f607(x75151,x75152)),x75152))
% 52.62/52.41 [7573]E(f332(f332(f332(f68(a845,x75731,f82(a845)),f332(f18(a845,x75731),f80(a845))),f2(a845)),x75732),f332(f43(x75731),x75732))+~P1(f332(f64(x75731),x75732))
% 52.62/52.41 [7574]E(f332(f332(f332(f68(a845,x75741,f82(a845)),f332(f18(a845,x75741),f80(a845))),f2(a845)),x75742),f332(f43(x75741),x75742))+~P1(f332(f64(x75741),x75742))
% 52.62/52.41 [7617]P31(a845,a845,f332(f332(f9(a845,a845,a845),f3(a845)),x76171),x76172)+~P1(f332(f332(f232(a845),x76171),f607(x76171,x76172)))
% 52.62/52.41 [7674]P38(x76741,x76742)+P1(f332(f332(f232(f853(x76741,a839)),f601(x76742,x76741)),f332(f277(x76741,x76741,x76742),f601(x76742,x76741))))
% 52.62/52.41 [7678]P60(x76781,x76782)+~P38(x76781,f332(f256(f852(x76781,x76781)),f332(f251(x76781,x76781,a839),x76782)))
% 52.62/52.41 [7750]P1(f332(f332(f232(a845),f332(a114,x77501)),x77502))+~P1(f175(a839,a178,f332(f232(a845),x77501),x77502))
% 52.62/52.41 [7806]P1(f332(f332(f334(f852(a845,a845)),f332(f332(f241(a845,a845),x78061),x78062)),f300(a845,a323)))+~P1(f332(f332(f232(a845),x78061),x78062))
% 52.62/52.41 [7900]P51(x79001,x79002)+~P49(x79001,f239(f853(x79001,a839)),f332(f256(f852(x79001,x79001)),f332(f251(x79001,x79001,a839),x79002)))
% 52.62/52.41 [8156]~P38(x81561,f332(f278(x81561,x81561),x81562))+P38(x81561,f332(f278(x81561,x81561),f332(f332(f281(x81561,x81561,x81561),x81562),f300(x81561,x81562))))
% 52.62/52.41 [8273]P1(f332(f64(f852(x82731,x82731)),f332(f332(f281(x82731,x82731,x82731),x82732),f300(x82731,x82732))))+~P1(f332(f64(f852(x82731,x82731)),x82732))
% 52.62/52.41 [8303]E(x83031,f2(a1))+P1(f332(f57(x83032,x83031),f332(f332(f241(a1,a1),f332(f332(f44(a1),x83032),x83031)),f53(a1,x83032,x83031))))
% 52.62/52.41 [8317]~P1(f332(f332(f334(f852(a845,a845)),f332(f332(f241(a845,a845),x83171),x83172)),f300(a845,a323)))+P1(f332(f332(f232(a845),x83171),x83172))
% 52.62/52.41 [8338]~P3(x83381)+E(f332(f132(x83381,x83381,f332(f9(x83381,x83381,x83381),f82(x83381)),f2(x83381)),f332(f142(x83381),x83382)),f332(f132(x83381,x83381,f82(x83381),f2(x83381)),x83382))
% 52.62/52.41 [8613]P1(f332(f332(f334(f852(a845,a845)),f332(f332(f241(a845,a845),x86131),x86132)),f332(f332(f281(a845,a845,a845),a323),f300(a845,a323))))+~P1(f332(f332(f233(a845),x86131),x86132))
% 52.62/52.41 [8655]~P1(f332(f64(f852(x86551,x86551)),f332(f332(f281(x86551,x86551,x86551),x86552),f300(x86551,x86552))))+P1(f332(f64(f852(x86551,x86551)),x86552))
% 52.62/52.41 [8875]P58(x88751,x88752)+P1(f332(f332(f334(f852(x88751,x88751)),f332(f332(f241(x88751,x88751),f631(x88752,x88751)),f631(x88752,x88751))),f332(f332(f281(x88751,x88751,x88751),x88752),f300(x88751,x88752))))
% 52.62/52.41 [8876]P58(x88761,x88762)+P1(f332(f332(f334(f852(x88761,x88761)),f332(f332(f241(x88761,x88761),f641(x88762,x88761)),f641(x88762,x88761))),f332(f332(f281(x88761,x88761,x88761),x88762),f300(x88761,x88762))))
% 52.62/52.41 [8985]~P1(f332(f332(f334(f852(a845,a845)),f332(f332(f241(a845,a845),x89851),x89852)),f332(f332(f281(a845,a845,a845),a323),f300(a845,a323))))+P1(f332(f332(f233(a845),x89851),x89852))
% 52.62/52.41 [4964]~P88(x49641)+E(f332(f332(f82(x49641),f332(f106(x49641),a85)),x49642),x49642)
% 52.62/52.41 [4994]~P69(x49941)+E(f332(f332(f82(x49941),f332(f81(x49941),x49942)),x49942),f2(x49941))
% 52.62/52.41 [4995]~P8(x49951)+E(f332(f332(f82(x49951),f332(f81(x49951),x49952)),x49952),f2(x49951))
% 52.62/52.41 [4996]~P90(x49961)+E(f332(f332(f103(x49961),f332(f81(x49961),x49962)),x49962),f239(x49961))
% 52.62/52.41 [4997]~P90(x49971)+E(f332(f332(f104(x49971),f332(f81(x49971),x49972)),x49972),f180(x49971))
% 52.62/52.41 [5027]~P88(x50271)+E(f332(f332(f83(x50271),f332(f106(x50271),a99)),x50272),f332(f81(x50271),x50272))
% 52.62/52.41 [5187]~P104(x51871)+E(f332(f332(f83(x51871),f332(f81(x51871),f80(x51871))),x51872),f332(f81(x51871),x51872))
% 52.62/52.41 [5229]E(f332(f77(a1),x52291),f80(a1))+~E(f332(f77(a1),f332(f332(f83(a1),x52291),x52292)),f80(a1))
% 52.62/52.41 [5316]~P88(x53161)+E(f332(f332(f82(x53161),f80(x53161)),f332(f106(x53161),x53162)),f332(f106(x53161),f332(f332(f3(a1),x53162),a99)))
% 52.62/52.41 [5371]~P93(x53711)+E(f15(x53711,f332(f332(f302(x53711),x53712),f180(f853(x53711,a839)))),x53712)
% 52.62/52.41 [5372]~P100(x53721)+E(f16(x53721,f332(f332(f302(x53721),x53722),f180(f853(x53721,a839)))),x53722)
% 52.62/52.41 [5373]~P100(x53731)+E(f17(x53731,f332(f332(f302(x53731),x53732),f180(f853(x53731,a839)))),x53732)
% 52.62/52.41 [5374]~P93(x53741)+E(f12(x53741,f332(f332(f302(x53741),x53742),f180(f853(x53741,a839)))),x53742)
% 52.62/52.41 [5375]~P11(x53751)+E(f46(x53751,f332(f332(f302(x53751),x53752),f180(f853(x53751,a839)))),x53752)
% 52.62/52.41 [5376]~P11(x53761)+E(f45(x53761,f332(f332(f302(x53761),x53762),f180(f853(x53761,a839)))),x53762)
% 52.62/52.41 [5398]E(f332(f332(f82(a845),x53981),f332(f332(f3(a845),x53982),x53981)),x53982)+P1(f332(f332(f233(a845),x53982),x53981))
% 52.62/52.41 [5430]E(x54301,f115(x54302))+P1(f332(f332(f233(a845),f2(a845)),f332(f181(f846(x54302)),x54301)))
% 52.62/52.41 [5548]~P100(x55481)+E(f13(x55481,f179(x55481),f332(f332(f302(x55481),x55482),f180(f853(x55481,a839)))),x55482)
% 52.62/52.41 [5549]~P100(x55491)+E(f14(x55491,f236(x55491),f332(f332(f302(x55491),x55492),f180(f853(x55491,a839)))),x55492)
% 52.62/52.41 [5610]E(f332(f332(f82(a845),x56101),f332(f332(f3(a845),x56102),x56101)),x56102)+~P1(f332(f332(f232(a845),x56101),x56102))
% 52.62/52.41 [5611]E(f332(f332(f83(a1),x56111),f332(f332(f44(a1),x56112),x56111)),x56112)+~P1(f332(f332(f279(a1),x56111),x56112))
% 52.62/52.41 [5612]E(f332(f332(f3(a845),x56121),f332(f332(f3(a845),x56121),x56122)),x56122)+~P1(f332(f332(f232(a845),x56122),x56121))
% 52.62/52.41 [5630]E(f53(a845,f332(f332(f3(a845),x56301),x56302),x56302),f53(a845,x56301,x56302))+P1(f332(f332(f233(a845),x56301),x56302))
% 52.62/52.41 [5631]E(f53(a845,f332(f332(f3(a845),x56311),x56312),x56312),f53(a845,x56311,x56312))+P1(f332(f332(f233(a845),x56311),x56312))
% 52.62/52.41 [5641]E(f332(f81(a1),f332(f332(f44(a1),x56411),f332(f81(a1),x56412))),f285(x56411,x56412))+P1(f332(f332(f232(a1),f2(a1)),x56412))
% 52.62/52.41 [5643]~E(x56432,f2(a845))+P1(f332(f332(f233(a845),f2(a845)),f332(f332(f242(a845),x56431),x56432)))
% 52.62/52.41 [5703]~P88(x57031)+E(f332(f332(f82(x57031),f332(f81(x57031),f80(x57031))),f332(f106(x57031),x57032)),f332(f106(x57031),f332(f332(f82(a1),x57032),a99)))
% 52.62/52.41 [5704]E(f332(f332(f242(a845),f332(f106(a845),x57041)),x57042),f332(f332(f242(a845),f2(a845)),x57042))+~P1(f332(a186,f332(f106(a1),x57041)))
% 52.62/52.41 [5805]E(f332(f131(a845),f130(a845,f332(f294(a845,x58051),x58052))),x58051)+~P1(f332(f332(f233(a845),x58051),x58052))
% 52.62/52.41 [5822]E(f332(f332(f83(a845),f332(f106(a845),x58221)),f332(f106(a845),x58222)),f332(f106(a845),f332(f332(f83(a1),x58221),x58222)))+P1(f332(f332(f233(a1),x58221),a85))
% 52.62/52.41 [5828]~P118(x58281)+P1(f332(f332(f232(x58281),f2(x58281)),f332(f332(f83(x58281),x58282),x58282)))
% 52.62/52.41 [5840]E(f332(f332(f3(a845),f332(a114,x58401)),x58402),f332(a114,f332(f332(f3(a845),x58401),x58402)))+~P1(f332(f332(f232(a845),x58402),x58401))
% 52.62/52.41 [5843]E(f53(a845,f332(f332(f3(a845),x58431),x58432),x58432),f53(a845,x58431,x58432))+~P1(f332(f332(f232(a845),x58432),x58431))
% 52.62/52.41 [5894]E(f332(f332(f242(a845),f332(a107,x58941)),x58942),f332(a107,f332(f332(f242(a1),x58941),x58942)))+~P1(f332(f332(f232(a1),f2(a1)),x58941))
% 52.62/52.41 [5895]E(f332(f332(f242(a845),f332(a107,x58951)),x58952),f332(a107,f332(f332(f242(a1),x58951),x58952)))+~P1(f332(f332(f232(a1),f2(a1)),x58951))
% 52.62/52.41 [5911]P1(f332(f127(x59111),x59112))+P1(f332(f332(f233(a845),f722(x59112,x59111)),f332(f181(f846(x59111)),x59112)))
% 52.62/52.41 [5912]P1(f332(f127(x59121),x59122))+P1(f332(f332(f233(a845),f726(x59122,x59121)),f332(f181(f846(x59121)),x59122)))
% 52.62/52.41 [5928]~P1(f332(f332(f279(a1),x59281),x59282))+P1(f332(f332(f279(a1),f332(f81(a1),x59281)),x59282))
% 52.62/52.41 [5931]~E(x59311,f115(x59312))+~P1(f332(f332(f233(a845),f2(a845)),f332(f181(f846(x59312)),x59311)))
% 52.62/52.41 [5944]E(f134(a845,f130(a845,f332(f294(a845,x59441),x59442))),f332(f332(f3(a845),x59442),f80(a845)))+~P1(f332(f332(f233(a845),x59441),x59442))
% 52.62/52.41 [5947]E(f332(f332(f82(a1),x59471),f332(f102(a1),f332(a114,f605(x59472,x59471)))),x59472)+~P1(f332(f332(f233(a1),x59471),x59472))
% 52.62/52.41 [5953]E(x59531,f2(a845))+E(f332(f332(f83(a845),x59532),f332(f332(f242(a845),x59532),f332(f332(f3(a845),x59531),f80(a845)))),f332(f332(f242(a845),x59532),x59531))
% 52.62/52.41 [5979]E(f332(f332(f83(a845),f332(a107,x59791)),f332(a107,x59792)),f332(a107,f332(f332(f83(a1),x59791),x59792)))+~P1(f332(f332(f232(a1),f2(a1)),x59791))
% 52.62/52.41 [5980]E(f332(f332(f44(a845),f332(a107,x59801)),f332(a107,x59802)),f332(a107,f332(f332(f44(a1),x59801),x59802)))+~P1(f332(f332(f232(a1),f2(a1)),x59801))
% 52.62/52.41 [5994]~P73(x59941)+E(f332(f332(f82(x59941),x59942),x59942),f332(f332(f83(x59941),f332(f332(f82(x59941),f80(x59941)),f80(x59941))),x59942))
% 52.62/52.41 [6013]E(f332(f332(f44(a1),f332(f77(a1),x60131)),f332(f77(a1),x60132)),f332(f77(a1),f332(f332(f44(a1),x60131),x60132)))+~P1(f332(f332(f279(a1),x60132),x60131))
% 52.62/52.41 [6014]E(f332(f332(f3(a1),f332(f102(a1),x60141)),f332(f102(a1),x60142)),f332(f102(a1),f332(f332(f3(a845),x60141),x60142)))+~P1(f332(f332(f232(a845),x60142),x60141))
% 52.62/52.41 [6016]E(f332(f332(f241(a1,a1),f332(f106(a1),a99)),f332(f332(f82(a1),x60161),x60162)),f58(x60161,x60162))+~P1(f332(f332(f232(a1),x60162),f2(a1)))
% 52.62/52.41 [6055]E(f164(x60551,x60552),f115(f846(x60551)))+P1(f332(f332(f334(f846(x60551)),f721(x60552,x60551)),f332(f158(f846(x60551)),x60552)))
% 52.62/52.41 [6121]~P1(f332(f332(f279(a845),x61211),x61212))+P1(f332(f332(f279(a845),x61211),f332(f332(f82(a845),x61212),x61211)))
% 52.62/52.41 [6143]E(f332(f332(f140(a1),x61431),f163(f332(f332(f82(a1),x61431),f80(a1)),x61432)),f163(x61431,x61432))+~P1(f332(f332(f232(a1),x61431),x61432))
% 52.62/52.41 [6181]~P1(f332(f332(f233(a845),x61812),x61811))+P1(f332(f332(f233(a845),f2(a845)),f332(f332(f3(a845),x61811),x61812)))
% 52.62/52.41 [6213]~P1(f332(f332(f233(a845),x62131),f332(a107,x62132)))+P1(f332(f332(f233(a1),f332(f102(a1),x62131)),x62132))
% 52.62/52.41 [6214]P1(f332(f332(f279(a1),x62141),x62142))+~P1(f332(f332(f279(a1),f332(f81(a1),x62141)),x62142))
% 52.62/52.41 [6244]~P100(x62441)+E(f332(f332(f103(f853(x62441,a839)),f332(f257(x62441),x62442)),f332(f332(f302(x62441),x62442),f180(f853(x62441,a839)))),f332(f293(x62441),x62442))
% 52.62/52.41 [6245]~P1(f332(f332(f233(a845),f2(a845)),x62452))+P1(f332(f332(f233(a845),f2(a845)),f332(f332(f82(a845),x62451),x62452)))
% 52.62/52.41 [6246]~P1(f332(f332(f233(a845),f2(a845)),x62461))+P1(f332(f332(f233(a845),f2(a845)),f332(f332(f82(a845),x62461),x62462)))
% 52.62/52.41 [6247]~P1(f332(f332(f233(a845),f2(a845)),x62471))+P1(f332(f332(f233(a845),f2(a845)),f332(f332(f242(a845),x62471),x62472)))
% 52.62/52.41 [6248]~P1(f332(f332(f232(a1),f2(a1)),x62481))+P1(f332(f332(f232(a1),f2(a1)),f332(f332(f242(a1),x62481),x62482)))
% 52.62/52.41 [6276]~E(f332(x62761,f2(a845)),f2(a845))+E(f332(f332(f8(a845,a845),x62761),f295(a845,f332(a114,f2(a845)),x62762)),f332(f332(f8(a845,a845),x62761),f295(a845,f2(a845),x62762)))
% 52.62/52.41 [6342]~P88(x63421)+E(f332(f332(f83(x63421),f332(f332(f82(x63421),f80(x63421)),f80(x63421))),f332(f106(x63421),x63422)),f332(f106(x63421),f332(f332(f82(a1),x63422),x63422)))
% 52.62/52.41 [6364]E(f332(f332(f302(a1),x63641),f295(a1,f332(f332(f82(a1),x63641),f80(a1)),x63642)),f295(a1,x63641,x63642))+P1(f332(f332(f233(a1),x63642),x63641))
% 52.62/52.41 [6365]P1(f332(f332(f233(a845),x63651),f332(a107,x63652)))+~P1(f332(f332(f233(a1),f332(f102(a1),x63651)),x63652))
% 52.62/52.41 [6467]P1(f332(f332(f279(a845),x64671),x64672))+~P1(f332(f332(f279(a845),x64671),f332(f332(f82(a845),x64672),x64671)))
% 52.62/52.41 [6473]E(f332(a107,f332(f332(f44(a1),f332(f106(a1),x64731)),f332(f106(a1),x64732))),f332(f332(f44(a845),f332(f106(a845),x64731)),f332(f106(a845),x64732)))+P1(f332(a186,f332(f106(a1),x64731)))
% 52.62/52.41 [6474]E(f332(a107,f332(f332(f242(a1),f332(f106(a1),x64741)),f332(f106(a845),x64742))),f332(f332(f242(a845),f332(f106(a845),x64741)),f332(f106(a845),x64742)))+P1(f332(a186,f332(f106(a1),x64741)))
% 52.62/52.41 [6533]P1(f332(f332(f233(a845),x65331),x65332))+~P1(f332(f332(f233(a845),f2(a845)),f332(f332(f3(a845),x65332),x65331)))
% 52.62/52.41 [6576]P1(f332(f332(f233(a845),f2(a845)),x65761))+~P1(f332(f332(f233(a845),f2(a845)),f332(f332(f83(a845),x65762),x65761)))
% 52.62/52.41 [6577]P1(f332(f332(f233(a845),f2(a845)),x65771))+~P1(f332(f332(f233(a845),f2(a845)),f332(f332(f83(a845),x65771),x65772)))
% 52.62/52.41 [6591]E(f130(a845,f332(f294(a845,f332(f106(a845),x65911)),f332(f106(a845),x65912))),f115(a845))+P1(f332(f332(f233(a845),f332(f106(a845),x65911)),f332(f106(a845),x65912)))
% 52.62/52.41 [6593]~P1(f332(f332(f232(a1),x65931),f2(a1)))+E(f332(f332(f83(a845),f332(a107,f332(f81(a1),x65931))),f332(a107,f332(f81(a1),x65932))),f332(a107,f332(f332(f83(a1),x65931),x65932)))
% 52.62/52.41 [6659]~E(x66592,f180(f853(x66591,a839)))+P1(f332(f332(f232(f853(x66591,a839)),x66592),f332(f81(f853(x66591,a839)),x66592)))
% 52.62/52.41 [6722]~P88(x67221)+E(f332(f332(f82(x67221),f332(f332(f82(x67221),f2(x67221)),f332(f106(x67221),x67222))),f332(f106(x67221),x67222)),f332(f106(x67221),f332(f332(f82(a1),x67222),x67222)))
% 52.62/52.41 [6731]~P1(f332(f332(f279(a1),f332(f102(a1),x67311)),x67312))+P1(f332(f332(f279(a845),x67311),f332(a107,f332(f77(a1),x67312))))
% 52.62/52.41 [6781]~P1(f332(f332(f233(a1),x67811),x67812))+P1(f332(f332(f232(a1),f332(f332(f82(a1),x67811),f80(a1))),x67812))
% 52.62/52.41 [6782]~P1(f332(f332(f233(a1),x67821),x67822))+P1(f332(f332(f232(a1),f332(f332(f82(a1),x67821),f80(a1))),x67822))
% 52.62/52.41 [6821]P1(f332(f332(f279(a1),f332(f102(a1),x68211)),x68212))+~P1(f332(f332(f279(a845),x68211),f332(a107,f332(f77(a1),x68212))))
% 52.62/52.41 [6855]E(x68551,f2(a845))+~P1(f332(f332(f232(a1),f332(f102(a1),x68552)),f332(f81(a1),f332(f102(a1),x68551))))
% 52.62/52.41 [6856]E(x68561,f2(a845))+~P1(f332(f332(f232(a1),f332(f102(a1),x68561)),f332(f81(a1),f332(f102(a1),x68562))))
% 52.62/52.41 [6961]E(f332(f332(f241(a1,a1),f332(f106(a1),a99)),f332(f332(f82(a1),x69611),x69612)),f58(x69611,x69612))+~P1(f332(f332(f232(a1),f2(a1)),f332(f332(f82(a1),x69611),x69612)))
% 52.62/52.41 [6998]~P32(x69981,x69982)+P38(x69981,f332(f240(f853(f852(x69981,x69981),a839),f853(f852(x69981,x69981),a839)),x69982))
% 52.62/52.41 [7019]~P1(f332(f332(f232(a845),f332(a114,f2(a845))),x70191))+P1(f332(f332(f232(a845),f332(a114,f2(a845))),f332(f332(f242(a845),x70191),x70192)))
% 52.62/52.41 [7188]~P1(f332(f332(f233(a1),x71881),x71882))+P1(f332(f332(f233(a1),f332(f332(f82(a1),x71881),x71881)),f332(f332(f82(a1),x71882),x71882)))
% 52.62/52.41 [7189]~P1(f332(f332(f233(a1),x71891),x71892))+P1(f332(f332(f233(a1),f332(f332(f82(a1),x71891),x71891)),f332(f332(f82(a1),x71892),x71892)))
% 52.62/52.41 [7200]~P1(f332(f332(f232(a1),x72001),x72002))+P1(f332(f332(f232(a1),f332(f332(f82(a1),x72001),x72001)),f332(f332(f82(a1),x72002),x72002)))
% 52.62/52.41 [7201]~P1(f332(f332(f232(a1),x72011),x72012))+P1(f332(f332(f232(a1),f332(f332(f82(a1),x72011),x72011)),f332(f332(f82(a1),x72012),x72012)))
% 52.62/52.41 [7268]~P1(f332(f332(f233(a845),f2(a845)),x72681))+P1(f332(f332(f233(a845),f332(f332(f3(a845),x72681),f332(a114,x72682))),x72681))
% 52.62/52.41 [7305]P1(f332(f332(f232(a845),f332(a114,f2(a845))),x73051))+~P1(f332(f332(f232(a845),f332(a114,f2(a845))),f332(f332(f83(a845),x73052),x73051)))
% 52.62/52.41 [7306]P1(f332(f332(f232(a845),f332(a114,f2(a845))),x73061))+~P1(f332(f332(f232(a845),f332(a114,f2(a845))),f332(f332(f83(a845),x73061),x73062)))
% 52.62/52.41 [7310]P1(f332(f332(f232(a845),f332(f332(f152(a845),x73101),x73102)),f332(f154(a845),x73101)))+~P1(f332(f332(f233(a845),x73102),f332(f181(f846(a845)),x73101)))
% 52.62/52.41 [7354]P1(f332(f332(f233(a1),x73541),x73542))+~P1(f332(f332(f232(a1),f332(f332(f82(a1),x73541),f80(a1))),x73542))
% 52.62/52.41 [7363]~P1(f332(f332(f334(a845),x73631),x73632))+P1(f332(f332(f334(a1),f332(f102(a1),x73631)),f332(f303(a845,a1,f102(a1)),x73632)))
% 52.62/52.41 [7400]P1(f332(f64(x74001),f239(f853(x74001,a839))))+~P1(f332(f64(f853(x74002,x74001)),f239(f853(f853(x74002,x74001),a839))))
% 52.62/52.41 [7401]P1(f332(f64(x74011),f239(f853(x74011,a839))))+~P1(f332(f64(f854(x74012,x74011)),f239(f853(f854(x74012,x74011),a839))))
% 52.62/52.41 [7402]P1(f332(f64(x74021),f239(f853(x74021,a839))))+~P1(f332(f64(f854(x74021,x74022)),f239(f853(f854(x74021,x74022),a839))))
% 52.62/52.41 [7441]E(x74411,f180(f853(x74412,a839)))+~P1(f332(f332(f232(f853(x74412,a839)),x74411),f332(f81(f853(x74412,a839)),x74411)))
% 52.62/52.41 [7584]E(f332(f132(f846(x75841),f846(x75841),f125(x75841),f115(x75841)),x75842),f115(x75841))+P1(f332(f332(f334(f846(x75841)),f771(x75842,x75841)),f332(f158(f846(x75841)),x75842)))
% 52.62/52.41 [7585]E(f332(f132(f846(x75851),f846(x75851),f125(x75851),f115(x75851)),x75852),f115(x75851))+P1(f332(f332(f334(f846(x75851)),f772(x75852,x75851)),f332(f158(f846(x75851)),x75852)))
% 52.62/52.41 [7721]E(f164(x77211,f332(f332(f140(f846(x77211)),f115(x77211)),x77212)),f164(x77211,x77212))+~P1(f332(f321(f846(f846(x77211)),f165(x77211)),f332(f332(f140(f846(x77211)),f115(x77211)),x77212)))
% 52.62/52.41 [7825]P1(f332(f332(f233(a1),x78251),x78252))+~P1(f332(f332(f233(a1),f332(f332(f82(a1),x78251),x78251)),f332(f332(f82(a1),x78252),x78252)))
% 52.62/52.41 [7826]P1(f332(f332(f233(a1),x78261),x78262))+~P1(f332(f332(f233(a1),f332(f332(f82(a1),x78261),x78261)),f332(f332(f82(a1),x78262),x78262)))
% 52.62/52.41 [7828]P1(f332(f332(f232(a1),x78281),x78282))+~P1(f332(f332(f232(a1),f332(f332(f82(a1),x78281),x78281)),f332(f332(f82(a1),x78282),x78282)))
% 52.62/52.41 [7829]P1(f332(f332(f232(a1),x78291),x78292))+~P1(f332(f332(f232(a1),f332(f332(f82(a1),x78291),x78291)),f332(f332(f82(a1),x78292),x78292)))
% 52.62/52.41 [7921]~P73(x79211)+E(f332(f332(f83(x79211),f332(f332(f82(x79211),f80(x79211)),f80(x79211))),f332(f332(f8(a845,x79211),f102(x79211)),f295(a845,f80(a845),x79212))),f332(f332(f83(x79211),f332(f102(x79211),x79212)),f332(f332(f82(x79211),f332(f102(x79211),x79212)),f80(x79211))))
% 52.62/52.41 [7962]E(f332(f332(f140(a1),f332(f106(a1),x79621)),f163(f332(f332(f82(a1),f332(f106(a1),x79621)),f80(a1)),f332(f106(a1),x79622))),f163(f332(f106(a1),x79621),f332(f106(a1),x79622)))+~P1(f332(f332(f232(a1),f332(f106(a1),x79621)),f332(f106(a1),x79622)))
% 52.62/52.41 [7977]P1(f332(f332(f334(a845),x79771),x79772))+~P1(f332(f332(f334(a1),f332(f102(a1),x79771)),f332(f303(a845,a1,f102(a1)),x79772)))
% 52.62/52.41 [8127]~P1(f332(f64(x81271),x81272))+E(f332(f303(a845,x81271,f582(x81272,x81271)),f332(f256(a845),f332(f332(f9(a845,a845,a839),f233(a845)),f583(x81272,x81271)))),x81272)
% 52.62/52.41 [8411]P50(x84111,x84112)+P1(f332(f332(f334(f852(x84111,x84111)),f332(f332(f241(x84111,x84111),f474(x84112,x84111)),f474(x84112,x84111))),x84112))
% 52.62/52.41 [8547]~P88(x85471)+E(f332(f332(f3(x85471),f80(x85471)),f332(f106(x85471),x85472)),f332(f106(x85471),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f81(a1),x85472))))
% 52.62/52.41 [8651]~P1(f332(f332(f233(f853(a845,a839)),x86511),x86512))+P1(f332(f332(f233(f853(a1,a839)),f332(f303(a845,a1,f102(a1)),x86511)),f332(f303(a845,a1,f102(a1)),x86512)))
% 52.62/52.41 [8652]~P1(f332(f332(f232(f853(a845,a839)),x86521),x86522))+P1(f332(f332(f232(f853(a1,a839)),f332(f303(a845,a1,f102(a1)),x86521)),f332(f303(a845,a1,f102(a1)),x86522)))
% 52.62/52.41 [8677]~P1(f332(f332(f233(a1),x86771),x86772))+P1(f332(f332(f233(a1),f332(f332(f3(a1),f332(f332(f82(a1),x86771),x86771)),a99)),f332(f332(f82(a1),x86772),x86772)))
% 52.62/52.41 [8678]~P1(f332(f332(f233(a1),x86781),x86782))+P1(f332(f332(f233(a1),f332(f332(f3(a1),f332(f332(f82(a1),x86781),x86781)),a99)),f332(f332(f82(a1),x86782),x86782)))
% 52.62/52.41 [8679]~P1(f332(f332(f233(a1),x86791),x86792))+P1(f332(f332(f232(a1),f332(f332(f3(a1),f332(f332(f82(a1),x86791),x86791)),a99)),f332(f332(f82(a1),x86792),x86792)))
% 52.62/52.41 [8680]~P1(f332(f332(f233(a1),x86801),x86802))+P1(f332(f332(f232(a1),f332(f332(f3(a1),f332(f332(f82(a1),x86801),x86801)),a99)),f332(f332(f82(a1),x86802),x86802)))
% 52.62/52.41 [8747]~P1(f332(f332(f334(a845),x87471),f332(f158(a845),x87472)))+P1(f332(f332(f232(a845),x87471),f332(f132(a845,a845,f82(a845),f2(a845)),x87472)))
% 52.62/52.41 [8819]P46(x88191,x88192)+~P1(f332(f332(f334(f852(x88191,x88191)),f332(f332(f241(x88191,x88191),f428(x88192,x88191)),f428(x88192,x88191))),x88192))
% 52.62/52.41 [8952]~P1(f332(f332(f233(f853(a1,a839)),f332(f303(a845,a1,f102(a1)),x89521)),f332(f303(a845,a1,f102(a1)),x89522)))+P1(f332(f332(f233(f853(a845,a839)),x89521),x89522))
% 52.62/52.41 [8953]~P1(f332(f332(f232(f853(a1,a839)),f332(f303(a845,a1,f102(a1)),x89531)),f332(f303(a845,a1,f102(a1)),x89532)))+P1(f332(f332(f232(f853(a845,a839)),x89531),x89532))
% 52.62/52.41 [9034]P1(f332(f332(f233(a1),x90341),x90342))+~P1(f332(f332(f233(a1),f332(f332(f3(a1),f332(f332(f82(a1),x90341),x90341)),a99)),f332(f332(f82(a1),x90342),x90342)))
% 52.62/52.41 [9035]P1(f332(f332(f233(a1),x90351),x90352))+~P1(f332(f332(f233(a1),f332(f332(f3(a1),f332(f332(f82(a1),x90351),x90351)),a99)),f332(f332(f82(a1),x90352),x90352)))
% 52.62/52.41 [9036]P1(f332(f332(f233(a1),x90361),x90362))+~P1(f332(f332(f232(a1),f332(f332(f3(a1),f332(f332(f82(a1),x90361),x90361)),a99)),f332(f332(f82(a1),x90362),x90362)))
% 52.62/52.41 [9037]P1(f332(f332(f233(a1),x90371),x90372))+~P1(f332(f332(f232(a1),f332(f332(f3(a1),f332(f332(f82(a1),x90371),x90371)),a99)),f332(f332(f82(a1),x90372),x90372)))
% 52.62/52.41 [9891]~P1(f332(f64(x98911),x98912))+E(f332(f181(f846(x98911)),f92(f846(x98911),f332(f332(f20(f846(x98911),a839,a839),f332(f332(f10(a839,f853(a839,a839),f846(x98911)),a330),f332(f332(f9(f846(x98911),f853(x98911,a839),a839),f332(f332(f10(f853(x98911,a839),f853(f853(x98911,a839),a839),f846(x98911)),a329),f158(x98911))),x98912))),f127(x98911)))),f209(x98911,x98912))
% 52.62/52.41 [5943]E(f332(f332(f82(a845),f332(f332(f3(a845),x59431),x59432)),x59432),x59431)+~P1(f332(f332(f232(a845),x59432),x59431))
% 52.62/52.41 [6009]E(f332(f332(f44(a845),f332(f332(f83(a845),x60091),x60092)),x60092),x60091)+~P1(f332(f332(f233(a845),f2(a845)),x60092))
% 52.62/52.41 [6010]E(f332(f332(f44(a845),f332(f332(f83(a845),x60101),x60102)),x60101),x60102)+~P1(f332(f332(f233(a845),f2(a845)),x60101))
% 52.62/52.41 [6015]~P4(x60151)+E(f332(f332(f8(a845,x60151),f332(f152(x60151),x60152)),f332(f294(a845,f2(a845)),f332(f181(f846(x60151)),x60152))),f332(f154(x60151),x60152))
% 52.62/52.41 [6135]E(f53(a845,f332(a114,f332(f332(f83(a845),x61351),x61352)),x61351),f80(a845))+~P1(f332(f332(f233(a845),f80(a845)),x61351))
% 52.62/52.41 [6141]E(f332(a114,f332(f332(f82(a845),f332(f106(a845),x61411)),x61412)),f332(f332(f82(a845),f80(a845)),x61412))+~P1(f332(a186,f332(f106(a1),x61411)))
% 52.62/52.41 [6167]E(f332(a107,f332(f332(f242(a1),f332(f106(a1),x61671)),x61672)),f332(f332(f242(a845),f332(f106(a845),x61671)),x61672))+P1(f332(a186,f332(f106(a1),x61671)))
% 52.62/52.41 [6420]E(f332(f332(f3(a845),x64201),f332(f106(a845),f332(f332(f82(a1),x64202),a99))),f332(f332(f3(a845),f332(a114,x64201)),f332(f106(a845),x64202)))+~P1(f332(f332(f233(a1),a85),x64202))
% 52.62/52.41 [6502]E(x65021,f2(a845))+E(f332(a114,f332(f332(f82(a845),f332(f332(f3(a845),x65021),f80(a845))),x65022)),f332(f332(f82(a845),x65021),x65022))
% 52.62/52.41 [6547]E(x65471,f2(a1))+P1(f332(f332(f233(a1),f2(a1)),f332(f332(f242(a1),f332(f77(a1),x65471)),x65472)))
% 52.62/52.41 [6562]~E(x65622,f2(a845))+P1(f332(f332(f233(a1),f2(a1)),f332(f332(f242(a1),f332(f77(a1),x65621)),x65622)))
% 52.62/52.41 [6598]E(x65981,f2(a845))+E(f332(f332(f82(a845),x65982),f332(f332(f83(a845),f332(f332(f3(a845),x65981),f80(a845))),x65982)),f332(f332(f83(a845),x65981),x65982))
% 52.62/52.41 [6653]~P1(f332(f332(f232(a1),x66531),x66532))+P1(f332(f332(f233(a1),f332(f332(f82(a1),x66531),a99)),x66532))
% 52.62/52.41 [6785]E(f332(f332(f140(a845),x67851),f130(a845,f332(f294(a845,f332(a114,x67851)),x67852))),f130(a845,f332(f294(a845,x67851),x67852)))+~P1(f332(f332(f233(a845),x67851),x67852))
% 52.62/52.41 [6786]E(f332(f332(f140(a845),x67861),f130(a845,f332(f294(a845,f332(a114,x67861)),x67862))),f130(a845,f332(f294(a845,x67861),x67862)))+~P1(f332(f332(f233(a845),x67861),x67862))
% 52.62/52.41 [6955]~P1(f332(f332(f279(a1),x69551),f332(f102(a1),x69552)))+P1(f332(f332(f279(a845),f332(a107,f332(f77(a1),x69551))),x69552))
% 52.62/52.41 [6989]E(x69891,x69892)+~E(f332(f332(f3(a1),f332(f332(f82(a1),x69891),x69891)),a99),f332(f332(f3(a1),f332(f332(f82(a1),x69892),x69892)),a99))
% 52.62/52.41 [6992]E(x69921,f115(x69922))+E(f263(x69922,f332(f332(f143(x69922,f852(a101,x69922)),f332(f241(a101,x69922),f80(a101))),x69921)),f270(x69922,x69921))
% 52.62/52.41 [7231]P1(f332(f332(f232(a1),x72311),x72312))+~P1(f332(f332(f233(a1),f332(f332(f82(a1),x72311),a99)),x72312))
% 52.62/52.41 [7373]P1(f332(f332(f279(a1),x73731),f332(f102(a1),x73732)))+~P1(f332(f332(f279(a845),f332(a107,f332(f77(a1),x73731))),x73732))
% 52.62/52.41 [7723]~P1(f332(f332(f233(a845),x77231),x77232))+P1(f332(f332(f334(f852(a845,a845)),f332(f332(f241(a845,a845),x77231),x77232)),a237))
% 52.62/52.41 [7951]~P1(f332(f332(f233(a101),f2(a101)),x79511))+P1(f332(f332(f233(a101),f332(f240(a101,f852(a101,a101)),f332(f264(x79511),x79512))),x79511))
% 52.62/52.41 [8252]~P80(x82521)+P1(f332(f332(f232(x82521),f332(f77(x82521),f332(f154(x82521),x82522))),f332(f154(x82521),f332(f332(f143(x82521,x82521),f77(x82521)),x82522))))
% 52.62/52.41 [8275]P1(f332(f332(f233(a845),x82751),x82752))+~P1(f332(f332(f334(f852(a845,a845)),f332(f332(f241(a845,a845),x82751),x82752)),a237))
% 52.62/52.41 [8435]E(f332(f332(f241(x84351,x84351),f652(x84352,x84351)),f652(x84352,x84351)),x84352)+~P1(f332(f332(f334(f852(x84351,x84351)),x84352),f300(x84351,f180(f853(f852(x84351,x84351),a839)))))
% 52.62/52.41 [8480]E(f332(f294(a845,x84801),f332(f332(f82(a845),x84801),f332(f43(a845),x84802))),x84802)+~P1(f332(f332(f232(f853(a845,a839)),x84802),f332(f294(a845,x84801),f332(f332(f82(a845),x84801),f332(f43(a845),x84802)))))
% 52.62/52.41 [8501]E(f332(f332(f140(a845),f332(f106(a845),x85011)),f130(a845,f332(f294(a845,f332(a114,f332(f106(a845),x85011))),f332(f106(a845),x85012)))),f130(a845,f332(f294(a845,f332(f106(a845),x85011)),f332(f106(a845),x85012))))+~P1(f332(f332(f233(a845),f332(f106(a845),x85011)),f332(f106(a845),x85012)))
% 52.62/52.41 [8780]E(f332(f332(f44(a1),f332(f106(a1),f332(f332(f3(a1),f332(f332(f82(a1),x87801),x87801)),a99))),f332(f106(a1),f332(f332(f82(a1),x87802),x87802))),f332(f332(f44(a1),f332(f106(a1),x87801)),f332(f106(a1),x87802)))+~P1(f332(f332(f232(a1),f2(a1)),f332(f106(a1),x87802)))
% 52.62/52.41 [8885]E(f162(f846(x88851),f332(f332(f10(a839,a839,f846(x88851)),a328),f332(f332(f9(f846(x88851),f846(x88851),a839),a329),f115(x88851))),x88852),f164(x88851,f164(x88851,x88852)))+~P20(a845,f332(f142(a845),f332(f332(f143(f846(x88851),a845),f181(f846(x88851))),x88852)))
% 52.62/52.41 [8888]E(f332(f332(f44(a1),f332(f106(a1),f332(f332(f3(a1),f332(f332(f82(a1),x88881),x88881)),a99))),f332(f106(a1),f332(f332(f82(a1),x88882),x88882))),f332(f332(f44(a1),f332(f332(f82(a1),f332(f106(a1),x88881)),f80(a1))),f332(f106(a1),x88882)))+P1(f332(f332(f232(a1),f2(a1)),f332(f106(a1),x88882)))
% 52.62/52.41 [9660]P1(f332(a186,x96602))+E(f332(f332(f88(a1,a845),f332(f332(f3(a1),x96601),x96602)),f332(f332(f20(a1,a845,a845),f332(f332(f9(a1,a845,f853(a845,a845)),f332(f332(f10(a839,f853(a845,f853(a845,a845)),a1),f98(a845)),a186)),f2(a845))),a107)),f332(f332(f3(a845),f332(a107,x96601)),f332(a107,x96602)))
% 52.62/52.41 [9664]E(f332(f332(f88(a1,a845),f332(f106(a1),f332(f332(f82(a1),x96641),f332(f81(a1),x96642)))),f332(f332(f20(a1,a845,a845),f332(f332(f9(a1,a845,f853(a845,a845)),f332(f332(f10(a839,f853(a845,f853(a845,a845)),a1),f98(a845)),a186)),f2(a845))),a107)),f332(f332(f3(a845),f332(f106(a845),x96641)),f332(f106(a845),x96642)))+P1(f332(f332(f233(a1),x96642),a85))
% 52.62/52.41 [9665]~P32(x96651,x96652)+P1(f332(f332(f232(f853(f852(x96651,x96651),a839)),f332(f332(f281(x96651,x96651,x96651),f332(f240(f853(f852(x96651,x96651),a839),f853(f852(x96651,x96651),a839)),x96652)),f332(f250(f853(f852(x96651,x96651),a839),f853(f852(x96651,x96651),a839)),x96652))),f332(f240(f853(f852(x96651,x96651),a839),f853(f852(x96651,x96651),a839)),x96652)))
% 52.62/52.41 [9722]~E(f332(f43(a845),f332(f256(a845),f332(f332(f20(a845,a839,a839),f332(f332(f10(a839,f853(a839,a839),a845),a330),f332(f332(f9(a845,f853(a845,a839),a839),f334(a845)),x97221))),f332(f332(f9(a845,a845,a839),f233(a845)),f332(a114,x97222))))),f2(a845))+~P1(f332(f332(f334(a845),f2(a845)),x97221))
% 52.62/52.41 [9735]E(f291(a845,f332(f332(f20(a845,f853(a845,a839),f853(a845,a839)),f332(f332(f10(f853(a845,f853(a839,a839)),f853(f853(a845,a839),f853(a845,a839)),a845),f20(a845,a839,a839)),f332(f332(f10(f853(a845,a839),f853(a845,f853(a839,a839)),a845),f332(f10(a839,f853(a839,a839),a845),a330)),f279(a845)))),f332(f332(f10(f853(a845,a839),f853(a845,a839),a845),f332(f10(a839,a839,a845),a328)),f332(f9(a845,a845,a839),f279(a845)))),x97351,x97352),f180(f853(a845,a839)))+~P1(f332(f332(f279(a845),x97352),x97351))
% 52.62/52.41 [9741]E(f289(a845,f279(a845),f332(f332(f20(a845,f853(a845,a839),f853(a845,a839)),f332(f332(f10(f853(a845,f853(a839,a839)),f853(f853(a845,a839),f853(a845,a839)),a845),f20(a845,a839,a839)),f332(f332(f10(f853(a845,a839),f853(a845,f853(a839,a839)),a845),f332(f10(a839,f853(a839,a839),a845),a330)),f279(a845)))),f332(f332(f10(f853(a845,a839),f853(a845,a839),a845),f332(f10(a839,a839,a845),a328)),f332(f9(a845,a845,a839),f279(a845)))),x97411,x97412),f180(f853(a845,a839)))+P1(f332(f332(f279(a845),x97411),x97412))
% 52.62/52.41 [9742]E(f292(a845,f279(a845),f332(f332(f20(a845,f853(a845,a839),f853(a845,a839)),f332(f332(f10(f853(a845,f853(a839,a839)),f853(f853(a845,a839),f853(a845,a839)),a845),f20(a845,a839,a839)),f332(f332(f10(f853(a845,a839),f853(a845,f853(a839,a839)),a845),f332(f10(a839,f853(a839,a839),a845),a330)),f279(a845)))),f332(f332(f10(f853(a845,a839),f853(a845,a839),a845),f332(f10(a839,a839,a845),a328)),f332(f9(a845,a845,a839),f279(a845)))),x97421,x97422),f180(f853(a845,a839)))+P1(f332(f332(f279(a845),x97421),x97422))
% 52.62/52.41 [9743]E(f289(a845,f279(a845),f332(f332(f20(a845,f853(a845,a839),f853(a845,a839)),f332(f332(f10(f853(a845,f853(a839,a839)),f853(f853(a845,a839),f853(a845,a839)),a845),f20(a845,a839,a839)),f332(f332(f10(f853(a845,a839),f853(a845,f853(a839,a839)),a845),f332(f10(a839,f853(a839,a839),a845),a330)),f279(a845)))),f332(f332(f10(f853(a845,a839),f853(a845,a839),a845),f332(f10(a839,a839,a845),a328)),f332(f9(a845,a845,a839),f279(a845)))),x97431,x97432),f180(f853(a845,a839)))+P1(f332(f332(f279(a845),x97431),x97432))
% 52.62/52.41 [9744]E(f292(a845,f279(a845),f332(f332(f20(a845,f853(a845,a839),f853(a845,a839)),f332(f332(f10(f853(a845,f853(a839,a839)),f853(f853(a845,a839),f853(a845,a839)),a845),f20(a845,a839,a839)),f332(f332(f10(f853(a845,a839),f853(a845,f853(a839,a839)),a845),f332(f10(a839,f853(a839,a839),a845),a330)),f279(a845)))),f332(f332(f10(f853(a845,a839),f853(a845,a839),a845),f332(f10(a839,a839,a845),a328)),f332(f9(a845,a845,a839),f279(a845)))),x97441,x97442),f180(f853(a845,a839)))+P1(f332(f332(f279(a845),x97441),x97442))
% 52.62/52.41 [9745]E(f289(a845,f279(a845),f332(f332(f20(a845,f853(a845,a839),f853(a845,a839)),f332(f332(f10(f853(a845,f853(a839,a839)),f853(f853(a845,a839),f853(a845,a839)),a845),f20(a845,a839,a839)),f332(f332(f10(f853(a845,a839),f853(a845,f853(a839,a839)),a845),f332(f10(a839,f853(a839,a839),a845),a330)),f279(a845)))),f332(f332(f10(f853(a845,a839),f853(a845,a839),a845),f332(f10(a839,a839,a845),a328)),f332(f9(a845,a845,a839),f279(a845)))),x97451,x97452),f180(f853(a845,a839)))+~P1(f332(f332(f279(a845),x97452),x97451))
% 52.62/52.41 [9746]E(f292(a845,f279(a845),f332(f332(f20(a845,f853(a845,a839),f853(a845,a839)),f332(f332(f10(f853(a845,f853(a839,a839)),f853(f853(a845,a839),f853(a845,a839)),a845),f20(a845,a839,a839)),f332(f332(f10(f853(a845,a839),f853(a845,f853(a839,a839)),a845),f332(f10(a839,f853(a839,a839),a845),a330)),f279(a845)))),f332(f332(f10(f853(a845,a839),f853(a845,a839),a845),f332(f10(a839,a839,a845),a328)),f332(f9(a845,a845,a839),f279(a845)))),x97461,x97462),f180(f853(a845,a839)))+~P1(f332(f332(f279(a845),x97462),x97461))
% 52.62/52.41 [9747]E(f289(a845,f279(a845),f332(f332(f20(a845,f853(a845,a839),f853(a845,a839)),f332(f332(f10(f853(a845,f853(a839,a839)),f853(f853(a845,a839),f853(a845,a839)),a845),f20(a845,a839,a839)),f332(f332(f10(f853(a845,a839),f853(a845,f853(a839,a839)),a845),f332(f10(a839,f853(a839,a839),a845),a330)),f279(a845)))),f332(f332(f10(f853(a845,a839),f853(a845,a839),a845),f332(f10(a839,a839,a845),a328)),f332(f9(a845,a845,a839),f279(a845)))),x97471,x97472),f180(f853(a845,a839)))+~P1(f332(f332(f279(a845),x97472),x97471))
% 52.62/52.41 [9748]E(f289(a845,f279(a845),f332(f332(f20(a845,f853(a845,a839),f853(a845,a839)),f332(f332(f10(f853(a845,f853(a839,a839)),f853(f853(a845,a839),f853(a845,a839)),a845),f20(a845,a839,a839)),f332(f332(f10(f853(a845,a839),f853(a845,f853(a839,a839)),a845),f332(f10(a839,f853(a839,a839),a845),a330)),f279(a845)))),f332(f332(f10(f853(a845,a839),f853(a845,a839),a845),f332(f10(a839,a839,a845),a328)),f332(f9(a845,a845,a839),f279(a845)))),x97481,x97482),f180(f853(a845,a839)))+~P1(f332(f332(f279(a845),x97482),x97481))
% 52.62/52.41 [9749]E(f292(a845,f279(a845),f332(f332(f20(a845,f853(a845,a839),f853(a845,a839)),f332(f332(f10(f853(a845,f853(a839,a839)),f853(f853(a845,a839),f853(a845,a839)),a845),f20(a845,a839,a839)),f332(f332(f10(f853(a845,a839),f853(a845,f853(a839,a839)),a845),f332(f10(a839,f853(a839,a839),a845),a330)),f279(a845)))),f332(f332(f10(f853(a845,a839),f853(a845,a839),a845),f332(f10(a839,a839,a845),a328)),f332(f9(a845,a845,a839),f279(a845)))),x97491,x97492),f180(f853(a845,a839)))+~P1(f332(f332(f279(a845),x97492),x97491))
% 52.62/52.41 [9750]E(f292(a845,f279(a845),f332(f332(f20(a845,f853(a845,a839),f853(a845,a839)),f332(f332(f10(f853(a845,f853(a839,a839)),f853(f853(a845,a839),f853(a845,a839)),a845),f20(a845,a839,a839)),f332(f332(f10(f853(a845,a839),f853(a845,f853(a839,a839)),a845),f332(f10(a839,f853(a839,a839),a845),a330)),f279(a845)))),f332(f332(f10(f853(a845,a839),f853(a845,a839),a845),f332(f10(a839,a839,a845),a328)),f332(f9(a845,a845,a839),f279(a845)))),x97501,x97502),f180(f853(a845,a839)))+~P1(f332(f332(f279(a845),x97502),x97501))
% 52.62/52.41 [9793]E(f53(a1,f332(f106(a1),f332(f332(f3(a1),f332(f332(f82(a1),x97931),x97931)),a99)),f332(f106(a1),f332(f332(f82(a1),x97932),x97932))),f332(f332(f82(a1),f332(f332(f83(a1),f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f53(a1,f332(f106(a1),x97931),f332(f106(a1),x97932)))),f80(a1)))+~P1(f332(f332(f232(a1),f2(a1)),f332(f106(a1),x97932)))
% 52.62/52.41 [9802]E(f53(a1,f332(f106(a1),f332(f332(f3(a1),f332(f332(f82(a1),x98021),x98021)),a99)),f332(f106(a1),f332(f332(f82(a1),x98022),x98022))),f332(f332(f3(a1),f332(f332(f83(a1),f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f53(a1,f332(f332(f82(a1),f332(f106(a1),x98021)),f80(a1)),f332(f106(a1),x98022)))),f80(a1)))+P1(f332(f332(f232(a1),f2(a1)),f332(f106(a1),x98022)))
% 52.62/52.41 [9860]~P11(x98601)+E(f45(x98601,f332(f256(x98601),f332(f332(f10(f853(x98601,a839),a839,x98601),f90(x98601)),f332(f332(f10(f853(x98601,a839),f853(x98601,a839),x98601),f332(f20(x98601,a839,a839),f332(f332(f10(a839,f853(a839,a839),x98601),a335),f332(f332(f9(x98601,f853(x98601,a839),a839),f334(x98601)),x98602)))),f232(x98601))))),f46(x98601,x98602))
% 52.62/52.41 [9884]~P38(x98841,x98842)+P60(x98841,f332(f332(f9(x98841,f853(f852(x98841,x98841),a839),f853(x98841,a839)),f332(f332(f10(f853(x98841,f853(f853(f852(x98841,x98841),a839),a839)),f853(f853(f852(x98841,x98841),a839),f853(x98841,a839)),x98841),f9(x98841,f853(f852(x98841,x98841),a839),a839)),f332(f332(f10(f853(x98841,f852(x98841,x98841)),f853(x98841,f853(f853(f852(x98841,x98841),a839),a839)),x98841),f332(f10(f852(x98841,x98841),f853(f853(f852(x98841,x98841),a839),a839),x98841),f334(f852(x98841,x98841)))),f241(x98841,x98841)))),x98842))
% 52.62/52.41 [9885]~P14(x98851,f239(f853(x98851,a839)),x98852)+P13(x98851,f332(f332(f9(x98851,f853(f852(x98851,x98851),a839),f853(x98851,a839)),f332(f332(f10(f853(x98851,f853(f853(f852(x98851,x98851),a839),a839)),f853(f853(f852(x98851,x98851),a839),f853(x98851,a839)),x98851),f9(x98851,f853(f852(x98851,x98851),a839),a839)),f332(f332(f10(f853(x98851,f852(x98851,x98851)),f853(x98851,f853(f853(f852(x98851,x98851),a839),a839)),x98851),f332(f10(f852(x98851,x98851),f853(f853(f852(x98851,x98851),a839),a839),x98851),f334(f852(x98851,x98851)))),f241(x98851,x98851)))),x98852))
% 52.62/52.41 [9922]P38(x99221,x99222)+~P60(x99221,f332(f332(f9(x99221,f853(f852(x99221,x99221),a839),f853(x99221,a839)),f332(f332(f10(f853(x99221,f853(f853(f852(x99221,x99221),a839),a839)),f853(f853(f852(x99221,x99221),a839),f853(x99221,a839)),x99221),f9(x99221,f853(f852(x99221,x99221),a839),a839)),f332(f332(f10(f853(x99221,f852(x99221,x99221)),f853(x99221,f853(f853(f852(x99221,x99221),a839),a839)),x99221),f332(f10(f852(x99221,x99221),f853(f853(f852(x99221,x99221),a839),a839),x99221),f334(f852(x99221,x99221)))),f241(x99221,x99221)))),x99222))
% 52.62/52.41 [9923]P14(x99231,f239(f853(x99231,a839)),x99232)+~P13(x99231,f332(f332(f9(x99231,f853(f852(x99231,x99231),a839),f853(x99231,a839)),f332(f332(f10(f853(x99231,f853(f853(f852(x99231,x99231),a839),a839)),f853(f853(f852(x99231,x99231),a839),f853(x99231,a839)),x99231),f9(x99231,f853(f852(x99231,x99231),a839),a839)),f332(f332(f10(f853(x99231,f852(x99231,x99231)),f853(x99231,f853(f853(f852(x99231,x99231),a839),a839)),x99231),f332(f10(f852(x99231,x99231),f853(f853(f852(x99231,x99231),a839),a839),x99231),f334(f852(x99231,x99231)))),f241(x99231,x99231)))),x99232))
% 52.62/52.41 [7177]E(f332(f332(f82(a845),f332(f106(a845),f332(f332(f3(a1),x71771),a99))),x71772),f332(a114,f332(f332(f82(a845),f332(f106(a845),x71771)),x71772)))+P1(f332(a186,f332(f106(a1),x71771)))
% 52.62/52.41 [7642]~P88(x76421)+E(f332(f332(f82(x76421),f332(f332(f82(x76421),f80(x76421)),f332(f106(x76421),x76422))),f332(f106(x76421),x76422)),f332(f106(x76421),f332(f332(f3(a1),f332(f332(f82(a1),x76422),x76422)),a99)))
% 52.62/52.41 [8276]~P1(f332(f332(f232(a1),x82761),x82762))+P1(f332(f332(f233(a1),f332(f332(f82(a1),x82761),x82761)),f332(f332(f3(a1),f332(f332(f82(a1),x82762),x82762)),a99)))
% 52.62/52.41 [8277]~P1(f332(f332(f232(a1),x82771),x82772))+P1(f332(f332(f233(a1),f332(f332(f82(a1),x82771),x82771)),f332(f332(f3(a1),f332(f332(f82(a1),x82772),x82772)),a99)))
% 52.62/52.41 [8278]~P1(f332(f332(f232(a1),x82781),x82782))+P1(f332(f332(f232(a1),f332(f332(f82(a1),x82781),x82781)),f332(f332(f3(a1),f332(f332(f82(a1),x82782),x82782)),a99)))
% 52.62/52.41 [8279]~P1(f332(f332(f232(a1),x82791),x82792))+P1(f332(f332(f232(a1),f332(f332(f82(a1),x82791),x82791)),f332(f332(f3(a1),f332(f332(f82(a1),x82792),x82792)),a99)))
% 52.62/52.41 [8681]P1(f332(f332(f232(a1),x86811),x86812))+~P1(f332(f332(f233(a1),f332(f332(f82(a1),x86811),x86811)),f332(f332(f3(a1),f332(f332(f82(a1),x86812),x86812)),a99)))
% 52.62/52.41 [8682]P1(f332(f332(f232(a1),x86821),x86822))+~P1(f332(f332(f233(a1),f332(f332(f82(a1),x86821),x86821)),f332(f332(f3(a1),f332(f332(f82(a1),x86822),x86822)),a99)))
% 52.62/52.41 [8683]P1(f332(f332(f232(a1),x86831),x86832))+~P1(f332(f332(f232(a1),f332(f332(f82(a1),x86831),x86831)),f332(f332(f3(a1),f332(f332(f82(a1),x86832),x86832)),a99)))
% 52.62/52.41 [8684]P1(f332(f332(f232(a1),x86841),x86842))+~P1(f332(f332(f232(a1),f332(f332(f82(a1),x86841),x86841)),f332(f332(f3(a1),f332(f332(f82(a1),x86842),x86842)),a99)))
% 52.62/52.41 [8942]~P1(f332(f332(f233(a1),x89421),x89422))+P1(f332(f332(f233(a1),f332(f332(f3(a1),f332(f332(f82(a1),x89421),x89421)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),x89422),x89422)),a99)))
% 52.62/52.41 [8943]~P1(f332(f332(f233(a1),x89431),x89432))+P1(f332(f332(f233(a1),f332(f332(f3(a1),f332(f332(f82(a1),x89431),x89431)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),x89432),x89432)),a99)))
% 52.62/52.41 [8944]~P1(f332(f332(f232(a1),x89441),x89442))+P1(f332(f332(f232(a1),f332(f332(f3(a1),f332(f332(f82(a1),x89441),x89441)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),x89442),x89442)),a99)))
% 52.62/52.41 [8945]~P1(f332(f332(f232(a1),x89451),x89452))+P1(f332(f332(f232(a1),f332(f332(f3(a1),f332(f332(f82(a1),x89451),x89451)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),x89452),x89452)),a99)))
% 52.62/52.41 [9178]P1(f332(f332(f233(a1),x91781),x91782))+~P1(f332(f332(f233(a1),f332(f332(f3(a1),f332(f332(f82(a1),x91781),x91781)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),x91782),x91782)),a99)))
% 52.62/52.41 [9179]P1(f332(f332(f233(a1),x91791),x91792))+~P1(f332(f332(f233(a1),f332(f332(f3(a1),f332(f332(f82(a1),x91791),x91791)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),x91792),x91792)),a99)))
% 52.62/52.41 [9180]P1(f332(f332(f232(a1),x91801),x91802))+~P1(f332(f332(f232(a1),f332(f332(f3(a1),f332(f332(f82(a1),x91801),x91801)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),x91802),x91802)),a99)))
% 52.62/52.41 [9181]P1(f332(f332(f232(a1),x91811),x91812))+~P1(f332(f332(f232(a1),f332(f332(f3(a1),f332(f332(f82(a1),x91811),x91811)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),x91812),x91812)),a99)))
% 52.62/52.41 [9212]~P1(f332(f64(x92121),x92122))+P1(f332(f64(f853(x92121,a839)),f332(f256(f853(x92121,a839)),f332(f332(f9(f853(x92121,a839),f853(x92121,a839),a839),f232(f853(x92121,a839))),x92122))))
% 52.62/52.41 [9259]~E(f332(f277(f852(a845,a845),f852(a845,a845),a111),f332(f332(f302(f852(a845,a845)),x92591),f180(f853(f852(a845,a845),a839)))),f332(f277(f852(a845,a845),f852(a845,a845),a111),f332(f332(f302(f852(a845,a845)),x92592),f180(f853(f852(a845,a845),a839)))))+P1(f332(f332(f334(f852(f852(a845,a845),f852(a845,a845))),f332(f332(f241(f852(a845,a845),f852(a845,a845)),x92591),x92592)),a111))
% 52.62/52.41 [9345]E(f332(f277(f852(a845,a845),f852(a845,a845),a111),f332(f332(f302(f852(a845,a845)),x93451),f180(f853(f852(a845,a845),a839)))),f332(f277(f852(a845,a845),f852(a845,a845),a111),f332(f332(f302(f852(a845,a845)),x93452),f180(f853(f852(a845,a845),a839)))))+~P1(f332(f332(f334(f852(f852(a845,a845),f852(a845,a845))),f332(f332(f241(f852(a845,a845),f852(a845,a845)),x93451),x93452)),a111))
% 52.62/52.41 [9379]P1(f332(f332(f232(a1),f2(a1)),f698(x93791,x93792)))+E(f332(f256(a1),f332(f332(f20(a1,a839,a839),f332(f332(f10(a839,f853(a839,a839),a1),a330),f332(f232(a1),f2(a1)))),x93791)),f332(f256(a1),f332(f332(f20(a1,a839,a839),f332(f332(f10(a839,f853(a839,a839),a1),a330),f332(f232(a1),f2(a1)))),x93792)))
% 52.62/52.41 [9870]~P11(x98701)+E(f46(x98701,f332(f256(x98701),f332(f332(f10(f853(x98701,a839),a839,x98701),f90(x98701)),f332(f332(f10(f853(x98701,a839),f853(x98701,a839),x98701),f332(f20(x98701,a839,a839),f332(f332(f10(a839,f853(a839,a839),x98701),a335),f332(f332(f9(x98701,f853(x98701,a839),a839),f334(x98701)),x98702)))),f332(f9(x98701,x98701,a839),f232(x98701)))))),f45(x98701,x98702))
% 52.62/52.41 [9890]P1(f332(f332(f334(a845),f2(a845)),x98901))+E(f332(f43(a845),f332(f256(a845),f332(f332(f20(a845,a839,a839),f332(f332(f10(a839,f853(a839,a839),a845),a330),f332(f332(f9(a845,f853(a845,a839),a839),f332(f332(f10(a845,f853(f853(a845,a839),a839),a845),f334(a845)),a114)),x98901))),f332(f332(f9(a845,a845,a839),f233(a845)),x98902)))),f332(f43(a845),f332(f256(a845),f332(f332(f20(a845,a839,a839),f332(f332(f10(a839,f853(a839,a839),a845),a330),f332(f332(f9(a845,f853(a845,a839),a839),f334(a845)),x98901))),f332(f332(f9(a845,a845,a839),f233(a845)),f332(a114,x98902))))))
% 52.62/52.41 [9937]P1(f332(f332(f279(a845),x99371),x99372))+~P1(f332(f332(f334(a845),x99372),f287(a845,f332(f332(f20(a845,f853(a845,a839),f853(a845,a839)),f332(f332(f10(f853(a845,f853(a839,a839)),f853(f853(a845,a839),f853(a845,a839)),a845),f20(a845,a839,a839)),f332(f332(f10(f853(a845,a839),f853(a845,f853(a839,a839)),a845),f332(f10(a839,f853(a839,a839),a845),a330)),f279(a845)))),f332(f332(f10(f853(a845,a839),f853(a845,a839),a845),f332(f10(a839,a839,a845),a328)),f332(f9(a845,a845,a839),f279(a845)))),x99371)))
% 52.62/52.41 [9938]P1(f332(f332(f279(a845),x99381),x99382))+~P1(f332(f332(f334(a845),x99381),f290(a845,f332(f332(f20(a845,f853(a845,a839),f853(a845,a839)),f332(f332(f10(f853(a845,f853(a839,a839)),f853(f853(a845,a839),f853(a845,a839)),a845),f20(a845,a839,a839)),f332(f332(f10(f853(a845,a839),f853(a845,f853(a839,a839)),a845),f332(f10(a839,f853(a839,a839),a845),a330)),f279(a845)))),f332(f332(f10(f853(a845,a839),f853(a845,a839),a845),f332(f10(a839,a839,a845),a328)),f332(f9(a845,a845,a839),f279(a845)))),x99382)))
% 52.62/52.41 [9939]~P1(f332(f332(f279(a845),x99391),x99392))+~P1(f332(f332(f334(a845),x99392),f290(a845,f332(f332(f20(a845,f853(a845,a839),f853(a845,a839)),f332(f332(f10(f853(a845,f853(a839,a839)),f853(f853(a845,a839),f853(a845,a839)),a845),f20(a845,a839,a839)),f332(f332(f10(f853(a845,a839),f853(a845,f853(a839,a839)),a845),f332(f10(a839,f853(a839,a839),a845),a330)),f279(a845)))),f332(f332(f10(f853(a845,a839),f853(a845,a839),a845),f332(f10(a839,a839,a845),a328)),f332(f9(a845,a845,a839),f279(a845)))),x99391)))
% 52.62/52.41 [9940]~P1(f332(f332(f279(a845),x99401),x99402))+~P1(f332(f332(f334(a845),x99401),f287(a845,f332(f332(f20(a845,f853(a845,a839),f853(a845,a839)),f332(f332(f10(f853(a845,f853(a839,a839)),f853(f853(a845,a839),f853(a845,a839)),a845),f20(a845,a839,a839)),f332(f332(f10(f853(a845,a839),f853(a845,f853(a839,a839)),a845),f332(f10(a839,f853(a839,a839),a845),a330)),f279(a845)))),f332(f332(f10(f853(a845,a839),f853(a845,a839),a845),f332(f10(a839,a839,a845),a328)),f332(f9(a845,a845,a839),f279(a845)))),x99402)))
% 52.62/52.41 [7509]~P88(x75091)+E(f332(f332(f83(x75091),x75092),f332(f106(x75091),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))),x75092)
% 52.62/52.41 [7776]~P88(x77761)+E(f332(f332(f82(x77761),f332(f106(x77761),x77762)),f80(x77761)),f332(f106(x77761),f332(f332(f82(a1),x77762),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))
% 52.62/52.41 [7920]P1(f332(f332(f232(a1),f2(a1)),f332(f106(a1),x79202)))+E(f332(f332(f242(a1),x79201),f332(f106(a845),f332(f332(f3(a1),f332(f332(f82(a1),x79202),x79202)),a99))),f80(a1))
% 52.62/52.41 [9236]~P1(f332(f332(f232(a1),f2(a1)),f332(f106(a1),x92362)))+E(f332(f332(f242(a1),x92361),f332(f106(a845),f332(f332(f3(a1),f332(f332(f82(a1),x92362),x92362)),a99))),f332(f332(f88(a1,a1),f332(f332(f242(a1),x92361),f332(f106(a845),x92362))),f332(f332(f20(a1,a1,a1),f332(f332(f10(a1,f853(a1,a1),a1),f83(a1)),f332(f83(a1),x92361))),f7(a1))))
% 52.62/52.41 [9712]~P1(f332(f332(f233(a845),f332(f106(a845),x97121)),f332(a114,x97122)))+P1(f332(f332(f88(a1,a839),f332(f106(a1),f332(f332(f82(a1),x97121),a99))),f332(f332(f20(a1,a839,a839),f332(f332(f10(a839,f853(a839,a839),a1),a335),f332(f332(f10(a839,a839,a1),a328),a186))),f332(f332(f9(a1,a845,a839),f332(f332(f10(a845,f853(a845,a839),a1),f233(a845)),a107)),x97122))))
% 52.62/52.41 [9713]~P1(f332(f332(f232(a845),f332(f106(a845),x97131)),f332(a114,x97132)))+P1(f332(f332(f88(a1,a839),f332(f106(a1),f332(f332(f82(a1),x97131),a99))),f332(f332(f20(a1,a839,a839),f332(f332(f10(a839,f853(a839,a839),a1),a335),f332(f332(f10(a839,a839,a1),a328),a186))),f332(f332(f9(a1,a845,a839),f332(f332(f10(a845,f853(a845,a839),a1),f232(a845)),a107)),x97132))))
% 52.62/52.41 [9777]P1(f332(f332(f233(a845),f332(f106(a845),x97771)),f332(a114,x97772)))+~P1(f332(f332(f88(a1,a839),f332(f106(a1),f332(f332(f82(a1),x97771),a99))),f332(f332(f20(a1,a839,a839),f332(f332(f10(a839,f853(a839,a839),a1),a335),f332(f332(f10(a839,a839,a1),a328),a186))),f332(f332(f9(a1,a845,a839),f332(f332(f10(a845,f853(a845,a839),a1),f233(a845)),a107)),x97772))))
% 52.62/52.41 [9778]P1(f332(f332(f232(a845),f332(f106(a845),x97781)),f332(a114,x97782)))+~P1(f332(f332(f88(a1,a839),f332(f106(a1),f332(f332(f82(a1),x97781),a99))),f332(f332(f20(a1,a839,a839),f332(f332(f10(a839,f853(a839,a839),a1),a335),f332(f332(f10(a839,a839,a1),a328),a186))),f332(f332(f9(a1,a845,a839),f332(f332(f10(a845,f853(a845,a839),a1),f232(a845)),a107)),x97782))))
% 52.62/52.41 [9808]~P1(f332(f332(f233(a845),f332(a114,x98082)),f332(f106(a845),x98081)))+P1(f332(f332(f88(a1,a839),f332(f106(a1),f332(f332(f82(a1),x98081),a99))),f332(f332(f20(a1,a839,a839),f332(f332(f10(a839,f853(a839,a839),a1),a330),f332(f332(f10(a839,a839,a1),a328),a186))),f332(f332(f20(a1,a839,a839),f332(f332(f10(a839,f853(a839,a839),a1),a335),f332(f332(f10(a839,a839,a1),a328),a186))),f332(f332(f10(a845,a839,a1),f332(f233(a845),x98082)),a107)))))
% 52.62/52.41 [9809]~P1(f332(f332(f232(a845),f332(a114,x98092)),f332(f106(a845),x98091)))+P1(f332(f332(f88(a1,a839),f332(f106(a1),f332(f332(f82(a1),x98091),a99))),f332(f332(f20(a1,a839,a839),f332(f332(f10(a839,f853(a839,a839),a1),a330),f332(f332(f10(a839,a839,a1),a328),a186))),f332(f332(f20(a1,a839,a839),f332(f332(f10(a839,f853(a839,a839),a1),a335),f332(f332(f10(a839,a839,a1),a328),a186))),f332(f332(f10(a845,a839,a1),f332(f232(a845),x98092)),a107)))))
% 52.62/52.41 [9858]P1(f332(f332(f233(a845),f332(a114,x98581)),f332(f106(a845),x98582)))+~P1(f332(f332(f88(a1,a839),f332(f106(a1),f332(f332(f82(a1),x98582),a99))),f332(f332(f20(a1,a839,a839),f332(f332(f10(a839,f853(a839,a839),a1),a330),f332(f332(f10(a839,a839,a1),a328),a186))),f332(f332(f20(a1,a839,a839),f332(f332(f10(a839,f853(a839,a839),a1),a335),f332(f332(f10(a839,a839,a1),a328),a186))),f332(f332(f10(a845,a839,a1),f332(f233(a845),x98581)),a107)))))
% 52.62/52.41 [9859]P1(f332(f332(f232(a845),f332(a114,x98591)),f332(f106(a845),x98592)))+~P1(f332(f332(f88(a1,a839),f332(f106(a1),f332(f332(f82(a1),x98592),a99))),f332(f332(f20(a1,a839,a839),f332(f332(f10(a839,f853(a839,a839),a1),a330),f332(f332(f10(a839,a839,a1),a328),a186))),f332(f332(f20(a1,a839,a839),f332(f332(f10(a839,f853(a839,a839),a1),a335),f332(f332(f10(a839,a839,a1),a328),a186))),f332(f332(f10(a845,a839,a1),f332(f232(a845),x98591)),a107)))))
% 52.62/52.41 [9930]~P1(f332(f332(f334(a845),f2(a845)),x99301))+E(f332(a114,f332(f43(a845),f332(f256(a845),f332(f332(f20(a845,a839,a839),f332(f332(f10(a839,f853(a839,a839),a845),a330),f332(f332(f9(a845,f853(a845,a839),a839),f332(f332(f10(a845,f853(f853(a845,a839),a839),a845),f334(a845)),a114)),x99301))),f332(f332(f9(a845,a845,a839),f233(a845)),x99302))))),f332(f43(a845),f332(f256(a845),f332(f332(f20(a845,a839,a839),f332(f332(f10(a839,f853(a839,a839),a845),a330),f332(f332(f9(a845,f853(a845,a839),a839),f334(a845)),x99301))),f332(f332(f9(a845,a845,a839),f233(a845)),f332(a114,x99302))))))
% 52.62/52.41 [8461]~P88(x84611)+E(f332(f332(f83(x84611),f332(f106(x84611),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))),x84612),x84612)
% 52.62/52.41 [8521]~P88(x85211)+E(f332(f332(f82(x85211),f80(x85211)),f332(f106(x85211),x85212)),f332(f106(x85211),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),x85212)))
% 52.62/52.41 [8567]~P88(x85671)+E(f332(f332(f3(x85671),f332(f106(x85671),x85672)),f80(x85671)),f332(f106(x85671),f332(f332(f82(a1),x85672),f332(f81(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))))
% 52.62/52.41 [8700]~P1(f332(f332(f233(a845),f332(f106(a845),a85)),x87002))+E(f332(f332(f3(a845),x87001),f332(f332(f3(a845),x87002),f332(f106(a845),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f332(f332(f3(a845),f332(a114,x87001)),x87002))
% 52.62/52.41 [9275]~P73(x92751)+E(f332(f332(f83(x92751),x92752),x92752),f332(f332(f242(x92751),x92752),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))))
% 52.62/52.41 [9276]~P76(x92761)+E(f332(f332(f242(x92761),x92762),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f332(f332(f83(x92761),x92762),x92762))
% 52.62/52.41 [9278]~P88(x92781)+E(f332(f332(f83(x92781),x92782),f332(f106(x92781),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f332(f332(f82(x92781),x92782),x92782))
% 52.62/52.41 [9511]~P133(x95111)+E(f332(f332(f242(x95111),f332(f81(x95111),x95112)),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f332(f332(f242(x95111),x95112),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))))
% 52.62/52.41 [9512]~P110(x95121)+E(f332(f332(f242(x95121),f332(f77(x95121),x95122)),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f332(f332(f242(x95121),x95122),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))))
% 52.62/52.41 [9508]~P88(x95081)+E(f332(f332(f83(x95081),f332(f106(x95081),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),x95082),f332(f332(f82(x95081),x95082),x95082))
% 52.62/52.41 [9622]~P110(x96221)+E(f332(f77(x96221),f332(f332(f242(x96221),x96222),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))),f332(f332(f242(x96221),x96222),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))))
% 52.62/52.41 [9672]~P110(x96721)+P1(f332(f332(f232(x96721),f2(x96721)),f332(f332(f242(x96721),x96722),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))))
% 52.62/52.41 [9849]~E(f332(a114,x98492),f332(f106(a845),x98491))+P1(f332(f332(f88(a1,a839),f332(f106(a1),f332(f332(f82(a1),x98491),a99))),f332(f332(f20(a1,a839,a839),f332(f332(f10(a839,f853(a839,a839),a1),a330),f332(f332(f10(a839,a839,a1),a328),a186))),f332(f332(f20(a1,a839,a839),f332(f332(f10(a839,f853(a839,a839),a1),a335),f332(f332(f10(a839,a839,a1),a328),a186))),f332(f332(f9(a1,a845,a839),f332(f332(f10(a845,f853(a845,a839),a1),a329),a107)),x98492)))))
% 52.62/52.41 [9850]~E(f332(f106(a845),x98501),f332(a114,x98502))+P1(f332(f332(f88(a1,a839),f332(f106(a1),f332(f332(f82(a1),x98501),a99))),f332(f332(f20(a1,a839,a839),f332(f332(f10(a839,f853(a839,a839),a1),a330),f332(f332(f10(a839,a839,a1),a328),a186))),f332(f332(f20(a1,a839,a839),f332(f332(f10(a839,f853(a839,a839),a1),a335),f332(f332(f10(a839,a839,a1),a328),a186))),f332(f332(f9(a1,a845,a839),f332(f332(f10(a845,f853(a845,a839),a1),a329),a107)),x98502)))))
% 52.62/52.41 [9893]E(f332(a114,x98931),f332(f106(a845),x98932))+~P1(f332(f332(f88(a1,a839),f332(f106(a1),f332(f332(f82(a1),x98932),a99))),f332(f332(f20(a1,a839,a839),f332(f332(f10(a839,f853(a839,a839),a1),a330),f332(f332(f10(a839,a839,a1),a328),a186))),f332(f332(f20(a1,a839,a839),f332(f332(f10(a839,f853(a839,a839),a1),a335),f332(f332(f10(a839,a839,a1),a328),a186))),f332(f332(f9(a1,a845,a839),f332(f332(f10(a845,f853(a845,a839),a1),a329),a107)),x98931)))))
% 52.62/52.41 [9894]E(f332(f106(a845),x98941),f332(a114,x98942))+~P1(f332(f332(f88(a1,a839),f332(f106(a1),f332(f332(f82(a1),x98941),a99))),f332(f332(f20(a1,a839,a839),f332(f332(f10(a839,f853(a839,a839),a1),a330),f332(f332(f10(a839,a839,a1),a328),a186))),f332(f332(f20(a1,a839,a839),f332(f332(f10(a839,f853(a839,a839),a1),a335),f332(f332(f10(a839,a839,a1),a328),a186))),f332(f332(f9(a1,a845,a839),f332(f332(f10(a845,f853(a845,a839),a1),a329),a107)),x98942)))))
% 52.62/52.41 [9670]~P88(x96701)+E(f332(f332(f242(x96701),f332(f106(x96701),a99)),f332(f332(f83(a845),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),x96702)),f80(x96701))
% 52.62/52.41 [9671]~P133(x96711)+E(f332(f332(f242(x96711),f332(f81(x96711),f80(x96711))),f332(f332(f83(a845),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),x96712)),f80(x96711))
% 52.62/52.41 [9674]~P76(x96741)+E(f332(f332(f242(x96741),x96742),f332(f106(a845),f332(f332(f3(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))),a99))),f332(f332(f83(x96741),f332(f332(f83(x96741),x96742),x96742)),x96742))
% 52.62/52.41 [9873]~P1(f332(f332(f232(a1),f2(a1)),x98732))+E(f53(a1,f332(f332(f82(a1),f80(a1)),f332(f332(f83(a1),f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),x98731)),f332(f332(f83(a1),f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),x98732)),f332(f332(f82(a1),f80(a1)),f332(f332(f83(a1),f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f53(a1,x98731,x98732))))
% 52.62/52.41 [9896]~P1(f332(f332(f232(a1),f2(a1)),x98962))+E(f332(f332(f44(a1),f332(f332(f82(a1),f80(a1)),f332(f332(f83(a1),f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),x98961))),f332(f332(f83(a1),f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),x98962)),f332(f332(f44(a1),x98961),x98962))
% 52.62/52.41 [9898]~P1(f332(f332(f232(a1),x98982),f2(a1)))+E(f332(f332(f44(a1),f332(f332(f82(a1),f80(a1)),f332(f332(f83(a1),f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),x98981))),f332(f332(f83(a1),f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),x98982)),f332(f332(f44(a1),f332(f332(f82(a1),x98981),f80(a1))),x98982))
% 52.62/52.41 [9899]~P1(f332(f332(f232(a1),x98992),f2(a1)))+E(f53(a1,f332(f332(f82(a1),f80(a1)),f332(f332(f83(a1),f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),x98991)),f332(f332(f83(a1),f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),x98992)),f332(f332(f3(a1),f332(f332(f83(a1),f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f53(a1,f332(f332(f82(a1),x98991),f80(a1)),x98992))),f80(a1)))
% 52.62/52.41 [9768]~P88(x97681)+E(f332(f332(f242(x97681),f332(f106(x97681),a99)),f332(a114,f332(f332(f83(a845),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),x97682))),f332(f106(x97681),a99))
% 52.62/52.41 [9770]~P133(x97701)+E(f332(f332(f242(x97701),f332(f81(x97701),f80(x97701))),f332(a114,f332(f332(f83(a845),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),x97702))),f332(f81(x97701),f80(x97701)))
% 52.62/52.41 [5995]E(x59951,x59952)+~P41(a25,x59951,x59953,x59952)
% 52.62/52.41 [5005]~P38(x50051,x50053)+P38(x50051,f327(x50051,x50052,x50053))
% 52.62/52.41 [5170]P33(x51701,x51702,x51703)+~P33(x51701,f332(a114,x51702),x51703)
% 52.62/52.41 [5253]~P14(x52531,x52532,x52533)+P14(f846(x52531),f149(x52531,x52532),f147(x52531,x52533))
% 52.62/52.41 [5254]~P49(x52541,x52542,x52543)+P49(f846(x52541),f149(x52541,x52542),f147(x52541,x52543))
% 52.62/52.41 [5363]P56(x53631,x53632,x53633)+~E(f637(x53633,x53632,x53631),f638(x53633,x53632,x53631))
% 52.62/52.41 [5364]P55(x53641,x53642,x53643)+~E(f639(x53643,x53642,x53641),f640(x53643,x53642,x53641))
% 52.62/52.41 [6319]P34(x63191,x63192,x63193)+~P33(x63191,f805(x63193,x63192,x63191),f816(x63193,x63192,x63191))
% 52.62/52.41 [4563]~E(x45631,f183(x45632))+~E(x45631,f332(f227(x45632),x45633))
% 52.62/52.41 [4564]~E(x45641,f183(x45642))+~E(x45641,f332(f227(x45642),x45643))
% 52.62/52.41 [4611]~E(f332(f142(x46112),x46111),x46113)+E(x46111,f332(f142(x46112),x46113))
% 52.62/52.41 [4612]~E(x46122,f332(f142(x46121),x46123))+E(f332(f142(x46121),x46122),x46123)
% 52.62/52.41 [4656]E(x46561,x46562)+~E(f332(f227(x46563),x46561),f332(f227(x46563),x46562))
% 52.62/52.41 [4657]E(x46571,x46572)+~E(f332(f142(x46573),x46571),f332(f142(x46573),x46572))
% 52.62/52.41 [4855]~P13(x48553,x48551)+P1(f332(f332(x48551,x48552),x48552))
% 52.62/52.41 [4856]~P51(x48563,x48561)+P1(f332(f332(x48561,x48562),x48562))
% 52.62/52.41 [4857]~P60(x48571,x48572)+P1(f332(f321(x48571,x48572),x48573))
% 52.62/52.41 [4858]~P60(x48581,x48582)+P1(f332(f321(x48581,x48582),x48583))
% 52.62/52.41 [4920]~P38(x49201,x49202)+P38(f846(x49201),f332(f133(x49201,x49202),x49203))
% 52.62/52.41 [4924]~P1(f332(x49242,x49243))+~E(f332(f256(x49241),x49242),f180(f853(x49241,a839)))
% 52.62/52.41 [4925]~P1(f332(x49252,x49253))+~E(f180(f853(x49251,a839)),f332(f256(x49251),x49252))
% 52.62/52.41 [4958]~P1(f332(x49581,x49583))+P1(f332(x49581,f92(x49582,x49581)))
% 52.62/52.41 [4959]~P1(f332(x49591,x49593))+P1(f332(x49591,f92(x49592,x49591)))
% 52.62/52.41 [4960]~P1(f332(x49601,x49603))+P1(f332(x49601,f92(x49602,x49601)))
% 52.62/52.41 [4961]~P1(f332(x49611,x49613))+P1(f332(x49611,f92(x49612,x49611)))
% 52.62/52.41 [5085]~E(x50852,x50853)+P1(f332(f332(f334(x50851),x50852),f332(a329,x50853)))
% 52.62/52.41 [5139]E(f332(f142(x51391),x51392),f332(f332(f140(x51391),x51393),f115(x51391)))+~E(x51392,f332(f332(f140(x51391),x51393),f115(x51391)))
% 52.62/52.41 [5140]~E(x51403,f332(f332(f140(x51401),x51402),f115(x51401)))+E(f332(f332(f140(x51401),x51402),f115(x51401)),f332(f142(x51401),x51403))
% 52.62/52.41 [5165]~E(x51653,f332(f18(f849(x51652),x51651),f183(x51652)))+E(f169(x51651,x51652,x51653),f180(f853(x51651,a839)))
% 52.62/52.41 [5186]E(f332(f43(x51861),f380(x51862,x51863,x51861)),x51862)+~E(f332(f43(x51861),x51863),f332(a114,x51862))
% 52.62/52.41 [5191]~P38(x51911,x51913)+P1(f332(f332(f334(x51911),x51912),f322(x51911,x51913)))
% 52.62/52.41 [5192]~P38(x51921,x51923)+P1(f332(f332(f334(x51921),x51922),f322(x51921,x51923)))
% 52.62/52.41 [5195]~E(f332(f142(x51952),x51951),f332(f332(f140(x51952),x51953),f115(x51952)))+E(x51951,f332(f332(f140(x51952),x51953),f115(x51952)))
% 52.62/52.41 [5196]~E(f332(f332(f140(x51962),x51963),f115(x51962)),f332(f142(x51962),x51961))+E(x51961,f332(f332(f140(x51962),x51963),f115(x51962)))
% 52.62/52.41 [5211]E(x52111,f332(f18(f849(x52112),x52113),f183(x52112)))+~E(f169(x52113,x52112,x52111),f180(f853(x52113,a839)))
% 52.62/52.41 [5217]E(f87(f852(a845,a845),f56(x52171,x52172)),x52173)+~P1(f332(f56(x52171,x52172),x52173))
% 52.62/52.41 [5225]~E(x52253,f332(f227(x52251),x52252))+P1(f332(f332(f334(x52251),x52252),f226(x52251,x52253)))
% 52.62/52.41 [5315]~E(x53152,f115(x53151))+P1(f332(f332(f334(f846(x53151)),x53152),f149(x53151,x53153)))
% 52.62/52.41 [5323]~P49(x53231,x53232,x53233)+P49(x53231,x53232,f332(f278(x53231,x53231),x53233))
% 52.62/52.41 [5324]~P56(x53241,x53242,x53243)+P56(x53241,x53242,f332(f278(x53241,x53241),x53243))
% 52.62/52.41 [5344]~P9(x53441)+E(f53(x53441,f53(x53441,x53442,x53443),x53443),f53(x53441,x53442,x53443))
% 52.62/52.41 [5441]E(x54411,x54412)+~P1(f332(f332(f334(x54413),x54411),f332(a329,x54412)))
% 52.62/52.41 [5484]~P2(x54841)+E(f182(x54841,x54842,f2(a845),x54843),x54843)
% 52.62/52.41 [5504]P49(x55041,x55042,x55043)+~P49(x55041,x55042,f332(f278(x55041,x55041),x55043))
% 52.62/52.41 [5505]P56(x55051,x55052,x55053)+~P56(x55051,x55052,f332(f278(x55051,x55051),x55053))
% 52.62/52.41 [5526]E(x55261,f332(f227(x55262),x55263))+~P1(f332(f332(f334(x55262),x55263),f226(x55262,x55261)))
% 52.62/52.41 [5607]~P1(f332(a26,x56073))+P1(f332(a26,f32(x56071,x56072,x56073)))
% 52.62/52.41 [5608]~P1(f332(a26,x56083))+P1(f332(a26,f32(x56081,x56082,x56083)))
% 52.62/52.41 [5620]E(f332(f126(x56201,x56202),x56203),f115(x56201))+P1(f332(x56202,f746(x56203,x56202,x56201)))
% 52.62/52.41 [5776]~P1(f332(f127(x57761),x57763))+P1(f332(f127(x57761),f151(x57761,x57762,x57763)))
% 52.62/52.41 [5777]~P1(f332(f127(x57771),x57772))+P1(f332(f127(x57771),f160(x57771,x57772,x57773)))
% 52.62/52.41 [5778]~P1(f332(f127(x57781),x57783))+P1(f332(f127(x57781),f162(x57781,x57782,x57783)))
% 52.62/52.41 [5779]~P140(x57791,x57792,x57793)+P1(f332(x57791,f53(a1,x57792,x57793)))
% 52.62/52.41 [5877]P1(f332(a26,f31(x58771,x58772,x58773)))+~P1(f332(a26,f332(a27,x58772)))
% 52.62/52.41 [5878]P1(f332(a26,f31(x58781,x58782,x58783)))+~P1(f332(a26,f332(a27,x58782)))
% 52.62/52.41 [5890]~P99(x58901)+E(f332(f332(f104(f853(x58901,a839)),f332(f257(x58901),x58902)),f295(x58901,x58902,x58903)),f180(f853(x58901,a839)))
% 52.62/52.41 [5891]~P99(x58911)+E(f332(f332(f104(f853(x58911,a839)),f332(f293(x58911),x58912)),f297(x58911,x58912,x58913)),f180(f853(x58911,a839)))
% 52.62/52.41 [5892]~P99(x58921)+E(f332(f332(f104(f853(x58921,a839)),f332(f293(x58921),x58922)),f298(x58921,x58922,x58923)),f180(f853(x58921,a839)))
% 52.62/52.41 [6043]P1(f332(a26,x60431))+~P1(f332(a26,f32(x60432,x60433,x60431)))
% 52.62/52.41 [6044]P1(f332(a26,x60441))+~P1(f332(a26,f32(x60442,x60443,x60441)))
% 52.62/52.41 [6045]P1(f332(a26,x60451))+~P1(f332(a26,f33(x60452,x60453,x60451)))
% 52.62/52.41 [6046]P1(f332(a26,x60461))+~P1(f332(a26,f33(x60462,x60463,x60461)))
% 52.62/52.41 [6047]P1(f332(a26,x60471))+~P1(f332(a26,f33(x60472,x60471,x60473)))
% 52.62/52.41 [6048]P1(f332(a26,x60481))+~P1(f332(a26,f33(x60482,x60481,x60483)))
% 52.62/52.41 [6130]E(f332(f126(x61301,x61302),x61303),x61303)+~P1(f332(x61302,f758(x61303,x61302,x61301)))
% 52.62/52.41 [6132]E(f332(f332(f302(x61321),f416(x61322,x61323,x61321)),f380(x61322,x61323,x61321)),x61323)+~E(f332(f43(x61321),x61323),f332(a114,x61322))
% 52.62/52.41 [6147]P140(x61471,x61472,x61473)+~P1(f332(x61471,f53(a1,x61472,x61473)))
% 52.62/52.41 [6199]E(f162(x61991,x61992,x61993),x61993)+~P1(f332(x61992,f770(x61993,x61992,x61991)))
% 52.62/52.41 [6239]~P1(f332(a26,f31(x62392,x62391,x62393)))+P1(f332(a26,f332(a27,x62391)))
% 52.62/52.41 [6240]~P1(f332(a26,f31(x62402,x62401,x62403)))+P1(f332(a26,f332(a27,x62401)))
% 52.62/52.41 [6288]~P1(f332(x62882,f815(x62883,x62882,x62881)))+P1(f332(f245(x62881,x62882),x62883))
% 52.62/52.41 [6548]~P1(f332(f321(x65481,x65482),f817(x65483,x65482,x65481)))+P1(f332(f321(x65481,x65482),x65483))
% 52.62/52.41 [6549]~P1(f332(f321(x65491,x65492),f818(x65493,x65492,x65491)))+P1(f332(f321(x65491,x65492),x65493))
% 52.62/52.41 [7178]~P9(x71781)+E(f332(f332(f82(x71781),f332(f332(f83(x71781),x71782),f332(f332(f44(x71781),x71783),x71782))),f53(x71781,x71783,x71782)),x71783)
% 52.62/52.41 [7666]E(f332(f332(f241(x76661,x76661),f463(x76662,x76663,x76661)),f463(x76662,x76663,x76661)),x76663)+~P1(f332(f332(f334(f852(x76661,x76661)),x76663),f260(x76661,x76662)))
% 52.62/52.41 [7785]~P1(f332(f332(f334(x77851),f527(x77853,x77852,x77851)),f322(x77851,x77853)))+P1(f332(f332(f334(x77851),x77852),f322(x77851,x77853)))
% 52.62/52.41 [7786]~P1(f332(f332(f334(x77861),f620(x77863,x77862,x77861)),f322(x77861,x77863)))+P1(f332(f332(f334(x77861),x77862),f322(x77861,x77863)))
% 52.62/52.41 [7787]~P1(f332(f332(f334(x77871),f622(x77873,x77872,x77871)),f322(x77871,x77873)))+P1(f332(f332(f334(x77871),x77872),f322(x77871,x77873)))
% 52.62/52.41 [7972]~P9(x79721)+E(f332(f332(f82(x79721),f332(f332(f83(x79721),f332(f332(f44(x79721),x79722),x79723)),x79723)),f53(x79721,x79722,x79723)),x79722)
% 52.62/52.41 [7973]~P9(x79731)+E(f332(f332(f82(x79731),f332(f332(f83(x79731),f332(f332(f44(x79731),x79732),x79733)),x79733)),f53(x79731,x79732,x79733)),x79732)
% 52.62/52.41 [8014]~E(f332(f43(x80141),x80142),f332(a114,x80143))+~P1(f332(f332(f334(x80141),f416(x80143,x80142,x80141)),f380(x80143,x80142,x80141)))
% 52.62/52.41 [8615]P1(f332(f332(f232(f853(f852(x86151,x86151),a839)),f300(x86151,x86152)),f300(x86151,x86153)))+~P1(f332(f332(f232(f853(f852(x86151,x86151),a839)),x86152),f300(x86151,x86153)))
% 52.62/52.41 [8853]E(x88531,f115(x88532))+~P1(f332(f332(f334(f852(f846(x88532),f846(x88532))),f332(f332(f241(f846(x88532),f846(x88532)),x88531),f115(x88532))),f147(x88532,x88533)))
% 52.62/52.41 [8879]E(x88791,f115(x88792))+~P1(f332(f332(f334(f852(f846(x88792),f846(x88792))),f332(f332(f241(f846(x88792),f846(x88792)),f115(x88792)),x88791)),f147(x88792,x88793)))
% 52.62/52.41 [9006]E(f332(f332(f140(x90061),f749(x90062,x90063,x90061)),f750(x90062,x90063,x90061)),x90063)+~P1(f332(f332(f334(f852(f846(x90061),f846(x90061))),f332(f332(f241(f846(x90061),f846(x90061)),f115(x90061)),x90063)),f137(x90061,x90062)))
% 52.62/52.41 [9205]~P118(x92051)+~P1(f332(f332(f233(x92051),f332(f332(f82(x92051),f332(f332(f83(x92051),x92052),x92052)),f332(f332(f83(x92051),x92053),x92053))),f2(x92051)))
% 52.62/52.41 [9254]P1(f332(f64(x92541),x92542))+~P1(f332(f332(f334(f852(f853(x92541,a839),f853(x92541,a839))),f332(f332(f241(f853(x92541,a839),f853(x92541,a839)),x92543),x92542)),f299(x92541)))
% 52.62/52.41 [9532]~P47(x95321,x95322,x95323)+P1(f332(f332(f233(a1),f332(f332(f75(f852(a1,a1),a1,x95321,f240(a1,a1)),f207(x95321)),f224(x95321,x95322,f221(x95321,x95323)))),f2(a1)))
% 52.62/52.41 [9533]~P48(x95331,x95332,x95333)+P1(f332(f332(f232(a1),f332(f332(f75(f852(a1,a1),a1,x95331,f240(a1,a1)),f207(x95331)),f224(x95331,x95332,f221(x95331,x95333)))),f2(a1)))
% 52.62/52.41 [9647]P47(x96471,x96472,x96473)+~P1(f332(f332(f233(a1),f332(f332(f75(f852(a1,a1),a1,x96471,f240(a1,a1)),f207(x96471)),f224(x96471,x96472,f221(x96471,x96473)))),f2(a1)))
% 52.62/52.41 [9648]P48(x96481,x96482,x96483)+~P1(f332(f332(f232(a1),f332(f332(f75(f852(a1,a1),a1,x96481,f240(a1,a1)),f207(x96481)),f224(x96481,x96482,f221(x96481,x96483)))),f2(a1)))
% 52.62/52.41 [9979]~P110(x99791)+~P1(f332(f332(f233(x99791),f332(f332(f82(x99791),f332(f332(f242(x99791),x99792),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))),f332(f332(f242(x99791),x99793),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))))),f2(x99791)))
% 52.62/52.41 [4638]~E(x46383,f115(x46381))+E(f332(f332(f125(x46381),x46382),x46383),x46382)
% 52.62/52.41 [4639]~E(x46392,f115(x46391))+E(f332(f332(f125(x46391),x46392),x46393),x46393)
% 52.62/52.41 [4640]~E(x46403,f115(x46401))+E(f332(f332(f125(x46401),x46402),x46403),x46402)
% 52.62/52.41 [4641]~E(x46412,f115(x46411))+E(f332(f332(f125(x46411),x46412),x46413),x46413)
% 52.62/52.41 [4647]~E(x46472,f2(a845))+E(f332(f332(f159(x46471),x46472),x46473),f115(x46471))
% 52.62/52.41 [4651]~E(x46513,f115(x46511))+E(f332(f332(f159(x46511),x46512),x46513),f115(x46511))
% 52.62/52.41 [4690]~E(x46901,x46903)+E(x46901,f332(f332(f125(x46902),f115(x46902)),x46903))
% 52.62/52.41 [4771]~P106(x47712)+E(f332(f239(f853(x47711,x47712)),x47713),f239(x47712))
% 52.62/52.41 [4772]~P101(x47722)+E(f332(f180(f853(x47721,x47722)),x47723),f180(x47722))
% 52.62/52.41 [4773]~P101(x47732)+E(f332(f180(f853(x47731,x47732)),x47733),f180(x47732))
% 52.62/52.41 [4790]E(x47901,f115(x47902))+~E(f332(f332(f125(x47902),x47901),x47903),x47903)
% 52.62/52.41 [4791]E(x47911,f115(x47912))+~E(f332(f332(f125(x47912),x47913),x47911),x47913)
% 52.62/52.41 [4792]E(x47921,f115(x47922))+~E(f332(f332(f125(x47922),x47923),x47921),x47923)
% 52.62/52.41 [4793]E(x47931,f115(x47932))+~E(f332(f332(f125(x47932),x47931),x47933),x47933)
% 52.62/52.41 [4799]E(x47991,f115(x47992))+~E(f332(f332(f125(x47992),x47993),x47991),f115(x47992))
% 52.62/52.41 [4800]E(x48001,f115(x48002))+~E(f332(f332(f125(x48002),x48001),x48003),f115(x48002))
% 52.62/52.41 [4801]E(x48011,f115(x48012))+~E(f332(f332(f125(x48012),x48013),x48011),f115(x48012))
% 52.62/52.41 [4802]E(x48021,f115(x48022))+~E(f332(f332(f125(x48022),x48021),x48023),f115(x48022))
% 52.62/52.41 [4827]~E(x48272,f2(a845))+E(f332(f332(f83(a845),x48271),x48272),f332(f332(f83(a845),x48273),x48272))
% 52.62/52.41 [4828]~E(x48281,f2(a845))+E(f332(f332(f83(a845),x48281),x48282),f332(f332(f83(a845),x48281),x48283))
% 52.62/52.41 [4829]~E(x48291,f2(a845))+E(f332(f332(f83(a845),x48291),x48292),f332(f332(f83(a845),x48291),x48293))
% 52.62/52.41 [4882]~P73(x48821)+E(f332(f332(f82(x48821),x48822),x48823),f332(f332(f82(x48821),x48823),x48822))
% 52.62/52.41 [4883]~P73(x48831)+E(f332(f332(f83(x48831),x48832),x48833),f332(f332(f83(x48831),x48833),x48832))
% 52.62/52.41 [4884]~P100(x48841)+E(f332(f332(f236(x48841),x48842),x48843),f332(f332(f236(x48841),x48843),x48842))
% 52.62/52.41 [4885]~P100(x48851)+E(f332(f332(f236(x48851),x48852),x48853),f332(f332(f236(x48851),x48853),x48852))
% 52.62/52.41 [4886]~P100(x48861)+E(f332(f332(f179(x48861),x48862),x48863),f332(f332(f179(x48861),x48863),x48862))
% 52.62/52.41 [4887]~P100(x48871)+E(f332(f332(f179(x48871),x48872),x48873),f332(f332(f179(x48871),x48873),x48872))
% 52.62/52.41 [4888]~P92(x48881)+E(f332(f332(f103(x48881),x48882),x48883),f332(f332(f103(x48881),x48883),x48882))
% 52.62/52.41 [4889]~P92(x48891)+E(f332(f332(f103(x48891),x48892),x48893),f332(f332(f103(x48891),x48893),x48892))
% 52.62/52.41 [4890]~P93(x48901)+E(f332(f332(f103(x48901),x48902),x48903),f332(f332(f103(x48901),x48903),x48902))
% 52.62/52.41 [4891]~P93(x48911)+E(f332(f332(f104(x48911),x48912),x48913),f332(f332(f104(x48911),x48913),x48912))
% 52.62/52.41 [4892]~P98(x48921)+E(f332(f332(f104(x48921),x48922),x48923),f332(f332(f104(x48921),x48923),x48922))
% 52.62/52.41 [4893]~P98(x48931)+E(f332(f332(f104(x48931),x48932),x48933),f332(f332(f104(x48931),x48933),x48932))
% 52.62/52.41 [4956]E(f53(a845,x49561,x49562),f2(a845))+~E(x49561,f332(f332(f83(a845),x49562),x49563))
% 52.62/52.41 [4957]E(f53(a1,x49571,x49572),f2(a1))+~E(x49571,f332(f332(f83(a1),x49572),x49573))
% 52.62/52.41 [5017]E(x50171,x50172)+~E(f332(f332(f82(a845),x50173),x50171),f332(f332(f82(a845),x50173),x50172))
% 52.62/52.41 [5018]E(x50181,x50182)+~E(f332(f332(f82(a845),x50181),x50183),f332(f332(f82(a845),x50182),x50183))
% 52.62/52.41 [5028]~P69(x50281)+E(f332(f332(f82(x50281),x50282),f332(f81(x50281),x50283)),f332(f332(f3(x50281),x50282),x50283))
% 52.62/52.41 [5029]~P104(x50291)+E(f332(f332(f82(x50291),x50292),f332(f81(x50291),x50293)),f332(f332(f3(x50291),x50292),x50293))
% 52.62/52.41 [5030]~P8(x50301)+E(f332(f332(f82(x50301),x50302),f332(f81(x50301),x50303)),f332(f332(f3(x50301),x50302),x50303))
% 52.62/52.41 [5031]~P90(x50311)+E(f332(f332(f104(x50311),x50312),f332(f81(x50311),x50313)),f332(f332(f3(x50311),x50312),x50313))
% 52.62/52.41 [5032]~P69(x50321)+E(f332(f332(f3(x50321),x50322),f332(f81(x50321),x50323)),f332(f332(f82(x50321),x50322),x50323))
% 52.62/52.41 [5079]~P1(f332(x50793,x50792))+P1(f332(f332(f334(x50791),x50792),x50793))
% 52.62/52.41 [5080]~P4(x50802)+E(f332(f332(f8(x50801,x50802),x50803),f180(f853(x50801,a839))),f2(x50802))
% 52.62/52.41 [5081]~P4(x50812)+E(f332(f332(f8(x50811,x50812),x50813),f180(f853(x50811,a839))),f2(x50812))
% 52.62/52.41 [5082]~P70(x50822)+E(f332(f332(f11(x50821,x50822),x50823),f180(f853(x50821,a839))),f80(x50822))
% 52.62/52.41 [5083]~P70(x50832)+E(f332(f332(f11(x50831,x50832),x50833),f180(f853(x50831,a839))),f80(x50832))
% 52.62/52.41 [5128]~E(x51282,f332(f332(f82(a845),x51281),x51283))+P1(f332(f332(f232(a845),x51281),x51282))
% 52.62/52.41 [5130]~E(x51302,f180(f853(x51301,a839)))+E(f332(f332(f62(x51301),x51302),x51303),f180(f853(f853(x51301,a839),a839)))
% 52.62/52.41 [5131]~E(x51312,f180(f853(x51311,a839)))+E(f180(f853(f853(x51311,a839),a839)),f332(f332(f62(x51311),x51312),x51313))
% 52.62/52.41 [5199]~E(f332(f259(x51992,x51993),x51991),f180(f853(x51993,a839)))+E(x51991,f180(f853(f852(x51992,x51993),a839)))
% 52.62/52.41 [5200]~E(f332(f261(x52002,x52003),x52001),f180(f853(x52002,a839)))+E(x52001,f180(f853(f852(x52002,x52003),a839)))
% 52.62/52.41 [5231]E(f332(f259(x52311,x52312),x52313),f180(f853(x52312,a839)))+~E(x52313,f180(f853(f852(x52311,x52312),a839)))
% 52.62/52.41 [5232]E(f332(f261(x52321,x52322),x52323),f180(f853(x52321,a839)))+~E(x52323,f180(f853(f852(x52321,x52322),a839)))
% 52.62/52.41 [5235]E(f269(x52351,x52352,x52353),f332(f332(f3(a101),x52352),x52353))+P1(f332(f332(f233(a101),x52352),x52353))
% 52.62/52.41 [5251]P1(f332(x52511,x52512))+~P1(f332(f332(f334(x52513),x52512),x52511))
% 52.62/52.41 [5287]E(x52871,x52872)+~E(f332(f81(f853(x52873,a839)),x52871),f332(f81(f853(x52873,a839)),x52872))
% 52.62/52.41 [5292]E(f307(x52921,x52922,x52923),f183(f846(a837)))+~P1(f332(f332(f233(a1),x52922),x52923))
% 52.62/52.41 [5295]~E(x52951,f180(f853(x52952,a839)))+~P1(f332(f332(f334(x52952),x52953),x52951))
% 52.62/52.41 [5296]~E(x52961,f180(f853(x52962,a839)))+~P1(f332(f332(f334(x52962),x52963),x52961))
% 52.62/52.41 [5297]~E(x52971,f180(f853(x52972,a839)))+~P1(f332(f332(f334(x52972),x52973),x52971))
% 52.62/52.41 [5325]~E(x53252,f332(f332(f82(a1),x53251),f332(f102(a1),x53253)))+P1(f332(f332(f232(a1),x53251),x53252))
% 52.62/52.41 [5341]E(f332(f332(f302(x53411),x53412),x53413),x53413)+~P1(f332(f332(f334(x53411),x53412),x53413))
% 52.62/52.41 [5353]E(x53531,f180(f853(x53532,a839)))+~E(f332(f332(f62(x53532),x53531),x53533),f180(f853(f853(x53532,a839),a839)))
% 52.62/52.41 [5354]E(x53541,f180(f853(x53542,a839)))+~E(f180(f853(f853(x53542,a839),a839)),f332(f332(f62(x53542),x53541),x53543))
% 52.62/52.41 [5360]~P121(x53601)+E(f332(f332(f83(x53601),f332(f81(x53601),x53602)),f332(f81(x53601),x53603)),f332(f332(f83(x53601),x53602),x53603))
% 52.62/52.41 [5362]~P62(x53621)+E(f332(f332(f283(x53621),f332(f81(x53621),x53622)),f332(f81(x53621),x53623)),f332(f332(f283(x53621),x53622),x53623))
% 52.62/52.41 [5393]~P1(f332(x53933,x53932))+P1(f332(f332(f334(x53931),x53932),f332(f256(x53931),x53933)))
% 52.62/52.41 [5394]~P1(f332(x53943,x53942))+P1(f332(f332(f334(x53941),x53942),f332(f256(x53941),x53943)))
% 52.62/52.41 [5434]E(f151(x54341,x54342,x54343),x54343)+P1(f332(f332(f334(x54341),x54342),f332(f158(x54341),x54343)))
% 52.62/52.41 [5512]~P1(f332(f127(x55121),x55123))+P1(f332(f127(x55121),f332(f126(x55121,x55122),x55123)))
% 52.62/52.41 [5554]~P9(x55541)+E(f332(f332(f44(x55541),f53(x55541,x55542,x55543)),x55543),f2(x55541))
% 52.62/52.41 [5572]E(f160(x55721,f332(f332(f140(x55721),x55722),f115(x55721)),x55723),f115(x55721))+P1(f332(f332(f334(a845),f2(a845)),x55723))
% 52.62/52.41 [5637]E(x56371,x56372)+~E(f332(f332(f83(a845),f332(a114,x56373)),x56371),f332(f332(f83(a845),f332(a114,x56373)),x56372))
% 52.62/52.41 [5638]~E(x56382,f332(f332(f82(a1),x56381),f332(f102(a1),f332(a114,x56383))))+P1(f332(f332(f233(a1),x56381),x56382))
% 52.62/52.41 [5756]~E(x57563,f115(x57561))+E(f332(f332(f332(f173(f846(x57561),f846(x57561)),x57562),f141(x57561)),x57563),f115(x57561))
% 52.62/52.41 [5758]P1(f332(x57581,x57582))+~P1(f332(f332(f334(x57583),x57582),f332(f256(x57583),x57581)))
% 52.62/52.41 [5759]P1(f332(x57591,x57592))+~P1(f332(f332(f334(x57593),x57592),f332(f256(x57593),x57591)))
% 52.62/52.41 [5760]P1(f332(x57601,x57602))+~P1(f332(f332(f334(x57603),x57602),f332(f256(x57603),x57601)))
% 52.62/52.41 [5794]E(x57941,x57942)+~E(f332(f332(f302(x57943),x57941),f180(f853(x57943,a839))),f332(f332(f302(x57943),x57942),f180(f853(x57943,a839))))
% 52.62/52.41 [5804]~P99(x58041)+E(f332(f332(f104(f853(x58041,a839)),f332(f257(x58041),x58042)),f332(f294(x58041,x58042),x58043)),f180(f853(x58041,a839)))
% 52.62/52.41 [5864]~P78(x58641)+E(f332(f303(x58641,x58641,f81(x58641)),f332(f294(x58641,x58642),x58643)),f297(x58641,f332(f81(x58641),x58643),f332(f81(x58641),x58642)))
% 52.62/52.41 [5872]E(f332(f181(f846(x58721)),f151(x58721,x58722,x58723)),f332(f181(f846(x58721)),x58723))+P1(f332(f332(f334(x58721),x58722),f332(f158(x58721),x58723)))
% 52.62/52.41 [5893]P1(f332(x58931,x58932))+~P1(f332(f332(f334(x58933),x58932),f180(f853(x58933,a839))))
% 52.62/52.41 [5930]~P99(x59301)+E(f332(f332(f104(f853(x59301,a839)),f332(f294(x59301,x59302),x59303)),f332(f258(x59301),x59303)),f180(f853(x59301,a839)))
% 52.62/52.41 [5951]~P78(x59511)+E(f332(f303(x59511,x59511,f81(x59511)),f295(x59511,x59512,x59513)),f295(x59511,f332(f81(x59511),x59513),f332(f81(x59511),x59512)))
% 52.62/52.41 [5952]~P78(x59521)+E(f332(f303(x59521,x59521,f81(x59521)),f298(x59521,x59522,x59523)),f298(x59521,f332(f81(x59521),x59523),f332(f81(x59521),x59522)))
% 52.62/52.41 [6011]E(f160(x60111,f332(f332(f140(x60111),x60112),f115(x60111)),x60113),f332(f332(f140(x60111),x60112),f115(x60111)))+~P1(f332(f332(f334(a845),f2(a845)),x60113))
% 52.62/52.41 [6019]~P78(x60191)+E(f332(f303(x60191,x60191,f81(x60191)),f297(x60191,x60192,x60193)),f332(f294(x60191,f332(f81(x60191),x60193)),f332(f81(x60191),x60192)))
% 52.62/52.41 [6039]~P10(x60391)+E(f53(x60391,f332(f81(x60391),f53(x60391,x60392,x60393)),x60393),f53(x60391,f332(f81(x60391),x60392),x60393))
% 52.62/52.41 [6145]~P1(f332(f64(f852(x61452,x61451)),x61453))+P1(f332(f64(x61451),f332(f259(x61452,x61451),x61453)))
% 52.62/52.41 [6146]~P1(f332(f64(f852(x61461,x61462)),x61463))+P1(f332(f64(x61461),f332(f261(x61461,x61462),x61463)))
% 52.62/52.41 [6151]~P99(x61511)+E(f332(f332(f104(f853(x61511,a839)),f295(x61511,x61512,x61513)),f332(f296(x61511),x61513)),f180(f853(x61511,a839)))
% 52.62/52.41 [6152]~P99(x61521)+E(f332(f332(f104(f853(x61521,a839)),f297(x61521,x61522,x61523)),f332(f296(x61521),x61523)),f180(f853(x61521,a839)))
% 52.62/52.41 [6153]~P99(x61531)+E(f332(f332(f104(f853(x61531,a839)),f298(x61531,x61532,x61533)),f332(f258(x61531),x61533)),f180(f853(x61531,a839)))
% 52.62/52.41 [6222]E(f332(f332(f152(x62221),x62222),f729(x62222,x62223,x62221)),x62223)+~P1(f332(f332(f334(x62221),x62223),f332(f158(x62221),x62222)))
% 52.62/52.41 [6374]E(x63741,f115(x63742))+~E(f332(f332(f332(f173(f846(x63742),f846(x63742)),x63743),f141(x63742)),x63741),f115(x63742))
% 52.62/52.41 [6453]P41(x64531,x64532,f404(x64533,x64532,x64531),x64533)+~P1(f332(f332(f187(x64531),x64532),x64533))
% 52.62/52.41 [6454]P41(x64541,x64542,f462(x64543,x64542,x64541),x64543)+~P1(f332(f332(f187(x64541),x64542),x64543))
% 52.62/52.41 [6484]~P1(f332(f64(f852(x64842,x64841)),x64843))+P1(f332(f64(f852(x64841,x64842)),f332(f278(x64842,x64841),x64843)))
% 52.62/52.41 [6506]E(x65061,x65062)+~E(f282(a845,f279(a845),x65063,x65061),f332(f332(f302(a845),x65062),f180(f853(a845,a839))))
% 52.62/52.41 [6507]E(x65071,x65072)+~E(f282(a845,f279(a845),x65071,x65072),f332(f332(f302(a845),x65073),f180(f853(a845,a839))))
% 52.62/52.41 [6642]P56(x66421,x66422,x66423)+P1(f332(f332(f334(x66421),f638(x66423,x66422,x66421)),x66422))
% 52.62/52.41 [6643]P56(x66431,x66432,x66433)+P1(f332(f332(f334(x66431),f637(x66433,x66432,x66431)),x66432))
% 52.62/52.41 [6655]P1(f332(f321(x66551,x66552),x66553))+P1(f332(f332(x66552,f817(x66553,x66552,x66551)),x66553))
% 52.62/52.41 [6656]P1(f332(f321(x66561,x66562),x66563))+P1(f332(f332(x66562,f818(x66563,x66562,x66561)),x66563))
% 52.62/52.41 [6687]E(f332(f181(f846(x66871)),f151(x66871,x66872,x66873)),f332(f332(f3(a845),f332(f181(f846(x66871)),x66873)),f80(a845)))+~P1(f332(f332(f334(x66871),x66872),f332(f158(x66871),x66873)))
% 52.62/52.41 [6727]P1(f332(f245(x67271,x67272),x67273))+P1(f332(f332(f334(x67271),f815(x67273,x67272,x67271)),x67273))
% 52.62/52.41 [6739]~P1(f332(f64(f852(x67392,x67391)),f332(f278(x67391,x67392),x67393)))+P1(f332(f64(f852(x67391,x67392)),x67393))
% 52.62/52.41 [6800]~P1(f332(f332(f334(x68001),x68002),f332(f158(x68001),f116(x68001,x68003))))+P1(f332(f332(f334(x68001),x68002),f332(f158(x68001),x68003)))
% 52.62/52.41 [6807]P34(x68071,x68072,x68073)+P1(f332(f332(f334(f844(x68071)),f816(x68073,x68072,x68071)),x68073))
% 52.62/52.41 [6836]E(f332(f126(x68361,x68362),x68363),x68363)+P1(f332(f332(f334(x68361),f758(x68363,x68362,x68361)),f332(f158(x68361),x68363)))
% 52.62/52.41 [6853]E(f332(f126(x68531,x68532),x68533),f115(x68531))+P1(f332(f332(f334(x68531),f746(x68533,x68532,x68531)),f332(f158(x68531),x68533)))
% 52.62/52.41 [6881]E(f162(x68811,x68812,x68813),x68813)+P1(f332(f332(f334(x68811),f770(x68813,x68812,x68811)),f332(f158(x68811),x68813)))
% 52.62/52.41 [7002]P1(f332(f332(f334(x70021),x70022),f696(x70023,x70022,x70021)))+~P1(f332(f332(f334(x70021),x70022),f45(f853(x70021,a839),x70023)))
% 52.62/52.41 [7004]~P4(x70041)+E(f332(f332(f82(x70041),f332(f332(f8(a845,x70041),x70042),f332(f257(a845),x70043))),f332(x70042,x70043)),f332(f332(f8(a845,x70041),x70042),f332(f257(a845),f332(a114,x70043))))
% 52.62/52.41 [7108]~P1(f332(f332(f334(x71081),x71082),f685(x71082,x71083,x71081)))+P1(f332(f332(f334(x71081),x71082),f46(f853(x71081,a839),x71083)))
% 52.62/52.41 [7137]~P4(x71371)+E(f332(f332(f82(x71371),f332(f332(f8(a845,x71371),x71372),f332(f293(a845),x71373))),f332(x71372,f332(a114,x71373))),f332(f332(f8(a845,x71371),x71372),f332(f293(a845),f332(a114,x71373))))
% 52.62/52.41 [7291]P1(f332(f332(f334(f846(x72911)),x72912),f149(x72911,x72913)))+P1(f332(f332(f334(x72911),f745(x72913,x72912,x72911)),f332(f158(x72911),x72912)))
% 52.62/52.41 [7308]~P1(f332(f332(f334(f846(x73081)),x73082),f149(x73081,f322(x73081,x73083))))+P1(f332(f332(f334(f846(x73081)),x73082),f322(f846(x73081),f146(x73081,x73083))))
% 52.62/52.41 [7336]~P1(f332(f332(f334(f846(x73361)),x73362),f322(f846(x73361),f146(x73361,x73363))))+P1(f332(f332(f334(f846(x73361)),x73362),f149(x73361,f322(x73361,x73363))))
% 52.62/52.41 [7376]E(f332(f332(f332(f173(f846(x73761),f846(x73761)),x73762),f141(x73761)),x73763),x73763)+~P1(f332(f332(f232(a845),f332(f181(f846(x73761)),x73763)),f80(a845)))
% 52.62/52.41 [7429]~P31(x74291,x74292,x74293,f239(f853(x74291,a839)))+P31(f846(x74291),f846(x74292),f332(f143(x74291,x74292),x74293),f239(f853(f846(x74291),a839)))
% 52.62/52.41 [7430]~P31(x74301,x74302,x74303,f239(f853(x74301,a839)))+P31(f846(x74301),f846(x74302),f332(f143(x74301,x74302),x74303),f239(f853(f846(x74301),a839)))
% 52.62/52.41 [7587]E(x75871,f332(f332(f82(a845),f332(f332(f83(a845),f332(f240(a845,a845),x75872)),x75873)),f332(f250(a845,a845),x75872)))+~P1(f332(f56(x75871,x75873),x75872))
% 52.62/52.41 [7594]P31(x75941,x75942,x75943,f239(f853(x75941,a839)))+~P31(f846(x75941),f846(x75942),f332(f143(x75941,x75942),x75943),f239(f853(f846(x75941),a839)))
% 52.62/52.41 [7595]P31(x75951,x75952,x75953,f239(f853(x75951,a839)))+~P31(f846(x75951),f846(x75952),f332(f143(x75951,x75952),x75953),f239(f853(f846(x75951),a839)))
% 52.62/52.41 [7638]P1(f332(f332(f334(f853(x76381,a839)),f685(x76382,x76383,x76381)),x76383))+P1(f332(f332(f334(x76381),x76382),f46(f853(x76381,a839),x76383)))
% 52.62/52.41 [7727]P1(f332(f332(f334(f846(x77271)),x77272),f149(x77271,x77273)))+~P1(f332(f332(f334(x77271),f745(x77273,x77272,x77271)),x77273))
% 52.62/52.41 [7858]E(x78581,x78582)+~E(f332(f332(f9(x78583,f853(x78583,a839),a839),f334(x78583)),x78581),f332(f332(f9(x78583,f853(x78583,a839),a839),f334(x78583)),x78582))
% 52.62/52.41 [7864]~P1(f332(f332(f334(f852(x78641,x78641)),x78643),f260(x78641,x78642)))+P1(f332(f332(f334(x78641),f463(x78642,x78643,x78641)),x78642))
% 52.62/52.41 [7866]~P1(f332(f332(f334(x78661),x78663),f45(f853(x78661,a839),x78662)))+P1(f332(f332(f334(f853(x78661,a839)),f696(x78662,x78663,x78661)),x78662))
% 52.62/52.41 [8126]E(f332(f229(f849(f846(a837)),f846(a837),f307(x81261,x81262,f332(f332(f82(a1),x81263),f80(a1))),f227(f846(a837))),f332(x81261,x81263)),f307(x81261,x81262,x81263))+P1(f332(f332(f233(a1),x81262),x81263))
% 52.62/52.41 [8225]E(x82251,f115(x82252))+P1(f332(f332(f334(x82252),f332(f240(x82252,f852(a101,a101)),f332(f270(x82252,x82251),x82253))),f332(f158(x82252),x82251)))
% 52.62/52.41 [8323]~P7(x83231)+E(f332(f132(x83231,x83231,f332(f9(x83231,x83231,x83231),f82(x83231)),x83232),f332(f142(x83231),x83233)),f332(f132(x83231,x83231,f82(x83231),x83232),x83233))
% 52.62/52.41 [8784]~P100(x87841)+E(f332(f158(x87841),f139(x87841,x87841,f7(x87841),x87842,x87843)),f332(f332(f302(x87841),x87842),f332(f158(x87841),x87843)))
% 52.62/52.41 [8793]P1(f332(f332(f233(a845),f2(a845)),f635(x87931,x87932,x87933)))+~P1(f332(f332(f334(f852(x87933,x87933)),x87932),f332(f332(f281(x87933,x87933,x87933),x87931),f300(x87933,x87931))))
% 52.62/52.41 [9056]~P58(x90561,x90562)+~P1(f332(f332(f334(f852(x90561,x90561)),f332(f332(f241(x90561,x90561),x90563),x90563)),f332(f332(f281(x90561,x90561,x90561),x90562),f300(x90561,x90562))))
% 52.62/52.41 [9167]~E(f332(f332(f104(f853(f852(x91671,x91671),a839)),f332(f278(x91671,x91671),x91672)),f300(x91671,x91672)),f180(f853(f852(x91671,x91671),a839)))+~P1(f332(f332(f334(f852(x91671,x91671)),f332(f332(f241(x91671,x91671),x91673),x91673)),f332(f332(f281(x91671,x91671,x91671),x91672),f300(x91671,x91672))))
% 52.62/52.41 [9341]~P1(f332(f64(x93411),x93412))+P1(f332(f332(f232(a845),f332(f43(x93411),f332(f332(f3(f853(x93411,a839)),x93412),f332(f332(f302(x93411),x93413),f180(f853(x93411,a839)))))),f332(f43(x93411),x93412)))
% 52.62/52.41 [4939]~E(x49393,f115(x49391))+E(f134(x49391,f332(f332(f140(x49391),x49392),x49393)),x49392)
% 52.62/52.41 [4940]~E(x49403,f115(x49401))+E(f134(x49401,f332(f332(f140(x49401),x49402),x49403)),x49402)
% 52.62/52.41 [4953]~E(x49533,f115(x49531))+E(f116(x49531,f332(f332(f140(x49531),x49532),x49533)),f115(x49531))
% 52.62/52.41 [4981]E(x49811,f115(x49812))+E(f134(x49812,f332(f332(f140(x49812),x49813),x49811)),f134(x49812,x49811))
% 52.62/52.41 [4982]E(x49821,f115(x49822))+E(f134(x49822,f332(f332(f140(x49822),x49823),x49821)),f134(x49822,x49821))
% 52.62/52.41 [4983]E(x49831,f115(x49832))+E(f134(x49832,f332(f332(f125(x49832),x49833),x49831)),f134(x49832,x49831))
% 52.62/52.41 [4984]E(x49841,f115(x49842))+E(f134(x49842,f332(f332(f125(x49842),x49843),x49841)),f134(x49842,x49841))
% 52.62/52.41 [4990]~E(x49903,f115(x49901))+E(f134(x49901,f332(f332(f125(x49901),x49902),x49903)),f134(x49901,x49902))
% 52.62/52.41 [4991]~E(x49913,f115(x49911))+E(f134(x49911,f332(f332(f125(x49911),x49912),x49913)),f134(x49911,x49912))
% 52.62/52.41 [4992]~E(x49923,f115(x49921))+E(f116(x49921,f332(f332(f125(x49921),x49922),x49923)),f116(x49921,x49922))
% 52.62/52.41 [5021]E(x50211,f115(x50212))+E(f332(f131(x50212),f332(f332(f125(x50212),x50211),x50213)),f332(f131(x50212),x50211))
% 52.62/52.41 [5022]E(x50221,f115(x50222))+E(f332(f131(x50222),f332(f332(f125(x50222),x50221),x50223)),f332(f131(x50222),x50221))
% 52.62/52.41 [5053]~E(x50532,f115(x50531))+E(f332(f131(x50531),f332(f332(f125(x50531),x50532),x50533)),f332(f131(x50531),x50533))
% 52.62/52.41 [5104]~P100(x51041)+E(f332(f332(f236(x51041),x51042),f332(f332(f179(x51041),x51042),x51043)),x51042)
% 52.62/52.41 [5105]~P100(x51051)+E(f332(f332(f179(x51051),x51052),f332(f332(f236(x51051),x51052),x51053)),x51052)
% 52.62/52.41 [5106]~P93(x51061)+E(f332(f332(f103(x51061),x51062),f332(f332(f104(x51061),x51062),x51063)),x51062)
% 52.62/52.41 [5107]~P93(x51071)+E(f332(f332(f104(x51071),x51072),f332(f332(f103(x51071),x51072),x51073)),x51072)
% 52.62/52.41 [5126]~P9(x51261)+E(f53(x51261,f332(f332(f83(x51261),x51262),x51263),x51263),f2(x51261))
% 52.62/52.41 [5127]~P9(x51271)+E(f53(x51271,f332(f332(f83(x51271),x51272),x51273),x51272),f2(x51271))
% 52.62/52.41 [5194]~P8(x51941)+E(f332(f81(x51941),f332(f332(f3(x51941),x51942),x51943)),f332(f332(f3(x51941),x51943),x51942))
% 52.62/52.41 [5255]E(x52551,f115(x52552))+E(f116(x52552,f332(f332(f140(x52552),x52553),x52551)),f332(f332(f140(x52552),x52553),f116(x52552,x52551)))
% 52.62/52.41 [5256]E(x52561,f115(x52562))+E(f116(x52562,f332(f332(f125(x52562),x52563),x52561)),f332(f332(f125(x52562),x52563),f116(x52562,x52561)))
% 52.62/52.41 [5257]~P11(x52571)+E(f46(x52571,f332(f332(f302(x52571),x52572),x52573)),f332(f332(f104(x52571),x52572),f46(x52571,x52573)))
% 52.62/52.41 [5258]~P11(x52581)+E(f45(x52581,f332(f332(f302(x52581),x52582),x52583)),f332(f332(f103(x52581),x52582),f45(x52581,x52583)))
% 52.62/52.41 [5301]~P91(x53011)+E(f332(f332(f83(x53011),x53012),f332(f332(f83(x53011),x53012),x53013)),f332(f332(f83(x53011),x53012),x53013))
% 52.62/52.41 [5302]~P100(x53021)+E(f332(f332(f236(x53021),x53022),f332(f332(f236(x53021),x53022),x53023)),f332(f332(f236(x53021),x53022),x53023))
% 52.62/52.41 [5303]~P100(x53031)+E(f332(f332(f236(x53031),x53032),f332(f332(f236(x53031),x53032),x53033)),f332(f332(f236(x53031),x53032),x53033))
% 52.62/52.41 [5304]~P100(x53041)+E(f332(f332(f179(x53041),x53042),f332(f332(f179(x53041),x53042),x53043)),f332(f332(f179(x53041),x53042),x53043))
% 52.62/52.41 [5305]~P100(x53051)+E(f332(f332(f179(x53051),x53052),f332(f332(f179(x53051),x53052),x53053)),f332(f332(f179(x53051),x53052),x53053))
% 52.62/52.41 [5306]~P92(x53061)+E(f332(f332(f103(x53061),x53062),f332(f332(f103(x53061),x53062),x53063)),f332(f332(f103(x53061),x53062),x53063))
% 52.62/52.41 [5307]~P92(x53071)+E(f332(f332(f103(x53071),x53072),f332(f332(f103(x53071),x53072),x53073)),f332(f332(f103(x53071),x53072),x53073))
% 52.62/52.41 [5308]~P93(x53081)+E(f332(f332(f103(x53081),x53082),f332(f332(f103(x53081),x53082),x53083)),f332(f332(f103(x53081),x53082),x53083))
% 52.62/52.41 [5309]~P93(x53091)+E(f332(f332(f104(x53091),x53092),f332(f332(f104(x53091),x53092),x53093)),f332(f332(f104(x53091),x53092),x53093))
% 52.62/52.41 [5310]~P98(x53101)+E(f332(f332(f104(x53101),x53102),f332(f332(f104(x53101),x53102),x53103)),f332(f332(f104(x53101),x53102),x53103))
% 52.62/52.41 [5311]~P98(x53111)+E(f332(f332(f104(x53111),x53112),f332(f332(f104(x53111),x53112),x53113)),f332(f332(f104(x53111),x53112),x53113))
% 52.62/52.41 [5318]~P9(x53181)+E(f53(x53181,f332(f332(f82(x53181),x53182),x53183),x53183),f53(x53181,x53182,x53183))
% 52.62/52.41 [5319]~P9(x53191)+E(f53(x53191,f332(f332(f82(x53191),x53192),x53193),x53192),f53(x53191,x53193,x53192))
% 52.62/52.41 [5326]~P121(x53261)+E(f332(f332(f83(x53261),x53262),f332(f81(x53261),x53263)),f332(f81(x53261),f332(f332(f83(x53261),x53262),x53263)))
% 52.62/52.41 [5327]~P62(x53271)+E(f332(f332(f283(x53271),x53272),f332(f81(x53271),x53273)),f332(f81(x53271),f332(f332(f283(x53271),x53272),x53273)))
% 52.62/52.41 [5328]~P3(x53281)+E(f332(f332(f82(x53281),x53282),f332(f154(x53281),x53283)),f332(f154(x53281),f332(f332(f140(x53281),x53282),x53283)))
% 52.62/52.41 [5359]~P121(x53591)+E(f332(f332(f83(x53591),f332(f81(x53591),x53592)),x53593),f332(f332(f83(x53591),x53592),f332(f81(x53591),x53593)))
% 52.62/52.41 [5365]~P14(x53651,x53652,x53653)+E(f45(f853(x53651,a839),f332(f332(f62(x53651),x53652),x53653)),x53652)
% 52.62/52.41 [5425]~P73(x54251)+E(f332(f332(f83(x54251),x54252),f332(f332(f242(x54251),x54252),x54253)),f332(f332(f242(x54251),x54252),f332(a114,x54253)))
% 52.62/52.41 [5426]~P105(x54261)+E(f332(f332(f83(x54261),x54262),f332(f332(f242(x54261),x54262),x54263)),f332(f332(f242(x54261),x54262),f332(a114,x54263)))
% 52.62/52.41 [5427]~P73(x54271)+E(f332(f332(f83(x54271),x54272),f332(f332(f242(x54271),x54272),x54273)),f332(f332(f242(x54271),x54272),f332(a114,x54273)))
% 52.62/52.41 [5437]~P69(x54371)+E(f332(f332(f82(x54371),f332(f81(x54371),x54372)),f332(f332(f82(x54371),x54372),x54373)),x54373)
% 52.62/52.41 [5456]~P2(x54561)+E(f332(f332(f242(x54561),f332(f102(x54561),x54562)),x54563),f332(f102(x54561),f332(f332(f242(a845),x54562),x54563)))
% 52.62/52.41 [5457]~P133(x54571)+E(f332(f332(f242(x54571),f332(f105(x54571),x54572)),x54573),f332(f105(x54571),f332(f332(f242(a1),x54572),x54573)))
% 52.62/52.41 [5462]~P80(x54621)+E(f332(f77(x54621),f332(f332(f3(x54621),x54622),x54623)),f332(f77(x54621),f332(f332(f3(x54621),x54623),x54622)))
% 52.62/52.41 [5465]~P110(x54651)+E(f332(f332(f83(x54651),f84(x54651,x54652)),f84(x54651,x54653)),f84(x54651,f332(f332(f83(x54651),x54652),x54653)))
% 52.62/52.41 [5469]E(x54691,f115(x54692))+E(f332(f332(f125(x54692),f332(f157(x54692),x54691)),x54693),f332(f157(x54692),f332(f332(f125(x54692),x54691),x54693)))
% 52.62/52.41 [5475]~E(x54752,f332(a114,f332(f332(f82(a845),x54751),x54753)))+P1(f332(f332(f233(a845),x54751),x54752))
% 52.62/52.41 [5476]~P121(x54761)+E(f332(f332(f83(x54761),f332(f81(x54761),x54762)),x54763),f332(f81(x54761),f332(f332(f83(x54761),x54762),x54763)))
% 52.62/52.41 [5477]~P113(x54771)+E(f332(f332(f283(x54771),f332(f81(x54771),x54772)),x54773),f332(f81(x54771),f332(f332(f283(x54771),x54772),x54773)))
% 52.62/52.41 [5478]~P110(x54781)+E(f332(f332(f242(x54781),f332(f77(x54781),x54782)),x54783),f332(f77(x54781),f332(f332(f242(x54781),x54782),x54783)))
% 52.62/52.41 [5571]E(f493(x55711,x55712,x55713),f498(x55711,x55712,x55713))+E(f332(f332(f104(f853(x55713,a839)),x55712),x55711),f180(f853(x55713,a839)))
% 52.62/52.41 [5585]~P4(x55852)+E(f332(f332(f8(x55851,x55852),f332(f18(x55852,x55851),f2(x55852))),x55853),f2(x55852))
% 52.62/52.41 [5586]~P70(x55862)+E(f332(f332(f11(x55861,x55862),f332(f18(x55862,x55861),f80(x55862))),x55863),f80(x55862))
% 52.62/52.41 [5588]~P2(x55881)+E(f332(f332(f82(x55881),f332(f102(x55881),x55882)),f332(f102(x55881),x55883)),f332(f102(x55881),f332(f332(f82(a845),x55882),x55883)))
% 52.62/52.41 [5589]~P2(x55891)+E(f332(f332(f83(x55891),f332(f102(x55891),x55892)),f332(f102(x55891),x55893)),f332(f102(x55891),f332(f332(f83(a845),x55892),x55893)))
% 52.62/52.41 [5590]~P133(x55901)+E(f332(f332(f82(x55901),f332(f105(x55901),x55902)),f332(f105(x55901),x55903)),f332(f105(x55901),f332(f332(f82(a1),x55902),x55903)))
% 52.62/52.41 [5591]~P133(x55911)+E(f332(f332(f83(x55911),f332(f105(x55911),x55912)),f332(f105(x55911),x55913)),f332(f105(x55911),f332(f332(f83(a1),x55912),x55913)))
% 52.62/52.41 [5592]~P133(x55921)+E(f332(f332(f3(x55921),f332(f105(x55921),x55922)),f332(f105(x55921),x55923)),f332(f105(x55921),f332(f332(f3(a1),x55922),x55923)))
% 52.62/52.41 [5593]~P88(x55931)+E(f332(f332(f82(x55931),f332(f106(x55931),x55932)),f332(f106(x55931),x55933)),f332(f106(x55931),f332(f332(f82(a1),x55932),x55933)))
% 52.62/52.41 [5594]~P88(x55941)+E(f332(f332(f83(x55941),f332(f106(x55941),x55942)),f332(f106(x55941),x55943)),f332(f106(x55941),f332(f332(f83(a1),x55942),x55943)))
% 52.62/52.41 [5595]~P88(x55951)+E(f332(f332(f3(x55951),f332(f106(x55951),x55952)),f332(f106(x55951),x55953)),f332(f106(x55951),f332(f332(f3(a1),x55952),x55953)))
% 52.62/52.41 [5596]~P88(x55961)+E(f332(f332(f82(x55961),f332(f106(x55961),x55962)),f332(f106(x55961),x55963)),f332(f106(x55961),f332(f332(f82(a1),x55962),x55963)))
% 52.62/52.41 [5597]~P88(x55971)+E(f332(f332(f83(x55971),f332(f106(x55971),x55972)),f332(f106(x55971),x55973)),f332(f106(x55971),f332(f332(f83(a1),x55972),x55973)))
% 52.62/52.41 [5644]~E(x56443,x56442)+P1(f332(f332(f232(f853(x56441,a839)),x56442),x56443))
% 52.62/52.41 [5645]~E(x56452,x56453)+P1(f332(f332(f232(f853(x56451,a839)),x56452),x56453))
% 52.62/52.41 [5646]~E(x56462,x56463)+P1(f332(f332(f232(f853(x56461,a839)),x56462),x56463))
% 52.62/52.41 [5647]~E(x56472,x56473)+P1(f332(f332(f232(f853(x56471,a839)),x56472),x56473))
% 52.62/52.41 [5648]~E(x56482,x56483)+P1(f332(f332(f232(f853(x56481,a839)),x56482),x56483))
% 52.62/52.41 [5649]~E(x56492,x56493)+P1(f332(f332(f232(f853(x56491,a839)),x56492),x56493))
% 52.62/52.41 [5650]~E(x56502,x56503)+P1(f332(f332(f232(f853(x56501,a839)),x56502),x56503))
% 52.62/52.41 [5655]~P69(x56551)+E(f332(f332(f82(x56551),f332(f81(x56551),x56552)),f332(f81(x56551),x56553)),f332(f81(x56551),f332(f332(f82(x56551),x56553),x56552)))
% 52.62/52.41 [5656]~P8(x56561)+E(f332(f332(f82(x56561),f332(f81(x56561),x56562)),f332(f81(x56561),x56563)),f332(f81(x56561),f332(f332(f82(x56561),x56562),x56563)))
% 52.62/52.41 [5657]~P68(x56571)+E(f332(f332(f179(x56571),f332(f81(x56571),x56572)),f332(f81(x56571),x56573)),f332(f81(x56571),f332(f332(f236(x56571),x56572),x56573)))
% 52.62/52.41 [5658]~P68(x56581)+E(f332(f332(f236(x56581),f332(f81(x56581),x56582)),f332(f81(x56581),x56583)),f332(f81(x56581),f332(f332(f179(x56581),x56582),x56583)))
% 52.62/52.41 [5659]~P90(x56591)+E(f332(f332(f104(x56591),f332(f81(x56591),x56592)),f332(f81(x56591),x56593)),f332(f81(x56591),f332(f332(f103(x56591),x56592),x56593)))
% 52.62/52.41 [5660]~P90(x56601)+E(f332(f332(f103(x56601),f332(f81(x56601),x56602)),f332(f81(x56601),x56603)),f332(f81(x56601),f332(f332(f104(x56601),x56602),x56603)))
% 52.62/52.41 [5661]~P110(x56611)+E(f332(f332(f83(x56611),f332(f77(x56611),x56612)),f332(f77(x56611),x56613)),f332(f77(x56611),f332(f332(f83(x56611),x56612),x56613)))
% 52.62/52.41 [5662]~P64(x56621)+E(f332(f332(f283(x56621),f332(f77(x56621),x56622)),f332(f77(x56621),x56623)),f332(f77(x56621),f332(f332(f283(x56621),x56622),x56623)))
% 52.62/52.41 [5663]~P3(x56631)+E(f332(f332(f82(x56631),f332(f154(x56631),x56632)),f332(f154(x56631),x56633)),f332(f154(x56631),f332(f332(f125(x56631),x56632),x56633)))
% 52.62/52.41 [5664]E(x56641,f180(f853(x56642,a839)))+~E(f332(f332(f103(f853(x56642,a839)),x56643),x56641),f180(f853(x56642,a839)))
% 52.62/52.41 [5665]E(x56651,f180(f853(x56652,a839)))+~E(f332(f332(f103(f853(x56652,a839)),x56651),x56653),f180(f853(x56652,a839)))
% 52.62/52.41 [5666]~P141(x56661,x56662,x56663)+P1(f332(x56661,f332(f332(f44(a1),x56662),x56663)))
% 52.62/52.41 [5727]~P1(f332(f64(x57271),x57273))+P1(f332(f64(x57271),f332(f332(f302(x57271),x57272),x57273)))
% 52.62/52.41 [5728]~P1(f332(f64(x57281),x57283))+P1(f332(f64(x57281),f332(f332(f302(x57281),x57282),x57283)))
% 52.62/52.41 [5729]~P1(f332(f127(x57291),x57293))+P1(f332(f127(x57291),f332(f332(f159(x57291),x57292),x57293)))
% 52.62/52.41 [5730]~P1(f332(f127(x57301),x57303))+P1(f332(f127(x57301),f332(f332(f128(x57301),x57302),x57303)))
% 52.62/52.41 [5761]~P100(x57611)+P1(f332(f332(f232(x57611),x57612),f332(f332(f179(x57611),x57613),x57612)))
% 52.62/52.41 [5762]~P100(x57621)+P1(f332(f332(f232(x57621),x57622),f332(f332(f179(x57621),x57622),x57623)))
% 52.62/52.41 [5763]~P92(x57631)+P1(f332(f332(f232(x57631),x57632),f332(f332(f103(x57631),x57633),x57632)))
% 52.62/52.41 [5764]~P93(x57641)+P1(f332(f332(f232(x57641),x57642),f332(f332(f103(x57641),x57643),x57642)))
% 52.62/52.41 [5765]~P92(x57651)+P1(f332(f332(f232(x57651),x57652),f332(f332(f103(x57651),x57652),x57653)))
% 52.62/52.41 [5766]~P93(x57661)+P1(f332(f332(f232(x57661),x57662),f332(f332(f103(x57661),x57662),x57663)))
% 52.62/52.41 [5767]~P73(x57671)+P1(f332(f332(f279(x57671),x57672),f332(f332(f83(x57671),x57673),x57672)))
% 52.62/52.41 [5768]~P73(x57681)+P1(f332(f332(f279(x57681),x57682),f332(f332(f83(x57681),x57682),x57683)))
% 52.62/52.41 [5781]~E(x57811,f2(a845))+E(f332(f332(f44(a845),f332(f332(f83(a845),x57811),x57812)),f332(f332(f83(a845),x57811),x57813)),f2(a845))
% 52.62/52.41 [5844]P1(f332(x58441,x58442))+P1(f332(f332(f187(f35(x58441,x58443)),x58442),x58442))
% 52.62/52.41 [5845]P1(f332(x58451,x58452))+P1(f332(f332(f187(f35(x58451,x58453)),x58452),x58452))
% 52.62/52.41 [5857]~P88(x58571)+E(f332(f332(f3(x58571),f332(f106(x58571),x58572)),f332(f106(x58571),x58573)),f332(f106(x58571),f332(f332(f82(a1),x58572),f332(f81(a1),x58573))))
% 52.62/52.41 [5913]E(x59131,f2(a845))+E(f332(f332(f44(a845),f332(f332(f83(a845),x59131),x59132)),f332(f332(f83(a845),x59131),x59133)),f332(f332(f44(a845),x59132),x59133))
% 52.62/52.41 [5983]P141(x59831,x59832,x59833)+~P1(f332(x59831,f332(f332(f44(a1),x59832),x59833)))
% 52.62/52.41 [6060]E(x60601,f115(x60602))+E(f332(f332(f140(x60602),f332(f131(x60602),x60601)),f332(f332(f159(x60602),x60603),f332(f157(x60602),x60601))),f332(f332(f159(x60602),f332(a114,x60603)),x60601))
% 52.62/52.41 [6068]E(f332(f332(f3(f853(x60681,a839)),x60682),x60683),x60682)+~E(f332(f332(f104(f853(x60681,a839)),x60682),x60683),f180(f853(x60681,a839)))
% 52.62/52.41 [6113]~P1(f332(f332(f233(a845),x61131),x61133))+P1(f332(f332(f233(a845),x61131),f332(f332(f82(a845),x61132),x61133)))
% 52.62/52.41 [6114]~P1(f332(f332(f233(a845),x61141),x61143))+P1(f332(f332(f233(a845),x61141),f332(f332(f82(a845),x61142),x61143)))
% 52.62/52.41 [6115]~P1(f332(f332(f233(a845),x61151),x61152))+P1(f332(f332(f233(a845),x61151),f332(f332(f82(a845),x61152),x61153)))
% 52.62/52.41 [6116]~P1(f332(f332(f233(a845),x61161),x61162))+P1(f332(f332(f233(a845),x61161),f332(f332(f82(a845),x61162),x61163)))
% 52.62/52.41 [6117]~P1(f332(f332(f232(a845),x61171),x61173))+P1(f332(f332(f232(a845),x61171),f332(f332(f82(a845),x61172),x61173)))
% 52.62/52.41 [6118]~P1(f332(f332(f232(a845),x61181),x61183))+P1(f332(f332(f232(a845),x61181),f332(f332(f82(a845),x61182),x61183)))
% 52.62/52.41 [6119]~P1(f332(f332(f232(a845),x61191),x61192))+P1(f332(f332(f232(a845),x61191),f332(f332(f82(a845),x61192),x61193)))
% 52.62/52.41 [6120]~P1(f332(f332(f232(a845),x61201),x61202))+P1(f332(f332(f232(a845),x61201),f332(f332(f82(a845),x61202),x61203)))
% 52.62/52.41 [6159]P1(f332(f64(x61591),x61592))+~P1(f332(f64(x61591),f332(f332(f302(x61591),x61593),x61592)))
% 52.62/52.41 [6160]P1(f332(f127(x61601),x61602))+~P1(f332(f127(x61601),f332(f332(f140(x61601),x61603),x61602)))
% 52.62/52.41 [6161]P1(f332(f127(x61611),x61612))+~P1(f332(f127(x61611),f332(f332(f125(x61611),x61613),x61612)))
% 52.62/52.41 [6162]P1(f332(f127(x61621),x61622))+~P1(f332(f127(x61621),f332(f332(f125(x61621),x61622),x61623)))
% 52.62/52.41 [6207]~E(f53(a1,x62072,x62071),f53(a1,x62073,x62071))+P1(f332(f332(f279(a1),x62071),f332(f332(f3(a1),x62072),x62073)))
% 52.62/52.41 [6212]~P73(x62121)+E(f332(f332(f82(x62121),x62122),f332(f332(f83(x62121),x62123),x62122)),f332(f332(f83(x62121),f332(f332(f82(x62121),x62123),f80(x62121))),x62122))
% 52.62/52.41 [6261]~E(x62611,x62612)+~P1(f332(f332(f233(f853(x62613,a839)),x62611),x62612))
% 52.62/52.41 [6308]P1(f332(f332(f334(x63081),x63082),x63083))+P1(f332(f332(f334(x63081),x63082),f332(f81(f853(x63081,a839)),x63083)))
% 52.62/52.41 [6309]P1(f332(f332(f334(x63091),x63092),x63093))+P1(f332(f332(f334(x63091),x63092),f332(f81(f853(x63091,a839)),x63093)))
% 52.62/52.41 [6316]E(f134(x63161,f332(f332(f128(x63161),x63162),x63163)),f134(x63161,x63163))+~P1(f332(f332(f233(a845),x63162),f332(f181(f846(x63161)),x63163)))
% 52.62/52.41 [6317]E(f332(f332(f159(x63171),x63172),f116(x63171,x63173)),f332(f332(f159(x63171),x63172),x63173))+~P1(f332(f332(f233(a845),x63172),f332(f181(f846(x63171)),x63173)))
% 52.62/52.41 [6376]E(f332(f332(f332(f173(f846(x63761),f846(x63761)),x63762),f141(x63761)),x63763),x63763)+~E(f53(a845,x63762,f332(f181(f846(x63761)),x63763)),f2(a845))
% 52.62/52.41 [6385]~P14(x63851,x63853,x63852)+E(f332(f332(f281(x63851,x63851,x63851),f332(f278(x63851,x63851),x63852)),x63852),x63852)
% 52.62/52.41 [6428]~E(f332(f332(f103(f853(x64281,a839)),x64282),x64283),x64283)+P1(f332(f332(f232(f853(x64281,a839)),x64282),x64283))
% 52.62/52.41 [6433]~P55(x64331,x64331,x64333)+P55(x64331,x64331,f332(f332(f173(f852(x64331,x64331),a839),x64332),x64333))
% 52.62/52.41 [6435]~P1(f332(f332(f334(x64351),x64353),f332(f158(x64351),x64352)))+P1(f332(f332(f233(a845),f2(a845)),f332(f181(f846(x64351)),x64352)))
% 52.62/52.41 [6452]~E(x64522,x64523)+P1(f332(f332(f334(x64521),x64522),f332(f332(f302(x64521),x64523),f180(f853(x64521,a839)))))
% 52.62/52.41 [6465]~P80(x64651)+E(f332(f77(x64651),f332(f332(f82(x64651),f332(f77(x64651),x64652)),f332(f77(x64651),x64653))),f332(f332(f82(x64651),f332(f77(x64651),x64652)),f332(f77(x64651),x64653)))
% 52.62/52.41 [6477]E(f332(f332(f44(a845),f332(f332(f83(a845),x64771),x64772)),f332(f332(f83(a845),x64771),x64773)),f332(f332(f44(a845),x64772),x64773))+~P1(f332(f332(f233(a845),f2(a845)),x64771))
% 52.62/52.41 [6504]E(f53(a1,x65041,x65042),f53(a1,x65043,x65042))+~P1(f332(f332(f279(a1),x65042),f332(f332(f3(a1),x65041),x65043)))
% 52.62/52.41 [6617]~P1(f332(f64(x66171),x66173))+E(f332(f332(f67(x66171,f853(x66171,a839),f302(x66171)),x66172),x66173),f332(f332(f103(f853(x66171,a839)),x66173),x66172))
% 52.62/52.41 [6680]E(f332(f332(f103(f853(x66801,a839)),x66802),x66803),x66802)+~P1(f332(f332(f232(f853(x66801,a839)),x66803),x66802))
% 52.62/52.41 [6681]E(f332(f332(f103(f853(x66811,a839)),x66812),x66813),x66813)+~P1(f332(f332(f232(f853(x66811,a839)),x66812),x66813))
% 52.62/52.41 [6682]E(f332(f332(f103(f853(x66821,a839)),x66822),x66823),x66823)+~P1(f332(f332(f232(f853(x66821,a839)),x66822),x66823))
% 52.62/52.41 [6683]E(f332(f332(f104(f853(x66831,a839)),x66832),x66833),x66833)+~P1(f332(f332(f232(f853(x66831,a839)),x66833),x66832))
% 52.62/52.41 [6684]E(f332(f332(f104(f853(x66841,a839)),x66842),x66843),x66842)+~P1(f332(f332(f232(f853(x66841,a839)),x66842),x66843))
% 52.62/52.41 [6737]~P1(f332(f127(x67371),x67372))+E(f332(f332(f3(f853(x67371,a839)),f332(f158(x67371),x67372)),f332(f332(f302(x67371),x67373),f180(f853(x67371,a839)))),f332(f158(x67371),f151(x67371,x67373,x67372)))
% 52.62/52.41 [6795]P38(x67951,x67952)+~P38(x67951,f332(f332(f173(f852(x67951,x67951),a839),x67953),x67952))
% 52.62/52.41 [6811]~E(x68111,f2(a845))+P1(f332(f332(f279(a845),f332(f332(f83(a845),x68111),x68112)),f332(f332(f83(a845),x68111),x68113)))
% 52.62/52.41 [6865]P1(f332(f57(x68651,x68652),f332(a59,x68653)))+~P1(f332(f57(f332(f81(a1),x68651),f332(f81(a1),x68652)),x68653))
% 52.62/52.41 [6870]E(f332(f332(f3(f853(x68701,a839)),f332(f332(f302(x68701),x68702),x68703)),f332(f332(f302(x68701),x68702),f180(f853(x68701,a839)))),x68703)+P1(f332(f332(f334(x68701),x68702),x68703))
% 52.62/52.41 [6889]E(f332(f332(f104(f853(x68891,a839)),f332(f158(x68891),x68892)),f332(f158(x68891),x68893)),f180(f853(x68891,a839)))+~P1(f332(f127(x68891),f332(f332(f125(x68891),x68892),x68893)))
% 52.62/52.41 [6906]~P1(f332(f332(f334(x69061),x69062),f332(f158(x69061),x69063)))+~P1(f332(f127(x69061),f332(f332(f140(x69061),x69062),x69063)))
% 52.62/52.41 [6983]E(f332(f332(f104(f853(x69831,a839)),x69832),x69833),f180(f853(x69831,a839)))+P1(f332(f332(f334(x69831),f493(x69833,x69832,x69831)),x69832))
% 52.62/52.41 [6984]E(f332(f332(f104(f853(x69841,a839)),x69842),x69843),f180(f853(x69841,a839)))+P1(f332(f332(f334(x69841),f498(x69843,x69842,x69841)),x69843))
% 52.62/52.41 [6988]E(f116(x69881,f332(f332(f159(x69881),x69882),x69883)),f332(f332(f159(x69881),f332(f332(f3(a845),x69882),f80(a845))),x69883))+~P1(f332(f332(f232(a845),x69882),f332(f181(f846(x69881)),x69883)))
% 52.62/52.41 [7070]P1(f332(f332(f233(a845),f2(a845)),x70701))+P1(f332(f332(f232(a845),f332(f332(f83(a845),x70702),x70701)),f332(f332(f83(a845),x70703),x70701)))
% 52.62/52.41 [7071]P1(f332(f332(f233(a845),f2(a845)),x70711))+P1(f332(f332(f232(a845),f332(f332(f83(a845),x70711),x70712)),f332(f332(f83(a845),x70711),x70713)))
% 52.62/52.41 [7072]~P1(f332(f332(f334(x70721),x70722),x70723))+~P1(f332(f332(f334(x70721),x70722),f332(f81(f853(x70721,a839)),x70723)))
% 52.62/52.41 [7073]~P1(f332(f332(f334(x70731),x70732),x70733))+~P1(f332(f332(f334(x70731),x70732),f332(f81(f853(x70731,a839)),x70733)))
% 52.62/52.41 [7074]~P1(f332(f332(f334(x70741),x70742),x70743))+~P1(f332(f332(f334(x70741),x70742),f332(f81(f853(x70741,a839)),x70743)))
% 52.62/52.41 [7078]~P1(f332(f332(f233(f853(x70781,a839)),x70782),x70783))+P1(f332(f332(f232(f853(x70781,a839)),x70782),x70783))
% 52.62/52.41 [7079]~P1(f332(f332(f233(f853(x70791,a839)),x70792),x70793))+P1(f332(f332(f232(f853(x70791,a839)),x70792),x70793))
% 52.62/52.41 [7080]~P1(f332(f332(f233(f853(x70801,a839)),x70802),x70803))+P1(f332(f332(f232(f853(x70801,a839)),x70802),x70803))
% 52.62/52.41 [7185]~P1(f332(f332(f233(a845),x71852),x71853))+P1(f332(f332(f233(a845),f332(f332(f82(a845),x71851),x71852)),f332(f332(f82(a845),x71851),x71853)))
% 52.62/52.41 [7186]~P1(f332(f332(f233(a845),x71861),x71863))+P1(f332(f332(f233(a845),f332(f332(f82(a845),x71861),x71862)),f332(f332(f82(a845),x71863),x71862)))
% 52.62/52.41 [7187]~P1(f332(f332(f233(a1),x71871),x71873))+P1(f332(f332(f233(a1),f332(f332(f82(a1),x71871),x71872)),f332(f332(f82(a1),x71873),x71872)))
% 52.62/52.41 [7190]~P1(f332(f332(f232(a845),x71902),x71903))+P1(f332(f332(f232(a845),f332(f332(f82(a845),x71901),x71902)),f332(f332(f82(a845),x71901),x71903)))
% 52.62/52.41 [7191]~P1(f332(f332(f232(a845),x71911),x71913))+P1(f332(f332(f232(a845),f332(f332(f82(a845),x71911),x71912)),f332(f332(f82(a845),x71913),x71912)))
% 52.62/52.41 [7192]~P1(f332(f332(f232(a845),x71922),x71923))+P1(f332(f332(f232(a845),f332(f332(f83(a845),x71921),x71922)),f332(f332(f83(a845),x71921),x71923)))
% 52.62/52.41 [7193]~P1(f332(f332(f232(a845),x71932),x71933))+P1(f332(f332(f232(a845),f332(f332(f83(a845),x71931),x71932)),f332(f332(f83(a845),x71931),x71933)))
% 52.62/52.41 [7194]~P1(f332(f332(f232(a845),x71941),x71943))+P1(f332(f332(f232(a845),f332(f332(f83(a845),x71941),x71942)),f332(f332(f83(a845),x71943),x71942)))
% 52.62/52.41 [7195]~P1(f332(f332(f232(a845),x71951),x71953))+P1(f332(f332(f232(a845),f332(f332(f83(a845),x71951),x71952)),f332(f332(f83(a845),x71953),x71952)))
% 52.62/52.41 [7196]~P1(f332(f332(f232(a845),x71961),x71963))+P1(f332(f332(f232(a845),f332(f332(f44(a845),x71961),x71962)),f332(f332(f44(a845),x71963),x71962)))
% 52.62/52.41 [7197]~P1(f332(f332(f232(a845),x71973),x71972))+P1(f332(f332(f232(a845),f332(f332(f3(a845),x71971),x71972)),f332(f332(f3(a845),x71971),x71973)))
% 52.62/52.41 [7198]~P1(f332(f332(f232(a845),x71981),x71983))+P1(f332(f332(f232(a845),f332(f332(f3(a845),x71981),x71982)),f332(f332(f3(a845),x71983),x71982)))
% 52.62/52.41 [7199]~P1(f332(f332(f232(a1),x71992),x71993))+P1(f332(f332(f232(a1),f332(f332(f82(a1),x71991),x71992)),f332(f332(f82(a1),x71991),x71993)))
% 52.62/52.41 [7202]~P1(f332(f332(f279(a845),x72022),x72023))+P1(f332(f332(f279(a845),f332(f332(f83(a845),x72021),x72022)),f332(f332(f83(a845),x72021),x72023)))
% 52.62/52.41 [7289]E(x72891,x72892)+~P1(f332(f332(f334(x72893),x72891),f332(f332(f302(x72893),x72892),f180(f853(x72893,a839)))))
% 52.62/52.41 [7290]E(x72901,x72902)+~P1(f332(f332(f334(x72903),x72901),f332(f332(f302(x72903),x72902),f180(f853(x72903,a839)))))
% 52.62/52.41 [7292]~E(f332(f332(f104(f853(x72921,a839)),x72922),x72923),f180(f853(x72921,a839)))+P1(f332(f332(f232(f853(x72921,a839)),x72922),f332(f81(f853(x72921,a839)),x72923)))
% 52.62/52.41 [7298]P1(f332(f332(f334(f853(x72981,a839)),x72982),f332(f301(x72981),x72983)))+~P1(f332(f332(f232(f853(x72981,a839)),x72982),x72983))
% 52.62/52.41 [7299]P1(f332(f332(f334(f853(x72991,a839)),x72992),f332(f301(x72991),x72993)))+~P1(f332(f332(f232(f853(x72991,a839)),x72992),x72993))
% 52.62/52.41 [7356]E(f332(f332(f140(x73561),f332(f332(f152(x73561),x73562),x73563)),f332(f332(f128(x73561),f332(a114,x73563)),x73562)),f332(f332(f128(x73561),x73563),x73562))+~P1(f332(f332(f233(a845),x73563),f332(f181(f846(x73561)),x73562)))
% 52.62/52.41 [7386]P1(f332(f332(f334(f852(x73861,x73861)),x73862),f300(x73861,x73863)))+~P1(f332(f332(f334(f852(x73861,x73861)),x73862),x73863))
% 52.62/52.41 [7395]~P1(f332(f332(f334(f853(x73951,a839)),x73952),f332(f301(x73951),x73953)))+P1(f332(f332(f232(f853(x73951,a839)),x73952),x73953))
% 52.62/52.41 [7396]~P1(f332(f332(f334(f853(x73961,a839)),x73962),f332(f301(x73961),x73963)))+P1(f332(f332(f232(f853(x73961,a839)),x73962),x73963))
% 52.62/52.41 [7438]P1(f332(f332(f232(f853(x74381,a839)),x74382),f45(f853(x74381,a839),x74383)))+~P1(f332(f332(f334(f853(x74381,a839)),x74382),x74383))
% 52.62/52.41 [7466]~P133(x74661)+E(f332(f332(f83(x74661),f332(f332(f242(x74661),f332(f81(x74661),f80(x74661))),x74662)),f332(f332(f242(x74661),x74663),x74662)),f332(f332(f242(x74661),f332(f81(x74661),x74663)),x74662))
% 52.62/52.41 [7488]E(f332(f332(f152(x74881),x74882),f332(f332(f3(a845),f332(f181(f846(x74881)),x74882)),f332(a114,x74883))),f332(f332(f152(x74881),f332(f142(x74881),x74882)),x74883))+~P1(f332(f332(f233(a845),x74883),f332(f181(f846(x74881)),x74882)))
% 52.62/52.41 [7505]~E(f332(f332(f104(f853(x75051,a839)),f650(x75053,x75052,x75051)),x75053),f180(f853(x75051,a839)))+E(f332(f332(f104(f853(x75051,a839)),f45(f853(x75051,a839),x75052)),x75053),f180(f853(x75051,a839)))
% 52.62/52.41 [7569]~P1(f332(f332(f334(x75693),x75692),f332(f158(x75693),x75691)))+P1(f332(f332(f233(a845),f729(x75691,x75692,x75693)),f332(f181(f846(x75693)),x75691)))
% 52.62/52.41 [7577]P1(f332(f332(f334(x75771),f332(f332(f152(x75771),x75772),x75773)),f332(f158(x75771),x75772)))+~P1(f332(f332(f233(a845),x75773),f332(f181(f846(x75771)),x75772)))
% 52.62/52.41 [7686]P1(f332(f332(f232(f853(f846(x76861),a839)),f149(x76861,x76862)),f149(x76861,x76863)))+~P1(f332(f332(f232(f853(x76861,a839)),x76862),x76863))
% 52.62/52.41 [7715]E(f332(f332(f104(f853(x77151,a839)),f45(f853(x77151,a839),x77152)),x77153),f180(f853(x77151,a839)))+P1(f332(f332(f334(f853(x77151,a839)),f650(x77153,x77152,x77151)),x77152))
% 52.62/52.41 [7717]~P1(f332(f332(f334(f853(x77171,a839)),x77173),x77172))+P1(f332(f332(f232(f853(x77171,a839)),f46(f853(x77171,a839),x77172)),x77173))
% 52.62/52.41 [7719]E(f332(f332(f104(f853(x77191,a839)),x77192),x77193),f180(f853(x77191,a839)))+~P1(f332(f332(f232(f853(x77191,a839)),x77192),f332(f81(f853(x77191,a839)),x77193)))
% 52.62/52.41 [7772]E(f332(f332(f3(a845),f332(f332(f82(a845),f332(f154(a845),x77721)),x77722)),f332(f332(f152(a845),x77721),x77723)),f332(f154(a845),f332(f332(f148(a845,x77721),x77723),x77722)))+~P1(f332(f332(f233(a845),x77723),f332(f181(f846(a845)),x77721)))
% 52.62/52.41 [7822]P1(f332(f332(f233(a845),x78221),x78222))+~P1(f332(f332(f233(a845),f332(f332(f82(a845),x78223),x78221)),f332(f332(f82(a845),x78223),x78222)))
% 52.62/52.41 [7823]P1(f332(f332(f233(a845),x78231),x78232))+~P1(f332(f332(f233(a845),f332(f332(f83(a845),x78233),x78231)),f332(f332(f83(a845),x78233),x78232)))
% 52.62/52.41 [7824]P1(f332(f332(f233(a845),x78241),x78242))+~P1(f332(f332(f233(a845),f332(f332(f83(a845),x78241),x78243)),f332(f332(f83(a845),x78242),x78243)))
% 52.62/52.41 [7827]P1(f332(f332(f232(a845),x78271),x78272))+~P1(f332(f332(f232(a845),f332(f332(f82(a845),x78273),x78271)),f332(f332(f82(a845),x78273),x78272)))
% 52.62/52.41 [7856]P1(f332(f332(f233(a845),f2(a845)),x78561))+~P1(f332(f332(f233(a845),f332(f332(f83(a845),x78562),x78561)),f332(f332(f83(a845),x78563),x78561)))
% 52.62/52.41 [7857]P1(f332(f332(f233(a845),f2(a845)),x78571))+~P1(f332(f332(f233(a845),f332(f332(f83(a845),x78571),x78572)),f332(f332(f83(a845),x78571),x78573)))
% 52.62/52.41 [7930]E(f244(x79301,x79302,x79303),x79302)+~P1(f332(f332(f232(f853(x79301,a839)),x79303),f332(f332(f302(x79301),x79302),f180(f853(x79301,a839)))))
% 52.62/52.41 [8009]E(f332(f332(f125(x80091),f332(f332(f159(x80091),x80092),x80093)),f332(f332(f140(x80091),f332(f332(f152(x80091),x80093),x80092)),f115(x80091))),f332(f332(f159(x80091),f332(a114,x80092)),x80093))+~P1(f332(f332(f233(a845),x80092),f332(f181(f846(x80091)),x80093)))
% 52.62/52.41 [8078]P1(f332(f332(f232(f853(f853(x80781,a839),a839)),f245(x80781,x80782)),f245(x80781,x80783)))+~P1(f332(f332(f232(f853(x80781,a839)),x80782),x80783))
% 52.62/52.41 [8117]~P1(f332(f127(x81171),x81173))+P1(f332(f127(x81171),f332(f332(f332(f173(f846(x81171),f846(x81171)),x81172),f141(x81171)),x81173)))
% 52.62/52.41 [8122]~P1(f332(f332(f233(a845),x81222),x81223))+P1(f332(f332(f233(a845),f332(f332(f83(a845),f332(a114,x81221)),x81222)),f332(f332(f83(a845),f332(a114,x81221)),x81223)))
% 52.62/52.41 [8123]~P1(f332(f332(f232(a845),x81232),x81233))+P1(f332(f332(f232(a845),f332(f332(f83(a845),f332(a114,x81231)),x81232)),f332(f332(f83(a845),f332(a114,x81231)),x81233)))
% 52.62/52.41 [8145]P1(f332(f332(f232(f853(f853(x81451,a839),a839)),f332(f301(x81451),x81452)),f332(f301(x81451),x81453)))+~P1(f332(f332(f232(f853(x81451,a839)),x81452),x81453))
% 52.62/52.41 [8301]~P1(f332(f332(f232(f853(x83011,a839)),x83013),x83012))+P1(f332(f332(f232(f853(x83011,a839)),f332(f81(f853(x83011,a839)),x83012)),f332(f81(f853(x83011,a839)),x83013)))
% 52.62/52.41 [8302]~P1(f332(f332(f232(f853(x83021,a839)),x83023),x83022))+P1(f332(f332(f232(f853(x83021,a839)),f332(f81(f853(x83021,a839)),x83022)),f332(f81(f853(x83021,a839)),x83023)))
% 52.62/52.41 [8341]E(f332(f303(a845,a845,f332(f332(f9(a845,a845,a845),f3(a845)),x83411)),f332(f294(a845,x83412),x83413)),f332(f294(a845,f332(f332(f3(a845),x83412),x83411)),f332(f332(f3(a845),x83413),x83411)))+~P1(f332(f332(f233(a845),x83411),x83413))
% 52.62/52.41 [8367]~P3(x83671)+E(f332(f332(f82(x83671),x83672),f332(f132(x83671,x83671,f82(x83671),f2(x83671)),x83673)),f332(f132(x83671,x83671,f82(x83671),x83672),x83673))
% 52.62/52.41 [8448]~P80(x84481)+P1(f332(f332(f232(x84481),f332(f77(x84481),f332(f332(f82(x84481),x84482),x84483))),f332(f332(f82(x84481),f332(f77(x84481),x84482)),f332(f77(x84481),x84483))))
% 52.62/52.41 [8449]~P80(x84491)+P1(f332(f332(f232(x84491),f332(f77(x84491),f332(f332(f3(x84491),x84492),x84493))),f332(f332(f82(x84491),f332(f77(x84491),x84492)),f332(f77(x84491),x84493))))
% 52.62/52.41 [8459]E(f332(f332(f82(a1),f332(f332(f83(a1),x84591),f53(a1,f332(f332(f44(a1),x84592),x84591),x84593))),f53(a1,x84592,x84591)),f53(a1,x84592,f332(f332(f83(a1),x84591),x84593)))+~P1(f332(f332(f233(a1),f2(a1)),x84593))
% 52.62/52.41 [8468]E(f332(f332(f125(x84681),f332(f332(f159(x84681),x84682),x84683)),f332(f332(f140(x84681),f332(f131(x84681),f332(f332(f128(x84681),x84682),x84683))),f115(x84681))),f332(f332(f159(x84681),f332(a114,x84682)),x84683))+~P1(f332(f332(f233(a845),x84682),f332(f181(f846(x84681)),x84683)))
% 52.62/52.41 [8487]E(f332(f265(x84871,f332(f332(f143(x84871,f852(a101,x84871)),f332(f241(a101,x84871),f80(a101))),x84872)),f332(a5,x84873)),f332(f332(f152(x84871),x84872),x84873))+~P1(f332(f332(f233(a845),x84873),f332(f181(f846(x84871)),x84872)))
% 52.62/52.41 [8544]P1(f332(f332(f334(f852(x85441,x85441)),x85442),f332(f332(f281(x85441,x85441,x85441),x85443),f300(x85441,x85443))))+~P1(f332(f332(f334(f852(x85441,x85441)),x85442),x85443))
% 52.62/52.41 [8560]P1(f332(f332(f233(a845),x85601),x85602))+~P1(f332(f332(f233(a845),f332(f332(f83(a845),f332(a114,x85603)),x85601)),f332(f332(f83(a845),f332(a114,x85603)),x85602)))
% 52.62/52.41 [8561]P1(f332(f332(f232(a845),x85611),x85612))+~P1(f332(f332(f232(a845),f332(f332(f83(a845),f332(a114,x85613)),x85611)),f332(f332(f83(a845),f332(a114,x85613)),x85612)))
% 52.62/52.41 [8572]P1(f332(f332(f232(f853(x85721,a839)),x85722),x85723))+~P1(f332(f332(f232(f853(x85721,a839)),f332(f81(f853(x85721,a839)),x85723)),f332(f81(f853(x85721,a839)),x85722)))
% 52.62/52.41 [8590]P1(f332(f127(x85901),x85902))+~P1(f332(f127(x85901),f332(f332(f332(f173(f846(x85901),f846(x85901)),x85903),f141(x85901)),x85902)))
% 52.62/52.41 [8656]E(f332(f277(x86561,x86561,f300(x86561,x86562)),x86563),x86563)+~P1(f332(f332(f232(f853(x86561,a839)),f332(f277(x86561,x86561,x86562),x86563)),x86563))
% 52.62/52.41 [8658]E(f332(f303(f852(x86581,x86582),x86582,f250(x86581,x86582)),f332(f158(f852(x86581,x86582)),x86583)),f171(x86581,x86582,f166(x86581,x86582,x86583)))+~P1(f332(f127(x86581),f332(f332(f143(f852(x86581,x86582),x86581),f240(x86581,x86582)),x86583)))
% 52.62/52.41 [8697]~P100(x86971)+P20(x86971,f332(f126(x86971,f332(f332(f9(x86971,x86971,a839),a329),f332(x86972,x86973))),x86973))
% 52.62/52.41 [8702]~P1(f332(f332(f232(a845),x87021),x87022))+P1(f332(f332(f232(a845),x87021),f332(f132(a845,a845,f82(a845),x87022),x87023)))
% 52.62/52.41 [8773]~P1(f332(f332(f334(f852(x87731,x87731)),x87732),f300(x87731,x87733)))+P1(f332(f332(f334(f852(x87731,x87731)),x87732),f332(f332(f173(f852(x87731,x87731),a839),f630(x87733,x87732,x87731)),x87733)))
% 52.62/52.41 [8842]~P3(x88421)+E(f332(f332(f82(x88421),x88422),f332(f132(x88421,x88421,f332(f9(x88421,x88421,x88421),f82(x88421)),f2(x88421)),f332(f142(x88421),x88423))),f332(f132(x88421,x88421,f82(x88421),x88422),x88423))
% 52.62/52.41 [9101]P55(x91011,x91012,x91013)+P1(f332(f332(f334(f852(x91011,x91012)),f332(f332(f241(x91011,x91012),f646(x91013,x91012,x91011)),f640(x91013,x91012,x91011))),x91013))
% 52.62/52.41 [9102]P55(x91021,x91022,x91023)+P1(f332(f332(f334(f852(x91021,x91022)),f332(f332(f241(x91021,x91022),f646(x91023,x91022,x91021)),f639(x91023,x91022,x91021))),x91023))
% 52.62/52.41 [9157]~P1(f332(f332(f334(f852(x91571,x91571)),x91572),f332(f332(f281(x91571,x91571,x91571),x91573),f300(x91571,x91573))))+P1(f332(f332(f334(f852(x91571,x91571)),x91572),f332(f332(f173(f852(x91571,x91571),a839),f635(x91573,x91572,x91571)),x91573)))
% 52.62/52.41 [9158]~P1(f332(x91581,f332(f332(f152(x91582),x91583),f332(f181(f846(x91582)),f162(x91582,x91581,x91583)))))+~P1(f332(f332(f233(a845),f332(f181(f846(x91582)),f162(x91582,x91581,x91583))),f332(f181(f846(x91582)),x91583)))
% 52.62/52.41 [9234]~P1(f332(f332(f232(f853(x92341,a839)),x92342),x92343))+P1(f332(f332(f232(f853(x92341,a839)),f332(f332(f9(x92341,f853(x92341,a839),a839),f334(x92341)),x92342)),f332(f332(f9(x92341,f853(x92341,a839),a839),f334(x92341)),x92343)))
% 52.62/52.41 [9290]~P1(f332(f332(f334(f852(f853(x92901,a839),f853(x92901,a839))),f332(f332(f241(f853(x92901,a839),f853(x92901,a839)),x92902),x92903)),f299(x92901)))+P1(f332(f332(f233(f853(x92901,a839)),x92902),x92903))
% 52.62/52.41 [9316]P56(x93161,x93162,x93163)+~P1(f332(f332(f334(f852(x93161,x93161)),f332(f332(f241(x93161,x93161),f638(x93163,x93162,x93161)),f637(x93163,x93162,x93161))),x93163))
% 52.62/52.41 [9317]P56(x93171,x93172,x93173)+~P1(f332(f332(f334(f852(x93171,x93171)),f332(f332(f241(x93171,x93171),f637(x93173,x93172,x93171)),f638(x93173,x93172,x93171))),x93173))
% 52.62/52.41 [9351]~P1(f332(f332(f334(f852(f846(x93511),f846(x93511))),f332(f332(f241(f846(x93511),f846(x93511)),x93512),x93512)),f137(x93511,x93513)))+P1(f332(f332(f334(f852(x93511,x93511)),f332(f332(f241(x93511,x93511),f754(x93512,x93513,x93511)),f754(x93512,x93513,x93511))),x93513))
% 52.62/52.41 [9396]P1(f332(f332(f232(f853(x93961,a839)),x93962),x93963))+~P1(f332(f332(f232(f853(x93961,a839)),f332(f332(f9(x93961,f853(x93961,a839),a839),f334(x93961)),x93962)),f332(f332(f9(x93961,f853(x93961,a839),a839),f334(x93961)),x93963)))
% 52.62/52.41 [9482]E(f332(f332(f3(a845),f332(f332(f8(a845,a845),x94821),f332(f257(a845),x94822))),f332(f332(f8(a845,a845),x94823),f332(f257(a845),x94822))),f332(f332(f8(a845,a845),f332(f332(f20(a845,a845,a845),f332(f332(f10(a845,f853(a845,a845),a845),f3(a845)),x94821)),x94823)),f332(f257(a845),x94822)))+~P1(f332(f332(f232(a845),f332(x94823,f341(x94822,x94821,x94823))),f332(x94821,f341(x94822,x94821,x94823))))
% 52.62/52.41 [9765]E(f332(f256(f852(x97651,x97652)),f332(f251(x97651,x97652,a839),f332(f332(f9(x97651,f853(x97652,f849(x97652)),f853(x97652,a839)),f332(f332(f10(f853(f849(x97652),a839),f853(f853(x97652,f849(x97652)),f853(x97652,a839)),x97651),f10(f849(x97652),a839,x97652)),f332(f332(f10(f849(x97652),f853(f849(x97652),a839),x97651),a329),f166(x97651,x97652,x97653)))),f227(x97652)))),f332(f158(f852(x97651,x97652)),x97653))+~P1(f332(f127(x97651),f332(f332(f143(f852(x97651,x97652),x97651),f240(x97651,x97652)),x97653)))
% 52.62/52.41 [5509]~P69(x55091)+E(f332(f332(f82(x55091),f332(f332(f3(x55091),x55092),x55093)),x55093),x55092)
% 52.62/52.41 [5510]~P69(x55101)+E(f332(f332(f3(x55101),f332(f332(f82(x55101),x55102),x55103)),x55103),x55102)
% 52.62/52.41 [5736]~P69(x57361)+E(f332(f332(f82(x57361),x57362),f332(f332(f82(x57361),f332(f81(x57361),x57362)),x57363)),x57363)
% 52.62/52.41 [5819]~P76(x58191)+E(f332(f332(f83(x58191),f332(f332(f242(x58191),x58192),x58193)),x58192),f332(f332(f242(x58191),x58192),f332(a114,x58193)))
% 52.62/52.41 [5820]~P73(x58201)+E(f332(f332(f83(x58201),f332(f332(f242(x58201),x58202),x58203)),x58202),f332(f332(f242(x58201),x58202),f332(a114,x58203)))
% 52.62/52.41 [6036]~P110(x60361)+E(f332(f77(x60361),f332(f332(f242(x60361),f332(f81(x60361),x60362)),x60363)),f332(f77(x60361),f332(f332(f242(x60361),x60362),x60363)))
% 52.62/52.41 [6088]~P76(x60881)+E(f332(f332(f83(x60881),f332(f332(f242(x60881),x60882),x60883)),x60882),f332(f332(f83(x60881),x60882),f332(f332(f242(x60881),x60882),x60883)))
% 52.62/52.41 [6150]E(f332(f332(f3(a101),f332(f332(f82(a101),x61501),x61502)),x61503),f269(x61501,x61502,x61503))+~P1(f332(f332(f233(a101),x61502),x61503))
% 52.62/52.41 [6172]~E(f332(f332(f128(x61721),x61723),x61722),f115(x61721))+P1(f332(f332(f232(a845),f332(f181(f846(x61721)),x61722)),x61723))
% 52.62/52.41 [6314]E(f332(f332(f83(a845),f332(f106(a845),x63141)),f332(f332(f83(a845),f332(f106(a845),x63142)),x63143)),f2(a845))+~P1(f332(f332(f233(a1),x63141),a85))
% 52.62/52.41 [6330]~P62(x63301)+E(f332(f332(f242(x63301),f332(f332(f283(x63301),f80(x63301)),x63302)),x63303),f332(f332(f283(x63301),f80(x63301)),f332(f332(f242(x63301),x63302),x63303)))
% 52.62/52.41 [6414]E(f332(f332(f3(a845),f332(f332(f82(a845),x64141),x64142)),x64143),f332(f332(f82(a845),x64141),f332(f332(f3(a845),x64142),x64143)))+~P1(f332(f332(f232(a845),x64143),x64142))
% 52.62/52.41 [6415]E(f332(f332(f3(a845),f332(f332(f82(a845),x64151),x64152)),x64153),f332(f332(f3(a845),x64151),f332(f332(f3(a845),x64153),x64152)))+~P1(f332(f332(f232(a845),x64152),x64153))
% 52.62/52.41 [6416]E(f332(f332(f3(a845),f332(f332(f82(a845),x64161),x64162)),x64163),f332(f332(f82(a845),x64161),f332(f332(f3(a845),x64162),x64163)))+~P1(f332(f332(f232(a845),x64163),x64162))
% 52.62/52.41 [6456]~P100(x64561)+P1(f332(f332(f232(x64561),f332(f332(f236(x64561),x64562),x64563)),x64563))
% 52.62/52.41 [6457]~P100(x64571)+P1(f332(f332(f232(x64571),f332(f332(f236(x64571),x64572),x64573)),x64572))
% 52.62/52.41 [6458]~P93(x64581)+P1(f332(f332(f232(x64581),f332(f332(f104(x64581),x64582),x64583)),x64583))
% 52.62/52.41 [6459]~P98(x64591)+P1(f332(f332(f232(x64591),f332(f332(f104(x64591),x64592),x64593)),x64593))
% 52.62/52.41 [6460]~P93(x64601)+P1(f332(f332(f232(x64601),f332(f332(f104(x64601),x64602),x64603)),x64602))
% 52.62/52.41 [6461]~P98(x64611)+P1(f332(f332(f232(x64611),f332(f332(f104(x64611),x64612),x64613)),x64612))
% 52.62/52.41 [6476]E(f332(f332(f44(a1),f332(f332(f44(a1),x64761),x64762)),x64763),f332(f332(f44(a1),x64761),f332(f332(f83(a1),x64762),x64763)))+~P1(f332(f332(f233(a1),f2(a1)),x64763))
% 52.62/52.41 [6529]~P73(x65291)+E(f332(f332(f82(x65291),f332(f332(f83(x65291),x65292),x65293)),x65293),f332(f332(f83(x65291),f332(f332(f82(x65291),x65292),f80(x65291))),x65293))
% 52.62/52.41 [6530]~P88(x65301)+E(f332(f332(f83(x65301),f332(f81(x65301),f332(f106(x65301),x65302))),x65303),f332(f332(f83(x65301),f332(f106(x65301),f332(f81(a1),x65302))),x65303))
% 52.62/52.41 [6602]~P3(x66021)+E(f332(f154(x66021),f332(f332(f143(x66022,x66021),f332(f18(x66021,x66022),f2(x66021))),x66023)),f2(x66021))
% 52.62/52.41 [6621]E(f332(f332(f82(a845),f332(f106(a845),x66211)),f332(f332(f82(a845),f332(f106(a845),x66212)),x66213)),f332(f332(f82(a845),f332(f106(a845),x66212)),x66213))+~P1(f332(a186,f332(f106(a1),x66211)))
% 52.62/52.41 [6636]~P11(x66361)+E(f46(x66361,f332(f332(f302(x66361),x66362),f332(f332(f302(x66361),x66363),f180(f853(x66361,a839))))),f332(f332(f104(x66361),x66362),x66363))
% 52.62/52.41 [6637]~P11(x66371)+E(f45(x66371,f332(f332(f302(x66371),x66372),f332(f332(f302(x66371),x66373),f180(f853(x66371,a839))))),f332(f332(f103(x66371),x66372),x66373))
% 52.62/52.41 [6662]E(f332(f332(f159(x66621),x66622),x66623),x66623)+~P1(f332(f332(f232(a845),f332(f181(f846(x66621)),x66623)),x66622))
% 52.62/52.41 [6673]E(f332(f332(f128(x66731),x66732),x66733),f115(x66731))+~P1(f332(f332(f232(a845),f332(f181(f846(x66731)),x66733)),x66732))
% 52.62/52.41 [6674]E(f332(f332(f128(x66741),x66742),x66743),f115(x66741))+~P1(f332(f332(f232(a845),f332(f181(f846(x66741)),x66743)),x66742))
% 52.62/52.41 [6685]E(f332(f332(f3(a845),f332(f332(f82(a845),x66851),x66852)),x66853),f332(f332(f82(a845),f332(f332(f3(a845),x66851),x66853)),x66852))+~P1(f332(f332(f232(a845),x66853),x66851))
% 52.62/52.41 [6686]E(f332(f332(f3(a845),f332(f332(f82(a845),x66861),x66862)),x66863),f332(f332(f82(a845),f332(f332(f3(a845),x66861),x66863)),x66862))+~P1(f332(f332(f232(a845),x66863),x66861))
% 52.62/52.41 [6700]~P1(f332(f332(f233(a845),x67001),x67003))+P1(f332(f332(f233(a845),f332(f332(f3(a845),x67001),x67002)),x67003))
% 52.62/52.41 [6728]~P100(x67281)+E(f151(x67281,x67282,f332(f332(f138(x67281,x67281,f7(x67281)),x67282),x67283)),x67283)
% 52.62/52.41 [6825]E(f332(f332(f3(a845),f332(f332(f82(a845),x68251),x68252)),f332(a114,x68253)),f332(f332(f3(a845),x68251),f332(a114,f332(f332(f3(a845),x68253),x68252))))+~P1(f332(f332(f232(a845),x68252),x68253))
% 52.62/52.41 [6826]~P110(x68261)+P1(f332(f332(f232(x68261),f2(x68261)),f332(f332(f242(x68261),f332(f77(x68261),x68262)),x68263)))
% 52.62/52.41 [6877]P30(x68771,x68772,x68773)+~P1(f332(f332(f232(f853(f844(x68771),a839)),x68773),x68772))
% 52.62/52.41 [6918]~P1(f332(f64(x69181),x69182))+P1(f332(f64(x69181),f332(f332(f3(f853(x69181,a839)),x69182),x69183)))
% 52.62/52.41 [6919]~P1(f332(f64(x69191),x69193))+P1(f332(f64(x69191),f332(f332(f104(f853(x69191,a839)),x69192),x69193)))
% 52.62/52.41 [6920]~P1(f332(f64(x69201),x69202))+P1(f332(f64(x69201),f332(f332(f104(f853(x69201,a839)),x69202),x69203)))
% 52.62/52.41 [7059]~P38(x70591,x70593)+P38(x70591,f332(f332(f104(f853(f852(x70591,x70591),a839)),x70592),x70593))
% 52.62/52.41 [7060]~P38(x70601,x70602)+P38(x70601,f332(f332(f104(f853(f852(x70601,x70601),a839)),x70602),x70603))
% 52.62/52.41 [7180]~P93(x71801)+E(f15(x71801,f332(f158(x71801),f332(f332(f140(x71801),x71802),x71803))),f332(f132(x71801,x71801,f103(x71801),x71802),x71803))
% 52.62/52.41 [7181]~P100(x71811)+E(f16(x71811,f332(f158(x71811),f332(f332(f140(x71811),x71812),x71813))),f332(f132(x71811,x71811,f179(x71811),x71812),x71813))
% 52.62/52.41 [7182]~P100(x71821)+E(f17(x71821,f332(f158(x71821),f332(f332(f140(x71821),x71822),x71823))),f332(f132(x71821,x71821,f236(x71821),x71822),x71823))
% 52.62/52.41 [7183]~P93(x71831)+E(f12(x71831,f332(f158(x71831),f332(f332(f140(x71831),x71832),x71833))),f332(f132(x71831,x71831,f104(x71831),x71832),x71833))
% 52.62/52.41 [7184]~P1(f332(f332(f279(a1),x71841),x71842))+P1(f332(f332(f279(a1),x71841),f332(f332(f82(a1),x71842),f332(f332(f83(a1),x71841),x71843))))
% 52.62/52.41 [7254]~P1(f332(f64(x72541),x72542))+P1(f332(f332(f232(a845),f332(f43(x72541),x72542)),f332(f43(x72541),f332(f332(f302(x72541),x72543),x72542))))
% 52.62/52.41 [7261]E(f332(f332(f103(f853(a845,a839)),f332(f294(a845,x72611),x72612)),f332(f294(a845,x72612),f332(f332(f82(a845),x72612),x72613))),f332(f294(a845,x72611),f332(f332(f82(a845),x72612),x72613)))+~P1(f332(f332(f232(a845),x72611),x72612))
% 52.62/52.41 [7271]P1(f332(f332(f233(a845),x72711),x72712))+~P1(f332(f332(f233(a845),f332(f332(f82(a845),x72711),x72713)),x72712))
% 52.62/52.41 [7272]P1(f332(f332(f232(a845),x72721),x72722))+~P1(f332(f332(f232(a845),f332(f332(f82(a845),x72723),x72721)),x72722))
% 52.62/52.41 [7273]P1(f332(f332(f232(a845),x72731),x72732))+~P1(f332(f332(f232(a845),f332(f332(f82(a845),x72731),x72733)),x72732))
% 52.62/52.41 [7274]P1(f332(f332(f232(a845),x72741),x72742))+~P1(f332(f332(f232(a845),f332(f332(f82(a845),x72743),x72741)),x72742))
% 52.62/52.41 [7275]P1(f332(f332(f232(a845),x72751),x72752))+~P1(f332(f332(f232(a845),f332(f332(f82(a845),x72751),x72753)),x72752))
% 52.62/52.41 [7317]~P100(x73171)+E(f13(x73171,f179(x73171),f332(f158(x73171),f332(f332(f140(x73171),x73172),x73173))),f332(f132(x73171,x73171,f179(x73171),x73172),x73173))
% 52.62/52.41 [7318]~P100(x73181)+E(f14(x73181,f236(x73181),f332(f158(x73181),f332(f332(f140(x73181),x73182),x73183))),f332(f132(x73181,x73181,f236(x73181),x73182),x73183))
% 52.62/52.41 [7322]~E(x73222,f180(f853(f852(x73221,x73221),a839)))+P1(f332(f332(f232(f853(f852(x73221,x73221),a839)),x73222),x73223))
% 52.62/52.41 [7431]E(f332(f332(f103(f853(x74311,a839)),x74312),f332(f332(f3(f853(x74311,a839)),x74313),x74312)),x74313)+~P1(f332(f332(f232(f853(x74311,a839)),x74312),x74313))
% 52.62/52.41 [7434]~P1(f332(f332(f233(a845),x74341),f332(f332(f3(a845),x74343),x74342)))+P1(f332(f332(f233(a845),f332(f332(f82(a845),x74341),x74342)),x74343))
% 52.62/52.41 [7435]~P1(f332(f332(f232(a845),x74351),f332(f332(f82(a845),x74353),x74352)))+P1(f332(f332(f232(a845),f332(f332(f3(a845),x74351),x74352)),x74353))
% 52.62/52.41 [7495]E(x74951,f115(x74952))+E(f332(f131(x74952),f332(f332(f332(f173(f846(x74952),f846(x74952)),x74953),f141(x74952)),x74951)),f332(f332(f152(x74952),x74951),f53(a845,x74953,f332(f181(f846(x74952)),x74951))))
% 52.62/52.41 [7504]E(f332(f332(f302(x75041),x75042),f332(f332(f3(f853(x75041,a839)),x75043),f332(f332(f302(x75041),x75042),f180(f853(x75041,a839))))),x75043)+~P1(f332(f332(f334(x75041),x75042),x75043))
% 52.62/52.41 [7668]P1(f332(f332(f233(a845),x76681),f332(f332(f3(a845),x76682),x76683)))+~P1(f332(f332(f233(a845),f332(f332(f82(a845),x76681),x76683)),x76682))
% 52.62/52.41 [7669]P1(f332(f332(f232(a845),x76691),f332(f332(f82(a845),x76692),x76693)))+~P1(f332(f332(f232(a845),f332(f332(f3(a845),x76691),x76693)),x76692))
% 52.62/52.41 [7689]P1(f332(f64(x76891),x76892))+~P1(f332(f64(x76891),f332(f332(f103(f853(x76891,a839)),x76893),x76892)))
% 52.62/52.41 [7690]P1(f332(f64(x76901),x76902))+~P1(f332(f64(x76901),f332(f332(f103(f853(x76901,a839)),x76902),x76903)))
% 52.62/52.41 [7771]~P46(x77711,x77713)+P1(f332(f332(f334(f852(x77711,x77711)),f332(f332(f241(x77711,x77711),x77712),x77712)),x77713))
% 52.62/52.41 [7821]P1(f332(f332(f279(a1),x78211),x78212))+~P1(f332(f332(f279(a1),x78211),f332(f332(f82(a1),x78212),f332(f332(f83(a1),x78211),x78213))))
% 52.62/52.41 [7901]E(f332(f332(f152(a845),f130(a845,f332(f294(a845,x79011),x79012))),x79013),f332(f332(f82(a845),x79011),x79013))+~P1(f332(f332(f233(a845),f332(f332(f82(a845),x79011),x79013)),x79012))
% 52.62/52.41 [7970]~P1(f332(f332(f187(f332(a27,x79701)),x79702),x79703))+P1(f332(f332(f187(f332(f231(a840),f332(a30,x79701))),x79702),x79703))
% 52.62/52.41 [7971]~P1(f332(f332(f187(f332(a27,x79711)),x79712),x79713))+P1(f332(f332(f187(f332(f231(a840),f332(a30,x79711))),x79712),x79713))
% 52.62/52.41 [7975]E(f332(f332(f159(a845),x79751),f130(a845,f332(f294(a845,x79752),x79753))),f130(a845,f332(f294(a845,x79752),f332(f332(f82(a845),x79752),x79751))))+~P1(f332(f332(f232(a845),f332(f332(f82(a845),x79752),x79751)),x79753))
% 52.62/52.41 [8024]~P88(x80241)+E(f332(f332(f242(x80241),x80242),f332(f106(a845),f332(f332(f82(a1),x80243),x80243))),f332(f332(f88(x80241,x80241),f332(f332(f242(x80241),x80242),f332(f106(a845),x80243))),f332(f332(f20(x80241,x80241,x80241),f83(x80241)),f7(x80241))))
% 52.62/52.41 [8223]P1(f332(f332(f187(f332(a27,x82231)),x82232),x82233))+~P1(f332(f332(f187(f332(f231(a840),f332(a30,x82231))),x82232),x82233))
% 52.62/52.41 [8224]P1(f332(f332(f187(f332(a27,x82241)),x82242),x82243))+~P1(f332(f332(f187(f332(f231(a840),f332(a30,x82241))),x82242),x82243))
% 52.62/52.41 [8281]E(f332(f332(f125(x82811),f332(f332(f159(x82811),x82812),x82813)),f332(f332(f140(x82811),f332(f332(f152(x82811),x82813),x82812)),f332(f332(f128(x82811),f332(a114,x82812)),x82813))),x82813)+~P1(f332(f332(f233(a845),x82812),f332(f181(f846(x82811)),x82813)))
% 52.62/52.41 [8288]P1(f332(f332(f232(f853(x82881,a839)),f321(x82881,x82882)),f321(x82881,x82883)))+~P1(f332(f332(f232(f853(x82881,f853(x82881,a839))),x82883),x82882))
% 52.62/52.41 [8289]~P56(x82891,x82892,x82893)+P56(x82891,x82892,f332(f332(f3(f853(f852(x82891,x82891),a839)),x82893),f300(x82891,f180(f853(f852(x82891,x82891),a839)))))
% 52.62/52.41 [8311]P1(f332(f332(f232(f853(x83111,a839)),f322(x83111,x83112)),f322(x83111,x83113)))+~P1(f332(f332(f232(f853(f852(x83111,x83111),a839)),x83113),x83112))
% 52.62/52.41 [8318]~P118(x83181)+P1(f332(f332(f232(x83181),f2(x83181)),f332(f332(f82(x83181),f332(f332(f83(x83181),x83182),x83182)),f332(f332(f83(x83181),x83183),x83183))))
% 52.62/52.41 [8350]~P88(x83501)+E(f332(f332(f242(x83501),f332(f106(x83501),x83502)),f332(f106(a845),f332(f332(f82(a1),x83503),x83503))),f332(f332(f88(x83501,x83501),f332(f332(f242(x83501),f332(f106(x83501),x83502)),f332(f106(a845),x83503))),f332(f332(f20(x83501,x83501,x83501),f83(x83501)),f7(x83501))))
% 52.62/52.41 [8355]P1(f332(f332(f232(f853(x83551,a839)),f332(f276(x83551),x83552)),f332(f276(x83551),x83553)))+~P1(f332(f332(f232(f853(f852(x83551,x83551),a839)),x83552),x83553))
% 52.62/52.41 [8387]~P50(x83871,x83872)+~P1(f332(f332(f334(f852(x83871,x83871)),f332(f332(f241(x83871,x83871),x83873),x83873)),x83872))
% 52.62/52.41 [8388]~P38(x83881,x83882)+~P1(f332(f332(f334(f852(x83881,x83881)),f332(f332(f241(x83881,x83881),x83883),x83883)),x83882))
% 52.62/52.41 [8389]~P38(x83891,x83892)+~P1(f332(f332(f334(f852(x83891,x83891)),f332(f332(f241(x83891,x83891),x83893),x83893)),x83892))
% 52.62/52.41 [8429]~E(x84292,x84293)+P1(f332(f332(f334(f852(x84291,x84291)),f332(f332(f241(x84291,x84291),x84292),x84293)),f300(x84291,f180(f853(f852(x84291,x84291),a839)))))
% 52.62/52.41 [8450]P1(f332(f332(f232(f853(x84501,a839)),f46(f853(x84501,a839),x84502)),f46(f853(x84501,a839),x84503)))+~P1(f332(f332(f232(f853(f853(x84501,a839),a839)),x84503),x84502))
% 52.62/52.41 [8451]P1(f332(f332(f232(f853(x84511,a839)),f45(f853(x84511,a839),x84512)),f45(f853(x84511,a839),x84513)))+~P1(f332(f332(f232(f853(f853(x84511,a839),a839)),x84512),x84513))
% 52.62/52.41 [8506]~P14(x85061,x85063,x85062)+P1(f332(f332(f232(f853(f852(x85061,x85061),a839)),x85062),f332(f332(f248(x85061,x85061),x85063),f332(f18(f853(x85061,a839),x85061),x85063))))
% 52.62/52.41 [8507]~P49(x85071,x85073,x85072)+P1(f332(f332(f232(f853(f852(x85071,x85071),a839)),x85072),f332(f332(f248(x85071,x85071),x85073),f332(f18(f853(x85071,a839),x85071),x85073))))
% 52.62/52.41 [8545]~P80(x85451)+P1(f332(f332(f232(x85451),f332(f332(f3(x85451),f332(f77(x85451),x85452)),f332(f77(x85451),x85453))),f332(f77(x85451),f332(f332(f3(x85451),x85453),x85452))))
% 52.62/52.41 [8546]~P80(x85461)+P1(f332(f332(f232(x85461),f332(f332(f3(x85461),f332(f77(x85461),x85462)),f332(f77(x85461),x85463))),f332(f77(x85461),f332(f332(f3(x85461),x85462),x85463))))
% 52.62/52.41 [8570]P1(f332(f332(f232(f853(f852(x85701,x85701),a839)),f300(x85701,x85702)),f300(x85701,x85703)))+~P1(f332(f332(f232(f853(f852(x85701,x85701),a839)),x85702),x85703))
% 52.62/52.41 [8716]P56(x87161,x87162,x87163)+~P56(x87161,x87162,f332(f332(f3(f853(f852(x87161,x87161),a839)),x87163),f300(x87161,f180(f853(f852(x87161,x87161),a839)))))
% 52.62/52.41 [8735]P1(f332(f332(f232(f853(f852(f846(x87351),f846(x87351)),a839)),f147(x87351,x87352)),f147(x87351,x87353)))+~P1(f332(f332(f232(f853(f852(x87351,x87351),a839)),x87352),x87353))
% 52.62/52.41 [8736]P1(f332(f332(f232(f853(f852(f846(x87361),f846(x87361)),a839)),f146(x87361,x87362)),f146(x87361,x87363)))+~P1(f332(f332(f232(f853(f852(x87361,x87361),a839)),x87362),x87363))
% 52.62/52.41 [8753]~P49(x87531,x87533,x87532)+P1(f332(f332(f232(f853(f852(x87531,x87531),a839)),x87532),f332(f332(f281(x87531,x87531,x87531),f332(f278(x87531,x87531),x87532)),x87532)))
% 52.62/52.41 [8794]~P1(f332(f127(x87941),x87942))+E(f332(f126(x87941,f332(f332(f9(x87941,f853(x87941,a839),a839),f334(x87941)),f332(f158(x87941),f160(x87941,x87942,x87943)))),x87942),f160(x87941,x87942,x87943))
% 52.62/52.41 [8840]E(x88401,x88402)+~P1(f332(f332(f334(f852(x88403,x88403)),f332(f332(f241(x88403,x88403),x88401),x88402)),f300(x88403,f180(f853(f852(x88403,x88403),a839)))))
% 52.62/52.41 [8922]P1(f332(f332(f334(x89221),x89222),f322(x89221,x89223)))+P1(f332(f332(f334(f852(x89221,x89221)),f332(f332(f241(x89221,x89221),f527(x89223,x89222,x89221)),x89222)),x89223))
% 52.62/52.41 [8923]P1(f332(f332(f334(x89231),x89232),f322(x89231,x89233)))+P1(f332(f332(f334(f852(x89231,x89231)),f332(f332(f241(x89231,x89231),f620(x89233,x89232,x89231)),x89232)),x89233))
% 52.62/52.41 [8924]P1(f332(f332(f334(x89241),x89242),f322(x89241,x89243)))+P1(f332(f332(f334(f852(x89241,x89241)),f332(f332(f241(x89241,x89241),f622(x89243,x89242,x89241)),x89242)),x89243))
% 52.62/52.41 [9028]P1(f332(x90283,x90282))+E(f332(f256(x90281),f332(f332(f20(x90281,a839,a839),f332(f332(f10(a839,f853(a839,a839),x90281),a330),f332(a329,x90282))),x90283)),f180(f853(x90281,a839)))
% 52.62/52.41 [9047]~P80(x90471)+P1(f332(f332(f232(x90471),f332(f77(x90471),f332(f332(f3(x90471),f332(f77(x90471),x90472)),f332(f77(x90471),x90473)))),f332(f77(x90471),f332(f332(f3(x90471),x90472),x90473))))
% 52.62/52.41 [9060]~P1(f332(x90603,x90602))+E(f332(f256(x90601),f332(f332(f20(x90601,a839,a839),f332(f332(f10(a839,f853(a839,a839),x90601),a330),f332(a329,x90602))),x90603)),f332(f332(f302(x90601),x90602),f180(f853(x90601,a839))))
% 52.62/52.41 [9066]~P1(f332(f332(f334(f853(x90661,a839)),x90663),f332(f301(x90661),x90662)))+P1(f332(f245(x90661,f332(f332(f9(x90661,f853(x90661,a839),a839),f334(x90661)),x90662)),x90663))
% 52.62/52.41 [9100]P38(x91001,x91002)+P1(f332(f332(f334(f852(x91001,x91001)),f332(f332(f241(x91001,x91001),f332(f588(x91002,x91001),f332(a114,x91003))),f332(f588(x91002,x91001),x91003))),x91002))
% 52.62/52.41 [9226]P1(f332(f332(f334(f853(x92261,a839)),x92262),f332(f301(x92261),x92263)))+~P1(f332(f245(x92261,f332(f332(f9(x92261,f853(x92261,a839),a839),f334(x92261)),x92263)),x92262))
% 52.62/52.41 [9286]P1(f332(f332(f334(x92861),f332(f265(x92861,x92862),x92863)),f332(f158(x92861),f332(f332(f143(f852(a101,x92861),x92861),f250(a101,x92861)),x92862))))+~P1(f332(f332(f233(a101),x92863),f332(f154(a101),f332(f332(f143(f852(a101,x92861),a101),f240(a101,x92861)),x92862))))
% 52.62/52.41 [9334]P1(f332(f332(f232(f853(f852(f846(x93341),f846(x93341)),a839)),f147(x93341,x93342)),f332(f332(f248(f846(x93341),f846(x93341)),f149(x93341,x93343)),f332(f18(f853(f846(x93341),a839),f846(x93341)),f149(x93341,x93343)))))+~P1(f332(f332(f232(f853(f852(x93341,x93341),a839)),x93342),f332(f332(f248(x93341,x93341),x93343),f332(f18(f853(x93341,a839),x93341),x93343))))
% 52.62/52.41 [9354]P1(f332(f332(f334(x93541),f332(f240(x93541,f852(a101,a101)),f332(f263(x93541,x93542),x93543))),f332(f158(x93541),f332(f332(f143(f852(a101,x93541),x93541),f250(a101,x93541)),x93542))))+~P1(f332(f332(f233(a101),f2(a101)),f332(f154(a101),f332(f332(f143(f852(a101,x93541),a101),f240(a101,x93541)),x93542))))
% 52.62/52.41 [9369]~P1(f332(f332(f232(f853(f852(x93691,x93691),a839)),x93692),f332(f332(f248(x93691,x93691),x93693),f332(f18(f853(x93691,a839),x93691),x93693))))+P1(f332(f332(f232(f853(f852(x93691,x93691),a839)),f332(f332(f281(x93691,x93691,x93691),x93692),f300(x93691,x93692))),f332(f332(f248(x93691,x93691),x93693),f332(f18(f853(x93691,a839),x93691),x93693))))
% 52.62/52.41 [9650]~P38(x96501,x96502)+~P1(f332(f332(f334(f852(x96501,x96501)),f332(f332(f241(x96501,x96501),f332(x96503,f332(a114,f589(x96502,x96501,x96503)))),f332(x96503,f589(x96502,x96501,x96503)))),x96502))
% 52.62/52.41 [9651]~P38(x96511,x96512)+~P1(f332(f332(f334(f852(x96511,x96511)),f332(f332(f241(x96511,x96511),f332(x96513,f332(a114,f632(x96513,x96512,x96511)))),f332(x96513,f632(x96513,x96512,x96511)))),x96512))
% 52.62/52.41 [9907]P1(f332(f332(f232(f853(f852(f853(x99071,a839),f853(x99071,a839)),a839)),f332(f332(f281(f853(x99071,a839),f853(x99071,a839),f853(x99071,a839)),f324(x99071,x99072)),f332(f332(f103(f853(f852(f853(x99071,a839),f853(x99071,a839)),a839)),f324(x99071,x99073)),f332(f332(f302(f852(f853(x99071,a839),f853(x99071,a839))),f332(f332(f241(f853(x99071,a839),f853(x99071,a839)),f180(f853(x99071,a839))),f180(f853(x99071,a839)))),f180(f853(f852(f853(x99071,a839),f853(x99071,a839)),a839)))))),f324(x99071,x99072)))+~P1(f332(f332(f232(f853(f852(x99071,x99071),a839)),f332(f332(f281(x99071,x99071,x99071),x99072),x99073)),x99072))
% 52.62/52.41 [9908]P1(f332(f332(f232(f853(f852(f853(x99081,a839),f853(x99081,a839)),a839)),f332(f332(f281(f853(x99081,a839),f853(x99081,a839),f853(x99081,a839)),f325(x99081,x99082)),f332(f332(f103(f853(f852(f853(x99081,a839),f853(x99081,a839)),a839)),f325(x99081,x99083)),f332(f332(f302(f852(f853(x99081,a839),f853(x99081,a839))),f332(f332(f241(f853(x99081,a839),f853(x99081,a839)),f180(f853(x99081,a839))),f180(f853(x99081,a839)))),f180(f853(f852(f853(x99081,a839),f853(x99081,a839)),a839)))))),f325(x99081,x99082)))+~P1(f332(f332(f232(f853(f852(x99081,x99081),a839)),f332(f332(f281(x99081,x99081,x99081),x99082),x99083)),x99082))
% 52.62/52.41 [7179]~P1(f332(f332(f232(a845),x71792),x71791))+E(f332(f332(f3(a845),f332(a114,f332(f332(f3(a845),x71791),x71792))),x71793),f332(f332(f3(a845),f332(a114,x71791)),f332(f332(f82(a845),x71792),x71793)))
% 52.62/52.41 [7219]~P9(x72191)+E(f332(f332(f82(x72191),f53(x72191,x72192,x72193)),f332(f332(f83(x72191),f332(f332(f44(x72191),x72192),x72193)),x72193)),x72192)
% 52.62/52.41 [7439]E(f332(f332(f83(a845),f332(f106(a845),x74391)),f332(f332(f83(a845),f332(f106(a845),x74392)),x74393)),f332(f332(f83(a845),f332(f106(a845),f332(f332(f83(a1),x74391),x74392))),x74393))+P1(f332(f332(f233(a1),x74391),a85))
% 52.62/52.41 [7912]~P1(f332(f332(f232(a845),x79123),x79122))+P1(f332(f332(f232(a845),x79121),f332(f332(f3(a845),f332(f332(f82(a845),x79122),x79121)),x79123)))
% 52.62/52.41 [8107]~P1(f332(f332(f232(a845),x81071),x81072))+E(f332(f332(f125(a845),f130(a845,f332(f294(a845,x81071),x81072))),f130(a845,f332(f294(a845,x81072),f332(f332(f82(a845),x81072),x81073)))),f130(a845,f332(f294(a845,x81071),f332(f332(f82(a845),x81072),x81073))))
% 52.62/52.41 [8364]~P1(f332(f64(x83641),x83642))+E(f332(a114,f332(f43(x83641),f332(f332(f3(f853(x83641,a839)),x83642),f332(f332(f302(x83641),x83643),f180(f853(x83641,a839)))))),f332(f43(x83641),f332(f332(f302(x83641),x83643),x83642)))
% 52.62/52.41 [8408]~P1(f332(f64(x84081),x84082))+E(f332(f332(f82(a845),f80(a845)),f332(f43(x84081),f332(f332(f3(f853(x84081,a839)),x84082),f332(f332(f302(x84081),x84083),f180(f853(x84081,a839)))))),f332(f43(x84081),f332(f332(f302(x84081),x84083),x84082)))
% 52.62/52.41 [8579]E(f332(f332(f3(a845),f332(f43(x85791),x85792)),f332(f43(x85791),f332(f332(f104(f853(x85791,a839)),x85792),x85793))),f332(f43(x85791),f332(f332(f3(f853(x85791,a839)),x85792),x85793)))+~P1(f332(f64(x85791),f332(f332(f104(f853(x85791,a839)),x85792),x85793)))
% 52.62/52.41 [8791]~P12(f332(x87912,f406(x87912,x87913,x87911)))+E(f332(f102(a1),f332(f332(f8(x87911,a845),f332(f332(f10(a1,a845,x87911),a107),x87912)),x87913)),f332(f332(f8(x87911,a1),x87912),x87913))
% 52.62/52.41 [8792]~P12(f332(x87922,f466(x87922,x87923,x87921)))+E(f332(f102(a1),f332(f332(f11(x87921,a845),f332(f332(f10(a1,a845,x87921),a107),x87922)),x87923)),f332(f332(f11(x87921,a1),x87922),x87923))
% 52.62/52.41 [8824]~P1(f332(f64(x88241),x88243))+P1(f332(f332(f232(a845),f332(f332(f3(a845),f332(f43(x88241),x88242)),f332(f43(x88241),x88243))),f332(f43(x88241),f332(f332(f3(f853(x88241,a839)),x88242),x88243))))
% 52.62/52.41 [8848]P1(f332(f332(f334(x88481),f406(x88482,x88483,x88481)),x88483))+E(f332(f102(a1),f332(f332(f8(x88481,a845),f332(f332(f10(a1,a845,x88481),a107),x88482)),x88483)),f332(f332(f8(x88481,a1),x88482),x88483))
% 52.62/52.41 [8849]P1(f332(f332(f334(x88491),f466(x88492,x88493,x88491)),x88493))+E(f332(f102(a1),f332(f332(f11(x88491,a845),f332(f332(f10(a1,a845,x88491),a107),x88492)),x88493)),f332(f332(f11(x88491,a1),x88492),x88493))
% 52.62/52.41 [8916]E(f87(x89161,f332(f332(f9(x89161,f853(x89161,a839),a839),f334(x89161)),f332(f332(f3(f853(x89161,a839)),x89162),f332(f332(f302(x89161),x89163),f180(f853(x89161,a839)))))),f244(x89161,x89163,x89162))+P1(f332(f332(f232(f853(x89161,a839)),x89162),f332(f332(f302(x89161),x89163),f180(f853(x89161,a839)))))
% 52.62/52.41 [9227]E(f332(f332(f143(f846(x92271),x92271),f332(f332(f9(f846(x92271),a845,x92271),f152(x92271)),x92272)),f332(f126(f846(x92271),f332(f332(f10(a845,a839,f846(x92271)),f332(f233(a845),x92272)),f181(f846(x92271)))),x92273)),f332(f332(f152(f846(x92271)),f164(x92271,x92273)),x92272))+~P1(f332(f332(f233(a845),x92272),f332(f181(f846(f846(x92271))),f164(x92271,x92273))))
% 52.62/52.41 [9526]~P1(f332(f332(f334(f852(x95261,x95261)),x95262),f300(x95261,x95263)))+P1(f332(f332(f334(f852(x95261,x95261)),x95262),f332(f332(f47(a845,f853(f852(x95261,x95261),a839)),f239(f853(a845,a839))),f332(f332(f9(a845,f853(f852(x95261,x95261),a839),f853(f852(x95261,x95261),a839)),f173(f852(x95261,x95261),a839)),x95263))))
% 52.62/52.41 [9579]~P1(f332(f332(f232(f853(x95791,a839)),f332(f332(f47(a845,f853(x95791,a839)),f332(f294(a845,f2(a845)),f398(x95793,x95792,x95791))),x95792)),x95793))+P1(f332(f332(f232(f853(x95791,a839)),f332(f332(f47(a845,f853(x95791,a839)),f239(f853(a845,a839))),x95792)),x95793))
% 52.62/52.41 [9627]~P1(f332(f332(f233(a1),f2(a1)),x96273))+P1(f332(f332(f233(a1),x96271),f332(f332(f82(a1),x96272),f332(f332(f83(a1),f332(f332(f82(a1),f332(f77(a1),f332(f332(f3(a1),x96272),x96271))),f80(a1))),x96273))))
% 52.62/52.41 [9637]~P38(x96371,f332(f332(f103(f853(f852(x96371,x96371),a839)),x96372),x96373))+P38(x96371,f332(f332(f103(f853(f852(x96371,x96371),a839)),f332(f332(f103(f853(f852(x96371,x96371),a839)),f332(f332(f281(x96371,x96371,x96371),x96372),x96372)),f332(f332(f281(x96371,x96371,x96371),x96373),x96372))),x96373))
% 52.62/52.41 [9703]P38(x97031,f332(f332(f103(f853(f852(x97031,x97031),a839)),x97032),x97033))+~P38(x97031,f332(f332(f103(f853(f852(x97031,x97031),a839)),f332(f332(f103(f853(f852(x97031,x97031),a839)),f332(f332(f281(x97031,x97031,x97031),x97032),x97032)),f332(f332(f281(x97031,x97031,x97031),x97033),x97032))),x97033))
% 52.62/52.41 [9308]~P133(x93081)+E(f332(f105(x93081),f332(a91,f332(f277(f852(a845,a845),f852(a845,a845),a111),f332(f332(f302(f852(a845,a845)),f332(f332(f241(a845,a845),x93082),x93083)),f180(f853(f852(a845,a845),a839)))))),f332(f332(f3(x93081),f332(f102(x93081),x93082)),f332(f102(x93081),x93083)))
% 52.62/52.41 [9387]P1(f332(x93873,x93872))+E(f332(f256(x93871),f332(f332(f20(x93871,a839,a839),f332(f332(f10(a839,f853(a839,a839),x93871),a330),f332(f332(f9(x93871,x93871,a839),a329),x93872))),x93873)),f180(f853(x93871,a839)))
% 52.62/52.41 [9389]~P1(f332(x93893,x93892))+E(f332(f256(x93891),f332(f332(f20(x93891,a839,a839),f332(f332(f10(a839,f853(a839,a839),x93891),a330),f332(f332(f9(x93891,x93891,a839),a329),x93892))),x93893)),f332(f332(f302(x93891),x93892),f180(f853(x93891,a839))))
% 52.62/52.41 [9695]~P1(f332(f64(x96951),x96953))+E(f332(f332(f67(x96951,f853(x96951,a839),f332(f332(f10(f853(x96951,a839),f853(f853(x96951,a839),f853(x96951,a839)),x96951),f332(f9(f853(x96951,a839),f853(x96951,a839),f853(x96951,a839)),f3(f853(x96951,a839)))),f332(f332(f9(x96951,f853(x96951,a839),f853(x96951,a839)),f302(x96951)),f180(f853(x96951,a839))))),x96952),x96953),f332(f332(f3(f853(x96951,a839)),x96952),x96953))
% 52.62/52.41 [9729]~P1(f332(f332(f233(a1),f2(a1)),x97293))+P1(f332(f332(f233(a1),f332(f332(f3(a1),x97291),f332(f332(f83(a1),f332(f332(f82(a1),f332(f77(a1),f332(f332(f3(a1),x97291),x97292))),f80(a1))),x97293))),x97292))
% 52.62/52.41 [9975]~P1(f332(f332(f334(x99751),x99753),f322(x99751,x99752)))+P1(f332(f321(x99751,f332(f332(f9(x99751,f853(f852(x99751,x99751),a839),f853(x99751,a839)),f332(f332(f10(f853(x99751,f853(f853(f852(x99751,x99751),a839),a839)),f853(f853(f852(x99751,x99751),a839),f853(x99751,a839)),x99751),f9(x99751,f853(f852(x99751,x99751),a839),a839)),f332(f332(f10(f853(x99751,f852(x99751,x99751)),f853(x99751,f853(f853(f852(x99751,x99751),a839),a839)),x99751),f332(f10(f852(x99751,x99751),f853(f853(f852(x99751,x99751),a839),a839),x99751),f334(f852(x99751,x99751)))),f241(x99751,x99751)))),x99752)),x99753))
% 52.62/52.41 [9987]P1(f332(f332(f334(x99871),x99872),f322(x99871,x99873)))+~P1(f332(f321(x99871,f332(f332(f9(x99871,f853(f852(x99871,x99871),a839),f853(x99871,a839)),f332(f332(f10(f853(x99871,f853(f853(f852(x99871,x99871),a839),a839)),f853(f853(f852(x99871,x99871),a839),f853(x99871,a839)),x99871),f9(x99871,f853(f852(x99871,x99871),a839),a839)),f332(f332(f10(f853(x99871,f852(x99871,x99871)),f853(x99871,f853(f853(f852(x99871,x99871),a839),a839)),x99871),f332(f10(f852(x99871,x99871),f853(f853(f852(x99871,x99871),a839),a839),x99871),f334(f852(x99871,x99871)))),f241(x99871,x99871)))),x99873)),x99872))
% 52.62/52.41 [9577]~P1(f332(f64(x95771),f332(f256(x95771),x95773)))+P1(f332(f64(x95771),f332(f256(x95771),f332(f332(f20(x95771,a839,a839),f332(f332(f10(a839,f853(a839,a839),x95771),a330),x95772)),x95773))))
% 52.62/52.41 [9578]~P1(f332(f64(x95781),f332(f256(x95781),x95782)))+P1(f332(f64(x95781),f332(f256(x95781),f332(f332(f20(x95781,a839,a839),f332(f332(f10(a839,f853(a839,a839),x95781),a330),x95782)),x95783))))
% 52.62/52.41 [9662]P1(f332(f64(x96621),f332(f256(x96621),x96622)))+~P1(f332(f64(x96621),f332(f256(x96621),f332(f332(f20(x96621,a839,a839),f332(f332(f10(a839,f853(a839,a839),x96621),a331),x96623)),x96622))))
% 52.62/52.41 [9663]P1(f332(f64(x96631),f332(f256(x96631),x96632)))+~P1(f332(f64(x96631),f332(f256(x96631),f332(f332(f20(x96631,a839,a839),f332(f332(f10(a839,f853(a839,a839),x96631),a331),x96632)),x96633))))
% 52.62/52.41 [9960]~P1(f332(f64(x99601),x99602))+P1(f332(f64(f846(x99601)),f332(f256(f846(x99601)),f332(f332(f20(f846(x99601),a839,a839),f332(f332(f10(a839,f853(a839,a839),f846(x99601)),a330),f332(f332(f9(f846(x99601),f853(x99601,a839),a839),f332(f332(f10(f853(x99601,a839),f853(f853(x99601,a839),a839),f846(x99601)),f232(f853(x99601,a839))),f158(x99601))),x99602))),f332(f332(f9(f846(x99601),a845,a839),f332(f332(f10(a845,f853(a845,a839),f846(x99601)),a329),f181(f846(x99601)))),x99603)))))
% 52.62/52.41 [9961]~P1(f332(f64(x99611),x99612))+P1(f332(f64(f846(x99611)),f332(f256(f846(x99611)),f332(f332(f20(f846(x99611),a839,a839),f332(f332(f10(a839,f853(a839,a839),f846(x99611)),a330),f332(f332(f9(f846(x99611),f853(x99611,a839),a839),f332(f332(f10(f853(x99611,a839),f853(f853(x99611,a839),a839),f846(x99611)),f232(f853(x99611,a839))),f158(x99611))),x99612))),f332(f332(f9(f846(x99611),a845,a839),f332(f332(f10(a845,f853(a845,a839),f846(x99611)),f232(a845)),f181(f846(x99611)))),x99613)))))
% 52.62/52.41 [9676]~P73(x96761)+E(f332(f332(f242(x96761),x96762),f332(f332(f83(a845),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),x96763)),f332(f332(f83(x96761),f332(f332(f242(x96761),x96762),x96763)),f332(f332(f242(x96761),x96762),x96763)))
% 52.62/52.41 [9708]~P76(x97081)+E(f332(f332(f242(x97081),f332(f332(f242(x97081),x97082),x97083)),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f332(f332(f242(x97081),x97082),f332(f332(f83(a845),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),x97083)))
% 52.62/52.41 [9769]~P133(x97691)+E(f332(f332(f242(x97691),f332(f81(x97691),x97692)),f332(f332(f83(a845),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),x97693)),f332(f332(f242(x97691),x97692),f332(f332(f83(a845),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),x97693)))
% 52.62/52.41 [9912]~P110(x99121)+P1(f332(f332(f232(x99121),f2(x99121)),f332(f332(f82(x99121),f332(f332(f242(x99121),x99122),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))),f332(f332(f242(x99121),x99123),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))))))
% 52.62/52.41 [9779]~P73(x97791)+E(f332(f332(f242(x97791),x97792),f332(a114,f332(f332(f83(a845),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),x97793))),f332(f332(f83(x97791),x97792),f332(f332(f83(x97791),f332(f332(f242(x97791),x97792),x97793)),f332(f332(f242(x97791),x97792),x97793))))
% 52.62/52.41 [9828]~P76(x98281)+E(f332(f332(f83(x98281),x98282),f332(f332(f242(x98281),f332(f332(f242(x98281),x98282),x98283)),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))),f332(f332(f242(x98281),x98282),f332(a114,f332(f332(f83(a845),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),x98283))))
% 52.62/52.41 [9872]~P110(x98721)+P1(f332(f332(f232(x98721),f2(x98721)),f332(f332(f242(x98721),x98722),f332(f332(f83(a845),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),x98723))))
% 52.62/52.41 [9941]~P88(x99411)+E(f332(f332(f82(x99411),f332(f332(f82(x99411),f332(f332(f242(x99411),x99412),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))),f332(f332(f242(x99411),x99413),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))))),f332(f332(f83(x99411),f332(f332(f83(x99411),f332(f106(x99411),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),x99412)),x99413)),f332(f332(f242(x99411),f332(f332(f82(x99411),x99412),x99413)),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))))
% 52.62/52.41 [9942]~P88(x99421)+E(f332(f332(f3(x99421),f332(f332(f82(x99421),f332(f332(f242(x99421),x99422),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))),f332(f332(f242(x99421),x99423),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))))),f332(f332(f83(x99421),f332(f332(f83(x99421),f332(f106(x99421),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),x99422)),x99423)),f332(f332(f242(x99421),f332(f332(f3(x99421),x99422),x99423)),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))))
% 52.62/52.41 [4579]E(x45791,x45792)+~E(f36(x45793,x45791),f36(x45794,x45792))
% 52.62/52.41 [4580]E(x45801,x45802)+~E(f36(x45801,x45803),f36(x45802,x45804))
% 52.62/52.41 [4581]E(x45811,x45812)+~E(f35(x45813,x45811),f35(x45814,x45812))
% 52.62/52.41 [4582]E(x45821,x45822)+~E(f35(x45821,x45823),f35(x45822,x45824))
% 52.62/52.41 [4583]E(x45831,x45832)+~E(f28(x45833,x45831),f28(x45834,x45832))
% 52.62/52.41 [4584]E(x45841,x45842)+~E(f28(x45841,x45843),f28(x45842,x45844))
% 52.62/52.41 [5700]P41(f35(x57001,x57003),x57002,x57004,x57002)+P1(f332(x57001,x57002))
% 52.62/52.41 [5701]P41(f35(x57011,x57013),x57012,x57014,x57012)+P1(f332(x57011,x57012))
% 52.62/52.41 [6864]~P41(x68641,x68642,x68643,x68644)+P41(x68641,x68642,f332(a114,x68643),x68644)
% 52.62/52.41 [7709]P31(x77091,x77092,x77093,x77094)+~E(f516(x77094,x77093,x77092,x77091),f519(x77094,x77093,x77092,x77091))
% 52.62/52.41 [8209]~P31(x82091,f849(x82092),x82094,f169(x82091,x82092,x82094))+P31(x82091,f849(x82092),f170(x82091,x82092,x82093,x82094),f169(x82091,x82092,x82094))
% 52.62/52.41 [8423]~P31(x84231,f849(x84232),f170(x84231,x84232,x84234,x84233),f169(x84231,x84232,x84233))+P31(x84231,f849(x84232),x84233,f169(x84231,x84232,x84233))
% 52.62/52.41 [4945]~P23(x49453,x49451,x49454)+E(f332(f332(x49451,x49452),x49452),x49452)
% 52.62/52.41 [4947]E(x49471,x49472)+~E(f332(f304(x49473,x49474),x49471),f332(f304(x49473,x49474),x49472))
% 52.62/52.41 [4948]E(x49481,x49482)+~E(f332(f304(x49483,x49484),x49481),f332(f304(x49483,x49484),x49482))
% 52.62/52.41 [4949]E(x49491,x49492)+~E(f332(f313(x49493,x49494),x49491),f332(f313(x49493,x49494),x49492))
% 52.62/52.41 [4950]E(x49501,x49502)+~E(f332(f313(x49503,x49504),x49501),f332(f313(x49503,x49504),x49502))
% 52.62/52.41 [5227]~E(x52274,f180(f853(x52271,a839)))+E(f332(f303(x52271,x52272,x52273),x52274),f180(f853(x52272,a839)))
% 52.62/52.41 [5228]~E(x52284,f180(f853(x52281,a839)))+E(f332(f303(x52281,x52282,x52283),x52284),f180(f853(x52282,a839)))
% 52.62/52.41 [5490]~E(f332(f303(x54902,x54903,x54904),x54901),f180(f853(x54903,a839)))+E(x54901,f180(f853(x54902,a839)))
% 52.62/52.41 [5491]~E(f332(f303(x54912,x54913,x54914),x54911),f180(f853(x54913,a839)))+E(x54911,f180(f853(x54912,a839)))
% 52.62/52.41 [5782]~P100(x57822)+E(f332(f332(f138(x57821,x57822,x57823),x57824),f115(x57821)),f332(f332(f140(x57821),x57824),f115(x57821)))
% 52.62/52.41 [5817]E(f332(x58171,x58172),f183(x58173))+P1(f332(f332(f334(x58174),x58172),f169(x58174,x58173,x58171)))
% 52.62/52.41 [6144]~E(x61441,f180(f853(x61442,a839)))+~P1(f332(f65(x61442,x61443,x61441),x61444))
% 52.62/52.41 [6165]~P59(x61651,x61653,x61654,x61652)+P1(f332(f64(x61651),x61652))
% 52.62/52.41 [6166]~P59(x61661,x61663,x61662,x61664)+P1(f332(f64(x61661),x61662))
% 52.62/52.41 [6173]~P59(x61732,x61733,x61734,x61731)+~E(x61731,f180(f853(x61732,a839)))
% 52.62/52.41 [6205]~P99(x62051)+E(f332(f332(f104(f853(x62051,a839)),f332(f294(x62051,x62052),x62053)),f295(x62051,x62053,x62054)),f180(f853(x62051,a839)))
% 52.62/52.41 [6234]~P1(f332(f332(x62343,x62344),x62342))+P1(f332(f332(f334(x62341),x62342),f287(x62341,x62343,x62344)))
% 52.62/52.41 [6235]~P1(f332(f332(x62353,x62354),x62352))+P1(f332(f332(f334(x62351),x62352),f286(x62351,x62353,x62354)))
% 52.62/52.41 [6236]~P1(f332(f332(x62363,x62362),x62364))+P1(f332(f332(f334(x62361),x62362),f290(x62361,x62363,x62364)))
% 52.62/52.41 [6237]~P1(f332(f332(x62373,x62372),x62374))+P1(f332(f332(f334(x62371),x62372),f288(x62371,x62373,x62374)))
% 52.62/52.41 [6389]~P99(x63891)+E(f332(f332(f104(f853(x63891,a839)),f295(x63891,x63892,x63893)),f297(x63891,x63893,x63894)),f180(f853(x63891,a839)))
% 52.62/52.41 [6390]~P99(x63901)+E(f332(f332(f104(f853(x63901,a839)),f295(x63901,x63902,x63903)),f298(x63901,x63903,x63904)),f180(f853(x63901,a839)))
% 52.62/52.41 [6391]~P99(x63911)+E(f332(f332(f104(f853(x63911,a839)),f297(x63911,x63912,x63913)),f297(x63911,x63913,x63914)),f180(f853(x63911,a839)))
% 52.62/52.41 [6392]~P99(x63921)+E(f332(f332(f104(f853(x63921,a839)),f297(x63921,x63922,x63923)),f298(x63921,x63923,x63924)),f180(f853(x63921,a839)))
% 52.62/52.41 [6393]~P99(x63931)+E(f332(f332(f104(f853(x63931,a839)),f298(x63931,x63932,x63933)),f295(x63931,x63933,x63934)),f180(f853(x63931,a839)))
% 52.62/52.41 [6431]P1(f332(f332(x64311,x64312),f596(x64312,x64311)))+~P1(f332(f246(x64313,x64314,x64311),x64312))
% 52.62/52.41 [6485]~E(f332(x64851,x64852),f183(x64853))+~P1(f332(f332(f334(x64854),x64852),f169(x64854,x64853,x64851)))
% 52.62/52.41 [6567]~P2(x65671)+E(f182(x65671,x65672,f332(a114,x65673),x65674),f182(x65671,x65672,x65673,f332(x65672,x65674)))
% 52.62/52.41 [6630]~P1(f332(f332(f334(x66304),x66303),f287(x66304,x66301,x66302)))+P1(f332(f332(x66301,x66302),x66303))
% 52.62/52.41 [6631]~P1(f332(f332(f334(x66314),x66313),f286(x66314,x66311,x66312)))+P1(f332(f332(x66311,x66312),x66313))
% 52.62/52.41 [6632]~P1(f332(f332(f334(x66324),x66322),f290(x66324,x66321,x66323)))+P1(f332(f332(x66321,x66322),x66323))
% 52.62/52.41 [6633]~P1(f332(f332(f334(x66334),x66332),f288(x66334,x66331,x66333)))+P1(f332(f332(x66331,x66332),x66333))
% 52.62/52.41 [6715]E(f332(f43(f854(x67151,x67152)),f314(x67151,x67152,x67153,x67154)),f2(a845))+P1(f332(f64(x67152),x67154))
% 52.62/52.41 [6716]E(f332(f43(f854(x67161,x67162)),f314(x67161,x67162,x67163,x67164)),f2(a845))+P1(f332(f64(x67161),x67163))
% 52.62/52.41 [6926]~P21(x69264,x69261,x69262)+E(f332(f75(x69261,x69261,x69261,f332(x69262,x69263)),f332(x69262,x69263)),f332(x69262,x69263))
% 52.62/52.41 [7164]E(f272(x71641,x71642,x71643,x71644),f332(f241(f853(a101,f853(a839,f849(f847(x71641)))),f852(a101,a101)),f49(x71641)))+~P1(f332(f332(f232(a101),x71643),f2(a101)))
% 52.62/52.41 [7230]~P41(f332(a27,x72301),x72302,f332(a114,x72303),x72304)+P41(f332(f231(a840),f332(a30,x72301)),x72302,x72303,x72304)
% 52.62/52.41 [7266]P41(f332(a27,x72661),x72662,f332(a114,x72663),x72664)+~P41(f332(f231(a840),f332(a30,x72661)),x72662,x72663,x72664)
% 52.62/52.41 [7267]P41(f332(a27,x72671),x72672,f332(a114,x72673),x72674)+~P41(f332(f231(a840),f332(a30,x72671)),x72672,x72673,x72674)
% 52.62/52.41 [7567]~P41(f332(a27,x75674),x75673,x75672,x75671)+E(f332(a114,f494(x75671,x75672,x75673,x75674)),x75672)
% 52.62/52.41 [7837]~E(x78372,x78373)+P1(f332(f332(f334(f852(x78371,x78371)),f332(f332(f241(x78371,x78371),x78372),x78373)),f300(x78371,x78374)))
% 52.62/52.41 [7863]~P31(x78631,x78632,x78633,f239(f853(x78631,a839)))+E(f332(f79(x78631,x78632,f239(f853(x78631,a839)),x78633),f332(x78633,x78634)),x78634)
% 52.62/52.41 [7955]~P1(f332(f332(f334(f846(x79551)),f332(f332(f140(x79551),x79554),x79552)),f149(x79551,x79553)))+P1(f332(f332(f334(f846(x79551)),x79552),f149(x79551,x79553)))
% 52.62/52.41 [7956]~P1(f332(f332(f334(f846(x79561)),f332(f332(f125(x79561),x79564),x79562)),f149(x79561,x79563)))+P1(f332(f332(f334(f846(x79561)),x79562),f149(x79561,x79563)))
% 52.62/52.41 [7957]~P1(f332(f332(f334(f846(x79571)),f332(f332(f125(x79571),x79572),x79574)),f149(x79571,x79573)))+P1(f332(f332(f334(f846(x79571)),x79572),f149(x79571,x79573)))
% 52.62/52.41 [8031]~P41(f332(a27,x80311),x80312,x80314,x80313)+P41(f332(f231(a840),f332(a30,x80311)),x80312,f494(x80313,x80314,x80312,x80311),x80313)
% 52.62/52.41 [8068]P31(x80684,x80683,x80681,x80682)+E(f332(x80681,f516(x80682,x80681,x80683,x80684)),f332(x80681,f519(x80682,x80681,x80683,x80684)))
% 52.62/52.41 [8077]E(f170(x80771,x80772,x80773,x80774),f170(x80771,x80772,x80774,x80773))+~E(f332(f332(f104(f853(x80771,a839)),f169(x80771,x80772,x80773)),f169(x80771,x80772,x80774)),f180(f853(x80771,a839)))
% 52.62/52.41 [8174]~P31(x81742,x81741,x81744,x81743)+P31(x81741,x81742,f79(x81742,x81741,x81743,x81744),f332(f303(x81742,x81741,x81744),x81743))
% 52.62/52.41 [8309]P38(f852(x83092,x83094),f275(x83092,x83094,x83091,x83093))+P1(f332(x83091,f593(x83092,x83093,x83094,x83091)))
% 52.62/52.41 [8430]E(x84301,x84302)+~P1(f332(f332(f334(f852(x84303,x84303)),f332(f332(f241(x84303,x84303),x84301),x84302)),f260(x84303,x84304)))
% 52.62/52.41 [8464]~E(f332(x84641,f460(x84643,x84642,x84644,x84641)),f332(f174(x84644,x84642,x84643),f460(x84643,x84642,x84644,x84641)))+E(f332(x84641,f2(a845)),x84642)
% 52.62/52.41 [8496]~P1(f332(f64(f854(x84963,x84961)),f314(x84963,x84961,x84964,x84962)))+P1(f332(f64(x84961),x84962))
% 52.62/52.41 [8497]~P1(f332(f64(f854(x84971,x84973)),f314(x84971,x84973,x84972,x84974)))+P1(f332(f64(x84971),x84972))
% 52.62/52.41 [8498]~P1(f332(f64(f854(x84983,x84981)),f314(x84983,x84981,x84984,x84982)))+P1(f332(f64(x84981),x84982))
% 52.62/52.41 [8499]~P1(f332(f64(f854(x84991,x84993)),f314(x84991,x84993,x84992,x84994)))+P1(f332(f64(x84991),x84992))
% 52.62/52.41 [8660]P38(f852(x86601,x86602),f275(x86601,x86602,x86603,x86604))+~P38(x86602,f332(x86604,f593(x86601,x86604,x86602,x86603)))
% 52.62/52.41 [9161]E(f332(f332(f148(x91611,x91612),f737(x91613,x91614,x91612,x91611)),f738(x91613,x91614,x91612,x91611)),x91614)+~P1(f332(f332(f334(f852(f846(x91611),f846(x91611))),f332(f332(f241(f846(x91611),f846(x91611)),x91612),x91614)),f146(x91611,x91613)))
% 52.62/52.41 [9165]~P1(f332(f332(f334(f852(f846(x91651),f846(x91651))),f332(f332(f241(f846(x91651),f846(x91651)),x91652),x91653)),f135(x91651,x91654)))+P1(f332(f332(f334(f852(f846(x91651),f846(x91651))),f332(f332(f241(f846(x91651),f846(x91651)),x91652),x91653)),f137(x91651,x91654)))
% 52.62/52.41 [9262]P1(f332(f64(x92621),x92622))+~P1(f332(f332(f334(f852(f853(x92621,a839),f853(x92621,a839))),f332(f332(f241(f853(x92621,a839),f853(x92621,a839)),x92623),x92622)),f325(x92621,x92624)))
% 52.62/52.41 [9263]P1(f332(f64(x92631),x92632))+~P1(f332(f332(f334(f852(f853(x92631,a839),f853(x92631,a839))),f332(f332(f241(f853(x92631,a839),f853(x92631,a839)),x92632),x92633)),f325(x92631,x92634)))
% 52.62/52.41 [9266]~E(x92661,f180(f853(x92662,a839)))+~P1(f332(f332(f334(f852(f853(x92662,a839),f853(x92662,a839))),f332(f332(f241(f853(x92662,a839),f853(x92662,a839)),x92663),x92661)),f325(x92662,x92664)))
% 52.62/52.41 [9883]P18(x98831,x98832,x98833,x98834)+~P1(f332(f332(f251(x98831,x98831,a839),f332(f332(f9(x98831,f853(x98831,x98832),f853(x98831,a839)),f332(f332(f10(f853(x98832,a839),f853(f853(x98831,x98832),f853(x98831,a839)),x98831),f10(x98832,a839,x98831)),f332(f332(f10(x98832,f853(x98832,a839),x98831),a329),x98834))),x98834)),f499(x98834,x98833,x98832,x98831)))
% 52.62/52.41 [4847]~E(x48474,f115(x48471))+E(f332(f332(f143(x48471,x48472),x48473),x48474),f115(x48472))
% 52.62/52.41 [4848]~E(x48484,f115(x48481))+E(f332(f332(f143(x48481,x48482),x48483),x48484),f115(x48482))
% 52.62/52.41 [4849]~E(x48494,f183(x48491))+E(f332(f332(f196(x48491,x48492),x48493),x48494),f183(x48492))
% 52.62/52.41 [4850]~E(x48502,f115(x48501))+E(f332(f332(f148(x48501,x48502),x48503),x48504),f115(x48501))
% 52.62/52.41 [5086]E(x50861,f115(x50862))+~E(f332(f332(f143(x50862,x50863),x50864),x50861),f115(x50863))
% 52.62/52.41 [5087]E(x50871,f183(x50872))+~E(f332(f332(f196(x50872,x50873),x50874),x50871),f183(x50873))
% 52.62/52.41 [5088]E(x50881,f115(x50882))+~E(f332(f332(f143(x50882,x50883),x50884),x50881),f115(x50883))
% 52.62/52.41 [5089]E(x50891,f115(x50892))+~E(f332(f332(f148(x50892,x50891),x50893),x50894),f115(x50892))
% 52.62/52.41 [5119]E(x51191,x51192)+~E(f332(f332(f125(x51193),x51194),x51191),f332(f332(f125(x51193),x51194),x51192))
% 52.62/52.41 [5120]E(x51201,x51202)+~E(f332(f332(f125(x51203),x51201),x51204),f332(f332(f125(x51203),x51202),x51204))
% 52.62/52.41 [5263]P1(f332(x52633,x52632))+E(f151(x52631,x52632,f332(f126(x52631,x52633),x52634)),f332(f126(x52631,x52633),x52634))
% 52.62/52.41 [5274]E(x52741,x52742)+~E(f130(a845,f332(f294(a845,x52741),x52743)),f332(f332(f140(a845),x52742),x52744))
% 52.62/52.41 [5321]~P32(x53212,x53213)+P32(x53211,f332(f332(f76(x53212,x53211),x53213),x53214))
% 52.62/52.41 [5322]~P38(x53222,x53223)+P38(x53221,f332(f332(f280(x53222,x53221),x53223),x53224))
% 52.62/52.41 [5531]~E(x55311,f115(x55312))+~E(f332(f332(f125(x55312),x55313),f332(f332(f140(x55312),x55314),f115(x55312))),x55311)
% 52.62/52.41 [5564]E(f134(x55641,x55642),x55643)+~E(f332(f332(f125(x55641),x55644),f332(f332(f140(x55641),x55643),f115(x55641))),x55642)
% 52.62/52.41 [5565]E(f116(x55651,x55652),x55653)+~E(f332(f332(f125(x55651),x55653),f332(f332(f140(x55651),x55654),f115(x55651))),x55652)
% 52.62/52.41 [5673]~E(f130(a845,f332(f294(a845,x56731),x56732)),f332(f332(f140(a845),x56733),x56734))+P1(f332(f332(f233(a845),x56731),x56732))
% 52.62/52.41 [5772]~E(f332(f106(a845),x57724),f2(a845))+E(f332(f332(f152(x57721),f332(f332(f140(x57721),x57722),x57723)),f332(f106(a845),x57724)),x57722)
% 52.62/52.41 [5880]E(x58801,f332(f332(f125(x58802),f332(f142(x58802),x58803)),f332(f332(f140(x58802),x58804),f115(x58802))))+~E(f332(f142(x58802),x58801),f332(f332(f140(x58802),x58804),x58803))
% 52.62/52.41 [6064]~P99(x60641)+E(f332(f332(f104(f853(x60641,a839)),f332(f294(x60641,x60642),x60643)),f332(f294(x60641,x60643),x60644)),f180(f853(x60641,a839)))
% 52.62/52.41 [6099]~P4(x60991)+E(f332(f154(x60991),f332(f332(f143(a1,x60991),x60992),f163(x60993,x60994))),f332(f332(f8(a1,x60991),x60992),f332(f158(a1),f163(x60993,x60994))))
% 52.62/52.41 [6100]~P4(x61001)+E(f332(f332(f8(a1,x61001),x61002),f332(f158(a1),f163(x61003,x61004))),f332(f154(x61001),f332(f332(f143(a1,x61001),x61002),f163(x61003,x61004))))
% 52.62/52.41 [6249]~E(x62492,f332(f332(f125(x62491),f332(f142(x62491),x62494)),f332(f332(f140(x62491),x62493),f115(x62491))))+E(f332(f142(x62491),x62492),f332(f332(f140(x62491),x62493),x62494))
% 52.62/52.41 [6265]~P25(x62652,x62653,x62654,x62651)+E(f332(x62651,f180(f853(x62652,a839))),f39(x62653))
% 52.62/52.41 [6295]~P99(x62951)+E(f332(f332(f104(f853(x62951,a839)),f298(x62951,x62952,x62953)),f332(f294(x62951,x62953),x62954)),f180(f853(x62951,a839)))
% 52.62/52.41 [6381]~P41(x63811,x63812,x63814,x63813)+P1(f332(f332(f187(x63811),x63812),x63813))
% 52.62/52.41 [6382]~P41(x63821,x63822,x63824,x63823)+P1(f332(f332(f187(x63821),x63822),x63823))
% 52.62/52.41 [6516]E(x65161,f180(f853(x65162,a839)))+~E(f314(x65163,x65162,x65164,x65161),f180(f853(f854(x65163,x65162),a839)))
% 52.62/52.41 [6517]E(x65171,f180(f853(x65172,a839)))+~E(f314(x65172,x65173,x65171,x65174),f180(f853(f854(x65172,x65173),a839)))
% 52.62/52.41 [6596]~P1(f332(f247(x65963,x65964,x65961),x65962))+P1(f332(f332(x65961,f592(x65962,x65961)),x65962))
% 52.62/52.41 [6626]E(f332(f106(a845),x66261),f2(a845))+E(f332(f332(f152(x66262),f332(f332(f140(x66262),x66263),x66264)),f332(f106(a845),x66261)),f332(f332(f152(x66262),x66264),f332(f332(f3(a845),f332(f106(a845),x66261)),f80(a845))))
% 52.62/52.41 [6644]~P1(f332(f64(x66442),x66444))+P1(f332(f64(x66441),f332(f303(x66442,x66441,x66443),x66444)))
% 52.62/52.41 [6885]~P31(x68852,x68851,x68853,x68854)+E(f332(f43(x68851),f332(f303(x68852,x68851,x68853),x68854)),f332(f43(x68852),x68854))
% 52.62/52.41 [6905]E(f332(f303(x69051,x69052,x69053),f332(f305(x69051,x69052,x69053),x69054)),x69054)+~E(f332(f303(x69051,x69052,x69053),f239(f853(x69051,a839))),f239(f853(x69052,a839)))
% 52.62/52.41 [7331]~P31(x73311,x73312,x73313,f239(f853(x73311,a839)))+E(f332(f305(x73311,x73312,x73313),f332(f303(x73311,x73312,x73313),x73314)),x73314)
% 52.62/52.41 [7671]P1(f332(x76711,x76712))+~P1(f332(f332(f334(x76713),x76712),f332(f158(x76713),f162(x76713,x76711,x76714))))
% 52.62/52.41 [7781]~P1(f332(f332(f334(f846(x77811)),f332(f332(f140(x77811),x77812),x77814)),f149(x77811,x77813)))+P1(f332(f332(f334(x77811),x77812),x77813))
% 52.62/52.41 [7908]~P1(f332(f332(f334(x79081),x79082),f332(f158(x79081),f151(x79081,x79084,x79083))))+P1(f332(f332(f334(x79081),x79082),f332(f158(x79081),x79083)))
% 52.62/52.41 [7909]~P1(f332(f332(f334(x79091),x79092),f332(f158(x79091),f160(x79091,x79093,x79094))))+P1(f332(f332(f334(x79091),x79092),f332(f158(x79091),x79093)))
% 52.62/52.41 [7910]~P1(f332(f332(f334(x79101),x79102),f332(f158(x79101),f160(x79101,x79103,x79104))))+P1(f332(f332(f334(x79101),x79102),f332(f158(x79101),x79103)))
% 52.62/52.41 [7911]~P1(f332(f332(f334(x79111),x79112),f332(f158(x79111),f162(x79111,x79114,x79113))))+P1(f332(f332(f334(x79111),x79112),f332(f158(x79111),x79113)))
% 52.62/52.41 [8124]E(f332(f332(f152(x81241),f162(x81241,x81242,x81243)),x81244),f332(f332(f152(x81241),x81243),x81244))+~P1(f332(f332(f233(a845),x81244),f332(f181(f846(x81241)),f162(x81241,x81242,x81243))))
% 52.62/52.41 [8207]~P4(x82071)+E(f332(f332(f8(a845,x82071),f332(f332(f10(a845,x82071,a845),x82072),a114)),f332(f294(a845,x82073),x82074)),f332(f332(f8(a845,x82071),x82072),f332(f294(a845,f332(a114,x82073)),f332(a114,x82074))))
% 52.62/52.41 [8216]~P4(x82161)+E(f332(f332(f8(a845,x82161),f332(f332(f10(a845,x82161,a845),x82162),a114)),f295(a845,x82163,x82164)),f332(f332(f8(a845,x82161),x82162),f295(a845,f332(a114,x82163),f332(a114,x82164))))
% 52.62/52.41 [8348]~P31(x83481,x83483,x83484,f239(f853(x83481,a839)))+P31(x83481,f853(x83482,x83483),f332(f332(f10(x83483,f853(x83482,x83483),x83481),f18(x83483,x83482)),x83484),f239(f853(x83481,a839)))
% 52.62/52.41 [8439]~P31(x84392,x84391,x84394,x84393)+E(f332(f303(x84391,x84392,f79(x84392,x84391,x84393,x84394)),f332(f303(x84392,x84391,x84394),x84393)),x84393)
% 52.62/52.41 [8500]~P1(f332(f332(f334(f852(x85001,x85001)),f332(f332(f241(x85001,x85001),x85002),x85004)),f260(x85001,x85003)))+P1(f332(f332(f334(x85001),x85002),x85003))
% 52.62/52.41 [8575]E(f332(f332(f332(f74(x85751,f849(x85752)),f332(f18(f849(x85752),x85751),f183(x85752))),x85753),f332(f227(x85752),f529(x85753,x85754,x85752,x85751))),x85754)+~E(f169(x85751,x85752,x85754),f332(f332(f302(x85751),x85753),f180(f853(x85751,a839))))
% 52.62/52.41 [8693]~E(f332(f332(f8(x86931,a845),x86934),x86933),f332(a114,x86932))+P1(f332(f332(f334(x86931),f358(x86932,x86933,x86934,x86931)),x86933))
% 52.62/52.41 [8709]~E(f332(f332(f8(x87094,a845),x87091),x87093),f332(a114,x87092))+P1(f332(f332(f233(a845),f2(a845)),f332(x87091,f358(x87092,x87093,x87091,x87094))))
% 52.62/52.41 [8719]~P1(f332(f64(x87192),x87194))+P1(f332(f332(f232(a845),f332(f43(x87191),f332(f303(x87192,x87191,x87193),x87194))),f332(f43(x87192),x87194)))
% 52.62/52.41 [8720]E(f332(f332(f241(x87201,x87202),f700(x87203,x87204,x87202,x87201)),f701(x87203,x87204,x87202,x87201)),x87204)+~P1(f332(f332(f334(f852(x87201,x87202)),x87204),f332(f278(x87202,x87201),x87203)))
% 52.62/52.41 [8729]P31(x87291,x87292,x87293,x87294)+P1(f332(f332(f334(x87291),f516(x87294,x87293,x87292,x87291)),x87294))
% 52.62/52.41 [8730]P31(x87301,x87302,x87303,x87304)+P1(f332(f332(f334(x87301),f519(x87304,x87303,x87302,x87301)),x87304))
% 52.62/52.41 [8783]P18(x87831,x87832,x87833,x87834)+P1(f332(f332(f334(f852(x87831,x87831)),f499(x87834,x87833,x87832,x87831)),x87833))
% 52.62/52.41 [8830]P1(f332(x88301,x88302))+~P1(f332(x88301,f332(f332(f241(x88303,x88304),f826(x88304,x88303,x88301)),f827(x88304,x88303,x88301))))
% 52.62/52.41 [8843]E(f332(f181(f846(x88431)),x88432),f332(f181(f846(x88431)),x88433))+~P1(f332(f332(f334(f852(f846(x88431),f846(x88431))),f332(f332(f241(f846(x88431),f846(x88431)),x88432),x88433)),f135(x88431,x88434)))
% 52.62/52.41 [8844]E(f332(f181(f846(x88441)),x88442),f332(f181(f846(x88441)),x88443))+~P1(f332(f332(f334(f852(f846(x88441),f846(x88441))),f332(f332(f241(f846(x88441),f846(x88441)),x88442),x88443)),f147(x88441,x88444)))
% 52.62/52.41 [8845]E(f332(f181(f846(x88451)),x88452),f332(f181(f846(x88451)),x88453))+~P1(f332(f332(f334(f852(f846(x88451),f846(x88451))),f332(f332(f241(f846(x88451),f846(x88451)),x88452),x88453)),f147(x88451,x88454)))
% 52.62/52.41 [8846]E(f332(f181(f846(x88461)),x88462),f332(f181(f846(x88461)),x88463))+~P1(f332(f332(f334(f852(f846(x88461),f846(x88461))),f332(f332(f241(f846(x88461),f846(x88461)),x88462),x88463)),f147(x88461,x88464)))
% 52.62/52.41 [8847]E(f332(f181(f846(x88471)),x88472),f332(f181(f846(x88471)),x88473))+~P1(f332(f332(f334(f852(f846(x88471),f846(x88471))),f332(f332(f241(f846(x88471),f846(x88471)),x88472),x88473)),f146(x88471,x88474)))
% 52.62/52.41 [8920]P1(f332(f332(f232(a845),f144(x89201,x89202,x89203)),f144(x89201,x89204,x89203)))+P1(f332(f332(f334(x89201),f757(x89204,x89202,x89203,x89201)),f332(f158(x89201),x89203)))
% 52.62/52.41 [8921]E(f332(f181(f846(x89211)),x89212),f332(f181(f846(x89211)),x89213))+~P1(f332(f332(f334(f852(f846(x89211),f846(x89211))),f332(f332(f241(f846(x89211),f846(x89211)),x89212),x89213)),f300(f846(x89211),f146(x89211,x89214))))
% 52.62/52.41 [9033]P1(f332(f332(f279(a845),x90331),x90332))+P1(f332(f332(f232(f853(a845,a839)),f282(a845,f279(a845),x90331,x90332)),f282(a845,f279(a845),x90333,x90334)))
% 52.62/52.41 [9141]~P31(x91411,x91412,x91413,x91414)+~P1(f332(f332(f233(a845),f332(f43(x91412),f332(f303(x91411,x91412,x91413),x91414))),f332(f43(x91411),x91414)))
% 52.62/52.41 [9171]~P1(f332(f332(f334(f852(f846(x91711),f846(x91711))),f332(f332(f241(f846(x91711),f846(x91711)),x91712),x91713)),f146(x91711,x91714)))+P1(f332(f332(f334(f852(f846(x91711),f846(x91711))),f332(f332(f241(f846(x91711),f846(x91711)),x91712),x91713)),f147(x91711,f300(x91711,x91714))))
% 52.62/52.41 [9174]~P1(f332(f332(f334(f852(f846(x91741),f846(x91741))),f332(f332(f241(f846(x91741),f846(x91741)),x91742),x91743)),f147(x91741,x91744)))+P1(f332(f332(f334(f852(f846(x91741),f846(x91741))),f332(f332(f241(f846(x91741),f846(x91741)),x91742),x91743)),f300(f846(x91741),f146(x91741,x91744))))
% 52.62/52.41 [9189]P1(f332(f332(f334(f852(x91891,x91891)),f332(f332(f241(x91891,x91891),x91892),x91893)),f300(x91891,x91894)))+~P1(f332(f332(f334(f852(x91891,x91891)),f332(f332(f241(x91891,x91891),x91892),x91893)),f332(f332(f281(x91891,x91891,x91891),x91894),f300(x91891,x91894))))
% 52.62/52.41 [9258]P1(f332(f332(f279(a845),x92581),x92582))+~P1(f332(f332(f233(f853(a845,a839)),f282(a845,f279(a845),x92583,x92584)),f282(a845,f279(a845),x92581,x92582)))
% 52.62/52.41 [9370]E(f332(f332(f125(x93701),f741(x93702,x93703,x93704,x93701)),f332(f332(f140(x93701),f742(x93702,x93703,x93704,x93701)),f744(x93702,x93703,x93704,x93701))),x93704)+~P1(f332(f332(f334(f852(f846(x93701),f846(x93701))),f332(f332(f241(f846(x93701),f846(x93701)),x93704),x93703)),f146(x93701,x93702)))
% 52.62/52.41 [9371]E(f332(f332(f125(x93711),f741(x93712,x93713,x93714,x93711)),f332(f332(f140(x93711),f743(x93712,x93713,x93714,x93711)),f744(x93712,x93713,x93714,x93711))),x93713)+~P1(f332(f332(f334(f852(f846(x93711),f846(x93711))),f332(f332(f241(f846(x93711),f846(x93711)),x93714),x93713)),f146(x93711,x93712)))
% 52.62/52.41 [9444]P1(f332(f332(f334(f852(x94441,x94441)),f332(f332(f241(x94441,x94441),x94442),f654(x94443,x94444,x94442,x94441))),f300(x94441,x94443)))+~P1(f332(f332(f334(f852(x94441,x94441)),f332(f332(f241(x94441,x94441),x94442),x94444)),f332(f332(f281(x94441,x94441,x94441),x94443),f300(x94441,x94443))))
% 52.62/52.41 [9509]P1(f332(f332(f232(a845),f144(x95091,x95092,x95093)),f144(x95091,x95094,x95093)))+~P1(f332(f332(f233(a845),f332(x95092,f757(x95094,x95092,x95093,x95091))),f332(x95094,f757(x95094,x95092,x95093,x95091))))
% 52.62/52.41 [9575]P1(f332(f332(f334(f852(x95751,x95751)),f332(f332(f241(x95751,x95751),f653(x95752,x95753,x95754,x95751)),x95753)),f300(x95751,x95752)))+~P1(f332(f332(f334(f852(x95751,x95751)),f332(f332(f241(x95751,x95751),x95754),x95753)),f332(f332(f281(x95751,x95751,x95751),x95752),f300(x95751,x95752))))
% 52.62/52.41 [5099]~E(x50992,x50993)+E(f151(x50991,x50992,f332(f332(f140(x50991),x50993),x50994)),x50994)
% 52.62/52.41 [5113]~E(x51132,f2(a845))+E(f332(f332(f159(x51131),x51132),f332(f332(f140(x51131),x51133),x51134)),f115(x51131))
% 52.62/52.41 [5220]P1(f332(x52202,x52203))+E(f162(x52201,x52202,f332(f332(f140(x52201),x52203),x52204)),f115(x52201))
% 52.62/52.41 [5285]~P85(x52852)+E(f332(f332(f81(f853(x52851,x52852)),x52853),x52854),f332(f81(x52852),f332(x52853,x52854)))
% 52.62/52.41 [5286]~P85(x52862)+E(f332(f332(f81(f853(x52861,x52862)),x52863),x52864),f332(f81(x52862),f332(x52863,x52864)))
% 52.62/52.41 [5298]~E(x52982,f2(a845))+E(f332(f332(f128(x52981),x52982),f332(f332(f140(x52981),x52983),x52984)),f332(f332(f140(x52981),x52983),x52984))
% 52.62/52.41 [5299]P1(f332(x52992,x52993))+E(f332(f126(x52991,x52992),f332(f332(f140(x52991),x52993),x52994)),f332(f126(x52991,x52992),x52994))
% 52.62/52.41 [5432]~E(x54322,x54324)+P1(f332(f332(f332(f302(x54321),x54322),x54323),x54324))
% 52.62/52.41 [5440]E(x54401,f115(x54402))+E(f134(x54403,f332(f332(f143(x54402,x54403),x54404),x54401)),f332(x54404,f134(x54402,x54401)))
% 52.62/52.41 [5451]~E(x54511,f66(x54512,x54514))+E(f332(x54511,f332(f332(f302(x54512),x54513),f180(f853(x54512,a839)))),x54513)
% 52.62/52.41 [5466]~E(f332(f106(a845),x54662),f2(a845))+E(f332(f332(f159(x54661),f332(f106(a845),x54662)),f332(f332(f140(x54661),x54663),x54664)),f115(x54661))
% 52.62/52.41 [5486]E(x54861,f115(x54862))+E(f332(f131(x54863),f332(f332(f143(x54862,x54863),x54864),x54861)),f332(x54864,f332(f131(x54862),x54861)))
% 52.62/52.41 [5583]~P1(f332(x55833,x55834))+P1(f332(f332(f332(f302(x55831),x55832),x55833),x55834))
% 52.62/52.41 [5690]~E(f332(f106(a845),x56902),f2(a845))+E(f332(f332(f128(x56901),f332(f106(a845),x56902)),f332(f332(f140(x56901),x56903),x56904)),f332(f332(f140(x56901),x56903),x56904))
% 52.62/52.41 [5708]~P24(x57082,x57084,x57081)+E(f332(x57081,f332(f332(f302(x57082),x57083),f180(f853(x57082,a839)))),x57083)
% 52.62/52.41 [5732]~E(x57322,x57323)+P1(f332(f332(f334(x57321),x57322),f332(f332(f302(x57321),x57323),x57324)))
% 52.62/52.41 [5733]~E(x57332,x57333)+P1(f332(f332(f334(x57331),x57332),f332(f332(f302(x57331),x57333),x57334)))
% 52.62/52.41 [5737]~P73(x57371)+E(f332(f332(f82(x57371),x57372),f332(f332(f82(x57371),x57373),x57374)),f332(f332(f82(x57371),x57373),f332(f332(f82(x57371),x57372),x57374)))
% 52.62/52.41 [5738]~P73(x57381)+E(f332(f332(f83(x57381),x57382),f332(f332(f83(x57381),x57383),x57384)),f332(f332(f83(x57381),x57383),f332(f332(f83(x57381),x57382),x57384)))
% 52.62/52.41 [5739]~P100(x57391)+E(f332(f332(f236(x57391),x57392),f332(f332(f236(x57391),x57393),x57394)),f332(f332(f236(x57391),x57393),f332(f332(f236(x57391),x57392),x57394)))
% 52.62/52.41 [5740]~P100(x57401)+E(f332(f332(f236(x57401),x57402),f332(f332(f236(x57401),x57403),x57404)),f332(f332(f236(x57401),x57403),f332(f332(f236(x57401),x57402),x57404)))
% 52.62/52.41 [5741]~P100(x57411)+E(f332(f332(f179(x57411),x57412),f332(f332(f179(x57411),x57413),x57414)),f332(f332(f179(x57411),x57413),f332(f332(f179(x57411),x57412),x57414)))
% 52.62/52.41 [5742]~P100(x57421)+E(f332(f332(f179(x57421),x57422),f332(f332(f179(x57421),x57423),x57424)),f332(f332(f179(x57421),x57423),f332(f332(f179(x57421),x57422),x57424)))
% 52.62/52.41 [5743]~P92(x57431)+E(f332(f332(f103(x57431),x57432),f332(f332(f103(x57431),x57433),x57434)),f332(f332(f103(x57431),x57433),f332(f332(f103(x57431),x57432),x57434)))
% 52.62/52.41 [5744]~P92(x57441)+E(f332(f332(f103(x57441),x57442),f332(f332(f103(x57441),x57443),x57444)),f332(f332(f103(x57441),x57443),f332(f332(f103(x57441),x57442),x57444)))
% 52.62/52.41 [5745]~P93(x57451)+E(f332(f332(f103(x57451),x57452),f332(f332(f103(x57451),x57453),x57454)),f332(f332(f103(x57451),x57453),f332(f332(f103(x57451),x57452),x57454)))
% 52.62/52.41 [5746]~P93(x57461)+E(f332(f332(f104(x57461),x57462),f332(f332(f104(x57461),x57463),x57464)),f332(f332(f104(x57461),x57463),f332(f332(f104(x57461),x57462),x57464)))
% 52.62/52.41 [5747]~P98(x57471)+E(f332(f332(f104(x57471),x57472),f332(f332(f104(x57471),x57473),x57474)),f332(f332(f104(x57471),x57473),f332(f332(f104(x57471),x57472),x57474)))
% 52.62/52.41 [5748]~P98(x57481)+E(f332(f332(f104(x57481),x57482),f332(f332(f104(x57481),x57483),x57484)),f332(f332(f104(x57481),x57483),f332(f332(f104(x57481),x57482),x57484)))
% 52.62/52.41 [5755]E(x57551,x57552)+E(f151(x57553,x57551,f332(f332(f140(x57553),x57552),x57554)),f332(f332(f140(x57553),x57552),f151(x57553,x57551,x57554)))
% 52.62/52.41 [5770]~P1(f332(x57702,x57703))+E(f332(f126(x57701,x57702),f332(f332(f140(x57701),x57703),x57704)),f332(f332(f140(x57701),x57703),f332(f126(x57701,x57702),x57704)))
% 52.62/52.41 [5856]~E(x58564,f180(f853(x58561,a839)))+E(f332(f303(x58561,x58562,f332(f18(x58562,x58561),x58563)),x58564),f180(f853(x58562,a839)))
% 52.62/52.41 [5901]~P1(f332(x59012,x59013))+E(f162(x59011,x59012,f332(f332(f140(x59011),x59013),x59014)),f332(f332(f140(x59011),x59013),f162(x59011,x59012,x59014)))
% 52.62/52.41 [5954]P30(x59541,x59542,x59543)+~P30(x59541,x59542,f332(f332(f302(f844(x59541)),x59544),x59543))
% 52.62/52.41 [5967]E(x59671,f180(f853(x59672,a839)))+E(f332(f332(f47(x59672,f853(x59673,a839)),x59671),f332(f18(f853(x59673,a839),x59672),x59674)),x59674)
% 52.62/52.41 [5968]E(x59681,f180(f853(x59682,a839)))+E(f332(f332(f48(x59682,f853(x59683,a839)),x59681),f332(f18(f853(x59683,a839),x59682),x59684)),x59684)
% 52.62/52.41 [5977]~E(x59774,f180(f853(x59772,a839)))+E(f332(f332(f248(x59771,x59772),x59773),f332(f18(f853(x59772,a839),x59771),x59774)),f180(f853(f852(x59771,x59772),a839)))
% 52.62/52.41 [5978]~E(x59783,f180(f853(x59781,a839)))+E(f332(f332(f248(x59781,x59782),x59783),f332(f18(f853(x59782,a839),x59781),x59784)),f180(f853(f852(x59781,x59782),a839)))
% 52.62/52.41 [6029]E(x60291,f2(a845))+E(f332(f332(f128(x60292),x60291),f332(f332(f140(x60292),x60293),x60294)),f332(f332(f128(x60292),f332(f332(f3(a845),x60291),f80(a845))),x60294))
% 52.62/52.41 [6056]E(x60561,f180(f853(x60562,a839)))+E(f332(f303(x60562,x60563,f332(f18(x60563,x60562),x60564)),x60561),f332(f332(f302(x60563),x60564),f180(f853(x60563,a839))))
% 52.62/52.41 [6059]E(f332(f305(x60591,x60592,f332(f18(x60592,x60591),x60593)),x60594),f180(f853(x60591,a839)))+P1(f332(f332(f334(x60592),x60593),x60594))
% 52.62/52.41 [6128]~E(x61283,f180(f853(x61281,a839)))+E(f332(f332(f47(x61281,f853(x61282,a839)),x61283),f332(f18(f853(x61282,a839),x61281),x61284)),f180(f853(x61282,a839)))
% 52.62/52.41 [6129]~E(x61293,f180(f853(x61291,a839)))+E(f332(f332(f48(x61291,f853(x61292,a839)),x61293),f332(f18(f853(x61292,a839),x61291),x61294)),f239(f853(x61292,a839)))
% 52.62/52.41 [6131]~P9(x61311)+E(f53(x61311,f332(f332(f83(x61311),x61312),x61313),f332(f332(f83(x61311),x61312),x61314)),f332(f332(f83(x61311),x61312),f53(x61311,x61313,x61314)))
% 52.62/52.41 [6305]E(f332(f305(x63051,x63052,f332(f18(x63052,x63051),x63053)),x63054),f239(f853(x63051,a839)))+~P1(f332(f332(f334(x63052),x63053),x63054))
% 52.62/52.41 [6326]~P1(f332(f332(f334(x63261),x63262),x63264))+P1(f332(f332(f334(x63261),x63262),f332(f332(f302(x63261),x63263),x63264)))
% 52.62/52.41 [6327]~P1(f332(f332(f334(x63271),x63272),x63274))+P1(f332(f332(f334(x63271),x63272),f332(f332(f302(x63271),x63273),x63274)))
% 52.62/52.41 [6328]~P1(f332(f332(f334(x63281),x63282),x63284))+P1(f332(f332(f334(x63281),x63282),f332(f332(f302(x63281),x63283),x63284)))
% 52.62/52.41 [6341]~E(x63413,f332(f332(f3(a845),f332(f181(f846(x63411)),x63412)),f80(a845)))+E(f116(x63411,f332(f332(f148(x63411,x63412),x63413),x63414)),f116(x63411,x63412))
% 52.62/52.41 [6366]~P100(x63661)+E(f332(f332(f104(f853(x63661,a839)),f332(f293(x63661),x63662)),f295(x63661,x63663,x63664)),f295(x63661,x63663,f332(f332(f236(x63661),x63662),x63664)))
% 52.62/52.41 [6367]~P100(x63671)+E(f332(f332(f104(f853(x63671,a839)),f332(f258(x63671),x63672)),f295(x63671,x63673,x63674)),f295(x63671,f332(f332(f179(x63671),x63672),x63673),x63674))
% 52.62/52.41 [6383]E(f332(f332(f104(f853(x63831,a839)),x63832),f332(f332(f302(x63831),x63833),x63834)),f332(f332(f104(f853(x63831,a839)),x63832),x63834))+P1(f332(f332(f334(x63831),x63833),x63832))
% 52.62/52.41 [6384]E(f332(f332(f104(f853(x63841,a839)),x63842),f332(f332(f302(x63841),x63843),x63844)),f332(f332(f104(f853(x63841,a839)),x63842),x63844))+P1(f332(f332(f334(x63841),x63843),x63842))
% 52.62/52.41 [6396]E(f151(x63961,x63962,f332(f332(f125(x63961),x63963),x63964)),f332(f332(f125(x63961),x63963),f151(x63961,x63962,x63964)))+P1(f332(f332(f334(x63961),x63962),f332(f158(x63961),x63963)))
% 52.62/52.41 [6401]~P76(x64011)+E(f332(f332(f83(x64011),f332(f332(f242(x64011),x64012),x64013)),f332(f332(f242(x64011),x64012),x64014)),f332(f332(f242(x64011),x64012),f332(f332(f82(a845),x64013),x64014)))
% 52.62/52.41 [6402]~P73(x64021)+E(f332(f332(f83(x64021),f332(f332(f242(x64021),x64022),x64023)),f332(f332(f242(x64021),x64022),x64024)),f332(f332(f242(x64021),x64022),f332(f332(f82(a845),x64023),x64024)))
% 52.62/52.41 [6438]~P73(x64381)+E(f332(f332(f82(x64381),f332(f332(f83(x64381),x64382),x64383)),f332(f332(f83(x64381),x64382),x64384)),f332(f332(f83(x64381),x64382),f332(f332(f82(x64381),x64383),x64384)))
% 52.62/52.41 [6439]~P100(x64391)+E(f332(f332(f179(x64391),f332(f332(f236(x64391),x64392),x64393)),f332(f332(f236(x64391),x64392),x64394)),f332(f332(f236(x64391),x64392),f332(f332(f179(x64391),x64393),x64394)))
% 52.62/52.41 [6440]~P100(x64401)+E(f332(f332(f236(x64401),f332(f332(f179(x64401),x64402),x64403)),f332(f332(f179(x64401),x64402),x64404)),f332(f332(f179(x64401),x64402),f332(f332(f236(x64401),x64403),x64404)))
% 52.62/52.41 [6441]~P97(x64411)+E(f332(f332(f104(x64411),f332(f332(f103(x64411),x64412),x64413)),f332(f332(f103(x64411),x64412),x64414)),f332(f332(f103(x64411),x64412),f332(f332(f104(x64411),x64413),x64414)))
% 52.62/52.41 [6442]~P97(x64421)+E(f332(f332(f103(x64421),f332(f332(f104(x64421),x64422),x64423)),f332(f332(f104(x64421),x64422),x64424)),f332(f332(f104(x64421),x64422),f332(f332(f103(x64421),x64423),x64424)))
% 52.62/52.41 [6479]~P9(x64791)+E(f53(x64791,f332(f332(f83(x64791),x64792),x64793),f332(f332(f83(x64791),x64794),x64793)),f332(f332(f83(x64791),f53(x64791,x64792,x64794)),x64793))
% 52.62/52.41 [6482]~E(f332(f181(f846(x64821)),x64823),f332(f181(f846(x64822)),x64824))+E(f332(f332(f143(f852(x64821,x64822),x64822),f250(x64821,x64822)),f332(f332(f167(x64821,x64822),x64823),x64824)),x64824)
% 52.62/52.41 [6483]~E(f332(f181(f846(x64831)),x64833),f332(f181(f846(x64832)),x64834))+E(f332(f332(f143(f852(x64831,x64832),x64831),f240(x64831,x64832)),f332(f332(f167(x64831,x64832),x64833),x64834)),x64833)
% 52.62/52.41 [6493]~P9(x64931)+E(f53(x64931,f332(f332(f82(x64931),x64932),f53(x64931,x64933,x64934)),x64934),f53(x64931,f332(f332(f82(x64931),x64932),x64933),x64934))
% 52.62/52.41 [6494]~P9(x64941)+E(f53(x64941,f332(f332(f83(x64941),x64942),f53(x64941,x64943,x64944)),x64944),f53(x64941,f332(f332(f83(x64941),x64942),x64943),x64944))
% 52.62/52.41 [6495]~P10(x64951)+E(f53(x64951,f332(f332(f3(x64951),x64952),f53(x64951,x64953,x64954)),x64954),f53(x64951,f332(f332(f3(x64951),x64952),x64953),x64954))
% 52.62/52.41 [6496]~P9(x64961)+E(f53(x64961,f332(f332(f82(x64961),x64962),f53(x64961,x64963,x64964)),x64964),f53(x64961,f332(f332(f82(x64961),x64962),x64963),x64964))
% 52.62/52.41 [6579]~P100(x65791)+E(f332(f332(f104(f853(x65791,a839)),f295(x65791,x65792,x65793)),f332(f293(x65791),x65794)),f295(x65791,x65792,f332(f332(f236(x65791),x65793),x65794)))
% 52.62/52.41 [6580]~P100(x65801)+E(f332(f332(f104(f853(x65801,a839)),f295(x65801,x65802,x65803)),f332(f258(x65801),x65804)),f295(x65801,f332(f332(f179(x65801),x65802),x65804),x65803))
% 52.62/52.41 [6583]~E(f332(f181(f846(x65831)),x65833),f332(f181(f846(x65832)),x65834))+E(f332(f332(f167(x65831,x65832),f332(f142(x65831),x65833)),f332(f142(x65832),x65834)),f332(f142(f852(x65831,x65832)),f332(f332(f167(x65831,x65832),x65833),x65834)))
% 52.62/52.41 [6592]E(x65921,f332(f332(f3(a845),f332(f181(f846(x65922)),x65923)),f80(a845)))+E(f116(x65922,f332(f332(f148(x65922,x65923),x65921),x65924)),f332(f332(f148(x65922,f116(x65922,x65923)),x65921),x65924))
% 52.62/52.41 [6609]~P1(f332(f127(x66092),x66094))+P1(f332(f127(f852(x66091,x66092)),f332(f332(f167(x66091,x66092),x66093),x66094)))
% 52.62/52.41 [6610]~P1(f332(f127(x66101),x66103))+P1(f332(f127(f852(x66101,x66102)),f332(f332(f167(x66101,x66102),x66103),x66104)))
% 52.62/52.41 [6708]E(x67081,f332(f332(f332(a189,x67082),x67083),f332(x67084,x67082)))+~P1(f332(f332(f187(f28(x67083,x67084)),x67082),x67081))
% 52.62/52.41 [6888]E(f332(f332(f44(a845),x68881),x68882),x68883)+~P1(f332(f56(x68881,x68882),f332(f332(f241(a845,a845),x68883),x68884)))
% 52.62/52.41 [6914]E(f53(a845,x69141,x69142),x69143)+~P1(f332(f56(x69141,x69142),f332(f332(f241(a845,a845),x69144),x69143)))
% 52.62/52.41 [6917]P1(f332(f127(x69171),x69172))+~P1(f332(f127(x69173),f332(f332(f143(x69171,x69173),x69174),x69172)))
% 52.62/52.41 [6925]~P30(x69251,x69252,f332(f332(f302(f844(x69251)),x69253),x69254))+P30(x69251,x69252,f332(f332(f302(f844(x69251)),x69253),f180(f853(f844(x69251),a839))))
% 52.62/52.41 [6997]E(f151(x69971,x69972,f332(f332(f125(x69971),x69973),x69974)),f332(f332(f125(x69971),f151(x69971,x69972,x69973)),x69974))+~P1(f332(f332(f334(x69971),x69972),f332(f158(x69971),x69973)))
% 52.62/52.41 [7065]E(f332(f106(a845),x70651),f2(a845))+E(f332(f332(f128(x70652),f332(f106(a845),x70651)),f332(f332(f140(x70652),x70653),x70654)),f332(f332(f128(x70652),f332(f332(f3(a845),f332(f106(a845),x70651)),f80(a845))),x70654))
% 52.62/52.41 [7091]~P9(x70911)+E(f53(x70911,f332(f332(f82(x70911),f53(x70911,x70912,x70913)),x70914),x70913),f53(x70911,f332(f332(f82(x70911),x70912),x70914),x70913))
% 52.62/52.41 [7092]~P9(x70921)+E(f53(x70921,f332(f332(f83(x70921),f53(x70921,x70922,x70923)),x70924),x70923),f53(x70921,f332(f332(f83(x70921),x70922),x70924),x70923))
% 52.62/52.41 [7093]~P10(x70931)+E(f53(x70931,f332(f332(f3(x70931),f53(x70931,x70932,x70933)),x70934),x70933),f53(x70931,f332(f332(f3(x70931),x70932),x70934),x70933))
% 52.62/52.41 [7094]~P9(x70941)+E(f53(x70941,f332(f332(f82(x70941),f53(x70941,x70942,x70943)),x70944),x70943),f53(x70941,f332(f332(f82(x70941),x70942),x70944),x70943))
% 52.62/52.41 [7095]~P9(x70951)+E(f53(x70951,f332(f332(f83(x70951),f53(x70951,x70952,x70953)),x70954),x70953),f53(x70951,f332(f332(f83(x70951),x70952),x70954),x70953))
% 52.62/52.41 [7301]~E(x73011,f332(f332(f140(x73012),x73013),x73014))+~P1(f332(f332(f232(a845),f332(f181(f846(x73012)),x73011)),f332(f181(f846(x73012)),x73014)))
% 52.62/52.41 [7473]~E(f166(x74731,x74732,x74733),f166(x74731,x74732,x74734))+E(f332(f303(f852(x74731,x74732),x74731,f240(x74731,x74732)),f332(f158(f852(x74731,x74732)),x74733)),f332(f303(f852(x74731,x74732),x74731,f240(x74731,x74732)),f332(f158(f852(x74731,x74732)),x74734)))
% 52.62/52.41 [7516]P31(x75161,x75162,x75163,f332(f158(x75161),x75164))+~P1(f332(f127(x75162),f332(f332(f143(x75161,x75162),x75163),x75164)))
% 52.62/52.41 [7593]~P1(f332(f332(f232(f853(x75931,a839)),x75932),x75934))+P1(f332(f332(f232(f853(x75931,a839)),x75932),f332(f332(f302(x75931),x75933),x75934)))
% 52.62/52.41 [7628]~P9(x76281)+E(f53(x76281,f332(f332(f82(x76281),f53(x76281,x76282,x76283)),f53(x76281,x76284,x76283)),x76283),f53(x76281,f332(f332(f82(x76281),x76282),x76284),x76283))
% 52.62/52.41 [7629]~P9(x76291)+E(f53(x76291,f332(f332(f83(x76291),f53(x76291,x76292,x76293)),f53(x76291,x76294,x76293)),x76293),f53(x76291,f332(f332(f83(x76291),x76292),x76294),x76293))
% 52.62/52.41 [7630]~P10(x76301)+E(f53(x76301,f332(f332(f3(x76301),f53(x76301,x76302,x76303)),f53(x76301,x76304,x76303)),x76303),f53(x76301,f332(f332(f3(x76301),x76302),x76304),x76303))
% 52.62/52.41 [7731]~E(f332(x77314,f651(x77314,x77313,x77311,x77312)),f239(f853(x77312,a839)))+E(f332(f332(f48(x77311,f853(x77312,a839)),x77313),x77314),f239(f853(x77312,a839)))
% 52.62/52.41 [7732]~E(f332(x77324,f387(x77324,x77323,x77321,x77322)),f180(f853(x77322,a839)))+E(f332(f332(f47(x77321,f853(x77322,a839)),x77323),x77324),f180(f853(x77322,a839)))
% 52.62/52.41 [7733]~E(f332(x77334,f401(x77334,x77333,x77332,x77331)),f180(f853(x77332,a839)))+E(f332(f332(f47(x77331,f853(x77332,a839)),x77333),x77334),f180(f853(x77332,a839)))
% 52.62/52.41 [7734]~E(f332(x77344,f664(x77344,x77343,x77342,x77341)),f239(f853(x77342,a839)))+E(f332(f332(f48(x77341,f853(x77342,a839)),x77343),x77344),f239(f853(x77342,a839)))
% 52.62/52.41 [8125]P1(f332(x81251,x81252))+~P1(f332(f332(f334(x81253),x81252),f332(f332(f104(f853(x81253,a839)),x81254),f332(f256(x81253),x81251))))
% 52.62/52.41 [8164]~P1(f332(f332(f232(f853(x81641,a839)),x81643),x81644))+P1(f332(f332(f232(f853(x81641,a839)),f332(f332(f302(x81641),x81642),x81643)),f332(f332(f302(x81641),x81642),x81644)))
% 52.62/52.41 [8205]P1(f332(f332(f334(x82051),x82052),x82053))+~P1(f332(f332(f334(x82051),x82052),f332(f332(f104(f853(x82051,a839)),x82053),f332(f256(x82051),x82054))))
% 52.62/52.41 [8331]P1(f332(f332(f187(x83311),x83312),f433(x83313,x83312,x83314,x83311)))+~P1(f332(f332(f187(f36(x83311,x83314)),x83312),x83313))
% 52.62/52.41 [8332]P1(f332(f332(f187(x83321),x83322),f441(x83323,x83322,x83324,x83321)))+~P1(f332(f332(f187(f36(x83321,x83324)),x83322),x83323))
% 52.62/52.41 [8453]~P1(f332(f332(f233(a845),f332(x84534,x84532)),f332(x84534,x84533)))+P1(f332(f332(f334(f852(x84531,x84531)),f332(f332(f241(x84531,x84531),x84532),x84533)),f332(f332(f280(a845,x84531),a237),x84534)))
% 52.62/52.41 [8600]P31(f846(x86001),f846(x86002),f332(f143(x86001,x86002),x86003),x86004)+~P31(x86001,x86002,x86003,f45(f853(x86001,a839),f332(f303(f846(x86001),f853(x86001,a839),f158(x86001)),x86004)))
% 52.62/52.41 [8710]E(f332(f332(f48(x87101,f853(x87102,a839)),x87103),x87104),f239(f853(x87102,a839)))+P1(f332(f332(f334(x87101),f651(x87104,x87103,x87101,x87102)),x87103))
% 52.62/52.41 [8711]E(f332(f332(f47(x87111,f853(x87112,a839)),x87113),x87114),f180(f853(x87112,a839)))+P1(f332(f332(f334(x87111),f387(x87114,x87113,x87111,x87112)),x87113))
% 52.62/52.41 [8712]E(f332(f332(f47(x87121,f853(x87122,a839)),x87123),x87124),f180(f853(x87122,a839)))+P1(f332(f332(f334(x87121),f401(x87124,x87123,x87122,x87121)),x87123))
% 52.62/52.41 [8713]E(f332(f332(f48(x87131,f853(x87132,a839)),x87133),x87134),f239(f853(x87132,a839)))+P1(f332(f332(f334(x87131),f664(x87134,x87133,x87132,x87131)),x87133))
% 52.62/52.41 [8748]P1(f332(f332(f233(a845),f332(x87481,x87482)),f332(x87481,x87483)))+~P1(f332(f332(f334(f852(x87484,x87484)),f332(f332(f241(x87484,x87484),x87482),x87483)),f332(f332(f280(a845,x87484),a237),x87481)))
% 52.62/52.41 [8797]P1(f332(f332(f187(x87971),f433(x87972,x87973,x87971,x87974)),x87972))+~P1(f332(f332(f187(f36(x87974,x87971)),x87973),x87972))
% 52.62/52.41 [8798]P1(f332(f332(f187(x87981),f441(x87982,x87983,x87981,x87984)),x87982))+~P1(f332(f332(f187(f36(x87984,x87981)),x87983),x87982))
% 52.62/52.41 [8909]P1(f332(f332(f334(x89091),f495(x89092,x89093,x89094,x89091)),x89093))+~P1(f332(f332(f334(f853(x89091,a839)),x89094),f332(f332(f62(x89091),x89093),x89092)))
% 52.62/52.41 [8912]E(x89121,x89122)+~P1(f332(f332(f334(f852(x89123,x89123)),f332(f332(f241(x89123,x89123),x89121),x89122)),f332(f332(f173(f852(x89123,x89123),a839),f2(a845)),x89124)))
% 52.62/52.41 [8984]E(f332(f277(x89841,x89841,x89842),f332(f332(f302(x89841),f495(x89842,x89843,x89844,x89841)),f180(f853(x89841,a839)))),x89844)+~P1(f332(f332(f334(f853(x89841,a839)),x89844),f332(f332(f62(x89841),x89843),x89842)))
% 52.62/52.41 [8995]~P1(f332(f332(f334(f852(x89951,x89951)),f332(f332(f241(x89951,x89951),x89953),x89952)),f300(x89951,x89954)))+P1(f332(f332(f334(f852(x89951,x89951)),f332(f332(f241(x89951,x89951),x89952),x89953)),f300(x89951,f332(f278(x89951,x89951),x89954))))
% 52.62/52.41 [9008]~P9(x90081)+E(f332(f332(f82(x90081),f332(f332(f82(x90081),f332(f332(f83(x90081),x90082),f332(f332(f44(x90081),x90083),x90082))),f53(x90081,x90083,x90082))),x90084),f332(f332(f82(x90081),x90083),x90084))
% 52.62/52.41 [9015]~P1(f332(f332(f334(x90151),x90153),x90154))+P1(f332(f332(f334(f853(x90151,a839)),f332(f277(x90151,x90151,x90152),f332(f332(f302(x90151),x90153),f180(f853(x90151,a839))))),f332(f332(f62(x90151),x90154),x90152)))
% 52.62/52.41 [9025]P1(f332(f332(f334(f852(x90251,x90251)),f332(f332(f241(x90251,x90251),x90252),x90253)),f300(x90251,x90254)))+~P1(f332(f332(f334(f852(x90251,x90251)),f332(f332(f241(x90251,x90251),x90253),x90252)),f300(x90251,f332(f278(x90251,x90251),x90254))))
% 52.62/52.41 [9108]E(f332(f332(f148(x91081,f332(f142(x91081),x91082)),f332(f332(f3(a845),f332(f332(f3(a845),f332(f181(f846(x91081)),x91082)),x91083)),f80(a845))),x91084),f332(f142(x91081),f332(f332(f148(x91081,x91082),x91083),x91084)))+~P1(f332(f332(f233(a845),x91083),f332(f181(f846(x91081)),x91082)))
% 52.62/52.41 [9145]~P31(x91452,x91451,x91453,f239(f853(x91452,a839)))+P1(f332(f332(f232(f853(x91451,a839)),f332(f303(x91452,x91451,x91453),f332(f81(f853(x91452,a839)),x91454))),f332(f81(f853(x91451,a839)),f332(f303(x91452,x91451,x91453),x91454))))
% 52.62/52.41 [9153]~P11(x91531)+E(f332(f132(x91531,x91532,f332(f9(x91532,x91531,x91531),f332(f332(f10(x91531,f853(x91531,x91531),x91532),f103(x91531)),x91533)),f180(x91531)),x91534),f332(f332(f47(x91532,x91531),f332(f158(x91532),x91534)),x91533))
% 52.62/52.41 [9154]~P11(x91541)+E(f332(f132(x91541,x91542,f332(f9(x91542,x91541,x91541),f332(f332(f10(x91541,f853(x91541,x91541),x91542),f104(x91541)),x91543)),f239(x91541)),x91544),f332(f332(f48(x91542,x91541),f332(f158(x91542),x91544)),x91543))
% 52.62/52.41 [9220]~P1(f332(f332(f334(f852(f846(x92204),f846(x92204))),f332(f332(f241(f846(x92204),f846(x92204)),x92203),x92202)),f146(x92204,x92201)))+P1(f332(f332(f233(a845),f737(x92201,x92202,x92203,x92204)),f332(f181(f846(x92204)),x92203)))
% 52.62/52.41 [9221]~P9(x92211)+E(f332(f332(f82(x92211),f332(f332(f82(x92211),f332(f332(f83(x92211),f332(f332(f44(x92211),x92212),x92213)),x92213)),f53(x92211,x92212,x92213))),x92214),f332(f332(f82(x92211),x92212),x92214))
% 52.62/52.41 [9250]~P1(f332(f332(f334(f852(f846(x92501),f846(x92501))),f332(f332(f241(f846(x92501),f846(x92501)),x92502),x92503)),f332(f278(f846(x92501),f846(x92501)),f146(x92501,x92504))))+P1(f332(f332(f334(f852(f846(x92501),f846(x92501))),f332(f332(f241(f846(x92501),f846(x92501)),x92502),x92503)),f146(x92501,f332(f278(x92501,x92501),x92504))))
% 52.62/52.41 [9251]P1(f332(f332(f334(f852(f846(x92511),f846(x92511))),f332(f332(f241(f846(x92511),f846(x92511)),x92512),x92513)),f332(f278(f846(x92511),f846(x92511)),f146(x92511,x92514))))+~P1(f332(f332(f334(f852(f846(x92511),f846(x92511))),f332(f332(f241(f846(x92511),f846(x92511)),x92512),x92513)),f146(x92511,f332(f278(x92511,x92511),x92514))))
% 52.62/52.41 [9288]~P1(f332(f332(f334(x92881),x92883),f332(f261(x92881,x92882),x92884)))+P1(f332(f332(f334(f852(x92881,x92882)),f332(f332(f241(x92881,x92882),x92883),f597(x92884,x92882,x92883,x92881))),x92884))
% 52.62/52.41 [9289]~P1(f332(f332(f334(x92891),x92893),f332(f261(x92891,x92892),x92894)))+P1(f332(f332(f334(f852(x92891,x92892)),f332(f332(f241(x92891,x92892),x92893),f598(x92894,x92892,x92893,x92891))),x92894))
% 52.62/52.41 [9415]~P1(f332(f64(f849(x94151)),f332(f303(x94152,f849(x94151),x94153),f239(f853(x94152,a839)))))+P1(f332(f64(f849(x94151)),f332(f303(x94152,f849(x94151),f170(x94152,x94151,x94153,f166(x94152,x94151,x94154))),f239(f853(x94152,a839)))))
% 52.62/52.41 [9439]~P1(f332(f332(f334(f852(x94391,x94391)),f332(f332(f241(x94391,x94391),x94392),x94394)),f332(f332(f281(x94391,x94391,x94391),x94393),f300(x94391,x94393))))+P1(f332(f332(f334(f852(x94391,x94391)),f332(f332(f241(x94391,x94391),x94392),f653(x94393,x94394,x94392,x94391))),x94393))
% 52.62/52.41 [9597]~P1(f332(f332(f334(f852(x95972,x95971)),x95974),f332(f278(x95971,x95972),x95973)))+P1(f332(f332(f334(f852(x95971,x95972)),f332(f332(f241(x95971,x95972),f701(x95973,x95974,x95971,x95972)),f700(x95973,x95974,x95971,x95972))),x95973))
% 52.62/52.41 [9621]~P1(f332(f332(f334(f852(f846(x96211),f846(x96211))),f332(f332(f241(f846(x96211),f846(x96211)),x96214),x96213)),f146(x96211,x96212)))+P1(f332(f332(f334(f852(x96211,x96211)),f332(f332(f241(x96211,x96211),f742(x96212,x96213,x96214,x96211)),f743(x96212,x96213,x96214,x96211))),x96212))
% 52.62/52.41 [9697]~P1(f332(f332(f334(f852(f846(x96971),f846(x96971))),f332(f332(f241(f846(x96971),f846(x96971)),x96972),x96974)),f146(x96971,x96973)))+P1(f332(f332(f334(f852(x96971,x96971)),f332(f332(f241(x96971,x96971),f332(f332(f152(x96971),x96972),f737(x96973,x96974,x96972,x96971))),f738(x96973,x96974,x96972,x96971))),x96973))
% 52.62/52.41 [9719]~P1(f332(f64(x97192),x97194))+E(f332(f332(f332(f68(f853(x97191,a839),x97192,f103(f853(x97191,a839))),f332(f332(f9(x97192,f853(x97191,a839),f853(x97191,a839)),f332(f332(f10(x97191,f853(f853(x97191,a839),f853(x97191,a839)),x97192),f302(x97191)),x97193)),f180(f853(x97191,a839)))),f180(f853(x97191,a839))),x97194),f332(f303(x97192,x97191,x97193),x97194))
% 52.62/52.41 [9835]~P31(x98351,x98352,x98353,f239(f853(x98351,a839)))+P1(f332(f332(f232(f853(x98351,a839)),f332(f305(x98351,x98352,x98353),f332(f332(f302(x98352),x98354),f180(f853(x98352,a839))))),f332(f332(f302(x98351),f87(x98351,f332(f332(f9(x98351,x98352,a839),f332(f332(f10(x98352,f853(x98352,a839),x98351),a329),x98353)),x98354))),f180(f853(x98351,a839)))))
% 52.62/52.41 [5495]~E(f332(f332(f125(x54951),x54952),x54954),x54953)+E(f332(f332(f159(x54951),f332(f181(f846(x54951)),x54952)),x54953),x54952)
% 52.62/52.41 [5496]~E(f332(f332(f125(x54962),x54963),x54961),x54964)+E(x54961,f332(f332(f128(x54962),f332(f181(f846(x54962)),x54963)),x54964))
% 52.62/52.41 [5507]~E(x55074,f2(a845))+E(f332(f332(f152(x55071),f332(f332(f140(x55071),x55072),x55073)),x55074),x55072)
% 52.62/52.41 [6040]~P73(x60401)+E(f332(f332(f242(x60401),f332(f332(f242(x60401),x60402),x60403)),x60404),f332(f332(f242(x60401),x60402),f332(f332(f83(a845),x60403),x60404)))
% 52.62/52.41 [6041]~P76(x60411)+E(f332(f332(f242(x60411),f332(f332(f242(x60411),x60412),x60413)),x60414),f332(f332(f242(x60411),x60412),f332(f332(f83(a845),x60413),x60414)))
% 52.62/52.41 [6057]E(x60571,f2(a845))+E(f332(f332(f152(x60572),f332(f332(f140(x60572),x60573),x60574)),x60571),f332(f332(f152(x60572),x60574),f332(f332(f3(a845),x60571),f80(a845))))
% 52.62/52.41 [6081]~P73(x60811)+E(f332(f332(f82(x60811),f332(f332(f82(x60811),x60812),x60813)),x60814),f332(f332(f82(x60811),x60812),f332(f332(f82(x60811),x60813),x60814)))
% 52.62/52.41 [6082]~P73(x60821)+E(f332(f332(f83(x60821),f332(f332(f83(x60821),x60822),x60823)),x60824),f332(f332(f83(x60821),x60822),f332(f332(f83(x60821),x60823),x60824)))
% 52.62/52.41 [6083]~P113(x60831)+E(f332(f332(f283(x60831),f332(f332(f83(x60831),x60832),x60833)),x60834),f332(f332(f83(x60831),x60832),f332(f332(f283(x60831),x60833),x60834)))
% 52.62/52.41 [6084]~P73(x60841)+E(f332(f332(f82(x60841),f332(f332(f82(x60841),x60842),x60843)),x60844),f332(f332(f82(x60841),x60842),f332(f332(f82(x60841),x60843),x60844)))
% 52.62/52.41 [6085]~P7(x60851)+E(f332(f332(f82(x60851),f332(f332(f82(x60851),x60852),x60853)),x60854),f332(f332(f82(x60851),x60852),f332(f332(f82(x60851),x60853),x60854)))
% 52.62/52.41 [6086]~P73(x60861)+E(f332(f332(f83(x60861),f332(f332(f83(x60861),x60862),x60863)),x60864),f332(f332(f83(x60861),x60862),f332(f332(f83(x60861),x60863),x60864)))
% 52.62/52.41 [6087]~P66(x60871)+E(f332(f332(f83(x60871),f332(f332(f83(x60871),x60872),x60873)),x60874),f332(f332(f83(x60871),x60872),f332(f332(f83(x60871),x60873),x60874)))
% 52.62/52.41 [6089]~P100(x60891)+E(f332(f332(f236(x60891),f332(f332(f236(x60891),x60892),x60893)),x60894),f332(f332(f236(x60891),x60892),f332(f332(f236(x60891),x60893),x60894)))
% 52.62/52.41 [6090]~P100(x60901)+E(f332(f332(f236(x60901),f332(f332(f236(x60901),x60902),x60903)),x60904),f332(f332(f236(x60901),x60902),f332(f332(f236(x60901),x60903),x60904)))
% 52.62/52.41 [6091]~P100(x60911)+E(f332(f332(f179(x60911),f332(f332(f179(x60911),x60912),x60913)),x60914),f332(f332(f179(x60911),x60912),f332(f332(f179(x60911),x60913),x60914)))
% 52.62/52.41 [6092]~P100(x60921)+E(f332(f332(f179(x60921),f332(f332(f179(x60921),x60922),x60923)),x60924),f332(f332(f179(x60921),x60922),f332(f332(f179(x60921),x60923),x60924)))
% 52.62/52.41 [6093]~P92(x60931)+E(f332(f332(f103(x60931),f332(f332(f103(x60931),x60932),x60933)),x60934),f332(f332(f103(x60931),x60932),f332(f332(f103(x60931),x60933),x60934)))
% 52.62/52.41 [6094]~P92(x60941)+E(f332(f332(f103(x60941),f332(f332(f103(x60941),x60942),x60943)),x60944),f332(f332(f103(x60941),x60942),f332(f332(f103(x60941),x60943),x60944)))
% 52.62/52.41 [6095]~P93(x60951)+E(f332(f332(f103(x60951),f332(f332(f103(x60951),x60952),x60953)),x60954),f332(f332(f103(x60951),x60952),f332(f332(f103(x60951),x60953),x60954)))
% 52.62/52.41 [6096]~P93(x60961)+E(f332(f332(f104(x60961),f332(f332(f104(x60961),x60962),x60963)),x60964),f332(f332(f104(x60961),x60962),f332(f332(f104(x60961),x60963),x60964)))
% 52.62/52.41 [6097]~P98(x60971)+E(f332(f332(f104(x60971),f332(f332(f104(x60971),x60972),x60973)),x60974),f332(f332(f104(x60971),x60972),f332(f332(f104(x60971),x60973),x60974)))
% 52.62/52.41 [6098]~P98(x60981)+E(f332(f332(f104(x60981),f332(f332(f104(x60981),x60982),x60983)),x60984),f332(f332(f104(x60981),x60982),f332(f332(f104(x60981),x60983),x60984)))
% 52.62/52.41 [6111]~P9(x61111)+E(f53(x61111,f332(f332(f82(x61111),x61112),f332(f332(f83(x61111),x61113),x61114)),x61114),f53(x61111,x61112,x61114))
% 52.62/52.41 [6112]~P9(x61121)+E(f53(x61121,f332(f332(f82(x61121),x61122),f332(f332(f83(x61121),x61123),x61124)),x61123),f53(x61121,x61122,x61123))
% 52.62/52.41 [6250]E(f332(f332(f152(x62501),f332(f332(f159(x62501),x62502),x62503)),x62504),f332(f332(f152(x62501),x62503),x62504))+~P1(f332(f332(f233(a845),x62504),x62502))
% 52.62/52.41 [6436]~P73(x64361)+E(f332(f332(f82(x64361),f332(f332(f82(x64361),x64362),x64363)),x64364),f332(f332(f82(x64361),f332(f332(f82(x64361),x64362),x64364)),x64363))
% 52.62/52.41 [6437]~P73(x64371)+E(f332(f332(f83(x64371),f332(f332(f83(x64371),x64372),x64373)),x64374),f332(f332(f83(x64371),f332(f332(f83(x64371),x64372),x64374)),x64373))
% 52.62/52.41 [6499]~P2(x64992)+E(f332(f332(f8(x64991,x64992),f332(f18(x64992,x64991),x64993)),x64994),f332(f332(f83(x64992),f332(f102(x64992),f332(f43(x64991),x64994))),x64993))
% 52.62/52.41 [6676]E(f332(f332(f104(f853(x66761,a839)),f332(f332(f302(x66761),x66762),x66763)),x66764),f332(f332(f104(f853(x66761,a839)),x66763),x66764))+P1(f332(f332(f334(x66761),x66762),x66764))
% 52.62/52.41 [6677]E(f332(f332(f104(f853(x66771,a839)),f332(f332(f302(x66771),x66772),x66773)),x66774),f332(f332(f104(f853(x66771,a839)),x66773),x66774))+P1(f332(f332(f334(x66771),x66772),x66774))
% 52.62/52.41 [6751]~P75(x67511)+E(f332(f332(f236(x67511),f332(f332(f82(x67511),x67512),x67513)),f332(f332(f82(x67511),x67514),x67513)),f332(f332(f82(x67511),f332(f332(f236(x67511),x67512),x67514)),x67513))
% 52.62/52.41 [6752]~P75(x67521)+E(f332(f332(f179(x67521),f332(f332(f82(x67521),x67522),x67523)),f332(f332(f82(x67521),x67524),x67523)),f332(f332(f82(x67521),f332(f332(f179(x67521),x67522),x67524)),x67523))
% 52.62/52.41 [6753]~P73(x67531)+E(f332(f332(f82(x67531),f332(f332(f83(x67531),x67532),x67533)),f332(f332(f83(x67531),x67534),x67533)),f332(f332(f83(x67531),f332(f332(f82(x67531),x67532),x67534)),x67533))
% 52.62/52.41 [6754]~P109(x67541)+E(f332(f332(f82(x67541),f332(f332(f83(x67541),x67542),x67543)),f332(f332(f83(x67541),x67544),x67543)),f332(f332(f83(x67541),f332(f332(f82(x67541),x67542),x67544)),x67543))
% 52.62/52.41 [6755]~P78(x67551)+E(f332(f332(f236(x67551),f332(f332(f3(x67551),x67552),x67553)),f332(f332(f3(x67551),x67554),x67553)),f332(f332(f3(x67551),f332(f332(f236(x67551),x67552),x67554)),x67553))
% 52.62/52.41 [6756]~P78(x67561)+E(f332(f332(f179(x67561),f332(f332(f3(x67561),x67562),x67563)),f332(f332(f3(x67561),x67564),x67563)),f332(f332(f3(x67561),f332(f332(f179(x67561),x67562),x67564)),x67563))
% 52.62/52.41 [6757]~P73(x67571)+E(f332(f332(f83(x67571),f332(f332(f242(x67571),x67572),x67573)),f332(f332(f242(x67571),x67574),x67573)),f332(f332(f242(x67571),f332(f332(f83(x67571),x67572),x67574)),x67573))
% 52.62/52.41 [6758]~P70(x67581)+E(f332(f332(f83(x67581),f332(f332(f242(x67581),x67582),x67583)),f332(f332(f242(x67581),x67584),x67583)),f332(f332(f242(x67581),f332(f332(f83(x67581),x67582),x67584)),x67583))
% 52.62/52.41 [6759]~P62(x67591)+E(f332(f332(f283(x67591),f332(f332(f242(x67591),x67592),x67593)),f332(f332(f242(x67591),x67594),x67593)),f332(f332(f242(x67591),f332(f332(f283(x67591),x67592),x67594)),x67593))
% 52.62/52.41 [6760]~P113(x67601)+E(f332(f332(f82(x67601),f332(f332(f283(x67601),x67602),x67603)),f332(f332(f283(x67601),x67604),x67603)),f332(f332(f283(x67601),f332(f332(f82(x67601),x67602),x67604)),x67603))
% 52.62/52.41 [6761]~P113(x67611)+E(f332(f332(f3(x67611),f332(f332(f283(x67611),x67612),x67613)),f332(f332(f283(x67611),x67614),x67613)),f332(f332(f283(x67611),f332(f332(f3(x67611),x67612),x67614)),x67613))
% 52.62/52.41 [6762]~P100(x67621)+E(f332(f332(f179(x67621),f332(f332(f236(x67621),x67622),x67623)),f332(f332(f236(x67621),x67624),x67623)),f332(f332(f236(x67621),f332(f332(f179(x67621),x67622),x67624)),x67623))
% 52.62/52.41 [6763]~P100(x67631)+E(f332(f332(f236(x67631),f332(f332(f179(x67631),x67632),x67633)),f332(f332(f179(x67631),x67634),x67633)),f332(f332(f179(x67631),f332(f332(f236(x67631),x67632),x67634)),x67633))
% 52.62/52.41 [6764]~P97(x67641)+E(f332(f332(f104(x67641),f332(f332(f103(x67641),x67642),x67643)),f332(f332(f103(x67641),x67644),x67643)),f332(f332(f103(x67641),f332(f332(f104(x67641),x67642),x67644)),x67643))
% 52.62/52.41 [6765]~P97(x67651)+E(f332(f332(f103(x67651),f332(f332(f104(x67651),x67652),x67653)),f332(f332(f104(x67651),x67654),x67653)),f332(f332(f104(x67651),f332(f332(f103(x67651),x67652),x67654)),x67653))
% 52.62/52.41 [6766]~P73(x67661)+E(f332(f332(f82(x67661),f332(f332(f83(x67661),x67662),x67663)),f332(f332(f83(x67661),x67664),x67663)),f332(f332(f83(x67661),f332(f332(f82(x67661),x67662),x67664)),x67663))
% 52.62/52.41 [6801]E(f332(f332(f148(x68011,x68012),x68013),x68014),x68012)+~P1(f332(f332(f232(a845),f332(f181(f846(x68011)),x68012)),x68013))
% 52.62/52.41 [6827]~P1(f332(x68273,x68274))+P1(f332(f332(f332(f103(f853(x68271,a839)),x68272),x68273),x68274))
% 52.62/52.41 [6828]~P1(f332(x68283,x68284))+P1(f332(f332(f332(f103(f853(x68281,a839)),x68282),x68283),x68284))
% 52.62/52.41 [6829]~P1(f332(x68292,x68294))+P1(f332(f332(f332(f103(f853(x68291,a839)),x68292),x68293),x68294))
% 52.62/52.41 [6830]~P1(f332(x68302,x68304))+P1(f332(f332(f332(f103(f853(x68301,a839)),x68302),x68303),x68304))
% 52.62/52.41 [6852]E(f332(f332(f152(x68521),f332(f332(f125(x68521),x68522),x68523)),x68524),f332(f332(f152(x68521),x68522),x68524))+~P1(f332(f332(f233(a845),x68524),f332(f181(f846(x68521)),x68522)))
% 52.62/52.41 [6861]E(f332(f332(f3(f853(x68611,a839)),f332(f332(f302(x68611),x68612),x68613)),x68614),f332(f332(f3(f853(x68611,a839)),x68613),x68614))+~P1(f332(f332(f334(x68611),x68612),x68614))
% 52.62/52.41 [6862]E(f332(f332(f3(f853(x68621,a839)),f332(f332(f302(x68621),x68622),x68623)),x68624),f332(f332(f3(f853(x68621,a839)),x68623),x68624))+~P1(f332(f332(f334(x68621),x68622),x68624))
% 52.62/52.41 [6903]~E(f130(a845,f332(f294(a845,x69031),x69032)),f332(f332(f140(a845),x69034),x69033))+E(f130(a845,f332(f294(a845,f332(f332(f82(a845),x69031),f80(a845))),x69032)),x69033)
% 52.62/52.41 [6972]E(x69721,f2(a845))+E(f332(f332(f140(x69722),x69723),f332(f332(f159(x69722),f332(f332(f3(a845),x69721),f80(a845))),x69724)),f332(f332(f159(x69722),x69721),f332(f332(f140(x69722),x69723),x69724)))
% 52.62/52.41 [7076]E(f332(f332(f152(x70761),x70762),f332(f332(f3(a845),x70763),f332(f181(f846(x70761)),x70764))),f332(f332(f152(x70761),f332(f332(f125(x70761),x70764),x70762)),x70763))+P1(f332(f332(f233(a845),x70763),f332(f181(f846(x70761)),x70764)))
% 52.62/52.41 [7103]E(f332(f332(f104(f853(x71031,a839)),x71032),f332(f332(f302(x71031),x71033),x71034)),f332(f332(f302(x71031),x71033),f332(f332(f104(f853(x71031,a839)),x71032),x71034)))+~P1(f332(f332(f334(x71031),x71033),x71032))
% 52.62/52.41 [7104]E(f332(f332(f104(f853(x71041,a839)),x71042),f332(f332(f302(x71041),x71043),x71044)),f332(f332(f302(x71041),x71043),f332(f332(f104(f853(x71041,a839)),x71042),x71044)))+~P1(f332(f332(f334(x71041),x71043),x71042))
% 52.62/52.41 [7138]E(f332(f332(f152(x71381),f332(f332(f148(x71381,x71382),x71383),x71384)),x71383),x71384)+~P1(f332(f332(f233(a845),x71383),f332(f181(f846(x71381)),x71382)))
% 52.62/52.41 [7159]E(x71591,f180(f853(x71592,a839)))+E(f332(f303(f852(x71593,x71592),x71593,f240(x71593,x71592)),f332(f332(f248(x71593,x71592),x71594),f332(f18(f853(x71592,a839),x71593),x71591))),x71594)
% 52.62/52.41 [7160]E(x71601,f180(f853(x71602,a839)))+E(f332(f303(f852(x71602,x71603),x71603,f250(x71602,x71603)),f332(f332(f248(x71602,x71603),x71601),f332(f18(f853(x71603,a839),x71602),x71604))),x71604)
% 52.62/52.41 [7244]E(f332(f332(f3(f853(x72441,a839)),f332(f332(f302(x72441),x72442),x72443)),x72444),f332(f332(f302(x72441),x72442),f332(f332(f3(f853(x72441,a839)),x72443),x72444)))+P1(f332(f332(f334(x72441),x72442),x72444))
% 52.62/52.41 [7285]~E(x72854,f180(f853(x72852,a839)))+E(f332(f303(f852(x72851,x72852),x72851,f240(x72851,x72852)),f332(f332(f248(x72851,x72852),x72853),f332(f18(f853(x72852,a839),x72851),x72854))),f180(f853(x72851,a839)))
% 52.62/52.41 [7286]~E(x72863,f180(f853(x72861,a839)))+E(f332(f303(f852(x72861,x72862),x72862,f250(x72861,x72862)),f332(f332(f248(x72861,x72862),x72863),f332(f18(f853(x72862,a839),x72861),x72864))),f180(f853(x72862,a839)))
% 52.62/52.41 [7343]~P1(f332(f332(f334(x73431),x73432),x73434))+P1(f332(f332(f334(x73431),x73432),f332(f332(f103(f853(x73431,a839)),x73433),x73434)))
% 52.62/52.41 [7344]~P1(f332(f332(f334(x73441),x73442),x73444))+P1(f332(f332(f334(x73441),x73442),f332(f332(f103(f853(x73441,a839)),x73443),x73444)))
% 52.62/52.41 [7345]~P1(f332(f332(f334(x73451),x73452),x73454))+P1(f332(f332(f334(x73451),x73452),f332(f332(f103(f853(x73451,a839)),x73453),x73454)))
% 52.62/52.41 [7346]~P1(f332(f332(f334(x73461),x73462),x73463))+P1(f332(f332(f334(x73461),x73462),f332(f332(f103(f853(x73461,a839)),x73463),x73464)))
% 52.62/52.41 [7347]~P1(f332(f332(f334(x73471),x73472),x73473))+P1(f332(f332(f334(x73471),x73472),f332(f332(f103(f853(x73471,a839)),x73473),x73474)))
% 52.62/52.41 [7348]~P1(f332(f332(f334(x73481),x73482),x73483))+P1(f332(f332(f334(x73481),x73482),f332(f332(f103(f853(x73481,a839)),x73483),x73484)))
% 52.62/52.41 [7369]E(f332(f332(f104(f853(x73691,a839)),f332(f332(f302(x73691),x73692),x73693)),x73694),f332(f332(f302(x73691),x73692),f332(f332(f104(f853(x73691,a839)),x73693),x73694)))+~P1(f332(f332(f334(x73691),x73692),x73694))
% 52.62/52.41 [7370]E(f332(f332(f104(f853(x73701,a839)),f332(f332(f302(x73701),x73702),x73703)),x73704),f332(f332(f302(x73701),x73702),f332(f332(f104(f853(x73701,a839)),x73703),x73704)))+~P1(f332(f332(f334(x73701),x73702),x73704))
% 52.62/52.41 [7647]P1(f332(x76471,x76472))+~P1(f332(f332(f332(f104(f853(x76473,a839)),x76474),x76471),x76472))
% 52.62/52.41 [7648]P1(f332(x76481,x76482))+~P1(f332(f332(f332(f104(f853(x76483,a839)),x76481),x76484),x76482))
% 52.62/52.41 [7649]P1(f332(x76491,x76492))+~P1(f332(f332(f332(f104(f853(x76493,a839)),x76494),x76491),x76492))
% 52.62/52.41 [7650]P1(f332(x76501,x76502))+~P1(f332(f332(f332(f104(f853(x76503,a839)),x76501),x76504),x76502))
% 52.62/52.41 [7653]E(f332(f332(f8(x76531,a845),x76532),f332(f332(f3(f853(x76531,a839)),x76533),f332(f332(f302(x76531),x76534),f180(f853(x76531,a839))))),f332(f332(f8(x76531,a845),x76532),x76533))+P1(f332(f332(f334(x76531),x76534),x76533))
% 52.62/52.41 [7659]~P4(x76591)+E(f332(f154(x76591),f332(f332(f143(a845,x76591),x76592),f130(a845,f332(f294(a845,x76593),x76594)))),f332(f332(f8(a845,x76591),x76592),f332(f158(a845),f130(a845,f332(f294(a845,x76593),x76594)))))
% 52.62/52.41 [7660]~P4(x76601)+E(f332(f332(f8(a845,x76601),x76602),f332(f158(a845),f130(a845,f332(f294(a845,x76603),x76604)))),f332(f154(x76601),f332(f332(f143(a845,x76601),x76602),f130(a845,f332(f294(a845,x76603),x76604)))))
% 52.62/52.41 [7774]~E(x77743,x77744)+P1(f332(f65(x77741,x77742,f332(f332(f302(x77741),x77743),f180(f853(x77741,a839)))),x77744))
% 52.62/52.41 [7870]P1(f332(f332(f334(x78701),x78702),f332(f158(x78701),x78703)))+~P1(f332(f332(f334(x78701),x78702),f332(f158(x78701),f332(f332(f159(x78701),x78704),x78703))))
% 52.62/52.41 [7871]P1(f332(f332(f334(x78711),x78712),f332(f158(x78711),x78713)))+~P1(f332(f332(f334(x78711),x78712),f332(f158(x78711),f332(f332(f128(x78711),x78714),x78713))))
% 52.62/52.41 [7942]P1(f332(f332(f334(x79421),x79422),x79423))+~P1(f332(f332(f334(x79421),x79422),f332(f332(f104(f853(x79421,a839)),x79424),x79423)))
% 52.62/52.41 [7943]P1(f332(f332(f334(x79431),x79432),x79433))+~P1(f332(f332(f334(x79431),x79432),f332(f332(f3(f853(x79431,a839)),x79433),x79434)))
% 52.62/52.41 [7944]P1(f332(f332(f334(x79441),x79442),x79443))+~P1(f332(f332(f334(x79441),x79442),f332(f332(f3(f853(x79441,a839)),x79443),x79444)))
% 52.62/52.41 [7945]P1(f332(f332(f334(x79451),x79452),x79453))+~P1(f332(f332(f334(x79451),x79452),f332(f332(f3(f853(x79451,a839)),x79453),x79454)))
% 52.62/52.41 [7946]P1(f332(f332(f334(x79461),x79462),x79463))+~P1(f332(f332(f334(x79461),x79462),f332(f332(f104(f853(x79461,a839)),x79464),x79463)))
% 52.62/52.41 [7947]P1(f332(f332(f334(x79471),x79472),x79473))+~P1(f332(f332(f334(x79471),x79472),f332(f332(f104(f853(x79471,a839)),x79474),x79473)))
% 52.62/52.41 [7948]P1(f332(f332(f334(x79481),x79482),x79483))+~P1(f332(f332(f334(x79481),x79482),f332(f332(f104(f853(x79481,a839)),x79483),x79484)))
% 52.62/52.41 [7949]P1(f332(f332(f334(x79491),x79492),x79493))+~P1(f332(f332(f334(x79491),x79492),f332(f332(f104(f853(x79491,a839)),x79493),x79494)))
% 52.62/52.41 [7950]P1(f332(f332(f334(x79501),x79502),x79503))+~P1(f332(f332(f334(x79501),x79502),f332(f332(f104(f853(x79501,a839)),x79503),x79504)))
% 52.62/52.41 [7967]E(f332(f332(f125(x79671),f332(f332(f159(x79671),x79672),x79673)),f332(f332(f140(x79671),x79674),f332(f332(f128(x79671),f332(a114,x79672)),x79673))),f332(f332(f148(x79671,x79673),x79672),x79674))+~P1(f332(f332(f233(a845),x79672),f332(f181(f846(x79671)),x79673)))
% 52.62/52.41 [7990]P1(f332(f332(f334(x79901),x79902),x79903))+~P1(f332(f332(f232(f853(x79901,a839)),f332(f332(f302(x79901),x79902),x79904)),x79903))
% 52.62/52.41 [8018]~P1(f332(f332(f334(x80181),x80182),x80183))+~P1(f332(f332(f334(x80181),x80182),f332(f332(f3(f853(x80181,a839)),x80184),x80183)))
% 52.62/52.41 [8019]~P1(f332(f332(f334(x80191),x80192),x80193))+~P1(f332(f332(f334(x80191),x80192),f332(f332(f3(f853(x80191,a839)),x80194),x80193)))
% 52.62/52.41 [8020]~P1(f332(f332(f334(x80201),x80202),x80203))+~P1(f332(f332(f334(x80201),x80202),f332(f332(f3(f853(x80201,a839)),x80204),x80203)))
% 52.62/52.41 [8053]~P1(f332(f332(f233(a845),x80534),f332(f181(f846(x80531)),x80533)))+P1(f332(f332(f334(x80531),x80532),f332(f158(x80531),f332(f332(f148(x80531,x80533),x80534),x80532))))
% 52.62/52.41 [8094]E(f332(f106(a845),x80941),f2(a845))+E(f332(f332(f140(x80942),x80943),f332(f332(f159(x80942),f332(f332(f3(a845),f332(f106(a845),x80941)),f80(a845))),x80944)),f332(f332(f159(x80942),f332(f106(a845),x80941)),f332(f332(f140(x80942),x80943),x80944)))
% 52.62/52.41 [8103]E(f332(f332(f152(x81031),f332(f332(f128(x81031),x81032),x81033)),x81034),f332(f332(f152(x81031),x81033),f332(f332(f82(a845),x81032),x81034)))+~P1(f332(f332(f232(a845),f332(f332(f82(a845),x81032),x81034)),f332(f181(f846(x81031)),x81033)))
% 52.62/52.41 [8112]~P2(x81122)+E(f332(f332(f8(x81121,x81122),f332(f332(f10(a845,x81122,x81121),f102(x81122)),x81123)),x81124),f332(f102(x81122),f332(f332(f8(x81121,a845),x81123),x81124)))
% 52.62/52.41 [8113]~P133(x81132)+E(f332(f332(f8(x81131,x81132),f332(f332(f10(a1,x81132,x81131),f105(x81132)),x81133)),x81134),f332(f105(x81132),f332(f332(f8(x81131,a1),x81133),x81134)))
% 52.62/52.41 [8166]~P65(x81662)+E(f332(f332(f11(x81661,x81662),f332(f332(f10(x81662,x81662,x81661),f77(x81662)),x81663)),x81664),f332(f77(x81662),f332(f332(f11(x81661,x81662),x81663),x81664)))
% 52.62/52.41 [8167]~P8(x81672)+E(f332(f332(f8(x81671,x81672),f332(f332(f10(x81672,x81672,x81671),f81(x81672)),x81673)),x81674),f332(f81(x81672),f332(f332(f8(x81671,x81672),x81673),x81674)))
% 52.62/52.41 [8169]E(f332(f332(f8(x81691,a845),x81692),f332(f332(f3(f853(x81691,a839)),x81693),f332(f332(f302(x81691),x81694),f180(f853(x81691,a839))))),f332(f332(f3(a845),f332(f332(f8(x81691,a845),x81692),x81693)),f332(x81692,x81694)))+~P1(f332(f332(f334(x81691),x81694),x81693))
% 52.62/52.41 [8188]P1(f332(f332(f232(f853(x81881,a839)),x81882),x81883))+~P1(f332(f332(f232(f853(x81881,a839)),f332(f332(f302(x81881),x81884),x81882)),x81883))
% 52.62/52.41 [8396]P38(x83961,x83962)+~P38(x83961,f332(f332(f302(f852(x83961,x83961)),f332(f332(f241(x83961,x83961),x83963),x83964)),x83962))
% 52.62/52.41 [8397]P58(x83971,x83972)+~P58(x83971,f332(f332(f302(f852(x83971,x83971)),f332(f332(f241(x83971,x83971),x83973),x83974)),x83972))
% 52.62/52.41 [8405]~P100(x84051)+E(f332(f332(f138(x84051,x84051,f7(x84051)),x84052),f332(f332(f138(x84051,x84051,f7(x84051)),x84053),x84054)),f332(f332(f138(x84051,x84051,f7(x84051)),x84053),f332(f332(f138(x84051,x84051,f7(x84051)),x84052),x84054)))
% 52.62/52.41 [8415]E(x84151,x84152)+~P1(f332(f65(x84153,x84154,f332(f332(f302(x84153),x84151),f180(f853(x84153,a839)))),x84152))
% 52.62/52.41 [8420]E(f332(f166(x84201,x84202,x84203),x84204),f183(x84202))+P1(f332(f332(f334(x84201),x84204),f332(f303(f852(x84201,x84202),x84201,f240(x84201,x84202)),f332(f158(f852(x84201,x84202)),x84203))))
% 52.62/52.41 [8426]E(f332(f332(f125(x84261),f332(f332(f159(x84261),x84262),x84263)),f332(f332(f159(x84261),x84264),f332(f332(f128(x84261),x84262),x84263))),f332(f332(f159(x84261),f332(f332(f82(a845),x84262),x84264)),x84263))+~P1(f332(f332(f232(a845),f332(f332(f82(a845),x84262),x84264)),f332(f181(f846(x84261)),x84263)))
% 52.62/52.41 [8469]P1(f332(f64(x84691),x84692))+~E(x84692,f332(f303(a845,x84691,x84693),f332(f256(a845),f332(f332(f9(a845,a845,a839),f233(a845)),x84694))))
% 52.62/52.41 [8470]P1(f332(f64(x84701),x84702))+~E(x84702,f332(f303(a845,x84701,x84703),f332(f256(a845),f332(f332(f9(a845,a845,a839),f233(a845)),x84704))))
% 52.62/52.41 [8490]~P84(x84901)+E(f332(f132(x84901,x84901,f82(x84901),f332(f332(f82(x84901),x84902),x84903)),x84904),f332(f332(f82(x84901),x84902),f332(f132(x84901,x84901,f82(x84901),x84903),x84904)))
% 52.62/52.41 [8522]P1(f332(f332(f232(f853(x85221,a839)),f332(f261(x85221,x85222),x85223)),f332(f261(x85221,x85222),x85224)))+~P1(f332(f332(f232(f853(f852(x85221,x85222),a839)),x85223),x85224))
% 52.62/52.41 [8533]~P1(f332(f332(f232(a845),x85332),x85334))+P1(f332(f332(f232(f853(x85331,a839)),f332(f158(x85331),f332(f332(f159(x85331),x85332),x85333))),f332(f158(x85331),f332(f332(f159(x85331),x85334),x85333))))
% 52.62/52.41 [8534]~P1(f332(f332(f232(a845),x85344),x85342))+P1(f332(f332(f232(f853(x85341,a839)),f332(f158(x85341),f332(f332(f128(x85341),x85342),x85343))),f332(f158(x85341),f332(f332(f128(x85341),x85344),x85343))))
% 52.62/52.41 [8577]~P1(f332(f64(x85771),f332(f332(f3(f853(x85771,a839)),x85772),x85774)))+P1(f332(f64(x85771),f332(f332(f3(f853(x85771,a839)),x85772),f332(f332(f302(x85771),x85773),x85774))))
% 52.62/52.41 [8610]P1(f332(f332(f334(f852(x86101,x86101)),x86102),f300(x86101,x86103)))+~P1(f332(f332(f334(f852(x86101,x86101)),x86102),f332(f332(f173(f852(x86101,x86101),a839),x86104),x86103)))
% 52.62/52.41 [8611]P1(f332(f332(f334(f852(x86111,x86111)),x86112),f300(x86111,x86113)))+~P1(f332(f332(f334(f852(x86111,x86111)),x86112),f332(f332(f173(f852(x86111,x86111),a839),x86114),x86113)))
% 52.62/52.41 [8686]~P1(f332(f64(x86861),f332(f332(f3(f853(x86861,a839)),x86862),f332(f332(f302(x86861),x86864),x86863))))+P1(f332(f64(x86861),f332(f332(f3(f853(x86861,a839)),x86862),x86863)))
% 52.62/52.41 [8752]P1(f332(f332(f334(f852(x87521,x87522)),f332(f332(f241(x87521,x87522),x87523),x87524)),f180(f853(f852(x87521,x87522),a839))))+~P1(f332(f332(f180(f853(x87521,f853(x87522,a839))),x87523),x87524))
% 52.62/52.41 [8829]~E(f332(f166(x88291,x88292,x88293),x88294),f183(x88292))+~P1(f332(f332(f334(x88291),x88294),f332(f303(f852(x88291,x88292),x88291,f240(x88291,x88292)),f332(f158(f852(x88291,x88292)),x88293))))
% 52.62/52.41 [8866]~P100(x88661)+P1(f332(f332(f232(x88661),f332(f332(f179(x88661),x88662),f332(f332(f236(x88661),x88663),x88664))),f332(f332(f236(x88661),f332(f332(f179(x88661),x88662),x88663)),f332(f332(f179(x88661),x88662),x88664))))
% 52.62/52.41 [8867]~P93(x88671)+P1(f332(f332(f232(x88671),f332(f332(f103(x88671),x88672),f332(f332(f104(x88671),x88673),x88674))),f332(f332(f104(x88671),f332(f332(f103(x88671),x88672),x88673)),f332(f332(f103(x88671),x88672),x88674))))
% 52.62/52.41 [8886]~P1(f332(f332(f334(f852(x88861,x88862)),f332(f332(f241(x88861,x88862),x88863),x88864)),f180(f853(f852(x88861,x88862),a839))))+P1(f332(f332(f180(f853(x88861,f853(x88862,a839))),x88863),x88864))
% 52.62/52.41 [9011]E(x90111,x90112)+~P1(f332(f332(f334(f852(x90113,x90113)),f332(f332(f241(x90113,x90113),x90111),x90112)),f332(f158(f852(x90113,x90113)),f332(f332(f167(x90113,x90113),x90114),x90114))))
% 52.62/52.41 [9041]~P1(f332(f332(f334(f852(x90411,x90411)),f332(f332(f241(x90411,x90411),x90413),x90412)),f300(x90411,x90414)))+~P38(x90411,f332(f332(f302(f852(x90411,x90411)),f332(f332(f241(x90411,x90411),x90412),x90413)),x90414))
% 52.62/52.41 [9042]~P1(f332(f332(f334(f852(x90421,x90421)),f332(f332(f241(x90421,x90421),x90423),x90422)),f300(x90421,x90424)))+~P58(x90421,f332(f332(f302(f852(x90421,x90421)),f332(f332(f241(x90421,x90421),x90422),x90423)),x90424))
% 52.62/52.41 [9055]P1(f332(f332(f334(x90551),x90552),f332(f158(x90551),x90553)))+~P1(f332(f332(f334(f852(x90551,x90551)),f332(f332(f241(x90551,x90551),x90552),x90554)),f332(f158(f852(x90551,x90551)),f332(f332(f167(x90551,x90551),x90553),x90553))))
% 52.62/52.41 [9086]~P100(x90861)+P1(f332(f332(f232(x90861),f332(f332(f179(x90861),f332(f332(f236(x90861),x90862),x90863)),f332(f332(f236(x90861),x90862),x90864))),f332(f332(f236(x90861),x90862),f332(f332(f179(x90861),x90863),x90864))))
% 52.62/52.41 [9087]~P93(x90871)+P1(f332(f332(f232(x90871),f332(f332(f103(x90871),f332(f332(f104(x90871),x90872),x90873)),f332(f332(f104(x90871),x90872),x90874))),f332(f332(f104(x90871),x90872),f332(f332(f103(x90871),x90873),x90874))))
% 52.62/52.41 [9123]P1(f332(f332(f334(f852(x91231,x91231)),f332(f332(f241(x91231,x91231),x91232),x91233)),f332(f332(f281(x91231,x91231,x91231),x91234),f300(x91231,x91234))))+~P1(f332(f332(f334(f852(x91231,x91231)),f332(f332(f241(x91231,x91231),x91232),x91233)),x91234))
% 52.62/52.41 [9150]~E(f332(f303(x91502,x91501,x91503),f239(f853(x91502,a839))),f239(f853(x91501,a839)))+P1(f332(f332(f232(f853(x91501,a839)),f332(f81(f853(x91501,a839)),f332(f303(x91502,x91501,x91503),x91504))),f332(f303(x91502,x91501,x91503),f332(f81(f853(x91502,a839)),x91504))))
% 52.62/52.41 [9453]P1(f332(f332(f334(f852(x94531,x94531)),f332(f332(f241(x94531,x94531),x94532),x94533)),f332(f278(x94531,x94531),f332(f332(f281(x94531,x94531,x94531),x94534),f300(x94531,x94534)))))+~P1(f332(f332(f334(f852(x94531,x94531)),f332(f332(f241(x94531,x94531),x94532),x94533)),f332(f332(f281(x94531,x94531,x94531),f332(f278(x94531,x94531),x94534)),f300(x94531,f332(f278(x94531,x94531),x94534)))))
% 52.62/52.41 [9454]~P1(f332(f332(f334(f852(x94541,x94541)),f332(f332(f241(x94541,x94541),x94542),x94543)),f332(f278(x94541,x94541),f332(f332(f281(x94541,x94541,x94541),x94544),f300(x94541,x94544)))))+P1(f332(f332(f334(f852(x94541,x94541)),f332(f332(f241(x94541,x94541),x94542),x94543)),f332(f332(f281(x94541,x94541,x94541),f332(f278(x94541,x94541),x94544)),f300(x94541,f332(f278(x94541,x94541),x94544)))))
% 52.62/52.41 [9479]~P1(f332(f332(f334(x94792),x94794),f332(f259(x94791,x94792),x94793)))+P1(f332(f332(f334(f852(x94791,x94792)),f332(f332(f241(x94791,x94792),f594(x94793,x94791,x94794,x94792)),x94794)),x94793))
% 52.62/52.41 [9480]~P1(f332(f332(f334(x94802),x94804),f332(f259(x94801,x94802),x94803)))+P1(f332(f332(f334(f852(x94801,x94802)),f332(f332(f241(x94801,x94802),f595(x94803,x94801,x94804,x94802)),x94804)),x94803))
% 52.62/52.41 [9499]~P1(f332(f332(f334(x94991),x94994),f332(f332(f103(f853(x94991,a839)),x94992),x94993)))+P1(f332(f332(f332(f103(f853(x94991,a839)),f332(f332(f9(x94991,f853(x94991,a839),a839),f334(x94991)),x94992)),f332(f332(f9(x94991,f853(x94991,a839),a839),f334(x94991)),x94993)),x94994))
% 52.62/52.41 [9500]~P1(f332(f332(f334(x95001),x95004),f332(f332(f104(f853(x95001,a839)),x95002),x95003)))+P1(f332(f332(f332(f104(f853(x95001,a839)),f332(f332(f9(x95001,f853(x95001,a839),a839),f334(x95001)),x95002)),f332(f332(f9(x95001,f853(x95001,a839),a839),f334(x95001)),x95003)),x95004))
% 52.62/52.41 [9573]~P1(f332(f332(f334(f852(x95731,x95731)),f332(f332(f241(x95731,x95731),x95734),x95733)),f332(f332(f281(x95731,x95731,x95731),x95732),f300(x95731,x95732))))+P1(f332(f332(f334(f852(x95731,x95731)),f332(f332(f241(x95731,x95731),f654(x95732,x95733,x95734,x95731)),x95733)),x95732))
% 52.62/52.41 [9608]P1(f332(f332(f334(x96081),x96082),f332(f332(f103(f853(x96081,a839)),x96083),x96084)))+~P1(f332(f332(f332(f103(f853(x96081,a839)),f332(f332(f9(x96081,f853(x96081,a839),a839),f334(x96081)),x96083)),f332(f332(f9(x96081,f853(x96081,a839),a839),f334(x96081)),x96084)),x96082))
% 52.62/52.41 [9609]P1(f332(f332(f334(x96091),x96092),f332(f332(f104(f853(x96091,a839)),x96093),x96094)))+~P1(f332(f332(f332(f104(f853(x96091,a839)),f332(f332(f9(x96091,f853(x96091,a839),a839),f334(x96091)),x96093)),f332(f332(f9(x96091,f853(x96091,a839),a839),f334(x96091)),x96094)),x96092))
% 52.62/52.41 [9888]P36(x98881,f332(f332(f9(x98881,f853(f852(x98881,x98881),a839),f853(x98881,a839)),f332(f332(f10(f853(x98881,f853(f853(f852(x98881,x98881),a839),a839)),f853(f853(f852(x98881,x98881),a839),f853(x98881,a839)),x98881),f9(x98881,f853(f852(x98881,x98881),a839),a839)),f332(f332(f10(f853(x98881,f852(x98881,x98881)),f853(x98881,f853(f853(f852(x98881,x98881),a839),a839)),x98881),f332(f10(f852(x98881,x98881),f853(f853(f852(x98881,x98881),a839),a839),x98881),f334(f852(x98881,x98881)))),f241(x98881,x98881)))),x98882),x98883,x98884)+~P1(f332(f332(f334(f852(f846(x98881),f846(x98881))),f332(f332(f241(f846(x98881),f846(x98881)),x98883),x98884)),f147(x98881,x98882)))
% 52.62/52.41 [9892]P59(x98921,f332(f332(f9(x98921,f853(f852(x98921,x98921),a839),f853(x98921,a839)),f332(f332(f10(f853(x98921,f853(f853(f852(x98921,x98921),a839),a839)),f853(f853(f852(x98921,x98921),a839),f853(x98921,a839)),x98921),f9(x98921,f853(f852(x98921,x98921),a839),a839)),f332(f332(f10(f853(x98921,f852(x98921,x98921)),f853(x98921,f853(f853(f852(x98921,x98921),a839),a839)),x98921),f332(f10(f852(x98921,x98921),f853(f853(f852(x98921,x98921),a839),a839),x98921),f334(f852(x98921,x98921)))),f241(x98921,x98921)))),x98922),x98923,x98924)+~P1(f332(f332(f334(f852(f853(x98921,a839),f853(x98921,a839))),f332(f332(f241(f853(x98921,a839),f853(x98921,a839)),x98923),x98924)),f325(x98921,x98922)))
% 52.62/52.41 [9921]E(x99211,x99212)+~E(f332(f332(f9(x99213,f853(f852(x99213,x99214),a839),f853(x99214,a839)),f332(f332(f10(f853(x99214,f853(f853(f852(x99213,x99214),a839),a839)),f853(f853(f852(x99213,x99214),a839),f853(x99214,a839)),x99213),f9(x99214,f853(f852(x99213,x99214),a839),a839)),f332(f332(f10(f853(x99214,f852(x99213,x99214)),f853(x99214,f853(f853(f852(x99213,x99214),a839),a839)),x99213),f332(f10(f852(x99213,x99214),f853(f853(f852(x99213,x99214),a839),a839),x99214),f334(f852(x99213,x99214)))),f241(x99213,x99214)))),x99211),f332(f332(f9(x99213,f853(f852(x99213,x99214),a839),f853(x99214,a839)),f332(f332(f10(f853(x99214,f853(f853(f852(x99213,x99214),a839),a839)),f853(f853(f852(x99213,x99214),a839),f853(x99214,a839)),x99213),f9(x99214,f853(f852(x99213,x99214),a839),a839)),f332(f332(f10(f853(x99214,f852(x99213,x99214)),f853(x99214,f853(f853(f852(x99213,x99214),a839),a839)),x99213),f332(f10(f852(x99213,x99214),f853(f853(f852(x99213,x99214),a839),a839),x99214),f334(f852(x99213,x99214)))),f241(x99213,x99214)))),x99212))
% 52.62/52.41 [9924]~P36(x99241,f332(f332(f9(x99241,f853(f852(x99241,x99241),a839),f853(x99241,a839)),f332(f332(f10(f853(x99241,f853(f853(f852(x99241,x99241),a839),a839)),f853(f853(f852(x99241,x99241),a839),f853(x99241,a839)),x99241),f9(x99241,f853(f852(x99241,x99241),a839),a839)),f332(f332(f10(f853(x99241,f852(x99241,x99241)),f853(x99241,f853(f853(f852(x99241,x99241),a839),a839)),x99241),f332(f10(f852(x99241,x99241),f853(f853(f852(x99241,x99241),a839),a839),x99241),f334(f852(x99241,x99241)))),f241(x99241,x99241)))),x99244),x99242,x99243)+P1(f332(f332(f334(f852(f846(x99241),f846(x99241))),f332(f332(f241(f846(x99241),f846(x99241)),x99242),x99243)),f147(x99241,x99244)))
% 52.62/52.41 [9925]~P59(x99251,f332(f332(f9(x99251,f853(f852(x99251,x99251),a839),f853(x99251,a839)),f332(f332(f10(f853(x99251,f853(f853(f852(x99251,x99251),a839),a839)),f853(f853(f852(x99251,x99251),a839),f853(x99251,a839)),x99251),f9(x99251,f853(f852(x99251,x99251),a839),a839)),f332(f332(f10(f853(x99251,f852(x99251,x99251)),f853(x99251,f853(f853(f852(x99251,x99251),a839),a839)),x99251),f332(f10(f852(x99251,x99251),f853(f853(f852(x99251,x99251),a839),a839),x99251),f334(f852(x99251,x99251)))),f241(x99251,x99251)))),x99254),x99252,x99253)+P1(f332(f332(f334(f852(f853(x99251,a839),f853(x99251,a839))),f332(f332(f241(f853(x99251,a839),f853(x99251,a839)),x99252),x99253)),f325(x99251,x99254)))
% 52.62/52.41 [7418]~P88(x74181)+E(f332(f332(f82(x74181),f332(f106(x74181),x74182)),f332(f332(f82(x74181),f332(f106(x74181),x74183)),x74184)),f332(f332(f82(x74181),f332(f106(x74181),f332(f332(f82(a1),x74182),x74183))),x74184))
% 52.62/52.41 [7419]~P88(x74191)+E(f332(f332(f82(x74191),f332(f106(x74191),x74192)),f332(f332(f3(x74191),f332(f106(x74191),x74193)),x74194)),f332(f332(f3(x74191),f332(f106(x74191),f332(f332(f82(a1),x74192),x74193))),x74194))
% 52.62/52.41 [7420]~P88(x74201)+E(f332(f332(f83(x74201),f332(f106(x74201),x74202)),f332(f332(f83(x74201),f332(f106(x74201),x74203)),x74204)),f332(f332(f83(x74201),f332(f106(x74201),f332(f332(f83(a1),x74202),x74203))),x74204))
% 52.62/52.41 [7467]~P2(x74671)+E(f332(f154(x74671),f332(f332(f143(x74672,x74671),f332(f18(x74671,x74672),x74673)),x74674)),f332(f332(f83(x74671),f332(f102(x74671),f332(f181(f846(x74672)),x74674))),x74673))
% 52.62/52.41 [7703]E(f332(f265(x77031,f332(f332(f140(f852(a101,x77031)),x77032),x77033)),x77034),f332(f250(a101,x77031),x77032))+~P1(f332(f332(f233(a101),x77034),f332(f240(a101,x77031),x77032)))
% 52.62/52.41 [7751]~P88(x77511)+E(f332(f332(f82(x77511),f332(f106(x77511),x77512)),f332(f332(f3(x77511),x77513),f332(f106(x77511),x77514))),f332(f332(f82(x77511),f332(f106(x77511),f332(f332(f82(a1),x77512),f332(f81(a1),x77514)))),x77513))
% 52.62/52.41 [7882]E(f332(f265(x78821,x78822),f332(f332(f3(a101),x78823),f332(f240(a101,x78821),x78824))),f332(f265(x78821,f332(f332(f140(f852(a101,x78821)),x78824),x78822)),x78823))+P1(f332(f332(f233(a101),x78823),f332(f240(a101,x78821),x78824)))
% 52.62/52.41 [8313]~P1(f332(f332(f334(x83131),x83132),f332(f158(x83131),f116(x83131,x83134))))+P1(f332(f332(f334(x83131),x83132),f332(f158(x83131),f116(x83131,f332(f332(f125(x83131),x83133),x83134)))))
% 52.62/52.41 [8314]~P1(f332(f332(f334(x83141),x83142),f332(f158(x83141),f116(x83141,x83143))))+P1(f332(f332(f334(x83141),x83142),f332(f158(x83141),f116(x83141,f332(f332(f125(x83141),x83143),x83144)))))
% 52.62/52.41 [8337]E(f332(f332(f103(f853(x83371,a839)),f332(f332(f104(f853(x83371,a839)),x83372),x83373)),x83374),f332(f332(f104(f853(x83371,a839)),x83372),f332(f332(f103(f853(x83371,a839)),x83373),x83374)))+~P1(f332(f332(f232(f853(x83371,a839)),x83374),x83372))
% 52.62/52.41 [8624]~E(f332(f332(f103(f853(x86241,a839)),f332(f332(f104(f853(x86241,a839)),x86243),x86244)),x86242),f332(f332(f104(f853(x86241,a839)),x86243),f332(f332(f103(f853(x86241,a839)),x86244),x86242)))+P1(f332(f332(f232(f853(x86241,a839)),x86242),x86243))
% 52.62/52.41 [8873]~P1(f332(f332(f232(f853(x88731,a839)),x88732),f332(f332(f103(f853(x88731,a839)),x88733),x88734)))+P1(f332(f332(f232(f853(x88731,a839)),f332(f332(f3(f853(x88731,a839)),x88732),x88733)),x88734))
% 52.62/52.41 [8992]P1(f332(f332(f232(f853(x89921,a839)),x89922),f332(f332(f103(f853(x89921,a839)),x89923),x89924)))+~P1(f332(f332(f232(f853(x89921,a839)),f332(f332(f3(f853(x89921,a839)),x89922),x89923)),x89924))
% 52.62/52.41 [9068]~P80(x90681)+E(f332(f77(x90681),f332(f332(f8(x90682,x90681),f332(f332(f10(x90681,x90681,x90682),f77(x90681)),x90683)),x90684)),f332(f332(f8(x90682,x90681),f332(f332(f10(x90681,x90681,x90682),f77(x90681)),x90683)),x90684))
% 52.62/52.41 [9213]~P80(x92131)+P1(f332(f332(f232(x92131),f2(x92131)),f332(f332(f8(x92132,x92131),f332(f332(f10(x92131,x92131,x92132),f77(x92131)),x92133)),x92134)))
% 52.62/52.41 [9216]~P8(x92161)+E(f332(f154(x92161),f332(f332(f143(x92162,x92161),f332(f75(x92161,x92161,x92162,f81(x92161)),x92163)),x92164)),f332(f81(x92161),f332(f154(x92161),f332(f332(f143(x92162,x92161),x92163),x92164))))
% 52.62/52.41 [9353]~P80(x93531)+P1(f332(f332(f232(x93531),f332(f77(x93531),f332(f332(f8(x93532,x93531),x93533),x93534))),f332(f332(f8(x93532,x93531),f332(f332(f10(x93531,x93531,x93532),f77(x93531)),x93533)),x93534)))
% 52.62/52.41 [9381]~E(f332(f332(f82(a845),x93811),x93814),f332(f332(f82(a845),x93813),x93812))+P1(f332(f332(f334(f852(f852(a845,a845),f852(a845,a845))),f332(f332(f241(f852(a845,a845),f852(a845,a845)),f332(f332(f241(a845,a845),x93811),x93812)),f332(f332(f241(a845,a845),x93813),x93814))),a111))
% 52.62/52.41 [9382]~P1(f332(f332(f233(a845),x93821),x93823))+P1(f332(f332(f334(f852(f852(a845,a845),f852(a845,a845))),f332(f332(f241(f852(a845,a845),f852(a845,a845)),f332(f332(f241(a845,a845),x93821),x93822)),f332(f332(f241(a845,a845),x93823),x93824))),a40))
% 52.62/52.41 [9383]~P1(f332(f332(f233(a845),x93831),x93833))+P1(f332(f332(f334(f852(f852(a845,a845),f852(a845,a845))),f332(f332(f241(f852(a845,a845),f852(a845,a845)),f332(f332(f241(a845,a845),x93831),x93832)),f332(f332(f241(a845,a845),x93833),x93834))),a72))
% 52.62/52.41 [9522]E(f332(f332(f82(a845),x95221),x95222),f332(f332(f82(a845),x95223),x95224))+~P1(f332(f332(f334(f852(f852(a845,a845),f852(a845,a845))),f332(f332(f241(f852(a845,a845),f852(a845,a845)),f332(f332(f241(a845,a845),x95221),x95224)),f332(f332(f241(a845,a845),x95223),x95222))),a111))
% 52.62/52.41 [9566]~P1(f332(f332(f334(x95662),x95664),f332(f332(f47(x95661,f853(x95662,a839)),f239(f853(x95661,a839))),x95663)))+P1(f332(f332(f332(f47(x95661,f853(x95662,a839)),f239(f853(x95661,a839))),f332(f332(f10(f853(x95662,a839),f853(x95662,a839),x95661),f332(f9(x95662,f853(x95662,a839),a839),f334(x95662))),x95663)),x95664))
% 52.62/52.41 [9567]~P1(f332(f332(f334(x95672),x95674),f332(f332(f48(x95671,f853(x95672,a839)),f239(f853(x95671,a839))),x95673)))+P1(f332(f332(f332(f48(x95671,f853(x95672,a839)),f239(f853(x95671,a839))),f332(f332(f10(f853(x95672,a839),f853(x95672,a839),x95671),f332(f9(x95672,f853(x95672,a839),a839),f334(x95672))),x95673)),x95674))
% 52.62/52.41 [9633]~P1(f332(f57(x96331,x96332),f332(f332(f241(a1,a1),x96334),x96333)))+P1(f332(f57(f332(f81(a1),x96331),x96332),f332(f332(f241(a1,a1),f332(f332(f332(f98(a1),f332(f332(a329,x96333),f2(a1))),f332(f81(a1),x96334)),f332(f332(f3(a1),f332(f81(a1),x96334)),f80(a1)))),f332(f332(f332(f98(a1),f332(f332(a329,x96333),f2(a1))),f2(a1)),f332(f332(f3(a1),x96332),x96333)))))
% 52.62/52.41 [9642]P1(f332(f332(f334(x96421),x96422),f332(f332(f47(x96423,f853(x96421,a839)),f239(f853(x96423,a839))),x96424)))+~P1(f332(f332(f332(f47(x96423,f853(x96421,a839)),f239(f853(x96423,a839))),f332(f332(f10(f853(x96421,a839),f853(x96421,a839),x96423),f332(f9(x96421,f853(x96421,a839),a839),f334(x96421))),x96424)),x96422))
% 52.62/52.41 [9643]P1(f332(f332(f334(x96431),x96432),f332(f332(f48(x96433,f853(x96431,a839)),f239(f853(x96433,a839))),x96434)))+~P1(f332(f332(f332(f48(x96433,f853(x96431,a839)),f239(f853(x96433,a839))),f332(f332(f10(f853(x96431,a839),f853(x96431,a839),x96433),f332(f9(x96431,f853(x96431,a839),a839),f334(x96431))),x96434)),x96432))
% 52.62/52.41 [9654]E(f332(f332(f47(a845,f853(x96541,a839)),f239(f853(a845,a839))),x96542),f332(f332(f47(a845,f853(x96541,a839)),f239(f853(a845,a839))),x96543))+~E(f332(f332(f47(a845,f853(x96541,a839)),f332(f294(a845,f2(a845)),f399(x96542,x96544,x96543,x96541))),x96543),f332(f332(f47(a845,f853(x96541,a839)),f332(f294(a845,f2(a845)),f332(f332(f82(a845),f399(x96542,x96544,x96543,x96541)),x96544))),x96542))
% 52.62/52.41 [9985]~P1(f332(f332(f232(f853(f852(x99851,x99852),a839)),x99853),x99854))+P1(f332(f332(f232(f853(x99851,f853(x99852,a839))),f332(f332(f9(x99851,f853(f852(x99851,x99852),a839),f853(x99852,a839)),f332(f332(f10(f853(x99852,f853(f853(f852(x99851,x99852),a839),a839)),f853(f853(f852(x99851,x99852),a839),f853(x99852,a839)),x99851),f9(x99852,f853(f852(x99851,x99852),a839),a839)),f332(f332(f10(f853(x99852,f852(x99851,x99852)),f853(x99852,f853(f853(f852(x99851,x99852),a839),a839)),x99851),f332(f10(f852(x99851,x99852),f853(f853(f852(x99851,x99852),a839),a839),x99852),f334(f852(x99851,x99852)))),f241(x99851,x99852)))),x99853)),f332(f332(f9(x99851,f853(f852(x99851,x99852),a839),f853(x99852,a839)),f332(f332(f10(f853(x99852,f853(f853(f852(x99851,x99852),a839),a839)),f853(f853(f852(x99851,x99852),a839),f853(x99852,a839)),x99851),f9(x99852,f853(f852(x99851,x99852),a839),a839)),f332(f332(f10(f853(x99852,f852(x99851,x99852)),f853(x99852,f853(f853(f852(x99851,x99852),a839),a839)),x99851),f332(f10(f852(x99851,x99852),f853(f853(f852(x99851,x99852),a839),a839),x99852),f334(f852(x99851,x99852)))),f241(x99851,x99852)))),x99854)))
% 52.62/52.41 [10001]P1(f332(f332(f232(f853(f852(x100011,x100012),a839)),x100013),x100014))+~P1(f332(f332(f232(f853(x100011,f853(x100012,a839))),f332(f332(f9(x100011,f853(f852(x100011,x100012),a839),f853(x100012,a839)),f332(f332(f10(f853(x100012,f853(f853(f852(x100011,x100012),a839),a839)),f853(f853(f852(x100011,x100012),a839),f853(x100012,a839)),x100011),f9(x100012,f853(f852(x100011,x100012),a839),a839)),f332(f332(f10(f853(x100012,f852(x100011,x100012)),f853(x100012,f853(f853(f852(x100011,x100012),a839),a839)),x100011),f332(f10(f852(x100011,x100012),f853(f853(f852(x100011,x100012),a839),a839),x100012),f334(f852(x100011,x100012)))),f241(x100011,x100012)))),x100013)),f332(f332(f9(x100011,f853(f852(x100011,x100012),a839),f853(x100012,a839)),f332(f332(f10(f853(x100012,f853(f853(f852(x100011,x100012),a839),a839)),f853(f853(f852(x100011,x100012),a839),f853(x100012,a839)),x100011),f9(x100012,f853(f852(x100011,x100012),a839),a839)),f332(f332(f10(f853(x100012,f852(x100011,x100012)),f853(x100012,f853(f853(f852(x100011,x100012),a839),a839)),x100011),f332(f10(f852(x100011,x100012),f853(f853(f852(x100011,x100012),a839),a839),x100012),f334(f852(x100011,x100012)))),f241(x100011,x100012)))),x100014)))
% 52.62/52.41 [9113]~P1(f332(f332(f334(f852(x91131,x91131)),x91132),f300(x91131,x91134)))+P1(f332(f332(f334(f852(x91131,x91131)),x91132),f300(x91131,f332(f332(f103(f853(f852(x91131,x91131),a839)),x91133),x91134))))
% 52.62/52.41 [9114]~P1(f332(f332(f334(f852(x91141,x91141)),x91142),f300(x91141,x91143)))+P1(f332(f332(f334(f852(x91141,x91141)),x91142),f300(x91141,f332(f332(f103(f853(f852(x91141,x91141),a839)),x91143),x91144))))
% 52.62/52.41 [9445]~E(f332(f158(x94451),x94454),f169(x94451,x94452,x94453))+E(f166(x94451,x94452,f332(f332(f143(x94451,f852(x94451,x94452)),f332(f332(f20(x94451,x94452,f852(x94451,x94452)),f241(x94451,x94452)),f332(f332(f10(f849(x94452),x94452,x94451),f231(x94452)),x94453))),x94454)),x94453)
% 52.62/52.41 [9737]~P1(f332(f332(f233(a845),f332(f332(f82(a845),x97371),x97374)),f332(f332(f82(a845),x97373),x97372)))+P1(f332(f332(f233(a1),f332(a91,f332(f277(f852(a845,a845),f852(a845,a845),a111),f332(f332(f302(f852(a845,a845)),f332(f332(f241(a845,a845),x97371),x97372)),f180(f853(f852(a845,a845),a839)))))),f332(a91,f332(f277(f852(a845,a845),f852(a845,a845),a111),f332(f332(f302(f852(a845,a845)),f332(f332(f241(a845,a845),x97373),x97374)),f180(f853(f852(a845,a845),a839)))))))
% 52.62/52.41 [9738]~P1(f332(f332(f232(a845),f332(f332(f82(a845),x97381),x97384)),f332(f332(f82(a845),x97383),x97382)))+P1(f332(f332(f232(a1),f332(a91,f332(f277(f852(a845,a845),f852(a845,a845),a111),f332(f332(f302(f852(a845,a845)),f332(f332(f241(a845,a845),x97381),x97382)),f180(f853(f852(a845,a845),a839)))))),f332(a91,f332(f277(f852(a845,a845),f852(a845,a845),a111),f332(f332(f302(f852(a845,a845)),f332(f332(f241(a845,a845),x97383),x97384)),f180(f853(f852(a845,a845),a839)))))))
% 52.62/52.41 [9826]P1(f332(f332(f233(a845),f332(f332(f82(a845),x98261),x98262)),f332(f332(f82(a845),x98263),x98264)))+~P1(f332(f332(f233(a1),f332(a91,f332(f277(f852(a845,a845),f852(a845,a845),a111),f332(f332(f302(f852(a845,a845)),f332(f332(f241(a845,a845),x98261),x98264)),f180(f853(f852(a845,a845),a839)))))),f332(a91,f332(f277(f852(a845,a845),f852(a845,a845),a111),f332(f332(f302(f852(a845,a845)),f332(f332(f241(a845,a845),x98263),x98262)),f180(f853(f852(a845,a845),a839)))))))
% 52.62/52.41 [9827]P1(f332(f332(f232(a845),f332(f332(f82(a845),x98271),x98272)),f332(f332(f82(a845),x98273),x98274)))+~P1(f332(f332(f232(a1),f332(a91,f332(f277(f852(a845,a845),f852(a845,a845),a111),f332(f332(f302(f852(a845,a845)),f332(f332(f241(a845,a845),x98271),x98274)),f180(f853(f852(a845,a845),a839)))))),f332(a91,f332(f277(f852(a845,a845),f852(a845,a845),a111),f332(f332(f302(f852(a845,a845)),f332(f332(f241(a845,a845),x98273),x98272)),f180(f853(f852(a845,a845),a839)))))))
% 52.62/52.41 [9874]P1(f332(f332(f232(f853(x98741,a839)),f332(f332(f47(a845,f853(x98741,a839)),f239(f853(a845,a839))),x98742)),f332(f332(f47(a845,f853(x98741,a839)),f239(f853(a845,a839))),x98743)))+~P1(f332(f332(f232(f853(x98741,a839)),f332(f332(f47(a845,f853(x98741,a839)),f332(f294(a845,f2(a845)),f400(x98743,x98744,x98742,x98741))),x98742)),f332(f332(f47(a845,f853(x98741,a839)),f332(f294(a845,f2(a845)),f332(f332(f82(a845),f400(x98743,x98744,x98742,x98741)),x98744))),x98743)))
% 52.62/52.41 [9927]P1(f332(f332(f232(a101),x99274),f2(a101)))+E(f332(f332(f253(f852(a101,a101),f852(x99271,f853(a848,a837)),f852(a101,a101),f852(f853(a101,f853(a839,f849(f847(x99271)))),f852(a101,a101))),f332(x99272,x99273)),f332(f332(f10(f853(f853(a101,f853(a839,f849(f847(x99271)))),f853(f852(a101,a101),f852(f853(a101,f853(a839,f849(f847(x99271)))),f852(a101,a101)))),f853(f852(a101,a101),f852(f853(a101,f853(a839,f849(f847(x99271)))),f852(a101,a101))),f852(x99271,f853(a848,a837))),f332(f253(f852(a101,a101),f853(a101,f853(a839,f849(f847(x99271)))),f852(a101,a101),f852(f853(a101,f853(a839,f849(f847(x99271)))),f852(a101,a101))),f272(x99271,x99272,f332(f332(f3(a101),x99274),f80(a101)),x99273))),f332(f332(f10(f853(f853(a101,f853(a839,f849(f847(x99271)))),f853(a101,f853(a839,f849(f847(x99271))))),f853(f853(a101,f853(a839,f849(f847(x99271)))),f853(f852(a101,a101),f852(f853(a101,f853(a839,f849(f847(x99271)))),f852(a101,a101)))),f852(x99271,f853(a848,a837))),f332(f10(f853(a101,f853(a839,f849(f847(x99271)))),f853(f852(a101,a101),f852(f853(a101,f853(a839,f849(f847(x99271)))),f852(a101,a101))),f853(a101,f853(a839,f849(f847(x99271))))),f241(f853(a101,f853(a839,f849(f847(x99271)))),f852(a101,a101)))),f332(f332(f10(f853(a101,f853(a839,f849(f847(x99271)))),f853(f853(a101,f853(a839,f849(f847(x99271)))),f853(a101,f853(a839,f849(f847(x99271))))),f852(x99271,f853(a848,a837))),f52(x99271)),f332(f332(f10(x99271,f853(a101,f853(a839,f849(f847(x99271)))),f852(x99271,f853(a848,a837))),f50(x99271)),f240(x99271,f853(a848,a837))))))),f272(x99271,x99272,x99274,x99273))
% 52.62/52.41 [9976]~P1(f332(f332(f334(x99762),x99764),f332(f259(x99761,x99762),x99763)))+P1(f332(f247(x99761,x99762,f332(f332(f9(x99761,f853(f852(x99761,x99762),a839),f853(x99762,a839)),f332(f332(f10(f853(x99762,f853(f853(f852(x99761,x99762),a839),a839)),f853(f853(f852(x99761,x99762),a839),f853(x99762,a839)),x99761),f9(x99762,f853(f852(x99761,x99762),a839),a839)),f332(f332(f10(f853(x99762,f852(x99761,x99762)),f853(x99762,f853(f853(f852(x99761,x99762),a839),a839)),x99761),f332(f10(f852(x99761,x99762),f853(f853(f852(x99761,x99762),a839),a839),x99762),f334(f852(x99761,x99762)))),f241(x99761,x99762)))),x99763)),x99764))
% 52.62/52.41 [9977]~P1(f332(f332(f334(x99771),x99774),f332(f261(x99771,x99772),x99773)))+P1(f332(f246(x99771,x99772,f332(f332(f9(x99771,f853(f852(x99771,x99772),a839),f853(x99772,a839)),f332(f332(f10(f853(x99772,f853(f853(f852(x99771,x99772),a839),a839)),f853(f853(f852(x99771,x99772),a839),f853(x99772,a839)),x99771),f9(x99772,f853(f852(x99771,x99772),a839),a839)),f332(f332(f10(f853(x99772,f852(x99771,x99772)),f853(x99772,f853(f853(f852(x99771,x99772),a839),a839)),x99771),f332(f10(f852(x99771,x99772),f853(f853(f852(x99771,x99772),a839),a839),x99772),f334(f852(x99771,x99772)))),f241(x99771,x99772)))),x99773)),x99774))
% 52.62/52.41 [9988]P1(f332(f332(f334(x99881),x99882),f332(f259(x99883,x99881),x99884)))+~P1(f332(f247(x99883,x99881,f332(f332(f9(x99883,f853(f852(x99883,x99881),a839),f853(x99881,a839)),f332(f332(f10(f853(x99881,f853(f853(f852(x99883,x99881),a839),a839)),f853(f853(f852(x99883,x99881),a839),f853(x99881,a839)),x99883),f9(x99881,f853(f852(x99883,x99881),a839),a839)),f332(f332(f10(f853(x99881,f852(x99883,x99881)),f853(x99881,f853(f853(f852(x99883,x99881),a839),a839)),x99883),f332(f10(f852(x99883,x99881),f853(f853(f852(x99883,x99881),a839),a839),x99881),f334(f852(x99883,x99881)))),f241(x99883,x99881)))),x99884)),x99882))
% 52.62/52.41 [9989]P1(f332(f332(f334(x99891),x99892),f332(f261(x99891,x99893),x99894)))+~P1(f332(f246(x99891,x99893,f332(f332(f9(x99891,f853(f852(x99891,x99893),a839),f853(x99893,a839)),f332(f332(f10(f853(x99893,f853(f853(f852(x99891,x99893),a839),a839)),f853(f853(f852(x99891,x99893),a839),f853(x99893,a839)),x99891),f9(x99893,f853(f852(x99891,x99893),a839),a839)),f332(f332(f10(f853(x99893,f852(x99891,x99893)),f853(x99893,f853(f853(f852(x99891,x99893),a839),a839)),x99891),f332(f10(f852(x99891,x99893),f853(f853(f852(x99891,x99893),a839),a839),x99893),f334(f852(x99891,x99893)))),f241(x99891,x99893)))),x99894)),x99892))
% 52.62/52.41 [9751]~P73(x97511)+E(f332(f332(f83(x97511),f332(f332(f82(x97511),f80(x97511)),f80(x97511))),f332(f332(f8(a845,x97511),f332(f332(f10(x97511,x97511,a845),f332(f82(x97511),x97512)),f332(f332(f9(a845,x97511,x97511),f332(f332(f10(x97511,f853(x97511,x97511),a845),f83(x97511)),f102(x97511))),x97513))),f332(f257(a845),x97514))),f332(f332(f83(x97511),f332(f102(x97511),x97514)),f332(f332(f82(x97511),x97512),f332(f332(f82(x97511),x97512),f332(f332(f83(x97511),f332(f102(x97511),f332(f332(f3(a845),x97514),f80(a845)))),x97513)))))
% 52.62/52.41 [9895]P1(f332(x98951,f590(x98952,x98953,x98954,x98951)))+P38(x98952,f332(f256(f852(x98952,x98952)),f332(f251(x98952,x98952,a839),f332(f332(f10(f853(x98952,a839),f853(x98952,a839),x98952),f332(f20(x98952,a839,a839),f332(f332(f10(a839,f853(a839,a839),x98952),a330),x98951))),f332(f332(f9(x98952,f853(x98952,x98952),f853(x98952,a839)),f332(f332(f10(f853(x98952,a839),f853(f853(x98952,x98952),f853(x98952,a839)),x98952),f10(x98952,a839,x98952)),a329)),x98953)))))
% 52.62/52.41 [9909]~P1(f332(f332(f233(a845),f332(x99094,f332(x99093,f590(x99091,x99093,x99094,x99092)))),f332(x99094,f590(x99091,x99093,x99094,x99092))))+P38(x99091,f332(f256(f852(x99091,x99091)),f332(f251(x99091,x99091,a839),f332(f332(f10(f853(x99091,a839),f853(x99091,a839),x99091),f332(f20(x99091,a839,a839),f332(f332(f10(a839,f853(a839,a839),x99091),a330),x99092))),f332(f332(f9(x99091,f853(x99091,x99091),f853(x99091,a839)),f332(f332(f10(f853(x99091,a839),f853(f853(x99091,x99091),f853(x99091,a839)),x99091),f10(x99091,a839,x99091)),a329)),x99093)))))
% 52.62/52.41 [10013]~P1(f332(f332(f334(f852(x100131,x100131)),f332(f332(f241(x100131,x100131),x100133),x100134)),f332(f332(f103(f853(f852(x100131,x100131),a839)),x100132),f300(x100131,f180(f853(f852(x100131,x100131),a839))))))+P1(f332(f332(f332(f332(f103(f853(x100131,f853(x100131,a839))),f332(f332(f9(x100131,f853(f852(x100131,x100131),a839),f853(x100131,a839)),f332(f332(f10(f853(x100131,f853(f853(f852(x100131,x100131),a839),a839)),f853(f853(f852(x100131,x100131),a839),f853(x100131,a839)),x100131),f9(x100131,f853(f852(x100131,x100131),a839),a839)),f332(f332(f10(f853(x100131,f852(x100131,x100131)),f853(x100131,f853(f853(f852(x100131,x100131),a839),a839)),x100131),f332(f10(f852(x100131,x100131),f853(f853(f852(x100131,x100131),a839),a839),x100131),f334(f852(x100131,x100131)))),f241(x100131,x100131)))),x100132)),a329),x100133),x100134))
% 52.62/52.41 [10022]P1(f332(f332(f334(f852(x100221,x100221)),f332(f332(f241(x100221,x100221),x100222),x100223)),f332(f332(f103(f853(f852(x100221,x100221),a839)),x100224),f300(x100221,f180(f853(f852(x100221,x100221),a839))))))+~P1(f332(f332(f332(f332(f103(f853(x100221,f853(x100221,a839))),f332(f332(f9(x100221,f853(f852(x100221,x100221),a839),f853(x100221,a839)),f332(f332(f10(f853(x100221,f853(f853(f852(x100221,x100221),a839),a839)),f853(f853(f852(x100221,x100221),a839),f853(x100221,a839)),x100221),f9(x100221,f853(f852(x100221,x100221),a839),a839)),f332(f332(f10(f853(x100221,f852(x100221,x100221)),f853(x100221,f853(f853(f852(x100221,x100221),a839),a839)),x100221),f332(f10(f852(x100221,x100221),f853(f853(f852(x100221,x100221),a839),a839),x100221),f334(f852(x100221,x100221)))),f241(x100221,x100221)))),x100224)),a329),x100222),x100223))
% 52.62/52.41 [9973]E(f332(f332(f140(f846(x99731)),f332(f332(f140(x99731),x99732),f332(f132(f846(x99731),f846(x99731),f125(x99731),f115(x99731)),f332(f332(f143(f846(x99731),f846(x99731)),f145(f846(x99731),x99731,f115(x99731),f332(f332(f10(f846(x99731),f853(f846(x99731),f846(x99731)),x99731),f18(f846(x99731),f846(x99731))),f332(f332(f9(x99731,f846(x99731),f846(x99731)),f140(x99731)),f115(x99731))))),x99733)))),f164(x99731,f332(f332(f140(f846(x99731)),x99734),f332(f132(f846(f846(x99731)),f846(f846(x99731)),f125(f846(x99731)),f115(f846(x99731))),f332(f332(f143(f846(x99731),f846(f846(x99731))),f145(f846(f846(x99731)),x99731,f115(f846(x99731)),f332(f18(f853(f846(x99731),f846(f846(x99731))),x99731),f332(f332(f9(f846(x99731),f846(f846(x99731)),f846(f846(x99731))),f140(f846(x99731))),f115(f846(x99731)))))),x99733))))),f164(x99731,f332(f332(f140(f846(x99731)),f332(f332(f140(x99731),x99732),x99734)),x99733)))+~P1(f332(f321(f846(f846(x99731)),f165(x99731)),f332(f332(f140(f846(x99731)),f332(f332(f140(x99731),x99732),x99734)),x99733)))
% 52.62/52.41 [10012]~P1(f332(f64(x100122),f332(f256(x100122),x100124)))+P1(f332(f64(x100121),f332(f256(x100121),f332(f332(f10(f853(x100122,a839),a839,x100121),f89(x100122)),f332(f332(f9(x100121,f853(x100122,a839),f853(x100122,a839)),f332(f332(f10(f853(x100122,f853(a839,a839)),f853(f853(x100122,a839),f853(x100122,a839)),x100121),f20(x100122,a839,a839)),f332(f332(f10(f853(x100122,a839),f853(x100122,f853(a839,a839)),x100121),f332(f10(a839,f853(a839,a839),x100122),a330)),f332(f332(f9(x100121,f853(x100122,x100121),f853(x100122,a839)),f332(f332(f10(f853(x100121,a839),f853(f853(x100122,x100121),f853(x100122,a839)),x100121),f10(x100121,a839,x100122)),a329)),x100123)))),x100124)))))
% 52.62/52.41 [7173]E(x71731,x71732)+~E(f316(x71733,x71734,x71735,x71731),f316(x71733,x71734,x71735,x71732))
% 52.62/52.41 [7174]E(x71741,x71742)+~E(f317(x71743,x71744,x71745,x71741),f317(x71743,x71744,x71745,x71742))
% 52.62/52.41 [8986]~P41(f36(x89861,x89865),x89862,x89863,x89864)+P41(x89861,x89862,x89863,f361(x89864,x89863,x89862,x89865,x89861))
% 52.62/52.41 [8987]~P41(f36(x89871,x89875),x89872,x89873,x89874)+P41(x89871,x89872,x89873,f373(x89874,x89873,x89872,x89875,x89871))
% 52.62/52.41 [8988]~P41(f36(x89885,x89881),x89884,x89883,x89882)+P41(x89881,f361(x89882,x89883,x89884,x89881,x89885),x89883,x89882)
% 52.62/52.41 [8989]~P41(f36(x89895,x89891),x89894,x89893,x89892)+P41(x89891,f373(x89892,x89893,x89894,x89891,x89895),x89893,x89892)
% 52.62/52.41 [5519]E(f332(f332(f302(x55191),x55192),f169(x55191,x55193,x55194)),f169(x55191,x55193,x55194))+~E(f332(x55194,x55192),f332(f227(x55193),x55195))
% 52.62/52.41 [5933]P1(f332(f247(x59331,x59332,x59333),x59334))+~P1(f332(f332(x59333,x59335),x59334))
% 52.62/52.41 [5934]P1(f332(f247(x59341,x59342,x59343),x59344))+~P1(f332(f332(x59343,x59345),x59344))
% 52.62/52.41 [5935]P1(f332(f246(x59351,x59352,x59353),x59354))+~P1(f332(f332(x59353,x59354),x59355))
% 52.62/52.41 [5936]P1(f332(f246(x59361,x59362,x59363),x59364))+~P1(f332(f332(x59363,x59364),x59365))
% 52.62/52.41 [5939]~E(f332(x59394,x59392),f332(f227(x59393),x59395))+P1(f332(f332(f334(x59391),x59392),f169(x59391,x59393,x59394)))
% 52.62/52.41 [5940]~E(f332(x59404,x59405),f332(f227(x59401),x59402))+P1(f332(f332(f334(x59401),x59402),f171(x59403,x59401,x59404)))
% 52.62/52.41 [6426]~E(x64265,f2(a101))+E(f332(f193(x64261,x64262,x64263,x64264),x64265),f117(x64262))
% 52.62/52.41 [6427]~E(x64275,f2(a101))+E(f332(f191(x64271,x64272,x64273,x64274),x64275),f124(x64272))
% 52.62/52.41 [6523]~P41(f28(x65233,x65234),x65232,x65235,x65231)+E(x65231,f332(f332(f332(a189,x65232),x65233),f332(x65234,x65232)))
% 52.62/52.41 [6568]~E(x65683,f2(a101))+E(f332(f268(x65681,x65682,x65683,x65684),x65685),f332(f241(x65681,x65682),x65685))
% 52.62/52.41 [6646]~E(f332(x66464,x66465),f183(x66462))+E(f332(f229(f849(x66461),x66462,f183(x66461),x66463),f332(x66464,x66465)),f183(x66461))
% 52.62/52.41 [6647]~E(f332(x66474,x66475),f183(x66472))+E(f332(f229(f849(x66471),x66472,f183(x66471),x66473),f332(x66474,x66475)),f183(x66471))
% 52.62/52.41 [7296]E(f332(x72961,x72962),f183(x72963))+~E(f332(f170(x72964,x72963,x72965,x72961),x72962),f183(x72963))
% 52.62/52.41 [7297]E(f332(x72971,x72972),f183(x72973))+~E(f332(f170(x72974,x72973,x72971,x72975),x72972),f183(x72973))
% 52.62/52.41 [7337]E(f332(f170(x73371,x73372,x73373,x73374),x73375),f332(x73373,x73375))+P1(f332(f332(f334(x73371),x73375),f169(x73371,x73372,x73374)))
% 52.62/52.41 [7338]E(f332(f170(x73381,x73382,x73383,x73384),x73385),f332(x73384,x73385))+P1(f332(f332(f334(x73381),x73385),f169(x73381,x73382,x73383)))
% 52.62/52.41 [7664]~P26(x76644,x76641,x76642,x76645)+E(f332(f75(x76641,x76641,x76641,f332(x76642,x76643)),f332(x76642,x76643)),f332(x76642,x76643))
% 52.62/52.41 [7707]E(f332(f170(x77071,x77072,x77073,x77074),x77075),f332(x77074,x77075))+~P1(f332(f332(f334(x77071),x77075),f169(x77071,x77072,x77074)))
% 52.62/52.41 [8054]~P22(x80545,x80541,x80542)+E(f332(f75(x80541,x80541,x80541,f332(x80542,x80543)),f332(x80542,x80544)),f332(f75(x80541,x80541,x80541,f332(x80542,x80544)),f332(x80542,x80543)))
% 52.62/52.41 [8376]P1(f332(f332(f334(f852(x83761,x83761)),f332(f332(f241(x83761,x83761),x83762),x83763)),f327(x83761,x83764,x83765)))+~P1(f332(f332(f233(a845),f332(x83764,x83762)),f332(x83764,x83763)))
% 52.62/52.41 [8476]~P1(f332(f332(f334(x84764),x84763),f282(x84764,x84761,x84762,x84765)))+P1(f332(f332(x84761,x84762),x84763))
% 52.62/52.41 [8477]~P1(f332(f332(f334(x84774),x84773),f291(x84774,x84771,x84772,x84775)))+P1(f332(f332(x84771,x84772),x84773))
% 52.62/52.41 [8478]~P1(f332(f332(f334(x84784),x84782),f282(x84784,x84781,x84785,x84783)))+P1(f332(f332(x84781,x84782),x84783))
% 52.62/52.41 [8479]~P1(f332(f332(f334(x84794),x84792),f291(x84794,x84791,x84795,x84793)))+P1(f332(f332(x84791,x84792),x84793))
% 52.62/52.41 [8601]~P57(x86012,x86011,x86015,x86013,x86014)+E(f332(f303(x86011,x86012,x86013),x86014),f239(f853(x86012,a839)))
% 52.62/52.41 [9372]P1(f332(f332(f334(f852(f846(x93721),f846(x93721))),f332(f332(f241(f846(x93721),f846(x93721)),f332(f332(f140(x93721),x93722),x93723)),f332(f332(f140(x93721),x93722),x93724))),f146(x93721,x93725)))+~P1(f332(f332(f334(f852(f846(x93721),f846(x93721))),f332(f332(f241(f846(x93721),f846(x93721)),x93723),x93724)),f146(x93721,x93725)))
% 52.62/52.41 [9373]P1(f332(f332(f334(f852(f846(x93731),f846(x93731))),f332(f332(f241(f846(x93731),f846(x93731)),f332(f332(f125(x93731),x93732),x93733)),f332(f332(f125(x93731),x93732),x93734))),f137(x93731,x93735)))+~P1(f332(f332(f334(f852(f846(x93731),f846(x93731))),f332(f332(f241(f846(x93731),f846(x93731)),x93733),x93734)),f137(x93731,x93735)))
% 52.62/52.41 [9424]~E(f332(x94243,f397(x94242,x94241,x94244,x94245,x94243)),f332(f174(x94245,x94244,x94241),f397(x94242,x94241,x94244,x94245,x94243)))+E(f332(f332(x94241,x94242),f332(x94243,x94242)),f332(x94243,f332(a114,x94242)))
% 52.62/52.41 [9549]E(f332(f332(f140(x95491),f717(x95492,x95493,x95494,x95495,x95491)),f720(x95492,x95493,x95494,x95495,x95491)),x95495)+~P1(f332(f332(f334(f852(f846(x95491),f846(x95491))),f332(f332(f241(f846(x95491),f846(x95491)),x95495),f332(f332(f140(x95491),x95494),x95493))),f147(x95491,x95492)))
% 52.62/52.41 [9576]E(f332(f332(f140(x95761),f718(x95762,x95763,x95764,x95765,x95761)),f719(x95762,x95763,x95764,x95765,x95761)),x95763)+~P1(f332(f332(f334(f852(f846(x95761),f846(x95761))),f332(f332(f241(f846(x95761),f846(x95761)),f332(f332(f140(x95761),x95765),x95764)),x95763)),f147(x95761,x95762)))
% 52.62/52.41 [9709]~P1(f332(f332(f334(f852(f846(x97091),f846(x97091))),f332(f332(f241(f846(x97091),f846(x97091)),f332(f332(f140(x97091),x97095),x97092)),x97094)),f147(x97091,x97093)))+P1(f332(f332(f334(f852(f846(x97091),f846(x97091))),f332(f332(f241(f846(x97091),f846(x97091)),x97092),f719(x97093,x97094,x97092,x97095,x97091))),f147(x97091,x97093)))
% 52.62/52.41 [9794]~P1(f332(f332(f334(f852(f846(x97941),f846(x97941))),f332(f332(f241(f846(x97941),f846(x97941)),x97945),f332(f332(f140(x97941),x97944),x97943))),f147(x97941,x97942)))+P1(f332(f332(f334(f852(f846(x97941),f846(x97941))),f332(f332(f241(f846(x97941),f846(x97941)),f720(x97942,x97943,x97944,x97945,x97941)),x97943)),f147(x97941,x97942)))
% 52.62/52.41 [9967]P1(f332(f332(f334(f852(x99671,x99671)),f332(f332(f241(x99671,x99671),f332(x99672,f332(f332(f82(a845),x99673),x99674))),f332(x99672,x99673))),f300(x99671,x99675)))+~P1(f332(f332(f334(f852(x99671,x99671)),f332(f332(f241(x99671,x99671),f332(x99672,f332(a114,f634(x99674,x99673,x99675,x99672,x99671)))),f332(x99672,f634(x99674,x99673,x99675,x99672,x99671)))),f300(x99671,x99675)))
% 52.62/52.41 [9991]E(x99911,f2(a101))+E(f332(f229(f852(f846(x99912),x99913),f852(x99912,x99913),f332(f332(f241(f846(x99912),x99913),f115(x99912)),x99914),f332(f251(x99912,x99913,f852(f846(x99912),x99913)),f332(f332(f9(x99912,f853(x99913,f852(f846(x99912),x99913)),f853(x99913,f852(f846(x99912),x99913))),f332(f332(f10(f853(f852(f846(x99912),x99913),f852(f846(x99912),x99913)),f853(f853(x99913,f852(f846(x99912),x99913)),f853(x99913,f852(f846(x99912),x99913))),x99912),f10(f852(f846(x99912),x99913),f852(f846(x99912),x99913),x99913)),f332(f332(f10(f853(f846(x99912),f853(x99913,f852(f846(x99912),x99913))),f853(f852(f846(x99912),x99913),f852(f846(x99912),x99913)),x99912),f251(f846(x99912),x99913,f852(f846(x99912),x99913))),f332(f332(f10(f853(f846(x99912),f846(x99912)),f853(f846(x99912),f853(x99913,f852(f846(x99912),x99913))),x99912),f332(f10(f846(x99912),f853(x99913,f852(f846(x99912),x99913)),f846(x99912)),f241(f846(x99912),x99913))),f140(x99912))))),f119(x99913,x99912,x99915,f332(f332(f3(a101),x99911),f80(a101)))))),f332(x99915,x99914)),f332(f119(x99913,x99912,x99915,x99911),x99914))
% 52.62/52.41 [5121]E(x51211,x51212)+~E(f332(f332(f140(x51213),x51214),x51211),f332(f332(f140(x51213),x51215),x51212))
% 52.62/52.41 [5122]E(x51221,x51222)+~E(f332(f332(f140(x51223),x51221),x51224),f332(f332(f140(x51223),x51222),x51225))
% 52.62/52.41 [5317]~E(f332(f332(f128(x53171),x53173),x53172),f332(f332(f140(x53171),x53174),x53175))+E(f332(f332(f152(x53171),x53172),x53173),x53174)
% 52.62/52.41 [5450]~P21(x54504,x54505,x54501)+E(f332(f332(x54501,x54502),f332(f332(x54501,x54502),x54503)),f332(f332(x54501,x54502),x54503))
% 52.62/52.41 [5815]~E(f332(x58153,x58154),f332(f227(x58152),x58155))+E(f332(f332(f332(f74(x58151,f849(x58152)),x58153),x58154),f332(f227(x58152),x58155)),x58153)
% 52.62/52.41 [6067]~P100(x60672)+~E(f332(f332(f138(x60671,x60672,x60673),x60674),x60675),f115(x60671))
% 52.62/52.41 [6468]E(x64681,x64682)+~E(f332(f332(f125(x64683),x64684),f332(f332(f140(x64683),x64681),f115(x64683))),f332(f332(f125(x64683),x64685),f332(f332(f140(x64683),x64682),f115(x64683))))
% 52.62/52.41 [6469]E(x64691,x64692)+~E(f332(f332(f125(x64693),x64691),f332(f332(f140(x64693),x64694),f115(x64693))),f332(f332(f125(x64693),x64692),f332(f332(f140(x64693),x64695),f115(x64693))))
% 52.62/52.41 [6729]E(f332(f172(x67291,x67292,x67293,x67294),x67295),f183(x67292))+P1(f332(f332(f334(x67291),x67295),x67294))
% 52.62/52.41 [6730]E(f332(f172(x67301,x67302,x67303,x67304),x67305),f183(x67302))+P1(f332(f332(f334(x67301),x67305),x67304))
% 52.62/52.41 [6799]E(f332(f332(f302(x67991),f332(x67992,x67993)),f332(f303(x67994,x67991,x67992),x67995)),f332(f303(x67994,x67991,x67992),x67995))+~P1(f332(f332(f334(x67994),x67993),x67995))
% 52.62/52.41 [6808]~P1(f332(x68084,f332(x68083,x68085)))+P1(f332(f332(f305(x68081,x68082,x68083),x68084),x68085))
% 52.62/52.41 [6813]~E(x68134,f2(a101))+E(f332(f119(x68131,x68132,x68133,x68134),x68135),f332(f332(f241(f846(x68132),x68131),f115(x68132)),x68135))
% 52.62/52.41 [6907]~E(f332(f303(x69071,x69072,x69073),x69074),x69075)+E(f332(f303(f853(x69071,a839),f853(x69072,a839),f303(x69071,x69072,x69073)),f332(f301(x69071),x69074)),f332(f301(x69072),x69075))
% 52.62/52.41 [6937]E(f332(f172(x69371,x69372,x69373,x69374),x69375),f332(x69373,x69375))+~P1(f332(f332(f334(x69371),x69375),x69374))
% 52.62/52.41 [6938]E(f332(f172(x69381,x69382,x69383,x69384),x69385),f332(x69383,x69385))+~P1(f332(f332(f334(x69381),x69385),x69384))
% 52.62/52.41 [7253]P31(x72531,x72532,x72533,x72534)+~P31(x72531,x72532,x72533,f332(f332(f302(x72531),x72535),x72534))
% 52.62/52.41 [7324]P1(f332(x73241,x73242))+~P1(f332(f332(f94(x73243,x73244,x73241),x73245),x73242))
% 52.62/52.41 [7375]~P1(f332(f332(f334(x73754),x73753),x73755))+P1(f332(f332(f334(x73751),f332(x73752,x73753)),f332(f303(x73754,x73751,x73752),x73755)))
% 52.62/52.41 [7427]P1(f332(x74271,f332(x74272,x74273)))+~P1(f332(f332(f305(x74274,x74275,x74272),x74271),x74273))
% 52.62/52.41 [7428]P1(f332(f332(x74281,x74282),x74283))+~P1(f332(f332(f94(x74284,x74281,x74285),x74282),x74283))
% 52.62/52.41 [7496]~P1(f332(f332(f334(x74963),f332(x74964,x74962)),x74965))+P1(f332(f332(f334(x74961),x74962),f332(f305(x74961,x74963,x74964),x74965)))
% 52.62/52.41 [7497]~P1(f332(f332(f334(x74973),f332(x74974,x74972)),x74975))+P1(f332(f332(f334(x74971),x74972),f332(f305(x74971,x74973,x74974),x74975)))
% 52.62/52.41 [7895]~P1(f332(f332(f334(x78955),x78953),f332(f305(x78955,x78951,x78952),x78954)))+P1(f332(f332(f334(x78951),f332(x78952,x78953)),x78954))
% 52.62/52.41 [7896]~P1(f332(f332(f334(x78965),x78963),f332(f305(x78965,x78961,x78962),x78964)))+P1(f332(f332(f334(x78961),f332(x78962,x78963)),x78964))
% 52.62/52.41 [8114]~E(x81143,f332(f332(f332(f74(x81141,f849(x81142)),f332(f18(f849(x81142),x81141),f183(x81142))),x81144),f332(f227(x81142),x81145)))+E(f169(x81141,x81142,x81143),f332(f332(f302(x81141),x81144),f180(f853(x81141,a839))))
% 52.62/52.41 [8210]E(f332(x82101,f405(x82102,x82101,x82103,x82104)),x82104)+~P1(f332(f332(f334(x82105),x82104),f332(f303(x82103,x82105,x82101),x82102)))
% 52.62/52.41 [8462]P1(f332(f332(f334(f854(x84621,x84622)),f332(f313(x84622,x84621),x84623)),f314(x84621,x84622,x84624,x84625)))+~P1(f332(f332(f334(x84622),x84623),x84625))
% 52.62/52.41 [8463]P1(f332(f332(f334(f854(x84631,x84632)),f332(f304(x84631,x84632),x84633)),f314(x84631,x84632,x84634,x84635)))+~P1(f332(f332(f334(x84631),x84633),x84634))
% 52.62/52.41 [8520]~E(x85202,f332(f332(f140(x85201),x85204),x85205))+P1(f332(f332(f334(f852(f846(x85201),f846(x85201))),f332(f332(f241(f846(x85201),f846(x85201)),f115(x85201)),x85202)),f137(x85201,x85203)))
% 52.62/52.41 [8571]P1(f332(f332(f232(f853(x85711,a839)),f332(f332(f48(x85712,f853(x85711,a839)),x85713),x85714)),f332(x85714,x85715)))+~P1(f332(f332(f334(x85712),x85715),x85713))
% 52.62/52.41 [8617]~P57(x86171,x86172,x86173,x86175,x86174)+E(f332(f303(x86171,x86172,x86173),f239(f853(x86171,a839))),x86174)
% 52.62/52.41 [8806]E(f332(f332(f332(f74(x88061,f849(x88062)),f172(x88061,x88062,x88063,x88064)),x88065),f183(x88062)),f172(x88061,x88062,x88063,x88064))+P1(f332(f332(f334(x88061),x88065),x88064))
% 52.62/52.41 [8809]E(f332(x88091,f702(x88092,x88093,x88091,x88094,x88095)),x88092)+~E(f332(f332(f196(x88095,x88094),x88091),x88093),f332(f227(x88094),x88092))
% 52.62/52.41 [8812]E(f332(f227(x88121),f702(x88122,x88123,x88124,x88125,x88121)),x88123)+~E(f332(f332(f196(x88121,x88125),x88124),x88123),f332(f227(x88125),x88122))
% 52.62/52.41 [8896]E(f332(f181(f846(x88961)),x88962),x88963)+~P1(f332(f332(f334(f852(f846(x88961),f846(x88961))),f332(f332(f241(f846(x88961),f846(x88961)),x88964),x88962)),f332(f133(x88961,x88965),x88963)))
% 52.62/52.41 [8897]E(f332(f181(f846(x88971)),x88972),x88973)+~P1(f332(f332(f334(f852(f846(x88971),f846(x88971))),f332(f332(f241(f846(x88971),f846(x88971)),x88972),x88974)),f332(f133(x88971,x88975),x88973)))
% 52.62/52.41 [8958]P1(f332(f332(f334(x89581),f405(x89582,x89583,x89581,x89584)),x89582))+~P1(f332(f332(f334(x89585),x89584),f332(f303(x89581,x89585,x89583),x89582)))
% 52.62/52.41 [9111]E(f332(f303(x91111,x91112,x91113),f364(x91114,x91113,x91111,x91115,x91112)),x91115)+~P1(f332(f332(f232(f853(x91112,a839)),x91115),f332(f303(x91111,x91112,x91113),x91114)))
% 52.62/52.41 [9344]E(f332(x93441,f536(x93442,x93441,x93443,x93444,x93445)),f332(f227(x93445),x93444))+~P1(f332(f332(f334(x93445),x93444),f171(x93443,x93445,f172(x93443,x93445,x93441,x93442))))
% 52.62/52.41 [9388]P1(f332(f332(f334(f852(f846(x93881),f846(x93881))),f332(f332(f241(f846(x93881),f846(x93881)),f332(f332(f140(x93881),x93882),x93883)),f332(f332(f140(x93881),x93882),x93884))),f300(f846(x93881),f146(x93881,x93885))))+~P1(f332(f332(f334(f852(f846(x93881),f846(x93881))),f332(f332(f241(f846(x93881),f846(x93881)),x93883),x93884)),f300(f846(x93881),f146(x93881,x93885))))
% 52.62/52.41 [9417]~E(f332(x94173,f703(x94175,x94174,x94173,x94172,x94171)),f332(x94175,f703(x94175,x94174,x94173,x94172,x94171)))+E(f332(f332(f143(x94171,x94172),x94173),x94174),f332(f332(f143(x94171,x94172),x94175),x94174))
% 52.62/52.41 [9495]E(f332(f332(f143(x94951,x94952),x94953),x94954),f332(f332(f143(x94951,x94952),x94955),x94954))+P1(f332(f332(f334(x94951),f703(x94953,x94954,x94955,x94952,x94951)),f332(f158(x94951),x94954)))
% 52.62/52.41 [9523]~P1(f332(f332(f334(x95235),x95234),f332(f277(x95231,x95235,x95233),x95232)))+P1(f332(f332(f334(x95231),f488(x95232,x95233,x95231,x95234,x95235)),x95232))
% 52.62/52.41 [9524]~P1(f332(f332(f334(x95245),x95244),f332(f277(x95241,x95245,x95243),x95242)))+P1(f332(f332(f334(x95241),f534(x95242,x95243,x95241,x95244,x95245)),x95242))
% 52.62/52.41 [9547]~P1(f332(f332(f232(f853(x95475,a839)),x95474),f332(f303(x95471,x95475,x95473),x95472)))+P1(f332(f332(f232(f853(x95471,a839)),f364(x95472,x95473,x95471,x95474,x95475)),x95472))
% 52.62/52.41 [9591]~P1(f332(f332(f334(x95915),x95914),f171(x95911,x95915,f172(x95911,x95915,x95913,x95912))))+P1(f332(f332(f334(x95911),f536(x95912,x95913,x95911,x95914,x95915)),x95912))
% 52.62/52.41 [5330]~E(f332(x53303,x53304),x53305)+E(f332(f332(f332(f74(x53301,x53302),x53303),x53304),x53305),x53303)
% 52.62/52.41 [5331]~E(f332(x53313,x53314),x53315)+E(f332(f332(f332(f74(x53311,x53312),x53313),x53314),x53315),x53313)
% 52.62/52.41 [5780]E(f332(x57801,x57802),x57803)+~E(f332(f332(f332(f74(x57804,x57805),x57801),x57802),x57803),x57801)
% 52.62/52.41 [5869]E(x58691,x58692)+~E(f332(f250(x58693,x58694),f332(f332(f241(x58693,x58694),x58695),x58691)),x58692)
% 52.62/52.41 [5870]E(x58701,x58702)+~E(f332(f240(x58703,x58704),f332(f332(f241(x58703,x58704),x58701),x58705)),x58702)
% 52.62/52.41 [6556]E(f332(f303(x65561,x65562,f332(f18(x65562,x65561),x65563)),x65564),f332(f332(f302(x65562),x65563),f180(f853(x65562,a839))))+~P1(f332(f332(f334(x65561),x65565),x65564))
% 52.62/52.41 [6629]E(f332(f332(f103(f853(x66291,a839)),f332(f158(x66291),x66292)),f332(f158(x66291),x66293)),f332(f158(x66291),x66294))+~E(f155(x66291,x66295,x66294),f332(f332(f241(f846(x66291),f846(x66291)),x66292),x66293))
% 52.62/52.41 [6736]~P100(x67362)+E(f332(f181(f846(x67361)),f332(f332(f138(x67361,x67362,x67363),x67364),x67365)),f332(a114,f332(f181(f846(x67361)),x67365)))
% 52.62/52.41 [6750]~P100(x67502)+E(f332(f158(x67501),f332(f332(f138(x67501,x67502,x67503),x67504),x67505)),f332(f332(f302(x67501),x67504),f332(f158(x67501),x67505)))
% 52.62/52.41 [7028]~P73(x70281)+E(f332(f332(f82(x70281),f332(f332(f82(x70281),x70282),x70283)),f332(f332(f82(x70281),x70284),x70285)),f332(f332(f82(x70281),f332(f332(f82(x70281),x70282),x70284)),f332(f332(f82(x70281),x70283),x70285)))
% 52.62/52.41 [7029]~P73(x70291)+E(f332(f332(f83(x70291),f332(f332(f83(x70291),x70292),x70293)),f332(f332(f83(x70291),x70294),x70295)),f332(f332(f83(x70291),f332(f332(f83(x70291),x70292),x70294)),f332(f332(f83(x70291),x70293),x70295)))
% 52.62/52.41 [7030]~P62(x70301)+E(f332(f332(f283(x70301),f332(f332(f83(x70301),x70302),x70303)),f332(f332(f83(x70301),x70304),x70305)),f332(f332(f83(x70301),f332(f332(f283(x70301),x70302),x70304)),f332(f332(f283(x70301),x70303),x70305)))
% 52.62/52.41 [7044]~P100(x70441)+E(f295(x70441,f332(f332(f179(x70441),x70442),x70443),f332(f332(f236(x70441),x70444),x70445)),f332(f332(f104(f853(x70441,a839)),f295(x70441,x70442,x70444)),f295(x70441,x70443,x70445)))
% 52.62/52.41 [7045]~P100(x70451)+E(f297(x70451,f332(f332(f179(x70451),x70452),x70453),f332(f332(f236(x70451),x70454),x70455)),f332(f332(f104(f853(x70451,a839)),f297(x70451,x70452,x70454)),f297(x70451,x70453,x70455)))
% 52.62/52.41 [7046]~P100(x70461)+E(f298(x70461,f332(f332(f179(x70461),x70462),x70463),f332(f332(f236(x70461),x70464),x70465)),f332(f332(f104(f853(x70461,a839)),f298(x70461,x70462,x70464)),f298(x70461,x70463,x70465)))
% 52.62/52.41 [7047]~P100(x70471)+E(f332(f332(f104(f853(x70471,a839)),f332(f294(x70471,x70472),x70473)),f332(f294(x70471,x70474),x70475)),f332(f294(x70471,f332(f332(f179(x70471),x70472),x70474)),f332(f332(f236(x70471),x70473),x70475)))
% 52.62/52.41 [7165]~P1(f332(x71651,f820(x71653,x71652,x71651)))+P1(f332(x71651,f332(f332(f241(x71652,x71653),x71654),x71655)))
% 52.62/52.41 [7265]~E(f332(x72653,x72654),f183(x72652))+E(f171(x72651,x72652,f332(f332(f332(f74(x72651,f849(x72652)),x72653),x72654),f332(f227(x72652),x72655))),f332(f332(f302(x72652),x72655),f171(x72651,x72652,x72653)))
% 52.62/52.41 [7288]~E(x72882,f332(x72884,x72885))+P1(f332(f332(f334(x72881),x72882),f332(f303(x72883,x72881,x72884),f239(f853(x72883,a839)))))
% 52.62/52.41 [7349]~E(f332(x73493,x73494),f183(x73492))+E(f332(f332(f3(f853(x73491,a839)),f169(x73491,x73492,x73493)),f332(f332(f302(x73491),x73494),x73495)),f332(f332(f3(f853(x73491,a839)),f169(x73491,x73492,x73493)),x73495))
% 52.62/52.41 [7371]~P21(x73713,x73712,x73714)+P21(x73711,x73712,f332(f332(f10(x73713,f853(x73712,x73712),x73711),x73714),x73715))
% 52.62/52.41 [7372]~P22(x73723,x73722,x73724)+P22(x73721,x73722,f332(f332(f10(x73723,f853(x73722,x73722),x73721),x73724),x73725))
% 52.62/52.41 [7513]~P31(x75131,x75132,x75133,x75134)+P31(x75131,x75132,x75133,f332(f332(f3(f853(x75131,a839)),x75134),x75135))
% 52.62/52.41 [7672]~P1(f332(f332(x76723,x76724),x76725))+P1(f332(f332(f251(x76721,x76722,a839),x76723),f332(f332(f241(x76721,x76722),x76724),x76725)))
% 52.62/52.41 [7673]~P1(f332(f332(x76733,x76734),x76735))+P1(f332(f332(f251(x76731,x76732,a839),x76733),f332(f332(f241(x76731,x76732),x76734),x76735)))
% 52.62/52.41 [7807]P31(x78071,x78072,x78073,x78074)+~P31(x78071,x78072,x78073,f332(f332(f103(f853(x78071,a839)),x78075),x78074))
% 52.62/52.41 [7808]P31(x78081,x78082,x78083,x78084)+~P31(x78081,x78082,x78083,f332(f332(f103(f853(x78081,a839)),x78084),x78085))
% 52.62/52.41 [8013]~P33(x80131,f332(a114,x80132),f332(f332(f332(f93(x80131),x80133),f332(a27,x80134)),x80135))+P33(x80131,x80132,f332(f332(f332(f93(x80131),x80133),f332(f231(a840),f332(a30,x80134))),x80135))
% 52.62/52.41 [8141]P33(x81411,f332(a114,x81412),f332(f332(f332(f93(x81411),x81413),f332(a27,x81414)),x81415))+~P33(x81411,x81412,f332(f332(f332(f93(x81411),x81413),f332(f231(a840),f332(a30,x81414))),x81415))
% 52.62/52.41 [8170]~P21(x81702,x81701,x81703)+E(f332(f132(x81701,x81702,f332(f9(x81702,x81701,x81701),x81703),x81704),x81705),f332(f332(f67(x81702,x81701,x81703),x81704),f332(f158(x81702),x81705)))
% 52.62/52.41 [8220]P1(f332(f332(x82201,x82202),x82203))+~P1(f332(f332(f251(x82204,x82205,a839),x82201),f332(f332(f241(x82204,x82205),x82202),x82203)))
% 52.62/52.41 [8291]P41(x82914,f672(x82915,x82914,x82913,x82912),x82912,f782(x82915,x82914,x82913,x82912))+P33(x82911,x82912,f332(f332(f332(f93(x82911),x82913),x82914),x82915))
% 52.62/52.41 [8306]~E(f332(f166(x83061,x83062,x83065),x83063),f332(f227(x83062),x83064))+P1(f332(f332(f334(f852(x83061,x83062)),f332(f332(f241(x83061,x83062),x83063),x83064)),f332(f158(f852(x83061,x83062)),x83065)))
% 52.62/52.41 [8307]~E(f332(f166(x83071,x83072,x83075),x83073),f332(f227(x83072),x83074))+P1(f332(f332(f334(f852(x83071,x83072)),f332(f332(f241(x83071,x83072),x83073),x83074)),f332(f158(f852(x83071,x83072)),x83075)))
% 52.62/52.41 [8670]P1(f332(f332(f232(f853(x86701,a839)),f332(f303(x86702,x86701,x86703),x86704)),f332(f303(x86702,x86701,x86703),x86705)))+~P1(f332(f332(f232(f853(x86702,a839)),x86704),x86705))
% 52.62/52.41 [8671]P1(f332(f332(f232(f853(x86711,a839)),f332(f305(x86711,x86712,x86713),x86714)),f332(f305(x86711,x86712,x86713),x86715)))+~P1(f332(f332(f232(f853(x86712,a839)),x86714),x86715))
% 52.62/52.41 [8742]E(x87421,f2(a101))+E(f332(f332(f253(x87422,x87423,x87422,f852(x87423,x87422)),f332(x87424,x87425)),f268(x87423,x87422,f332(f332(f3(a101),x87421),f80(a101)),x87424)),f332(f268(x87423,x87422,x87421,x87424),x87425))
% 52.62/52.41 [8828]P1(f332(f332(f249(x88281,x88282,a839,x88283),x88284),x88285))+~P1(f332(x88283,f332(f332(f241(x88281,x88282),x88284),x88285)))
% 52.62/52.41 [9029]P33(x90291,x90292,f332(f332(f332(f93(x90291),x90293),x90294),x90295))+P1(f332(f332(x90293,f561(x90295,x90294,x90293,x90292)),f672(x90295,x90294,x90293,x90292)))
% 52.62/52.41 [9089]~P1(f332(f332(f249(x90892,x90893,a839,x90891),x90894),x90895))+P1(f332(x90891,f332(f332(f241(x90892,x90893),x90894),x90895)))
% 52.62/52.41 [9090]~P1(f332(f332(f249(x90902,x90903,a839,x90901),x90904),x90905))+P1(f332(x90901,f332(f332(f241(x90902,x90903),x90904),x90905)))
% 52.62/52.41 [9199]E(f332(f227(x91991),f714(x91992,x91993,x91994,x91991,x91995)),f332(f166(x91995,x91991,x91992),x91994))+~P1(f332(f332(f334(f852(x91995,x91991)),f332(f332(f241(x91995,x91991),x91994),x91993)),f332(f158(f852(x91995,x91991)),x91992)))
% 52.62/52.41 [9242]P33(x92421,x92422,f332(f332(f332(f93(x92421),x92423),x92424),x92425))+~P1(f332(f332(x92425,f561(x92425,x92424,x92423,x92422)),f782(x92425,x92424,x92423,x92422)))
% 52.62/52.41 [9309]~P30(x93091,x93092,f332(f332(f302(f844(x93091)),f332(f332(f332(f93(x93091),x93093),f332(f231(a840),f332(a30,x93094))),x93095)),f180(f853(f844(x93091),a839))))+P30(x93091,x93092,f332(f332(f302(f844(x93091)),f332(f332(f332(f93(x93091),x93093),f332(a27,x93094)),x93095)),f180(f853(f844(x93091),a839))))
% 52.62/52.41 [9336]~P1(f332(f64(x93363),f332(f303(x93362,x93363,x93365),f239(f853(x93362,a839)))))+P1(f332(f64(x93361),f332(f303(x93362,x93361,f332(f332(f10(x93363,x93361,x93362),x93364),x93365)),f239(f853(x93362,a839)))))
% 52.62/52.41 [9358]P1(f332(f332(f232(f853(f853(x93581,a839),a839)),f332(f303(f853(x93582,a839),f853(x93581,a839),f303(x93582,x93581,x93583)),f332(f301(x93582),x93584))),f332(f301(x93581),x93585)))+~P1(f332(f332(f232(f853(x93581,a839)),f332(f303(x93582,x93581,x93583),x93584)),x93585))
% 52.62/52.41 [9368]~P1(f332(f64(f849(x93681)),f332(f303(x93682,f849(x93681),x93683),f239(f853(x93682,a839)))))+P1(f332(f64(f849(x93681)),f332(f303(x93682,f849(x93681),f332(f332(f332(f74(x93682,f849(x93681)),x93683),x93684),f332(f227(x93681),x93685))),f239(f853(x93682,a839)))))
% 52.62/52.41 [9427]E(x94271,x94272)+~P1(f332(f69(x94273,x94274,x94275,x94271,f180(f853(x94273,a839))),x94272))
% 52.62/52.41 [9440]E(f332(f332(f241(x94401,x94402),f569(x94403,x94404,x94405,x94402,x94401)),f570(x94403,x94404,x94405,x94402,x94401)),x94405)+~P1(f332(f332(f334(f852(x94401,x94402)),x94405),f332(f332(f248(x94401,x94402),x94404),x94403)))
% 52.62/52.41 [9528]P1(f332(f332(f334(x95281),f569(x95282,x95283,x95284,x95285,x95281)),x95283))+~P1(f332(f332(f334(f852(x95281,x95285)),x95284),f332(f332(f248(x95281,x95285),x95283),x95282)))
% 52.62/52.41 [9624]P30(x96245,x96244,f332(f332(f302(f844(x96245)),f332(f332(f332(f93(x96245),x96241),x96243),x96242)),f180(f853(f844(x96245),a839))))+P1(f332(f332(x96241,f486(x96242,x96243,x96244,x96245,x96241)),f487(x96242,x96243,x96244,x96245,x96241)))
% 52.62/52.41 [9666]P1(f332(f332(f334(x96661),f570(x96662,x96663,x96664,x96661,x96665)),f332(x96662,f569(x96662,x96663,x96664,x96661,x96665))))+~P1(f332(f332(f334(f852(x96665,x96661)),x96664),f332(f332(f248(x96665,x96661),x96663),x96662)))
% 52.62/52.41 [9685]P1(f332(f332(f334(f852(x96851,x96851)),f332(f332(f241(x96851,x96851),x96852),f657(x96853,x96854,x96855,x96852,x96851))),x96853))+~P1(f332(f332(f334(f852(x96851,x96851)),f332(f332(f241(x96851,x96851),x96852),x96855)),f332(f332(f173(f852(x96851,x96851),a839),f332(a114,x96854)),x96853)))
% 52.62/52.41 [9686]P1(f332(f332(f334(f852(x96861,x96861)),f332(f332(f241(x96861,x96861),x96862),f659(x96863,x96864,x96865,x96862,x96861))),x96863))+~P1(f332(f332(f334(f852(x96861,x96861)),f332(f332(f241(x96861,x96861),x96862),x96865)),f332(f332(f173(f852(x96861,x96861),a839),f332(a114,x96864)),x96863)))
% 52.62/52.41 [9704]~P1(f332(f332(f334(f852(f846(x97041),f846(x97041))),f332(f332(f241(f846(x97041),f846(x97041)),f332(f332(f140(x97041),x97042),x97045)),x97044)),f147(x97041,x97043)))+P1(f332(f332(f334(f852(x97041,x97041)),f332(f332(f241(x97041,x97041),x97042),f718(x97043,x97044,x97045,x97042,x97041))),x97043))
% 52.62/52.41 [9706]~P34(x97061,x97062,f332(f332(f302(f844(x97061)),f332(f332(f332(f93(x97061),f94(x97061,x97063,x97064)),x97065),x97063)),f180(f853(f844(x97061),a839))))+P34(x97061,x97062,f332(f332(f302(f844(x97061)),f332(f332(f332(f93(x97061),x97063),f35(x97064,x97065)),f94(x97061,x97063,f332(f75(a839,a839,a842,a328),x97064)))),f180(f853(f844(x97061),a839))))
% 52.62/52.41 [9707]~P30(x97071,x97072,f332(f332(f302(f844(x97071)),f332(f332(f332(f93(x97071),f94(x97071,x97073,x97074)),x97075),x97073)),f180(f853(f844(x97071),a839))))+P30(x97071,x97072,f332(f332(f302(f844(x97071)),f332(f332(f332(f93(x97071),x97073),f35(x97074,x97075)),f94(x97071,x97073,f332(f75(a839,a839,a842,a328),x97074)))),f180(f853(f844(x97071),a839))))
% 52.62/52.41 [9992]P30(x99921,x99922,f332(f332(f302(f844(x99921)),f332(f332(f332(f93(x99921),x99923),x99924),x99925)),f180(f853(f844(x99921),a839))))+~P30(x99921,x99922,f332(f332(f302(f844(x99921)),f332(f332(f332(f93(x99921),f332(f18(f853(a842,a839),x99921),f332(f332(f9(a842,a842,a839),a329),f487(x99925,x99924,x99922,x99921,x99923)))),x99924),f332(f18(f853(a842,a839),x99921),f332(x99925,f486(x99925,x99924,x99922,x99921,x99923))))),f180(f853(f844(x99921),a839))))
% 52.62/52.41 [6220]P1(f332(x62202,x62204))+E(f162(x62201,x62202,f332(f332(f125(x62201),x62203),f332(f332(f140(x62201),x62204),x62205))),f162(x62201,x62202,x62203))
% 52.62/52.41 [6269]~P71(x62692)+E(f332(f332(f332(f3(f853(x62691,x62692)),x62693),x62694),x62695),f332(f332(f3(x62692),f332(x62693,x62695)),f332(x62694,x62695)))
% 52.62/52.41 [6270]~P71(x62702)+E(f332(f332(f332(f3(f853(x62701,x62702)),x62703),x62704),x62705),f332(f332(f3(x62702),f332(x62703,x62705)),f332(x62704,x62705)))
% 52.62/52.41 [6271]~P93(x62712)+E(f332(f332(f332(f103(f853(x62711,x62712)),x62713),x62714),x62715),f332(f332(f103(x62712),f332(x62713,x62715)),f332(x62714,x62715)))
% 52.62/52.41 [6272]~P93(x62722)+E(f332(f332(f332(f103(f853(x62721,x62722)),x62723),x62724),x62725),f332(f332(f103(x62722),f332(x62723,x62725)),f332(x62724,x62725)))
% 52.62/52.41 [6273]~P93(x62732)+E(f332(f332(f332(f104(f853(x62731,x62732)),x62733),x62734),x62735),f332(f332(f104(x62732),f332(x62733,x62735)),f332(x62734,x62735)))
% 52.62/52.41 [6274]~P93(x62742)+E(f332(f332(f332(f104(f853(x62741,x62742)),x62743),x62744),x62745),f332(f332(f104(x62742),f332(x62743,x62745)),f332(x62744,x62745)))
% 52.62/52.41 [6296]E(x62961,x62962)+E(f332(f332(f152(x62963),f332(f332(f148(x62963,x62964),x62961),x62965)),x62962),f332(f332(f152(x62963),x62964),x62962))
% 52.62/52.41 [6573]~E(x65734,f180(f853(x65733,a839)))+E(f332(f332(f3(f853(x65731,a839)),x65732),f332(f332(f47(x65733,f853(x65731,a839)),x65734),x65735)),x65732)
% 52.62/52.41 [6574]~E(x65744,f180(f853(x65743,a839)))+E(f332(f332(f103(f853(x65741,a839)),x65742),f332(f332(f47(x65743,f853(x65741,a839)),x65744),x65745)),x65742)
% 52.62/52.41 [6575]~E(x65754,f180(f853(x65753,a839)))+E(f332(f332(f104(f853(x65751,a839)),x65752),f332(f332(f48(x65753,f853(x65751,a839)),x65754),x65755)),x65752)
% 52.62/52.41 [6588]~E(x65884,f180(f853(x65883,a839)))+E(f332(f332(f302(x65881),x65882),f332(f332(f47(x65883,f853(x65881,a839)),x65884),x65885)),f332(f332(f302(x65881),x65882),f180(f853(x65881,a839))))
% 52.62/52.41 [7027]~P73(x70271)+E(f332(f332(f83(x70271),f332(f332(f83(x70271),x70272),x70273)),f332(f332(f83(x70271),x70274),x70275)),f332(f332(f83(x70271),x70272),f332(f332(f83(x70271),x70273),f332(f332(f83(x70271),x70274),x70275))))
% 52.62/52.41 [7416]E(f332(f332(f152(x74161),f332(f332(f143(x74162,x74161),x74163),x74164)),x74165),f332(x74163,f332(f332(f152(x74162),x74164),x74165)))+~P1(f332(f332(f233(a845),x74165),f332(f181(f846(x74162)),x74164)))
% 52.62/52.41 [7485]E(f332(f332(f103(f853(x74851,a839)),f332(x74852,x74853)),f332(f332(f47(x74854,f853(x74851,a839)),x74855),x74852)),f332(f332(f47(x74854,f853(x74851,a839)),x74855),x74852))+~P1(f332(f332(f334(x74854),x74853),x74855))
% 52.62/52.41 [7486]E(f332(f332(f104(f853(x74861,a839)),f332(x74862,x74863)),f332(f332(f48(x74864,f853(x74861,a839)),x74865),x74862)),f332(f332(f48(x74864,f853(x74861,a839)),x74865),x74862))+~P1(f332(f332(f334(x74864),x74863),x74865))
% 52.62/52.41 [8089]~E(x80893,f180(f853(x80891,a839)))+E(f332(f332(f47(x80891,f853(x80892,a839)),x80893),f332(f332(f10(f853(x80892,a839),f853(x80892,a839),x80891),f332(f302(x80892),x80894)),x80895)),f180(f853(x80892,a839)))
% 52.62/52.41 [8095]~P1(f332(f332(f334(x80954),x80953),x80955))+P1(f332(f332(f232(f853(x80951,a839)),f332(x80952,x80953)),f332(f332(f47(x80954,f853(x80951,a839)),x80955),x80952)))
% 52.62/52.41 [8219]~E(f332(x82194,x82192),x82195)+P1(f332(f332(f334(x82191),x82192),f332(f305(x82191,x82193,x82194),f332(f332(f302(x82193),x82195),f180(f853(x82193,a839))))))
% 52.62/52.41 [8265]~P55(x82651,x82652,f332(f278(x82652,x82651),x82653))+E(f332(f332(f104(f853(x82651,a839)),f332(f277(x82652,x82651,x82653),x82654)),f332(f277(x82652,x82651,x82653),x82655)),f332(f277(x82652,x82651,x82653),f332(f332(f104(f853(x82652,a839)),x82654),x82655)))
% 52.62/52.41 [8290]E(x82901,f2(a101))+E(f118(x82902,x82903,f332(x82904,f332(f332(f3(a101),x82901),f80(a101))),f332(f332(f9(x82902,a101,f847(x82903)),x82905),x82901)),f332(f193(x82902,x82903,x82904,x82905),x82901))
% 52.62/52.41 [8385]E(x83851,f180(f853(x83852,a839)))+E(f332(f332(f47(x83852,f853(x83853,a839)),x83851),f332(f332(f10(f853(x83853,a839),f853(x83853,a839),x83852),f332(f302(x83853),x83854)),x83855)),f332(f332(f302(x83853),x83854),f332(f332(f47(x83852,f853(x83853,a839)),x83851),x83855)))
% 52.62/52.41 [8386]E(x83861,f180(f853(x83862,a839)))+E(f332(f332(f47(x83862,f853(x83863,a839)),x83861),f332(f332(f10(f853(x83863,a839),f853(x83863,a839),x83862),f332(f302(x83863),x83864)),x83865)),f332(f332(f302(x83863),x83864),f332(f332(f47(x83862,f853(x83863,a839)),x83861),x83865)))
% 52.62/52.41 [8440]~P31(x84402,x84401,x84403,f239(f853(x84402,a839)))+E(f332(f332(f3(f853(x84401,a839)),f332(f303(x84402,x84401,x84403),x84404)),f332(f303(x84402,x84401,x84403),x84405)),f332(f303(x84402,x84401,x84403),f332(f332(f3(f853(x84402,a839)),x84404),x84405)))
% 52.62/52.41 [8441]~P31(x84412,x84411,x84413,f239(f853(x84412,a839)))+E(f332(f332(f104(f853(x84411,a839)),f332(f303(x84412,x84411,x84413),x84414)),f332(f303(x84412,x84411,x84413),x84415)),f332(f303(x84412,x84411,x84413),f332(f332(f104(f853(x84412,a839)),x84414),x84415)))
% 52.62/52.41 [8508]~P1(f332(f332(f70(x85081,x85082,x85085),x85083),x85084))+P1(f332(f332(f334(f852(x85081,x85082)),f332(f332(f241(x85081,x85082),x85083),x85084)),x85085))
% 52.62/52.41 [8535]P1(f332(f332(f334(x85351),x85352),f332(f259(x85353,x85351),x85354)))+~P1(f332(f332(f334(f852(x85353,x85351)),f332(f332(f241(x85353,x85351),x85355),x85352)),x85354))
% 52.62/52.41 [8536]P1(f332(f332(f334(x85361),x85362),f332(f259(x85363,x85361),x85364)))+~P1(f332(f332(f334(f852(x85363,x85361)),f332(f332(f241(x85363,x85361),x85365),x85362)),x85364))
% 52.62/52.41 [8537]P1(f332(f332(f334(x85371),x85372),f332(f261(x85371,x85373),x85374)))+~P1(f332(f332(f334(f852(x85371,x85373)),f332(f332(f241(x85371,x85373),x85372),x85375)),x85374))
% 52.62/52.41 [8538]P1(f332(f332(f334(x85381),x85382),f332(f261(x85381,x85383),x85384)))+~P1(f332(f332(f334(f852(x85381,x85383)),f332(f332(f241(x85381,x85383),x85382),x85385)),x85384))
% 52.62/52.41 [8659]P1(f332(f332(f70(x86591,x86592,x86593),x86594),x86595))+~P1(f332(f332(f334(f852(x86591,x86592)),f332(f332(f241(x86591,x86592),x86594),x86595)),x86593))
% 52.62/52.41 [8692]E(f332(x86921,x86922),x86923)+~P1(f332(f332(f334(x86924),x86922),f332(f305(x86924,x86925,x86921),f332(f332(f302(x86925),x86923),f180(f853(x86925,a839))))))
% 52.62/52.41 [8892]P1(f332(f332(f334(f852(x88921,x88922)),f332(f332(f241(x88921,x88922),x88923),x88924)),f332(f278(x88922,x88921),x88925)))+~P1(f332(f332(f334(f852(x88922,x88921)),f332(f332(f241(x88922,x88921),x88924),x88923)),x88925))
% 52.62/52.41 [8893]P1(f332(f332(f334(f852(x88931,x88932)),f332(f332(f241(x88931,x88932),x88933),x88934)),f332(f278(x88932,x88931),x88935)))+~P1(f332(f332(f334(f852(x88932,x88931)),f332(f332(f241(x88932,x88931),x88934),x88933)),x88935))
% 52.62/52.41 [8911]~P1(f332(f332(x89111,x89115),x89114))+P1(f332(f332(x89111,f332(f250(x89112,x89113),f332(f332(f241(x89112,x89113),x89114),x89115))),f332(f240(x89112,x89113),f332(f332(f241(x89112,x89113),x89114),x89115))))
% 52.62/52.41 [8937]~P1(f332(f332(f334(f852(x89372,x89371)),f332(f332(f241(x89372,x89371),x89374),x89373)),f332(f278(x89371,x89372),x89375)))+P1(f332(f332(f334(f852(x89371,x89372)),f332(f332(f241(x89371,x89372),x89373),x89374)),x89375))
% 52.62/52.41 [8938]~P1(f332(f332(f334(f852(x89382,x89381)),f332(f332(f241(x89382,x89381),x89384),x89383)),f332(f278(x89381,x89382),x89385)))+P1(f332(f332(f334(f852(x89381,x89382)),f332(f332(f241(x89381,x89382),x89383),x89384)),x89385))
% 52.62/52.41 [8966]~P1(f332(f332(f334(f852(x89663,x89661)),f332(f332(f241(x89663,x89661),x89665),x89662)),x89664))+P1(f332(f332(f334(x89661),x89662),f332(f277(x89663,x89661,x89664),f332(f332(f302(x89663),x89665),f180(f853(x89663,a839))))))
% 52.62/52.41 [9013]P1(f332(f332(f334(f852(x90131,x90132)),f332(f332(f241(x90131,x90132),x90133),x90134)),x90135))+~P1(f332(f332(f334(x90132),x90134),f332(f277(x90131,x90132,x90135),f332(f332(f302(x90131),x90133),f180(f853(x90131,a839))))))
% 52.62/52.41 [9032]E(f332(f332(f332(f74(x90321,f849(x90322)),f172(x90321,x90322,x90323,x90324)),x90325),f183(x90322)),f172(x90321,x90322,x90323,f332(f332(f3(f853(x90321,a839)),x90324),f332(f332(f302(x90321),x90325),f180(f853(x90321,a839))))))+~P1(f332(f332(f334(x90321),x90325),x90324))
% 52.62/52.41 [9096]~P4(x90961)+E(f332(f332(f8(a845,x90961),x90962),f295(a845,f332(f332(f82(a845),x90963),x90964),f332(f332(f82(a845),x90965),x90964))),f332(f332(f8(a845,x90961),f332(f332(f10(a845,x90961,a845),x90962),f332(f332(f9(a845,a845,a845),f82(a845)),x90964))),f295(a845,x90963,x90965)))
% 52.62/52.41 [9115]~P4(x91151)+E(f332(f332(f8(a845,x91151),x91152),f332(f294(a845,f332(f332(f82(a845),x91153),x91154)),f332(f332(f82(a845),x91155),x91154))),f332(f332(f8(a845,x91151),f332(f332(f10(a845,x91151,a845),x91152),f332(f332(f9(a845,a845,a845),f82(a845)),x91154))),f332(f294(a845,x91153),x91155)))
% 52.62/52.41 [9324]P1(f332(f332(f334(f852(f846(x93241),f846(x93241))),f332(f332(f241(f846(x93241),f846(x93241)),f332(f332(f140(x93241),x93242),x93243)),f332(f332(f140(x93241),x93244),x93243))),f146(x93241,x93245)))+~P1(f332(f332(f334(f852(x93241,x93241)),f332(f332(f241(x93241,x93241),x93242),x93244)),x93245))
% 52.62/52.41 [9425]P30(x94251,x94252,f332(f332(f302(f844(x94251)),f332(f332(f332(f93(x94251),x94253),f332(a27,x94254)),x94255)),f180(f853(f844(x94251),a839))))+~P30(x94251,f332(f332(f302(f844(x94251)),f332(f332(f332(f93(x94251),x94253),f332(a27,x94254)),x94255)),x94252),f332(f332(f302(f844(x94251)),f332(f332(f332(f93(x94251),x94253),f332(f231(a840),f332(a30,x94254))),x94255)),f180(f853(f844(x94251),a839))))
% 52.62/52.41 [9436]E(f332(f332(f302(x94361),f540(x94362,x94363,x94364,x94365,x94361)),f545(x94362,x94363,x94364,x94365,x94361)),f332(f332(f302(x94361),x94364),x94363))+~P1(f332(f65(x94361,x94365,f332(f332(f302(x94361),x94364),x94363)),x94362))
% 52.62/52.41 [9437]E(f332(f332(f302(x94371),f546(x94372,x94373,x94374,x94375,x94371)),f551(x94372,x94373,x94374,x94375,x94371)),f332(f332(f302(x94371),x94374),x94373))+~P1(f332(f65(x94371,x94375,f332(f332(f302(x94371),x94374),x94373)),x94372))
% 52.62/52.41 [9514]P1(f332(f332(f334(x95141),f666(x95142,x95143,x95144,x95145,x95141)),x95144))+P1(f332(f332(f332(f48(x95141,f853(x95145,a839)),x95144),x95143),x95142))
% 52.62/52.41 [9519]P1(f332(f332(f334(x95191),f660(x95192,x95193,x95191,x95194,x95195)),x95193))+P1(f332(f332(f334(x95195),x95194),f332(f332(f48(x95191,f853(x95195,a839)),x95193),x95192)))
% 52.62/52.41 [9527]P1(f332(f332(f334(x95271),f667(x95272,x95273,x95271,x95274,x95275)),x95273))+P1(f332(f332(f232(f853(x95275,a839)),x95274),f332(f332(f48(x95271,f853(x95275,a839)),x95273),x95272)))
% 52.62/52.41 [9529]P1(f332(f332(x95291,f390(x95292,x95291,x95293,x95294,x95295)),x95292))+~P1(f332(f332(f332(f47(x95295,f853(x95294,a839)),x95293),x95291),x95292))
% 52.62/52.41 [9531]P1(f332(f332(f334(x95311),f390(x95312,x95313,x95314,x95315,x95311)),x95314))+~P1(f332(f332(f332(f47(x95311,f853(x95315,a839)),x95314),x95313),x95312))
% 52.62/52.41 [9541]P1(f332(f332(f334(x95411),f407(x95412,x95413,x95411,x95414,x95415)),x95413))+~P1(f332(f332(f334(x95415),x95414),f332(f332(f47(x95411,f853(x95415,a839)),x95413),x95412)))
% 52.62/52.41 [9546]P1(f332(f332(f334(x95461),x95462),f332(x95463,f407(x95463,x95464,x95465,x95462,x95461))))+~P1(f332(f332(f334(x95461),x95462),f332(f332(f47(x95465,f853(x95461,a839)),x95464),x95463)))
% 52.62/52.41 [9628]~P1(f332(f332(x96284,f666(x96285,x96284,x96283,x96282,x96281)),x96285))+P1(f332(f332(f332(f48(x96281,f853(x96282,a839)),x96283),x96284),x96285))
% 52.62/52.41 [9631]~P1(f332(f332(f334(x96311),x96312),f332(x96315,f660(x96315,x96314,x96313,x96312,x96311))))+P1(f332(f332(f334(x96311),x96312),f332(f332(f48(x96313,f853(x96311,a839)),x96314),x96315)))
% 52.62/52.41 [9634]~P1(f332(f332(f232(f853(x96341,a839)),x96342),f332(x96345,f667(x96345,x96344,x96343,x96342,x96341))))+P1(f332(f332(f232(f853(x96341,a839)),x96342),f332(f332(f48(x96343,f853(x96341,a839)),x96344),x96345)))
% 52.62/52.41 [9689]~P1(f332(f332(f334(x96891),f540(x96895,x96894,x96893,x96892,x96891)),f545(x96895,x96894,x96893,x96892,x96891)))+~P1(f332(f65(x96891,x96892,f332(f332(f302(x96891),x96893),x96894)),x96895))
% 52.62/52.41 [9690]~P1(f332(f332(f334(x96901),f546(x96905,x96904,x96903,x96902,x96901)),f551(x96905,x96904,x96903,x96902,x96901)))+~P1(f332(f65(x96901,x96902,f332(f332(f302(x96901),x96903),x96904)),x96905))
% 52.62/52.41 [9691]~P1(f332(f332(f334(f852(x96911,x96911)),f332(f332(f241(x96911,x96911),x96912),x96915)),f332(f332(f173(f852(x96911,x96911),a839),f332(a114,x96914)),x96913)))+P1(f332(f332(f334(f852(x96911,x96911)),f332(f332(f241(x96911,x96911),x96912),f658(x96913,x96914,x96915,x96912,x96911))),f332(f332(f173(f852(x96911,x96911),a839),x96914),x96913)))
% 52.62/52.41 [9698]P1(f332(f69(x96981,x96981,x96982,f540(x96983,x96984,x96985,x96982,x96981),f545(x96983,x96984,x96985,x96982,x96981)),x96983))+~P1(f332(f65(x96981,x96982,f332(f332(f302(x96981),x96985),x96984)),x96983))
% 52.62/52.41 [9699]P1(f332(f69(x96991,x96991,x96992,f546(x96993,x96994,x96995,x96992,x96991),f551(x96993,x96994,x96995,x96992,x96991)),x96993))+~P1(f332(f65(x96991,x96992,f332(f332(f302(x96991),x96995),x96994)),x96993))
% 52.62/52.41 [9711]~P100(x97111)+P20(x97111,f332(f332(f143(x97112,x97111),x97113),f332(f126(x97112,f332(f332(f9(x97112,x97111,a839),f332(f332(f10(x97111,f853(x97111,a839),x97112),a329),x97113)),f332(x97114,x97115))),x97115)))
% 52.62/52.41 [9766]~P1(f332(f332(f334(x97662),x97665),f332(f277(x97661,x97662,x97664),x97663)))+P1(f332(f332(f334(f852(x97661,x97662)),f332(f332(f241(x97661,x97662),f488(x97663,x97664,x97661,x97665,x97662)),x97665)),x97664))
% 52.62/52.41 [9767]~P1(f332(f332(f334(x97672),x97675),f332(f277(x97671,x97672,x97674),x97673)))+P1(f332(f332(f334(f852(x97671,x97672)),f332(f332(f241(x97671,x97672),f534(x97673,x97674,x97671,x97675,x97672)),x97675)),x97674))
% 52.62/52.41 [9787]~P1(f332(f332(f334(f852(x97871,x97871)),f332(f332(f241(x97871,x97871),x97875),x97874)),f332(f332(f173(f852(x97871,x97871),a839),f332(a114,x97873)),x97872)))+P1(f332(f332(f334(f852(x97871,x97871)),f332(f332(f241(x97871,x97871),f658(x97872,x97873,x97874,x97875,x97871)),x97874)),x97872))
% 52.62/52.41 [9790]~P1(f332(f332(f334(f852(x97901,x97901)),f332(f332(f241(x97901,x97901),x97905),x97904)),f332(f332(f173(f852(x97901,x97901),a839),f332(a114,x97903)),x97902)))+P1(f332(f332(f334(f852(x97901,x97901)),f332(f332(f241(x97901,x97901),f657(x97902,x97903,x97904,x97905,x97901)),x97904)),f332(f332(f173(f852(x97901,x97901),a839),x97903),x97902)))
% 52.62/52.41 [9791]~P1(f332(f332(f334(f852(x97911,x97911)),f332(f332(f241(x97911,x97911),x97915),x97914)),f332(f332(f173(f852(x97911,x97911),a839),f332(a114,x97913)),x97912)))+P1(f332(f332(f334(f852(x97911,x97911)),f332(f332(f241(x97911,x97911),f659(x97912,x97913,x97914,x97915,x97911)),x97914)),f332(f332(f173(f852(x97911,x97911),a839),x97913),x97912)))
% 52.62/52.41 [9792]~P1(f332(f332(f334(f852(f846(x97921),f846(x97921))),f332(f332(f241(f846(x97921),f846(x97921)),x97925),f332(f332(f140(x97921),x97924),x97923))),f147(x97921,x97922)))+P1(f332(f332(f334(f852(x97921,x97921)),f332(f332(f241(x97921,x97921),f717(x97922,x97923,x97924,x97925,x97921)),x97924)),x97922))
% 52.62/52.41 [6987]E(x69871,f183(x69872))+E(f169(x69873,x69872,f332(f332(f332(f74(x69873,f849(x69872)),x69874),x69875),x69871)),f332(f332(f302(x69873),x69875),f169(x69873,x69872,x69874)))
% 52.62/52.41 [7506]~E(x75063,f180(f853(x75062,a839)))+E(f332(f332(f103(f853(x75061,a839)),f332(f332(f47(x75062,f853(x75061,a839)),x75063),x75064)),x75065),x75065)
% 52.62/52.41 [7507]~E(x75073,f180(f853(x75072,a839)))+E(f332(f332(f104(f853(x75071,a839)),f332(f332(f48(x75072,f853(x75071,a839)),x75073),x75074)),x75075),x75075)
% 52.62/52.41 [7559]~P73(x75591)+E(f332(f332(f83(x75591),f332(f332(f83(x75591),x75592),x75593)),f332(f332(f83(x75591),x75594),x75595)),f332(f332(f83(x75591),x75594),f332(f332(f83(x75591),f332(f332(f83(x75591),x75592),x75593)),x75595)))
% 52.62/52.41 [7869]~E(x78695,f183(x78692))+E(f169(x78691,x78692,f332(f332(f332(f74(x78691,f849(x78692)),x78693),x78694),x78695)),f332(f332(f3(f853(x78691,a839)),f169(x78691,x78692,x78693)),f332(f332(f302(x78691),x78694),f180(f853(x78691,a839)))))
% 52.62/52.41 [7939]~E(x79393,f180(f853(x79392,a839)))+E(f332(f332(f3(f853(x79391,a839)),f332(f332(f48(x79392,f853(x79391,a839)),x79393),x79394)),x79395),f332(f332(f3(f853(x79391,a839)),f239(f853(x79391,a839))),x79395))
% 52.62/52.41 [8066]E(f332(f332(f148(x80661,f332(f332(f125(x80661),x80662),x80663)),x80664),x80665),f332(f332(f125(x80661),f332(f332(f148(x80661,x80662),x80664),x80665)),x80663))+~P1(f332(f332(f233(a845),x80664),f332(f181(f846(x80661)),x80662)))
% 52.62/52.41 [8067]E(f332(f332(f148(x80671,f332(f332(f125(x80671),x80672),x80673)),x80674),x80675),f332(f332(f125(x80671),f332(f332(f148(x80671,x80672),x80674),x80675)),x80673))+~P1(f332(f332(f233(a845),x80674),f332(f181(f846(x80671)),x80672)))
% 52.62/52.41 [8197]P1(f332(f332(f334(x81971),x81975),f332(f158(x81971),x81973)))+E(f332(f166(x81971,x81972,f332(f332(f167(x81971,x81972),x81973),f332(f332(f143(x81971,x81972),x81974),x81973))),x81975),f183(x81972))
% 52.62/52.41 [8305]~P1(f332(f332(f334(x83051),x83055),f332(f158(x83051),x83053)))+E(f332(f166(x83051,x83052,f332(f332(f167(x83051,x83052),x83053),f332(f332(f143(x83051,x83052),x83054),x83053))),x83055),f332(f227(x83052),f332(x83054,x83055)))
% 52.62/52.41 [8336]E(f332(f332(f152(x83361),f332(f332(f143(a845,x83361),x83362),f130(a845,f332(f294(a845,x83363),x83364)))),x83365),f332(x83362,f332(f332(f82(a845),x83363),x83365)))+~P1(f332(f332(f233(a845),x83365),f332(f332(f3(a845),x83364),x83363)))
% 52.62/52.41 [8349]E(x83491,f2(a101))+E(f121(x83492,x83493,f332(x83494,f332(f332(f3(a101),x83491),f80(a101))),f332(f332(f9(x83492,a101,f847(f849(x83493))),x83495),x83491)),f332(f191(x83492,x83493,x83494,x83495),x83491))
% 52.62/52.41 [8373]~E(x83733,f180(f853(x83731,a839)))+E(f332(f332(f47(x83731,f853(x83732,a839)),x83733),f332(f332(f10(f853(x83732,a839),f853(x83732,a839),x83731),f332(f103(f853(x83732,a839)),x83734)),x83735)),f180(f853(x83732,a839)))
% 52.62/52.41 [8374]~E(x83743,f180(f853(x83741,a839)))+E(f332(f332(f48(x83741,f853(x83742,a839)),x83743),f332(f332(f10(f853(x83742,a839),f853(x83742,a839),x83741),f332(f3(f853(x83742,a839)),x83744)),x83745)),f239(f853(x83742,a839)))
% 52.62/52.41 [8375]~E(x83753,f180(f853(x83751,a839)))+E(f332(f332(f48(x83751,f853(x83752,a839)),x83753),f332(f332(f10(f853(x83752,a839),f853(x83752,a839),x83751),f332(f104(f853(x83752,a839)),x83754)),x83755)),f239(f853(x83752,a839)))
% 52.62/52.41 [8380]~P136(x83802)+E(f332(f332(f8(x83801,x83802),f332(f332(f10(x83802,x83802,x83801),f332(f83(x83802),x83803)),x83804)),x83805),f332(f332(f83(x83802),x83803),f332(f332(f8(x83801,x83802),x83804),x83805)))
% 52.62/52.41 [8641]E(x86411,f180(f853(x86412,a839)))+E(f332(f332(f48(x86412,f853(x86413,a839)),x86411),f332(f332(f10(f853(x86413,a839),f853(x86413,a839),x86412),f332(f3(f853(x86413,a839)),x86414)),x86415)),f332(f332(f3(f853(x86413,a839)),x86414),f332(f332(f47(x86412,f853(x86413,a839)),x86411),x86415)))
% 52.62/52.41 [8642]E(x86421,f180(f853(x86422,a839)))+E(f332(f332(f47(x86422,f853(x86423,a839)),x86421),f332(f332(f10(f853(x86423,a839),f853(x86423,a839),x86422),f332(f103(f853(x86423,a839)),x86424)),x86425)),f332(f332(f103(f853(x86423,a839)),x86424),f332(f332(f47(x86422,f853(x86423,a839)),x86421),x86425)))
% 52.62/52.41 [8643]E(x86431,f180(f853(x86432,a839)))+E(f332(f332(f48(x86432,f853(x86433,a839)),x86431),f332(f332(f10(f853(x86433,a839),f853(x86433,a839),x86432),f332(f104(f853(x86433,a839)),x86434)),x86435)),f332(f332(f104(f853(x86433,a839)),x86434),f332(f332(f48(x86432,f853(x86433,a839)),x86431),x86435)))
% 52.62/52.41 [8644]E(x86441,f180(f853(x86442,a839)))+E(f332(f332(f47(x86442,f853(x86443,a839)),x86441),f332(f332(f10(f853(x86443,a839),f853(x86443,a839),x86442),f332(f103(f853(x86443,a839)),x86444)),x86445)),f332(f332(f103(f853(x86443,a839)),x86444),f332(f332(f47(x86442,f853(x86443,a839)),x86441),x86445)))
% 52.62/52.41 [8645]E(x86451,f180(f853(x86452,a839)))+E(f332(f332(f48(x86452,f853(x86453,a839)),x86451),f332(f332(f10(f853(x86453,a839),f853(x86453,a839),x86452),f332(f3(f853(x86453,a839)),x86454)),x86455)),f332(f332(f3(f853(x86453,a839)),x86454),f332(f332(f47(x86452,f853(x86453,a839)),x86451),x86455)))
% 52.62/52.41 [8646]E(x86461,f180(f853(x86462,a839)))+E(f332(f332(f48(x86462,f853(x86463,a839)),x86461),f332(f332(f10(f853(x86463,a839),f853(x86463,a839),x86462),f332(f104(f853(x86463,a839)),x86464)),x86465)),f332(f332(f104(f853(x86463,a839)),x86464),f332(f332(f48(x86462,f853(x86463,a839)),x86461),x86465)))
% 52.62/52.41 [9065]~P31(x90652,x90651,x90653,f332(f332(f103(f853(x90652,a839)),x90654),x90655))+E(f332(f332(f104(f853(x90651,a839)),f332(f303(x90652,x90651,x90653),f332(f332(f3(f853(x90652,a839)),x90654),x90655))),f332(f303(x90652,x90651,x90653),f332(f332(f3(f853(x90652,a839)),x90655),x90654))),f180(f853(x90651,a839)))
% 52.62/52.41 [9320]~P1(f332(f332(f232(f853(x93203,a839)),f332(f277(x93201,x93203,x93204),x93202)),x93205))+P1(f332(f332(f232(f853(x93201,a839)),x93202),f332(f81(f853(x93201,a839)),f332(f277(x93203,x93201,f332(f278(x93201,x93203),x93204)),f332(f81(f853(x93203,a839)),x93205)))))
% 52.62/52.41 [9343]~P31(x93431,x93432,x93433,f332(f332(f302(x93431),x93434),x93435))+~P1(f332(f332(f334(x93432),f332(x93433,x93434)),f332(f303(x93431,x93432,x93433),f332(f332(f3(f853(x93431,a839)),x93435),f332(f332(f302(x93431),x93434),f180(f853(x93431,a839)))))))
% 52.62/52.41 [9392]P1(f332(f332(f232(f853(x93921,a839)),f332(f277(x93922,x93921,x93923),x93924)),x93925))+~P1(f332(f332(f232(f853(x93922,a839)),x93924),f332(f81(f853(x93922,a839)),f332(f277(x93921,x93922,f332(f278(x93922,x93921),x93923)),f332(f81(f853(x93921,a839)),x93925)))))
% 52.62/52.41 [9465]~P80(x94651)+P1(f332(f332(f232(x94651),f332(f77(x94651),f332(f332(f3(x94651),f332(f332(f82(x94651),x94652),x94653)),f332(f332(f82(x94651),x94654),x94655)))),f332(f332(f82(x94651),f332(f77(x94651),f332(f332(f3(x94651),x94652),x94654))),f332(f77(x94651),f332(f332(f3(x94651),x94653),x94655)))))
% 52.62/52.41 [9558]P1(f332(f332(f334(x95581),f395(x95582,x95583,x95584,x95581,x95585)),x95584))+P1(f332(f332(f232(f853(x95585,a839)),f332(f332(f47(x95581,f853(x95585,a839)),x95584),x95583)),x95582))
% 52.62/52.41 [9731]~P1(f332(f332(f232(f853(x97311,a839)),f332(x97314,f395(x97315,x97314,x97313,x97312,x97311))),x97315))+P1(f332(f332(f232(f853(x97311,a839)),f332(f332(f47(x97312,f853(x97311,a839)),x97313),x97314)),x97315))
% 52.62/52.41 [8489]E(f332(f332(f125(x84891),x84892),f332(f332(f148(x84891,x84893),f332(f332(f3(a845),x84894),f332(f181(f846(x84891)),x84892))),x84895)),f332(f332(f148(x84891,f332(f332(f125(x84891),x84892),x84893)),x84894),x84895))+P1(f332(f332(f233(a845),x84894),f332(f181(f846(x84891)),x84892)))
% 52.62/52.41 [8514]~P135(x85141)+E(f332(f332(f82(x85141),f332(f332(f83(x85141),x85142),x85143)),f332(f332(f82(x85141),f332(f332(f83(x85141),x85144),x85143)),x85145)),f332(f332(f82(x85141),f332(f332(f83(x85141),f332(f332(f82(x85141),x85142),x85144)),x85143)),x85145))
% 52.62/52.41 [9022]~P136(x90221)+E(f332(f154(x90221),f332(f332(f143(x90222,x90221),f332(f332(f10(x90221,x90221,x90222),f332(f83(x90221),x90223)),x90224)),x90225)),f332(f332(f83(x90221),x90223),f332(f154(x90221),f332(f332(f143(x90222,x90221),x90224),x90225))))
% 52.62/52.41 [9399]~P136(x93992)+E(f332(f332(f8(x93991,x93992),f332(f332(f9(x93991,x93992,x93992),f332(f332(f10(x93992,f853(x93992,x93992),x93991),f83(x93992)),x93993)),x93994)),x93995),f332(f332(f83(x93992),f332(f332(f8(x93991,x93992),x93993),x93995)),x93994))
% 52.62/52.41 [9400]~P63(x94002)+E(f332(f332(f8(x94001,x94002),f332(f332(f9(x94001,x94002,x94002),f332(f332(f10(x94002,f853(x94002,x94002),x94001),f283(x94002)),x94003)),x94004)),x94005),f332(f332(f283(x94002),f332(f332(f8(x94001,x94002),x94003),x94005)),x94004))
% 52.62/52.41 [9407]~P4(x94072)+E(f332(f332(f8(x94071,x94072),f332(f332(f20(x94071,x94072,x94072),f332(f332(f10(x94072,f853(x94072,x94072),x94071),f82(x94072)),x94073)),x94074)),x94075),f332(f332(f82(x94072),f332(f332(f8(x94071,x94072),x94073),x94075)),f332(f332(f8(x94071,x94072),x94074),x94075)))
% 52.62/52.41 [9408]~P8(x94082)+E(f332(f332(f8(x94081,x94082),f332(f332(f20(x94081,x94082,x94082),f332(f332(f10(x94082,f853(x94082,x94082),x94081),f3(x94082)),x94083)),x94084)),x94085),f332(f332(f3(x94082),f332(f332(f8(x94081,x94082),x94083),x94085)),f332(f332(f8(x94081,x94082),x94084),x94085)))
% 52.62/52.41 [9409]~P70(x94092)+E(f332(f332(f11(x94091,x94092),f332(f332(f20(x94091,x94092,x94092),f332(f332(f10(x94092,f853(x94092,x94092),x94091),f83(x94092)),x94093)),x94094)),x94095),f332(f332(f83(x94092),f332(f332(f11(x94091,x94092),x94093),x94095)),f332(f332(f11(x94091,x94092),x94094),x94095)))
% 52.62/52.41 [9448]~E(x94483,f180(f853(x94481,a839)))+E(f332(f332(f47(x94481,f853(x94482,a839)),x94483),f332(f332(f9(x94481,f853(x94482,a839),f853(x94482,a839)),f332(f332(f10(f853(x94482,a839),f853(f853(x94482,a839),f853(x94482,a839)),x94481),f103(f853(x94482,a839))),x94484)),x94485)),f180(f853(x94482,a839)))
% 52.62/52.41 [9449]~E(x94493,f180(f853(x94491,a839)))+E(f332(f332(f48(x94491,f853(x94492,a839)),x94493),f332(f332(f9(x94491,f853(x94492,a839),f853(x94492,a839)),f332(f332(f10(f853(x94492,a839),f853(f853(x94492,a839),f853(x94492,a839)),x94491),f3(f853(x94492,a839))),x94494)),x94495)),f239(f853(x94492,a839)))
% 52.62/52.41 [9450]~E(x94503,f180(f853(x94501,a839)))+E(f332(f332(f48(x94501,f853(x94502,a839)),x94503),f332(f332(f9(x94501,f853(x94502,a839),f853(x94502,a839)),f332(f332(f10(f853(x94502,a839),f853(f853(x94502,a839),f853(x94502,a839)),x94501),f104(f853(x94502,a839))),x94504)),x94505)),f239(f853(x94502,a839)))
% 52.62/52.41 [9472]E(x94721,f180(f853(x94722,a839)))+E(f332(f332(f48(x94722,f853(x94723,a839)),x94721),f332(f332(f9(x94722,f853(x94723,a839),f853(x94723,a839)),f332(f332(f10(f853(x94723,a839),f853(f853(x94723,a839),f853(x94723,a839)),x94722),f3(f853(x94723,a839))),x94724)),x94725)),f332(f332(f3(f853(x94723,a839)),f332(f332(f48(x94722,f853(x94723,a839)),x94721),x94724)),x94725))
% 52.62/52.41 [9473]E(x94731,f180(f853(x94732,a839)))+E(f332(f332(f47(x94732,f853(x94733,a839)),x94731),f332(f332(f9(x94732,f853(x94733,a839),f853(x94733,a839)),f332(f332(f10(f853(x94733,a839),f853(f853(x94733,a839),f853(x94733,a839)),x94732),f103(f853(x94733,a839))),x94734)),x94735)),f332(f332(f103(f853(x94733,a839)),f332(f332(f47(x94732,f853(x94733,a839)),x94731),x94734)),x94735))
% 52.62/52.41 [9474]E(x94741,f180(f853(x94742,a839)))+E(f332(f332(f48(x94742,f853(x94743,a839)),x94741),f332(f332(f9(x94742,f853(x94743,a839),f853(x94743,a839)),f332(f332(f10(f853(x94743,a839),f853(f853(x94743,a839),f853(x94743,a839)),x94742),f104(f853(x94743,a839))),x94744)),x94745)),f332(f332(f104(f853(x94743,a839)),f332(f332(f48(x94742,f853(x94743,a839)),x94741),x94744)),x94745))
% 52.62/52.41 [9475]E(x94751,f180(f853(x94752,a839)))+E(f332(f332(f47(x94752,f853(x94753,a839)),x94751),f332(f332(f9(x94752,f853(x94753,a839),f853(x94753,a839)),f332(f332(f10(f853(x94753,a839),f853(f853(x94753,a839),f853(x94753,a839)),x94752),f103(f853(x94753,a839))),x94754)),x94755)),f332(f332(f103(f853(x94753,a839)),f332(f332(f47(x94752,f853(x94753,a839)),x94751),x94754)),x94755))
% 52.62/52.41 [9476]E(x94761,f180(f853(x94762,a839)))+E(f332(f332(f48(x94762,f853(x94763,a839)),x94761),f332(f332(f9(x94762,f853(x94763,a839),f853(x94763,a839)),f332(f332(f10(f853(x94763,a839),f853(f853(x94763,a839),f853(x94763,a839)),x94762),f3(f853(x94763,a839))),x94764)),x94765)),f332(f332(f3(f853(x94763,a839)),f332(f332(f48(x94762,f853(x94763,a839)),x94761),x94764)),x94765))
% 52.62/52.41 [9477]E(x94771,f180(f853(x94772,a839)))+E(f332(f332(f48(x94772,f853(x94773,a839)),x94771),f332(f332(f9(x94772,f853(x94773,a839),f853(x94773,a839)),f332(f332(f10(f853(x94773,a839),f853(f853(x94773,a839),f853(x94773,a839)),x94772),f104(f853(x94773,a839))),x94774)),x94775)),f332(f332(f104(f853(x94773,a839)),f332(f332(f48(x94772,f853(x94773,a839)),x94771),x94774)),x94775))
% 52.62/52.41 [9069]~P1(f332(f332(f232(a845),x90691),x90694))+E(f332(f332(f3(a845),f332(f332(f82(a845),f332(f332(f83(a845),x90691),x90692)),x90693)),f332(f332(f82(a845),f332(f332(f83(a845),x90694),x90692)),x90695)),f332(f332(f3(a845),x90693),f332(f332(f82(a845),f332(f332(f83(a845),f332(f332(f3(a845),x90694),x90691)),x90692)),x90695)))
% 52.62/52.41 [9611]~P136(x96111)+E(f332(f154(x96111),f332(f332(f143(x96112,x96111),f332(f332(f9(x96112,x96111,x96111),f332(f332(f10(x96111,f853(x96111,x96111),x96112),f83(x96111)),x96113)),x96114)),x96115)),f332(f332(f83(x96111),f332(f154(x96111),f332(f332(f143(x96112,x96111),x96113),x96115))),x96114))
% 52.62/52.41 [9617]~P4(x96171)+E(f332(f154(x96171),f332(f332(f143(x96172,x96171),f332(f332(f20(x96172,x96171,x96171),f332(f332(f10(x96171,f853(x96171,x96171),x96172),f82(x96171)),x96173)),x96174)),x96175)),f332(f332(f82(x96171),f332(f154(x96171),f332(f332(f143(x96172,x96171),x96173),x96175))),f332(f154(x96171),f332(f332(f143(x96172,x96171),x96174),x96175))))
% 52.62/52.41 [9618]~P8(x96181)+E(f332(f154(x96181),f332(f332(f143(x96182,x96181),f332(f332(f20(x96182,x96181,x96181),f332(f332(f10(x96181,f853(x96181,x96181),x96182),f3(x96181)),x96183)),x96184)),x96185)),f332(f332(f3(x96181),f332(f154(x96181),f332(f332(f143(x96182,x96181),x96183),x96185))),f332(f154(x96181),f332(f332(f143(x96182,x96181),x96184),x96185))))
% 52.62/52.41 [9287]~P1(f332(f332(f232(a845),x92874),x92871))+E(f332(f332(f3(a845),f332(f332(f82(a845),f332(f332(f83(a845),x92871),x92872)),x92873)),f332(f332(f82(a845),f332(f332(f83(a845),x92874),x92872)),x92875)),f332(f332(f3(a845),f332(f332(f82(a845),f332(f332(f83(a845),f332(f332(f3(a845),x92871),x92874)),x92872)),x92873)),x92875))
% 52.62/52.41 [10016]P34(x100161,x100162,f332(f303(a841,f844(x100161),f332(f332(f20(a841,f853(x100161,f853(a842,a839)),f844(x100161)),f332(f332(f20(a841,a840,f853(f853(x100161,f853(a842,a839)),f844(x100161))),f332(f332(f10(f853(x100161,f853(a842,a839)),f853(a840,f853(f853(x100161,f853(a842,a839)),f844(x100161))),a841),f93(x100161)),x100163)),a27)),x100164)),x100165))+~P34(x100161,f332(f332(f103(f853(f844(x100161),a839)),x100162),f332(f303(a841,f844(x100161),f332(f332(f20(a841,f853(x100161,f853(a842,a839)),f844(x100161)),f332(f332(f20(a841,a840,f853(f853(x100161,f853(a842,a839)),f844(x100161))),f332(f332(f10(f853(x100161,f853(a842,a839)),f853(a840,f853(f853(x100161,f853(a842,a839)),f844(x100161))),a841),f93(x100161)),x100163)),a27)),x100164)),x100165)),f332(f303(a841,f844(x100161),f332(f332(f20(a841,f853(x100161,f853(a842,a839)),f844(x100161)),f332(f332(f20(a841,a840,f853(f853(x100161,f853(a842,a839)),f844(x100161))),f332(f332(f10(f853(x100161,f853(a842,a839)),f853(a840,f853(f853(x100161,f853(a842,a839)),f844(x100161))),a841),f93(x100161)),x100163)),f332(f332(f10(f849(a840),a840,a841),f231(a840)),a30))),x100164)),x100165))
% 52.62/52.41 [10017]P30(x100171,x100172,f332(f303(a841,f844(x100171),f332(f332(f20(a841,f853(x100171,f853(a842,a839)),f844(x100171)),f332(f332(f20(a841,a840,f853(f853(x100171,f853(a842,a839)),f844(x100171))),f332(f332(f10(f853(x100171,f853(a842,a839)),f853(a840,f853(f853(x100171,f853(a842,a839)),f844(x100171))),a841),f93(x100171)),x100173)),a27)),x100174)),x100175))+~P30(x100171,f332(f332(f103(f853(f844(x100171),a839)),x100172),f332(f303(a841,f844(x100171),f332(f332(f20(a841,f853(x100171,f853(a842,a839)),f844(x100171)),f332(f332(f20(a841,a840,f853(f853(x100171,f853(a842,a839)),f844(x100171))),f332(f332(f10(f853(x100171,f853(a842,a839)),f853(a840,f853(f853(x100171,f853(a842,a839)),f844(x100171))),a841),f93(x100171)),x100173)),a27)),x100174)),x100175)),f332(f303(a841,f844(x100171),f332(f332(f20(a841,f853(x100171,f853(a842,a839)),f844(x100171)),f332(f332(f20(a841,a840,f853(f853(x100171,f853(a842,a839)),f844(x100171))),f332(f332(f10(f853(x100171,f853(a842,a839)),f853(a840,f853(f853(x100171,f853(a842,a839)),f844(x100171))),a841),f93(x100171)),x100173)),f332(f332(f10(f849(a840),a840,a841),f231(a840)),a30))),x100174)),x100175))
% 52.62/52.41 [5147]E(x51471,x51472)+~E(f33(x51473,x51474,x51471),f33(x51475,x51476,x51472))
% 52.62/52.41 [5148]E(x51481,x51482)+~E(f33(x51483,x51481,x51484),f33(x51485,x51482,x51486))
% 52.62/52.41 [5149]E(x51491,x51492)+~E(f33(x51491,x51493,x51494),f33(x51492,x51495,x51496))
% 52.62/52.41 [5150]E(x51501,x51502)+~E(f32(x51503,x51504,x51501),f32(x51505,x51506,x51502))
% 52.62/52.41 [5151]E(x51511,x51512)+~E(f32(x51513,x51511,x51514),f32(x51515,x51512,x51516))
% 52.62/52.41 [5152]E(x51521,x51522)+~E(f32(x51521,x51523,x51524),f32(x51522,x51525,x51526))
% 52.62/52.41 [5153]E(x51531,x51532)+~E(f31(x51533,x51534,x51531),f31(x51535,x51536,x51532))
% 52.62/52.41 [5154]E(x51541,x51542)+~E(f31(x51543,x51541,x51544),f31(x51545,x51542,x51546))
% 52.62/52.41 [5155]E(x51551,x51552)+~E(f31(x51551,x51553,x51554),f31(x51552,x51555,x51556))
% 52.62/52.41 [7175]E(x71751,x71752)+~E(f215(x71753,x71754,x71755,x71751),f215(x71753,x71754,x71756,x71752))
% 52.62/52.41 [7176]E(x71761,x71762)+~E(f215(x71763,x71764,x71761,x71765),f215(x71763,x71764,x71762,x71766))
% 52.62/52.41 [6618]E(f332(f170(x66181,x66182,x66183,x66184),x66185),f332(f227(x66182),x66186))+~E(f332(x66184,x66185),f332(f227(x66182),x66186))
% 52.62/52.41 [6619]E(f332(f170(x66191,x66192,x66193,x66194),x66195),f332(f227(x66192),x66196))+~E(f332(x66194,x66195),f332(f227(x66192),x66196))
% 52.62/52.41 [6770]E(f332(f229(f849(x67701),x67702,f183(x67701),x67703),f332(x67704,x67705)),f332(x67703,x67706))+~E(f332(x67704,x67705),f332(f227(x67702),x67706))
% 52.62/52.41 [8316]~P25(x83165,x83161,x83162,x83166)+E(f332(f75(x83161,x83161,x83161,f332(x83162,x83163)),f332(x83162,x83164)),f332(f75(x83161,x83161,x83161,f332(x83162,x83164)),f332(x83162,x83163)))
% 52.62/52.41 [8549]~P57(x85494,x85495,x85492,x85491,x85496)+E(f332(x85491,f332(x85492,x85493)),x85493)
% 52.62/52.41 [8690]P31(x86901,x86902,x86903,x86904)+~P31(x86901,x86905,f332(f75(x86902,x86905,x86901,x86906),x86903),x86904)
% 52.62/52.41 [8767]~P31(x87674,x87672,f332(f75(x87671,x87672,x87674,x87673),x87675),x87676)+P31(x87671,x87672,x87673,f332(f303(x87674,x87671,x87675),x87676))
% 52.62/52.41 [9410]P1(f332(f64(x94101),x94102))+~P1(f332(f69(x94101,x94103,x94104,x94105,x94102),x94106))
% 52.62/52.41 [9420]~P1(f332(f332(f334(x94204),x94203),f289(x94204,x94201,x94205,x94202,x94206)))+P1(f332(f332(x94201,x94202),x94203))
% 52.62/52.41 [9421]~P1(f332(f332(f334(x94214),x94213),f292(x94214,x94215,x94211,x94212,x94216)))+P1(f332(f332(x94211,x94212),x94213))
% 52.62/52.41 [9422]~P1(f332(f332(f334(x94224),x94222),f289(x94224,x94225,x94221,x94226,x94223)))+P1(f332(f332(x94221,x94222),x94223))
% 52.62/52.41 [9423]~P1(f332(f332(f334(x94234),x94232),f292(x94234,x94231,x94235,x94236,x94233)))+P1(f332(f332(x94231,x94232),x94233))
% 52.62/52.41 [5633]E(x56331,x56332)+~E(f332(f332(f241(x56333,x56334),x56335),x56331),f332(f332(f241(x56333,x56334),x56336),x56332))
% 52.62/52.41 [5634]E(x56341,x56342)+~E(f332(f332(f241(x56343,x56344),x56345),x56341),f332(f332(f241(x56343,x56344),x56346),x56342))
% 52.62/52.41 [5635]E(x56351,x56352)+~E(f332(f332(f241(x56353,x56354),x56351),x56355),f332(f332(f241(x56353,x56354),x56352),x56356))
% 52.62/52.41 [5636]E(x56361,x56362)+~E(f332(f332(f241(x56363,x56364),x56361),x56365),f332(f332(f241(x56363,x56364),x56362),x56366))
% 52.62/52.41 [5775]~P22(x57755,x57756,x57751)+E(f332(f332(x57751,x57752),f332(f332(x57751,x57753),x57754)),f332(f332(x57751,x57753),f332(f332(x57751,x57752),x57754)))
% 52.62/52.41 [7246]~P36(x72464,x72461,f332(f332(f140(x72464),x72462),x72465),f332(f332(f140(x72464),x72463),x72466))+P1(f332(f332(x72461,x72462),x72463))
% 52.62/52.41 [7625]P36(x76251,x76252,x76253,x76254)+~P36(x76251,x76252,f332(f332(f140(x76251),x76255),x76253),f332(f332(f140(x76251),x76256),x76254))
% 52.62/52.41 [8635]~P57(x86355,x86351,x86352,x86356,x86354)+P1(f332(f332(f334(x86351),f332(x86352,x86353)),x86354))
% 52.62/52.41 [8788]E(f332(f78(x87881,x87882,x87883,x87884,x87885),x87886),f332(x87883,x87886))+P1(f332(f332(f334(x87881),x87886),x87885))
% 52.62/52.41 [8789]E(f332(f78(x87891,x87892,x87893,x87894,x87895),x87896),f332(x87893,x87896))+P1(f332(f332(f334(x87891),x87896),x87895))
% 52.62/52.41 [8807]~E(x88073,f332(f332(f140(x88071),x88075),x88076))+P1(f332(f332(f334(f852(f846(x88071),f846(x88071))),f332(f332(f241(f846(x88071),f846(x88071)),x88072),f332(f332(f125(x88071),x88072),x88073))),f137(x88071,x88074)))
% 52.62/52.41 [8810]E(f332(f78(x88101,x88102,x88103,x88104,x88105),x88106),f332(x88104,x88106))+~P1(f332(f332(f334(x88101),x88106),x88105))
% 52.62/52.41 [8811]E(f332(f78(x88111,x88112,x88113,x88114,x88115),x88116),f332(x88114,x88116))+~P1(f332(f332(f334(x88111),x88116),x88115))
% 52.62/52.41 [9487]~P29(x94874,x94872,x94875,x94873,x94876,x94871)+E(f332(x94871,f180(f853(x94872,a839))),x94873)
% 52.62/52.41 [9692]~E(f332(x96924,f332(f240(x96921,x96923),x96925)),f332(x96926,f332(f240(x96921,x96923),x96925)))+E(f332(f252(x96921,x96922,x96923,x96923,x96924,f39(x96923)),x96925),f332(f252(x96921,x96922,x96923,x96923,x96926,f39(x96923)),x96925))
% 52.62/52.41 [9693]~E(f332(x96934,f332(f250(x96931,x96932),x96935)),f332(x96936,f332(f250(x96931,x96932),x96935)))+E(f332(f252(x96931,x96931,x96932,x96933,f39(x96931),x96934),x96935),f332(f252(x96931,x96931,x96932,x96933,f39(x96931),x96936),x96935))
% 52.62/52.41 [9754]~E(f332(f252(x97542,x97546,x97543,x97543,x97541,f39(x97543)),x97544),f332(f252(x97542,x97546,x97543,x97543,x97545,f39(x97543)),x97544))+E(f332(x97541,f332(f240(x97542,x97543),x97544)),f332(x97545,f332(f240(x97542,x97543),x97544)))
% 52.62/52.41 [9755]~E(f332(f252(x97552,x97552,x97553,x97556,f39(x97552),x97551),x97554),f332(f252(x97552,x97552,x97553,x97556,f39(x97552),x97555),x97554))+E(f332(x97551,f332(f250(x97552,x97553),x97554)),f332(x97555,f332(f250(x97552,x97553),x97554)))
% 52.62/52.41 [8722]P1(f332(f332(f334(x87221),x87222),x87223))+~P1(f332(f332(f334(f852(x87221,x87224)),f332(f332(f241(x87221,x87224),x87222),x87225)),f332(f332(f248(x87221,x87224),x87223),x87226)))
% 52.62/52.41 [8723]P1(f332(f332(f334(x87231),x87232),x87233))+~P1(f332(f332(f334(f852(x87231,x87234)),f332(f332(f241(x87231,x87234),x87232),x87235)),f332(f332(f248(x87231,x87234),x87233),x87236)))
% 52.62/52.41 [8724]P1(f332(f332(f334(x87241),x87242),x87243))+~P1(f332(f332(f334(f852(x87241,x87244)),f332(f332(f241(x87241,x87244),x87242),x87245)),f332(f332(f248(x87241,x87244),x87243),x87246)))
% 52.62/52.41 [8737]P1(f332(f332(f334(x87371),x87372),f332(x87373,x87374)))+~P1(f332(f332(f334(f852(x87375,x87371)),f332(f332(f241(x87375,x87371),x87374),x87372)),f332(f332(f248(x87375,x87371),x87376),x87373)))
% 52.62/52.41 [8738]P1(f332(f332(f334(x87381),x87382),f332(x87383,x87384)))+~P1(f332(f332(f334(f852(x87385,x87381)),f332(f332(f241(x87385,x87381),x87384),x87382)),f332(f332(f248(x87385,x87381),x87386),x87383)))
% 52.62/52.41 [8739]P1(f332(f332(f334(x87391),x87392),f332(x87393,x87394)))+~P1(f332(f332(f334(f852(x87395,x87391)),f332(f332(f241(x87395,x87391),x87394),x87392)),f332(f332(f248(x87395,x87391),x87396),x87393)))
% 52.62/52.41 [9045]P1(f332(f332(f334(x90451),x90454),f169(x90451,x90452,x90456)))+E(f170(x90451,x90452,f332(f332(f332(f74(x90451,f849(x90452)),x90453),x90454),f332(f227(x90452),x90455)),x90456),f332(f332(f332(f74(x90451,f849(x90452)),f170(x90451,x90452,x90453,x90456)),x90454),f332(f227(x90452),x90455)))
% 52.62/52.41 [9136]P1(f332(f332(f334(f852(x91361,x91361)),f332(f332(f241(x91361,x91361),f332(x91362,x91363)),f332(x91362,x91364))),x91365))+~P1(f332(f332(f334(f852(x91366,x91366)),f332(f332(f241(x91366,x91366),x91363),x91364)),f332(f332(f280(x91361,x91366),x91365),x91362)))
% 52.62/52.41 [9148]~P1(f332(f332(f334(f852(x91484,x91484)),f332(f332(f241(x91484,x91484),f332(x91486,x91482)),f332(x91486,x91483))),x91485))+P1(f332(f332(f334(f852(x91481,x91481)),f332(f332(f241(x91481,x91481),x91482),x91483)),f332(f332(f280(x91484,x91481),x91485),x91486)))
% 52.62/52.41 [9757]E(f332(f332(f241(x97571,x97572),f705(x97573,x97574,x97575,x97576,x97572,x97571)),f708(x97573,x97574,x97575,x97576,x97572,x97571)),x97576)+~P1(f332(f332(f334(f852(x97571,x97572)),x97576),f332(f332(f281(x97571,x97575,x97572),x97574),x97573)))
% 52.62/52.41 [9965]~P1(f332(f332(f334(f852(x99651,x99656)),x99655),f332(f332(f281(x99651,x99652,x99656),x99654),x99653)))+P1(f332(f332(f334(f852(x99651,x99652)),f332(f332(f241(x99651,x99652),f705(x99653,x99654,x99652,x99655,x99656,x99651)),f709(x99653,x99654,x99652,x99655,x99656,x99651))),x99654))
% 52.62/52.41 [9966]~P1(f332(f332(f334(f852(x99666,x99662)),x99665),f332(f332(f281(x99666,x99661,x99662),x99664),x99663)))+P1(f332(f332(f334(f852(x99661,x99662)),f332(f332(f241(x99661,x99662),f709(x99663,x99664,x99661,x99665,x99662,x99666)),f708(x99663,x99664,x99661,x99665,x99662,x99666))),x99663))
% 52.62/52.41 [6053]~E(x60536,x60534)+E(f332(f332(f332(f332(f74(x60531,x60532),x60533),x60534),x60535),x60536),x60535)
% 52.62/52.41 [6054]~E(x60546,x60544)+E(f332(f332(f332(f332(f74(x60541,x60542),x60543),x60544),x60545),x60546),x60545)
% 52.62/52.41 [6101]E(x61011,x61012)+E(f332(f332(f332(f332(f74(x61013,x61014),x61015),x61012),x61016),x61011),f332(x61015,x61011))
% 52.62/52.41 [6102]E(x61021,x61022)+E(f332(f332(f332(f332(f74(x61023,x61024),x61025),x61022),x61026),x61021),f332(x61025,x61021))
% 52.62/52.41 [6103]E(x61031,x61032)+E(f332(f332(f332(f332(f74(x61033,x61034),x61035),x61032),x61036),x61031),f332(x61035,x61031))
% 52.62/52.41 [7691]~P11(x76912)+E(f332(f332(f47(x76911,x76912),x76913),f332(f332(f9(x76911,x76914,x76912),x76915),x76916)),f332(f332(f332(f47(x76911,f853(x76914,x76912)),x76913),x76915),x76916))
% 52.62/52.41 [7692]~P11(x76922)+E(f332(f332(f48(x76921,x76922),x76923),f332(f332(f9(x76921,x76924,x76922),x76925),x76926)),f332(f332(f332(f48(x76921,f853(x76924,x76922)),x76923),x76925),x76926))
% 52.62/52.41 [8280]E(f332(f303(x82801,f849(x82802),f332(f332(f332(f74(x82801,f849(x82802)),x82803),x82804),f332(f227(x82802),x82805))),x82806),f332(f303(x82801,f849(x82802),x82803),x82806))+P1(f332(f332(f334(x82801),x82804),x82806))
% 52.62/52.41 [8471]E(f332(f332(f47(x84711,f853(x84712,a839)),x84713),f332(f332(f10(f853(x84712,a839),f853(x84712,a839),x84711),f332(f302(x84712),x84714)),x84715)),f332(f332(f302(x84712),x84714),f332(f332(f47(x84711,f853(x84712,a839)),x84713),x84715)))+~P1(f332(f332(f334(x84711),x84716),x84713))
% 52.62/52.41 [8472]E(f332(f332(f48(x84721,f853(x84722,a839)),x84723),f332(f332(f10(f853(x84722,a839),f853(x84722,a839),x84721),f332(f302(x84722),x84724)),x84725)),f332(f332(f302(x84722),x84724),f332(f332(f48(x84721,f853(x84722,a839)),x84723),x84725)))+~P1(f332(f332(f334(x84721),x84726),x84723))
% 52.62/52.41 [8851]~P11(x88512)+E(f332(f332(f47(x88511,x88512),x88513),f332(f332(f10(f853(x88514,x88512),x88512,x88511),f332(f47(x88514,x88512),x88515)),f332(f9(x88514,x88511,x88512),x88516))),f332(f332(f47(x88514,x88512),x88515),f332(f332(f10(f853(x88511,x88512),x88512,x88514),f332(f47(x88511,x88512),x88513)),x88516)))
% 52.62/52.41 [8852]~P11(x88522)+E(f332(f332(f48(x88521,x88522),x88523),f332(f332(f10(f853(x88524,x88522),x88522,x88521),f332(f48(x88524,x88522),x88525)),f332(f9(x88524,x88521,x88522),x88526))),f332(f332(f48(x88524,x88522),x88525),f332(f332(f10(f853(x88521,x88522),x88522,x88524),f332(f48(x88521,x88522),x88523)),x88526)))
% 52.62/52.41 [9051]P1(f332(f332(f334(x90511),x90512),f332(f158(x90511),x90513)))+~P1(f332(f332(f334(f852(x90514,x90511)),f332(f332(f241(x90514,x90511),x90515),x90512)),f332(f158(f852(x90514,x90511)),f332(f332(f167(x90514,x90511),x90516),x90513))))
% 52.62/52.41 [9052]P1(f332(f332(f334(x90521),x90522),f332(f158(x90521),x90523)))+~P1(f332(f332(f334(f852(x90521,x90524)),f332(f332(f241(x90521,x90524),x90522),x90525)),f332(f158(f852(x90521,x90524)),f332(f332(f167(x90521,x90524),x90523),x90526))))
% 52.62/52.41 [9053]P1(f332(f332(f334(x90531),x90532),f332(f158(x90531),x90533)))+~P1(f332(f332(f334(f852(x90534,x90531)),f332(f332(f241(x90534,x90531),x90535),x90532)),f332(f158(f852(x90534,x90531)),f332(f332(f167(x90534,x90531),x90536),x90533))))
% 52.62/52.41 [9054]P1(f332(f332(f334(x90541),x90542),f332(f158(x90541),x90543)))+~P1(f332(f332(f334(f852(x90541,x90544)),f332(f332(f241(x90541,x90544),x90542),x90545)),f332(f158(f852(x90541,x90544)),f332(f332(f167(x90541,x90544),x90543),x90546))))
% 52.62/52.41 [9146]P1(f332(f332(f232(f853(x91461,a839)),f332(f277(x91462,x91461,x91463),x91464)),x91465))+~P1(f332(f332(f232(f853(f852(x91462,x91461),a839)),x91463),f332(f332(f248(x91462,x91461),x91466),f332(f18(f853(x91461,a839),x91462),x91465))))
% 52.62/52.41 [9323]P1(f332(f332(f334(f852(f846(x93231),f846(x93231))),f332(f332(f241(f846(x93231),f846(x93231)),f332(f332(f140(x93231),x93232),x93233)),f332(f332(f140(x93231),x93234),x93235))),f137(x93231,x93236)))+~P1(f332(f332(f334(f852(x93231,x93231)),f332(f332(f241(x93231,x93231),x93232),x93234)),x93236))
% 52.62/52.41 [9753]E(f332(f332(f241(x97531,x97532),f612(x97533,x97534,x97535,x97532,x97531,x97536)),f613(x97533,x97534,x97535,x97532,x97531,x97536)),x97536)+P1(f332(f332(f334(x97535),x97534),f332(f332(f251(x97531,x97532,f853(x97535,a839)),x97533),x97536)))
% 52.62/52.41 [9758]E(f332(f332(f241(x97581,x97582),f614(x97583,x97584,x97582,x97581,x97585,x97586)),f615(x97583,x97584,x97582,x97581,x97585,x97586)),x97583)+~P1(f332(f332(f334(x97586),x97585),f332(f332(f251(x97581,x97582,f853(x97586,a839)),x97584),x97583)))
% 52.62/52.41 [9920]P1(f332(f332(f334(x99201),x99202),f332(f332(x99203,f614(x99204,x99203,x99205,x99206,x99202,x99201)),f615(x99204,x99203,x99205,x99206,x99202,x99201))))+~P1(f332(f332(f334(x99201),x99202),f332(f332(f251(x99206,x99205,f853(x99201,a839)),x99203),x99204)))
% 52.62/52.41 [9944]~P1(f332(f332(f334(x99441),x99442),f332(f332(x99445,f612(x99445,x99442,x99441,x99444,x99443,x99446)),f613(x99445,x99442,x99441,x99444,x99443,x99446))))+P1(f332(f332(f334(x99441),x99442),f332(f332(f251(x99443,x99444,f853(x99441,a839)),x99445),x99446)))
% 52.62/52.41 [7816]P1(f332(f332(f334(x78161),x78164),x78166))+E(f172(x78161,x78162,f332(f332(f332(f74(x78161,f849(x78162)),x78163),x78164),x78165),x78166),f172(x78161,x78162,x78163,x78166))
% 52.62/52.41 [7891]P1(f332(f332(f334(x78911),x78914),x78916))+E(f332(f303(x78911,x78912,f332(f332(f332(f74(x78911,x78912),x78913),x78914),x78915)),x78916),f332(f303(x78911,x78912,x78913),x78916))
% 52.62/52.41 [7919]P1(f332(f332(f334(x79191),x79194),f332(f158(x79191),x79196)))+E(f332(f332(f143(x79191,x79192),f332(f332(f332(f74(x79191,x79192),x79193),x79194),x79195)),x79196),f332(f332(f143(x79191,x79192),x79193),x79196))
% 52.62/52.41 [8366]E(x83661,x83662)+E(f332(f332(f148(x83663,f332(f332(f148(x83663,x83664),x83661),x83665)),x83662),x83666),f332(f332(f148(x83663,f332(f332(f148(x83663,x83664),x83662),x83666)),x83661),x83665))
% 52.62/52.41 [8857]~P1(f332(f332(f334(x88573),x88576),x88575))+E(f332(f332(f302(x88571),x88572),f332(f303(x88573,x88571,x88574),f332(f332(f3(f853(x88573,a839)),x88575),f332(f332(f302(x88573),x88576),f180(f853(x88573,a839)))))),f332(f303(x88573,x88571,f332(f332(f332(f74(x88573,x88571),x88574),x88576),x88572)),x88575))
% 52.62/52.41 [8685]~E(x86853,x86856)+E(f332(f166(x86851,x86852,f332(f332(f140(f852(x86851,x86852)),f332(f332(f241(x86851,x86852),x86853),x86854)),x86855)),x86856),f332(f227(x86852),x86854))
% 52.62/52.41 [8726]E(x87261,x87262)+E(f332(f166(x87263,x87264,f332(f332(f140(f852(x87263,x87264)),f332(f332(f241(x87263,x87264),x87261),x87265)),x87266)),x87262),f332(f166(x87263,x87264,x87266),x87262))
% 52.62/52.41 [8931]~P1(f332(f332(x89314,x89315),x89316))+P1(f332(f332(f332(f332(f103(f853(x89311,f853(x89312,a839))),x89313),x89314),x89315),x89316))
% 52.62/52.41 [8932]~P1(f332(f332(x89324,x89325),x89326))+P1(f332(f332(f332(f332(f103(f853(x89321,f853(x89322,a839))),x89323),x89324),x89325),x89326))
% 52.62/52.41 [8933]~P1(f332(f332(x89333,x89335),x89336))+P1(f332(f332(f332(f332(f103(f853(x89331,f853(x89332,a839))),x89333),x89334),x89335),x89336))
% 52.62/52.41 [8934]~P1(f332(f332(x89343,x89345),x89346))+P1(f332(f332(f332(f332(f103(f853(x89341,f853(x89342,a839))),x89343),x89344),x89345),x89346))
% 52.62/52.41 [8950]P1(f332(f332(f334(x89501),x89506),f332(f158(x89501),x89504)))+E(f332(f170(x89501,x89502,x89503,f166(x89501,x89502,f332(f142(f852(x89501,x89502)),f332(f332(f167(x89501,x89502),x89504),x89505)))),x89506),f332(x89503,x89506))
% 52.62/52.41 [9099]~E(f332(f181(f846(x90991)),x90994),f332(f181(f846(x90992)),x90995))+E(f170(x90991,x90992,x90993,f166(x90991,x90992,f332(f142(f852(x90991,x90992)),f332(f332(f167(x90991,x90992),x90994),f332(f332(f125(x90992),x90995),x90996))))),f170(x90991,x90992,x90993,f166(x90991,x90992,f332(f142(f852(x90991,x90992)),f332(f332(f167(x90991,x90992),x90994),x90995)))))
% 52.62/52.41 [9184]P1(f332(f332(x91841,x91842),x91843))+~P1(f332(f332(f332(f332(f104(f853(x91844,f853(x91845,a839))),x91846),x91841),x91842),x91843))
% 52.62/52.41 [9185]P1(f332(f332(x91851,x91852),x91853))+~P1(f332(f332(f332(f332(f104(f853(x91854,f853(x91855,a839))),x91851),x91856),x91852),x91853))
% 52.62/52.41 [9186]P1(f332(f332(x91861,x91862),x91863))+~P1(f332(f332(f332(f332(f104(f853(x91864,f853(x91865,a839))),x91866),x91861),x91862),x91863))
% 52.62/52.41 [9187]P1(f332(f332(x91871,x91872),x91873))+~P1(f332(f332(f332(f332(f104(f853(x91874,f853(x91875,a839))),x91871),x91876),x91872),x91873))
% 52.62/52.41 [9600]~P4(x96002)+E(f332(f332(f8(x96001,x96002),f332(f332(f9(x96001,f853(x96003,a839),x96002),f332(f332(f10(f853(x96003,x96002),f853(f853(x96003,a839),x96002),x96001),f8(x96003,x96002)),x96004)),x96005)),x96006),f332(f332(f8(f852(x96001,x96003),x96002),f332(f251(x96001,x96003,x96002),x96004)),f332(f332(f248(x96001,x96003),x96006),f332(f18(f853(x96003,a839),x96001),x96005))))
% 52.62/52.41 [9601]~P70(x96012)+E(f332(f332(f11(x96011,x96012),f332(f332(f9(x96011,f853(x96013,a839),x96012),f332(f332(f10(f853(x96013,x96012),f853(f853(x96013,a839),x96012),x96011),f11(x96013,x96012)),x96014)),x96015)),x96016),f332(f332(f11(f852(x96011,x96013),x96012),f332(f251(x96011,x96013,x96012),x96014)),f332(f332(f248(x96011,x96013),x96016),f332(f18(f853(x96013,a839),x96011),x96015))))
% 52.62/52.41 [9720]~P4(x97202)+E(f332(f332(f8(x97201,x97202),f332(f332(f9(x97201,f853(x97203,a839),x97202),f332(f332(f10(f853(x97203,x97202),f853(f853(x97203,a839),x97202),x97201),f8(x97203,x97202)),f332(f9(x97203,x97201,x97202),x97204))),x97205)),x97206),f332(f332(f8(x97203,x97202),f332(f332(f9(x97203,f853(x97201,a839),x97202),f332(f332(f10(f853(x97201,x97202),f853(f853(x97201,a839),x97202),x97203),f8(x97201,x97202)),x97204)),x97206)),x97205))
% 52.62/52.41 [9188]~E(f332(f181(f846(x91881)),x91884),f332(f181(f846(x91882)),x91886))+E(f170(x91881,x91882,x91883,f166(x91881,x91882,f332(f142(f852(x91881,x91882)),f332(f332(f167(x91881,x91882),f332(f332(f125(x91881),x91884),x91885)),x91886)))),f170(x91881,x91882,x91883,f166(x91881,x91882,f332(f142(f852(x91881,x91882)),f332(f332(f167(x91881,x91882),x91884),x91886)))))
% 52.62/52.41 [9452]~P1(f332(f332(f334(x94521),x94525),x94524))+E(f332(f332(f332(f74(x94521,f849(x94522)),f172(x94521,x94522,x94523,f332(f332(f3(f853(x94521,a839)),x94524),f332(f332(f302(x94521),x94525),f180(f853(x94521,a839)))))),x94525),x94526),f172(x94521,x94522,f332(f332(f332(f74(x94521,f849(x94522)),x94523),x94525),x94526),x94524))
% 52.62/52.41 [9504]~P1(f332(f332(f334(x95041),x95045),x95044))+E(f332(f332(f332(f74(x95041,f849(x95042)),f172(x95041,x95042,x95043,f332(f332(f3(f853(x95041,a839)),x95044),f332(f332(f302(x95041),x95045),f180(f853(x95041,a839)))))),x95045),x95046),f332(f332(f332(f74(x95041,f849(x95042)),f172(x95041,x95042,x95043,x95044)),x95045),x95046))
% 52.62/52.41 [9659]E(f170(x96591,x96592,x96593,f166(x96591,x96592,f332(f142(f852(x96591,x96592)),f332(f332(f167(x96591,x96592),f332(f332(f125(x96591),x96594),f332(f332(f140(x96591),x96595),f115(x96591)))),x96596)))),f332(f332(f332(f74(x96591,f849(x96592)),f170(x96591,x96592,x96593,f166(x96591,x96592,f332(f142(f852(x96591,x96592)),f332(f332(f167(x96591,x96592),x96594),x96596))))),x96595),f332(f227(x96592),f332(f332(f152(x96592),x96596),f332(f181(f846(x96591)),x96594)))))+~P1(f332(f332(f233(a845),f332(f181(f846(x96591)),x96594)),f332(f181(f846(x96592)),x96596)))
% 52.62/52.41 [10020]~P1(f332(f332(f334(f852(x100201,x100202)),f332(f332(f241(x100201,x100202),x100205),x100206)),f332(f332(f103(f853(f852(x100201,x100202),a839)),x100203),x100204)))+P1(f332(f332(f332(f332(f103(f853(x100201,f853(x100202,a839))),f332(f332(f9(x100201,f853(f852(x100201,x100202),a839),f853(x100202,a839)),f332(f332(f10(f853(x100202,f853(f853(f852(x100201,x100202),a839),a839)),f853(f853(f852(x100201,x100202),a839),f853(x100202,a839)),x100201),f9(x100202,f853(f852(x100201,x100202),a839),a839)),f332(f332(f10(f853(x100202,f852(x100201,x100202)),f853(x100202,f853(f853(f852(x100201,x100202),a839),a839)),x100201),f332(f10(f852(x100201,x100202),f853(f853(f852(x100201,x100202),a839),a839),x100202),f334(f852(x100201,x100202)))),f241(x100201,x100202)))),x100203)),f332(f332(f9(x100201,f853(f852(x100201,x100202),a839),f853(x100202,a839)),f332(f332(f10(f853(x100202,f853(f853(f852(x100201,x100202),a839),a839)),f853(f853(f852(x100201,x100202),a839),f853(x100202,a839)),x100201),f9(x100202,f853(f852(x100201,x100202),a839),a839)),f332(f332(f10(f853(x100202,f852(x100201,x100202)),f853(x100202,f853(f853(f852(x100201,x100202),a839),a839)),x100201),f332(f10(f852(x100201,x100202),f853(f853(f852(x100201,x100202),a839),a839),x100202),f334(f852(x100201,x100202)))),f241(x100201,x100202)))),x100204)),x100205),x100206))
% 52.62/52.41 [10021]~P1(f332(f332(f334(f852(x100211,x100212)),f332(f332(f241(x100211,x100212),x100215),x100216)),f332(f332(f104(f853(f852(x100211,x100212),a839)),x100213),x100214)))+P1(f332(f332(f332(f332(f104(f853(x100211,f853(x100212,a839))),f332(f332(f9(x100211,f853(f852(x100211,x100212),a839),f853(x100212,a839)),f332(f332(f10(f853(x100212,f853(f853(f852(x100211,x100212),a839),a839)),f853(f853(f852(x100211,x100212),a839),f853(x100212,a839)),x100211),f9(x100212,f853(f852(x100211,x100212),a839),a839)),f332(f332(f10(f853(x100212,f852(x100211,x100212)),f853(x100212,f853(f853(f852(x100211,x100212),a839),a839)),x100211),f332(f10(f852(x100211,x100212),f853(f853(f852(x100211,x100212),a839),a839),x100212),f334(f852(x100211,x100212)))),f241(x100211,x100212)))),x100213)),f332(f332(f9(x100211,f853(f852(x100211,x100212),a839),f853(x100212,a839)),f332(f332(f10(f853(x100212,f853(f853(f852(x100211,x100212),a839),a839)),f853(f853(f852(x100211,x100212),a839),f853(x100212,a839)),x100211),f9(x100212,f853(f852(x100211,x100212),a839),a839)),f332(f332(f10(f853(x100212,f852(x100211,x100212)),f853(x100212,f853(f853(f852(x100211,x100212),a839),a839)),x100211),f332(f10(f852(x100211,x100212),f853(f853(f852(x100211,x100212),a839),a839),x100212),f334(f852(x100211,x100212)))),f241(x100211,x100212)))),x100214)),x100215),x100216))
% 52.62/52.41 [10025]P1(f332(f332(f334(f852(x100251,x100252)),f332(f332(f241(x100251,x100252),x100253),x100254)),f332(f332(f103(f853(f852(x100251,x100252),a839)),x100255),x100256)))+~P1(f332(f332(f332(f332(f103(f853(x100251,f853(x100252,a839))),f332(f332(f9(x100251,f853(f852(x100251,x100252),a839),f853(x100252,a839)),f332(f332(f10(f853(x100252,f853(f853(f852(x100251,x100252),a839),a839)),f853(f853(f852(x100251,x100252),a839),f853(x100252,a839)),x100251),f9(x100252,f853(f852(x100251,x100252),a839),a839)),f332(f332(f10(f853(x100252,f852(x100251,x100252)),f853(x100252,f853(f853(f852(x100251,x100252),a839),a839)),x100251),f332(f10(f852(x100251,x100252),f853(f853(f852(x100251,x100252),a839),a839),x100252),f334(f852(x100251,x100252)))),f241(x100251,x100252)))),x100255)),f332(f332(f9(x100251,f853(f852(x100251,x100252),a839),f853(x100252,a839)),f332(f332(f10(f853(x100252,f853(f853(f852(x100251,x100252),a839),a839)),f853(f853(f852(x100251,x100252),a839),f853(x100252,a839)),x100251),f9(x100252,f853(f852(x100251,x100252),a839),a839)),f332(f332(f10(f853(x100252,f852(x100251,x100252)),f853(x100252,f853(f853(f852(x100251,x100252),a839),a839)),x100251),f332(f10(f852(x100251,x100252),f853(f853(f852(x100251,x100252),a839),a839),x100252),f334(f852(x100251,x100252)))),f241(x100251,x100252)))),x100256)),x100253),x100254))
% 52.62/52.41 [10026]P1(f332(f332(f334(f852(x100261,x100262)),f332(f332(f241(x100261,x100262),x100263),x100264)),f332(f332(f104(f853(f852(x100261,x100262),a839)),x100265),x100266)))+~P1(f332(f332(f332(f332(f104(f853(x100261,f853(x100262,a839))),f332(f332(f9(x100261,f853(f852(x100261,x100262),a839),f853(x100262,a839)),f332(f332(f10(f853(x100262,f853(f853(f852(x100261,x100262),a839),a839)),f853(f853(f852(x100261,x100262),a839),f853(x100262,a839)),x100261),f9(x100262,f853(f852(x100261,x100262),a839),a839)),f332(f332(f10(f853(x100262,f852(x100261,x100262)),f853(x100262,f853(f853(f852(x100261,x100262),a839),a839)),x100261),f332(f10(f852(x100261,x100262),f853(f853(f852(x100261,x100262),a839),a839),x100262),f334(f852(x100261,x100262)))),f241(x100261,x100262)))),x100265)),f332(f332(f9(x100261,f853(f852(x100261,x100262),a839),f853(x100262,a839)),f332(f332(f10(f853(x100262,f853(f853(f852(x100261,x100262),a839),a839)),f853(f853(f852(x100261,x100262),a839),f853(x100262,a839)),x100261),f9(x100262,f853(f852(x100261,x100262),a839),a839)),f332(f332(f10(f853(x100262,f852(x100261,x100262)),f853(x100262,f853(f853(f852(x100261,x100262),a839),a839)),x100261),f332(f10(f852(x100261,x100262),f853(f853(f852(x100261,x100262),a839),a839),x100262),f334(f852(x100261,x100262)))),f241(x100261,x100262)))),x100266)),x100263),x100264))
% 52.62/52.41 [10014]~P1(f332(f332(f334(f852(x100142,x100143)),f332(f332(f241(x100142,x100143),x100145),x100146)),f332(f332(f47(x100141,f853(f852(x100142,x100143),a839)),f239(f853(x100141,a839))),x100144)))+P1(f332(f332(f332(f332(f47(x100141,f853(x100142,f853(x100143,a839))),f239(f853(x100141,a839))),f332(f332(f10(f853(f852(x100142,x100143),a839),f853(x100142,f853(x100143,a839)),x100141),f332(f9(x100142,f853(f852(x100142,x100143),a839),f853(x100143,a839)),f332(f332(f10(f853(x100143,f853(f853(f852(x100142,x100143),a839),a839)),f853(f853(f852(x100142,x100143),a839),f853(x100143,a839)),x100142),f9(x100143,f853(f852(x100142,x100143),a839),a839)),f332(f332(f10(f853(x100143,f852(x100142,x100143)),f853(x100143,f853(f853(f852(x100142,x100143),a839),a839)),x100142),f332(f10(f852(x100142,x100143),f853(f853(f852(x100142,x100143),a839),a839),x100143),f334(f852(x100142,x100143)))),f241(x100142,x100143))))),x100144)),x100145),x100146))
% 52.62/52.41 [10015]~P1(f332(f332(f334(f852(x100152,x100153)),f332(f332(f241(x100152,x100153),x100155),x100156)),f332(f332(f48(x100151,f853(f852(x100152,x100153),a839)),f239(f853(x100151,a839))),x100154)))+P1(f332(f332(f332(f332(f48(x100151,f853(x100152,f853(x100153,a839))),f239(f853(x100151,a839))),f332(f332(f10(f853(f852(x100152,x100153),a839),f853(x100152,f853(x100153,a839)),x100151),f332(f9(x100152,f853(f852(x100152,x100153),a839),f853(x100153,a839)),f332(f332(f10(f853(x100153,f853(f853(f852(x100152,x100153),a839),a839)),f853(f853(f852(x100152,x100153),a839),f853(x100153,a839)),x100152),f9(x100153,f853(f852(x100152,x100153),a839),a839)),f332(f332(f10(f853(x100153,f852(x100152,x100153)),f853(x100153,f853(f853(f852(x100152,x100153),a839),a839)),x100152),f332(f10(f852(x100152,x100153),f853(f853(f852(x100152,x100153),a839),a839),x100153),f334(f852(x100152,x100153)))),f241(x100152,x100153))))),x100154)),x100155),x100156))
% 52.62/52.41 [10023]P1(f332(f332(f334(f852(x100231,x100232)),f332(f332(f241(x100231,x100232),x100233),x100234)),f332(f332(f47(x100235,f853(f852(x100231,x100232),a839)),f239(f853(x100235,a839))),x100236)))+~P1(f332(f332(f332(f332(f47(x100235,f853(x100231,f853(x100232,a839))),f239(f853(x100235,a839))),f332(f332(f10(f853(f852(x100231,x100232),a839),f853(x100231,f853(x100232,a839)),x100235),f332(f9(x100231,f853(f852(x100231,x100232),a839),f853(x100232,a839)),f332(f332(f10(f853(x100232,f853(f853(f852(x100231,x100232),a839),a839)),f853(f853(f852(x100231,x100232),a839),f853(x100232,a839)),x100231),f9(x100232,f853(f852(x100231,x100232),a839),a839)),f332(f332(f10(f853(x100232,f852(x100231,x100232)),f853(x100232,f853(f853(f852(x100231,x100232),a839),a839)),x100231),f332(f10(f852(x100231,x100232),f853(f853(f852(x100231,x100232),a839),a839),x100232),f334(f852(x100231,x100232)))),f241(x100231,x100232))))),x100236)),x100233),x100234))
% 52.62/52.41 [10024]P1(f332(f332(f334(f852(x100241,x100242)),f332(f332(f241(x100241,x100242),x100243),x100244)),f332(f332(f48(x100245,f853(f852(x100241,x100242),a839)),f239(f853(x100245,a839))),x100246)))+~P1(f332(f332(f332(f332(f48(x100245,f853(x100241,f853(x100242,a839))),f239(f853(x100245,a839))),f332(f332(f10(f853(f852(x100241,x100242),a839),f853(x100241,f853(x100242,a839)),x100245),f332(f9(x100241,f853(f852(x100241,x100242),a839),f853(x100242,a839)),f332(f332(f10(f853(x100242,f853(f853(f852(x100241,x100242),a839),a839)),f853(f853(f852(x100241,x100242),a839),f853(x100242,a839)),x100241),f9(x100242,f853(f852(x100241,x100242),a839),a839)),f332(f332(f10(f853(x100242,f852(x100241,x100242)),f853(x100242,f853(f853(f852(x100241,x100242),a839),a839)),x100241),f332(f10(f852(x100241,x100242),f853(f853(f852(x100241,x100242),a839),a839),x100242),f334(f852(x100241,x100242)))),f241(x100241,x100242))))),x100246)),x100243),x100244))
% 52.62/52.41 [9121]E(x91211,x91212)+~E(f319(x91213,x91214,x91215,x91216,x91211),f319(x91213,x91214,x91215,x91217,x91212))
% 52.62/52.41 [9122]E(x91221,x91222)+~E(f319(x91223,x91224,x91225,x91221,x91226),f319(x91223,x91224,x91225,x91222,x91227))
% 52.62/52.41 [7364]E(f332(x73641,f332(x73642,x73643)),f332(x73644,x73643))+~E(f332(f75(x73645,x73646,x73647,x73641),x73642),x73644)
% 52.62/52.41 [9486]~P28(x94863,x94864,x94861,x94865,x94866,x94867)+E(f332(f332(x94861,x94862),x94862),x94862)
% 52.62/52.41 [9813]~P53(x98135,x98136,x98137,x98131,x98134,x98132,x98133)+P1(f332(f332(x98131,x98132),f587(x98133,x98132,x98134,x98131)))
% 52.62/52.41 [9838]~E(f332(f229(f849(x98387),x98381,f183(x98387),x98385),f332(x98384,x98383)),f332(f227(x98387),x98382))+E(f332(f227(x98381),f712(x98382,x98383,x98384,x98385,x98386,x98387,x98381)),f332(x98384,x98383))
% 52.62/52.41 [9839]~E(f332(f229(f849(x98396),x98397,f183(x98396),x98391),f332(x98394,x98393)),f332(f227(x98396),x98392))+E(f332(x98391,f712(x98392,x98393,x98394,x98391,x98395,x98396,x98397)),f332(f227(x98396),x98392))
% 52.62/52.41 [5871]~E(f332(f332(f143(x58711,x58715),x58716),x58712),f332(f332(f143(x58713,x58715),x58717),x58714))+E(f332(f181(f846(x58711)),x58712),f332(f181(f846(x58713)),x58714))
% 52.62/52.41 [7440]E(x74401,x74402)+~E(f332(f332(f332(f74(x74403,f849(x74404)),x74405),x74406),f332(f227(x74404),x74401)),f332(f332(f332(f74(x74403,f849(x74404)),x74407),x74406),f332(f227(x74404),x74402)))
% 52.62/52.41 [8401]E(f332(x84011,f332(x84012,x84013)),f332(x84014,x84013))+~E(f332(f75(x84015,x84016,x84017,x84011),x84012),f332(f75(x84016,x84016,x84017,f39(x84016)),x84014))
% 52.62/52.41 [9818]~P53(x98185,x98186,x98187,x98184,x98181,x98183,x98182)+P1(f332(f332(x98181,f587(x98182,x98183,x98181,x98184)),x98182))
% 52.62/52.41 [5918]E(x59181,x59182)+~E(f332(f332(f332(f93(x59183),x59184),x59185),x59181),f332(f332(f332(f93(x59183),x59186),x59187),x59182))
% 52.62/52.41 [5919]E(x59191,x59192)+~E(f332(f332(f332(f93(x59193),x59194),x59191),x59195),f332(f332(f332(f93(x59193),x59196),x59192),x59197))
% 52.62/52.41 [5920]E(x59201,x59202)+~E(f332(f332(f332(f93(x59203),x59201),x59204),x59205),f332(f332(f332(f93(x59203),x59202),x59206),x59207))
% 52.62/52.41 [8814]~P26(x88146,x88141,x88143,x88147)+E(f332(f75(x88141,x88141,x88142,f332(x88143,x88144)),f332(f75(x88141,x88141,x88142,f332(x88143,x88144)),x88145)),f332(f75(x88141,x88141,x88142,f332(x88143,x88144)),x88145))
% 52.62/52.41 [8813]~P1(f332(f332(f334(x88131),x88132),f332(f332(x88135,x88136),x88137)))+P1(f332(f332(f334(x88131),x88132),f332(f332(f251(x88133,x88134,f853(x88131,a839)),x88135),f332(f332(f241(x88133,x88134),x88136),x88137))))
% 52.62/52.41 [9080]P1(f332(f332(f332(x90801,x90802),x90803),x90804))+~P1(f332(f332(f332(f251(x90805,x90806,f853(x90807,a839)),x90801),f332(f332(f241(x90805,x90806),x90802),x90803)),x90804))
% 52.62/52.41 [9200]P1(f332(f332(f334(x92001),f332(f332(x92002,x92003),x92004)),f332(f303(f852(x92005,x92006),x92001,f332(f251(x92005,x92006,x92001),x92002)),x92007)))+~P1(f332(f332(f334(f852(x92005,x92006)),f332(f332(f241(x92005,x92006),x92003),x92004)),x92007))
% 52.62/52.41 [9525]P1(f332(f332(f334(f852(f846(x95251),f846(x95251))),f332(f332(f241(f846(x95251),f846(x95251)),f332(f332(f125(x95251),x95252),f332(f332(f140(x95251),x95253),x95254))),f332(f332(f125(x95251),x95252),f332(f332(f140(x95251),x95255),x95256)))),f137(x95251,x95257)))+~P1(f332(f332(f334(f852(x95251,x95251)),f332(f332(f241(x95251,x95251),x95253),x95255)),x95257))
% 52.62/52.41 [9943]P53(x99431,x99432,x99433,f332(f332(f9(x99431,f853(f852(x99431,x99432),a839),f853(x99432,a839)),f332(f332(f10(f853(x99432,f853(f853(f852(x99431,x99432),a839),a839)),f853(f853(f852(x99431,x99432),a839),f853(x99432,a839)),x99431),f9(x99432,f853(f852(x99431,x99432),a839),a839)),f332(f332(f10(f853(x99432,f852(x99431,x99432)),f853(x99432,f853(f853(f852(x99431,x99432),a839),a839)),x99431),f332(f10(f852(x99431,x99432),f853(f853(f852(x99431,x99432),a839),a839),x99432),f334(f852(x99431,x99432)))),f241(x99431,x99432)))),x99434),f332(f332(f9(x99432,f853(f852(x99432,x99433),a839),f853(x99433,a839)),f332(f332(f10(f853(x99433,f853(f853(f852(x99432,x99433),a839),a839)),f853(f853(f852(x99432,x99433),a839),f853(x99433,a839)),x99432),f9(x99433,f853(f852(x99432,x99433),a839),a839)),f332(f332(f10(f853(x99433,f852(x99432,x99433)),f853(x99433,f853(f853(f852(x99432,x99433),a839),a839)),x99432),f332(f10(f852(x99432,x99433),f853(f853(f852(x99432,x99433),a839),a839),x99433),f334(f852(x99432,x99433)))),f241(x99432,x99433)))),x99435),x99436,x99437)+~P1(f332(f332(f334(f852(x99431,x99433)),f332(f332(f241(x99431,x99433),x99436),x99437)),f332(f332(f281(x99431,x99432,x99433),x99434),x99435)))
% 52.62/52.41 [9972]~P53(x99721,x99725,x99722,f332(f332(f9(x99721,f853(f852(x99721,x99725),a839),f853(x99725,a839)),f332(f332(f10(f853(x99725,f853(f853(f852(x99721,x99725),a839),a839)),f853(f853(f852(x99721,x99725),a839),f853(x99725,a839)),x99721),f9(x99725,f853(f852(x99721,x99725),a839),a839)),f332(f332(f10(f853(x99725,f852(x99721,x99725)),f853(x99725,f853(f853(f852(x99721,x99725),a839),a839)),x99721),f332(f10(f852(x99721,x99725),f853(f853(f852(x99721,x99725),a839),a839),x99725),f334(f852(x99721,x99725)))),f241(x99721,x99725)))),x99726),f332(f332(f9(x99725,f853(f852(x99725,x99722),a839),f853(x99722,a839)),f332(f332(f10(f853(x99722,f853(f853(f852(x99725,x99722),a839),a839)),f853(f853(f852(x99725,x99722),a839),f853(x99722,a839)),x99725),f9(x99722,f853(f852(x99725,x99722),a839),a839)),f332(f332(f10(f853(x99722,f852(x99725,x99722)),f853(x99722,f853(f853(f852(x99725,x99722),a839),a839)),x99725),f332(f10(f852(x99725,x99722),f853(f853(f852(x99725,x99722),a839),a839),x99722),f334(f852(x99725,x99722)))),f241(x99725,x99722)))),x99727),x99723,x99724)+P1(f332(f332(f334(f852(x99721,x99722)),f332(f332(f241(x99721,x99722),x99723),x99724)),f332(f332(f281(x99721,x99725,x99722),x99726),x99727)))
% 52.62/52.41 [9589]P1(f332(f332(f334(x95891),x95894),f332(f158(x95891),x95896)))+E(f170(x95891,x95892,f332(f332(f332(f74(x95891,f849(x95892)),x95893),x95894),f332(f227(x95892),x95895)),f166(x95891,x95892,f332(f142(f852(x95891,x95892)),f332(f332(f167(x95891,x95892),x95896),x95897)))),f332(f332(f332(f74(x95891,f849(x95892)),f170(x95891,x95892,x95893,f166(x95891,x95892,f332(f142(f852(x95891,x95892)),f332(f332(f167(x95891,x95892),x95896),x95897))))),x95894),f332(f227(x95892),x95895)))
% 52.62/52.41 [9075]E(x90751,x90752)+E(f332(f332(f332(f74(x90753,x90754),f332(f332(f332(f74(x90753,x90754),x90755),x90751),x90756)),x90752),x90757),f332(f332(f332(f74(x90753,x90754),f332(f332(f332(f74(x90753,x90754),x90755),x90752),x90757)),x90751),x90756))
% 52.62/52.41 [9327]E(f170(x93271,x93272,f332(f332(f332(f74(x93271,f849(x93272)),x93273),x93274),f332(f227(x93272),x93275)),f166(x93271,x93272,f332(f142(f852(x93271,x93272)),f332(f332(f167(x93271,x93272),x93276),x93277)))),f170(x93271,x93272,x93273,f166(x93271,x93272,f332(f142(f852(x93271,x93272)),f332(f332(f167(x93271,x93272),x93276),x93277)))))+~P1(f332(f332(f334(x93271),x93274),f332(f158(x93271),f332(f332(f159(x93271),f332(f181(f846(x93272)),x93277)),x93276))))
% 52.62/52.41 [9607]E(f170(x96071,x96072,f332(f332(f332(f74(x96071,f849(x96072)),x96073),x96074),f332(f227(x96072),x96075)),f166(x96071,x96072,f332(f142(f852(x96071,x96072)),f332(f332(f167(x96071,x96072),x96076),x96077)))),f332(f332(f332(f74(x96071,f849(x96072)),f170(x96071,x96072,x96073,f166(x96071,x96072,f332(f142(f852(x96071,x96072)),f332(f332(f167(x96071,x96072),x96076),x96077))))),x96074),f332(f227(x96072),x96075)))+P1(f332(f332(f334(x96071),x96074),f332(f158(x96071),f332(f332(f159(x96071),f332(f181(f846(x96072)),x96077)),x96076))))
% 52.62/52.41 [9954]P1(f332(f332(f334(x99541),f668(x99542,x99543,x99544,x99545,x99546,x99547,x99541)),x99545))+P1(f332(f332(f332(f332(f48(x99541,f853(x99547,f853(x99546,a839))),x99545),x99544),x99543),x99542))
% 52.62/52.41 [9955]P1(f332(f332(f334(x99551),f409(x99552,x99553,x99554,x99555,x99556,x99557,x99551)),x99555))+~P1(f332(f332(f332(f332(f47(x99551,f853(x99557,f853(x99556,a839))),x99555),x99554),x99553),x99552))
% 52.62/52.41 [9982]P1(f332(f332(f332(x99821,f409(x99822,x99823,x99821,x99824,x99825,x99826,x99827)),x99823),x99822))+~P1(f332(f332(f332(f332(f47(x99827,f853(x99826,f853(x99825,a839))),x99824),x99821),x99823),x99822))
% 52.62/52.41 [9999]~P1(f332(f332(f332(x99995,f668(x99997,x99996,x99995,x99994,x99993,x99992,x99991)),x99996),x99997))+P1(f332(f332(f332(f332(f48(x99991,f853(x99992,f853(x99993,a839))),x99994),x99995),x99996),x99997))
% 52.62/52.41 [9964]~P136(x99642)+E(f332(f332(f8(x99641,x99642),f332(f332(f9(x99641,f853(x99643,a839),x99642),f332(f332(f10(f853(x99643,x99642),f853(f853(x99643,a839),x99642),x99641),f8(x99643,x99642)),f332(f332(f9(x99641,f853(x99643,x99642),f853(x99643,x99642)),f332(f332(f10(f853(x99642,x99642),f853(f853(x99643,x99642),f853(x99643,x99642)),x99641),f10(x99642,x99642,x99643)),f332(f332(f10(x99642,f853(x99642,x99642),x99641),f83(x99642)),x99644))),x99645))),x99646)),x99647),f332(f332(f83(x99642),f332(f332(f8(x99641,x99642),x99644),x99647)),f332(f332(f8(x99643,x99642),x99645),x99646)))
% 52.62/52.41 [9112]~P25(x91127,x91121,x91123,x91128)+E(f332(f75(x91121,x91121,x91122,f332(x91123,x91124)),f332(f75(x91121,x91121,x91122,f332(x91123,x91125)),x91126)),f332(f75(x91121,x91121,x91122,f332(x91123,x91125)),f332(f75(x91121,x91121,x91122,f332(x91123,x91124)),x91126)))
% 52.62/52.41 [10018]E(f332(f332(f241(x100181,x100182),f332(x100183,f573(x100184,x100185,x100183,x100186,x100187,x100188,x100182,x100181))),f332(x100185,f574(x100184,x100185,x100183,x100186,x100187,x100188,x100182,x100181))),x100188)+~P1(f332(f332(f334(f852(x100181,x100182)),x100188),f332(f303(f852(x100187,x100186),f852(x100181,x100182),f252(x100187,x100181,x100186,x100182,x100183,x100185)),x100184)))
% 52.62/52.41 [10030]~P1(f332(f332(f334(f852(x100308,x100307)),x100306),f332(f303(f852(x100301,x100302),f852(x100308,x100307),f252(x100301,x100308,x100302,x100307,x100305,x100304)),x100303)))+P1(f332(f332(f334(f852(x100301,x100302)),f332(f332(f241(x100301,x100302),f573(x100303,x100304,x100305,x100302,x100301,x100306,x100307,x100308)),f574(x100303,x100304,x100305,x100302,x100301,x100306,x100307,x100308))),x100303))
% 52.62/52.41 [9515]P1(f332(f332(f334(f852(f852(x95151,x95152),f852(x95151,x95152))),f332(f332(f241(f852(x95151,x95152),f852(x95151,x95152)),f332(f332(f241(x95151,x95152),x95153),x95154)),f332(f332(f241(x95151,x95152),x95155),x95156))),f326(x95151,x95152,x95157,x95158)))+~P1(f332(f332(f334(f852(x95151,x95151)),f332(f332(f241(x95151,x95151),x95153),x95155)),x95157))
% 52.62/52.41 [8406]E(f332(x84061,f332(x84062,x84063)),f332(x84064,f332(x84065,x84063)))+~E(f332(f75(x84066,x84067,x84068,x84061),x84062),f332(f75(x84069,x84067,x84068,x84064),x84065))
% 52.62/52.41 [8407]E(f332(x84071,f332(x84072,x84073)),f332(x84074,f332(x84075,x84073)))+~E(f332(f75(x84076,x84077,x84078,x84071),x84072),f332(f75(x84079,x84077,x84078,x84074),x84075))
% 52.62/52.41 [9889]P1(f332(f332(f334(f852(x98891,x98892)),f332(f332(f241(x98891,x98892),f332(x98893,x98894)),f332(x98895,x98896))),f332(f303(f852(x98897,x98898),f852(x98891,x98892),f252(x98897,x98891,x98898,x98892,x98893,x98895)),x98899)))+~P1(f332(f332(f334(f852(x98897,x98898)),f332(f332(f241(x98897,x98898),x98894),x98896)),x98899))
% 52.62/52.41 [8666]~E(f332(x86664,f332(x86665,x86666)),f332(x86669,f332(x866610,x866611)))+E(f332(f332(f75(x86661,x86662,x86663,x86664),x86665),x86666),f332(f332(f75(x86667,x86662,x86668,x86669),x866610),x866611))
% 52.62/52.41 [9173]~P25(x91738,x91739,x917310,x917311)+E(f332(f75(x91731,x91732,x91733,x91734),f332(f75(x91735,x91731,x91733,x91736),x91737)),f332(f75(x91735,x91732,x91733,f332(f75(x91731,x91732,x91735,x91734),x91736)),x91737))
% 52.62/52.41 [4494]~P100(x44941)+~P92(x44941)+E(f179(x44941),f103(x44941))
% 52.62/52.41 [4495]~P100(x44951)+~P98(x44951)+E(f236(x44951),f104(x44951))
% 52.62/52.41 [4727]~P110(x47271)+~P88(x47271)+E(f332(f77(x47271),f332(f106(x47271),a99)),f80(x47271))
% 52.62/52.41 [5002]E(x50021,f2(a1))+E(f84(a1,x50021),f332(f81(a1),f80(a1)))+P1(f332(f332(f233(a1),f2(a1)),x50021))
% 52.62/52.41 [5205]E(x52051,f2(a1))+E(f84(a1,x52051),f80(a1))+~P1(f332(f332(f233(a1),f2(a1)),x52051))
% 52.62/52.41 [6526]~P40(x65261)+~P1(f332(f64(a1),x65261))+P1(f332(f64(a845),f332(f303(a1,a845,a107),x65261)))
% 52.62/52.41 [6904]E(f55(f80(a1),f332(f106(a1),x69041)),f332(f332(f241(a1,a1),f2(a1)),f80(a1)))+~P1(f332(f332(f233(a1),f2(a1)),f332(f106(a1),x69041)))+~P1(f332(f332(f233(a1),f80(a1)),f332(f106(a1),x69041)))
% 52.62/52.41 [7251]~P40(x72511)+P1(f332(f64(a1),x72511))+~P1(f332(f64(a845),f332(f303(a1,a845,a107),x72511)))
% 52.62/52.41 [8105]E(f332(f332(f241(a1,a1),f332(f106(a1),a99)),f332(f332(f82(a1),f80(a1)),f332(f106(a1),x81051))),f58(f80(a1),f332(f106(a1),x81051)))+~P1(f332(f332(f233(a1),f2(a1)),f332(f106(a1),x81051)))+~P1(f332(f332(f232(a1),f2(a1)),f332(f332(f82(a1),f80(a1)),f332(f106(a1),x81051))))
% 52.62/52.41 [8513]~P15(a500)+~P1(f332(f332(f334(f852(a841,a840)),x85131),f332(f158(f852(a841,a840)),a29)))+P1(f332(f332(f251(a841,a840,a839),f332(f18(f853(a840,a839),a841),a26)),x85131))
% 52.62/52.41 [9776]E(f332(f51(f332(f106(a1),x97761)),f55(f80(a1),f332(f332(f83(a1),f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f332(f106(a1),x97761)))),f55(f80(a1),f332(f106(a1),x97761)))+~P1(f332(f332(f233(a1),f2(a1)),f332(f106(a1),x97761)))+P1(f332(f332(f233(a1),f80(a1)),f332(f106(a1),x97761)))
% 52.62/52.41 [9782]E(f332(f51(f332(f106(a1),x97821)),f58(f80(a1),f332(f332(f83(a1),f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f332(f106(a1),x97821)))),f58(f80(a1),f332(f106(a1),x97821)))+~P1(f332(f332(f233(a1),f2(a1)),f332(f106(a1),x97821)))+P1(f332(f332(f232(a1),f2(a1)),f332(f332(f82(a1),f80(a1)),f332(f106(a1),x97821))))
% 52.62/52.41 [9485]E(x94851,f180(f853(f852(a845,a845),a839)))+~P1(f332(f64(f852(a845,a845)),x94851))+P1(f332(f332(f334(f852(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839))),f332(f332(f241(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839)),f180(f853(f852(a845,a845),a839))),x94851)),a42))
% 52.62/52.41 [9632]E(x96321,f2(a845))+E(x96321,f332(a114,f2(a845)))+~P1(f332(f332(f233(a845),x96321),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))))
% 52.62/52.41 [9915]E(x99151,f2(a101))+E(f332(f332(f82(a1),f332(f332(f83(a1),f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f332(a23,f332(f332(f44(a101),x99151),f332(f106(a101),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))))),f80(a1)),f332(a23,x99151))+E(f53(a101,x99151,f332(f106(a101),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f2(a101))
% 52.62/52.41 [9762]E(x97621,f2(a101))+~E(f53(a101,x97621,f332(f106(a101),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f2(a101))+E(f332(f332(f83(a1),f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f332(a23,f332(f332(f44(a101),x97621),f332(f106(a101),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))))),f332(a23,x97621))
% 52.62/52.41 [4565]~P58(x45651,x45652)+P44(x45651,x45652)+~P45(a839)
% 52.62/52.41 [4505]~P2(x45051)+P35(x45051,x45052)+~E(x45052,f2(x45051))
% 52.62/52.41 [4514]~P110(x45141)+~E(x45142,f2(x45141))+E(f84(x45141,x45142),f2(x45141))
% 52.62/52.41 [4515]~P83(x45151)+~E(x45152,f2(x45151))+E(f84(x45151,x45152),f2(x45151))
% 52.62/52.41 [4521]~P2(x45212)+~P35(x45212,x45211)+E(x45211,f2(x45212))
% 52.62/52.41 [4555]~P110(x45552)+~E(f84(x45552,x45551),f2(x45552))+E(x45551,f2(x45552))
% 52.62/52.41 [4572]~P12(x45722)+~P12(x45721)+P12(f188(x45721,x45722))
% 52.62/52.41 [4573]~P61(x45732)+~P61(x45731)+P61(f854(x45731,x45732))
% 52.62/52.41 [4574]~P61(x45742)+~P61(x45741)+P61(f853(x45741,x45742))
% 52.62/52.41 [4575]~P61(x45752)+~P61(x45751)+P61(f852(x45751,x45752))
% 52.62/52.41 [4576]~P139(x45762)+~P139(x45761)+P139(f852(x45761,x45762))
% 52.62/52.41 [4930]~P12(x49302)+~P12(x49301)+P12(f53(a1,x49301,x49302))
% 52.62/52.41 [4522]~P68(x45221)+~E(x45222,f2(x45221))+E(f332(f81(x45221),x45222),x45222)
% 52.62/52.41 [4523]~P68(x45231)+~E(x45232,f2(x45231))+E(f332(f81(x45231),x45232),x45232)
% 52.62/52.41 [4526]~P87(x45261)+~E(x45262,f2(a1))+E(f332(f105(x45261),x45262),f2(x45261))
% 52.62/52.41 [4527]~P87(x45271)+~E(x45272,f2(a1))+E(f332(f105(x45271),x45272),f2(x45271))
% 52.62/52.41 [4528]~P133(x45281)+~E(x45282,f2(a1))+E(f332(f105(x45281),x45282),f2(x45281))
% 52.62/52.41 [4552]~P69(x45521)+~E(f2(x45521),x45522)+E(f332(f81(x45521),x45522),f2(x45521))
% 52.62/52.41 [4553]~P69(x45531)+~E(x45532,f2(x45531))+E(f332(f81(x45531),x45532),f2(x45531))
% 52.62/52.41 [4554]~P80(x45541)+~E(x45542,f2(x45541))+E(f332(f77(x45541),x45542),f2(x45541))
% 52.62/52.41 [4577]~P68(x45772)+E(x45771,f2(x45772))+~E(f332(f81(x45772),x45771),x45771)
% 52.62/52.41 [4578]~P68(x45782)+E(x45781,f2(x45782))+~E(f332(f81(x45782),x45781),x45781)
% 52.62/52.41 [4586]E(x45861,f332(a107,x45862))+~E(x45861,f2(a845))+~E(x45862,f332(f102(a1),x45861))
% 52.62/52.41 [4587]E(f332(a107,x45871),x45872)+~E(x45872,f2(a845))+~E(x45871,f332(f102(a1),x45872))
% 52.62/52.41 [4590]~P87(x45902)+E(x45901,f2(a1))+~E(f332(f105(x45902),x45901),f2(x45902))
% 52.62/52.41 [4591]~P87(x45912)+E(x45911,f2(a1))+~E(f332(f105(x45912),x45911),f2(x45912))
% 52.62/52.41 [4596]~P69(x45962)+E(x45961,f2(x45962))+~E(f332(f81(x45962),x45961),f2(x45962))
% 52.62/52.41 [4597]~P80(x45972)+E(x45971,f2(x45972))+~E(f332(f77(x45972),x45971),f2(x45972))
% 52.62/52.41 [4598]~P69(x45981)+E(f2(x45981),x45982)+~E(f332(f81(x45981),x45982),f2(x45981))
% 52.62/52.41 [4731]~P15(a500)+~E(f332(a30,x47312),f332(f227(a840),x47311))+P1(f332(a26,x47311))
% 52.62/52.41 [4770]~P100(x47701)+~P20(x47701,x47702)+P20(x47701,f332(f157(x47701),x47702))
% 52.62/52.41 [4796]~P1(x47962)+~P1(x47961)+P1(f332(f332(a330,x47961),x47962))
% 52.62/52.41 [4830]~E(f80(a845),f2(a845))+E(f332(f43(x48301),x48302),f2(a845))+~P1(f332(f64(x48301),x48302))
% 52.62/52.41 [4861]~P105(x48611)+~P136(x48611)+E(f332(f332(f242(x48611),f2(x48611)),f332(a114,x48612)),f2(x48611))
% 52.62/52.41 [4901]~P100(x49011)+P20(x49011,f130(x49011,x49012))+~P1(f332(f64(x49011),x49012))
% 52.62/52.41 [4921]~P100(x49211)+E(f332(f158(x49211),f130(x49211,x49212)),x49212)+~P1(f332(f64(x49211),x49212))
% 52.62/52.41 [4955]P1(x49551)+P1(x49552)+~P1(f332(f332(a331,x49552),x49551))
% 52.62/52.41 [4967]E(x49671,f180(f853(x49672,a839)))+~E(f332(f43(x49672),x49671),f2(a845))+~P1(f332(f64(x49672),x49671))
% 52.62/52.41 [4972]P1(x49721)+~P1(x49722)+~P1(f332(f332(a335,x49722),x49721))
% 52.62/52.41 [5020]~P67(x50201)+E(f332(f77(x50201),x50202),x50202)+P1(f332(f332(f233(x50201),x50202),f2(x50201)))
% 52.62/52.41 [5116]~P1(f332(a26,x51162))+~P1(f332(a26,x51161))+P1(f332(a26,f36(x51161,x51162)))
% 52.62/52.41 [5117]~P1(f332(a26,x51172))+~P1(f332(a26,x51171))+P1(f332(a26,f36(x51171,x51172)))
% 52.62/52.41 [5124]E(x51241,f115(x51242))+P1(f332(f127(x51242),f116(x51242,x51241)))+~P1(f332(f127(x51242),x51241))
% 52.62/52.41 [5129]~P100(x51291)+~P1(f332(f64(x51291),x51292))+P1(f332(f127(x51291),f130(x51291,x51292)))
% 52.62/52.41 [5134]P1(f332(x51341,x51342))+P1(f332(x51341,f514(x51342,x51341)))+~P1(f332(x51341,f2(a845)))
% 52.62/52.41 [5136]~P133(x51361)+E(f332(f102(x51361),f332(a107,x51362)),f332(f105(x51361),x51362))+P1(f332(f332(f233(a1),x51362),f2(a1)))
% 52.62/52.41 [5162]P13(x51622,x51621)+E(f332(x51621,f515(x51621)),f332(x51621,f520(x51621)))+P1(f332(f332(x51621,f515(x51621)),f520(x51621)))
% 52.62/52.41 [5175]E(f332(f102(a1),f616(x51751,x51752)),x51751)+P1(f332(x51752,f332(a107,x51751)))+~P1(f332(x51752,f2(a845)))
% 52.62/52.41 [5215]~P110(x52151)+~E(f84(x52151,x52152),f332(f81(x52151),f80(x52151)))+P1(f332(f332(f233(x52151),x52152),f2(x52151)))
% 52.62/52.41 [5288]~E(x52882,f2(a1))+E(f210(x52881,x52882),f332(f332(f241(a1,a1),f2(a1)),f80(a1)))+P1(f332(f332(f233(a1),x52882),f2(a1)))
% 52.62/52.41 [5289]~E(x52891,f2(a1))+E(f210(x52891,x52892),f332(f332(f241(a1,a1),f2(a1)),f80(a1)))+P1(f332(f332(f233(a1),x52892),f2(a1)))
% 52.62/52.41 [5340]E(f332(f102(a1),f616(x53401,x53402)),x53401)+P1(f332(x53402,f332(a107,x53401)))+P1(f332(f332(f233(a1),x53401),f2(a1)))
% 52.62/52.41 [5405]~P110(x54051)+E(f84(x54051,x54052),f332(f81(x54051),f80(x54051)))+~P1(f332(f332(f233(x54051),x54052),f2(x54051)))
% 52.62/52.41 [5406]~P110(x54061)+E(f84(x54061,x54062),f332(f81(x54061),f80(x54061)))+~P1(f332(f332(f233(x54061),x54062),f2(x54061)))
% 52.62/52.41 [5407]~P80(x54071)+E(f332(f77(x54071),x54072),f332(f81(x54071),x54072))+~P1(f332(f332(f233(x54071),x54072),f2(x54071)))
% 52.62/52.41 [5408]~P80(x54081)+E(f332(f77(x54081),x54082),f332(f81(x54081),x54082))+~P1(f332(f332(f232(x54081),x54082),f2(x54081)))
% 52.62/52.41 [5409]~P67(x54091)+E(f332(f77(x54091),x54092),f332(f81(x54091),x54092))+~P1(f332(f332(f233(x54091),x54092),f2(x54091)))
% 52.62/52.41 [5501]~P1(f332(x55011,f616(x55012,x55011)))+P1(f332(x55011,f332(a107,x55012)))+~P1(f332(x55011,f2(a845)))
% 52.62/52.41 [5508]E(x55081,f2(a845))+E(f332(a114,f526(x55082,x55081)),x55081)+~P1(f332(f332(f233(a845),x55081),f332(a114,x55082)))
% 52.62/52.41 [5511]P13(x55111,x55112)+~E(f332(x55112,f515(x55112)),f332(x55112,f520(x55112)))+~P1(f332(f332(x55112,f515(x55112)),f520(x55112)))
% 52.62/52.41 [5530]~P100(x55301)+P20(x55301,x55302)+P1(f332(f332(f232(a845),f760(x55302,x55301)),f761(x55302,x55301)))
% 52.62/52.41 [5616]~P80(x56161)+~E(x56162,f2(x56161))+P1(f332(f332(f232(x56161),f332(f77(x56161),x56162)),f2(x56161)))
% 52.62/52.41 [5705]~P1(f332(x57051,f616(x57052,x57051)))+P1(f332(x57051,f332(a107,x57052)))+P1(f332(f332(f233(a1),x57052),f2(a1)))
% 52.62/52.41 [5731]~P1(f332(x57311,f332(a107,x57312)))+P1(f332(x57311,f2(a845)))+~P1(f332(f332(f233(a1),x57312),f2(a1)))
% 52.62/52.41 [6076]~P110(x60761)+~P1(f332(f332(f233(x60761),x60762),f2(x60761)))+P1(f332(f332(f233(x60761),f84(x60761,x60762)),f2(x60761)))
% 52.62/52.41 [6195]~P110(x61951)+P1(f332(f332(f233(x61951),f332(f105(x61951),x61952)),f2(x61951)))+~P1(f332(f332(f233(a1),x61952),f2(a1)))
% 52.62/52.41 [6196]~P110(x61961)+P1(f332(f332(f232(x61961),f332(f105(x61961),x61962)),f2(x61961)))+~P1(f332(f332(f232(a1),x61962),f2(a1)))
% 52.62/52.41 [6201]~P80(x62012)+E(x62011,f2(x62012))+~P1(f332(f332(f232(x62012),f332(f77(x62012),x62011)),f2(x62012)))
% 52.62/52.41 [6286]~P133(x62861)+~P1(f332(f332(f334(x62861),x62862),f112(x62861)))+P1(f332(f332(f334(x62861),f332(f81(x62861),x62862)),f112(x62861)))
% 52.62/52.41 [6318]~P110(x63181)+~P1(f332(f332(f233(x63181),f84(x63181,x63182)),f2(x63181)))+P1(f332(f332(f233(x63181),x63182),f2(x63181)))
% 52.62/52.41 [6399]~P99(x63991)+P52(a845,x63991,f279(a845),x63992)+P1(f332(f332(f279(a845),f383(x63992,x63991)),f385(x63992,x63991)))
% 52.62/52.41 [6497]~P110(x64972)+~P1(f332(f332(f233(x64972),f332(f105(x64972),x64971)),f2(x64972)))+P1(f332(f332(f233(a1),x64971),f2(a1)))
% 52.62/52.41 [6498]~P110(x64982)+~P1(f332(f332(f232(x64982),f332(f105(x64982),x64981)),f2(x64982)))+P1(f332(f332(f232(a1),x64981),f2(a1)))
% 52.62/52.41 [7021]~P68(x70211)+~P1(f332(f332(f233(x70211),x70212),f2(x70211)))+P1(f332(f332(f233(x70211),f332(f332(f82(x70211),x70212),x70212)),f2(x70211)))
% 52.62/52.41 [7022]~P110(x70221)+~P1(f332(f332(f233(x70221),x70222),f2(x70221)))+P1(f332(f332(f233(x70221),f332(f332(f82(x70221),x70222),x70222)),f2(x70221)))
% 52.62/52.41 [7023]~P68(x70231)+~P1(f332(f332(f232(x70231),x70232),f2(x70231)))+P1(f332(f332(f232(x70231),f332(f332(f82(x70231),x70232),x70232)),f2(x70231)))
% 52.62/52.41 [7618]~P68(x76181)+~P1(f332(f332(f233(x76181),f332(f332(f82(x76181),x76182),x76182)),f2(x76181)))+P1(f332(f332(f233(x76181),x76182),f2(x76181)))
% 52.62/52.41 [7619]~P110(x76191)+~P1(f332(f332(f233(x76191),f332(f332(f82(x76191),x76192),x76192)),f2(x76191)))+P1(f332(f332(f233(x76191),x76192),f2(x76191)))
% 52.62/52.41 [7620]~P68(x76201)+~P1(f332(f332(f232(x76201),f332(f332(f82(x76201),x76202),x76202)),f2(x76201)))+P1(f332(f332(f232(x76201),x76202),f2(x76201)))
% 52.62/52.41 [4633]~E(x46332,f80(a845))+~E(x46331,f80(a845))+E(f332(f332(f83(a845),x46331),x46332),f80(a845))
% 52.62/52.41 [4634]~E(x46342,f2(a845))+~E(x46341,f2(a845))+E(f332(f332(f82(a845),x46341),x46342),f2(a845))
% 52.62/52.41 [4635]~E(x46352,f80(a845))+~E(x46351,f80(a845))+E(f332(f332(f83(a845),x46351),x46352),f80(a845))
% 52.62/52.41 [4636]~E(x46362,f80(a1))+~E(x46361,f80(a1))+E(f332(f332(f83(a1),x46361),x46362),f80(a1))
% 52.62/52.41 [4686]~P9(x46862)+E(x46861,f2(x46862))+E(f332(f332(f44(x46862),x46861),x46861),f80(x46862))
% 52.62/52.41 [4687]~P113(x46872)+E(x46871,f2(x46872))+E(f332(f332(f283(x46872),x46871),x46871),f80(x46872))
% 52.62/52.41 [4688]~P114(x46882)+E(x46881,f2(x46882))+E(f332(f332(f283(x46882),x46881),x46881),f80(x46882))
% 52.62/52.41 [4702]~P68(x47021)+~E(x47022,f2(x47021))+E(f332(f332(f82(x47021),x47022),x47022),f2(x47021))
% 52.62/52.41 [4703]~P68(x47031)+~E(x47032,f2(x47031))+E(f332(f332(f82(x47031),x47032),x47032),f2(x47031))
% 52.62/52.41 [4706]~P120(x47061)+~E(x47062,f80(x47061))+E(f332(f332(f83(x47061),x47062),x47062),f80(x47061))
% 52.62/52.41 [4707]~P114(x47071)+~E(x47072,f2(x47071))+E(f332(f332(f283(x47071),x47072),x47072),f2(x47071))
% 52.62/52.41 [4751]~E(x47512,f2(a845))+~E(x47511,f2(a845))+E(f332(f81(a1),f332(f102(a1),x47511)),f332(f102(a1),x47512))
% 52.62/52.41 [4769]E(x47691,f80(a845))+E(x47692,f2(a845))+~E(f332(f332(f83(a845),x47692),x47691),x47692)
% 52.62/52.41 [4777]E(x47771,f2(a845))+E(x47772,f2(a845))+~E(f332(f332(f83(a845),x47772),x47771),f2(a845))
% 52.62/52.41 [4803]~E(x48032,f2(a845))+~E(x48031,f332(a114,f2(a845)))+E(f332(f332(f82(a845),x48031),x48032),f332(a114,f2(a845)))
% 52.62/52.41 [4804]~E(x48041,f2(a845))+~E(x48042,f332(a114,f2(a845)))+E(f332(f332(f82(a845),x48041),x48042),f332(a114,f2(a845)))
% 52.62/52.41 [4805]~E(x48052,f2(a845))+~E(x48051,f332(a114,f2(a845)))+E(f332(f332(f82(a845),x48051),x48052),f332(a114,f2(a845)))
% 52.62/52.41 [4806]~E(x48061,f2(a845))+~E(x48062,f332(a114,f2(a845)))+E(f332(f332(f82(a845),x48061),x48062),f332(a114,f2(a845)))
% 52.62/52.41 [4811]E(x48111,f80(a1))+E(x48112,f332(f106(a1),a99))+~E(f332(f332(f83(a1),x48111),x48112),f80(a1))
% 52.62/52.41 [4812]E(x48121,f80(a1))+E(x48122,f332(f106(a1),a99))+~E(f332(f332(f83(a1),x48122),x48121),f80(a1))
% 52.62/52.41 [4813]E(x48131,f80(a1))+E(x48131,f332(f106(a1),a99))+~E(f332(f332(f83(a1),x48132),x48131),f80(a1))
% 52.62/52.41 [4814]E(x48141,f80(a1))+E(x48141,f332(f106(a1),a99))+~E(f332(f332(f83(a1),x48141),x48142),f80(a1))
% 52.62/52.41 [4815]E(x48151,f80(a1))+E(x48151,f332(f106(a1),a99))+~E(f332(f332(f83(a1),x48151),x48152),f80(a1))
% 52.62/52.41 [4833]~P68(x48332)+E(x48331,f2(x48332))+~E(f332(f332(f82(x48332),x48331),x48331),f2(x48332))
% 52.62/52.41 [4834]~P68(x48342)+E(x48341,f2(x48342))+~E(f332(f332(f82(x48342),x48341),x48341),f2(x48342))
% 52.62/52.41 [4840]~E(x48401,f332(f106(a1),a99))+~E(x48402,f332(f106(a1),a99))+E(f332(f332(f83(a1),x48401),x48402),f80(a1))
% 52.62/52.41 [4851]E(x48511,f2(a845))+E(x48512,f2(a845))+~E(f332(f332(f82(a845),x48512),x48511),f332(a114,f2(a845)))
% 52.62/52.41 [4852]E(x48521,f2(a845))+E(x48522,f2(a845))+~E(f332(f332(f82(a845),x48522),x48521),f332(a114,f2(a845)))
% 52.62/52.41 [4860]~P88(x48601)+~P62(x48601)+E(f332(f332(f283(x48601),x48602),f332(f106(x48601),a85)),f2(x48601))
% 52.62/52.41 [4867]~P120(x48671)+~E(x48672,f332(f81(x48671),f80(x48671)))+E(f332(f332(f83(x48671),x48672),x48672),f80(x48671))
% 52.62/52.41 [4872]~P12(x48722)+~P12(x48721)+P12(f332(f332(f82(a1),x48721),x48722))
% 52.62/52.41 [4873]~P12(x48732)+~P12(x48731)+P12(f332(f332(f83(a1),x48731),x48732))
% 52.62/52.41 [4874]~P12(x48742)+~P12(x48741)+P12(f332(f332(f44(a1),x48741),x48742))
% 52.62/52.41 [4875]~E(x48752,f2(a1))+E(x48751,f2(a1))+E(f54(x48751,x48752),f332(f332(f241(a1,a1),f2(a1)),x48751))
% 52.62/52.41 [4876]~E(x48762,f2(a1))+E(x48761,f2(a1))+E(f54(x48761,x48762),f332(f332(f241(a1,a1),f2(a1)),x48761))
% 52.62/52.41 [4899]~E(x48992,f332(a114,f2(a845)))+~E(x48991,f332(a114,f2(a845)))+E(f332(f332(f83(a845),x48991),x48992),f332(a114,f2(a845)))
% 52.62/52.41 [4910]E(x49101,f2(a845))+E(x49101,f332(a114,f2(a845)))+~E(f332(f332(f82(a845),x49102),x49101),f332(a114,f2(a845)))
% 52.62/52.41 [4911]E(x49111,f2(a845))+E(x49111,f332(a114,f2(a845)))+~E(f332(f332(f82(a845),x49111),x49112),f332(a114,f2(a845)))
% 52.62/52.41 [4912]E(x49121,f2(a845))+E(x49122,f332(a114,f2(a845)))+~E(f332(f332(f242(a845),x49122),x49121),f332(a114,f2(a845)))
% 52.62/52.41 [4913]E(x49131,f2(a845))+E(x49131,f332(a114,f2(a845)))+~E(f332(f332(f82(a845),x49132),x49131),f332(a114,f2(a845)))
% 52.62/52.41 [4914]E(x49141,f2(a845))+E(x49141,f332(a114,f2(a845)))+~E(f332(f332(f82(a845),x49141),x49142),f332(a114,f2(a845)))
% 52.62/52.41 [4922]~P88(x49221)+~P62(x49221)+E(f332(f332(f283(x49221),x49222),f332(f106(x49221),a99)),f332(f81(x49221),x49222))
% 52.62/52.41 [4943]E(x49431,f332(a107,x49432))+~E(x49431,f2(a845))+P1(f332(f332(f232(a1),f2(a1)),x49432))
% 52.62/52.41 [4944]E(f332(a107,x49441),x49442)+~E(x49442,f2(a845))+P1(f332(f332(f232(a1),f2(a1)),x49441))
% 52.62/52.41 [4962]E(x49621,f332(a114,f2(a845)))+E(x49622,f332(a114,f2(a845)))+~E(f332(f332(f82(a845),x49621),x49622),f332(a114,f2(a845)))
% 52.62/52.41 [4963]E(x49631,f332(a114,f2(a845)))+E(x49632,f332(a114,f2(a845)))+~E(f332(f332(f82(a845),x49631),x49632),f332(a114,f2(a845)))
% 52.62/52.41 [4974]~E(x49741,f332(a107,x49742))+E(x49741,f2(a845))+P1(f332(f332(f232(a1),f2(a1)),x49742))
% 52.62/52.41 [4975]~E(f332(a107,x49752),x49751)+E(x49751,f2(a845))+P1(f332(f332(f232(a1),f2(a1)),x49752))
% 52.62/52.41 [4998]~P93(x49981)+E(f332(f66(x49981,f103(x49981)),x49982),f15(x49981,x49982))+~P1(f332(f64(x49981),x49982))
% 52.62/52.41 [4999]~P100(x49991)+E(f332(f66(x49991,f179(x49991)),x49992),f16(x49991,x49992))+~P1(f332(f64(x49991),x49992))
% 52.62/52.41 [5000]~P100(x50001)+E(f332(f66(x50001,f236(x50001)),x50002),f17(x50001,x50002))+~P1(f332(f64(x50001),x50002))
% 52.62/52.41 [5001]~P93(x50011)+E(f332(f66(x50011,f104(x50011)),x50012),f12(x50011,x50012))+~P1(f332(f64(x50011),x50012))
% 52.62/52.41 [5084]E(x50841,x50842)+~E(f332(f332(f3(a845),x50842),x50841),f2(a845))+~E(f332(f332(f3(a845),x50841),x50842),f2(a845))
% 52.62/52.41 [5094]P12(x50941)+~P40(x50942)+~P1(f332(f332(f334(a1),x50941),x50942))
% 52.62/52.41 [5125]~P110(x51251)+~E(f84(x51251,x51252),f80(x51251))+P1(f332(f332(f233(x51251),f2(x51251)),x51252))
% 52.62/52.41 [5137]~P88(x51371)+E(f332(f102(x51371),f332(f106(a845),x51372)),f332(f106(x51371),x51372))+P1(f332(a186,f332(f106(a1),x51372)))
% 52.62/52.41 [5142]~P44(x51421,x51422)+P45(a839)+P1(f332(f64(f852(x51421,x51421)),x51422))
% 52.62/52.41 [5207]~P100(x52071)+E(f332(f66(x52071,f179(x52071)),x52072),f13(x52071,f179(x52071),x52072))+~P1(f332(f64(x52071),x52072))
% 52.62/52.41 [5208]~P100(x52081)+E(f332(f66(x52081,f236(x52081)),x52082),f14(x52081,f236(x52081),x52082))+~P1(f332(f64(x52081),x52082))
% 52.62/52.41 [5221]E(x52211,x52212)+P1(f332(f332(f233(a845),x52212),x52211))+P1(f332(f332(f233(a845),x52211),x52212))
% 52.62/52.41 [5222]E(x52221,x52222)+P1(f332(f332(f233(a845),x52222),x52221))+P1(f332(f332(f233(a845),x52221),x52222))
% 52.62/52.41 [5223]E(x52231,x52232)+P1(f332(f332(f233(a1),x52232),x52231))+P1(f332(f332(f233(a1),x52231),x52232))
% 52.62/52.41 [5275]~P88(x52751)+E(f332(f102(x52751),f332(f106(a845),x52752)),f2(x52751))+~P1(f332(a186,f332(f106(a1),x52752)))
% 52.62/52.41 [5278]~E(x52782,f332(a107,x52781))+E(x52781,f332(f102(a1),x52782))+~P1(f332(f332(f232(a1),f2(a1)),x52781))
% 52.62/52.41 [5279]~E(f332(a107,x52791),x52792)+E(x52791,f332(f102(a1),x52792))+~P1(f332(f332(f232(a1),f2(a1)),x52791))
% 52.62/52.41 [5280]~E(x52801,f332(a107,x52802))+E(f332(f102(a1),x52801),x52802)+~P1(f332(f332(f232(a1),f2(a1)),x52802))
% 52.62/52.41 [5290]E(x52901,f332(a107,x52902))+~E(x52902,f332(f102(a1),x52901))+~P1(f332(f332(f232(a1),f2(a1)),x52902))
% 52.62/52.41 [5291]E(f332(a107,x52911),x52912)+~E(x52911,f332(f102(a1),x52912))+~P1(f332(f332(f232(a1),f2(a1)),x52911))
% 52.62/52.41 [5320]~P73(x53202)+E(x53201,f2(x53202))+~P1(f332(f332(f279(x53202),f2(x53202)),x53201))
% 52.62/52.41 [5329]~P80(x53292)+E(x53291,f2(x53292))+P1(f332(f332(f233(x53292),f2(x53292)),f332(f77(x53292),x53291)))
% 52.62/52.41 [5396]~P110(x53961)+E(f84(x53961,x53962),f80(x53961))+~P1(f332(f332(f233(x53961),f2(x53961)),x53962))
% 52.62/52.41 [5397]~P110(x53971)+E(f84(x53971,x53972),f80(x53971))+~P1(f332(f332(f233(x53971),f2(x53971)),x53972))
% 52.62/52.41 [5403]~P88(x54031)+E(f332(f102(x54031),f332(f106(a845),x54032)),f2(x54031))+P1(f332(f332(f232(a1),f2(a1)),f332(f106(a1),x54032)))
% 52.62/52.41 [5410]~P80(x54101)+E(f332(f77(x54101),x54102),x54102)+~P1(f332(f332(f233(x54101),f2(x54101)),x54102))
% 52.62/52.41 [5411]~P80(x54111)+E(f332(f77(x54111),x54112),x54112)+~P1(f332(f332(f232(x54111),f2(x54111)),x54112))
% 52.62/52.41 [5418]E(x54181,f2(a845))+~E(f130(a845,f332(f294(a845,x54182),x54181)),f115(a845))+P1(f332(f332(f232(a845),x54181),x54182))
% 52.62/52.41 [5428]~P4(x54281)+E(f332(f332(f8(x54281,x54281),f7(x54281)),f332(f158(x54281),x54282)),f332(f154(x54281),x54282))+~P1(f332(f127(x54281),x54282))
% 52.62/52.41 [5431]~P133(x54311)+E(f332(f102(x54311),f332(a107,x54312)),f332(f105(x54311),x54312))+~P1(f332(f332(f232(a1),f2(a1)),x54312))
% 52.62/52.41 [5433]~E(x54331,x54332)+P1(f332(f332(f233(a845),x54331),f332(a114,x54332)))+P1(f332(f332(f233(a845),x54331),x54332))
% 52.62/52.41 [5452]E(x54521,x54522)+P1(f332(f332(f233(a845),x54521),x54522))+~P1(f332(f332(f232(a845),x54521),x54522))
% 52.62/52.41 [5453]E(x54531,x54532)+P1(f332(f332(f233(a845),x54531),x54532))+~P1(f332(f332(f232(a845),x54531),x54532))
% 52.62/52.41 [5454]E(x54541,x54542)+P1(f332(f332(f233(a845),x54541),x54542))+~P1(f332(f332(f232(a845),x54541),x54542))
% 52.62/52.41 [5455]E(x54551,x54552)+P1(f332(f332(f233(a1),x54551),x54552))+~P1(f332(f332(f232(a1),x54551),x54552))
% 52.62/52.41 [5458]E(x54581,f80(a1))+~E(f332(f332(f83(a1),x54582),x54581),f80(a1))+~P1(f332(f332(f233(a1),f2(a1)),x54582))
% 52.62/52.41 [5459]E(x54591,f80(a1))+~E(f332(f332(f83(a1),x54591),x54592),f80(a1))+~P1(f332(f332(f233(a1),f2(a1)),x54591))
% 52.62/52.41 [5497]~P40(x54972)+P1(f332(f332(f232(a1),f2(a1)),x54971))+~P1(f332(f332(f334(a1),x54971),x54972))
% 52.62/52.41 [5498]~P40(x54982)+P1(f332(f332(f232(a1),f2(a1)),x54981))+~P1(f332(f332(f334(a1),x54981),x54982))
% 52.62/52.41 [5515]~P58(x55151,x55152)+P38(x55151,x55152)+~P1(f332(f64(f852(x55151,x55151)),x55152))
% 52.62/52.41 [5516]~P58(x55161,x55162)+P38(x55161,x55162)+~P1(f332(f64(f852(x55161,x55161)),x55162))
% 52.62/52.41 [5517]~P38(x55171,x55172)+P58(x55171,x55172)+~P1(f332(f64(f852(x55171,x55171)),x55172))
% 52.62/52.41 [5518]~P58(x55181,x55182)+P44(x55181,x55182)+~P1(f332(f64(f852(x55181,x55181)),x55182))
% 52.62/52.41 [5558]E(x55581,f180(f853(x55582,a839)))+~P1(f332(f64(x55582),x55581))+P1(f332(f332(f233(a845),f2(a845)),f332(f43(x55582),x55581)))
% 52.62/52.41 [5584]~P1(f332(x55841,x55842))+P1(f332(x55841,f2(a845)))+P1(f332(f332(f233(a845),f787(x55842,x55841)),x55842))
% 52.62/52.41 [5609]E(x56091,f2(a845))+~E(f332(f154(a845),x56092),f2(a845))+~P1(f332(f332(f334(a845),x56091),f332(f158(a845),x56092)))
% 52.62/52.41 [5642]~E(x56421,x56422)+P1(f332(f332(f233(a845),x56421),f332(a114,x56422)))+~P1(f332(f332(f232(a845),x56422),x56421))
% 52.62/52.41 [5671]~E(x56712,f2(a845))+P1(f332(f332(f232(a1),f2(a1)),x56711))+P1(f332(f332(f279(a845),f332(a107,x56711)),x56712))
% 52.62/52.41 [5674]E(x56741,x56742)+~P1(f332(f332(f232(a845),x56742),x56741))+~P1(f332(f332(f232(a845),x56741),x56742))
% 52.62/52.41 [5675]E(x56751,x56752)+~P1(f332(f332(f232(a1),x56752),x56751))+~P1(f332(f332(f232(a1),x56751),x56752))
% 52.62/52.41 [5676]E(x56761,x56762)+~P1(f332(f332(f279(a845),x56762),x56761))+~P1(f332(f332(f279(a845),x56761),x56762))
% 52.62/52.41 [5677]E(x56771,x56772)+~P1(f332(f332(f279(a845),x56772),x56771))+~P1(f332(f332(f279(a845),x56771),x56772))
% 52.62/52.41 [5678]E(x56781,x56782)+~P1(f332(f332(f279(a845),x56782),x56781))+~P1(f332(f332(f279(a845),x56781),x56782))
% 52.62/52.41 [5679]E(x56791,x56792)+~P1(f332(f332(f279(a845),x56792),x56791))+~P1(f332(f332(f279(a845),x56791),x56792))
% 52.62/52.41 [5680]E(x56801,x56802)+~P1(f332(f332(f279(a845),x56802),x56801))+~P1(f332(f332(f279(a845),x56801),x56802))
% 52.62/52.41 [5681]E(x56811,x56812)+~P1(f332(f332(f279(a845),x56812),x56811))+~P1(f332(f332(f279(a845),x56811),x56812))
% 52.62/52.41 [5682]E(x56821,x56822)+~P1(f332(f332(f279(a845),x56822),x56821))+~P1(f332(f332(f279(a845),x56821),x56822))
% 52.62/52.41 [5683]E(x56831,x56832)+~P1(f332(f332(f279(a845),x56832),x56831))+~P1(f332(f332(f279(a845),x56831),x56832))
% 52.62/52.41 [5684]E(x56841,x56842)+~P1(f332(f332(f279(a845),x56842),x56841))+~P1(f332(f332(f279(a845),x56841),x56842))
% 52.62/52.41 [5685]E(f332(f43(x56851),x56852),f2(a845))+~P1(f332(f64(x56851),x56852))+P1(f332(f332(f334(x56851),f619(x56852,x56851)),x56852))
% 52.62/52.41 [5691]E(f58(x56911,x56912),f54(x56911,x56912))+P1(f332(f332(f232(a1),f2(a1)),x56911))+~P1(f332(f332(f233(a1),f2(a1)),x56912))
% 52.62/52.41 [5720]~P1(f332(x57201,f768(x57201)))+P1(f332(x57201,f332(a107,x57202)))+~P1(f332(f332(f232(a1),f2(a1)),x57202))
% 52.62/52.41 [5722]P1(f332(f332(f233(a845),x57221),f403(x57222)))+~P1(f332(f64(a845),x57222))+~P1(f332(f332(f334(a845),x57221),x57222))
% 52.62/52.41 [5723]P1(f332(f332(f232(a845),x57231),f411(x57232)))+~P1(f332(f64(a845),x57232))+~P1(f332(f332(f334(a845),x57231),x57232))
% 52.62/52.41 [5749]E(x57491,x57492)+~P1(f332(f332(f233(a845),x57491),f332(a114,x57492)))+P1(f332(f332(f233(a845),x57491),x57492))
% 52.62/52.41 [5750]E(x57501,x57502)+~P1(f332(f332(f233(a845),x57501),f332(a114,x57502)))+P1(f332(f332(f233(a845),x57501),x57502))
% 52.62/52.41 [5751]E(x57511,x57512)+~P1(f332(f332(f233(a845),x57511),f332(a114,x57512)))+P1(f332(f332(f233(a845),x57511),x57512))
% 52.62/52.41 [5752]E(x57521,x57522)+~P1(f332(f332(f233(a845),x57521),f332(a114,x57522)))+P1(f332(f332(f233(a845),x57521),x57522))
% 52.62/52.41 [5789]E(x57891,f332(a114,x57892))+~P1(f332(f332(f232(a845),x57891),f332(a114,x57892)))+P1(f332(f332(f232(a845),x57891),x57892))
% 52.62/52.41 [5790]E(x57901,f332(a114,x57902))+~P1(f332(f332(f232(a845),x57901),f332(a114,x57902)))+P1(f332(f332(f232(a845),x57901),x57902))
% 52.62/52.41 [5800]P1(f332(x58001,f769(x58001)))+~P1(f332(x58001,f332(a107,x58002)))+~P1(f332(f332(f232(a1),f2(a1)),x58002))
% 52.62/52.41 [5802]E(f332(f77(a1),x58021),f332(f77(a1),x58022))+~P1(f332(f332(f279(a1),x58022),x58021))+~P1(f332(f332(f279(a1),x58021),x58022))
% 52.62/52.41 [5814]~P1(f332(x58141,x58142))+~P1(f332(f332(f232(a1),f2(a1)),x58142))+P1(f332(x58141,f332(f102(a1),f723(x58141))))
% 52.62/52.41 [5826]~P80(x58262)+~E(x58261,f2(x58262))+~P1(f332(f332(f233(x58262),f2(x58262)),f332(f77(x58262),x58261)))
% 52.62/52.41 [5851]~P58(x58511,x58512)+P38(x58511,f332(f278(x58511,x58511),x58512))+~P1(f332(f64(f852(x58511,x58511)),x58512))
% 52.62/52.41 [5859]~P88(x58591)+E(f332(f102(x58591),f332(f106(a845),x58592)),f332(f106(x58591),x58592))+~P1(f332(f332(f232(a1),f2(a1)),f332(f106(a1),x58592)))
% 52.62/52.41 [5863]E(f332(a114,x58631),x58632)+~P1(f332(f332(f233(a845),x58631),x58632))+P1(f332(f332(f233(a845),f332(a114,x58631)),x58632))
% 52.62/52.41 [5875]E(f332(f332(f44(a1),x58751),x58752),f2(a1))+~P1(f332(f332(f232(a1),x58751),f2(a1)))+~P1(f332(f332(f233(a1),x58752),x58751))
% 52.62/52.41 [5876]E(f332(f332(f44(a1),x58761),x58762),f2(a1))+~P1(f332(f332(f232(a1),x58761),f2(a1)))+~P1(f332(f332(f233(a1),x58762),x58761))
% 52.62/52.41 [5889]E(f53(a1,x58891,x58892),x58891)+~P1(f332(f332(f232(a1),x58891),f2(a1)))+~P1(f332(f332(f233(a1),x58892),x58891))
% 52.62/52.41 [5902]E(f55(x59021,x59022),f54(x59021,x59022))+~P1(f332(f332(f232(a1),f2(a1)),x59021))+~P1(f332(f332(f232(a1),f2(a1)),x59022))
% 52.62/52.41 [5908]E(f332(f332(f44(a845),x59081),x59082),f2(a845))+~P1(f332(f332(f233(a845),f2(a845)),x59082))+~P1(f332(f332(f233(a845),x59081),x59082))
% 52.62/52.41 [5909]E(f332(f332(f44(a1),x59091),x59092),f2(a1))+~P1(f332(f332(f232(a1),f2(a1)),x59091))+~P1(f332(f332(f233(a1),x59091),x59092))
% 52.62/52.41 [5910]E(f332(f332(f44(a1),x59101),x59102),f2(a1))+~P1(f332(f332(f232(a1),f2(a1)),x59101))+~P1(f332(f332(f233(a1),x59101),x59102))
% 52.62/52.41 [5924]E(f53(a845,f332(f106(a845),x59241),f332(f106(a845),x59242)),f332(f106(a845),x59241))+P1(f332(a186,f332(f106(a1),x59241)))+~P1(f332(a186,f332(f106(a1),x59242)))
% 52.62/52.41 [5926]E(f53(a1,x59261,x59262),x59261)+~P1(f332(f332(f232(a1),f2(a1)),x59261))+~P1(f332(f332(f233(a1),x59261),x59262))
% 52.62/52.41 [5927]P1(f332(x59271,x59272))+~P1(f332(x59271,f2(a845)))+~P1(f332(x59271,f332(a114,f514(x59272,x59271))))
% 52.62/52.41 [5929]E(x59291,x59292)+~P1(f332(f332(f233(a845),x59291),f332(a114,x59292)))+~P1(f332(f332(f232(a845),x59292),x59291))
% 52.62/52.41 [5941]E(f332(f106(a1),x59411),f332(f102(a1),x59412))+~E(x59412,f332(a107,f332(f106(a1),x59411)))+~P1(f332(f332(f232(a1),f2(a1)),f332(f106(a1),x59411)))
% 52.62/52.41 [5945]~P110(x59451)+~P1(f332(f332(f233(x59451),x59452),f2(x59451)))+P1(f332(f332(f233(x59451),x59452),f332(f81(x59451),x59452)))
% 52.62/52.41 [5946]~P68(x59461)+~P1(f332(f332(f232(x59461),x59462),f2(x59461)))+P1(f332(f332(f232(x59461),x59462),f332(f81(x59461),x59462)))
% 52.62/52.41 [5955]~P11(x59551)+E(f332(f332(f67(x59551,x59551,f104(x59551)),f239(x59551)),x59552),f46(x59551,x59552))+~P1(f332(f64(x59551),x59552))
% 52.62/52.41 [5956]~P11(x59561)+E(f332(f332(f67(x59561,x59561,f103(x59561)),f180(x59561)),x59562),f45(x59561,x59562))+~P1(f332(f64(x59561),x59562))
% 52.62/52.41 [5970]~P117(x59701)+~P1(f332(f332(f233(a845),f2(a845)),x59702))+P1(f332(f332(f233(x59701),f2(x59701)),f332(f102(x59701),x59702)))
% 52.62/52.41 [5971]~P110(x59711)+~P1(f332(f332(f233(a1),f2(a1)),x59712))+P1(f332(f332(f233(x59711),f2(x59711)),f332(f105(x59711),x59712)))
% 52.62/52.41 [5972]~P110(x59721)+~P1(f332(f332(f232(a1),f2(a1)),x59722))+P1(f332(f332(f232(x59721),f2(x59721)),f332(f105(x59721),x59722)))
% 52.62/52.41 [5975]~P12(x59752)+~P12(x59751)+E(f332(f303(a845,a1,f102(a1)),f295(a845,f332(a107,x59751),f332(a107,x59752))),f295(a1,x59751,x59752))
% 52.62/52.41 [5981]P1(f332(x59811,x59812))+~P1(f332(f332(f232(a1),f2(a1)),x59812))+~P1(f332(x59811,f332(f102(a1),f747(x59811))))
% 52.62/52.41 [6008]E(f332(f332(f82(a845),f332(f106(a845),x60081)),f332(f106(a845),x60082)),f332(f106(a845),x60081))+P1(f332(f332(f233(a1),x60081),a85))+~P1(f332(f332(f233(a1),x60082),a85))
% 52.62/52.41 [6012]~P110(x60121)+P1(f332(f332(f233(x60121),f2(x60121)),f84(x60121,x60122)))+~P1(f332(f332(f233(x60121),f2(x60121)),x60122))
% 52.62/52.41 [6026]~P78(x60261)+~P1(f332(f332(f233(x60261),x60262),f2(x60261)))+P1(f332(f332(f233(x60261),f2(x60261)),f332(f81(x60261),x60262)))
% 52.62/52.41 [6027]~P78(x60271)+~P1(f332(f332(f232(x60271),x60272),f2(x60271)))+P1(f332(f332(f232(x60271),f2(x60271)),f332(f81(x60271),x60272)))
% 52.62/52.41 [6030]E(x60301,f2(a845))+P1(f332(f332(f232(a1),f2(a1)),x60302))+~P1(f332(f332(f279(a845),f332(a107,x60302)),x60301))
% 52.62/52.41 [6031]E(x60311,f239(f853(x60312,a839)))+~E(f332(f43(x60312),x60311),f332(f43(x60312),f239(f853(x60312,a839))))+~P1(f332(f64(x60312),f239(f853(x60312,a839))))
% 52.62/52.41 [6062]~P1(f332(f332(f233(a845),f2(a845)),x60622))+~P1(f332(f332(f279(a845),x60621),x60622))+P1(f332(f332(f232(a845),x60621),x60622))
% 52.62/52.41 [6063]~P1(f332(f332(f233(a1),f2(a1)),x60632))+~P1(f332(f332(f279(a1),x60631),x60632))+P1(f332(f332(f232(a1),x60631),x60632))
% 52.62/52.41 [6069]~P110(x60691)+P1(f332(f332(f233(x60691),x60692),f2(x60691)))+~P1(f332(f332(f233(x60691),x60692),f332(f81(x60691),x60692)))
% 52.62/52.41 [6070]~P68(x60701)+P1(f332(f332(f232(x60701),x60702),f2(x60701)))+~P1(f332(f332(f232(x60701),x60702),f332(f81(x60701),x60702)))
% 52.62/52.41 [6075]E(f55(x60751,x60752),f332(f332(f241(a1,a1),f2(a1)),x60751))+~P1(f332(f332(f233(a1),f2(a1)),x60752))+~P1(f332(f332(f233(a1),x60751),x60752))
% 52.62/52.41 [6078]~P88(x60781)+P1(f332(f332(f334(x60781),f332(f106(x60781),x60782)),f176(x60781)))+~P1(f332(f332(f232(a1),a85),x60782))
% 52.62/52.41 [6110]E(x61101,f2(a845))+~P1(f332(f332(f233(a845),x61101),f332(a114,x61102)))+P1(f332(f332(f233(a845),f526(x61102,x61101)),x61102))
% 52.62/52.41 [6134]~P110(x61341)+~P1(f332(f332(f233(x61341),f2(x61341)),f84(x61341,x61342)))+P1(f332(f332(f233(x61341),f2(x61341)),x61342))
% 52.62/52.41 [6136]~E(f332(f106(a845),x61362),f332(f106(a845),x61361))+P1(f332(f332(f232(a1),f332(f106(a1),x61361)),f2(a1)))+~P1(f332(a186,f332(f106(a1),x61362)))
% 52.62/52.41 [6164]E(f332(f240(a1,a1),f58(x61641,x61642)),f332(f332(f44(a1),x61641),x61642))+~P1(f332(f332(f233(a1),x61641),f2(a1)))+~P1(f332(f332(f233(a1),f2(a1)),x61642))
% 52.62/52.41 [6198]E(f332(f250(a1,a1),f58(x61981,x61982)),f53(a1,x61981,x61982))+~P1(f332(f332(f233(a1),x61981),f2(a1)))+~P1(f332(f332(f233(a1),f2(a1)),x61982))
% 52.62/52.41 [6200]E(x62001,f2(a1))+~P1(f332(f332(f279(a1),x62002),x62001))+P1(f332(f332(f232(a1),f332(f77(a1),x62002)),f332(f77(a1),x62001)))
% 52.62/52.41 [6202]~P117(x62022)+~P1(f332(f332(f233(x62022),f2(x62022)),f332(f102(x62022),x62021)))+P1(f332(f332(f233(a845),f2(a845)),x62021))
% 52.62/52.41 [6203]~P110(x62032)+~P1(f332(f332(f233(x62032),f2(x62032)),f332(f105(x62032),x62031)))+P1(f332(f332(f233(a1),f2(a1)),x62031))
% 52.62/52.41 [6204]~P110(x62042)+~P1(f332(f332(f232(x62042),f2(x62042)),f332(f105(x62042),x62041)))+P1(f332(f332(f232(a1),f2(a1)),x62041))
% 52.62/52.41 [6208]~E(x62082,f2(a845))+P1(f332(f332(f279(a845),f332(a107,x62081)),x62082))+~P1(f332(f332(f279(a1),x62081),f332(f102(a1),x62082)))
% 52.62/52.41 [6209]E(f332(f240(a1,a1),f55(x62091,x62092)),f332(f332(f44(a1),x62091),x62092))+~P1(f332(f332(f233(a1),f2(a1)),x62091))+~P1(f332(f332(f232(a1),f2(a1)),x62092))
% 52.62/52.41 [6223]E(f332(f250(a1,a1),f55(x62231,x62232)),f53(a1,x62231,x62232))+~P1(f332(f332(f233(a1),f2(a1)),x62231))+~P1(f332(f332(f232(a1),f2(a1)),x62232))
% 52.62/52.41 [6241]~P78(x62411)+P1(f332(f332(f233(x62411),x62412),f2(x62411)))+~P1(f332(f332(f233(x62411),f2(x62411)),f332(f81(x62411),x62412)))
% 52.62/52.41 [6242]~P78(x62421)+P1(f332(f332(f232(x62421),x62422),f2(x62421)))+~P1(f332(f332(f232(x62421),f2(x62421)),f332(f81(x62421),x62422)))
% 52.62/52.41 [6268]P1(f332(f57(x62681,x62682),f58(x62681,x62682)))+~P1(f332(f332(f233(a1),x62681),f2(a1)))+~P1(f332(f332(f233(a1),f2(a1)),x62682))
% 52.62/52.41 [6284]~P1(f332(f332(f233(a845),f2(a845)),x62841))+~P1(f332(f332(f279(a845),x62842),x62841))+~P1(f332(f332(f233(a845),x62841),x62842))
% 52.62/52.41 [6285]~P1(f332(f332(f233(a1),f2(a1)),x62851))+~P1(f332(f332(f279(a1),x62852),x62851))+~P1(f332(f332(f233(a1),x62851),x62852))
% 52.62/52.41 [6297]P1(f332(f57(x62971,x62972),f55(x62971,x62972)))+~P1(f332(f332(f233(a1),f2(a1)),x62972))+~P1(f332(f332(f232(a1),f2(a1)),x62971))
% 52.62/52.41 [6339]~P78(x63391)+P1(f332(f332(f233(x63391),f332(f81(x63391),x63392)),f2(x63391)))+~P1(f332(f332(f233(x63391),f2(x63391)),x63392))
% 52.62/52.41 [6340]~P78(x63401)+P1(f332(f332(f232(x63401),f332(f81(x63401),x63402)),f2(x63401)))+~P1(f332(f332(f232(x63401),f2(x63401)),x63402))
% 52.62/52.41 [6362]E(f332(f332(f3(a845),f332(a107,x63621)),f332(a107,x63622)),f332(a107,f188(x63621,x63622)))+~P1(f332(f332(f232(a1),f2(a1)),x63622))+~P1(f332(f332(f232(a1),f2(a1)),x63621))
% 52.62/52.41 [6380]P1(f332(f332(f232(a1),f2(a1)),f188(x63801,x63802)))+~P1(f332(f332(f232(a1),f2(a1)),x63802))+~P1(f332(f332(f232(a1),f2(a1)),x63801))
% 52.62/52.41 [6419]~P1(f332(x64191,x64192))+P1(f332(x64191,f2(a845)))+P1(f332(x64191,f332(f332(f82(a845),f787(x64192,x64191)),f80(a845))))
% 52.62/52.41 [6425]E(f282(a845,f279(a845),x64251,x64252),f180(f853(a845,a839)))+P1(f332(f332(f279(a845),x64251),x64252))+~P1(f332(f332(f279(a845),x64252),x64251))
% 52.62/52.41 [6505]E(f332(f106(a845),x65051),f332(f106(a845),x65052))+~P1(f332(f332(f232(a1),f332(f106(a1),x65052)),f2(a1)))+~P1(f332(a186,f332(f106(a1),x65051)))
% 52.62/52.41 [6518]~E(x65181,f2(a845))+~E(f736(x65182,x65181),f2(a845))+E(f332(f132(a845,a845,f82(a845),x65181),x65182),f2(a845))
% 52.62/52.41 [6544]~P1(f332(f64(x65441),f669(x65442,x65441)))+~P1(f332(f64(f853(x65441,a839)),x65442))+P1(f332(f64(x65441),f45(f853(x65441,a839),x65442)))
% 52.62/52.41 [6550]E(x65501,x65502)+P1(f332(f332(f233(a1),x65501),x65502))+~P1(f332(f332(f233(a1),x65501),f332(f332(f82(a1),x65502),f80(a1))))
% 52.62/52.41 [6551]P1(f332(f332(f233(a845),f332(a107,x65511)),f332(a107,x65512)))+~P1(f332(f332(f233(a1),f2(a1)),x65512))+~P1(f332(f332(f233(a1),x65511),x65512))
% 52.62/52.41 [6552]P1(f332(f332(f233(a845),f332(a107,x65521)),f332(a107,x65522)))+~P1(f332(f332(f233(a1),f2(a1)),x65522))+~P1(f332(f332(f233(a1),x65521),x65522))
% 52.62/52.41 [6553]P1(f332(f332(f233(a845),f332(a107,x65531)),f332(a107,x65532)))+~P1(f332(f332(f232(a1),f2(a1)),x65531))+~P1(f332(f332(f233(a1),x65531),x65532))
% 52.62/52.41 [6554]P1(f332(f332(f232(a845),f332(a107,x65541)),f332(a107,x65542)))+~P1(f332(f332(f233(a1),f2(a1)),x65541))+~P1(f332(f332(f232(a1),x65541),x65542))
% 52.62/52.41 [6555]P1(f332(f332(f232(a845),f332(a107,x65551)),f332(a107,x65552)))+~P1(f332(f332(f232(a1),f2(a1)),x65552))+~P1(f332(f332(f232(a1),x65551),x65552))
% 52.62/52.41 [6565]E(f53(a845,f332(a107,x65651),f332(a107,x65652)),f332(a107,f53(a1,x65651,x65652)))+~P1(f332(f332(f232(a1),f2(a1)),x65652))+~P1(f332(f332(f232(a1),f2(a1)),x65651))
% 52.62/52.41 [6566]E(f53(a845,f332(a107,x65661),f332(a107,x65662)),f332(a107,f53(a1,x65661,x65662)))+~P1(f332(f332(f232(a1),f2(a1)),x65662))+~P1(f332(f332(f232(a1),f2(a1)),x65661))
% 52.62/52.41 [6586]~P78(x65861)+~P1(f332(f332(f233(x65861),f332(f81(x65861),x65862)),f2(x65861)))+P1(f332(f332(f233(x65861),f2(x65861)),x65862))
% 52.62/52.41 [6587]~P78(x65871)+~P1(f332(f332(f232(x65871),f332(f81(x65871),x65872)),f2(x65871)))+P1(f332(f332(f232(x65871),f2(x65871)),x65872))
% 52.62/52.41 [6604]~P1(f332(f332(f233(a1),a85),x66042))+~P1(f332(f332(f233(a1),x66041),x66042))+P1(f332(f332(f233(a845),f332(f106(a845),x66041)),f332(f106(a845),x66042)))
% 52.62/52.41 [6701]~P1(f332(f332(f232(a1),f2(a1)),x67011))+P1(f332(f332(f233(a845),f332(a107,x67011)),x67012))+~P1(f332(f332(f233(a1),x67011),f332(f102(a1),x67012)))
% 52.62/52.41 [6702]~P1(f332(f332(f232(a1),f2(a1)),x67021))+P1(f332(f332(f279(a845),f332(a107,x67021)),x67022))+~P1(f332(f332(f279(a1),x67021),f332(f102(a1),x67022)))
% 52.62/52.41 [6718]E(x67181,f2(a1))+E(f53(a1,x67182,x67181),f2(a1))+E(f332(f332(f3(a1),f332(f81(a1),f332(f332(f44(a1),x67182),x67181))),f80(a1)),f332(f332(f44(a1),x67182),f332(f81(a1),x67181)))
% 52.62/52.41 [6734]~P1(f332(f332(f232(a1),f2(a1)),x67341))+~P1(f332(f332(f233(a845),f332(a107,x67341)),x67342))+P1(f332(f332(f233(a1),x67341),f332(f102(a1),x67342)))
% 52.62/52.41 [6735]~P1(f332(f332(f232(a1),f2(a1)),x67351))+~P1(f332(f332(f279(a845),f332(a107,x67351)),x67352))+P1(f332(f332(f279(a1),x67351),f332(f102(a1),x67352)))
% 52.62/52.41 [6772]~P1(f332(f332(f233(a845),f332(a107,x67721)),f332(a107,x67722)))+~P1(f332(f332(f233(a1),f2(a1)),x67722))+P1(f332(f332(f233(a1),x67721),x67722))
% 52.62/52.41 [6773]~P1(f332(f332(f233(a845),f332(a107,x67731)),f332(a107,x67732)))+~P1(f332(f332(f232(a1),f2(a1)),x67731))+P1(f332(f332(f233(a1),x67731),x67732))
% 52.62/52.41 [6774]~P1(f332(f332(f232(a845),f332(a107,x67741)),f332(a107,x67742)))+~P1(f332(f332(f233(a1),f2(a1)),x67741))+P1(f332(f332(f232(a1),x67741),x67742))
% 52.62/52.41 [6775]~P1(f332(f332(f232(a845),f332(a107,x67751)),f332(a107,x67752)))+~P1(f332(f332(f232(a1),f2(a1)),x67752))+P1(f332(f332(f232(a1),x67751),x67752))
% 52.62/52.41 [6806]P1(f332(f332(f232(a1),x68061),x68062))+~P1(f332(f332(f232(a845),f332(f106(a845),x68061)),f332(f106(a845),x68062)))+P1(f332(f332(f232(a1),x68061),a85))
% 52.62/52.41 [6833]P1(f332(f332(f232(a1),f2(a1)),f53(a1,x68331,x68332)))+~P1(f332(f332(f232(a1),f2(a1)),x68332))+~P1(f332(f332(f232(a1),f2(a1)),x68331))
% 52.62/52.41 [6932]P1(f332(f332(f233(a1),a85),x69321))+~P1(f332(f332(f233(a1),x69322),x69321))+~P1(f332(f332(f233(a845),f332(f106(a845),x69322)),f332(f106(a845),x69321)))
% 52.62/52.41 [6980]E(f332(f332(f241(a1,a1),f332(f332(f44(a1),x69801),x69802)),f53(a1,x69801,x69802)),f58(x69801,x69802))+~P1(f332(f332(f233(a1),x69801),f2(a1)))+~P1(f332(f332(f233(a1),f2(a1)),x69802))
% 52.62/52.41 [7001]E(f332(f332(f241(a1,a1),f332(f332(f44(a1),x70011),x70012)),f53(a1,x70011,x70012)),f55(x70011,x70012))+~P1(f332(f332(f232(a1),f2(a1)),x70012))+~P1(f332(f332(f232(a1),f2(a1)),x70011))
% 52.62/52.41 [7056]~P91(x70562)+E(x70561,f115(x70562))+E(f332(f132(x70562,x70562,f83(x70562),f332(f131(x70562),x70561)),f332(f157(x70562),x70561)),f332(f66(x70562,f83(x70562)),f332(f158(x70562),x70561)))
% 52.62/52.41 [7170]~E(x71701,f2(a845))+E(f332(f132(a845,a845,f82(a845),x71701),x71702),f2(a845))+P1(f332(f332(f334(a845),f736(x71702,x71701)),f332(f158(a845),x71702)))
% 52.62/52.41 [7224]~P1(f332(f332(f233(a1),x72242),f2(a1)))+P1(f332(f332(f233(a1),f332(f332(f44(a1),x72241),x72242)),f2(a1)))+~P1(f332(f332(f233(a1),f2(a1)),x72241))
% 52.62/52.41 [7225]~P1(f332(f332(f233(a1),x72251),f2(a1)))+P1(f332(f332(f233(a1),f332(f332(f44(a1),x72251),x72252)),f2(a1)))+~P1(f332(f332(f233(a1),f2(a1)),x72252))
% 52.62/52.41 [7226]~P1(f332(f332(f233(a1),x72261),f2(a1)))+P1(f332(f332(f233(a1),f332(f332(f44(a1),x72261),x72262)),f2(a1)))+~P1(f332(f332(f233(a1),f2(a1)),x72262))
% 52.62/52.41 [7227]~P1(f332(f332(f233(a1),x72272),f2(a1)))+P1(f332(f332(f232(a1),f332(f332(f44(a1),x72271),x72272)),f2(a1)))+~P1(f332(f332(f232(a1),f2(a1)),x72271))
% 52.62/52.41 [7228]~P1(f332(f332(f232(a1),x72281),f2(a1)))+P1(f332(f332(f232(a1),f332(f332(f44(a1),x72281),x72282)),f2(a1)))+~P1(f332(f332(f233(a1),f2(a1)),x72282))
% 52.62/52.41 [7237]P1(f332(f332(f334(f853(x72371,a839)),f669(x72372,x72371)),x72372))+~P1(f332(f64(f853(x72371,a839)),x72372))+P1(f332(f64(x72371),f45(f853(x72371,a839),x72372)))
% 52.62/52.41 [7342]P31(x73421,x73421,x73422,f239(f853(x73421,a839)))+~E(f332(f303(x73421,x73421,x73422),f239(f853(x73421,a839))),f239(f853(x73421,a839)))+~P1(f332(f64(x73421),f239(f853(x73421,a839))))
% 52.62/52.41 [7471]~P31(x74711,x74711,x74712,f239(f853(x74711,a839)))+E(f332(f303(x74711,x74711,x74712),f239(f853(x74711,a839))),f239(f853(x74711,a839)))+~P1(f332(f64(x74711),f239(f853(x74711,a839))))
% 52.62/52.41 [7494]E(f55(f332(f106(a1),x74941),f332(f106(a1),x74942)),f332(f332(f241(a1,a1),f2(a1)),f332(f106(a1),x74941)))+~P1(f332(f332(f233(a1),f2(a1)),f332(f106(a1),x74942)))+~P1(f332(f332(f233(a1),f332(f106(a1),x74941)),f332(f106(a1),x74942)))
% 52.62/52.41 [7612]E(f332(f332(f44(a1),x76121),x76122),f332(f106(a1),a99))+~P1(f332(f332(f232(a1),f332(f332(f82(a1),x76121),x76122)),f2(a1)))+~P1(f332(f332(f233(a1),f2(a1)),x76121))
% 52.62/52.41 [7670]~P1(f332(f332(f233(a1),x76702),f2(a1)))+~P1(f332(f332(f233(a1),f332(f332(f44(a1),x76701),x76702)),f2(a1)))+P1(f332(f332(f233(a1),f2(a1)),x76701))
% 52.62/52.41 [7675]E(f332(f332(f82(a1),x76751),x76752),f53(a1,x76751,x76752))+~P1(f332(f332(f232(a1),f332(f332(f82(a1),x76751),x76752)),f2(a1)))+~P1(f332(f332(f233(a1),f2(a1)),x76751))
% 52.62/52.41 [7677]P1(f332(f332(f233(a1),x76771),f2(a1)))+~P1(f332(f332(f233(a1),f332(f332(f44(a1),x76771),x76772)),f2(a1)))+~P1(f332(f332(f233(a1),f2(a1)),x76772))
% 52.62/52.41 [7929]~P99(x79291)+P52(a845,x79291,f279(a845),x79292)+~P1(f332(f332(f232(x79291),f332(x79292,f383(x79292,x79291))),f332(x79292,f385(x79292,x79291))))
% 52.62/52.41 [8371]~P100(x83711)+P20(x83711,x83712)+~P1(f332(f332(f232(x83711),f332(f332(f152(x83711),x83712),f760(x83712,x83711))),f332(f332(f152(x83711),x83712),f761(x83712,x83711))))
% 52.62/52.41 [5552]E(x55521,f2(a1))+~E(f53(a1,x55522,x55521),f2(a1))+E(f332(f332(f44(a1),x55522),f332(f81(a1),x55521)),f332(f81(a1),f332(f332(f44(a1),x55522),x55521)))
% 52.62/52.41 [5569]~P40(x55692)+~P40(x55691)+P40(f332(f332(f103(f853(a1,a839)),x55691),x55692))
% 52.62/52.41 [5570]~P40(x55702)+~P40(x55701)+P40(f332(f332(f104(f853(a1,a839)),x55701),x55702))
% 52.62/52.41 [5587]~P88(x55871)+~P62(x55871)+E(f332(f81(x55871),f332(f332(f283(x55871),f80(x55871)),x55872)),f332(f332(f283(x55871),f332(f106(x55871),a99)),x55872))
% 52.62/52.41 [5712]E(x57121,f2(a1))+~E(f53(a1,x57122,x57121),f2(a1))+E(f332(f332(f44(a1),f332(f81(a1),x57122)),x57121),f332(f81(a1),f332(f332(f44(a1),x57122),x57121)))
% 52.62/52.41 [5846]~P100(x58461)+P20(x58461,x58462)+P1(f332(f332(f233(a845),f761(x58462,x58461)),f332(f181(f846(x58461)),x58462)))
% 52.62/52.41 [6004]~P88(x60041)+~E(f332(f106(x60041),x60042),f2(x60041))+P35(x60041,f332(f106(x60041),f332(f332(f82(a1),x60042),f332(f81(a1),a85))))
% 52.62/52.41 [6005]~P88(x60051)+~E(f332(f106(x60051),x60052),f2(x60051))+P35(x60051,f332(f106(x60051),f332(f332(f82(a1),a85),f332(f81(a1),x60052))))
% 52.62/52.41 [6007]E(f332(a59,f55(f332(f81(a1),x60071),f332(f81(a1),x60072))),f54(x60071,x60072))+P1(f332(f332(f233(a1),f2(a1)),x60072))+P1(f332(f332(f232(a1),f2(a1)),x60071))
% 52.62/52.41 [6142]~E(x61422,f2(a845))+~E(x61421,f2(a845))+P1(f332(f332(f232(a1),f332(f102(a1),x61421)),f332(f81(a1),f332(f102(a1),x61422))))
% 52.62/52.41 [6168]E(f332(f332(f82(a845),f332(f106(a845),x61681)),f332(f106(a845),x61682)),f332(f106(a845),f332(f332(f82(a1),x61681),x61682)))+P1(f332(f332(f233(a1),x61681),a85))+P1(f332(f332(f233(a1),x61682),a85))
% 52.62/52.41 [6306]~P68(x63061)+~P1(f332(f332(f233(x63061),f2(x63061)),x63062))+P1(f332(f332(f233(x63061),f332(f81(x63061),x63062)),x63062))
% 52.62/52.41 [6307]~P68(x63071)+~P1(f332(f332(f232(x63071),f2(x63071)),x63072))+P1(f332(f332(f232(x63071),f332(f81(x63071),x63072)),x63072))
% 52.62/52.41 [6490]E(f332(f332(f3(a845),f332(a107,x64901)),f332(a107,x64902)),f332(a107,f332(f332(f3(a1),x64901),x64902)))+~P1(f332(f332(f232(a1),f2(a1)),x64902))+~P1(f332(f332(f232(a1),x64902),x64901))
% 52.62/52.41 [6527]E(f332(a107,f53(a1,f332(f106(a1),x65271),f332(f106(a1),x65272))),f53(a845,f332(f106(a845),x65271),f332(f106(a845),x65272)))+P1(f332(a186,f332(f106(a1),x65271)))+P1(f332(a186,f332(f106(a1),x65272)))
% 52.62/52.41 [6545]~P68(x65451)+P1(f332(f332(f233(x65451),f2(x65451)),x65452))+~P1(f332(f332(f233(x65451),f332(f81(x65451),x65452)),x65452))
% 52.62/52.41 [6546]~P68(x65461)+P1(f332(f332(f232(x65461),f2(x65461)),x65462))+~P1(f332(f332(f232(x65461),f332(f81(x65461),x65462)),x65462))
% 52.62/52.41 [6557]~P68(x65571)+~P1(f332(f332(f233(x65571),f2(x65571)),x65572))+P1(f332(f332(f233(x65571),f2(x65571)),f332(f332(f82(x65571),x65572),x65572)))
% 52.62/52.41 [6559]~P68(x65591)+~P1(f332(f332(f232(x65591),f2(x65591)),x65592))+P1(f332(f332(f232(x65591),f2(x65591)),f332(f332(f82(x65591),x65592),x65592)))
% 52.62/52.41 [6569]E(f332(f332(f82(a845),f332(a107,x65691)),f332(a107,x65692)),f332(a107,f332(f332(f82(a1),x65691),x65692)))+~P1(f332(f332(f232(a1),f2(a1)),x65692))+~P1(f332(f332(f232(a1),f2(a1)),x65691))
% 52.62/52.41 [6570]E(f332(f332(f82(a845),f332(a107,x65701)),f332(a107,x65702)),f332(a107,f332(f332(f82(a1),x65701),x65702)))+~P1(f332(f332(f232(a1),f2(a1)),x65702))+~P1(f332(f332(f232(a1),f2(a1)),x65701))
% 52.62/52.41 [6571]E(f332(f332(f83(a845),f332(a107,x65711)),f332(a107,x65712)),f332(a107,f332(f332(f83(a1),x65711),x65712)))+~P1(f332(f332(f232(a1),f2(a1)),x65712))+~P1(f332(f332(f232(a1),f2(a1)),x65711))
% 52.62/52.41 [6572]E(f332(f332(f44(a845),f332(a107,x65721)),f332(a107,x65722)),f332(a107,f332(f332(f44(a1),x65721),x65722)))+~P1(f332(f332(f232(a1),f2(a1)),x65722))+~P1(f332(f332(f232(a1),f2(a1)),x65721))
% 52.62/52.41 [6582]E(x65821,f2(a845))+P1(f332(f332(f233(a845),f2(a845)),x65822))+~P1(f332(f332(f233(a845),f2(a845)),f332(f332(f242(a845),x65822),x65821)))
% 52.62/52.41 [6615]~P88(x66151)+E(f332(f106(x66151),x66152),f2(x66151))+~P35(x66151,f332(f106(x66151),f332(f332(f82(a1),a85),f332(f81(a1),x66152))))
% 52.62/52.41 [6616]~P88(x66161)+E(f332(f106(x66161),x66162),f2(x66161))+~P35(x66161,f332(f106(x66161),f332(f332(f82(a1),x66162),f332(f81(a1),a85))))
% 52.62/52.41 [6678]~P1(f332(f64(x66781),x66782))+~P1(f332(f64(x66781),f239(f853(x66781,a839))))+P1(f332(f64(x66781),f332(f81(f853(x66781,a839)),x66782)))
% 52.62/52.41 [6703]~P1(f332(f332(f233(a1),f2(a1)),x67032))+~P1(f332(f332(f232(a1),x67032),x67031))+P1(f332(f332(f233(a1),f2(a1)),f332(f332(f44(a1),x67031),x67032)))
% 52.62/52.41 [6704]~P1(f332(f332(f233(a1),x67042),f2(a1)))+~P1(f332(f332(f232(a1),x67041),f2(a1)))+P1(f332(f332(f232(a1),f2(a1)),f332(f332(f44(a1),x67041),x67042)))
% 52.62/52.41 [6745]~P1(f332(f332(f233(a845),f2(a845)),x67452))+~P1(f332(f332(f233(a845),f2(a845)),x67451))+P1(f332(f332(f233(a845),f2(a845)),f332(f332(f83(a845),x67451),x67452)))
% 52.62/52.41 [6746]~P1(f332(f332(f232(a1),f2(a1)),x67462))+~P1(f332(f332(f232(a1),f2(a1)),x67461))+P1(f332(f332(f232(a1),f2(a1)),f332(f332(f82(a1),x67461),x67462)))
% 52.62/52.41 [6747]~P1(f332(f332(f232(a1),f2(a1)),x67472))+~P1(f332(f332(f232(a1),f2(a1)),x67471))+P1(f332(f332(f232(a1),f2(a1)),f332(f332(f83(a1),x67471),x67472)))
% 52.62/52.41 [6748]~P1(f332(f332(f233(a1),f2(a1)),x67482))+~P1(f332(f332(f232(a1),f2(a1)),x67481))+P1(f332(f332(f232(a1),f2(a1)),f332(f332(f44(a1),x67481),x67482)))
% 52.62/52.41 [6749]~P1(f332(f332(f232(a1),f2(a1)),x67492))+~P1(f332(f332(f232(a1),f2(a1)),x67491))+P1(f332(f332(f232(a1),f2(a1)),f332(f332(f44(a1),x67491),x67492)))
% 52.62/52.41 [6818]E(x68181,f2(a1))+E(f53(a1,x68182,x68181),f2(a1))+E(f332(f332(f3(a1),f332(f81(a1),f332(f332(f44(a1),x68182),x68181))),f80(a1)),f332(f332(f44(a1),f332(f81(a1),x68182)),x68181))
% 52.62/52.41 [6878]P1(f332(f332(f233(a845),f2(a845)),x68781))+P1(f332(f332(f233(a845),f2(a845)),x68782))+~P1(f332(f332(f233(a845),f2(a845)),f332(f332(f82(a845),x68782),x68781)))
% 52.62/52.41 [6879]~P68(x68791)+P1(f332(f332(f233(x68791),f2(x68791)),x68792))+~P1(f332(f332(f233(x68791),f2(x68791)),f332(f332(f82(x68791),x68792),x68792)))
% 52.62/52.41 [6880]~P68(x68801)+P1(f332(f332(f232(x68801),f2(x68801)),x68802))+~P1(f332(f332(f232(x68801),f2(x68801)),f332(f332(f82(x68801),x68802),x68802)))
% 52.62/52.41 [6933]~P1(f332(f64(x69331),x69332))+P1(f332(f64(x69331),f239(f853(x69331,a839))))+~P1(f332(f64(x69331),f332(f81(f853(x69331,a839)),x69332)))
% 52.62/52.41 [6993]P1(f332(f332(f232(a1),x69931),f2(a1)))+~P1(f332(f332(f233(a1),x69932),f2(a1)))+~P1(f332(f332(f232(a1),f2(a1)),f332(f332(f44(a1),x69931),x69932)))
% 52.62/52.41 [6999]~P1(f332(f332(f233(a1),f2(a1)),x69991))+P1(f332(f332(f232(a1),x69991),x69992))+~P1(f332(f332(f233(a1),f2(a1)),f332(f332(f44(a1),x69992),x69991)))
% 52.62/52.41 [7000]~P1(f332(f332(f232(a1),f2(a1)),x70002))+P1(f332(f332(f232(a1),x70001),x70002))+~P1(f332(f332(f233(a1),f2(a1)),f332(f332(f44(a1),x70002),x70001)))
% 52.62/52.41 [7032]P1(f332(f332(f233(a1),f2(a1)),x70321))+~P1(f332(f332(f232(a1),f2(a1)),x70322))+~P1(f332(f332(f233(a1),f2(a1)),f332(f332(f44(a1),x70322),x70321)))
% 52.62/52.41 [7033]P1(f332(f332(f232(a1),f2(a1)),x70331))+~P1(f332(f332(f233(a1),f2(a1)),x70332))+~P1(f332(f332(f232(a1),f2(a1)),f332(f332(f44(a1),x70331),x70332)))
% 52.62/52.41 [7133]E(f211(x71331,x71332),x71331)+~E(x71332,f2(a845))+~P1(f332(f321(f852(a845,a845),a214),f332(f332(f241(a845,a845),x71331),x71332)))
% 52.62/52.41 [7362]E(f163(x73621,x73622),f115(a1))+P1(f332(f332(f232(a1),x73621),x73622))+~P1(f332(f321(f852(a1,a1),a168),f332(f332(f241(a1,a1),x73621),x73622)))
% 52.62/52.41 [7387]E(f332(f332(f241(a1,a1),f332(f106(a1),a99)),f332(f332(f82(a1),x73871),x73872)),f58(x73871,x73872))+~P1(f332(f332(f233(a1),f2(a1)),x73872))+~P1(f332(f332(f232(a1),f2(a1)),f332(f332(f82(a1),x73871),x73872)))
% 52.62/52.41 [7414]E(x74141,f2(a845))+E(f211(x74141,f53(a845,x74142,x74141)),f211(x74142,x74141))+~P1(f332(f321(f852(a845,a845),a214),f332(f332(f241(a845,a845),x74142),x74141)))
% 52.62/52.41 [7502]~P1(f332(f64(x75022),f239(f853(x75022,a839))))+~P1(f332(f64(x75021),f239(f853(x75021,a839))))+P1(f332(f64(f854(x75021,x75022)),f239(f853(f854(x75021,x75022),a839))))
% 52.62/52.41 [7503]~P1(f332(f64(x75032),f239(f853(x75032,a839))))+~P1(f332(f64(x75031),f239(f853(x75031,a839))))+P1(f332(f64(f852(x75031,x75032)),f239(f853(f852(x75031,x75032),a839))))
% 52.62/52.41 [7575]~P1(f332(f332(f233(a845),f332(a114,f2(a845))),x75751))+~P1(f332(f332(f233(a845),f332(a114,f2(a845))),x75752))+P1(f332(f332(f233(a845),x75751),f332(f332(f83(a845),x75752),x75751)))
% 52.62/52.41 [7576]~P1(f332(f332(f233(a845),f332(a114,f2(a845))),x75761))+~P1(f332(f332(f233(a845),f332(a114,f2(a845))),x75762))+P1(f332(f332(f233(a845),x75761),f332(f332(f83(a845),x75761),x75762)))
% 52.62/52.41 [7611]E(f332(f43(x76111),f239(f853(x76111,a839))),f332(a114,f2(a845)))+P1(f332(f64(x76112),f239(f853(x76112,a839))))+~P1(f332(f64(f853(x76112,x76111)),f239(f853(f853(x76112,x76111),a839))))
% 52.62/52.41 [7663]E(f55(x76631,x76632),f332(f332(f241(a1,a1),f2(a1)),x76631))+~P1(f332(f332(f233(a1),x76631),x76632))+~P1(f332(f321(f852(a1,a1),a63),f332(f332(f241(a1,a1),x76631),x76632)))
% 52.62/52.41 [7667]E(f210(f332(f81(a1),x76671),f332(f81(a1),x76672)),f210(x76671,x76672))+~P1(f332(f332(f233(a1),x76672),f2(a1)))+~P1(f332(f321(f852(a1,a1),a216),f332(f332(f241(a1,a1),x76671),x76672)))
% 52.62/52.41 [7684]E(f55(x76841,x76842),f332(f332(f241(a1,a1),f2(a1)),x76841))+~P1(f332(f332(f232(a1),x76842),f2(a1)))+~P1(f332(f321(f852(a1,a1),a63),f332(f332(f241(a1,a1),x76841),x76842)))
% 52.62/52.41 [7736]~P1(f332(f332(f233(a845),f332(a114,f2(a845))),x77362))+~P1(f332(f332(f233(a845),f332(a114,f2(a845))),x77361))+P1(f332(f332(f233(a845),f332(a114,f2(a845))),f332(f332(f83(a845),x77361),x77362)))
% 52.62/52.41 [7737]~P1(f332(f332(f232(a845),f332(a114,f2(a845))),x77371))+~P1(f332(f332(f232(a845),f332(a114,f2(a845))),x77372))+P1(f332(f332(f232(a845),f332(a114,f2(a845))),f332(f332(f83(a845),x77371),x77372)))
% 52.62/52.41 [7899]E(f332(f332(f241(a1,a1),f332(f106(a1),a99)),f332(f332(f82(a1),x78991),x78992)),f58(x78991,x78992))+~P1(f332(f332(f232(a1),x78992),f2(a1)))+~P1(f332(f321(f852(a1,a1),a60),f332(f332(f241(a1,a1),x78991),x78992)))
% 52.62/52.41 [7940]E(f332(f332(f140(a1),x79401),f163(f332(f332(f82(a1),x79401),f80(a1)),x79402)),f163(x79401,x79402))+~P1(f332(f332(f232(a1),x79401),x79402))+~P1(f332(f321(f852(a1,a1),a168),f332(f332(f241(a1,a1),x79401),x79402)))
% 52.62/52.41 [8212]E(f332(f332(f241(a1,a1),f332(f106(a1),a99)),f332(f332(f82(a1),x82121),x82122)),f58(x82121,x82122))+~P1(f332(f332(f232(a1),f2(a1)),f332(f332(f82(a1),x82121),x82122)))+~P1(f332(f321(f852(a1,a1),a60),f332(f332(f241(a1,a1),x82121),x82122)))
% 52.62/52.41 [8418]E(x84181,f115(x84182))+~P1(f332(f127(x84182),x84181))+E(f162(x84182,f332(f332(f10(a839,a839,x84182),a328),f332(f332(f9(x84182,x84182,a839),a329),f134(x84182,x84181))),x84181),f116(x84182,x84181))
% 52.62/52.41 [8495]E(f332(f332(f241(a1,a1),f332(f106(a1),a99)),f332(f332(f82(a1),f332(f106(a1),x84951)),f332(f106(a1),x84952))),f58(f332(f106(a1),x84951),f332(f106(a1),x84952)))+~P1(f332(f332(f233(a1),f2(a1)),f332(f106(a1),x84952)))+~P1(f332(f332(f232(a1),f2(a1)),f332(f332(f82(a1),f332(f106(a1),x84951)),f332(f106(a1),x84952))))
% 52.62/52.41 [8516]~P40(x85162)+~P40(x85161)+E(f332(f303(a845,a1,f102(a1)),f332(f332(f103(f853(a845,a839)),f332(f303(a1,a845,a107),x85161)),f332(f303(a1,a845,a107),x85162))),f332(f332(f103(f853(a1,a839)),x85161),x85162))
% 52.62/52.41 [8517]~P40(x85172)+~P40(x85171)+E(f332(f303(a845,a1,f102(a1)),f332(f332(f104(f853(a845,a839)),f332(f303(a1,a845,a107),x85171)),f332(f303(a1,a845,a107),x85172))),f332(f332(f104(f853(a1,a839)),x85171),x85172))
% 52.62/52.41 [9106]~P88(x91061)+~E(f332(f106(x91061),x91062),f80(x91061))+P35(x91061,f332(f106(x91061),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f81(a1),x91062))))
% 52.62/52.41 [9321]~P88(x93211)+E(f332(f106(x93211),x93212),f80(x93211))+~P35(x93211,f332(f106(x93211),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f81(a1),x93212))))
% 52.62/52.41 [9736]~P99(x97362)+P54(a845,x97362,f332(f332(f20(a845,f853(a845,a839),f853(a845,a839)),f332(f332(f10(f853(a845,f853(a839,a839)),f853(f853(a845,a839),f853(a845,a839)),a845),f20(a845,a839,a839)),f332(f332(f10(f853(a845,a839),f853(a845,f853(a839,a839)),a845),f332(f10(a839,f853(a839,a839),a845),a330)),f279(a845)))),f332(f332(f10(f853(a845,a839),f853(a845,a839),a845),f332(f10(a839,a839,a845),a328)),f332(f9(a845,a845,a839),f279(a845)))),x97361)+P1(f332(f332(f279(a845),f371(x97361,x97362)),f372(x97361,x97362)))
% 52.62/52.41 [9739]~P99(x97391)+P54(a845,x97391,f332(f332(f20(a845,f853(a845,a839),f853(a845,a839)),f332(f332(f10(f853(a845,f853(a839,a839)),f853(f853(a845,a839),f853(a845,a839)),a845),f20(a845,a839,a839)),f332(f332(f10(f853(a845,a839),f853(a845,f853(a839,a839)),a845),f332(f10(a839,f853(a839,a839),a845),a330)),f279(a845)))),f332(f332(f10(f853(a845,a839),f853(a845,a839),a845),f332(f10(a839,a839,a845),a328)),f332(f9(a845,a845,a839),f279(a845)))),x97392)+~P1(f332(f332(f279(a845),f372(x97392,x97391)),f371(x97392,x97391)))
% 52.62/52.41 [9740]~P99(x97401)+P54(a845,x97401,f332(f332(f20(a845,f853(a845,a839),f853(a845,a839)),f332(f332(f10(f853(a845,f853(a839,a839)),f853(f853(a845,a839),f853(a845,a839)),a845),f20(a845,a839,a839)),f332(f332(f10(f853(a845,a839),f853(a845,f853(a839,a839)),a845),f332(f10(a839,f853(a839,a839),a845),a330)),f279(a845)))),f332(f332(f10(f853(a845,a839),f853(a845,a839),a845),f332(f10(a839,a839,a845),a328)),f332(f9(a845,a845,a839),f279(a845)))),x97402)+~P1(f332(f332(f233(x97401),f332(x97402,f371(x97402,x97401))),f332(x97402,f372(x97402,x97401))))
% 52.62/52.41 [9829]~P99(x98291)+P52(a845,x98291,f279(a845),x98292)+~P54(a845,x98291,f332(f332(f20(a845,f853(a845,a839),f853(a845,a839)),f332(f332(f10(f853(a845,f853(a839,a839)),f853(f853(a845,a839),f853(a845,a839)),a845),f20(a845,a839,a839)),f332(f332(f10(f853(a845,a839),f853(a845,f853(a839,a839)),a845),f332(f10(a839,f853(a839,a839),a845),a330)),f279(a845)))),f332(f332(f10(f853(a845,a839),f853(a845,a839),a845),f332(f10(a839,a839,a845),a328)),f332(f9(a845,a845,a839),f279(a845)))),x98292)
% 52.62/52.41 [10028]E(x100281,f2(a1))+E(x100282,f2(a1))+E(f332(f252(a1,a1,a1,a1,f39(a1),f332(f83(a1),f84(a1,x100282))),f332(f332(f332(f98(f852(a1,a1)),f332(f332(a329,f84(a1,x100281)),f84(a1,x100282))),f61(x100281,x100282)),f332(f332(f251(a1,a1,f852(a1,a1)),f332(f332(f20(a1,f853(a1,f852(a1,a1)),f853(a1,f852(a1,a1))),f332(f332(f10(f853(a1,f853(f852(a1,a1),f852(a1,a1))),f853(f853(a1,f852(a1,a1)),f853(a1,f852(a1,a1))),a1),f20(a1,f852(a1,a1),f852(a1,a1))),f332(f332(f10(f852(a1,a1),f853(a1,f853(f852(a1,a1),f852(a1,a1))),a1),f332(f9(a1,f852(a1,a1),f853(f852(a1,a1),f852(a1,a1))),f332(f332(f10(a839,f853(f852(a1,a1),f853(f852(a1,a1),f852(a1,a1))),a1),f98(f852(a1,a1))),f332(f332(f9(a1,a1,a839),a329),f2(a1))))),f332(f332(f9(a1,a1,f852(a1,a1)),f332(f332(f10(a1,f853(a1,f852(a1,a1)),a1),f241(a1,a1)),f81(a1))),f2(a1))))),f332(f332(f9(a1,f853(a1,a1),f853(a1,f852(a1,a1))),f332(f332(f10(f853(a1,f852(a1,a1)),f853(f853(a1,a1),f853(a1,f852(a1,a1))),a1),f10(a1,f852(a1,a1),a1)),f332(f332(f10(a1,f853(a1,f852(a1,a1)),a1),f241(a1,a1)),f332(f332(f9(a1,a1,a1),f332(f332(f10(a1,f853(a1,a1),a1),f3(a1)),f81(a1))),f80(a1))))),f332(f3(a1),f332(f77(a1),x100282))))),f61(x100281,x100282)))),f54(x100281,x100282))
% 52.62/52.41 [10029]E(x100291,f2(a1))+E(x100292,f2(a1))+E(f332(f252(a1,a1,a1,a1,f39(a1),f332(f83(a1),f84(a1,x100292))),f332(f332(f332(f98(f852(a1,a1)),f332(f332(a331,f332(f332(a330,f332(f332(f233(a1),f2(a1)),x100292)),f332(f332(f232(a1),f2(a1)),x100291))),f332(f332(a330,f332(f332(f233(a1),x100292),f2(a1))),f332(f332(f233(a1),x100291),f2(a1))))),f61(x100291,x100292)),f332(f332(f251(a1,a1,f852(a1,a1)),f332(f332(f20(a1,f853(a1,f852(a1,a1)),f853(a1,f852(a1,a1))),f332(f332(f10(f853(a1,f853(f852(a1,a1),f852(a1,a1))),f853(f853(a1,f852(a1,a1)),f853(a1,f852(a1,a1))),a1),f20(a1,f852(a1,a1),f852(a1,a1))),f332(f332(f10(f852(a1,a1),f853(a1,f853(f852(a1,a1),f852(a1,a1))),a1),f332(f9(a1,f852(a1,a1),f853(f852(a1,a1),f852(a1,a1))),f332(f332(f10(a839,f853(f852(a1,a1),f853(f852(a1,a1),f852(a1,a1))),a1),f98(f852(a1,a1))),f332(f332(f9(a1,a1,a839),a329),f2(a1))))),f332(f332(f9(a1,a1,f852(a1,a1)),f332(f332(f10(a1,f853(a1,f852(a1,a1)),a1),f241(a1,a1)),f81(a1))),f2(a1))))),f332(f332(f9(a1,f853(a1,a1),f853(a1,f852(a1,a1))),f332(f332(f10(f853(a1,f852(a1,a1)),f853(f853(a1,a1),f853(a1,f852(a1,a1))),a1),f10(a1,f852(a1,a1),a1)),f332(f332(f10(a1,f853(a1,f852(a1,a1)),a1),f241(a1,a1)),f332(f332(f9(a1,a1,a1),f332(f332(f10(a1,f853(a1,a1),a1),f3(a1)),f81(a1))),f80(a1))))),f332(f3(a1),f332(f77(a1),x100292))))),f61(x100291,x100292)))),f54(x100291,x100292))
% 52.62/52.41 [5577]~P110(x55771)+~P88(x55771)+E(f332(f77(x55771),f332(f332(f242(x55771),f332(f106(x55771),a99)),x55772)),f80(x55771))
% 52.62/52.41 [6079]~P133(x60791)+~P1(f332(f332(f233(a1),x60792),f2(a1)))+E(f332(f81(x60791),f332(f102(x60791),f332(a107,f332(f81(a1),x60792)))),f332(f105(x60791),x60792))
% 52.62/52.41 [6290]P1(f332(f332(f232(a101),x62901),f80(a101)))+E(f332(f332(f82(a101),f80(a101)),f267(x62901,f332(f332(f44(a101),x62902),x62901))),f267(x62901,x62902))+P1(f332(f332(f233(a101),x62902),x62901))
% 52.62/52.41 [6363]E(x63631,f2(a1))+~E(f332(f77(a1),x63632),f80(a1))+P1(f332(f332(f279(a1),f332(f332(f83(a1),x63631),x63632)),x63631))
% 52.62/52.41 [6787]~E(x67872,f80(a845))+~P1(f332(f332(f233(a845),f2(a845)),x67871))+P1(f332(f332(f279(a845),f332(f332(f83(a845),x67871),x67872)),x67871))
% 52.62/52.41 [6788]~E(x67881,f80(a845))+~P1(f332(f332(f233(a845),f2(a845)),x67882))+P1(f332(f332(f279(a845),f332(f332(f83(a845),x67881),x67882)),x67882))
% 52.62/52.41 [6921]~P87(x69211)+~P1(f332(f332(f334(x69211),x69212),f112(x69211)))+~E(f332(f332(f82(x69211),f332(f332(f82(x69211),f80(x69211)),x69212)),x69212),f2(x69211))
% 52.62/52.41 [7034]~P1(f332(f332(f233(a1),x70341),f2(a1)))+~P1(f332(f332(f232(a1),x70342),f2(a1)))+E(f332(f240(a1,a1),f332(a59,f55(f332(f81(a1),x70341),f332(f81(a1),x70342)))),f332(f332(f44(a1),x70341),x70342))
% 52.62/52.41 [7050]~P1(f332(f332(f233(a1),x70501),f2(a1)))+~P1(f332(f332(f232(a1),x70502),f2(a1)))+E(f332(f250(a1,a1),f332(a59,f55(f332(f81(a1),x70501),f332(f81(a1),x70502)))),f53(a1,x70501,x70502))
% 52.62/52.41 [7058]~P1(f332(f332(f233(a1),x70582),f2(a1)))+E(f332(f240(a1,a1),f332(a59,f58(f332(f81(a1),x70581),f332(f81(a1),x70582)))),f332(f332(f44(a1),x70581),x70582))+~P1(f332(f332(f233(a1),f2(a1)),x70581))
% 52.62/52.41 [7062]E(x70621,f2(a1))+E(f332(f77(a1),x70622),f80(a1))+~P1(f332(f332(f279(a1),f332(f332(f83(a1),x70621),x70622)),x70621))
% 52.62/52.41 [7077]~P1(f332(f332(f233(a1),x70772),f2(a1)))+E(f332(f250(a1,a1),f332(a59,f58(f332(f81(a1),x70771),f332(f81(a1),x70772)))),f53(a1,x70771,x70772))+~P1(f332(f332(f233(a1),f2(a1)),x70771))
% 52.62/52.41 [7128]E(f332(f332(f44(a1),f332(f332(f242(a1),x71281),x71282)),x71281),f332(f332(f242(a1),x71281),f332(f332(f3(a845),x71282),f332(a114,f2(a845)))))+~P1(f332(f332(f233(a845),f2(a845)),x71282))+~P1(f332(f332(f233(a1),f2(a1)),x71281))
% 52.62/52.41 [7233]~P1(f332(f332(f233(a845),f2(a845)),x72331))+~P1(f332(f332(f233(a845),f80(a845)),x72332))+P1(f332(f332(f233(a845),f332(f332(f44(a845),x72331),x72332)),x72331))
% 52.62/52.41 [7234]~P1(f332(f332(f233(a845),f2(a845)),x72341))+~P1(f332(f332(f233(a845),f2(a845)),x72342))+P1(f332(f332(f233(a845),f332(f332(f3(a845),x72341),x72342)),x72341))
% 52.62/52.41 [7235]~P1(f332(f332(f233(a1),f2(a1)),x72351))+~P1(f332(f332(f233(a1),f80(a1)),x72352))+P1(f332(f332(f233(a1),f332(f332(f44(a1),x72351),x72352)),x72351))
% 52.62/52.41 [7394]E(x73941,f2(a845))+~E(x73942,f2(a1))+~P1(f332(f332(f233(a1),f2(a1)),f332(f332(f242(a1),f332(f77(a1),x73942)),x73941)))
% 52.62/52.41 [7432]E(x74321,f80(a845))+~P1(f332(f332(f233(a845),f2(a845)),x74322))+~P1(f332(f332(f279(a845),f332(f332(f83(a845),x74322),x74321)),x74322))
% 52.62/52.41 [7433]E(x74331,f80(a845))+~P1(f332(f332(f233(a845),f2(a845)),x74332))+~P1(f332(f332(f279(a845),f332(f332(f83(a845),x74331),x74332)),x74332))
% 52.62/52.41 [7819]~E(x78192,f115(f846(x78191)))+E(f332(f181(f846(f846(x78191))),f164(x78191,x78192)),f2(a845))+~P20(a845,f332(f142(a845),f332(f332(f143(f846(x78191),a845),f181(f846(x78191))),x78192)))
% 52.62/52.41 [8069]P1(f332(x80691,x80692))+~P1(f332(x80691,f332(a110,f575(x80691,x80692))))+~P1(f332(f332(f334(f853(f852(a845,a845),a839)),x80692),a100))
% 52.62/52.41 [8083]E(x80831,f115(f846(x80832)))+E(f332(f181(f846(x80832)),f332(f332(f152(f846(x80832)),x80831),f2(a845))),f332(f181(f846(f846(x80832))),f164(x80832,x80831)))+~P20(a845,f332(f142(a845),f332(f332(f143(f846(x80832),a845),f181(f846(x80832))),x80831)))
% 52.62/52.41 [8755]~P1(f332(f64(x87551),f332(f256(x87551),x87552)))+~P1(f332(f64(x87551),f239(f853(x87551,a839))))+P1(f332(f64(x87551),f332(f256(x87551),f332(f332(f10(a839,a839,x87551),a328),x87552))))
% 52.62/52.41 [8808]E(f332(f332(f241(a845,a845),f332(a114,f332(f332(f44(a845),f332(f332(f3(a845),x88081),x88082)),x88082))),f53(a845,f332(f332(f3(a845),x88081),x88082),x88082)),f87(f852(a845,a845),f56(x88081,x88082)))+~P1(f332(f332(f233(a845),f2(a845)),x88082))+~P1(f332(f332(f232(a845),x88082),x88081))
% 52.62/52.41 [9073]~P1(f332(f64(x90731),f332(f256(x90731),x90732)))+P1(f332(f64(x90731),f239(f853(x90731,a839))))+~P1(f332(f64(x90731),f332(f256(x90731),f332(f332(f10(a839,a839,x90731),a328),x90732))))
% 52.62/52.41 [9733]P32(x97331,x97332)+~P38(x97331,f332(f240(f853(f852(x97331,x97331),a839),f853(f852(x97331,x97331),a839)),x97332))+~P1(f332(f332(f232(f853(f852(x97331,x97331),a839)),f332(f332(f281(x97331,x97331,x97331),f332(f240(f853(f852(x97331,x97331),a839),f853(f852(x97331,x97331),a839)),x97332)),f332(f250(f853(f852(x97331,x97331),a839),f853(f852(x97331,x97331),a839)),x97332))),f332(f240(f853(f852(x97331,x97331),a839),f853(f852(x97331,x97331),a839)),x97332)))
% 52.62/52.41 [9780]E(f332(f51(f332(f106(a1),x97801)),f55(f332(f106(a1),x97802),f332(f332(f83(a1),f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f332(f106(a1),x97801)))),f55(f332(f106(a1),x97802),f332(f106(a1),x97801)))+~P1(f332(f332(f233(a1),f2(a1)),f332(f106(a1),x97801)))+P1(f332(f332(f233(a1),f332(f106(a1),x97802)),f332(f106(a1),x97801)))
% 52.62/52.41 [9786]E(f332(f51(f332(f106(a1),x97861)),f58(f332(f106(a1),x97862),f332(f332(f83(a1),f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f332(f106(a1),x97861)))),f58(f332(f106(a1),x97862),f332(f106(a1),x97861)))+~P1(f332(f332(f233(a1),f2(a1)),f332(f106(a1),x97861)))+P1(f332(f332(f232(a1),f2(a1)),f332(f332(f82(a1),f332(f106(a1),x97862)),f332(f106(a1),x97861))))
% 52.62/52.41 [9831]~E(f289(a845,f279(a845),f332(f332(f20(a845,f853(a845,a839),f853(a845,a839)),f332(f332(f10(f853(a845,f853(a839,a839)),f853(f853(a845,a839),f853(a845,a839)),a845),f20(a845,a839,a839)),f332(f332(f10(f853(a845,a839),f853(a845,f853(a839,a839)),a845),f332(f10(a839,f853(a839,a839),a845),a330)),f279(a845)))),f332(f332(f10(f853(a845,a839),f853(a845,a839),a845),f332(f10(a839,a839,a845),a328)),f332(f9(a845,a845,a839),f279(a845)))),x98312,x98311),f180(f853(a845,a839)))+~P1(f332(f332(f279(a845),x98312),x98311))+P1(f332(f332(f279(a845),x98311),x98312))
% 52.62/52.41 [9832]~E(f292(a845,f279(a845),f332(f332(f20(a845,f853(a845,a839),f853(a845,a839)),f332(f332(f10(f853(a845,f853(a839,a839)),f853(f853(a845,a839),f853(a845,a839)),a845),f20(a845,a839,a839)),f332(f332(f10(f853(a845,a839),f853(a845,f853(a839,a839)),a845),f332(f10(a839,f853(a839,a839),a845),a330)),f279(a845)))),f332(f332(f10(f853(a845,a839),f853(a845,a839),a845),f332(f10(a839,a839,a845),a328)),f332(f9(a845,a845,a839),f279(a845)))),x98322,x98321),f180(f853(a845,a839)))+~P1(f332(f332(f279(a845),x98322),x98321))+P1(f332(f332(f279(a845),x98321),x98322))
% 52.62/52.41 [9833]~E(f289(a845,f279(a845),f332(f332(f20(a845,f853(a845,a839),f853(a845,a839)),f332(f332(f10(f853(a845,f853(a839,a839)),f853(f853(a845,a839),f853(a845,a839)),a845),f20(a845,a839,a839)),f332(f332(f10(f853(a845,a839),f853(a845,f853(a839,a839)),a845),f332(f10(a839,f853(a839,a839),a845),a330)),f279(a845)))),f332(f332(f10(f853(a845,a839),f853(a845,a839),a845),f332(f10(a839,a839,a845),a328)),f332(f9(a845,a845,a839),f279(a845)))),x98332,x98331),f180(f853(a845,a839)))+~P1(f332(f332(f279(a845),x98332),x98331))+P1(f332(f332(f279(a845),x98331),x98332))
% 52.62/52.41 [9834]~E(f292(a845,f279(a845),f332(f332(f20(a845,f853(a845,a839),f853(a845,a839)),f332(f332(f10(f853(a845,f853(a839,a839)),f853(f853(a845,a839),f853(a845,a839)),a845),f20(a845,a839,a839)),f332(f332(f10(f853(a845,a839),f853(a845,f853(a839,a839)),a845),f332(f10(a839,f853(a839,a839),a845),a330)),f279(a845)))),f332(f332(f10(f853(a845,a839),f853(a845,a839),a845),f332(f10(a839,a839,a845),a328)),f332(f9(a845,a845,a839),f279(a845)))),x98342,x98341),f180(f853(a845,a839)))+~P1(f332(f332(f279(a845),x98342),x98341))+P1(f332(f332(f279(a845),x98341),x98342))
% 52.62/52.41 [7151]~P1(f332(f332(f233(a845),f2(a845)),x71512))+P1(f332(f332(f233(a845),x71511),x71512))+E(f332(a114,f332(f332(f44(a845),f332(f332(f3(a845),x71511),x71512)),x71512)),f332(f332(f44(a845),x71511),x71512))
% 52.62/52.41 [7152]~P1(f332(f332(f233(a845),f2(a845)),x71522))+P1(f332(f332(f233(a845),x71521),x71522))+E(f332(a114,f332(f332(f44(a845),f332(f332(f3(a845),x71521),x71522)),x71522)),f332(f332(f44(a845),x71521),x71522))
% 52.62/52.41 [7309]~P1(f332(f332(f233(a845),f2(a845)),x73092))+~P1(f332(f332(f232(a845),x73092),x73091))+E(f332(a114,f332(f332(f44(a845),f332(f332(f3(a845),x73091),x73092)),x73092)),f332(f332(f44(a845),x73091),x73092))
% 52.62/52.41 [8282]~P88(x82821)+~P87(x82821)+~P35(x82821,f332(f106(x82821),f332(f332(f3(a1),f332(f332(f82(a1),x82822),x82822)),a99)))
% 52.62/52.41 [8983]E(x89831,f2(a845))+E(f332(f332(f251(a845,a845,f852(a845,a845)),f332(f332(f10(a845,f853(a845,f852(a845,a845)),a845),f241(a845,a845)),a114)),f87(f852(a845,a845),f56(f332(f332(f3(a845),x89832),x89831),x89831))),f87(f852(a845,a845),f56(x89832,x89831)))+P1(f332(f332(f233(a845),x89832),x89831))
% 52.62/52.41 [9380]P1(f332(x93802,f698(x93802,x93801)))+P1(f332(x93801,f698(x93802,x93801)))+E(f332(f256(a1),f332(f332(f20(a1,a839,a839),f332(f332(f10(a839,f853(a839,a839),a1),a330),f332(f232(a1),f2(a1)))),x93801)),f332(f256(a1),f332(f332(f20(a1,a839,a839),f332(f332(f10(a839,f853(a839,a839),a1),a330),f332(f232(a1),f2(a1)))),x93802)))
% 52.62/52.41 [9384]~P1(f332(x93842,f698(x93842,x93841)))+~P1(f332(x93841,f698(x93842,x93841)))+E(f332(f256(a1),f332(f332(f20(a1,a839,a839),f332(f332(f10(a839,f853(a839,a839),a1),a330),f332(f232(a1),f2(a1)))),x93841)),f332(f256(a1),f332(f332(f20(a1,a839,a839),f332(f332(f10(a839,f853(a839,a839),a1),a330),f332(f232(a1),f2(a1)))),x93842)))
% 52.62/52.41 [9916]~P1(f332(f332(f279(a845),x99162),x99161))+P1(f332(f332(f279(a845),x99161),x99162))+P1(f332(f332(f334(a845),x99161),f287(a845,f332(f332(f20(a845,f853(a845,a839),f853(a845,a839)),f332(f332(f10(f853(a845,f853(a839,a839)),f853(f853(a845,a839),f853(a845,a839)),a845),f20(a845,a839,a839)),f332(f332(f10(f853(a845,a839),f853(a845,f853(a839,a839)),a845),f332(f10(a839,f853(a839,a839),a845),a330)),f279(a845)))),f332(f332(f10(f853(a845,a839),f853(a845,a839),a845),f332(f10(a839,a839,a845),a328)),f332(f9(a845,a845,a839),f279(a845)))),x99162)))
% 52.62/52.41 [9917]~P1(f332(f332(f279(a845),x99172),x99171))+P1(f332(f332(f279(a845),x99171),x99172))+P1(f332(f332(f334(a845),x99172),f290(a845,f332(f332(f20(a845,f853(a845,a839),f853(a845,a839)),f332(f332(f10(f853(a845,f853(a839,a839)),f853(f853(a845,a839),f853(a845,a839)),a845),f20(a845,a839,a839)),f332(f332(f10(f853(a845,a839),f853(a845,f853(a839,a839)),a845),f332(f10(a839,f853(a839,a839),a845),a330)),f279(a845)))),f332(f332(f10(f853(a845,a839),f853(a845,a839),a845),f332(f10(a839,a839,a845),a328)),f332(f9(a845,a845,a839),f279(a845)))),x99171)))
% 52.62/52.41 [7531]~P88(x75311)+~P63(x75311)+E(f332(f332(f283(x75311),x75312),f332(f106(x75311),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))),x75312)
% 52.62/52.41 [7532]~P88(x75321)+~P63(x75321)+E(f332(f332(f283(x75321),x75322),f332(f106(x75321),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))),x75322)
% 52.62/52.41 [9105]~P88(x91051)+~E(f332(f106(x91051),x91052),f80(x91051))+P35(x91051,f332(f106(x91051),f332(f332(f82(a1),x91052),f332(f81(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))))
% 52.62/52.41 [9260]~P120(x92601)+~E(x92602,f2(x92601))+E(f332(f332(f242(x92601),x92602),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f2(x92601))
% 52.62/52.41 [9261]~P120(x92611)+~E(x92612,f80(x92611))+E(f332(f332(f242(x92611),x92612),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f80(x92611))
% 52.62/52.41 [9274]~P120(x92741)+~E(x92742,f332(f81(x92741),f80(x92741)))+E(f332(f332(f242(x92741),x92742),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f80(x92741))
% 52.62/52.41 [9294]~P76(x92941)+~P89(x92941)+E(f332(f332(f242(x92941),f332(f106(x92941),x92942)),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f332(f332(f83(x92941),f332(f106(x92941),x92942)),f332(f106(x92941),x92942)))
% 52.62/52.41 [9322]~P88(x93221)+E(f332(f106(x93221),x93222),f80(x93221))+~P35(x93221,f332(f106(x93221),f332(f332(f82(a1),x93222),f332(f81(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))))
% 52.62/52.41 [9432]~P120(x94322)+E(x94321,f2(x94322))+~E(f332(f332(f242(x94322),x94321),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f2(x94322))
% 52.62/52.41 [9673]~P110(x96732)+E(x96731,f2(x96732))+P1(f332(f332(f233(x96732),f2(x96732)),f332(f332(f242(x96732),x96731),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))))
% 52.62/52.41 [9732]~P110(x97322)+~E(x97321,f2(x97322))+~P1(f332(f332(f233(x97322),f2(x97322)),f332(f332(f242(x97322),x97321),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))))
% 52.62/52.41 [9771]P1(f332(f332(f232(a1),x97711),f2(a1)))+P1(f332(f332(f233(a1),x97712),x97711))+E(f332(f51(x97711),f55(x97712,f332(f332(f83(a1),f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),x97711))),f55(x97712,x97711))
% 52.62/52.41 [9772]~P1(f332(f332(f233(a1),f2(a1)),x97721))+P1(f332(f332(f233(a1),x97722),x97721))+E(f332(f51(x97721),f55(x97722,f332(f332(f83(a1),f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),x97721))),f55(x97722,x97721))
% 52.62/52.41 [9773]P1(f332(f332(f232(a1),x97731),f2(a1)))+P1(f332(f332(f232(a1),f2(a1)),f332(f332(f82(a1),x97732),x97731)))+E(f332(f51(x97731),f58(x97732,f332(f332(f83(a1),f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),x97731))),f58(x97732,x97731))
% 52.62/52.41 [9774]~P1(f332(f332(f233(a1),f2(a1)),x97741))+P1(f332(f332(f232(a1),f2(a1)),f332(f332(f82(a1),x97742),x97741)))+E(f332(f51(x97741),f58(x97742,f332(f332(f83(a1),f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),x97741))),f58(x97742,x97741))
% 52.62/52.41 [9775]~P2(x97751)+~P1(f332(f332(f232(a1),f2(a1)),x97752))+E(f332(f102(x97751),f332(a107,f332(f332(f83(a1),f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),x97752))),f332(f332(f82(x97751),f332(f102(x97751),f332(a107,x97752))),f332(f102(x97751),f332(a107,x97752))))
% 52.62/52.41 [6106]P144(x61061,x61062)+~P142(x61061,x61063)+~P41(a857,x61063,a858,x61062)
% 52.62/52.41 [6107]P143(x61071,x61072)+~P144(x61071,x61073)+~P41(a859,x61073,a858,x61072)
% 52.62/52.41 [4931]~P140(x49311,x49312,x49313)+~E(x49313,f2(a1))+P1(f332(x49311,x49312))
% 52.62/52.41 [5057]~P100(x50571)+~P20(x50571,x50573)+P20(x50571,f151(x50571,x50572,x50573))
% 52.62/52.41 [5058]~P100(x50581)+~P20(x50581,x50583)+P20(x50581,f162(x50581,x50582,x50583))
% 52.62/52.41 [4643]~P69(x46432)+~E(x46433,f332(f81(x46432),x46431))+E(x46431,f332(f81(x46432),x46433))
% 52.62/52.41 [4644]~P69(x46442)+~E(x46443,f332(f81(x46442),x46441))+E(x46441,f332(f81(x46442),x46443))
% 52.62/52.41 [4645]~P69(x46451)+~E(f332(f81(x46451),x46453),x46452)+E(f332(f81(x46451),x46452),x46453)
% 52.62/52.41 [4646]~P69(x46461)+~E(f332(f81(x46461),x46463),x46462)+E(f332(f81(x46461),x46462),x46463)
% 52.62/52.41 [4717]~P86(x47173)+E(x47171,x47172)+~E(f332(f102(x47173),x47171),f332(f102(x47173),x47172))
% 52.62/52.41 [4718]~P87(x47183)+E(x47181,x47182)+~E(f332(f105(x47183),x47181),f332(f105(x47183),x47182))
% 52.62/52.41 [4719]~P69(x47193)+E(x47191,x47192)+~E(f332(f81(x47193),x47191),f332(f81(x47193),x47192))
% 52.62/52.41 [4720]~P90(x47203)+E(x47201,x47202)+~E(f332(f81(x47203),x47201),f332(f81(x47203),x47202))
% 52.62/52.41 [4721]~P100(x47213)+E(x47211,x47212)+~E(f332(f257(x47213),x47211),f332(f257(x47213),x47212))
% 52.62/52.41 [4722]~P100(x47223)+E(x47221,x47222)+~E(f332(f296(x47223),x47221),f332(f296(x47223),x47222))
% 52.62/52.41 [4723]~P100(x47233)+E(x47231,x47232)+~E(f332(f293(x47233),x47231),f332(f293(x47233),x47232))
% 52.62/52.41 [4724]~P100(x47243)+E(x47241,x47242)+~E(f332(f258(x47243),x47241),f332(f258(x47243),x47242))
% 52.62/52.41 [4954]~P141(x49541,x49543,x49542)+~E(x49542,f2(a1))+P1(f332(x49541,f2(a1)))
% 52.62/52.41 [4993]~E(x49931,f2(a845))+E(f380(x49931,x49932,x49933),f180(f853(x49933,a839)))+~E(f332(f43(x49933),x49932),f332(a114,x49931))
% 52.62/52.41 [5141]~E(x51412,f2(a845))+E(f332(f240(a845,a845),x51411),f2(a845))+~P1(f332(f56(x51413,x51412),x51411))
% 52.62/52.41 [5185]P1(f332(x51851,x51852))+~E(x51853,f332(f102(a1),x51852))+~P1(f332(x51851,f332(a107,x51853)))
% 52.62/52.41 [5639]~E(x56393,f2(a845))+~P1(f332(x56391,x56392))+P1(f332(x56391,f53(a845,x56392,x56393)))
% 52.62/52.41 [5785]~P1(f332(a26,x57853))+~P1(f332(a26,x57852))+P1(f332(a26,f33(x57851,x57852,x57853)))
% 52.62/52.41 [5786]~P1(f332(a26,x57863))+~P1(f332(a26,x57862))+P1(f332(a26,f33(x57861,x57862,x57863)))
% 52.62/52.41 [6061]~E(x60613,f2(a845))+P1(f332(x60611,x60612))+~P1(f332(x60611,f53(a845,x60612,x60613)))
% 52.62/52.41 [6771]E(x67711,f2(a845))+~P1(f332(x67712,f799(x67711,x67713,x67712)))+P1(f332(x67712,f53(a845,x67713,x67711)))
% 52.62/52.41 [6884]~P11(x68841)+~P1(f332(f332(f232(x68841),x68842),f671(x68843,x68842,x68841)))+P1(f332(f332(f232(x68841),x68842),f46(x68841,x68843)))
% 52.62/52.41 [6886]~P1(f332(x68861,x68862))+~P1(f332(x68861,f799(x68863,x68862,x68861)))+P1(f332(x68861,f53(a845,x68862,x68863)))
% 52.62/52.41 [6986]E(x69861,f115(x69862))+E(f332(f332(f140(x69862),f748(x69863,x69861,x69862)),f755(x69863,x69861,x69862)),x69861)+~P1(f332(f332(f334(f846(x69862)),x69861),f149(x69862,x69863)))
% 52.62/52.41 [7020]~P133(x70201)+~P1(f332(f332(f334(x70201),x70202),f112(x70201)))+P1(f332(f332(f334(x70201),f332(f332(f242(x70201),x70202),x70203)),f112(x70201)))
% 52.62/52.41 [7361]P38(x73611,x73612)+~P1(f332(f332(f334(x73611),x73613),f682(x73612,x73611)))+P1(f332(f332(f334(x73611),f697(x73612,x73611,x73613)),f682(x73612,x73611)))
% 52.62/52.41 [7637]E(x76371,f115(x76372))+~P1(f332(f332(f334(f846(x76372)),x76371),f149(x76372,x76373)))+P1(f332(f332(f334(f846(x76372)),f755(x76373,x76371,x76372)),f149(x76372,x76373)))
% 52.62/52.41 [7687]E(x76871,f2(a845))+E(f332(f332(f82(a845),f332(f332(f83(a845),x76871),f801(x76871,x76872,x76873))),f799(x76871,x76872,x76873)),x76872)+P1(f332(x76873,f53(a845,x76872,x76871)))
% 52.62/52.41 [7730]~P1(f332(x77303,x77302))+E(f332(f332(f82(a845),f332(f332(f83(a845),x77301),f801(x77301,x77302,x77303))),f799(x77301,x77302,x77303)),x77302)+P1(f332(x77303,f53(a845,x77302,x77301)))
% 52.62/52.41 [7874]P1(f332(f332(f233(a1),x78741),f789(x78742,x78743,x78741)))+P1(f332(f332(x78743,f332(f332(f44(a1),x78742),x78741)),f53(a1,x78742,x78741)))+~P1(f332(f332(f233(a1),x78741),f2(a1)))
% 52.62/52.41 [8140]P1(f332(f332(x81402,f332(f332(f44(a1),x81401),x81403)),f53(a1,x81401,x81403)))+~P1(f332(f332(f233(a1),x81403),f2(a1)))+P1(f332(f332(f232(a1),f789(x81401,x81402,x81403)),f2(a1)))
% 52.62/52.41 [8319]E(f332(f332(f82(a1),f332(f332(f83(a1),x83191),f792(x83192,x83193,x83191))),f789(x83192,x83193,x83191)),x83192)+P1(f332(f332(x83193,f332(f332(f44(a1),x83192),x83191)),f53(a1,x83192,x83191)))+~P1(f332(f332(f233(a1),x83191),f2(a1)))
% 52.62/52.41 [8554]~P1(f332(f332(x85541,f792(x85542,x85541,x85543)),f789(x85542,x85541,x85543)))+P1(f332(f332(x85541,f332(f332(f44(a1),x85542),x85543)),f53(a1,x85542,x85543)))+~P1(f332(f332(f233(a1),x85543),f2(a1)))
% 52.62/52.41 [8765]~P100(x87651)+~P20(x87651,x87653)+P20(x87651,f139(x87651,x87651,f7(x87651),x87652,x87653))
% 52.62/52.41 [9210]~P119(x92102)+E(x92101,f2(x92102))+~P1(f332(f332(f232(x92102),f332(f332(f82(x92102),f332(f332(f83(x92102),x92103),x92103)),f332(f332(f83(x92102),x92101),x92101))),f2(x92102)))
% 52.62/52.41 [9211]~P119(x92112)+E(x92111,f2(x92112))+~P1(f332(f332(f232(x92112),f332(f332(f82(x92112),f332(f332(f83(x92112),x92111),x92111)),f332(f332(f83(x92112),x92113),x92113))),f2(x92112)))
% 52.62/52.41 [9970]~P110(x99701)+~P1(f332(f332(f233(x99701),x99702),f2(x99701)))+P1(f332(f332(f233(x99701),f332(f332(f242(x99701),x99702),f332(a114,f332(f332(f83(a845),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),x99703)))),f2(x99701)))
% 52.62/52.41 [9980]~P110(x99802)+E(x99801,f2(x99802))+~P1(f332(f332(f232(x99802),f332(f332(f82(x99802),f332(f332(f242(x99802),x99803),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))),f332(f332(f242(x99802),x99801),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))))),f2(x99802)))
% 52.62/52.41 [9981]~P110(x99812)+E(x99811,f2(x99812))+~P1(f332(f332(f232(x99812),f332(f332(f82(x99812),f332(f332(f242(x99812),x99811),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))),f332(f332(f242(x99812),x99813),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))))),f2(x99812)))
% 52.62/52.41 [4675]~E(x46752,x46753)+~P69(x46751)+E(f332(f332(f3(x46751),x46752),x46753),f2(x46751))
% 52.62/52.41 [4676]~E(x46762,x46763)+~P8(x46761)+E(f332(f332(f3(x46761),x46762),x46763),f2(x46761))
% 52.62/52.41 [4689]~P137(x46891)+~E(x46893,f2(x46891))+E(f332(f332(f82(x46891),x46892),x46893),x46892)
% 52.62/52.41 [4704]~P134(x47041)+~E(x47043,f2(x47041))+E(f332(f332(f83(x47041),x47042),x47043),f2(x47041))
% 52.62/52.41 [4705]~P134(x47051)+~E(x47052,f2(x47051))+E(f332(f332(f83(x47051),x47052),x47053),f2(x47051))
% 52.62/52.41 [4725]~E(x47253,f115(x47251))+~E(x47252,f115(x47251))+E(f332(f332(f125(x47251),x47252),x47253),f115(x47251))
% 52.62/52.41 [4726]~E(x47263,f115(x47261))+~E(x47262,f115(x47261))+E(f332(f332(f125(x47261),x47262),x47263),f115(x47261))
% 52.62/52.41 [4809]~P137(x48092)+E(x48091,f2(x48092))+~E(f332(f332(f82(x48092),x48093),x48091),x48093)
% 52.62/52.41 [4810]~P69(x48101)+~E(x48102,f332(f81(x48101),x48103))+E(f332(f332(f82(x48101),x48102),x48103),f2(x48101))
% 52.62/52.41 [4817]E(x48171,f115(x48172))+E(x48173,f2(a845))+~E(f332(f332(f159(x48172),x48173),x48171),f115(x48172))
% 52.62/52.41 [4825]~P69(x48253)+E(x48251,x48252)+~E(f332(f332(f3(x48253),x48251),x48252),f2(x48253))
% 52.62/52.41 [4826]~P8(x48263)+E(x48261,x48262)+~E(f332(f332(f3(x48263),x48261),x48262),f2(x48263))
% 52.62/52.41 [4835]~P120(x48352)+E(x48351,f2(x48352))+~E(f332(f332(f242(x48352),x48351),x48353),f2(x48352))
% 52.62/52.41 [4836]~P94(x48362)+E(x48361,f239(x48362))+~E(f332(f332(f104(x48362),x48363),x48361),f239(x48362))
% 52.62/52.41 [4837]~P94(x48372)+E(x48371,f239(x48372))+~E(f332(f332(f104(x48372),x48371),x48373),f239(x48372))
% 52.62/52.41 [4838]~P95(x48382)+E(x48381,f180(x48382))+~E(f332(f332(f103(x48382),x48383),x48381),f180(x48382))
% 52.62/52.41 [4839]~P95(x48392)+E(x48391,f180(x48392))+~E(f332(f332(f103(x48392),x48391),x48393),f180(x48392))
% 52.62/52.41 [4904]~P69(x49042)+E(x49041,f332(f81(x49042),x49043))+~E(f332(f332(f82(x49042),x49041),x49043),f2(x49042))
% 52.62/52.41 [4905]~P69(x49051)+E(f332(f81(x49051),x49052),x49053)+~E(f332(f332(f82(x49051),x49052),x49053),f2(x49051))
% 52.62/52.41 [4906]~E(x49062,x49063)+~P99(x49061)+P1(f332(f332(f232(x49061),x49062),x49063))
% 52.62/52.41 [4907]~E(x49072,x49073)+~P99(x49071)+P1(f332(f332(f232(x49071),x49072),x49073))
% 52.62/52.41 [4908]~E(x49082,x49083)+~P99(x49081)+P1(f332(f332(f232(x49081),x49082),x49083))
% 52.62/52.41 [4909]~E(x49092,x49093)+~P103(x49091)+P1(f332(f332(f232(x49091),x49092),x49093))
% 52.62/52.41 [5007]~P111(x50071)+~E(x50072,f332(f81(x50071),x50073))+E(f332(f332(f83(x50071),x50072),x50072),f332(f332(f83(x50071),x50073),x50073))
% 52.62/52.41 [5015]~P100(x50151)+~P20(x50151,x50153)+P20(x50151,f332(f332(f159(x50151),x50152),x50153))
% 52.62/52.41 [5016]~P100(x50161)+~P20(x50161,x50163)+P20(x50161,f332(f332(f128(x50161),x50162),x50163))
% 52.62/52.41 [5054]E(x50541,x50542)+E(x50543,f2(a845))+~E(f332(f332(f83(a845),x50543),x50541),f332(f332(f83(a845),x50543),x50542))
% 52.62/52.41 [5055]E(x50551,x50552)+E(x50553,f2(a845))+~E(f332(f332(f83(a845),x50553),x50551),f332(f332(f83(a845),x50553),x50552))
% 52.62/52.41 [5056]E(x50561,x50562)+E(x50563,f2(a845))+~E(f332(f332(f83(a845),x50561),x50563),f332(f332(f83(a845),x50562),x50563))
% 52.62/52.41 [5132]~E(x51322,x51323)+~P99(x51321)+E(f295(x51321,x51322,x51323),f332(f332(f302(x51321),x51322),f180(f853(x51321,a839))))
% 52.62/52.41 [5173]~P110(x51731)+~E(f332(f77(x51731),x51732),f332(f77(x51731),x51733))+P1(f332(f332(f279(x51731),x51732),x51733))
% 52.62/52.41 [5177]~E(x51771,x51772)+~P99(x51773)+~P1(f332(f332(f233(x51773),x51771),x51772))
% 52.62/52.41 [5178]~E(x51781,x51782)+~P99(x51783)+~P1(f332(f332(f233(x51783),x51781),x51782))
% 52.62/52.41 [5179]~E(x51791,x51792)+~P99(x51793)+~P1(f332(f332(f233(x51793),x51791),x51792))
% 52.62/52.41 [5180]~E(x51801,x51802)+~P100(x51803)+~P1(f332(f332(f233(x51803),x51801),x51802))
% 52.62/52.41 [5181]~E(x51811,x51812)+~P100(x51813)+~P1(f332(f332(f233(x51813),x51811),x51812))
% 52.62/52.41 [5182]~E(x51821,x51822)+~P99(x51823)+~P1(f332(f332(f233(x51823),x51821),x51822))
% 52.62/52.41 [5183]~E(x51831,x51832)+~P100(x51833)+~P1(f332(f332(f233(x51833),x51831),x51832))
% 52.62/52.41 [5189]~P99(x51891)+E(f332(f294(x51891,x51892),x51893),f180(f853(x51891,a839)))+P1(f332(f332(f233(x51891),x51892),x51893))
% 52.62/52.41 [5190]~P99(x51901)+E(f332(f294(x51901,x51902),x51903),f180(f853(x51901,a839)))+P1(f332(f332(f233(x51901),x51902),x51903))
% 52.62/52.41 [5236]~P99(x52361)+E(f295(x52361,x52362,x52363),f180(f853(x52361,a839)))+P1(f332(f332(f232(x52361),x52362),x52363))
% 52.62/52.41 [5237]~P99(x52371)+E(f297(x52371,x52372,x52373),f180(f853(x52371,a839)))+P1(f332(f332(f233(x52371),x52372),x52373))
% 52.62/52.41 [5238]~P99(x52381)+E(f180(f853(x52381,a839)),f295(x52381,x52382,x52383))+P1(f332(f332(f232(x52381),x52382),x52383))
% 52.62/52.41 [5239]~P99(x52391)+E(f180(f853(x52391,a839)),f297(x52391,x52392,x52393))+P1(f332(f332(f233(x52391),x52392),x52393))
% 52.62/52.41 [5247]~P100(x52471)+~E(f332(f332(f236(x52471),x52472),x52473),x52472)+P1(f332(f332(f232(x52471),x52472),x52473))
% 52.62/52.41 [5248]~P100(x52481)+~E(f332(f332(f179(x52481),x52482),x52483),x52483)+P1(f332(f332(f232(x52481),x52482),x52483))
% 52.62/52.41 [5249]~P92(x52491)+~E(f332(f332(f103(x52491),x52492),x52493),x52493)+P1(f332(f332(f232(x52491),x52492),x52493))
% 52.62/52.41 [5250]~P98(x52501)+~E(f332(f332(f104(x52501),x52502),x52503),x52502)+P1(f332(f332(f232(x52501),x52502),x52503))
% 52.62/52.41 [5265]~P100(x52651)+P20(x52651,x52652)+~P20(x52651,f332(f332(f140(x52651),x52653),x52652))
% 52.62/52.41 [5266]~P100(x52661)+P20(x52661,x52662)+~P20(x52661,f332(f332(f140(x52661),x52663),x52662))
% 52.62/52.41 [5267]~P100(x52671)+P20(x52671,x52672)+~P20(x52671,f332(f332(f125(x52671),x52673),x52672))
% 52.62/52.41 [5268]~P100(x52681)+P20(x52681,x52682)+~P20(x52681,f332(f332(f125(x52681),x52682),x52683))
% 52.62/52.41 [5273]~P9(x52731)+~E(f53(x52731,x52733,x52732),f2(x52731))+P1(f332(f332(f279(x52731),x52732),x52733))
% 52.62/52.41 [5332]~P100(x53321)+P1(f332(f332(f232(x53321),x53323),x53322))+P1(f332(f332(f233(x53321),x53322),x53323))
% 52.62/52.41 [5333]~P100(x53331)+P1(f332(f332(f232(x53331),x53333),x53332))+P1(f332(f332(f233(x53331),x53332),x53333))
% 52.62/52.41 [5334]~P100(x53341)+P1(f332(f332(f232(x53341),x53343),x53342))+P1(f332(f332(f233(x53341),x53342),x53343))
% 52.62/52.41 [5335]~P100(x53351)+P1(f332(f332(f232(x53351),x53353),x53352))+P1(f332(f332(f233(x53351),x53352),x53353))
% 52.62/52.41 [5336]~P100(x53361)+P1(f332(f332(f232(x53361),x53363),x53362))+P1(f332(f332(f233(x53361),x53362),x53363))
% 52.62/52.41 [5337]~P100(x53371)+P1(f332(f332(f232(x53371),x53373),x53372))+P1(f332(f332(f232(x53371),x53372),x53373))
% 52.62/52.41 [5338]~P100(x53381)+P1(f332(f332(f232(x53381),x53383),x53382))+P1(f332(f332(f232(x53381),x53382),x53383))
% 52.62/52.42 [5377]~P100(x53771)+E(f332(f332(f236(x53771),x53772),x53773),x53773)+~P1(f332(f332(f232(x53771),x53773),x53772))
% 52.62/52.42 [5378]~P100(x53781)+E(f332(f332(f236(x53781),x53782),x53783),x53782)+~P1(f332(f332(f232(x53781),x53782),x53783))
% 52.62/52.42 [5379]~P100(x53791)+E(f332(f332(f236(x53791),x53792),x53793),x53792)+~P1(f332(f332(f232(x53791),x53792),x53793))
% 52.62/52.42 [5380]~P100(x53801)+E(f332(f332(f179(x53801),x53802),x53803),x53802)+~P1(f332(f332(f232(x53801),x53803),x53802))
% 52.62/52.42 [5381]~P100(x53811)+E(f332(f332(f179(x53811),x53812),x53813),x53813)+~P1(f332(f332(f232(x53811),x53812),x53813))
% 52.62/52.42 [5382]~P100(x53821)+E(f332(f332(f179(x53821),x53822),x53823),x53823)+~P1(f332(f332(f232(x53821),x53822),x53823))
% 52.62/52.42 [5383]~P92(x53831)+E(f332(f332(f103(x53831),x53832),x53833),x53832)+~P1(f332(f332(f232(x53831),x53833),x53832))
% 52.62/52.42 [5384]~P92(x53841)+E(f332(f332(f103(x53841),x53842),x53843),x53843)+~P1(f332(f332(f232(x53841),x53842),x53843))
% 52.62/52.42 [5385]~P92(x53851)+E(f332(f332(f103(x53851),x53852),x53853),x53853)+~P1(f332(f332(f232(x53851),x53852),x53853))
% 52.62/52.42 [5386]~P98(x53861)+E(f332(f332(f104(x53861),x53862),x53863),x53863)+~P1(f332(f332(f232(x53861),x53863),x53862))
% 52.62/52.42 [5387]~P98(x53871)+E(f332(f332(f104(x53871),x53872),x53873),x53872)+~P1(f332(f332(f232(x53871),x53872),x53873))
% 52.62/52.42 [5388]~P98(x53881)+E(f332(f332(f104(x53881),x53882),x53883),x53882)+~P1(f332(f332(f232(x53881),x53882),x53883))
% 52.62/52.42 [5395]~P113(x53952)+E(x53951,f2(x53952))+E(f332(f332(f283(x53952),f332(f81(x53952),x53953)),f332(f81(x53952),x53951)),f332(f332(f283(x53952),x53953),x53951))
% 52.62/52.42 [5401]~P9(x54011)+E(f53(x54011,x54012,x54013),f2(x54011))+~P1(f332(f332(f279(x54011),x54013),x54012))
% 52.62/52.42 [5402]~P9(x54021)+E(f53(x54021,x54022,x54023),f2(x54021))+~P1(f332(f332(f279(x54021),x54023),x54022))
% 52.62/52.42 [5442]~P99(x54421)+E(f332(f294(x54421,x54422),x54423),f180(f853(x54421,a839)))+~P1(f332(f332(f232(x54421),x54423),x54422))
% 52.62/52.42 [5471]~P99(x54711)+E(f295(x54711,x54712,x54713),f180(f853(x54711,a839)))+~P1(f332(f332(f233(x54711),x54713),x54712))
% 52.62/52.42 [5472]~P99(x54721)+E(f297(x54721,x54722,x54723),f180(f853(x54721,a839)))+~P1(f332(f332(f232(x54721),x54723),x54722))
% 52.62/52.42 [5473]~P99(x54731)+E(f298(x54731,x54732,x54733),f180(f853(x54731,a839)))+~P1(f332(f332(f232(x54731),x54733),x54732))
% 52.62/52.42 [5522]~E(f332(f332(f3(a845),x55221),x55223),x55222)+E(x55221,f332(f332(f82(a845),x55222),x55223))+~P1(f332(f332(f232(a845),x55223),x55221))
% 52.62/52.42 [5523]~E(x55231,f332(f332(f82(a845),x55233),x55232))+E(f332(f332(f3(a845),x55231),x55232),x55233)+~P1(f332(f332(f232(a845),x55232),x55231))
% 52.62/52.42 [5566]~P1(f332(x55661,x55663))+P1(f332(x55661,f794(x55661,x55662)))+~P1(f332(f332(f232(a845),x55663),x55662))
% 52.62/52.42 [5567]~P1(f332(x55671,x55673))+P1(f332(x55671,f339(x55671,x55672)))+~P1(f332(f332(f233(a845),x55673),x55672))
% 52.62/52.42 [5574]~P99(x55741)+~E(f332(f294(x55741,x55742),x55743),f180(f853(x55741,a839)))+~P1(f332(f332(f233(x55741),x55742),x55743))
% 52.62/52.42 [5575]~P99(x55751)+~E(f332(f294(x55751,x55752),x55753),f180(f853(x55751,a839)))+~P1(f332(f332(f233(x55751),x55752),x55753))
% 52.62/52.42 [5578]~P99(x55781)+~P1(f332(f332(f233(x55781),x55782),x55783))+P1(f332(f332(f232(x55781),x55782),x55783))
% 52.62/52.42 [5579]~P99(x55791)+~P1(f332(f332(f233(x55791),x55792),x55793))+P1(f332(f332(f232(x55791),x55792),x55793))
% 52.62/52.42 [5580]~P103(x55801)+~P1(f332(f332(f233(x55801),x55802),x55803))+P1(f332(f332(f232(x55801),x55802),x55803))
% 52.62/52.42 [5581]~P103(x55811)+~P1(f332(f332(f233(x55811),x55812),x55813))+P1(f332(f332(f232(x55811),x55812),x55813))
% 52.62/52.42 [5694]~P99(x56941)+~E(f295(x56941,x56942,x56943),f180(f853(x56941,a839)))+~P1(f332(f332(f232(x56941),x56942),x56943))
% 52.62/52.42 [5695]~P99(x56951)+~E(f297(x56951,x56952,x56953),f180(f853(x56951,a839)))+~P1(f332(f332(f233(x56951),x56952),x56953))
% 52.62/52.42 [5696]~P99(x56961)+~E(f180(f853(x56961,a839)),f295(x56961,x56962,x56963))+~P1(f332(f332(f232(x56961),x56962),x56963))
% 52.62/52.42 [5697]~P99(x56971)+~E(f180(f853(x56971,a839)),f297(x56971,x56972,x56973))+~P1(f332(f332(f233(x56971),x56972),x56973))
% 52.62/52.42 [5710]P1(f332(x57101,x57102))+~P1(f332(x57101,f795(x57101,x57103)))+~P1(f332(f332(f232(a845),x57102),x57103))
% 52.62/52.42 [5711]P1(f332(x57111,x57112))+~P1(f332(x57111,f342(x57111,x57113)))+~P1(f332(f332(f233(a845),x57112),x57113))
% 52.62/52.42 [5719]~E(x57191,f332(a114,x57193))+P1(f332(f332(f233(a845),x57191),f332(a114,x57192)))+~P1(f332(f332(f233(a845),x57193),x57192))
% 52.62/52.42 [5735]E(x57351,x57352)+~E(f332(f332(f83(a845),x57353),x57351),f332(f332(f83(a845),x57353),x57352))+~P1(f332(f332(f233(a845),f2(a845)),x57353))
% 52.62/52.42 [5796]E(f332(x57961,f412(x57961,x57962,x57963)),f80(a845))+~E(f332(f332(f8(x57963,a845),x57961),x57962),f80(a845))+~P1(f332(f64(x57963),x57962))
% 52.62/52.42 [5806]~P11(x58061)+P1(f332(f332(f232(x58061),x58062),f45(x58061,x58063)))+~P1(f332(f332(f334(x58061),x58062),x58063))
% 52.62/52.42 [5830]~P99(x58301)+~P1(f332(f332(f233(x58301),x58303),x58302))+~P1(f332(f332(f233(x58301),x58302),x58303))
% 52.62/52.42 [5831]~P103(x58311)+~P1(f332(f332(f233(x58311),x58313),x58312))+~P1(f332(f332(f233(x58311),x58312),x58313))
% 52.62/52.42 [5832]~P103(x58321)+~P1(f332(f332(f233(x58321),x58323),x58322))+~P1(f332(f332(f233(x58321),x58322),x58323))
% 52.62/52.42 [5833]~P103(x58331)+~P1(f332(f332(f233(x58331),x58333),x58332))+~P1(f332(f332(f233(x58331),x58332),x58333))
% 52.62/52.42 [5834]~P103(x58341)+~P1(f332(f332(f233(x58341),x58343),x58342))+~P1(f332(f332(f233(x58341),x58342),x58343))
% 52.62/52.42 [5835]~P103(x58351)+~P1(f332(f332(f232(x58351),x58353),x58352))+~P1(f332(f332(f233(x58351),x58352),x58353))
% 52.62/52.42 [5836]~P100(x58361)+~P1(f332(f332(f233(x58361),x58363),x58362))+~P1(f332(f332(f233(x58361),x58362),x58363))
% 52.62/52.42 [5837]~P100(x58371)+~P1(f332(f332(f232(x58371),x58373),x58372))+~P1(f332(f332(f233(x58371),x58372),x58373))
% 52.62/52.42 [5838]~P100(x58381)+~P1(f332(f332(f232(x58381),x58383),x58382))+~P1(f332(f332(f233(x58381),x58382),x58383))
% 52.62/52.42 [5839]~P100(x58391)+~P1(f332(f332(f232(x58391),x58393),x58392))+~P1(f332(f332(f233(x58391),x58392),x58393))
% 52.62/52.42 [5858]~E(x58582,x58583)+~E(x58581,x58582)+E(f282(a845,f279(a845),x58581,x58582),f332(f332(f302(a845),x58583),f180(f853(a845,a839))))
% 52.62/52.42 [5866]~E(f332(x58662,f413(x58662,x58663,x58661)),f2(a845))+E(f332(f332(f8(x58661,a845),x58662),x58663),f2(a845))+~P1(f332(f64(x58661),x58663))
% 52.62/52.42 [5867]~E(f332(x58672,f449(x58672,x58673,x58671)),f80(a845))+E(f332(f332(f11(x58671,a845),x58672),x58673),f80(a845))+~P1(f332(f64(x58671),x58673))
% 52.62/52.42 [5881]~P102(x58811)+~P1(f332(f332(f233(x58811),x58813),x58812))+P1(f332(f332(f334(x58811),x58812),f332(f296(x58811),x58813)))
% 52.62/52.42 [5882]~P102(x58821)+~P1(f332(f332(f232(x58821),x58823),x58822))+P1(f332(f332(f334(x58821),x58822),f332(f258(x58821),x58823)))
% 52.62/52.42 [5883]~P102(x58831)+~P1(f332(f332(f233(x58831),x58832),x58833))+P1(f332(f332(f334(x58831),x58832),f332(f257(x58831),x58833)))
% 52.62/52.42 [5884]~P102(x58841)+~P1(f332(f332(f232(x58841),x58842),x58843))+P1(f332(f332(f334(x58841),x58842),f332(f293(x58841),x58843)))
% 52.62/52.42 [5885]~P104(x58851)+~P1(f332(f332(f279(x58851),x58852),x58853))+P1(f332(f332(f279(x58851),x58852),f332(f81(x58851),x58853)))
% 52.62/52.42 [5886]~P110(x58861)+~P1(f332(f332(f279(x58861),x58862),x58863))+P1(f332(f332(f279(x58861),x58862),f332(f77(x58861),x58863)))
% 52.62/52.42 [5897]E(f332(x58971,f414(x58971,x58972,x58973)),f332(a114,f2(a845)))+~E(f332(f332(f8(x58973,a845),x58971),x58972),f332(a114,f2(a845)))+~P1(f332(f64(x58973),x58972))
% 52.62/52.42 [5982]~P11(x59821)+~P1(f332(f332(f334(x59821),x59823),x59822))+P1(f332(f332(f232(x59821),f46(x59821,x59822)),x59823))
% 52.62/52.42 [6000]~P1(f332(f332(f232(a845),x60001),x60003))+P1(f332(f332(f232(a845),x60001),x60002))+~P1(f332(f332(f232(a845),x60003),x60002))
% 52.62/52.42 [6001]~P1(f332(f332(f232(a1),x60011),x60013))+P1(f332(f332(f232(a1),x60011),x60012))+~P1(f332(f332(f232(a1),x60013),x60012))
% 52.62/52.42 [6002]~P1(f332(f332(f279(a845),x60021),x60023))+P1(f332(f332(f279(a845),x60021),x60022))+~P1(f332(f332(f279(a845),x60023),x60022))
% 52.62/52.42 [6020]~P102(x60201)+~P1(f332(f332(f334(x60201),x60203),f332(f296(x60201),x60202)))+P1(f332(f332(f233(x60201),x60202),x60203))
% 52.62/52.42 [6021]~P102(x60211)+~P1(f332(f332(f334(x60211),x60212),f332(f257(x60211),x60213)))+P1(f332(f332(f233(x60211),x60212),x60213))
% 52.62/52.42 [6022]~P102(x60221)+~P1(f332(f332(f334(x60221),x60223),f332(f258(x60221),x60222)))+P1(f332(f332(f232(x60221),x60222),x60223))
% 52.62/52.42 [6023]~P102(x60231)+~P1(f332(f332(f334(x60231),x60232),f332(f293(x60231),x60233)))+P1(f332(f332(f232(x60231),x60232),x60233))
% 52.62/52.42 [6024]~P110(x60241)+~P1(f332(f332(f279(x60241),x60242),f332(f77(x60241),x60243)))+P1(f332(f332(f279(x60241),x60242),x60243))
% 52.62/52.42 [6025]~P104(x60251)+~P1(f332(f332(f279(x60251),x60252),f332(f81(x60251),x60253)))+P1(f332(f332(f279(x60251),x60252),x60253))
% 52.62/52.42 [6251]~P64(x62511)+P1(f332(f332(f233(x62511),f2(x62511)),f797(x62513,x62512,x62511)))+P1(f332(f332(f232(x62511),x62512),x62513))
% 52.62/52.42 [6252]~P65(x62521)+P1(f332(f332(f233(x62521),f2(x62521)),f804(x62523,x62522,x62521)))+P1(f332(f332(f232(x62521),x62522),x62523))
% 52.62/52.42 [6322]~P78(x63221)+~P1(f332(f332(f233(x63221),x63223),f332(f81(x63221),x63222)))+P1(f332(f332(f233(x63221),x63222),f332(f81(x63221),x63223)))
% 52.62/52.42 [6323]~P78(x63231)+~P1(f332(f332(f233(x63231),x63233),f332(f81(x63231),x63232)))+P1(f332(f332(f233(x63231),x63232),f332(f81(x63231),x63233)))
% 52.62/52.42 [6324]~P78(x63241)+~P1(f332(f332(f232(x63241),x63243),f332(f81(x63241),x63242)))+P1(f332(f332(f232(x63241),x63242),f332(f81(x63241),x63243)))
% 52.62/52.42 [6325]~P78(x63251)+~P1(f332(f332(f232(x63251),x63253),f332(f81(x63251),x63252)))+P1(f332(f332(f232(x63251),x63252),f332(f81(x63251),x63253)))
% 52.62/52.42 [6336]~P1(f332(f332(f233(a845),x63361),x63363))+~P1(f332(f332(f233(a845),x63363),x63362))+P1(f332(f332(f233(a845),f332(a114,x63361)),x63362))
% 52.62/52.42 [6368]~P117(x63681)+P1(f332(f332(f233(x63681),f332(f102(x63681),x63682)),f332(f102(x63681),x63683)))+~P1(f332(f332(f233(a845),x63682),x63683))
% 52.62/52.42 [6369]~P110(x63691)+P1(f332(f332(f233(x63691),f332(f105(x63691),x63692)),f332(f105(x63691),x63693)))+~P1(f332(f332(f233(a1),x63692),x63693))
% 52.62/52.42 [6370]~P117(x63701)+P1(f332(f332(f233(x63701),f332(f102(x63701),x63702)),f332(f102(x63701),x63703)))+~P1(f332(f332(f233(a845),x63702),x63703))
% 52.62/52.42 [6371]~P117(x63711)+P1(f332(f332(f232(x63711),f332(f102(x63711),x63712)),f332(f102(x63711),x63713)))+~P1(f332(f332(f232(a845),x63712),x63713))
% 52.62/52.42 [6372]~P110(x63721)+P1(f332(f332(f232(x63721),f332(f105(x63721),x63722)),f332(f105(x63721),x63723)))+~P1(f332(f332(f232(a1),x63722),x63723))
% 52.62/52.42 [6378]~P100(x63781)+E(f332(f332(f103(f853(x63781,a839)),f332(f257(x63781),x63782)),f332(f294(x63781,x63782),x63783)),f332(f257(x63781),x63783))+~P1(f332(f332(f232(x63781),x63782),x63783))
% 52.62/52.42 [6409]~P78(x64091)+~P1(f332(f332(f233(x64091),x64093),x64092))+P1(f332(f332(f233(x64091),f332(f81(x64091),x64092)),f332(f81(x64091),x64093)))
% 52.62/52.42 [6410]~P78(x64101)+~P1(f332(f332(f232(x64101),x64103),x64102))+P1(f332(f332(f232(x64101),f332(f81(x64101),x64102)),f332(f81(x64101),x64103)))
% 52.62/52.42 [6411]~P78(x64111)+~P1(f332(f332(f232(x64111),x64113),x64112))+P1(f332(f332(f232(x64111),f332(f81(x64111),x64112)),f332(f81(x64111),x64113)))
% 52.62/52.42 [6412]~P90(x64121)+~P1(f332(f332(f232(x64121),x64123),x64122))+P1(f332(f332(f232(x64121),f332(f81(x64121),x64122)),f332(f81(x64121),x64123)))
% 52.62/52.42 [6413]~P90(x64131)+~P1(f332(f332(f232(x64131),x64133),x64132))+P1(f332(f332(f232(x64131),f332(f81(x64131),x64132)),f332(f81(x64131),x64133)))
% 52.62/52.42 [6448]~P100(x64481)+E(f332(f332(f103(f853(x64481,a839)),f332(f257(x64481),x64482)),f295(x64481,x64482,x64483)),f332(f293(x64481),x64483))+~P1(f332(f332(f232(x64481),x64482),x64483))
% 52.62/52.42 [6449]~P100(x64491)+E(f332(f332(f103(f853(x64491,a839)),f332(f293(x64491),x64492)),f297(x64491,x64492,x64493)),f332(f293(x64491),x64493))+~P1(f332(f332(f232(x64491),x64492),x64493))
% 52.62/52.42 [6450]~P100(x64501)+E(f332(f332(f103(f853(x64501,a839)),f332(f293(x64501),x64502)),f298(x64501,x64502,x64503)),f332(f257(x64501),x64503))+~P1(f332(f332(f233(x64501),x64502),x64503))
% 52.62/52.42 [6488]~P100(x64881)+E(f332(f332(f103(f853(x64881,a839)),f332(f294(x64881,x64882),x64883)),f332(f258(x64881),x64883)),f332(f258(x64881),x64882))+~P1(f332(f332(f232(x64881),x64882),x64883))
% 52.62/52.42 [6650]~P100(x66501)+E(f332(f332(f103(f853(x66501,a839)),f295(x66501,x66502,x66503)),f332(f296(x66501),x66503)),f332(f258(x66501),x66502))+~P1(f332(f332(f232(x66501),x66502),x66503))
% 52.62/52.42 [6651]~P100(x66511)+E(f332(f332(f103(f853(x66511,a839)),f297(x66511,x66512,x66513)),f332(f296(x66511),x66513)),f332(f296(x66511),x66512))+~P1(f332(f332(f232(x66511),x66512),x66513))
% 52.62/52.42 [6652]~P100(x66521)+E(f332(f332(f103(f853(x66521,a839)),f298(x66521,x66522,x66523)),f332(f258(x66521),x66523)),f332(f296(x66521),x66522))+~P1(f332(f332(f233(x66521),x66522),x66523))
% 52.62/52.42 [6669]P1(f332(x66691,x66692))+~P1(f332(f332(f232(a845),x66692),x66693))+P1(f332(f332(f334(a845),f795(x66691,x66693)),f295(a845,f2(a845),x66693)))
% 52.62/52.42 [6679]P1(f332(f332(f279(a1),x66791),f53(a1,x66792,x66793)))+~P1(f332(f332(f279(a1),x66791),x66792))+~P1(f332(f332(f279(a1),x66791),x66793))
% 52.62/52.42 [6705]E(x67051,x67052)+~E(f332(f332(f152(x67053),x67051),f730(x67053,x67052,x67051)),f332(f332(f152(x67053),x67052),f730(x67053,x67052,x67051)))+~E(f332(f181(f846(x67053)),x67051),f332(f181(f846(x67053)),x67052))
% 52.62/52.42 [6711]~E(x67113,f332(f332(f44(a845),x67111),x67112))+~P1(f332(f332(f233(a845),f2(a845)),x67112))+P1(f332(f332(f233(a845),x67111),f332(f332(f83(a845),x67112),f332(a114,x67113))))
% 52.62/52.42 [6726]~P1(f332(x67261,x67263))+~P1(f332(f332(f232(a845),x67263),x67262))+P1(f332(f332(f334(a845),f794(x67261,x67262)),f295(a845,f2(a845),x67262)))
% 52.62/52.42 [6768]~P1(f332(x67681,x67683))+P1(f332(x67681,f340(x67681,x67682)))+~P1(f332(f332(f334(a845),x67683),f295(a845,f2(a845),x67682)))
% 52.62/52.42 [6790]~P117(x67903)+~P1(f332(f332(f233(x67903),f332(f102(x67903),x67901)),f332(f102(x67903),x67902)))+P1(f332(f332(f233(a845),x67901),x67902))
% 52.62/52.42 [6791]~P117(x67913)+~P1(f332(f332(f233(x67913),f332(f102(x67913),x67911)),f332(f102(x67913),x67912)))+P1(f332(f332(f233(a845),x67911),x67912))
% 52.62/52.42 [6792]~P110(x67923)+~P1(f332(f332(f233(x67923),f332(f105(x67923),x67921)),f332(f105(x67923),x67922)))+P1(f332(f332(f233(a1),x67921),x67922))
% 52.62/52.42 [6793]~P117(x67933)+~P1(f332(f332(f232(x67933),f332(f102(x67933),x67931)),f332(f102(x67933),x67932)))+P1(f332(f332(f232(a845),x67931),x67932))
% 52.62/52.42 [6794]~P110(x67943)+~P1(f332(f332(f232(x67943),f332(f105(x67943),x67941)),f332(f105(x67943),x67942)))+P1(f332(f332(f232(a1),x67941),x67942))
% 52.62/52.42 [6810]~P117(x68101)+~P1(f332(f332(f233(x68101),f80(x68101)),x68102))+P1(f332(f332(f233(x68101),f80(x68101)),f332(f332(f242(x68101),x68102),f332(a114,x68103))))
% 52.62/52.42 [6814]~P78(x68141)+~P1(f332(f332(f233(x68141),f332(f81(x68141),x68143)),f332(f81(x68141),x68142)))+P1(f332(f332(f233(x68141),x68142),x68143))
% 52.62/52.42 [6815]~P78(x68151)+~P1(f332(f332(f232(x68151),f332(f81(x68151),x68153)),f332(f81(x68151),x68152)))+P1(f332(f332(f232(x68151),x68152),x68153))
% 52.62/52.42 [6816]~P90(x68161)+~P1(f332(f332(f232(x68161),f332(f81(x68161),x68163)),f332(f81(x68161),x68162)))+P1(f332(f332(f232(x68161),x68162),x68163))
% 52.62/52.42 [6842]P1(f332(x68421,x68422))+~P1(f332(x68421,f834(x68421,x68423)))+~P1(f332(f332(f334(a845),x68422),f295(a845,f2(a845),x68423)))
% 52.62/52.42 [6863]~P64(x68631)+P1(f332(f332(f233(x68631),f797(x68633,x68632,x68631)),f80(x68631)))+P1(f332(f332(f232(x68631),x68632),x68633))
% 52.62/52.42 [6882]~E(f53(a845,x68823,x68822),f53(a845,x68821,x68822))+E(f332(f332(f82(a845),x68821),f332(f332(f83(a845),x68822),f808(x68821,x68822,x68823))),x68823)+~P1(f332(f332(f232(a845),x68821),x68823))
% 52.62/52.42 [6900]E(f332(x69001,f606(x69001,x69002,x69003)),f183(x69002))+~P1(f332(f64(x69003),f169(x69003,x69002,x69001)))+P1(f332(f64(x69003),f239(f853(x69003,a839))))
% 52.62/52.42 [6941]E(f332(f332(f8(x69411,a845),x69412),x69413),f2(a845))+~P1(f332(f64(x69411),x69413))+P1(f332(f332(f334(x69411),f413(x69412,x69413,x69411)),x69413))
% 52.62/52.42 [6942]E(f332(f332(f11(x69421,a845),x69422),x69423),f80(a845))+~P1(f332(f64(x69421),x69423))+P1(f332(f332(f334(x69421),f449(x69422,x69423,x69421)),x69423))
% 52.62/52.42 [6964]~P100(x69641)+~P1(f332(f332(f233(x69641),x69642),x69643))+P1(f332(f332(f233(f853(x69641,a839)),f332(f257(x69641),x69642)),f332(f257(x69641),x69643)))
% 52.62/52.42 [6965]~P100(x69651)+~P1(f332(f332(f232(x69651),x69652),x69653))+P1(f332(f332(f232(f853(x69651,a839)),f332(f257(x69651),x69652)),f332(f257(x69651),x69653)))
% 52.62/52.42 [6966]~P100(x69661)+~P1(f332(f332(f232(x69661),x69663),x69662))+P1(f332(f332(f232(f853(x69661,a839)),f332(f296(x69661),x69662)),f332(f296(x69661),x69663)))
% 52.62/52.42 [6967]~P99(x69671)+~P1(f332(f332(f232(x69671),x69672),x69673))+P1(f332(f332(f232(f853(x69671,a839)),f332(f293(x69671),x69672)),f332(f293(x69671),x69673)))
% 52.62/52.42 [6968]~P99(x69681)+~P1(f332(f332(f232(x69681),x69683),x69682))+P1(f332(f332(f232(f853(x69681,a839)),f332(f258(x69681),x69682)),f332(f258(x69681),x69683)))
% 52.62/52.42 [6973]~P11(x69731)+P1(f332(f332(f232(x69731),x69732),f46(x69731,x69733)))+P1(f332(f332(f334(x69731),f671(x69733,x69732,x69731)),x69733))
% 52.62/52.42 [6978]~P78(x69781)+P1(f332(f332(f233(x69781),f332(f332(f3(x69781),x69782),x69783)),f2(x69781)))+~P1(f332(f332(f233(x69781),x69782),x69783))
% 52.62/52.42 [6979]~P78(x69791)+P1(f332(f332(f232(x69791),f332(f332(f3(x69791),x69792),x69793)),f2(x69791)))+~P1(f332(f332(f232(x69791),x69792),x69793))
% 52.62/52.42 [7017]~P1(f332(f332(f279(a1),x70171),f53(a1,x70172,x70173)))+~P1(f332(f332(f279(a1),x70171),x70173))+P1(f332(f332(f279(a1),x70171),x70172))
% 52.62/52.42 [7024]P1(f332(x70241,x70242))+P1(f332(f332(f232(a845),f834(x70241,x70243)),x70243))+~P1(f332(f332(f334(a845),x70242),f295(a845,f2(a845),x70243)))
% 52.62/52.42 [7066]~E(f332(f332(f8(x70661,a845),x70662),x70663),f80(a845))+~P1(f332(f64(x70661),x70663))+P1(f332(f332(f334(x70661),f412(x70662,x70663,x70661)),x70663))
% 52.62/52.42 [7067]~P1(f332(x70671,x70673))+P1(f332(f332(f232(a845),f340(x70671,x70672)),x70672))+~P1(f332(f332(f334(a845),x70673),f295(a845,f2(a845),x70672)))
% 52.62/52.42 [7105]~P11(x71051)+P1(f332(f332(f334(x71051),f673(x71053,x71052,x71051)),x71052))+P1(f332(f332(f232(x71051),f45(x71051,x71052)),x71053))
% 52.62/52.42 [7135]~E(f332(f332(f8(x71351,a845),x71352),x71353),f332(a114,f2(a845)))+~P1(f332(f64(x71351),x71353))+P1(f332(f332(f334(x71351),f414(x71352,x71353,x71351)),x71353))
% 52.62/52.42 [7146]E(x71461,f2(a845))+P1(f332(x71462,f53(a845,x71463,x71461)))+P1(f332(f332(f233(a845),f799(x71461,x71463,x71462)),x71461))
% 52.62/52.42 [7270]~P1(f332(x72701,x72702))+P1(f332(x72701,f53(a845,x72702,x72703)))+P1(f332(f332(f233(a845),f799(x72703,x72702,x72701)),x72703))
% 52.62/52.42 [7397]E(x73971,f115(x73972))+~P1(f332(f332(f334(f846(x73972)),x73971),f149(x73972,x73973)))+P1(f332(f332(f334(x73972),f748(x73973,x73971,x73972)),x73973))
% 52.62/52.42 [7417]~P100(x74171)+E(f332(f332(f103(f853(x74171,a839)),f332(f332(f302(x74171),x74172),f180(f853(x74171,a839)))),f298(x74171,x74172,x74173)),f332(f294(x74171,x74172),x74173))+~P1(f332(f332(f233(x74171),x74172),x74173))
% 52.62/52.42 [7442]~P100(x74421)+E(f332(f332(f103(f853(x74421,a839)),f332(f332(f302(x74421),x74422),f180(f853(x74421,a839)))),f297(x74421,x74422,x74423)),f295(x74421,x74422,x74423))+~P1(f332(f332(f232(x74421),x74422),x74423))
% 52.62/52.42 [7554]~P100(x75541)+P1(f332(f332(f233(x75541),x75542),x75543))+~P1(f332(f332(f233(f853(x75541,a839)),f332(f257(x75541),x75542)),f332(f257(x75541),x75543)))
% 52.62/52.42 [7555]~P99(x75551)+P1(f332(f332(f232(x75551),x75552),x75553))+~P1(f332(f332(f232(f853(x75551,a839)),f332(f258(x75551),x75553)),f332(f258(x75551),x75552)))
% 52.62/52.42 [7556]~P100(x75561)+P1(f332(f332(f232(x75561),x75562),x75563))+~P1(f332(f332(f232(f853(x75561,a839)),f332(f296(x75561),x75563)),f332(f296(x75561),x75562)))
% 52.62/52.42 [7557]~P99(x75571)+P1(f332(f332(f232(x75571),x75572),x75573))+~P1(f332(f332(f232(f853(x75571,a839)),f332(f293(x75571),x75572)),f332(f293(x75571),x75573)))
% 52.62/52.42 [7558]~P100(x75581)+P1(f332(f332(f232(x75581),x75582),x75583))+~P1(f332(f332(f232(f853(x75581,a839)),f332(f257(x75581),x75582)),f332(f257(x75581),x75583)))
% 52.62/52.42 [7582]~P78(x75821)+~P1(f332(f332(f233(x75821),f332(f332(f3(x75821),x75822),x75823)),f2(x75821)))+P1(f332(f332(f233(x75821),x75822),x75823))
% 52.62/52.42 [7583]~P78(x75831)+~P1(f332(f332(f232(x75831),f332(f332(f3(x75831),x75832),x75833)),f2(x75831)))+P1(f332(f332(f232(x75831),x75832),x75833))
% 52.62/52.42 [7743]E(x77431,f2(a845))+~E(f332(f132(a845,a845,f82(a845),x77432),x77433),f2(a845))+~P1(f332(f332(f334(a845),x77431),f332(f158(a845),x77433)))
% 52.62/52.42 [7747]~P11(x77471)+~P1(f332(f332(f232(x77471),f673(x77473,x77472,x77471)),x77473))+P1(f332(f332(f232(x77471),f45(x77471,x77472)),x77473))
% 52.62/52.42 [7898]P1(f332(f332(f232(a1),f2(a1)),f790(x78981,x78982,x78983)))+P1(f332(f332(x78982,f332(f332(f44(a1),x78981),x78983)),f53(a1,x78981,x78983)))+~P1(f332(f332(f233(a1),f2(a1)),x78983))
% 52.62/52.42 [7991]E(x79911,x79912)+~E(f332(f181(f846(x79913)),x79911),f332(f181(f846(x79913)),x79912))+~P1(f332(f332(f251(x79913,x79913,a839),a329),f713(x79913,x79911,x79912)))
% 52.62/52.42 [8057]~P38(x80572,x80573)+E(x80571,f180(f853(x80572,a839)))+~P1(f332(f332(f232(f853(x80572,a839)),x80571),f332(f277(x80572,x80572,x80573),x80571)))
% 52.62/52.42 [8085]~P65(x80851)+~P1(f332(f332(f232(x80851),x80852),f332(f332(f82(x80851),x80853),f804(x80853,x80852,x80851))))+P1(f332(f332(f232(x80851),x80852),x80853))
% 52.62/52.42 [8121]P49(x81211,x81212,x81213)+P1(f332(f332(f334(x81211),f504(x81213,x81212,x81211)),x81212))+P1(f332(f332(f334(f852(x81211,x81211)),f505(x81213,x81212,x81211)),x81213))
% 52.62/52.42 [8144]P1(f332(f332(x81442,f332(f332(f44(a1),x81441),x81443)),f53(a1,x81441,x81443)))+~P1(f332(f332(f233(a1),f2(a1)),x81443))+P1(f332(f332(f233(a1),f790(x81441,x81442,x81443)),x81443))
% 52.62/52.42 [8168]E(f332(f303(a845,a845,f332(f332(f9(a845,a845,a845),f3(a845)),x81681)),f332(f294(a845,x81682),x81683)),f180(f853(a845,a839)))+P1(f332(f332(f233(a845),x81681),x81683))+P1(f332(f332(f233(a845),x81682),x81683))
% 52.62/52.42 [8270]E(f332(f303(a845,a845,f332(f332(f9(a845,a845,a845),f3(a845)),x82701)),f332(f294(a845,x82702),x82703)),f332(f332(f302(a845),f2(a845)),f180(f853(a845,a839))))+P1(f332(f332(f233(a845),x82701),x82703))+~P1(f332(f332(f233(a845),x82702),x82703))
% 52.62/52.42 [8285]~P100(x82851)+E(f139(x82851,x82851,f7(x82851),x82852,x82853),x82853)+~P1(f332(f332(f334(x82851),x82852),f332(f158(x82851),x82853)))
% 52.62/52.42 [8300]P31(x83001,x83001,x83002,x83003)+~P1(f332(f64(x83001),x83003))+~P1(f332(f332(f232(f853(x83001,a839)),x83003),f332(f303(x83001,x83001,x83002),x83003)))
% 52.62/52.42 [8327]E(f332(f332(f82(a1),f332(f332(f83(a1),x83271),f791(x83272,x83273,x83271))),f790(x83272,x83273,x83271)),x83272)+P1(f332(f332(x83273,f332(f332(f44(a1),x83272),x83271)),f53(a1,x83272,x83271)))+~P1(f332(f332(f233(a1),f2(a1)),x83271))
% 52.62/52.42 [8559]~P1(f332(f332(x85591,f791(x85592,x85591,x85593)),f790(x85592,x85591,x85593)))+P1(f332(f332(x85591,f332(f332(f44(a1),x85592),x85593)),f53(a1,x85592,x85593)))+~P1(f332(f332(f233(a1),f2(a1)),x85593))
% 52.62/52.42 [9349]~P1(f332(f64(x93491),x93492))+~P1(f332(f332(f334(x93491),x93493),x93492))+P1(f332(f332(f233(a845),f332(f43(x93491),f332(f332(f3(f853(x93491,a839)),x93492),f332(f332(f302(x93491),x93493),f180(f853(x93491,a839)))))),f332(f43(x93491),x93492)))
% 52.62/52.42 [9926]P49(x99261,x99262,x99263)+~P1(f332(f332(f251(x99261,x99261,a839),f332(f332(f9(x99261,f853(x99261,a839),f853(x99261,a839)),f332(f332(f10(f853(a839,a839),f853(f853(x99261,a839),f853(x99261,a839)),x99261),f10(a839,a839,x99261)),f332(f332(f10(a839,f853(a839,a839),x99261),a330),f332(f332(f9(x99261,f853(x99261,a839),a839),f334(x99261)),x99262)))),f332(f332(f9(x99261,f853(x99261,a839),a839),f334(x99261)),x99262))),f505(x99263,x99262,x99261)))+P1(f332(f332(f334(x99261),f504(x99263,x99262,x99261)),x99262))
% 52.62/52.42 [5356]~P113(x53562)+E(x53561,f2(x53562))+E(f332(f332(f283(x53562),x53563),f332(f81(x53562),x53561)),f332(f81(x53562),f332(f332(f283(x53562),x53563),x53561)))
% 52.62/52.42 [5487]~E(x54873,f180(f853(x54871,a839)))+~E(x54872,f180(f853(x54871,a839)))+E(f332(f332(f103(f853(x54871,a839)),x54872),x54873),f180(f853(x54871,a839)))
% 52.62/52.42 [5540]~E(x55403,f2(a845))+~P1(f332(x55401,f2(a845)))+P1(f332(x55401,f332(f332(f44(a845),x55402),x55403)))
% 52.62/52.42 [5541]~E(x55413,f2(a845))+~P1(f332(x55411,f2(a845)))+P1(f332(x55411,f332(f332(f44(a845),x55412),x55413)))
% 52.62/52.42 [5689]~P65(x56892)+E(x56891,f2(x56892))+E(f332(f332(f283(x56892),f332(f77(x56892),x56893)),f332(f77(x56892),x56891)),f332(f77(x56892),f332(f332(f283(x56892),x56893),x56891)))
% 52.62/52.42 [5784]~P73(x57841)+~E(x57842,f80(x57841))+P1(f332(f332(f279(x57841),x57842),f332(f332(f242(x57841),x57842),x57843)))
% 52.62/52.42 [5801]~P9(x58011)+E(f332(f332(f83(x58011),x58012),f332(f332(f44(x58011),x58013),x58012)),x58013)+~P1(f332(f332(f279(x58011),x58012),x58013))
% 52.62/52.42 [5854]~P1(f332(f64(x58541),x58543))+E(f332(f43(x58541),f332(f332(f302(x58541),x58542),x58543)),f332(a114,f332(f43(x58541),x58543)))+P1(f332(f332(f334(x58541),x58542),x58543))
% 52.62/52.42 [5855]~P1(f332(f64(x58551),x58553))+E(f332(f43(x58551),f332(f332(f302(x58551),x58552),x58553)),f332(a114,f332(f43(x58551),x58553)))+P1(f332(f332(f334(x58551),x58552),x58553))
% 52.62/52.42 [5932]~E(x59322,f2(a845))+P1(f332(x59321,f2(a845)))+~P1(f332(x59321,f332(f332(f44(a845),x59323),x59322)))
% 52.62/52.42 [5950]~P1(f332(f64(x59501),x59503))+E(f332(f43(x59501),f332(f332(f302(x59501),x59502),x59503)),f332(f43(x59501),x59503))+~P1(f332(f332(f334(x59501),x59502),x59503))
% 52.62/52.42 [5984]~P1(f332(f64(x59841),x59843))+E(f332(f43(x59841),f332(f332(f302(x59841),x59842),x59843)),f332(f332(f82(a845),f80(a845)),f332(f43(x59841),x59843)))+P1(f332(f332(f334(x59841),x59842),x59843))
% 52.62/52.42 [5991]~P10(x59911)+E(f332(f332(f44(x59911),x59912),f332(f81(x59911),x59913)),f332(f81(x59911),f332(f332(f44(x59911),x59912),x59913)))+~P1(f332(f332(f279(x59911),x59913),x59912))
% 52.62/52.42 [6108]E(f332(f332(f82(a845),x61081),f796(x61081,x61082,x61083)),x61082)+~P1(f332(x61083,f2(a845)))+P1(f332(x61083,f332(f332(f3(a845),x61082),x61081)))
% 52.62/52.42 [6109]E(f332(f332(f82(a845),x61091),f803(x61091,x61092,x61093)),x61092)+~P1(f332(x61093,f2(a845)))+P1(f332(x61093,f332(f332(f3(a845),x61092),x61091)))
% 52.62/52.42 [6133]~P10(x61331)+E(f332(f332(f44(x61331),f332(f81(x61331),x61332)),x61333),f332(f81(x61331),f332(f332(f44(x61331),x61332),x61333)))+~P1(f332(f332(f279(x61331),x61333),x61332))
% 52.62/52.42 [6156]~P11(x61561)+~P1(f332(f64(x61561),x61563))+E(f332(f332(f67(x61561,x61561,f103(x61561)),x61562),x61563),f332(f332(f103(x61561),x61562),f45(x61561,x61563)))
% 52.62/52.42 [6157]~P11(x61571)+~P1(f332(f64(x61571),x61573))+E(f332(f332(f67(x61571,x61571,f104(x61571)),x61572),x61573),f332(f332(f104(x61571),x61572),f46(x61571,x61573)))
% 52.62/52.42 [6163]~P88(x61631)+~E(f332(f106(x61631),x61632),f332(f106(x61631),x61633))+P35(x61631,f332(f106(x61631),f332(f332(f82(a1),x61632),f332(f81(a1),x61633))))
% 52.62/52.42 [6170]~P133(x61701)+E(f332(f332(f3(x61701),f332(f102(x61701),x61702)),f332(f102(x61701),x61703)),f332(f102(x61701),f332(f332(f3(a845),x61702),x61703)))+~P1(f332(f332(f232(a845),x61703),x61702))
% 52.62/52.42 [6176]~P104(x61761)+~P1(f332(f332(f279(x61761),x61762),x61763))+P1(f332(f332(f279(x61761),f332(f81(x61761),x61762)),x61763))
% 52.62/52.42 [6177]~P110(x61771)+~P1(f332(f332(f279(x61771),x61772),x61773))+P1(f332(f332(f279(x61771),f332(f77(x61771),x61772)),x61773))
% 52.62/52.42 [6262]E(f332(f332(f82(a845),x62621),f796(x62621,x62622,x62623)),x62622)+P1(f332(f332(f233(a845),x62622),x62621))+P1(f332(x62623,f332(f332(f3(a845),x62622),x62621)))
% 52.62/52.42 [6263]E(f332(f332(f82(a845),x62631),f803(x62631,x62632,x62633)),x62632)+P1(f332(f332(f233(a845),x62632),x62631))+P1(f332(x62633,f332(f332(f3(a845),x62632),x62631)))
% 52.62/52.42 [6281]~P110(x62811)+E(f332(f332(f83(x62811),f332(f77(x62811),x62812)),x62813),f332(f77(x62811),f332(f332(f83(x62811),x62812),x62813)))+~P1(f332(f332(f232(x62811),f2(x62811)),x62813))
% 52.62/52.42 [6282]~P64(x62821)+E(f332(f332(f283(x62821),f332(f77(x62821),x62822)),x62823),f332(f77(x62821),f332(f332(f283(x62821),x62822),x62823)))+~P1(f332(f332(f233(x62821),f2(x62821)),x62823))
% 52.62/52.42 [6291]~P93(x62911)+~P1(f332(f64(x62911),x62913))+E(f332(f332(f67(x62911,x62911,f103(x62911)),x62912),x62913),f15(x62911,f332(f332(f302(x62911),x62912),x62913)))
% 52.62/52.42 [6292]~P100(x62921)+~P1(f332(f64(x62921),x62923))+E(f332(f332(f67(x62921,x62921,f179(x62921)),x62922),x62923),f16(x62921,f332(f332(f302(x62921),x62922),x62923)))
% 52.62/52.42 [6293]~P100(x62931)+~P1(f332(f64(x62931),x62933))+E(f332(f332(f67(x62931,x62931,f236(x62931)),x62932),x62933),f17(x62931,f332(f332(f302(x62931),x62932),x62933)))
% 52.62/52.42 [6294]~P93(x62941)+~P1(f332(f64(x62941),x62943))+E(f332(f332(f67(x62941,x62941,f104(x62941)),x62942),x62943),f12(x62941,f332(f332(f302(x62941),x62942),x62943)))
% 52.62/52.42 [6338]E(x63381,f115(x63382))+~E(f164(x63382,x63383),f115(f846(x63382)))+~P1(f332(f332(f334(f846(x63382)),x63381),f332(f158(f846(x63382)),x63383)))
% 52.62/52.42 [6357]~P73(x63571)+~P1(f332(f332(f233(a845),f2(a845)),x63573))+P1(f332(f332(f279(x63571),x63572),f332(f332(f242(x63571),x63572),x63573)))
% 52.62/52.42 [6388]~P1(f332(f127(x63881),x63883))+P1(f332(f332(f334(x63881),x63882),f332(f158(x63881),x63883)))+P1(f332(f127(x63881),f332(f332(f140(x63881),x63882),x63883)))
% 52.62/52.42 [6400]~P91(x64001)+~P1(f332(f64(x64001),x64003))+E(f332(f66(x64001,f83(x64001)),f332(f332(f302(x64001),x64002),x64003)),f332(f332(f67(x64001,x64001,f83(x64001)),x64002),x64003))
% 52.62/52.42 [6421]~P100(x64211)+~P1(f332(f64(x64211),x64213))+E(f13(x64211,f179(x64211),f332(f332(f302(x64211),x64212),x64213)),f332(f332(f67(x64211,x64211,f179(x64211)),x64212),x64213))
% 52.62/52.42 [6422]~P100(x64221)+~P1(f332(f64(x64221),x64223))+E(f14(x64221,f236(x64221),f332(f332(f302(x64221),x64222),x64223)),f332(f332(f67(x64221,x64221,f236(x64221)),x64222),x64223))
% 52.62/52.42 [6423]P1(f332(x64231,f2(a845)))+~P1(f332(f332(f233(a845),x64232),x64233))+~P1(f332(x64231,f332(f332(f3(a845),x64232),x64233)))
% 52.62/52.42 [6424]P1(f332(x64241,f2(a845)))+~P1(f332(f332(f233(a845),x64242),x64243))+~P1(f332(x64241,f332(f332(f3(a845),x64242),x64243)))
% 52.62/52.42 [6443]~P110(x64431)+P1(f332(f332(f233(x64431),x64432),x64433))+~P1(f332(f332(f233(x64431),f332(f77(x64431),x64432)),x64433))
% 52.62/52.42 [6444]~P80(x64441)+P1(f332(f332(f232(x64441),x64442),x64443))+~P1(f332(f332(f232(x64441),f332(f77(x64441),x64442)),x64443))
% 52.62/52.42 [6445]~P80(x64451)+P1(f332(f332(f232(x64451),x64452),x64453))+~P1(f332(f332(f232(x64451),f332(f77(x64451),x64452)),x64453))
% 52.62/52.42 [6446]~P110(x64461)+P1(f332(f332(f279(x64461),x64462),x64463))+~P1(f332(f332(f279(x64461),f332(f77(x64461),x64462)),x64463))
% 52.62/52.42 [6447]~P104(x64471)+P1(f332(f332(f279(x64471),x64472),x64473))+~P1(f332(f332(f279(x64471),f332(f81(x64471),x64472)),x64473))
% 52.62/52.42 [6466]E(x64661,f115(x64662))+E(f332(f131(x64662),f332(f332(f128(x64662),x64663),x64661)),f332(f332(f152(x64662),x64661),x64663))+~P1(f332(f332(f233(a845),x64663),f332(f181(f846(x64662)),x64661)))
% 52.62/52.42 [6520]~P1(f332(x65201,x65203))+P1(f332(x65201,f343(x65201,x65202)))+~P1(f332(f332(f334(a845),x65203),f332(f294(a845,f2(a845)),x65202)))
% 52.62/52.42 [6543]P1(f332(x65431,x65432))+~P1(f332(f332(f233(a845),x65432),x65433))+P1(f332(f332(f334(a845),f342(x65431,x65433)),f332(f294(a845,f2(a845)),x65433)))
% 52.62/52.42 [6558]~P117(x65581)+~P1(f332(f332(f233(x65581),f2(x65581)),x65582))+P1(f332(f332(f233(x65581),f2(x65581)),f332(f332(f242(x65581),x65582),x65583)))
% 52.62/52.42 [6560]~P117(x65601)+~P1(f332(f332(f232(x65601),f2(x65601)),x65602))+P1(f332(f332(f232(x65601),f2(x65601)),f332(f332(f242(x65601),x65602),x65603)))
% 52.62/52.42 [6561]~P117(x65611)+~P1(f332(f332(f232(x65611),f80(x65611)),x65612))+P1(f332(f332(f232(x65611),f80(x65611)),f332(f332(f242(x65611),x65612),x65613)))
% 52.62/52.42 [6585]~P1(f332(x65851,x65853))+~P1(f332(f332(f233(a845),x65853),x65852))+P1(f332(f332(f334(a845),f339(x65851,x65852)),f332(f294(a845,f2(a845)),x65852)))
% 52.62/52.42 [6589]P1(f332(f64(x65891),x65892))+~P1(f332(f64(x65891),x65893))+~P1(f332(f332(f232(f853(x65891,a839)),x65892),x65893))
% 52.62/52.42 [6590]P1(f332(f64(x65901),x65902))+~P1(f332(f64(x65901),x65903))+~P1(f332(f332(f232(f853(x65901,a839)),x65902),x65903))
% 52.62/52.42 [6599]~P1(f332(f332(f279(a845),x65991),x65992))+~P1(f332(f332(f279(a845),x65991),x65993))+P1(f332(f332(f279(a845),x65991),f332(f332(f3(a845),x65992),x65993)))
% 52.62/52.42 [6600]P1(f332(x66001,x66002))+~P1(f332(x66001,f344(x66001,x66003)))+~P1(f332(f332(f334(a845),x66002),f332(f294(a845,f2(a845)),x66003)))
% 52.62/52.42 [6613]E(x66131,f2(a845))+P1(f332(x66132,f788(x66131,x66133,x66132)))+~P1(f332(x66132,f332(f332(f44(a845),x66133),x66131)))
% 52.62/52.42 [6622]~P119(x66222)+E(x66221,f2(x66222))+~E(f332(f332(f82(x66222),f332(f332(f83(x66222),x66223),x66223)),f332(f332(f83(x66222),x66221),x66221)),f2(x66222))
% 52.62/52.42 [6623]~P119(x66232)+E(x66231,f2(x66232))+~E(f332(f332(f82(x66232),f332(f332(f83(x66232),x66231),x66231)),f332(f332(f83(x66232),x66233),x66233)),f2(x66232))
% 52.62/52.42 [6670]E(x66701,f2(a845))+~P1(f332(x66702,f798(x66701,x66703,x66702)))+P1(f332(x66702,f332(f332(f44(a845),x66703),x66701)))
% 52.62/52.42 [6675]~P100(x66751)+~P20(x66751,x66753)+P20(x66751,f332(f332(f138(x66751,x66751,f7(x66751)),x66752),x66753))
% 52.62/52.42 [6719]P1(f332(x67191,f788(x67192,x67193,x67191)))+P1(f332(x67191,f2(a845)))+~P1(f332(x67191,f332(f332(f44(a845),x67193),x67192)))
% 52.62/52.42 [6725]~P88(x67251)+E(f332(f106(x67251),x67252),f332(f106(x67251),x67253))+~P35(x67251,f332(f106(x67251),f332(f332(f82(a1),x67252),f332(f81(a1),x67253))))
% 52.62/52.42 [6797]E(x67971,f2(a1))+E(x67972,f2(a1))+~P1(f332(f57(x67972,x67972),f332(f332(f241(a1,a1),x67973),x67971)))
% 52.62/52.42 [6798]E(x67981,f80(a1))+E(x67982,f2(a1))+~P1(f332(f57(x67982,x67982),f332(f332(f241(a1,a1),x67981),x67983)))
% 52.62/52.42 [6812]P1(f332(x68121,x68122))+P1(f332(f332(f233(a845),f344(x68121,x68123)),x68123))+~P1(f332(f332(f334(a845),x68122),f332(f294(a845,f2(a845)),x68123)))
% 52.62/52.42 [6837]~P1(f332(x68371,f798(x68373,x68372,x68371)))+~P1(f332(x68371,f2(a845)))+P1(f332(x68371,f332(f332(f44(a845),x68372),x68373)))
% 52.62/52.42 [6838]~P1(f332(x68381,f796(x68383,x68382,x68381)))+~P1(f332(x68381,f2(a845)))+P1(f332(x68381,f332(f332(f3(a845),x68382),x68383)))
% 52.62/52.42 [6839]~P1(f332(x68391,f803(x68393,x68392,x68391)))+~P1(f332(x68391,f2(a845)))+P1(f332(x68391,f332(f332(f3(a845),x68392),x68393)))
% 52.62/52.42 [6859]~P1(f332(x68591,x68593))+P1(f332(f332(f233(a845),f343(x68591,x68592)),x68592))+~P1(f332(f332(f334(a845),x68593),f332(f294(a845,f2(a845)),x68592)))
% 52.62/52.42 [6860]E(f332(f332(f3(a845),f332(f332(f3(a845),x68601),x68602)),f332(f332(f3(a845),x68603),x68602)),f332(f332(f3(a845),x68601),x68603))+~P1(f332(f332(f232(a845),x68602),x68601))+~P1(f332(f332(f232(a845),x68602),x68603))
% 52.62/52.42 [6893]~P78(x68931)+~P1(f332(f332(f233(x68931),f332(f81(x68931),x68933)),x68932))+P1(f332(f332(f233(x68931),f332(f81(x68931),x68932)),x68933))
% 52.62/52.42 [6894]~P78(x68941)+~P1(f332(f332(f233(x68941),f332(f81(x68941),x68943)),x68942))+P1(f332(f332(f233(x68941),f332(f81(x68941),x68942)),x68943))
% 52.62/52.42 [6895]~P110(x68951)+~P1(f332(f332(f233(x68951),f332(f77(x68951),x68952)),x68953))+P1(f332(f332(f233(x68951),f332(f81(x68951),x68952)),x68953))
% 52.62/52.42 [6896]~P78(x68961)+~P1(f332(f332(f232(x68961),f332(f81(x68961),x68963)),x68962))+P1(f332(f332(f232(x68961),f332(f81(x68961),x68962)),x68963))
% 52.62/52.42 [6897]~P78(x68971)+~P1(f332(f332(f232(x68971),f332(f81(x68971),x68973)),x68972))+P1(f332(f332(f232(x68971),f332(f81(x68971),x68972)),x68973))
% 52.62/52.42 [6898]~P80(x68981)+~P1(f332(f332(f232(x68981),f332(f77(x68981),x68982)),x68983))+P1(f332(f332(f232(x68981),f332(f81(x68981),x68982)),x68983))
% 52.62/52.42 [6899]~P80(x68991)+~P1(f332(f332(f232(x68991),f332(f77(x68991),x68992)),x68993))+P1(f332(f332(f232(x68991),f332(f81(x68991),x68992)),x68993))
% 52.62/52.42 [6902]~P1(f332(f332(f279(a1),x69021),x69023))+P1(f332(f332(f279(a1),x69021),x69022))+~P1(f332(f332(f279(a1),x69021),f332(f332(f3(a1),x69022),x69023)))
% 52.62/52.42 [6935]~P1(f332(x69353,f796(x69352,x69351,x69353)))+P1(f332(f332(f233(a845),x69351),x69352))+P1(f332(x69353,f332(f332(f3(a845),x69351),x69352)))
% 52.62/52.42 [6936]~P1(f332(x69363,f803(x69362,x69361,x69363)))+P1(f332(f332(f233(a845),x69361),x69362))+P1(f332(x69363,f332(f332(f3(a845),x69361),x69362)))
% 52.62/52.42 [6982]~E(f684(x69823,x69822,x69821),f679(x69823,x69822,x69821))+E(f332(f332(f104(f853(x69821,a839)),x69822),f45(f853(x69821,a839),x69823)),f180(f853(x69821,a839)))+P1(f332(f332(f334(f853(x69821,a839)),x69822),x69823))
% 52.62/52.42 [6991]~P1(f332(f64(x69911),x69913))+P1(f332(f64(x69911),f46(f853(x69911,a839),x69912)))+~P1(f332(f332(f334(f853(x69911,a839)),x69913),x69912))
% 52.62/52.42 [7052]~P100(x70521)+E(f332(f332(f103(f853(x70521,a839)),f332(f294(x70521,x70522),x70523)),f332(f332(f302(x70521),x70523),f180(f853(x70521,a839)))),f295(x70521,x70522,x70523))+~P1(f332(f332(f232(x70521),x70522),x70523))
% 52.62/52.42 [7055]E(x70551,f2(a845))+P1(f332(f332(f233(a845),f800(x70551,x70553,x70552)),x70551))+P1(f332(x70552,f332(f332(f44(a845),x70553),x70551)))
% 52.62/52.42 [7089]E(x70891,x70892)+~P1(f332(f332(f232(f853(x70893,a839)),x70891),x70892))+P1(f332(f332(f233(f853(x70893,a839)),x70891),x70892))
% 52.62/52.42 [7090]E(x70901,x70902)+~P1(f332(f332(f232(f853(x70903,a839)),x70901),x70902))+P1(f332(f332(f233(f853(x70903,a839)),x70901),x70902))
% 52.62/52.42 [7102]E(x71021,x71022)+~E(f332(f181(f846(x71023)),x71021),f332(f181(f846(x71023)),x71022))+P1(f332(f332(f233(a845),f730(x71023,x71021,x71022)),f332(f181(f846(x71023)),x71022)))
% 52.62/52.42 [7147]P14(x71471,x71472,x71473)+~E(f332(f261(x71471,x71471),x71473),x71472)+~E(f332(f332(f281(x71471,x71471,x71471),f332(f278(x71471,x71471),x71473)),x71473),x71473)
% 52.62/52.42 [7229]E(x72291,f2(a1))+~P1(f332(f332(f279(a1),x72292),x72293))+P1(f332(f332(f279(a1),f332(f332(f83(a1),x72291),x72292)),f332(f332(f83(a1),x72291),x72293)))
% 52.62/52.42 [7232]~P1(f332(x72321,f2(a845)))+P1(f332(f332(f233(a845),f800(x72323,x72322,x72321)),x72323))+P1(f332(x72321,f332(f332(f44(a845),x72322),x72323)))
% 52.62/52.42 [7245]~P100(x72451)+E(f332(f332(f103(f853(x72451,a839)),f298(x72451,x72452,x72453)),f332(f332(f302(x72451),x72453),f180(f853(x72451,a839)))),f297(x72451,x72452,x72453))+~P1(f332(f332(f233(x72451),x72452),x72453))
% 52.62/52.42 [7350]~P1(f332(f64(x73501),x73503))+P1(f332(f332(f233(a845),f332(f43(x73501),x73502)),f332(f43(x73501),x73503)))+~P1(f332(f332(f233(f853(x73501,a839)),x73502),x73503))
% 52.62/52.42 [7351]~P1(f332(f64(x73511),x73513))+P1(f332(f332(f232(a845),f332(f43(x73511),x73512)),f332(f43(x73511),x73513)))+~P1(f332(f332(f232(f853(x73511,a839)),x73512),x73513))
% 52.62/52.42 [7392]~P1(f332(x73923,x73922))+P1(f332(f332(f187(x73921),x73922),f418(x73922,x73921,x73923)))+~P1(f332(f332(f187(f35(x73923,x73921)),x73922),x73922))
% 52.62/52.42 [7489]E(x74891,x74892)+~P1(f332(f332(f232(f853(x74893,a839)),x74892),x74891))+~P1(f332(f332(f232(f853(x74893,a839)),x74891),x74892))
% 52.62/52.42 [7490]E(x74901,x74902)+~P1(f332(f332(f232(f853(x74903,a839)),x74902),x74901))+~P1(f332(f332(f232(f853(x74903,a839)),x74901),x74902))
% 52.62/52.42 [7493]~P100(x74931)+P20(x74931,x74932)+~P20(x74931,f332(f332(f138(x74931,x74931,f7(x74931)),x74933),x74932))
% 52.62/52.42 [7562]~P1(f332(f332(f233(a845),x75623),x75622))+~P1(f332(f332(f233(a845),x75623),x75621))+P1(f332(f332(f233(a845),f332(f332(f3(a845),x75621),x75622)),f332(f332(f3(a845),x75621),x75623)))
% 52.62/52.42 [7563]~P1(f332(f332(f233(a845),x75631),x75633))+~P1(f332(f332(f232(a845),x75632),x75631))+P1(f332(f332(f233(a845),f332(f332(f3(a845),x75631),x75632)),f332(f332(f3(a845),x75633),x75632)))
% 52.62/52.42 [7580]~P1(f332(f332(f233(a1),x75802),f2(a1)))+~P1(f332(f332(f232(a1),x75803),x75801))+P1(f332(f332(f232(a1),f332(f332(f44(a1),x75801),x75802)),f332(f332(f44(a1),x75803),x75802)))
% 52.62/52.42 [7597]~P1(f332(f332(f233(a845),f2(a845)),x75971))+~P1(f332(f332(f233(a845),x75972),x75973))+P1(f332(f332(f233(a845),f332(f332(f83(a845),x75971),x75972)),f332(f332(f83(a845),x75971),x75973)))
% 52.62/52.42 [7598]~P1(f332(f332(f233(a845),f2(a845)),x75981))+~P1(f332(f332(f233(a845),x75982),x75983))+P1(f332(f332(f233(a845),f332(f332(f83(a845),x75981),x75982)),f332(f332(f83(a845),x75981),x75983)))
% 52.62/52.42 [7599]~P1(f332(f332(f233(a845),f2(a845)),x75992))+~P1(f332(f332(f233(a845),x75991),x75993))+P1(f332(f332(f233(a845),f332(f332(f83(a845),x75991),x75992)),f332(f332(f83(a845),x75993),x75992)))
% 52.62/52.42 [7600]~P1(f332(f332(f233(a845),f2(a845)),x76002))+~P1(f332(f332(f233(a845),x76001),x76003))+P1(f332(f332(f233(a845),f332(f332(f83(a845),x76001),x76002)),f332(f332(f83(a845),x76003),x76002)))
% 52.62/52.42 [7601]~P1(f332(f332(f233(a845),f2(a845)),x76011))+~P1(f332(f332(f233(a845),x76012),x76013))+P1(f332(f332(f233(a845),f332(f332(f83(a845),x76011),x76012)),f332(f332(f83(a845),x76011),x76013)))
% 52.62/52.42 [7602]~P1(f332(f332(f233(a1),f2(a1)),x76021))+~P1(f332(f332(f233(a1),x76022),x76023))+P1(f332(f332(f233(a1),f332(f332(f83(a1),x76021),x76022)),f332(f332(f83(a1),x76021),x76023)))
% 52.62/52.42 [7603]~P1(f332(f332(f233(a845),f2(a845)),x76031))+~P1(f332(f332(f232(a845),x76032),x76033))+P1(f332(f332(f232(a845),f332(f332(f83(a845),x76031),x76032)),f332(f332(f83(a845),x76031),x76033)))
% 52.62/52.42 [7604]~P1(f332(f332(f233(a845),f2(a845)),x76043))+~P1(f332(f332(f232(a845),x76043),x76042))+P1(f332(f332(f232(a845),f332(f332(f44(a845),x76041),x76042)),f332(f332(f44(a845),x76041),x76043)))
% 52.62/52.42 [7605]~P1(f332(f332(f233(a1),f2(a1)),x76052))+~P1(f332(f332(f232(a1),x76051),x76053))+P1(f332(f332(f232(a1),f332(f332(f44(a1),x76051),x76052)),f332(f332(f44(a1),x76053),x76052)))
% 52.62/52.42 [7606]~P1(f332(f332(f233(a845),f2(a845)),x76061))+~P1(f332(f332(f279(a845),x76062),x76063))+P1(f332(f332(f279(a845),f332(f332(f83(a845),x76061),x76062)),f332(f332(f83(a845),x76061),x76063)))
% 52.62/52.42 [7654]E(x76541,f2(a845))+E(f332(f332(f82(a845),f332(f332(f83(a845),x76541),f798(x76541,x76542,x76543))),f800(x76541,x76542,x76543)),x76542)+P1(f332(x76543,f332(f332(f44(a845),x76542),x76541)))
% 52.62/52.42 [7712]E(f332(f332(f82(a845),f332(f332(f83(a845),x77121),f798(x77121,x77122,x77123))),f800(x77121,x77122,x77123)),x77122)+~P1(f332(x77123,f2(a845)))+P1(f332(x77123,f332(f332(f44(a845),x77122),x77121)))
% 52.62/52.42 [7728]~P1(f332(f64(x77281),x77283))+P1(f332(f332(f334(x77281),f464(x77282,x77283,x77281)),x77283))+P1(f332(f332(f233(a845),f2(a845)),f332(f332(f11(x77281,a845),x77282),x77283)))
% 52.62/52.42 [7729]~P1(f332(f64(x77291),x77293))+P1(f332(f332(f334(x77291),f572(x77292,x77293,x77291)),x77293))+P1(f332(f332(f233(a845),f2(a845)),f332(f332(f11(x77291,a845),x77292),x77293)))
% 52.62/52.42 [7834]E(x78341,f2(a845))+P1(f332(f332(f279(a845),x78342),x78343))+~P1(f332(f332(f279(a845),f332(f332(f83(a845),x78341),x78342)),f332(f332(f83(a845),x78341),x78343)))
% 52.62/52.42 [7835]E(x78351,f2(a1))+P1(f332(f332(f279(a1),x78352),x78353))+~P1(f332(f332(f279(a1),f332(f332(f83(a1),x78351),x78352)),f332(f332(f83(a1),x78351),x78353)))
% 52.62/52.42 [7836]E(x78361,f2(a1))+P1(f332(f332(f279(a1),x78362),x78363))+~P1(f332(f332(f279(a1),f332(f332(f83(a1),x78361),x78362)),f332(f332(f83(a1),x78361),x78363)))
% 52.62/52.42 [8022]E(x80221,f180(f853(x80222,a839)))+E(x80221,f332(f332(f302(x80222),x80223),f180(f853(x80222,a839))))+~P1(f332(f332(f232(f853(x80222,a839)),x80221),f332(f332(f302(x80222),x80223),f180(f853(x80222,a839)))))
% 52.62/52.42 [8058]~P1(f332(f332(f233(a845),f2(a845)),x80583))+P1(f332(f332(f233(a845),x80581),x80582))+~P1(f332(f332(f233(a845),f332(f332(f83(a845),x80583),x80581)),f332(f332(f83(a845),x80583),x80582)))
% 52.62/52.42 [8059]~P1(f332(f332(f233(a845),f2(a845)),x80593))+P1(f332(f332(f233(a845),x80591),x80592))+~P1(f332(f332(f233(a845),f332(f332(f242(a845),x80593),x80591)),f332(f332(f242(a845),x80593),x80592)))
% 52.62/52.42 [8060]~P1(f332(f332(f233(a845),f2(a845)),x80603))+P1(f332(f332(f232(a845),x80601),x80602))+~P1(f332(f332(f232(a845),f332(f332(f83(a845),x80603),x80601)),f332(f332(f83(a845),x80603),x80602)))
% 52.62/52.42 [8061]~P1(f332(f332(f233(a845),f2(a845)),x80613))+P1(f332(f332(f232(a845),x80611),x80612))+~P1(f332(f332(f232(a845),f332(f332(f83(a845),x80613),x80611)),f332(f332(f83(a845),x80613),x80612)))
% 52.62/52.42 [8062]~P1(f332(f332(f233(a845),f80(a845)),x80623))+P1(f332(f332(f232(a845),x80621),x80622))+~P1(f332(f332(f279(a845),f332(f332(f242(a845),x80623),x80621)),f332(f332(f242(a845),x80623),x80622)))
% 52.62/52.42 [8063]~P1(f332(f332(f233(a845),f2(a845)),x80633))+P1(f332(f332(f232(a845),x80631),x80632))+~P1(f332(f332(f232(a845),f332(f332(f83(a845),x80631),x80633)),f332(f332(f83(a845),x80632),x80633)))
% 52.62/52.42 [8064]~P1(f332(f332(f233(a845),f2(a845)),x80643))+P1(f332(f332(f279(a845),x80641),x80642))+~P1(f332(f332(f279(a845),f332(f332(f83(a845),x80643),x80641)),f332(f332(f83(a845),x80643),x80642)))
% 52.62/52.42 [8065]~P1(f332(f332(f233(a845),f2(a845)),x80653))+P1(f332(f332(f279(a845),x80651),x80652))+~P1(f332(f332(f279(a845),f332(f332(f83(a845),x80653),x80651)),f332(f332(f83(a845),x80653),x80652)))
% 52.62/52.42 [8093]~P1(f332(x80931,x80933))+P1(f332(f332(f187(f35(x80931,x80932)),f418(x80933,x80932,x80931)),x80933))+~P1(f332(f332(f187(f35(x80931,x80932)),x80933),x80933))
% 52.62/52.42 [8101]~E(f332(f332(f104(f853(x81011,a839)),f679(x81013,x81012,x81011)),f684(x81013,x81012,x81011)),f180(f853(x81011,a839)))+E(f332(f332(f104(f853(x81011,a839)),x81012),f45(f853(x81011,a839),x81013)),f180(f853(x81011,a839)))+P1(f332(f332(f334(f853(x81011,a839)),x81012),x81013))
% 52.62/52.42 [8115]E(x81151,f115(x81152))+~E(f332(f132(f846(x81152),f846(x81152),f125(x81152),f115(x81152)),x81153),f115(x81152))+~P1(f332(f332(f334(f846(x81152)),x81151),f332(f158(f846(x81152)),x81153)))
% 52.62/52.42 [8116]E(x81161,f115(x81162))+~E(f332(f132(f846(x81162),f846(x81162),f125(x81162),f115(x81162)),x81163),f115(x81162))+~P1(f332(f332(f334(f846(x81162)),x81161),f332(f158(f846(x81162)),x81163)))
% 52.62/52.42 [8173]E(x81731,f180(f853(f853(x81732,a839),a839)))+P1(f332(f332(f334(f853(x81732,a839)),f686(x81733,x81731,x81732)),x81731))+P1(f332(f332(f232(f853(x81732,a839)),f46(f853(x81732,a839),x81731)),x81733))
% 52.62/52.42 [8179]~P4(x81791)+~P70(x81791)+E(f332(f332(f8(a1,x81791),f332(f332(f10(a845,x81791,a1),x81792),a107)),f332(f303(a845,a1,f102(a1)),x81793)),f332(f332(f8(a845,x81791),x81792),x81793))
% 52.62/52.42 [8180]~P4(x81801)+~P70(x81801)+E(f332(f332(f11(a1,x81801),f332(f332(f10(a845,x81801,a1),x81802),a107)),f332(f303(a845,a1,f102(a1)),x81803)),f332(f332(f11(a845,x81801),x81802),x81803))
% 52.62/52.42 [8217]~P1(f332(f64(x82171),x82173))+~P1(f332(f332(f233(a845),f2(a845)),f332(x82172,f464(x82172,x82173,x82171))))+P1(f332(f332(f233(a845),f2(a845)),f332(f332(f11(x82171,a845),x82172),x82173)))
% 52.62/52.42 [8218]~P1(f332(f64(x82181),x82183))+~P1(f332(f332(f233(a845),f2(a845)),f332(x82182,f572(x82182,x82183,x82181))))+P1(f332(f332(f233(a845),f2(a845)),f332(f332(f11(x82181,a845),x82182),x82183)))
% 52.62/52.42 [8253]~P63(x82532)+E(x82531,f80(x82532))+E(f332(f332(f283(x82532),f332(f332(f3(x82532),f332(f332(f242(x82532),x82531),x82533)),f80(x82532))),f332(f332(f3(x82532),x82531),f80(x82532))),f332(f332(f8(a845,x82532),f332(f242(x82532),x82531)),f332(f294(a845,f2(a845)),x82533)))
% 52.62/52.42 [8312]E(x83121,f2(a845))+~P1(f332(x83123,f332(f332(f44(a845),x83122),x83121)))+P1(f332(f332(f233(a845),x83122),f332(f332(f83(a845),x83121),f332(a114,f788(x83121,x83122,x83123)))))
% 52.62/52.42 [8333]P1(f332(x83331,f2(a845)))+~P1(f332(x83331,f332(f332(f44(a845),x83332),x83333)))+P1(f332(f332(f233(a845),x83332),f332(f332(f83(a845),x83333),f332(a114,f788(x83333,x83332,x83331)))))
% 52.62/52.42 [8372]E(x83721,f2(a845))+~P1(f332(x83723,f332(f332(f44(a845),x83722),x83721)))+P1(f332(f332(f232(a845),f332(f332(f83(a845),x83721),f788(x83721,x83722,x83723))),x83722))
% 52.62/52.42 [8409]P1(f332(x84091,f2(a845)))+~P1(f332(x84091,f332(f332(f44(a845),x84093),x84092)))+P1(f332(f332(f232(a845),f332(f332(f83(a845),x84092),f788(x84092,x84093,x84091))),x84093))
% 52.62/52.42 [8412]~P100(x84121)+E(f332(f332(f138(x84121,x84121,f7(x84121)),x84122),x84123),f139(x84121,x84121,f7(x84121),x84122,x84123))+P1(f332(f332(f334(x84121),x84122),f332(f158(x84121),x84123)))
% 52.62/52.42 [8452]~E(f332(x84523,f609(x84522,x84523,x84521)),f332(x84523,f611(x84522,x84523,x84521)))+~P60(x84521,f332(x84523,f610(x84522,x84523,x84521)))+P60(x84521,f332(f332(f47(x84522,f853(x84521,f853(x84521,a839))),f239(f853(x84522,a839))),x84523))
% 52.62/52.42 [8460]E(x84601,f180(f853(f853(x84602,a839),a839)))+~P1(f332(f332(f232(f853(x84602,a839)),f686(x84603,x84601,x84602)),x84603))+P1(f332(f332(f232(f853(x84602,a839)),f46(f853(x84602,a839),x84601)),x84603))
% 52.62/52.42 [8519]~P65(x85191)+~P1(f332(f332(f233(x85191),x85192),x85193))+P1(f332(f332(f233(x85191),x85192),f332(f332(f283(x85191),f332(f332(f82(x85191),x85192),x85193)),f332(f332(f82(x85191),f80(x85191)),f80(x85191)))))
% 52.62/52.42 [8562]~P1(f332(f332(x85621,f821(x85621,x85623,x85622)),f822(x85621,x85623,x85622)))+P1(f332(f332(x85621,x85622),x85623))+~P1(f332(f321(f852(a1,a1),a60),f332(f332(f241(a1,a1),x85622),x85623)))
% 52.62/52.42 [8563]~P1(f332(f332(x85631,f823(x85631,x85633,x85632)),f824(x85631,x85633,x85632)))+P1(f332(f332(x85631,x85632),x85633))+~P1(f332(f321(f852(a1,a1),a63),f332(f332(f241(a1,a1),x85632),x85633)))
% 52.62/52.42 [8564]~P1(f332(f332(x85641,f825(x85641,x85643,x85642)),f828(x85641,x85643,x85642)))+P1(f332(f332(x85641,x85642),x85643))+~P1(f332(f321(f852(a1,a1),a216),f332(f332(f241(a1,a1),x85642),x85643)))
% 52.62/52.42 [8565]~P1(f332(f332(x85651,f829(x85651,x85653,x85652)),f830(x85651,x85653,x85652)))+P1(f332(f332(x85651,x85652),x85653))+~P1(f332(f321(f852(a845,a845),a214),f332(f332(f241(a845,a845),x85652),x85653)))
% 52.62/52.42 [8566]~P1(f332(f332(x85661,f388(x85661,x85663,x85662)),f396(x85661,x85663,x85662)))+P1(f332(f332(x85661,x85662),x85663))+~P1(f332(f321(f852(a1,a1),a168),f332(f332(f241(a1,a1),x85662),x85663)))
% 52.62/52.42 [8800]P1(f332(f332(x88001,x88002),x88003))+P1(f332(f321(f852(a845,a845),a214),f332(f332(f241(a845,a845),f829(x88001,x88003,x88002)),f830(x88001,x88003,x88002))))+~P1(f332(f321(f852(a845,a845),a214),f332(f332(f241(a845,a845),x88002),x88003)))
% 52.62/52.42 [8801]P1(f332(f332(x88011,x88012),x88013))+P1(f332(f321(f852(a1,a1),a60),f332(f332(f241(a1,a1),f821(x88011,x88013,x88012)),f822(x88011,x88013,x88012))))+~P1(f332(f321(f852(a1,a1),a60),f332(f332(f241(a1,a1),x88012),x88013)))
% 52.62/52.42 [8802]P1(f332(f332(x88021,x88022),x88023))+P1(f332(f321(f852(a1,a1),a63),f332(f332(f241(a1,a1),f823(x88021,x88023,x88022)),f824(x88021,x88023,x88022))))+~P1(f332(f321(f852(a1,a1),a63),f332(f332(f241(a1,a1),x88022),x88023)))
% 52.62/52.42 [8803]P1(f332(f332(x88031,x88032),x88033))+P1(f332(f321(f852(a1,a1),a216),f332(f332(f241(a1,a1),f825(x88031,x88033,x88032)),f828(x88031,x88033,x88032))))+~P1(f332(f321(f852(a1,a1),a216),f332(f332(f241(a1,a1),x88032),x88033)))
% 52.62/52.42 [8804]P1(f332(f332(x88041,x88042),x88043))+P1(f332(f321(f852(a1,a1),a168),f332(f332(f241(a1,a1),f388(x88041,x88043,x88042)),f396(x88041,x88043,x88042))))+~P1(f332(f321(f852(a1,a1),a168),f332(f332(f241(a1,a1),x88042),x88043)))
% 52.62/52.42 [9116]~P1(f332(f64(x91161),x91163))+P1(f332(f332(f334(f852(f853(x91161,a839),f853(x91161,a839))),f332(f332(f241(f853(x91161,a839),f853(x91161,a839)),x91162),x91163)),f299(x91161)))+~P1(f332(f332(f233(f853(x91161,a839)),x91162),x91163))
% 52.62/52.42 [9169]~P60(x91691,f332(x91693,f610(x91692,x91693,x91691)))+P60(x91691,f332(f332(f47(x91692,f853(x91691,f853(x91691,a839))),f239(f853(x91692,a839))),x91693))+~E(f332(f332(f104(f853(x91691,a839)),f246(x91691,x91691,f332(x91693,f609(x91692,x91693,x91691)))),f247(x91691,x91691,f332(x91693,f611(x91692,x91693,x91691)))),f180(f853(x91691,a839)))
% 52.62/52.42 [9362]P49(x93621,x93622,x93623)+P1(f332(f332(f334(f852(x93621,x93621)),f505(x93623,x93622,x93621)),x93623))+~P1(f332(f332(f334(f852(x93621,x93621)),f332(f332(f241(x93621,x93621),f504(x93623,x93622,x93621)),f504(x93623,x93622,x93621))),x93623))
% 52.62/52.42 [9928]P49(x99281,x99282,x99283)+~P1(f332(f332(f251(x99281,x99281,a839),f332(f332(f9(x99281,f853(x99281,a839),f853(x99281,a839)),f332(f332(f10(f853(a839,a839),f853(f853(x99281,a839),f853(x99281,a839)),x99281),f10(a839,a839,x99281)),f332(f332(f10(a839,f853(a839,a839),x99281),a330),f332(f332(f9(x99281,f853(x99281,a839),a839),f334(x99281)),x99282)))),f332(f332(f9(x99281,f853(x99281,a839),a839),f334(x99281)),x99282))),f505(x99283,x99282,x99281)))+~P1(f332(f332(f334(f852(x99281,x99281)),f332(f332(f241(x99281,x99281),f504(x99283,x99282,x99281)),f504(x99283,x99282,x99281))),x99283))
% 52.62/52.42 [5524]~P9(x55242)+E(x55241,f2(x55242))+E(f332(f332(f44(x55242),f332(f332(f83(x55242),x55243),x55241)),x55241),x55243)
% 52.62/52.42 [5525]~P9(x55252)+E(x55251,f2(x55252))+E(f332(f332(f44(x55252),f332(f332(f83(x55252),x55251),x55253)),x55251),x55253)
% 52.62/52.42 [6171]~P9(x61711)+E(f332(f332(f83(x61711),f332(f332(f44(x61711),x61712),x61713)),x61713),x61712)+~P1(f332(f332(f279(x61711),x61713),x61712))
% 52.62/52.42 [6337]~P4(x63371)+~E(f332(x63372,f2(a845)),f2(x63371))+E(f332(f332(f8(a845,x63371),x63372),f332(f294(a845,f332(a114,f2(a845))),x63373)),f332(f332(f8(a845,x63371),x63372),f332(f294(a845,f2(a845)),x63373)))
% 52.62/52.42 [6480]~P9(x64802)+E(x64801,f2(x64802))+E(f332(f332(f44(x64802),f332(f332(f82(x64802),x64803),x64801)),x64801),f332(f332(f82(x64802),f332(f332(f44(x64802),x64803),x64801)),f80(x64802)))
% 52.62/52.42 [6481]~P9(x64812)+E(x64811,f2(x64812))+E(f332(f332(f44(x64812),f332(f332(f82(x64812),x64811),x64813)),x64811),f332(f332(f82(x64812),f332(f332(f44(x64812),x64813),x64811)),f80(x64812)))
% 52.62/52.42 [6709]~P1(f332(x67093,f2(a1)))+P1(f332(f332(f232(a845),x67091),x67092))+P1(f332(x67093,f332(f102(a1),f332(f332(f3(a845),x67092),x67091))))
% 52.62/52.42 [6819]P1(f332(f332(f232(a845),x68192),x68191))+P1(f332(f332(f233(a845),x68191),x68192))+P1(f332(x68193,f332(f102(a1),f332(f332(f3(a845),x68191),x68192))))
% 52.62/52.42 [6892]E(f332(f332(f82(a845),f332(f106(a845),x68921)),f332(f332(f82(a845),f332(f106(a845),x68922)),x68923)),f332(f332(f82(a845),f332(f106(a845),x68921)),x68923))+P1(f332(a186,f332(f106(a1),x68921)))+~P1(f332(a186,f332(f106(a1),x68922)))
% 52.62/52.42 [6970]~E(x69702,f332(f332(f44(a845),x69703),x69701))+~P1(f332(f332(f233(a845),f2(a845)),x69701))+P1(f332(f332(f232(a845),f332(f332(f83(a845),x69701),x69702)),x69703))
% 52.62/52.42 [7086]~P1(f332(f64(x70861),x70863))+~P1(f332(f64(x70861),x70862))+P1(f332(f64(x70861),f332(f332(f3(f853(x70861,a839)),x70862),x70863)))
% 52.62/52.42 [7087]~P1(f332(f64(x70871),x70873))+~P1(f332(f64(x70871),x70872))+P1(f332(f64(x70871),f332(f332(f103(f853(x70871,a839)),x70872),x70873)))
% 52.62/52.42 [7088]~P1(f332(f64(x70881),x70883))+~P1(f332(f64(x70881),x70882))+P1(f332(f64(x70881),f332(f332(f103(f853(x70881,a839)),x70882),x70883)))
% 52.62/52.42 [7403]~P100(x74031)+~P1(f332(f64(x74031),x74032))+E(f130(x74031,f332(f332(f3(f853(x74031,a839)),x74032),f332(f332(f302(x74031),x74033),f180(f853(x74031,a839))))),f151(x74031,x74033,f130(x74031,x74032)))
% 52.62/52.42 [7469]P1(f332(x74691,f2(a1)))+~P1(f332(f332(f233(a845),x74692),x74693))+~P1(f332(x74691,f332(f102(a1),f332(f332(f3(a845),x74692),x74693))))
% 52.62/52.42 [7487]~P1(f332(f64(x74871),x74872))+E(f332(f43(x74871),f332(f332(f3(f853(x74871,a839)),x74872),f332(f332(f302(x74871),x74873),f180(f853(x74871,a839))))),f332(f43(x74871),x74872))+P1(f332(f332(f334(x74871),x74873),x74872))
% 52.62/52.42 [7621]~P117(x76211)+~P1(f332(f332(f233(x76211),f80(x76211)),x76212))+P1(f332(f332(f233(x76211),f80(x76211)),f332(f332(f83(x76211),x76212),f332(f332(f242(x76211),x76212),x76213))))
% 52.62/52.42 [7665]~P1(f332(f64(x76651),x76653))+E(f332(f332(f3(a845),f332(f43(x76651),x76652)),f332(f43(x76651),x76653)),f332(f43(x76651),f332(f332(f3(f853(x76651,a839)),x76652),x76653)))+~P1(f332(f332(f232(f853(x76651,a839)),x76653),x76652))
% 52.62/52.42 [7720]~P1(f332(f332(f232(a845),x77202),x77203))+~P1(f332(f332(f232(a845),x77201),f332(f332(f3(a845),x77203),x77202)))+P1(f332(f332(f232(a845),f332(f332(f82(a845),x77201),x77202)),x77203))
% 52.62/52.42 [7777]P1(f332(f64(x77771),x77772))+~P1(f332(f64(x77771),x77773))+~P1(f332(f64(x77771),f332(f332(f3(f853(x77771,a839)),x77772),x77773)))
% 52.62/52.42 [7783]~P1(f332(f64(x77831),x77832))+E(f332(f43(x77831),f332(f332(f3(f853(x77831,a839)),x77832),f332(f332(f302(x77831),x77833),f180(f853(x77831,a839))))),f332(f332(f3(a845),f332(f43(x77831),x77832)),f80(a845)))+~P1(f332(f332(f334(x77831),x77833),x77832))
% 52.62/52.42 [7784]~P1(f332(f64(x77841),x77842))+E(f332(f43(x77841),f332(f332(f3(f853(x77841,a839)),x77842),f332(f332(f302(x77841),x77843),f180(f853(x77841,a839))))),f332(f332(f3(a845),f332(f43(x77841),x77842)),f80(a845)))+~P1(f332(f332(f334(x77841),x77843),x77842))
% 52.62/52.42 [7859]P60(x78591,x78592)+~P60(x78591,x78593)+~P1(f332(f332(f232(f853(x78591,f853(x78591,a839))),x78592),x78593))
% 52.62/52.42 [7897]~P1(f332(f332(f232(a845),x78973),x78972))+P1(f332(f332(f232(a845),x78971),f332(f332(f3(a845),x78972),x78973)))+~P1(f332(f332(f232(a845),f332(f332(f82(a845),x78971),x78973)),x78972))
% 52.62/52.42 [7917]P38(x79171,x79172)+~P38(x79171,x79173)+~P1(f332(f332(f232(f853(f852(x79171,x79171),a839)),x79172),x79173))
% 52.62/52.42 [7918]P58(x79181,x79182)+~P58(x79181,x79183)+~P1(f332(f332(f232(f853(f852(x79181,x79181),a839)),x79182),x79183))
% 52.62/52.42 [8151]~P117(x81511)+~P1(f332(f332(f233(x81511),f80(x81511)),x81512))+P1(f332(f332(f233(x81511),f332(f332(f242(x81511),x81512),x81513)),f332(f332(f83(x81511),x81512),f332(f332(f242(x81511),x81512),x81513))))
% 52.62/52.42 [8237]~P1(f332(x82371,f2(a1)))+~P1(f332(x82371,f332(f332(f3(a1),f332(f102(a1),x82372)),f332(f102(a1),x82373))))+P1(f332(x82371,f332(f102(a1),f332(f332(f3(a845),x82372),x82373))))
% 52.62/52.42 [8250]~P1(f332(f332(f232(a845),x82503),x82502))+P1(f332(x82501,f332(f332(f3(a1),f332(f102(a1),x82502)),f332(f102(a1),x82503))))+~P1(f332(x82501,f332(f102(a1),f332(f332(f3(a845),x82502),x82503))))
% 52.62/52.42 [8267]P1(f332(f332(f233(a845),x82671),x82672))+~P1(f332(x82673,f332(f332(f3(a1),f332(f102(a1),x82671)),f332(f102(a1),x82672))))+P1(f332(x82673,f332(f102(a1),f332(f332(f3(a845),x82671),x82672))))
% 52.62/52.42 [8324]~P119(x83242)+E(x83241,f2(x83242))+P1(f332(f332(f233(x83242),f2(x83242)),f332(f332(f82(x83242),f332(f332(f83(x83242),x83243),x83243)),f332(f332(f83(x83242),x83241),x83241))))
% 52.62/52.42 [8325]~P119(x83252)+E(x83251,f2(x83252))+P1(f332(f332(f233(x83252),f2(x83252)),f332(f332(f82(x83252),f332(f332(f83(x83252),x83251),x83251)),f332(f332(f83(x83252),x83253),x83253))))
% 52.62/52.42 [8431]~P1(f332(f332(f233(a845),f2(a845)),x84311))+~P1(f332(f332(f233(a1),x84312),x84313))+P1(f332(f332(f233(a1),f332(f332(f83(a1),f332(f102(a1),x84311)),x84312)),f332(f332(f83(a1),f332(f102(a1),x84311)),x84313)))
% 52.62/52.42 [8491]E(f332(f332(f104(f853(x84911,a839)),x84912),f45(f853(x84911,a839),x84913)),f180(f853(x84911,a839)))+P1(f332(f332(f334(f853(x84911,a839)),x84912),x84913))+P1(f332(f332(f334(f853(x84911,a839)),f679(x84913,x84912,x84911)),f332(f332(f302(f853(x84911,a839)),x84912),x84913)))
% 52.62/52.42 [8492]E(f332(f332(f104(f853(x84921,a839)),x84922),f45(f853(x84921,a839),x84923)),f180(f853(x84921,a839)))+P1(f332(f332(f334(f853(x84921,a839)),x84922),x84923))+P1(f332(f332(f334(f853(x84921,a839)),f684(x84923,x84922,x84921)),f332(f332(f302(f853(x84921,a839)),x84922),x84923)))
% 52.62/52.42 [8518]E(x85181,x85182)+~E(f332(f181(f846(x85183)),x85181),f332(f181(f846(x85183)),x85182))+P1(f332(f332(f334(f852(x85183,x85183)),f713(x85183,x85181,x85182)),f332(f158(f852(x85183,x85183)),f332(f332(f167(x85183,x85183),x85182),x85181))))
% 52.62/52.42 [8728]E(f300(x87281,x87282),f300(x87281,x87283))+~P1(f332(f332(f232(f853(f852(x87281,x87281),a839)),x87283),f300(x87281,x87282)))+~P1(f332(f332(f232(f853(f852(x87281,x87281),a839)),x87282),x87283))
% 52.62/52.42 [8781]~P49(x87811,f239(f853(x87811,a839)),x87813)+P1(f332(f332(f232(f853(f852(f846(x87811),f846(x87811)),a839)),f146(x87811,x87812)),f147(x87811,x87813)))+~P1(f332(f332(f232(f853(f852(x87811,x87811),a839)),x87812),x87813))
% 52.62/52.42 [8960]P38(x89601,x89602)+~P1(f332(f332(f334(x89601),x89603),f682(x89602,x89601)))+P1(f332(f332(f334(f852(x89601,x89601)),f332(f332(f241(x89601,x89601),f697(x89602,x89601,x89603)),x89603)),x89602))
% 52.62/52.42 [8999]~P1(f332(f64(x89991),x89992))+P1(f332(f64(f853(x89991,a839)),f332(f332(f62(x89991),x89992),x89993)))+~P1(f332(f332(f232(f853(f852(x89991,x89991),a839)),x89993),f332(f332(f248(x89991,x89991),x89992),f332(f18(f853(x89991,a839),x89991),x89992))))
% 52.62/52.42 [9030]P49(x90301,x90302,x90303)+P1(f332(f332(f334(x90301),f550(x90303,x90302,x90301)),x90302))+~P1(f332(f332(f232(f853(f852(x90301,x90301),a839)),x90303),f332(f332(f248(x90301,x90301),x90302),f332(f18(f853(x90301,a839),x90301),x90302))))
% 52.62/52.42 [9031]P49(x90311,x90312,x90313)+P1(f332(f332(f334(x90311),f558(x90312,x90313,x90311)),x90312))+~P1(f332(f332(f232(f853(f852(x90311,x90311),a839)),x90313),f332(f332(f248(x90311,x90311),x90312),f332(f18(f853(x90311,a839),x90311),x90312))))
% 52.62/52.42 [9064]~P65(x90641)+~P1(f332(f332(f233(x90641),x90642),x90643))+P1(f332(f332(f233(x90641),f332(f332(f283(x90641),f332(f332(f82(x90641),x90642),x90643)),f332(f332(f82(x90641),f80(x90641)),f80(x90641)))),x90643))
% 52.62/52.42 [9091]~P64(x90911)+P1(f332(f332(f232(x90911),x90912),x90913))+~P1(f332(f332(f232(x90911),f332(f332(f83(x90911),f797(x90913,x90912,x90911)),x90912)),x90913))
% 52.62/52.42 [9198]E(f307(x91981,x91982,x91983),f183(f846(a837)))+~P1(f332(f332(f233(a1),x91982),x91983))+~P1(f332(f321(f852(f853(a1,f849(f846(a837))),f852(a1,a1)),a311),f332(f332(f241(f853(a1,f849(f846(a837))),f852(a1,a1)),x91981),f332(f332(f241(a1,a1),x91982),x91983))))
% 52.62/52.42 [9201]E(f332(f181(f846(f846(x92011))),f332(f126(f846(x92011),f332(f332(f10(a845,a839,f846(x92011)),f332(f233(a845),x92012)),f181(f846(x92011)))),f164(x92011,x92013))),f332(f181(f846(x92011)),f332(f332(f152(f846(x92011)),x92013),x92012)))+~P20(a845,f332(f142(a845),f332(f332(f143(f846(x92011),a845),f181(f846(x92011))),x92013)))+~P1(f332(f332(f233(a845),x92012),f332(f181(f846(f846(x92011))),x92013)))
% 52.62/52.42 [9312]~P38(x93121,x93122)+P32(x93121,f332(f332(f241(f853(f852(x93121,x93121),a839),f853(f852(x93121,x93121),a839)),x93122),x93123))+~P1(f332(f332(f232(f853(f852(x93121,x93121),a839)),f332(f332(f281(x93121,x93121,x93121),x93122),x93123)),x93122))
% 52.62/52.42 [9314]E(f332(f229(f849(f846(a837)),f846(a837),f307(x93141,x93142,f332(f332(f82(a1),x93143),f80(a1))),f227(f846(a837))),f332(x93141,x93143)),f307(x93141,x93142,x93143))+P1(f332(f332(f233(a1),x93142),x93143))+~P1(f332(f321(f852(f853(a1,f849(f846(a837))),f852(a1,a1)),a311),f332(f332(f241(f853(a1,f849(f846(a837))),f852(a1,a1)),x93141),f332(f332(f241(a1,a1),x93142),x93143))))
% 52.62/52.42 [9319]E(f332(f332(f143(f846(x93191),x93191),f332(f332(f9(f846(x93191),a845,x93191),f152(x93191)),x93192)),f332(f126(f846(x93191),f332(f332(f10(a845,a839,f846(x93191)),f332(f233(a845),x93192)),f181(f846(x93191)))),f164(x93191,x93193))),f332(f332(f152(f846(x93191)),x93193),x93192))+~P20(a845,f332(f142(a845),f332(f332(f143(f846(x93191),a845),f181(f846(x93191))),x93193)))+~P1(f332(f332(f233(a845),x93192),f332(f181(f846(f846(x93191))),x93193)))
% 52.62/52.42 [9446]P49(x94461,x94462,x94463)+~P1(f332(f332(f334(f852(x94461,x94461)),f332(f332(f241(x94461,x94461),f550(x94463,x94462,x94461)),f550(x94463,x94462,x94461))),x94463))+~P1(f332(f332(f232(f853(f852(x94461,x94461),a839)),x94463),f332(f332(f248(x94461,x94461),x94462),f332(f18(f853(x94461,a839),x94461),x94462))))
% 52.62/52.42 [9447]P49(x94471,x94472,x94473)+~P1(f332(f332(f334(f852(x94471,x94471)),f332(f332(f241(x94471,x94471),f558(x94472,x94473,x94471)),f558(x94472,x94473,x94471))),x94473))+~P1(f332(f332(f232(f853(f852(x94471,x94471),a839)),x94473),f332(f332(f248(x94471,x94471),x94472),f332(f18(f853(x94471,a839),x94471),x94472))))
% 52.62/52.42 [9606]~P133(x96061)+~P116(x96061)+E(f332(f332(f283(x96061),f332(f105(x96061),f332(f332(f75(f852(a1,a1),a1,x96062,f240(a1,a1)),f207(x96062)),x96063))),f332(f105(x96061),f332(f332(f75(f852(a1,a1),a1,x96062,f250(a1,a1)),f207(x96062)),x96063))),f217(x96062,x96061,x96063))
% 52.62/52.42 [9803]~E(x98033,f2(a845))+~E(f332(f181(f846(x98031)),f332(f332(f152(f846(x98031)),x98032),f766(x98033,x98031,x98032))),x98033)+E(f332(f332(f143(a845,f846(x98031)),f332(f332(f9(a845,f846(a845),f846(x98031)),f332(f332(f10(f853(a845,x98031),f853(f846(a845),f846(x98031)),a845),f143(a845,x98031)),f332(f9(a845,a845,x98031),f332(f332(f10(f846(x98031),f853(a845,x98031),a845),f152(x98031)),f332(f152(f846(x98031)),x98032))))),f130(a845,f332(f294(a845,f2(a845)),f332(f181(f846(f846(x98031))),x98032))))),f130(a845,f332(f294(a845,f2(a845)),x98033))),f164(x98031,x98032))
% 52.62/52.42 [9804]E(x98041,f115(f846(x98042)))+~E(f332(f181(f846(x98042)),f332(f332(f152(f846(x98042)),x98041),f766(x98043,x98042,x98041))),x98043)+E(f332(f332(f143(a845,f846(x98042)),f332(f332(f9(a845,f846(a845),f846(x98042)),f332(f332(f10(f853(a845,x98042),f853(f846(a845),f846(x98042)),a845),f143(a845,x98042)),f332(f9(a845,a845,x98042),f332(f332(f10(f846(x98042),f853(a845,x98042),a845),f152(x98042)),f332(f152(f846(x98042)),x98041))))),f130(a845,f332(f294(a845,f2(a845)),f332(f181(f846(f846(x98042))),x98041))))),f130(a845,f332(f294(a845,f2(a845)),x98043))),f164(x98042,x98041))
% 52.62/52.42 [9805]~E(x98053,f2(a845))+E(f332(f332(f143(a845,f846(x98051)),f332(f332(f9(a845,f846(a845),f846(x98051)),f332(f332(f10(f853(a845,x98051),f853(f846(a845),f846(x98051)),a845),f143(a845,x98051)),f332(f9(a845,a845,x98051),f332(f332(f10(f846(x98051),f853(a845,x98051),a845),f152(x98051)),f332(f152(f846(x98051)),x98052))))),f130(a845,f332(f294(a845,f2(a845)),f332(f181(f846(f846(x98051))),x98052))))),f130(a845,f332(f294(a845,f2(a845)),x98053))),f164(x98051,x98052))+P1(f332(f332(f233(a845),f766(x98053,x98051,x98052)),f332(f181(f846(f846(x98051))),x98052)))
% 52.62/52.42 [9806]E(x98061,f115(f846(x98062)))+E(f332(f332(f143(a845,f846(x98062)),f332(f332(f9(a845,f846(a845),f846(x98062)),f332(f332(f10(f853(a845,x98062),f853(f846(a845),f846(x98062)),a845),f143(a845,x98062)),f332(f9(a845,a845,x98062),f332(f332(f10(f846(x98062),f853(a845,x98062),a845),f152(x98062)),f332(f152(f846(x98062)),x98061))))),f130(a845,f332(f294(a845,f2(a845)),f332(f181(f846(f846(x98062))),x98061))))),f130(a845,f332(f294(a845,f2(a845)),x98063))),f164(x98062,x98061))+P1(f332(f332(f233(a845),f766(x98063,x98062,x98061)),f332(f181(f846(f846(x98062))),x98061)))
% 52.62/52.42 [7662]E(f332(f332(f82(a845),f332(f106(a845),x76621)),f332(f332(f82(a845),f332(f106(a845),x76622)),x76623)),f332(f332(f82(a845),f332(f106(a845),f332(f332(f82(a1),x76621),x76622))),x76623))+P1(f332(a186,f332(f106(a1),x76621)))+P1(f332(a186,f332(f106(a1),x76622)))
% 52.62/52.42 [8422]~P1(f332(f64(x84221),x84222))+~P1(f332(f332(f334(x84221),x84223),x84222))+E(f332(a114,f332(f43(x84221),f332(f332(f3(f853(x84221,a839)),x84222),f332(f332(f302(x84221),x84223),f180(f853(x84221,a839)))))),f332(f43(x84221),x84222))
% 52.62/52.42 [8442]~P1(f332(f64(x84421),x84422))+~P1(f332(f332(f334(x84421),x84423),x84422))+E(f332(f332(f82(a845),f80(a845)),f332(f43(x84421),f332(f332(f3(f853(x84421,a839)),x84422),f332(f332(f302(x84421),x84423),f180(f853(x84421,a839)))))),f332(f43(x84421),x84422))
% 52.62/52.42 [8526]~P100(x85261)+~P1(f332(f64(x85261),x85263))+E(f332(f332(f138(x85261,x85261,f7(x85261)),x85262),f130(x85261,f332(f332(f3(f853(x85261,a839)),x85263),f332(f332(f302(x85261),x85262),f180(f853(x85261,a839)))))),f130(x85261,f332(f332(f302(x85261),x85262),x85263)))
% 52.62/52.42 [8663]~P1(f332(f64(x86631),x86633))+~P1(f332(f64(x86631),x86632))+E(f332(f332(f82(a845),f332(f43(x86631),f332(f332(f103(f853(x86631,a839)),x86632),x86633))),f332(f43(x86631),f332(f332(f104(f853(x86631,a839)),x86632),x86633))),f332(f332(f82(a845),f332(f43(x86631),x86632)),f332(f43(x86631),x86633)))
% 52.62/52.42 [8664]~P1(f332(f64(x86641),x86643))+~P1(f332(f64(x86641),x86642))+E(f332(f332(f82(a845),f332(f43(x86641),f332(f332(f103(f853(x86641,a839)),x86642),x86643))),f332(f43(x86641),f332(f332(f104(f853(x86641,a839)),x86642),x86643))),f332(f332(f82(a845),f332(f43(x86641),x86642)),f332(f43(x86641),x86643)))
% 52.62/52.42 [9752]~P31(x97521,f853(f853(x97521,a839),a839),f332(f332(f9(x97521,f853(f852(x97521,x97521),a839),f853(f853(x97521,a839),a839)),f332(f332(f10(f853(x97521,a839),f853(f853(f852(x97521,x97521),a839),f853(f853(x97521,a839),a839)),x97521),f62(x97521)),f332(f332(f9(x97521,f853(x97521,a839),f853(x97521,a839)),f302(x97521)),f180(f853(x97521,a839))))),x97523),x97522)+~P1(f332(f64(x97521),x97522))+E(f332(f43(f853(x97521,a839)),f332(f332(f62(x97521),x97522),x97523)),f332(f43(x97521),x97522))
% 52.62/52.42 [7934]~P88(x79341)+P1(f332(f332(f232(a1),f2(a1)),f332(f106(a1),x79343)))+E(f332(f332(f242(x79341),x79342),f332(f106(a845),f332(f332(f3(a1),f332(f332(f82(a1),x79343),x79343)),a99))),f80(x79341))
% 52.62/52.42 [8023]~P88(x80231)+P1(f332(f332(f232(a1),f2(a1)),f332(f106(a1),x80233)))+E(f332(f332(f242(x80231),f332(f106(x80231),x80232)),f332(f106(a845),f332(f332(f3(a1),f332(f332(f82(a1),x80233),x80233)),a99))),f80(x80231))
% 52.62/52.42 [9295]~P88(x92951)+~P1(f332(f332(f232(a1),f2(a1)),f332(f106(a1),x92953)))+E(f332(f332(f242(x92951),x92952),f332(f106(a845),f332(f332(f3(a1),f332(f332(f82(a1),x92953),x92953)),a99))),f332(f332(f88(x92951,x92951),f332(f332(f242(x92951),x92952),f332(f106(a845),x92953))),f332(f332(f20(x92951,x92951,x92951),f332(f332(f10(x92951,f853(x92951,x92951),x92951),f83(x92951)),f332(f83(x92951),x92952))),f7(x92951))))
% 52.62/52.42 [9361]~P88(x93611)+~P1(f332(f332(f232(a1),f2(a1)),f332(f106(a1),x93613)))+E(f332(f332(f242(x93611),f332(f106(x93611),x93612)),f332(f106(a845),f332(f332(f3(a1),f332(f332(f82(a1),x93613),x93613)),a99))),f332(f332(f88(x93611,x93611),f332(f332(f242(x93611),f332(f106(x93611),x93612)),f332(f106(a845),x93613))),f332(f332(f20(x93611,x93611,x93611),f332(f332(f10(x93611,f853(x93611,x93611),x93611),f83(x93611)),f332(f83(x93611),f332(f106(x93611),x93612)))),f7(x93611))))
% 52.62/52.42 [9717]P1(f332(f332(f232(f853(f852(x97171,x97171),a839)),f300(x97171,x97172)),x97173))+~P1(f332(f332(f232(f853(f852(x97171,x97171),a839)),f300(x97171,f180(f853(f852(x97171,x97171),a839)))),x97173))+~P1(f332(f332(f232(f853(f852(x97171,x97171),a839)),f332(f332(f281(x97171,x97171,x97171),f332(f332(f104(f853(f852(x97171,x97171),a839)),f300(x97171,x97172)),x97173)),x97172)),x97173))
% 52.62/52.42 [9582]~P1(f332(f64(x95821),f332(f256(x95821),x95823)))+~P1(f332(f64(x95821),f332(f256(x95821),x95822)))+P1(f332(f64(x95821),f332(f256(x95821),f332(f332(f20(x95821,a839,a839),f332(f332(f10(a839,f853(a839,a839),x95821),a331),x95822)),x95823))))
% 52.62/52.42 [9871]P1(f332(f332(f232(f853(f852(x98711,x98711),a839)),f332(f332(f281(x98711,x98711,x98711),x98712),f300(x98711,x98712))),x98713))+~P1(f332(f332(f232(f853(f852(x98711,x98711),a839)),x98712),x98713))+~P1(f332(f332(f232(f853(f852(x98711,x98711),a839)),f332(f332(f281(x98711,x98711,x98711),f332(f332(f104(f853(f852(x98711,x98711),a839)),f332(f332(f281(x98711,x98711,x98711),x98712),f300(x98711,x98712))),x98713)),x98712)),x98713))
% 52.62/52.42 [9819]~P110(x98192)+E(x98191,f2(x98192))+~E(f332(f332(f82(x98192),f332(f332(f242(x98192),x98193),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))),f332(f332(f242(x98192),x98191),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))),f2(x98192))
% 52.62/52.42 [9820]~P110(x98202)+E(x98201,f2(x98202))+~E(f332(f332(f82(x98202),f332(f332(f242(x98202),x98201),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))),f332(f332(f242(x98202),x98203),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))),f2(x98202))
% 52.62/52.42 [9913]~P110(x99132)+E(x99131,f2(x99132))+P1(f332(f332(f233(x99132),f2(x99132)),f332(f332(f82(x99132),f332(f332(f242(x99132),x99133),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))),f332(f332(f242(x99132),x99131),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))))))
% 52.62/52.42 [9914]~P110(x99142)+E(x99141,f2(x99142))+P1(f332(f332(f233(x99142),f2(x99142)),f332(f332(f82(x99142),f332(f332(f242(x99142),x99141),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))),f332(f332(f242(x99142),x99143),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))))))
% 52.62/52.42 [9962]~P110(x99621)+P1(f332(f332(f232(x99621),f2(x99621)),x99622))+~P1(f332(f332(f232(x99621),f2(x99621)),f332(f332(f242(x99621),x99622),f332(a114,f332(f332(f83(a845),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),x99623)))))
% 52.62/52.42 [5369]~P30(x53691,x53694,x53693)+P30(x53691,x53692,x53693)+~P30(x53691,x53692,x53694)
% 52.62/52.42 [4845]~E(x48452,f92(x48453,x48451))+P1(f332(x48451,x48452))+~P1(f332(x48451,x48454))
% 52.62/52.42 [6614]~P38(x66142,x66144)+~P38(x66141,x66143)+P38(f852(x66141,x66142),f326(x66141,x66142,x66143,x66144))
% 52.62/52.42 [8005]~P41(f35(x80054,x80051),x80052,x80053,x80052)+P41(x80051,x80052,x80053,f345(x80053,x80052,x80051,x80054))+~P1(f332(x80054,x80052))
% 52.62/52.42 [8032]~P41(f35(x80321,x80322),x80324,x80323,x80324)+P41(f35(x80321,x80322),f345(x80323,x80324,x80322,x80321),x80323,x80324)+~P1(f332(x80321,x80324))
% 52.62/52.42 [5026]~P13(x50264,x50261)+~E(f332(x50261,x50262),f332(x50261,x50263))+P1(f332(f332(x50261,x50262),x50263))
% 52.62/52.42 [5188]~P13(x51884,x51881)+E(f332(x51881,x51882),f332(x51881,x51883))+~P1(f332(f332(x51881,x51882),x51883))
% 52.62/52.42 [5276]~P24(x52763,x52764,x52761)+E(f332(x52761,x52762),f332(f66(x52763,x52764),x52762))+~P1(f332(f64(x52763),x52762))
% 52.62/52.42 [5277]~P16(x52773,x52774,x52771)+E(f332(x52771,x52772),f332(f66(x52773,x52774),x52772))+~P1(f332(f64(x52773),x52772))
% 52.62/52.42 [5404]~P13(x54044,x54041)+~P1(f332(f332(x54041,x54043),x54042))+P1(f332(f332(x54041,x54042),x54043))
% 52.62/52.42 [5467]E(x54671,x54672)+~E(f332(f240(x54673,x54674),x54671),f332(f240(x54673,x54674),x54672))+~E(f332(f250(x54673,x54674),x54671),f332(f250(x54673,x54674),x54672))
% 52.62/52.42 [5468]E(x54681,x54682)+~E(f332(f240(x54683,x54684),x54681),f332(f240(x54683,x54684),x54682))+~E(f332(f250(x54683,x54684),x54681),f332(f250(x54683,x54684),x54682))
% 52.62/52.42 [5494]E(x54941,x54942)+~P1(f332(f56(x54943,x54944),x54942))+~P1(f332(f56(x54943,x54944),x54941))
% 52.62/52.42 [5688]~P4(x56882)+E(f225(x56881,x56882,x56883,x56884),f2(x56882))+P1(f332(f64(x56881),x56884))
% 52.62/52.42 [5823]~P1(f332(f321(x58231,x58232),x58234))+P1(f332(f321(x58231,x58232),x58233))+~P1(f332(f332(x58232,x58233),x58234))
% 52.62/52.42 [5824]~P1(f332(f321(x58241,x58242),x58244))+P1(f332(f321(x58241,x58242),x58243))+~P1(f332(f332(x58242,x58243),x58244))
% 52.62/52.42 [5825]~P1(f332(f321(x58251,x58252),x58254))+P1(f332(f321(x58251,x58252),x58253))+~P1(f332(f332(x58252,x58253),x58254))
% 52.62/52.42 [8075]~P1(f332(f64(x80752),x80754))+~P1(f332(f64(x80751),x80753))+P1(f332(f64(f854(x80751,x80752)),f314(x80751,x80752,x80753,x80754)))
% 52.62/52.42 [8076]~P1(f332(f64(x80762),x80764))+~P1(f332(f64(x80761),x80763))+P1(f332(f64(f854(x80761,x80762)),f314(x80761,x80762,x80763,x80764)))
% 52.62/52.42 [8079]P1(f332(f332(f334(f846(x80791)),f332(f332(f125(x80791),x80792),x80793)),f149(x80791,x80794)))+~P1(f332(f332(f334(f846(x80791)),x80793),f149(x80791,x80794)))+~P1(f332(f332(f334(f846(x80791)),x80792),f149(x80791,x80794)))
% 52.62/52.42 [8653]~P1(f332(f332(f334(f852(x86531,x86531)),f332(f332(f241(x86531,x86531),x86532),x86534)),f300(x86531,x86533)))+P1(f332(f332(f334(x86531),x86532),f322(x86531,x86533)))+~P1(f332(f332(f334(x86531),x86534),f322(x86531,x86533)))
% 52.62/52.42 [8654]~P1(f332(f332(f334(f852(x86541,x86541)),f332(f332(f241(x86541,x86541),x86542),x86544)),f300(x86541,x86543)))+P1(f332(f332(f334(x86541),x86542),f322(x86541,x86543)))+~P1(f332(f332(f334(x86541),x86544),f322(x86541,x86543)))
% 52.62/52.42 [5008]~P4(x50082)+E(f332(f332(f8(x50081,x50082),x50083),x50084),f2(x50082))+P1(f332(f64(x50081),x50084))
% 52.62/52.42 [5009]~P4(x50092)+E(f332(f332(f8(x50091,x50092),x50093),x50094),f2(x50092))+P1(f332(f64(x50091),x50094))
% 52.62/52.42 [5010]~P4(x50102)+E(f332(f332(f8(x50101,x50102),x50103),x50104),f2(x50102))+P1(f332(f64(x50101),x50104))
% 52.62/52.42 [5011]~P70(x50112)+E(f332(f332(f11(x50111,x50112),x50113),x50114),f80(x50112))+P1(f332(f64(x50111),x50114))
% 52.62/52.42 [5012]~P70(x50122)+E(f332(f332(f11(x50121,x50122),x50123),x50124),f80(x50122))+P1(f332(f64(x50121),x50124))
% 52.62/52.42 [5013]~P70(x50132)+E(f332(f332(f11(x50131,x50132),x50133),x50134),f80(x50132))+P1(f332(f64(x50131),x50134))
% 52.62/52.42 [5156]~P5(x51563)+E(x51561,x51562)+~E(f332(f332(f82(x51563),x51564),x51561),f332(f332(f82(x51563),x51564),x51562))
% 52.62/52.42 [5157]~P5(x51573)+E(x51571,x51572)+~E(f332(f332(f82(x51573),x51574),x51571),f332(f332(f82(x51573),x51574),x51572))
% 52.62/52.42 [5158]~P6(x51583)+E(x51581,x51582)+~E(f332(f332(f82(x51583),x51584),x51581),f332(f332(f82(x51583),x51584),x51582))
% 52.62/52.42 [5159]~P5(x51593)+E(x51591,x51592)+~E(f332(f332(f82(x51593),x51591),x51594),f332(f332(f82(x51593),x51592),x51594))
% 52.62/52.42 [5160]~P5(x51603)+E(x51601,x51602)+~E(f332(f332(f82(x51603),x51601),x51604),f332(f332(f82(x51603),x51602),x51604))
% 52.62/52.42 [5246]~P112(x52461)+~E(x52463,f332(f332(f83(x52461),x52462),x52464))+P1(f332(f332(f279(x52461),x52462),x52463))
% 52.62/52.42 [5271]~P11(x52713)+E(x52711,f180(f853(x52712,a839)))+E(f332(f332(f47(x52712,x52713),x52711),f332(f18(x52713,x52712),x52714)),x52714)
% 52.62/52.42 [5272]~P11(x52723)+E(x52721,f180(f853(x52722,a839)))+E(f332(f332(f48(x52722,x52723),x52721),f332(f18(x52723,x52722),x52724)),x52724)
% 52.62/52.42 [5482]~P99(x54823)+E(x54821,x54822)+~E(f295(x54823,x54824,x54821),f332(f332(f302(x54823),x54822),f180(f853(x54823,a839))))
% 52.62/52.42 [5483]~P99(x54833)+E(x54831,x54832)+~E(f295(x54833,x54831,x54832),f332(f332(f302(x54833),x54834),f180(f853(x54833,a839))))
% 52.62/52.42 [5787]P1(f332(x57871,x57872))+~P1(f332(f245(x57873,x57871),x57874))+~P1(f332(f332(f334(x57873),x57872),x57874))
% 52.62/52.42 [5816]E(x58161,x58162)+~P1(f332(f332(f187(x58163),x58164),x58162))+~P1(f332(f332(f187(x58163),x58164),x58161))
% 52.62/52.42 [5898]~P4(x58981)+E(f332(f332(f8(a845,x58981),x58982),f332(f294(a845,x58983),f332(a114,x58984))),f2(x58981))+~P1(f332(f332(f233(a845),x58984),x58983))
% 52.62/52.42 [5903]~P10(x59031)+~E(f53(x59031,x59032,x59033),f53(x59031,x59034,x59033))+E(f53(x59031,f332(f81(x59031),x59032),x59033),f53(x59031,f332(f81(x59031),x59034),x59033))
% 52.62/52.42 [5973]P1(f332(x59731,x59732))+~E(f332(f126(x59733,x59731),x59734),x59734)+~P1(f332(f332(f334(x59733),x59732),f332(f158(x59733),x59734)))
% 52.62/52.42 [5992]~E(f332(f332(f82(a845),x59923),x59922),f332(f332(f82(a845),x59921),x59924))+~P1(f332(f332(f233(a845),x59923),x59924))+P1(f332(f332(f233(a845),x59921),x59922))
% 52.62/52.42 [5999]~P9(x59991)+E(f53(x59991,f53(x59991,x59992,x59993),x59994),f53(x59991,x59992,x59994))+~P1(f332(f332(f279(x59991),x59994),x59993))
% 52.62/52.42 [6037]~E(f332(f126(x60371,x60372),x60373),f115(x60371))+~P1(f332(x60372,x60374))+~P1(f332(f332(f334(x60371),x60374),f332(f158(x60371),x60373)))
% 52.62/52.42 [6038]~E(f162(x60383,x60381,x60384),x60384)+P1(f332(x60381,x60382))+~P1(f332(f332(f334(x60383),x60382),f332(f158(x60383),x60384)))
% 52.62/52.42 [6073]~E(x60734,f180(f853(x60732,a839)))+~E(x60733,f180(f853(x60731,a839)))+E(f314(x60731,x60732,x60733,x60734),f180(f853(f854(x60731,x60732),a839)))
% 52.62/52.42 [6509]~P4(x65091)+E(f332(f332(f8(a845,x65091),x65092),f295(a845,x65093,f332(a114,x65094))),f2(x65091))+~P1(f332(f332(f233(a845),f332(a114,x65094)),x65093))
% 52.62/52.42 [6657]~P100(x66571)+E(f332(f332(f3(f853(x66571,a839)),f332(f294(x66571,x66572),x66573)),f332(f294(x66571,x66572),x66574)),f332(f294(x66571,x66574),x66573))+~P1(f332(f332(f232(x66571),x66572),x66574))
% 52.62/52.42 [7018]~P1(f332(f332(f334(f846(x70181)),x70184),f149(x70181,x70183)))+P1(f332(f332(f334(x70181),x70182),x70183))+~P1(f332(f332(f334(x70181),x70182),f332(f158(x70181),x70184)))
% 52.62/52.42 [7025]~P38(x70251,x70252)+P1(f332(f332(f334(x70251),f694(x70252,x70251,x70253)),x70253))+~P1(f332(f332(f334(x70251),x70254),x70253))
% 52.62/52.42 [7057]~P31(x70572,x70571,x70573,x70574)+E(f332(f43(x70571),f332(f303(x70572,x70571,x70573),x70574)),f332(f43(x70572),x70574))+~P1(f332(f64(x70572),x70574))
% 52.62/52.42 [7081]~P4(x70811)+E(f332(f332(f332(f68(x70811,x70812,f82(x70811)),x70813),f2(x70811)),x70814),f332(f332(f8(x70812,x70811),x70813),x70814))+~P1(f332(f64(x70812),x70814))
% 52.62/52.42 [7082]~P4(x70821)+E(f332(f332(f332(f68(x70821,x70822,f82(x70821)),x70823),f2(x70821)),x70824),f332(f332(f8(x70822,x70821),x70823),x70824))+~P1(f332(f64(x70822),x70824))
% 52.62/52.42 [7083]~P70(x70831)+E(f332(f332(f332(f68(x70831,x70832,f83(x70831)),x70833),f80(x70831)),x70834),f332(f332(f11(x70832,x70831),x70833),x70834))+~P1(f332(f64(x70832),x70834))
% 52.62/52.42 [7084]~P70(x70841)+E(f332(f332(f332(f68(x70841,x70842,f83(x70841)),x70843),f80(x70841)),x70844),f332(f332(f11(x70842,x70841),x70843),x70844))+~P1(f332(f64(x70842),x70844))
% 52.62/52.42 [7110]P31(x71101,x71102,x71103,x71104)+~E(f332(f43(x71102),f332(f303(x71101,x71102,x71103),x71104)),f332(f43(x71101),x71104))+~P1(f332(f64(x71101),x71104))
% 52.62/52.42 [7111]P31(x71111,x71112,x71113,x71114)+~E(f332(f43(x71112),f332(f303(x71111,x71112,x71113),x71114)),f332(f43(x71111),x71114))+~P1(f332(f64(x71111),x71114))
% 52.62/52.42 [7315]~P4(x73151)+E(f332(f332(f82(x73151),f332(x73152,x73153)),f332(f332(f8(a845,x73151),x73152),f297(a845,x73153,x73154))),f332(f332(f8(a845,x73151),x73152),f295(a845,x73153,x73154)))+~P1(f332(f332(f232(a845),x73153),x73154))
% 52.62/52.42 [7325]~P4(x73251)+~P31(x73252,x73251,x73253,x73254)+E(f332(f332(f8(x73251,x73251),f39(x73251)),f332(f303(x73252,x73251,x73253),x73254)),f332(f332(f8(x73252,x73251),x73253),x73254))
% 52.62/52.42 [7326]~P70(x73261)+~P31(x73262,x73261,x73263,x73264)+E(f332(f332(f11(x73261,x73261),f39(x73261)),f332(f303(x73262,x73261,x73263),x73264)),f332(f332(f11(x73262,x73261),x73263),x73264))
% 52.62/52.42 [7384]E(f332(f43(f854(x73841,x73842)),f314(x73841,x73842,x73843,x73844)),f332(f332(f82(a845),f332(f43(x73841),x73843)),f332(f43(x73842),x73844)))+~P1(f332(f64(x73842),x73844))+~P1(f332(f64(x73841),x73843))
% 52.62/52.42 [7385]E(f332(f43(f854(x73851,x73852)),f314(x73851,x73852,x73853,x73854)),f332(f332(f82(a845),f332(f43(x73851),x73853)),f332(f43(x73852),x73854)))+~P1(f332(f64(x73852),x73854))+~P1(f332(f64(x73851),x73853))
% 52.62/52.42 [7470]E(x74701,x74702)+P1(f332(f332(f334(x74703),x74701),f332(f158(x74703),f151(x74703,x74702,x74704))))+~P1(f332(f332(f334(x74703),x74701),f332(f158(x74703),x74704)))
% 52.62/52.42 [7696]~P4(x76961)+E(f332(f332(f82(x76961),f332(f332(f8(a845,x76961),x76962),f332(f294(a845,x76963),x76964))),f332(x76962,x76964)),f332(f332(f8(a845,x76961),x76962),f332(f294(a845,x76963),f332(a114,x76964))))+P1(f332(f332(f233(a845),x76964),x76963))
% 52.62/52.42 [7753]~P31(x77531,x77532,x77533,f239(f853(x77531,a839)))+~P1(f332(f64(x77532),x77534))+P1(f332(f64(x77531),f332(f305(x77531,x77532,x77533),x77534)))
% 52.62/52.42 [7867]P1(f332(f332(f334(f846(x78671)),f332(f332(f140(x78671),x78672),x78673)),f149(x78671,x78674)))+~P1(f332(f332(f334(f846(x78671)),x78673),f149(x78671,x78674)))+~P1(f332(f332(f334(x78671),x78672),x78674))
% 52.62/52.42 [7916]E(x79161,x79162)+~P1(f332(f332(f334(x79163),x79161),f332(f158(x79163),f151(x79163,x79162,x79164))))+P1(f332(f332(f334(x79163),x79161),f332(f158(x79163),x79164)))
% 52.62/52.42 [7958]~E(f332(f303(x79583,x79581,x79584),f239(f853(x79583,a839))),f239(f853(x79581,a839)))+P1(f332(f64(x79581),x79582))+~P1(f332(f64(x79583),f332(f305(x79583,x79581,x79584),x79582)))
% 52.62/52.42 [8048]~P31(x80481,x80483,x80484,x80482)+P1(f332(f64(x80481),x80482))+~P1(f332(f64(x80483),f332(f303(x80481,x80483,x80484),x80482)))
% 52.62/52.42 [8070]~E(x80702,x80703)+P1(f332(f332(f334(f852(x80701,x80701)),f332(f332(f241(x80701,x80701),x80702),x80703)),f260(x80701,x80704)))+~P1(f332(f332(f334(x80701),x80702),x80704))
% 52.62/52.42 [8071]~E(x80712,x80713)+P1(f332(f332(f334(f852(x80711,x80711)),f332(f332(f241(x80711,x80711),x80712),x80713)),f260(x80711,x80714)))+~P1(f332(f332(f334(x80711),x80712),x80714))
% 52.62/52.42 [8102]~P4(x81021)+E(f332(f332(f82(x81021),f332(f332(f8(a845,x81021),x81022),f295(a845,x81023,x81024))),f332(x81022,f332(a114,x81024))),f332(f332(f8(a845,x81021),x81022),f295(a845,x81023,f332(a114,x81024))))+P1(f332(f332(f233(a845),f332(a114,x81024)),x81023))
% 52.62/52.42 [8163]~E(x81632,x81634)+P1(f332(f332(f334(f852(x81631,x81631)),f332(f332(f241(x81631,x81631),x81632),x81634)),f300(x81631,x81633)))+P1(f332(f332(f334(x81631),x81632),f332(f261(x81631,x81631),x81633)))
% 52.62/52.42 [8165]P1(f332(x81651,x81652))+~P1(f332(x81651,f332(f332(f152(x81653),x81654),f725(x81651,x81654,x81653))))+~P1(f332(f332(f334(x81653),x81652),f332(f158(x81653),x81654)))
% 52.62/52.42 [8299]~P1(f332(f332(f334(x82991),x82992),f322(x82991,x82994)))+P1(f332(f332(f334(f846(x82991)),f332(f332(f140(x82991),x82992),x82993)),f322(f846(x82991),f146(x82991,x82994))))+~P1(f332(f332(f334(f846(x82991)),x82993),f322(f846(x82991),f146(x82991,x82994))))
% 52.62/52.42 [8315]~P31(x83152,x83153,x83154,f687(x83154,x83153,x83152,x83151))+P31(x83152,x83153,x83154,f46(f853(x83152,a839),x83151))+E(x83151,f180(f853(f853(x83152,a839),a839)))
% 52.62/52.42 [8576]E(x85761,x85762)+~P1(f332(f332(f334(f852(x85763,x85763)),f332(f332(f241(x85763,x85763),x85761),x85762)),f300(x85763,x85764)))+P1(f332(f332(f334(x85763),x85761),f332(f261(x85763,x85763),x85764)))
% 52.62/52.42 [8823]P31(x88232,x88233,x88234,f46(f853(x88232,a839),x88231))+E(x88231,f180(f853(f853(x88232,a839),a839)))+P1(f332(f332(f334(f853(x88232,a839)),f687(x88234,x88233,x88232,x88231)),x88231))
% 52.62/52.42 [8951]P1(f332(f64(x89511),x89512))+~P1(f332(f64(x89514),f332(f303(x89511,x89514,x89513),x89512)))+P1(f332(f332(f334(x89511),f599(x89513,x89514,x89512,x89511)),x89512))
% 52.62/52.42 [9043]~P11(x90432)+E(f332(f332(f67(x90431,x90432,f332(f332(f10(x90432,f853(x90432,x90432),x90431),f103(x90432)),x90433)),f180(x90432)),x90434),f332(f332(f47(x90431,x90432),x90434),x90433))+~P1(f332(f64(x90431),x90434))
% 52.62/52.42 [9044]~P11(x90442)+E(f332(f332(f67(x90441,x90442,f332(f332(f10(x90442,f853(x90442,x90442),x90441),f104(x90442)),x90443)),f239(x90442)),x90444),f332(f332(f48(x90441,x90442),x90444),x90443))+~P1(f332(f64(x90441),x90444))
% 52.62/52.42 [9070]~P1(f332(f332(f279(a845),x90703),x90704))+P1(f332(f332(f279(a845),x90701),x90702))+P1(f332(f332(f233(f853(a845,a839)),f282(a845,f279(a845),x90701,x90702)),f282(a845,f279(a845),x90703,x90704)))
% 52.62/52.42 [9081]~P1(f332(f332(f279(a845),x90812),x90814))+~P1(f332(f332(f279(a845),x90813),x90811))+P1(f332(f332(f232(f853(a845,a839)),f282(a845,f279(a845),x90811,x90812)),f282(a845,f279(a845),x90813,x90814)))
% 52.62/52.42 [9138]E(x91381,x91382)+~P1(f332(f332(f334(f852(x91383,x91383)),f332(f332(f241(x91383,x91383),x91381),x91382)),f300(x91383,x91384)))+P1(f332(f332(f334(f852(x91383,x91383)),f332(f332(f241(x91383,x91383),x91381),x91382)),f332(f332(f281(x91383,x91383,x91383),x91384),f300(x91383,x91384))))
% 52.62/52.42 [9139]E(x91391,x91392)+~P1(f332(f332(f334(f852(x91393,x91393)),f332(f332(f241(x91393,x91393),x91391),x91392)),f300(x91393,x91394)))+P1(f332(f332(f334(f852(x91393,x91393)),f332(f332(f241(x91393,x91393),x91391),x91392)),f332(f332(f281(x91393,x91393,x91393),x91394),f300(x91393,x91394))))
% 52.62/52.42 [9170]~E(f332(f181(f846(x91701)),x91702),f332(f181(f846(x91701)),x91703))+~P1(f332(f332(f334(f852(f846(x91701),f846(x91701))),f332(f332(f241(f846(x91701),f846(x91701)),x91702),x91703)),f137(x91701,x91704)))+P1(f332(f332(f334(f852(f846(x91701),f846(x91701))),f332(f332(f241(f846(x91701),f846(x91701)),x91702),x91703)),f135(x91701,x91704)))
% 52.62/52.42 [9190]E(x91901,x91902)+P1(f332(f332(f334(f852(x91903,x91903)),f332(f332(f241(x91903,x91903),x91901),x91902)),f300(x91903,x91904)))+~P1(f332(f332(f334(f852(x91903,x91903)),f332(f332(f241(x91903,x91903),x91901),x91902)),f332(f332(f281(x91903,x91903,x91903),x91904),f300(x91903,x91904))))
% 52.62/52.42 [9282]P1(f332(f332(f279(a845),x92821),x92822))+~P1(f332(f332(f279(a845),x92823),x92821))+~P1(f332(f332(f233(f853(a845,a839)),f282(a845,f279(a845),x92823,x92821)),f282(a845,f279(a845),x92824,x92822)))
% 52.62/52.42 [9283]P1(f332(f332(f279(a845),x92831),x92832))+~P1(f332(f332(f279(a845),x92833),x92831))+~P1(f332(f332(f232(f853(a845,a839)),f282(a845,f279(a845),x92833,x92831)),f282(a845,f279(a845),x92834,x92832)))
% 52.62/52.42 [9284]P1(f332(f332(f279(a845),x92841),x92842))+~P1(f332(f332(f279(a845),x92842),x92843))+~P1(f332(f332(f233(f853(a845,a839)),f282(a845,f279(a845),x92842,x92843)),f282(a845,f279(a845),x92841,x92844)))
% 52.62/52.42 [9285]P1(f332(f332(f279(a845),x92851),x92852))+~P1(f332(f332(f279(a845),x92852),x92853))+~P1(f332(f332(f232(f853(a845,a839)),f282(a845,f279(a845),x92852,x92853)),f282(a845,f279(a845),x92851,x92854)))
% 52.62/52.42 [9585]~P8(x95851)+E(f332(f332(f8(a845,x95851),f332(f332(f20(a845,x95851,x95851),f332(f332(f10(x95851,f853(x95851,x95851),a845),f3(x95851)),x95852)),f332(f332(f10(a845,x95851,a845),x95852),f332(f332(f9(a845,a845,a845),f82(a845)),f80(a845))))),f295(a845,x95853,x95854)),f2(x95851))+P1(f332(f332(f232(a845),x95853),x95854))
% 52.62/52.42 [9817]~P38(x98172,x98174)+~P31(x98172,x98171,x98173,f239(f853(x98172,a839)))+P38(x98171,f332(f303(f852(x98172,x98172),f852(x98171,x98171),f252(x98172,x98171,x98172,x98171,x98173,x98173)),x98174))
% 52.62/52.42 [9990]~E(f332(f181(f846(x99901)),x99903),f332(f181(f846(x99901)),x99902))+P1(f332(f332(f334(f852(f846(x99901),f846(x99901))),f332(f332(f241(f846(x99901),f846(x99901)),x99902),x99903)),f147(x99901,x99904)))+~P1(f332(f332(f251(x99901,x99901,a839),f332(f332(f9(x99901,f853(f852(x99901,x99901),a839),f853(x99901,a839)),f332(f332(f10(f853(x99901,f853(f853(f852(x99901,x99901),a839),a839)),f853(f853(f852(x99901,x99901),a839),f853(x99901,a839)),x99901),f9(x99901,f853(f852(x99901,x99901),a839),a839)),f332(f332(f10(f853(x99901,f852(x99901,x99901)),f853(x99901,f853(f853(f852(x99901,x99901),a839),a839)),x99901),f332(f10(f852(x99901,x99901),f853(f853(f852(x99901,x99901),a839),a839),x99901),f334(f852(x99901,x99901)))),f241(x99901,x99901)))),x99904)),f716(x99904,x99903,x99902,x99901)))
% 52.62/52.42 [5862]~E(x58624,x58622)+P1(f332(x58621,x58622))+P1(f332(f332(f187(f35(x58621,x58623)),x58622),x58624))
% 52.62/52.42 [5957]~P9(x59571)+~E(x59572,f2(x59571))+E(f332(f332(f44(x59571),f332(f332(f83(x59571),x59572),x59573)),f332(f332(f83(x59571),x59572),x59574)),f2(x59571))
% 52.62/52.42 [5996]E(x59961,f115(x59962))+E(x59963,f332(f332(f3(a845),f332(f181(f846(x59962)),x59961)),f80(a845)))+E(f134(x59962,f332(f332(f148(x59962,x59961),x59963),x59964)),f134(x59962,x59961))
% 52.62/52.42 [6028]E(x60281,x60282)+P1(f332(x60283,x60282))+~P1(f332(f332(f332(f302(x60284),x60281),x60283),x60282))
% 52.62/52.42 [6042]~P4(x60421)+~P1(f332(f127(x60422),x60424))+E(f332(f154(x60421),f332(f332(f143(x60422,x60421),x60423),x60424)),f332(f332(f8(x60422,x60421),x60423),f332(f158(x60422),x60424)))
% 52.62/52.42 [6066]~P70(x60662)+~P1(f332(f64(x60661),x60664))+E(f332(f332(f11(x60661,x60662),f332(f18(x60662,x60661),x60663)),x60664),f332(f332(f242(x60662),x60663),f332(f43(x60661),x60664)))
% 52.62/52.42 [6122]~P9(x61222)+E(x61221,f2(x61222))+E(f332(f332(f44(x61222),f332(f332(f83(x61222),x61223),x61221)),f332(f332(f83(x61222),x61224),x61221)),f332(f332(f44(x61222),x61223),x61224))
% 52.62/52.42 [6123]~P9(x61232)+E(x61231,f2(x61232))+E(f332(f332(f44(x61232),f332(f332(f83(x61232),x61231),x61233)),f332(f332(f83(x61232),x61231),x61234)),f332(f332(f44(x61232),x61233),x61234))
% 52.62/52.42 [6124]~P62(x61242)+E(x61241,f2(x61242))+E(f332(f332(f283(x61242),f332(f332(f83(x61242),x61243),x61241)),f332(f332(f83(x61242),x61244),x61241)),f332(f332(f283(x61242),x61243),x61244))
% 52.62/52.42 [6125]~P62(x61252)+E(x61251,f2(x61252))+E(f332(f332(f283(x61252),f332(f332(f83(x61252),x61251),x61253)),f332(f332(f83(x61252),x61251),x61254)),f332(f332(f283(x61252),x61253),x61254))
% 52.62/52.42 [6126]~P9(x61262)+E(x61261,f2(x61262))+E(f332(f332(f44(x61262),f332(f332(f83(x61262),x61261),x61263)),f332(f332(f83(x61262),x61261),x61264)),f332(f332(f44(x61262),x61263),x61264))
% 52.62/52.42 [6191]P1(f332(x61911,x61912))+~E(x61913,f332(f332(f82(a845),x61914),x61912))+~P1(f332(x61911,f332(f332(f3(a845),x61913),x61914)))
% 52.62/52.42 [6192]P1(f332(x61921,x61922))+~E(x61923,f332(f332(f82(a845),x61924),x61922))+~P1(f332(x61921,f332(f332(f3(a845),x61923),x61924)))
% 52.62/52.42 [6275]P34(x62751,x62752,x62753)+P33(x62751,f805(x62753,x62752,x62751),x62754)+~P1(f332(f332(f334(f844(x62751)),x62754),x62752))
% 52.62/52.42 [6321]E(x63211,f115(x63212))+~E(x63213,f332(f332(f3(a845),f332(f181(f846(x63212)),x63211)),f80(a845)))+E(f134(x63212,f332(f332(f148(x63212,x63211),x63213),x63214)),x63214)
% 52.62/52.42 [6343]~P100(x63431)+~P1(f332(f332(f233(x63431),x63432),x63434))+P1(f332(f332(f233(x63431),x63432),f332(f332(f179(x63431),x63433),x63434)))
% 52.62/52.42 [6344]~P100(x63441)+~P1(f332(f332(f233(x63441),x63442),x63444))+P1(f332(f332(f233(x63441),x63442),f332(f332(f179(x63441),x63443),x63444)))
% 52.62/52.42 [6345]~P100(x63451)+~P1(f332(f332(f233(x63451),x63452),x63453))+P1(f332(f332(f233(x63451),x63452),f332(f332(f179(x63451),x63453),x63454)))
% 52.62/52.42 [6346]~P100(x63461)+~P1(f332(f332(f233(x63461),x63462),x63463))+P1(f332(f332(f233(x63461),x63462),f332(f332(f179(x63461),x63463),x63464)))
% 52.62/52.42 [6347]~P92(x63471)+~P1(f332(f332(f233(x63471),x63472),x63474))+P1(f332(f332(f233(x63471),x63472),f332(f332(f103(x63471),x63473),x63474)))
% 52.62/52.42 [6348]~P92(x63481)+~P1(f332(f332(f233(x63481),x63482),x63483))+P1(f332(f332(f233(x63481),x63482),f332(f332(f103(x63481),x63483),x63484)))
% 52.62/52.42 [6349]~P100(x63491)+~P1(f332(f332(f232(x63491),x63492),x63494))+P1(f332(f332(f232(x63491),x63492),f332(f332(f179(x63491),x63493),x63494)))
% 52.62/52.42 [6350]~P100(x63501)+~P1(f332(f332(f232(x63501),x63502),x63504))+P1(f332(f332(f232(x63501),x63502),f332(f332(f179(x63501),x63503),x63504)))
% 52.62/52.42 [6351]~P100(x63511)+~P1(f332(f332(f232(x63511),x63512),x63513))+P1(f332(f332(f232(x63511),x63512),f332(f332(f179(x63511),x63513),x63514)))
% 52.62/52.42 [6352]~P100(x63521)+~P1(f332(f332(f232(x63521),x63522),x63523))+P1(f332(f332(f232(x63521),x63522),f332(f332(f179(x63521),x63523),x63524)))
% 52.62/52.42 [6353]~P92(x63531)+~P1(f332(f332(f232(x63531),x63532),x63534))+P1(f332(f332(f232(x63531),x63532),f332(f332(f103(x63531),x63533),x63534)))
% 52.62/52.42 [6354]~P92(x63541)+~P1(f332(f332(f232(x63541),x63542),x63543))+P1(f332(f332(f232(x63541),x63542),f332(f332(f103(x63541),x63543),x63544)))
% 52.62/52.42 [6355]~P73(x63551)+~P1(f332(f332(f279(x63551),x63552),x63554))+P1(f332(f332(f279(x63551),x63552),f332(f332(f83(x63551),x63553),x63554)))
% 52.62/52.42 [6356]~P73(x63561)+~P1(f332(f332(f279(x63561),x63562),x63563))+P1(f332(f332(f279(x63561),x63562),f332(f332(f83(x63561),x63563),x63564)))
% 52.62/52.42 [6451]~E(f332(f332(f152(x64511),x64512),x64513),x64514)+E(f332(f332(f148(x64511,x64512),x64513),x64514),x64512)+~P1(f332(f332(f233(a845),x64513),f332(f181(f846(x64511)),x64512)))
% 52.62/52.42 [6470]E(x64701,x64702)+P1(f332(x64703,x64701))+~P1(f332(f332(f187(f35(x64703,x64704)),x64701),x64702))
% 52.62/52.42 [6471]E(x64711,x64712)+P1(f332(x64713,x64711))+~P1(f332(f332(f187(f35(x64713,x64714)),x64711),x64712))
% 52.62/52.42 [6491]P1(f332(x64911,x64912))+~P1(f332(x64913,x64912))+~P1(f332(f332(f232(f853(x64914,a839)),x64913),x64911))
% 52.62/52.42 [6492]P1(f332(x64921,x64922))+~P1(f332(x64923,x64922))+~P1(f332(f332(f232(f853(x64924,a839)),x64923),x64921))
% 52.62/52.42 [6528]~E(f332(f332(f148(x65281,x65282),x65283),x65284),x65282)+E(f332(f332(f152(x65281),x65282),x65283),x65284)+~P1(f332(f332(f233(a845),x65283),f332(f181(f846(x65281)),x65282)))
% 52.62/52.42 [6645]P33(x66451,x66452,x66453)+~P33(x66451,f332(a114,x66452),f819(x66452,x66454,x66451))+~P1(f332(f332(f334(f844(x66451)),x66453),x66454))
% 52.62/52.42 [6654]E(x66541,f180(f853(x66542,a839)))+E(x66543,f180(f853(x66544,a839)))+~E(f332(f332(f248(x66544,x66542),x66543),f332(f18(f853(x66542,a839),x66544),x66541)),f180(f853(f852(x66544,x66542),a839)))
% 52.62/52.42 [6671]E(x66711,x66712)+P1(f332(f332(f334(x66713),x66711),x66714))+~P1(f332(f332(f334(x66713),x66711),f332(f332(f302(x66713),x66712),x66714)))
% 52.62/52.42 [6672]E(x66721,x66722)+P1(f332(f332(f334(x66723),x66721),x66724))+~P1(f332(f332(f334(x66723),x66721),f332(f332(f302(x66723),x66722),x66724)))
% 52.62/52.42 [6689]~P100(x66891)+P1(f332(f332(f233(x66891),x66892),x66893))+~P1(f332(f332(f233(x66891),x66892),f332(f332(f236(x66891),x66894),x66893)))
% 52.62/52.42 [6690]~P100(x66901)+P1(f332(f332(f233(x66901),x66902),x66903))+~P1(f332(f332(f233(x66901),x66902),f332(f332(f236(x66901),x66903),x66904)))
% 52.62/52.42 [6691]~P100(x66911)+P1(f332(f332(f232(x66911),x66912),x66913))+~P1(f332(f332(f232(x66911),x66912),f332(f332(f236(x66911),x66914),x66913)))
% 52.62/52.42 [6692]~P100(x66921)+P1(f332(f332(f232(x66921),x66922),x66923))+~P1(f332(f332(f232(x66921),x66922),f332(f332(f236(x66921),x66924),x66923)))
% 52.62/52.42 [6693]~P100(x66931)+P1(f332(f332(f232(x66931),x66932),x66933))+~P1(f332(f332(f232(x66931),x66932),f332(f332(f236(x66931),x66933),x66934)))
% 52.62/52.42 [6694]~P100(x66941)+P1(f332(f332(f232(x66941),x66942),x66943))+~P1(f332(f332(f232(x66941),x66942),f332(f332(f236(x66941),x66943),x66944)))
% 52.62/52.42 [6695]~P98(x66951)+P1(f332(f332(f232(x66951),x66952),x66953))+~P1(f332(f332(f232(x66951),x66952),f332(f332(f104(x66951),x66954),x66953)))
% 52.62/52.42 [6696]~P98(x66961)+P1(f332(f332(f232(x66961),x66962),x66963))+~P1(f332(f332(f232(x66961),x66962),f332(f332(f104(x66961),x66964),x66963)))
% 52.62/52.42 [6697]~P98(x66971)+P1(f332(f332(f232(x66971),x66972),x66973))+~P1(f332(f332(f232(x66971),x66972),f332(f332(f104(x66971),x66973),x66974)))
% 52.62/52.42 [6698]~P98(x66981)+P1(f332(f332(f232(x66981),x66982),x66983))+~P1(f332(f332(f232(x66981),x66982),f332(f332(f104(x66981),x66983),x66984)))
% 52.62/52.42 [6720]~E(f332(f332(f152(x67201),x67203),x67204),x67202)+P1(f332(f332(f334(x67201),x67202),f332(f158(x67201),x67203)))+~P1(f332(f332(f233(a845),x67204),f332(f181(f846(x67201)),x67203)))
% 52.62/52.42 [6732]~P100(x67321)+~P20(x67321,f332(f332(f140(x67321),x67322),f332(f332(f140(x67321),x67323),x67324)))+P1(f332(f332(f232(x67321),x67322),x67323))
% 52.62/52.42 [6789]~P100(x67891)+P20(x67891,f332(f332(f140(x67891),x67892),x67893))+~P20(x67891,f332(f332(f140(x67891),x67894),f332(f332(f140(x67891),x67892),x67893)))
% 52.62/52.42 [6901]E(x69011,f2(a1))+E(f332(f332(f44(a1),x69012),x69011),x69013)+~P1(f332(f57(x69012,x69011),f332(f332(f241(a1,a1),x69013),x69014)))
% 52.62/52.42 [6924]E(f53(a1,x69242,x69241),x69243)+E(x69241,f2(a1))+~P1(f332(f57(x69242,x69241),f332(f332(f241(a1,a1),x69244),x69243)))
% 52.62/52.42 [7039]P1(f332(f332(f334(x70391),x70392),x70393))+~P1(f332(f332(f334(x70391),x70392),x70394))+~P1(f332(f332(f233(f853(x70391,a839)),x70394),x70393))
% 52.62/52.42 [7040]P1(f332(f332(f334(x70401),x70402),x70403))+~P1(f332(f332(f334(x70401),x70402),x70404))+~P1(f332(f332(f232(f853(x70401,a839)),x70404),x70403))
% 52.62/52.42 [7041]P1(f332(f332(f334(x70411),x70412),x70413))+~P1(f332(f332(f334(x70411),x70412),x70414))+~P1(f332(f332(f232(f853(x70411,a839)),x70414),x70413))
% 52.62/52.42 [7042]P1(f332(f332(f334(x70421),x70422),x70423))+~P1(f332(f332(f334(x70421),x70422),x70424))+~P1(f332(f332(f232(f853(x70421,a839)),x70424),x70423))
% 52.62/52.42 [7043]P1(f332(f332(f334(x70431),x70432),x70433))+~P1(f332(f332(f334(x70431),x70432),x70434))+~P1(f332(f332(f232(f853(x70431,a839)),x70434),x70433))
% 52.62/52.42 [7053]~P111(x70531)+~E(x70533,f2(x70531))+P1(f332(f332(f279(x70531),f332(f332(f83(x70531),x70532),x70533)),f332(f332(f83(x70531),x70534),x70533)))
% 52.62/52.42 [7054]~P111(x70541)+~E(x70542,f2(x70541))+P1(f332(f332(f279(x70541),f332(f332(f83(x70541),x70542),x70543)),f332(f332(f83(x70541),x70542),x70544)))
% 52.62/52.42 [7279]~P102(x72792)+~P1(f332(f332(f233(f853(x72791,x72792)),x72793),x72794))+P1(f332(f332(f232(f853(x72791,x72792)),x72793),x72794))
% 52.62/52.42 [7374]~P30(x73741,x73742,x73744)+P30(x73741,x73742,f332(f332(f302(f844(x73741)),x73743),x73744))+~P30(x73741,x73742,f332(f332(f302(f844(x73741)),x73743),f180(f853(f844(x73741),a839))))
% 52.62/52.42 [7413]~P1(f332(f332(f334(x74131),x74132),x74134))+P1(f332(f332(f334(x74131),x74132),f45(f853(x74131,a839),x74133)))+~P1(f332(f332(f334(f853(x74131,a839)),x74134),x74133))
% 52.62/52.42 [7415]~P73(x74151)+~P1(f332(f332(f232(a845),x74153),x74154))+P1(f332(f332(f279(x74151),f332(f332(f242(x74151),x74152),x74153)),f332(f332(f242(x74151),x74152),x74154)))
% 52.62/52.42 [7426]P33(x74261,x74262,x74263)+P1(f332(f332(f334(f844(x74261)),f819(x74262,x74264,x74261)),x74264))+~P1(f332(f332(f334(f844(x74261)),x74263),x74264))
% 52.62/52.42 [7445]~P75(x74451)+~P1(f332(f332(f233(x74451),x74453),x74454))+P1(f332(f332(f233(x74451),f332(f332(f82(x74451),x74452),x74453)),f332(f332(f82(x74451),x74452),x74454)))
% 52.62/52.42 [7446]~P81(x74461)+~P1(f332(f332(f233(x74461),x74463),x74464))+P1(f332(f332(f233(x74461),f332(f332(f82(x74461),x74462),x74463)),f332(f332(f82(x74461),x74462),x74464)))
% 52.62/52.42 [7447]~P75(x74471)+~P1(f332(f332(f233(x74471),x74472),x74474))+P1(f332(f332(f233(x74471),f332(f332(f82(x74471),x74472),x74473)),f332(f332(f82(x74471),x74474),x74473)))
% 52.62/52.42 [7448]~P81(x74481)+~P1(f332(f332(f233(x74481),x74482),x74484))+P1(f332(f332(f233(x74481),f332(f332(f82(x74481),x74482),x74483)),f332(f332(f82(x74481),x74484),x74483)))
% 52.62/52.42 [7449]~P75(x74491)+~P1(f332(f332(f232(x74491),x74493),x74494))+P1(f332(f332(f232(x74491),f332(f332(f82(x74491),x74492),x74493)),f332(f332(f82(x74491),x74492),x74494)))
% 52.62/52.42 [7450]~P79(x74501)+~P1(f332(f332(f232(x74501),x74503),x74504))+P1(f332(f332(f232(x74501),f332(f332(f82(x74501),x74502),x74503)),f332(f332(f82(x74501),x74502),x74504)))
% 52.62/52.42 [7451]~P75(x74511)+~P1(f332(f332(f232(x74511),x74512),x74514))+P1(f332(f332(f232(x74511),f332(f332(f82(x74511),x74512),x74513)),f332(f332(f82(x74511),x74514),x74513)))
% 52.62/52.42 [7452]~P79(x74521)+~P1(f332(f332(f232(x74521),x74522),x74524))+P1(f332(f332(f232(x74521),f332(f332(f82(x74521),x74522),x74523)),f332(f332(f82(x74521),x74524),x74523)))
% 52.62/52.42 [7453]~P111(x74531)+~P1(f332(f332(f279(x74531),x74533),x74534))+P1(f332(f332(f279(x74531),f332(f332(f83(x74531),x74532),x74533)),f332(f332(f83(x74531),x74532),x74534)))
% 52.62/52.42 [7454]~P111(x74541)+~P1(f332(f332(f279(x74541),x74542),x74544))+P1(f332(f332(f279(x74541),f332(f332(f83(x74541),x74542),x74543)),f332(f332(f83(x74541),x74544),x74543)))
% 52.62/52.42 [7455]~P73(x74551)+~P1(f332(f332(f279(x74551),x74552),x74554))+P1(f332(f332(f279(x74551),f332(f332(f242(x74551),x74552),x74553)),f332(f332(f242(x74551),x74554),x74553)))
% 52.62/52.42 [7464]~P135(x74641)+~P89(x74641)+E(f332(f332(f82(x74641),f332(f332(f83(x74641),x74642),f332(f106(x74641),x74643))),f332(f332(f83(x74641),x74644),f332(f106(x74641),x74643))),f332(f332(f83(x74641),f332(f332(f82(x74641),x74642),x74644)),f332(f106(x74641),x74643)))
% 52.62/52.42 [7465]~P121(x74651)+~P89(x74651)+E(f332(f332(f3(x74651),f332(f332(f83(x74651),x74652),f332(f106(x74651),x74653))),f332(f332(f83(x74651),x74654),f332(f106(x74651),x74653))),f332(f332(f83(x74651),f332(f332(f3(x74651),x74652),x74654)),f332(f106(x74651),x74653)))
% 52.62/52.42 [7501]~P4(x75011)+E(f332(f332(f82(x75011),f332(x75012,x75013)),f332(f332(f8(a845,x75011),x75012),f295(a845,f332(a114,x75013),x75014))),f332(f332(f8(a845,x75011),x75012),f295(a845,x75013,x75014)))+~P1(f332(f332(f232(a845),x75013),x75014))
% 52.62/52.42 [7512]~P31(x75122,x75121,x75123,f332(f158(x75122),x75124))+~P1(f332(f127(x75122),x75124))+P1(f332(f127(x75121),f332(f332(f143(x75122,x75121),x75123),x75124)))
% 52.62/52.42 [7561]~P1(f332(f332(f233(a845),x75612),x75614))+~P1(f332(f332(f233(a845),x75611),x75613))+P1(f332(f332(f233(a845),f332(f332(f82(a845),x75611),x75612)),f332(f332(f82(a845),x75613),x75614)))
% 52.62/52.42 [7564]~P1(f332(f332(f233(a1),x75641),x75643))+~P1(f332(f332(f232(a1),x75642),x75644))+P1(f332(f332(f233(a1),f332(f332(f82(a1),x75641),x75642)),f332(f332(f82(a1),x75643),x75644)))
% 52.62/52.42 [7565]~P1(f332(f332(f232(a845),x75652),x75654))+~P1(f332(f332(f232(a845),x75651),x75653))+P1(f332(f332(f232(a845),f332(f332(f82(a845),x75651),x75652)),f332(f332(f82(a845),x75653),x75654)))
% 52.62/52.42 [7566]~P1(f332(f332(f232(a845),x75662),x75664))+~P1(f332(f332(f232(a845),x75661),x75663))+P1(f332(f332(f232(a845),f332(f332(f83(a845),x75661),x75662)),f332(f332(f83(a845),x75663),x75664)))
% 52.62/52.42 [7615]P1(f332(f332(f334(x76151),x76152),x76153))+~P1(f332(f332(f334(x76151),x76152),f46(f853(x76151,a839),x76154)))+~P1(f332(f332(f334(f853(x76151,a839)),x76153),x76154))
% 52.62/52.42 [7616]P1(f332(f332(f334(x76161),x76162),x76163))+~P1(f332(f332(f334(x76161),x76162),f46(f853(x76161,a839),x76164)))+~P1(f332(f332(f334(f853(x76161,a839)),x76163),x76164))
% 52.62/52.42 [7632]~P1(f332(x76321,f724(x76321,x76323,x76322)))+P1(f332(x76321,f332(f332(f152(x76322),x76323),x76324)))+~P1(f332(f332(f233(a845),x76324),f332(f181(f846(x76322)),x76323)))
% 52.62/52.42 [7636]P1(f332(x76361,x76362))+~P1(f332(f332(f334(x76364),x76362),f332(f158(x76364),x76363)))+P1(f332(f332(f233(a845),f725(x76361,x76363,x76364)),f332(f181(f846(x76364)),x76363)))
% 52.62/52.42 [7655]~P1(f332(f332(f187(x76552),x76553),x76554))+~P1(f332(f332(f187(f35(x76551,x76552)),x76554),x76553))+P1(f332(f332(f187(f35(x76551,x76552)),x76553),x76553))
% 52.62/52.42 [7683]~P102(x76831)+~P1(f332(f332(f232(f853(x76832,x76831)),x76834),x76833))+~P1(f332(f332(f233(f853(x76832,x76831)),x76833),x76834))
% 52.62/52.42 [7726]~P1(f332(x77264,x77262))+~P1(f332(f332(f334(x77261),x77262),x77263))+P1(f332(f332(f334(x77261),x77262),f332(f332(f104(f853(x77261,a839)),x77263),f332(f256(x77261),x77264))))
% 52.62/52.42 [7745]P1(f332(f332(f334(x77451),x77452),x77453))+~P1(f332(f332(f232(f853(x77451,a839)),x77453),x77454))+P1(f332(f332(f232(f853(x77451,a839)),x77453),f332(f332(f302(x77451),x77452),x77454)))
% 52.62/52.42 [7746]P1(f332(f332(f334(x77461),x77462),x77463))+~P1(f332(f332(f232(f853(x77461,a839)),x77463),x77464))+P1(f332(f332(f232(f853(x77461,a839)),x77463),f332(f332(f302(x77461),x77462),x77464)))
% 52.62/52.42 [7875]~P1(f332(f332(f334(x78751),x78753),x78754))+~P1(f332(f332(f233(f853(x78751,a839)),x78752),x78754))+P1(f332(f332(f233(f853(x78751,a839)),x78752),f332(f332(f302(x78751),x78753),x78754)))
% 52.62/52.42 [7877]E(f332(f332(f104(f853(x78771,a839)),x78772),x78773),f180(f853(x78771,a839)))+~E(f332(f332(f104(f853(x78771,a839)),f45(f853(x78771,a839),x78774)),x78773),f180(f853(x78771,a839)))+~P1(f332(f332(f334(f853(x78771,a839)),x78772),x78774))
% 52.62/52.42 [7953]P1(f332(f332(f334(x79531),x79532),x79533))+~P1(f332(f332(f232(f853(x79531,a839)),x79533),f332(f332(f302(x79531),x79532),x79534)))+P1(f332(f332(f232(f853(x79531,a839)),x79533),x79534))
% 52.62/52.42 [7954]P1(f332(f332(f334(x79541),x79542),x79543))+~P1(f332(f332(f232(f853(x79541,a839)),x79543),f332(f332(f302(x79541),x79542),x79544)))+P1(f332(f332(f232(f853(x79541,a839)),x79543),x79544))
% 52.62/52.42 [7974]P1(f332(f332(f334(x79742),f724(x79741,x79743,x79742)),f332(f158(x79742),x79743)))+P1(f332(x79741,f332(f332(f152(x79742),x79743),x79744)))+~P1(f332(f332(f233(a845),x79744),f332(f181(f846(x79742)),x79743)))
% 52.62/52.42 [7982]~P1(f332(f332(f233(f853(x79821,a839)),x79822),x79824))+P1(f332(f332(f233(f853(x79821,a839)),x79822),x79823))+~P1(f332(f332(f233(f853(x79821,a839)),x79824),x79823))
% 52.62/52.42 [7983]~P1(f332(f332(f232(f853(x79831,a839)),x79832),x79834))+P1(f332(f332(f233(f853(x79831,a839)),x79832),x79833))+~P1(f332(f332(f233(f853(x79831,a839)),x79834),x79833))
% 52.62/52.42 [7984]~P1(f332(f332(f232(f853(x79841,a839)),x79844),x79843))+~P1(f332(f332(f233(f853(x79841,a839)),x79842),x79844))+P1(f332(f332(f233(f853(x79841,a839)),x79842),x79843))
% 52.62/52.42 [7985]~P1(f332(f332(f232(f853(x79851,a839)),x79852),x79854))+P1(f332(f332(f232(f853(x79851,a839)),x79852),x79853))+~P1(f332(f332(f232(f853(x79851,a839)),x79854),x79853))
% 52.62/52.42 [8021]~P1(f332(f332(f334(x80211),x80214),x80213))+~P1(f332(f332(f233(f853(x80211,a839)),x80212),f332(f332(f302(x80211),x80214),x80213)))+P1(f332(f332(f233(f853(x80211,a839)),x80212),x80213))
% 52.62/52.42 [8033]~P75(x80331)+P1(f332(f332(f233(x80331),x80332),x80333))+~P1(f332(f332(f233(x80331),f332(f332(f82(x80331),x80334),x80332)),f332(f332(f82(x80331),x80334),x80333)))
% 52.62/52.42 [8034]~P75(x80341)+P1(f332(f332(f233(x80341),x80342),x80343))+~P1(f332(f332(f233(x80341),f332(f332(f82(x80341),x80344),x80342)),f332(f332(f82(x80341),x80344),x80343)))
% 52.62/52.42 [8035]~P75(x80351)+P1(f332(f332(f233(x80351),x80352),x80353))+~P1(f332(f332(f233(x80351),f332(f332(f82(x80351),x80352),x80354)),f332(f332(f82(x80351),x80353),x80354)))
% 52.62/52.42 [8036]~P75(x80361)+P1(f332(f332(f233(x80361),x80362),x80363))+~P1(f332(f332(f233(x80361),f332(f332(f82(x80361),x80362),x80364)),f332(f332(f82(x80361),x80363),x80364)))
% 52.62/52.42 [8037]~P75(x80371)+P1(f332(f332(f232(x80371),x80372),x80373))+~P1(f332(f332(f232(x80371),f332(f332(f82(x80371),x80374),x80372)),f332(f332(f82(x80371),x80374),x80373)))
% 52.62/52.42 [8038]~P75(x80381)+P1(f332(f332(f232(x80381),x80382),x80383))+~P1(f332(f332(f232(x80381),f332(f332(f82(x80381),x80384),x80382)),f332(f332(f82(x80381),x80384),x80383)))
% 52.62/52.42 [8039]~P75(x80391)+P1(f332(f332(f232(x80391),x80392),x80393))+~P1(f332(f332(f232(x80391),f332(f332(f82(x80391),x80392),x80394)),f332(f332(f82(x80391),x80393),x80394)))
% 52.62/52.42 [8040]~P75(x80401)+P1(f332(f332(f232(x80401),x80402),x80403))+~P1(f332(f332(f232(x80401),f332(f332(f82(x80401),x80402),x80404)),f332(f332(f82(x80401),x80403),x80404)))
% 52.62/52.42 [8204]P1(f332(x82041,x82042))+~P1(f332(f332(f334(x82043),x82042),f332(f158(x82043),x82044)))+P1(f332(f332(f233(a845),f332(f181(f846(x82043)),f332(f126(x82043,x82041),x82044))),f332(f181(f846(x82043)),x82044)))
% 52.62/52.42 [8334]E(x83341,x83342)+P1(f332(f332(f187(x83343),x83341),f423(x83342,x83341,x83343,x83344)))+~P1(f332(f332(f187(f35(x83344,x83343)),x83341),x83342))
% 52.62/52.42 [8335]E(x83351,x83352)+P1(f332(f332(f187(x83353),x83351),f465(x83352,x83351,x83353,x83354)))+~P1(f332(f332(f187(f35(x83354,x83353)),x83351),x83352))
% 52.62/52.42 [8362]~P1(f332(x83624,x83622))+P1(f332(f332(f187(x83621),x83622),f423(x83623,x83622,x83621,x83624)))+~P1(f332(f332(f187(f35(x83624,x83621)),x83622),x83623))
% 52.62/52.42 [8363]~P1(f332(x83634,x83632))+P1(f332(f332(f187(x83631),x83632),f465(x83633,x83632,x83631,x83634)))+~P1(f332(f332(f187(f35(x83634,x83631)),x83632),x83633))
% 52.62/52.42 [8687]~P31(x86874,x86873,x86871,f239(f853(x86874,a839)))+E(f332(x86871,f522(x86872,x86871,x86873,x86874)),x86872)+~P1(f332(f332(f334(x86873),x86872),f332(f303(x86874,x86873,x86871),f239(f853(x86874,a839)))))
% 52.62/52.42 [8825]~P1(f332(f64(x88251),x88254))+P1(f332(f332(f334(x88251),f560(x88252,x88253,x88254,x88251)),x88254))+P1(f332(f64(f852(x88251,x88253)),f332(f332(f248(x88251,x88253),x88254),x88252)))
% 52.62/52.42 [8869]E(x88691,x88692)+P1(f332(f332(f187(f35(x88693,x88694)),f423(x88691,x88692,x88694,x88693)),x88691))+~P1(f332(f332(f187(f35(x88693,x88694)),x88692),x88691))
% 52.62/52.42 [8870]E(x88701,x88702)+P1(f332(f332(f187(f35(x88703,x88704)),f465(x88701,x88702,x88704,x88703)),x88701))+~P1(f332(f332(f187(f35(x88703,x88704)),x88702),x88701))
% 52.62/52.42 [8890]~P1(f332(x88901,x88904))+P1(f332(f332(f187(f35(x88901,x88902)),f423(x88903,x88904,x88902,x88901)),x88903))+~P1(f332(f332(f187(f35(x88901,x88902)),x88904),x88903))
% 52.62/52.42 [8891]~P1(f332(x88911,x88914))+P1(f332(f332(f187(f35(x88911,x88912)),f465(x88913,x88914,x88912,x88911)),x88913))+~P1(f332(f332(f187(f35(x88911,x88912)),x88914),x88913))
% 52.62/52.42 [9130]~P1(f332(f64(x91301),x91303))+~P1(f332(f64(x91302),f332(x91304,f560(x91304,x91302,x91303,x91301))))+P1(f332(f64(f852(x91301,x91302)),f332(f332(f248(x91301,x91302),x91303),x91304)))
% 52.62/52.42 [9144]~E(f332(f181(f846(x91444)),x91442),f332(f181(f846(x91444)),x91443))+P1(f332(f332(f334(f852(f846(x91444),f846(x91444))),f332(f332(f241(f846(x91444),f846(x91444)),x91443),x91442)),f147(x91444,x91441)))+P1(f332(f332(f233(a845),f733(x91441,x91442,x91443,x91444)),f332(f181(f846(x91444)),x91443)))
% 52.62/52.42 [9257]E(f332(f332(f159(x92571),f739(x92572,x92573,x92574,x92571)),x92573),f332(f332(f159(x92571),f739(x92572,x92573,x92574,x92571)),x92574))+~P1(f332(f332(f334(f852(f846(x92571),f846(x92571))),f332(f332(f241(f846(x92571),f846(x92571)),x92574),x92573)),f137(x92571,x92572)))+P1(f332(f332(f233(a845),f332(f181(f846(x92571)),x92574)),f332(f181(f846(x92571)),x92573)))
% 52.62/52.42 [9315]~P1(f332(f332(f233(a845),f2(a845)),x93153))+~P1(f332(f332(f233(a845),x93154),x93151))+P1(f332(f332(f233(a845),f332(f332(f82(a845),f332(f332(f83(a845),x93151),f53(a845,x93152,x93153))),x93154)),f332(f332(f83(a845),x93151),x93153)))
% 52.62/52.42 [9497]~P102(x94972)+~P1(f332(f332(f232(x94972),f332(x94973,f704(x94974,x94973,x94971,x94972))),f332(x94974,f704(x94974,x94973,x94971,x94972))))+P1(f332(f332(f232(f853(x94971,x94972)),x94973),x94974))
% 52.62/52.42 [9588]~P8(x95881)+E(f332(f332(f8(a845,x95881),f332(f332(f20(a845,x95881,x95881),f332(f332(f10(x95881,f853(x95881,x95881),a845),f3(x95881)),x95882)),f332(f332(f10(a845,x95881,a845),x95882),f332(f332(f9(a845,a845,a845),f82(a845)),f80(a845))))),f295(a845,x95883,x95884)),f332(f332(f3(x95881),f332(x95882,x95883)),f332(x95882,f332(f332(f82(a845),x95884),f80(a845)))))+~P1(f332(f332(f232(a845),x95883),x95884))
% 52.62/52.42 [6634]~P9(x66341)+E(f332(f332(f44(x66341),f332(f332(f83(x66341),x66342),x66343)),x66344),f332(f332(f83(x66341),x66342),f332(f332(f44(x66341),x66343),x66344)))+~P1(f332(f332(f279(x66341),x66344),x66343))
% 52.62/52.42 [6724]E(f332(f332(f125(x67241),x67242),x67243),x67244)+~E(x67243,f332(f332(f128(x67241),f332(f181(f846(x67241)),x67242)),x67244))+~E(f332(f332(f159(x67241),f332(f181(f846(x67241)),x67242)),x67244),x67242)
% 52.62/52.42 [6784]~P63(x67842)+E(x67841,f2(x67842))+E(f332(f332(f283(x67842),f332(f332(f242(x67842),x67843),x67844)),f332(f332(f242(x67842),x67841),x67844)),f332(f332(f242(x67842),f332(f332(f283(x67842),x67843),x67841)),x67844))
% 52.62/52.42 [6934]~P9(x69341)+E(f332(f332(f44(x69341),f332(f332(f83(x69341),x69342),x69343)),x69344),f332(f332(f83(x69341),f332(f332(f44(x69341),x69342),x69344)),x69343))+~P1(f332(f332(f279(x69341),x69344),x69342))
% 52.62/52.42 [6943]~P100(x69431)+~P1(f332(f332(f233(x69431),x69433),x69434))+P1(f332(f332(f233(x69431),f332(f332(f236(x69431),x69432),x69433)),x69434))
% 52.62/52.42 [6944]~P100(x69441)+~P1(f332(f332(f233(x69441),x69443),x69444))+P1(f332(f332(f233(x69441),f332(f332(f236(x69441),x69442),x69443)),x69444))
% 52.62/52.42 [6945]~P100(x69451)+~P1(f332(f332(f233(x69451),x69452),x69454))+P1(f332(f332(f233(x69451),f332(f332(f236(x69451),x69452),x69453)),x69454))
% 52.62/52.42 [6946]~P100(x69461)+~P1(f332(f332(f233(x69461),x69462),x69464))+P1(f332(f332(f233(x69461),f332(f332(f236(x69461),x69462),x69463)),x69464))
% 52.62/52.42 [6947]~P98(x69471)+~P1(f332(f332(f233(x69471),x69473),x69474))+P1(f332(f332(f233(x69471),f332(f332(f104(x69471),x69472),x69473)),x69474))
% 52.62/52.42 [6948]~P98(x69481)+~P1(f332(f332(f233(x69481),x69482),x69484))+P1(f332(f332(f233(x69481),f332(f332(f104(x69481),x69482),x69483)),x69484))
% 52.62/52.42 [6949]~P100(x69491)+~P1(f332(f332(f232(x69491),x69493),x69494))+P1(f332(f332(f232(x69491),f332(f332(f236(x69491),x69492),x69493)),x69494))
% 52.62/52.42 [6950]~P100(x69501)+~P1(f332(f332(f232(x69501),x69503),x69504))+P1(f332(f332(f232(x69501),f332(f332(f236(x69501),x69502),x69503)),x69504))
% 52.62/52.42 [6951]~P100(x69511)+~P1(f332(f332(f232(x69511),x69512),x69514))+P1(f332(f332(f232(x69511),f332(f332(f236(x69511),x69512),x69513)),x69514))
% 52.62/52.42 [6952]~P100(x69521)+~P1(f332(f332(f232(x69521),x69522),x69524))+P1(f332(f332(f232(x69521),f332(f332(f236(x69521),x69522),x69523)),x69524))
% 52.62/52.42 [6953]~P98(x69531)+~P1(f332(f332(f232(x69531),x69533),x69534))+P1(f332(f332(f232(x69531),f332(f332(f104(x69531),x69532),x69533)),x69534))
% 52.62/52.42 [6954]~P98(x69541)+~P1(f332(f332(f232(x69541),x69542),x69544))+P1(f332(f332(f232(x69541),f332(f332(f104(x69541),x69542),x69543)),x69544))
% 52.62/52.42 [6971]~P1(f332(x69713,x69714))+~P1(f332(x69712,x69714))+P1(f332(f332(f332(f104(f853(x69711,a839)),x69712),x69713),x69714))
% 52.62/52.42 [7003]~E(f332(f181(f846(x70031)),x70033),f332(f181(f846(x70032)),x70034))+~P1(f332(f127(x70031),x70033))+E(f169(x70031,x70032,f166(x70031,x70032,f332(f332(f167(x70031,x70032),x70033),x70034))),f332(f158(x70031),x70033))
% 52.62/52.42 [7097]P30(x70971,x70972,x70973)+~P30(x70971,x70974,x70973)+~P1(f332(f332(f232(f853(f844(x70971),a839)),x70974),x70972))
% 52.62/52.42 [7098]P30(x70981,x70982,x70983)+~P30(x70981,x70982,x70984)+~P1(f332(f332(f232(f853(f844(x70981),a839)),x70983),x70984))
% 52.62/52.42 [7236]~P9(x72361)+E(f332(f332(f44(x72361),f332(f332(f242(x72361),x72362),x72363)),f332(f332(f242(x72361),x72364),x72363)),f332(f332(f242(x72361),f332(f332(f44(x72361),x72362),x72364)),x72363))+~P1(f332(f332(f279(x72361),x72364),x72362))
% 52.62/52.42 [7491]~P4(x74911)+E(f332(f332(f82(x74911),f332(x74912,x74913)),f332(f332(f8(a845,x74911),x74912),f332(f294(a845,f332(a114,x74913)),x74914))),f332(f332(f8(a845,x74911),x74912),f332(f294(a845,x74913),x74914)))+~P1(f332(f332(f233(a845),x74913),x74914))
% 52.62/52.42 [7519]~P100(x75191)+P1(f332(f332(f233(x75191),x75192),x75193))+~P1(f332(f332(f233(x75191),f332(f332(f179(x75191),x75194),x75192)),x75193))
% 52.62/52.42 [7520]~P100(x75201)+P1(f332(f332(f233(x75201),x75202),x75203))+~P1(f332(f332(f233(x75201),f332(f332(f179(x75201),x75202),x75204)),x75203))
% 52.62/52.42 [7521]~P100(x75211)+P1(f332(f332(f232(x75211),x75212),x75213))+~P1(f332(f332(f232(x75211),f332(f332(f179(x75211),x75214),x75212)),x75213))
% 52.62/52.42 [7522]~P100(x75221)+P1(f332(f332(f232(x75221),x75222),x75223))+~P1(f332(f332(f232(x75221),f332(f332(f179(x75221),x75224),x75222)),x75223))
% 52.62/52.42 [7523]~P100(x75231)+P1(f332(f332(f232(x75231),x75232),x75233))+~P1(f332(f332(f232(x75231),f332(f332(f179(x75231),x75232),x75234)),x75233))
% 52.62/52.42 [7524]~P100(x75241)+P1(f332(f332(f232(x75241),x75242),x75243))+~P1(f332(f332(f232(x75241),f332(f332(f179(x75241),x75242),x75244)),x75243))
% 52.62/52.42 [7525]~P92(x75251)+P1(f332(f332(f232(x75251),x75252),x75253))+~P1(f332(f332(f232(x75251),f332(f332(f103(x75251),x75254),x75252)),x75253))
% 52.62/52.42 [7526]~P92(x75261)+P1(f332(f332(f232(x75261),x75262),x75263))+~P1(f332(f332(f232(x75261),f332(f332(f103(x75261),x75264),x75262)),x75263))
% 52.62/52.42 [7527]~P92(x75271)+P1(f332(f332(f232(x75271),x75272),x75273))+~P1(f332(f332(f232(x75271),f332(f332(f103(x75271),x75272),x75274)),x75273))
% 52.62/52.42 [7528]~P92(x75281)+P1(f332(f332(f232(x75281),x75282),x75283))+~P1(f332(f332(f232(x75281),f332(f332(f103(x75281),x75282),x75284)),x75283))
% 52.62/52.42 [7529]~P73(x75291)+P1(f332(f332(f279(x75291),x75292),x75293))+~P1(f332(f332(f279(x75291),f332(f332(f83(x75291),x75294),x75292)),x75293))
% 52.62/52.42 [7530]~P73(x75301)+P1(f332(f332(f279(x75301),x75302),x75303))+~P1(f332(f332(f279(x75301),f332(f332(f83(x75301),x75302),x75304)),x75303))
% 52.62/52.42 [7607]~P1(f332(f332(f334(x76071),x76072),x76074))+P1(f332(f332(f334(x76071),x76072),x76073))+P1(f332(f332(f334(x76071),x76072),f332(f332(f3(f853(x76071,a839)),x76074),x76073)))
% 52.62/52.42 [7608]~P1(f332(f332(f334(x76081),x76082),x76084))+P1(f332(f332(f334(x76081),x76082),x76083))+P1(f332(f332(f334(x76081),x76082),f332(f332(f3(f853(x76081,a839)),x76084),x76083)))
% 52.62/52.42 [7688]P1(f332(x76881,x76882))+P1(f332(x76883,x76882))+~P1(f332(f332(f332(f103(f853(x76884,a839)),x76883),x76881),x76882))
% 52.62/52.42 [7697]~P1(f332(f332(f334(x76971),x76972),x76974))+~P1(f332(f332(f334(x76971),x76972),x76973))+P1(f332(f332(f334(x76971),x76972),f332(f332(f104(f853(x76971,a839)),x76973),x76974)))
% 52.62/52.42 [7698]~P1(f332(f332(f334(x76981),x76982),x76984))+~P1(f332(f332(f334(x76981),x76982),x76983))+P1(f332(f332(f334(x76981),x76982),f332(f332(f104(f853(x76981,a839)),x76983),x76984)))
% 52.62/52.42 [7754]~P100(x77541)+~P1(f332(f64(x77541),x77544))+E(f332(f332(f67(x77541,x77541,f236(x77541)),x77542),f332(f332(f302(x77541),x77543),x77544)),f332(f332(f236(x77541),x77543),f332(f332(f67(x77541,x77541,f236(x77541)),x77542),x77544)))
% 52.62/52.42 [7755]~P100(x77551)+~P1(f332(f64(x77551),x77554))+E(f332(f332(f67(x77551,x77551,f179(x77551)),x77552),f332(f332(f302(x77551),x77553),x77554)),f332(f332(f179(x77551),x77553),f332(f332(f67(x77551,x77551,f179(x77551)),x77552),x77554)))
% 52.62/52.42 [7756]~P92(x77561)+~P1(f332(f64(x77561),x77564))+E(f332(f332(f67(x77561,x77561,f103(x77561)),x77562),f332(f332(f302(x77561),x77563),x77564)),f332(f332(f103(x77561),x77563),f332(f332(f67(x77561,x77561,f103(x77561)),x77562),x77564)))
% 52.62/52.42 [7757]~P98(x77571)+~P1(f332(f64(x77571),x77574))+E(f332(f332(f67(x77571,x77571,f104(x77571)),x77572),f332(f332(f302(x77571),x77573),x77574)),f332(f332(f104(x77571),x77573),f332(f332(f67(x77571,x77571,f104(x77571)),x77572),x77574)))
% 52.62/52.42 [7759]~P135(x77591)+~P89(x77591)+E(f332(f332(f82(x77591),f332(f332(f83(x77591),f332(f106(x77591),x77592)),x77593)),f332(f332(f83(x77591),f332(f106(x77591),x77592)),x77594)),f332(f332(f83(x77591),f332(f106(x77591),x77592)),f332(f332(f82(x77591),x77593),x77594)))
% 52.62/52.42 [7760]~P121(x77601)+~P89(x77601)+E(f332(f332(f3(x77601),f332(f332(f83(x77601),f332(f106(x77601),x77602)),x77603)),f332(f332(f83(x77601),f332(f106(x77601),x77602)),x77604)),f332(f332(f83(x77601),f332(f106(x77601),x77602)),f332(f332(f3(x77601),x77603),x77604)))
% 52.62/52.42 [7873]E(x78731,x78732)+P1(f332(f332(f334(x78733),x78731),f332(f158(x78733),x78734)))+~P1(f332(f332(f334(x78733),x78731),f332(f158(x78733),f332(f332(f140(x78733),x78732),x78734))))
% 52.62/52.42 [8044]P55(x80441,x80442,x80443)+~P55(x80441,x80442,x80444)+~P1(f332(f332(f232(f853(f852(x80441,x80442),a839)),x80443),x80444))
% 52.62/52.42 [8086]P1(f332(f332(f334(x80861),x80862),x80863))+P1(f332(f332(f334(x80861),x80862),x80864))+~P1(f332(f332(f334(x80861),x80862),f332(f332(f103(f853(x80861,a839)),x80864),x80863)))
% 52.62/52.42 [8087]P1(f332(f332(f334(x80871),x80872),x80873))+P1(f332(f332(f334(x80871),x80872),x80874))+~P1(f332(f332(f334(x80871),x80872),f332(f332(f103(f853(x80871,a839)),x80874),x80873)))
% 52.62/52.42 [8096]~P49(x80961,x80964,x80963)+~P1(f332(f332(f334(x80961),x80962),x80964))+P1(f332(f332(f334(f852(x80961,x80961)),f332(f332(f241(x80961,x80961),x80962),x80962)),x80963))
% 52.62/52.42 [8097]~P49(x80971,x80974,x80973)+~P1(f332(f332(f334(x80971),x80972),x80974))+P1(f332(f332(f334(f852(x80971,x80971)),f332(f332(f241(x80971,x80971),x80972),x80972)),x80973))
% 52.62/52.42 [8098]~P49(x80981,x80984,x80983)+~P1(f332(f332(f334(x80981),x80982),x80984))+P1(f332(f332(f334(f852(x80981,x80981)),f332(f332(f241(x80981,x80981),x80982),x80982)),x80983))
% 52.62/52.42 [8110]~P1(f332(f64(x81102),x81104))+~P1(f332(f64(x81101),x81103))+P1(f332(f64(f852(x81101,x81102)),f332(f332(f248(x81101,x81102),x81103),f332(f18(f853(x81102,a839),x81101),x81104))))
% 52.62/52.42 [8111]~P1(f332(f332(f334(x81111),x81112),x81114))+~P1(f332(f332(f232(f853(x81111,a839)),x81113),x81114))+P1(f332(f332(f232(f853(x81111,a839)),f332(f332(f302(x81111),x81112),x81113)),x81114))
% 52.62/52.42 [8119]~P2(x81192)+~P70(x81192)+E(f332(f332(f11(x81191,x81192),f332(f332(f10(a845,x81192,x81191),f102(x81192)),x81193)),x81194),f332(f102(x81192),f332(f332(f11(x81191,a845),x81193),x81194)))
% 52.62/52.42 [8120]~P70(x81202)+~P133(x81202)+E(f332(f332(f11(x81201,x81202),f332(f332(f10(a1,x81202,x81201),f105(x81202)),x81203)),x81204),f332(f105(x81202),f332(f332(f11(x81201,a1),x81203),x81204)))
% 52.62/52.42 [8146]E(f332(f332(f3(f853(x81461,a839)),x81462),f332(f332(f3(f853(x81461,a839)),x81463),x81464)),x81464)+~P1(f332(f332(f232(f853(x81461,a839)),x81462),x81463))+~P1(f332(f332(f232(f853(x81461,a839)),x81464),x81462))
% 52.62/52.42 [8238]~P1(f332(f64(x82381),x82384))+E(f332(f332(f3(a845),f332(f332(f8(x82381,a845),x82382),x82383)),f332(f332(f8(x82381,a845),x82382),x82384)),f332(f332(f8(x82381,a845),x82382),f332(f332(f3(f853(x82381,a839)),x82383),x82384)))+~P1(f332(f332(f232(f853(x82381,a839)),x82384),x82383))
% 52.62/52.42 [8395]~P14(x83951,x83954,x83953)+~P1(f332(f332(f334(x83951),x83952),x83954))+P1(f332(f332(f334(x83951),x83952),f332(f277(x83951,x83951,x83953),f332(f332(f302(x83951),x83952),f180(f853(x83951,a839))))))
% 52.62/52.42 [8458]~P1(f332(f332(f232(f853(x84581,a839)),x84582),x84583))+~P1(f332(f332(f232(f853(x84581,a839)),x84582),x84584))+P1(f332(f332(f232(f853(x84581,a839)),x84582),f332(f332(f104(f853(x84581,a839)),x84583),x84584)))
% 52.62/52.42 [8550]E(x85501,f180(f853(x85502,a839)))+P1(f332(f64(x85503),x85504))+~P1(f332(f64(f852(x85503,x85502)),f332(f332(f248(x85503,x85502),x85504),f332(f18(f853(x85502,a839),x85503),x85501))))
% 52.62/52.42 [8551]E(x85511,f180(f853(x85512,a839)))+P1(f332(f64(x85513),x85514))+~P1(f332(f64(f852(x85512,x85513)),f332(f332(f248(x85512,x85513),x85511),f332(f18(f853(x85513,a839),x85512),x85514))))
% 52.62/52.42 [8608]P1(f332(f332(f334(x86081),x86082),f322(x86081,x86083)))+~P1(f332(f332(f334(x86081),x86084),f322(x86081,x86083)))+~P1(f332(f332(f334(f852(x86081,x86081)),f332(f332(f241(x86081,x86081),x86082),x86084)),x86083))
% 52.62/52.42 [8609]P1(f332(f332(f334(x86091),x86092),f322(x86091,x86093)))+~P1(f332(f332(f334(x86091),x86094),f322(x86091,x86093)))+~P1(f332(f332(f334(f852(x86091,x86091)),f332(f332(f241(x86091,x86091),x86092),x86094)),x86093))
% 52.62/52.42 [8661]~P38(x86611,x86614)+P1(f332(f332(f334(f852(x86611,x86611)),f332(f332(f241(x86611,x86611),x86613),x86612)),f300(x86611,x86614)))+P38(x86611,f332(f332(f302(f852(x86611,x86611)),f332(f332(f241(x86611,x86611),x86612),x86613)),x86614))
% 52.62/52.42 [8662]~P58(x86621,x86624)+P1(f332(f332(f334(f852(x86621,x86621)),f332(f332(f241(x86621,x86621),x86623),x86622)),f300(x86621,x86624)))+P58(x86621,f332(f332(f302(f852(x86621,x86621)),f332(f332(f241(x86621,x86621),x86622),x86623)),x86624))
% 52.62/52.42 [8733]~E(x87332,x87333)+~P1(f332(f332(f334(x87331),x87332),f332(f158(x87331),x87334)))+P1(f332(f332(f334(f852(x87331,x87331)),f332(f332(f241(x87331,x87331),x87332),x87333)),f332(f158(f852(x87331,x87331)),f332(f332(f167(x87331,x87331),x87334),x87334))))
% 52.62/52.42 [8805]~E(x88053,x88054)+P1(f332(f332(f251(x88051,x88051,a839),a329),x88052))+~P1(f332(f332(f334(f852(x88051,x88051)),x88052),f332(f158(f852(x88051,x88051)),f332(f332(f167(x88051,x88051),x88053),x88054))))
% 52.62/52.42 [8841]P1(f332(f332(f334(f852(f846(x88411),f846(x88411))),f332(f332(f241(f846(x88411),f846(x88411)),x88412),x88413)),f137(x88411,x88414)))+~E(f332(f332(f159(x88411),f332(f181(f846(x88411)),x88412)),x88413),x88412)+~P1(f332(f332(f233(a845),f332(f181(f846(x88411)),x88412)),f332(f181(f846(x88411)),x88413)))
% 52.62/52.42 [8935]~P1(f332(f64(x89351),x89354))+P1(f332(f332(f334(x89351),f408(x89352,x89353,x89354,x89351)),x89354))+P1(f332(f64(x89353),f332(f332(f47(x89351,f853(x89353,a839)),x89354),x89352)))
% 52.62/52.42 [8936]~P1(f332(f64(x89361),x89364))+P1(f332(f332(f334(x89361),f608(x89362,x89363,x89364,x89361)),x89364))+P1(f332(f64(x89363),f332(f332(f47(x89361,f853(x89363,a839)),x89364),x89362)))
% 52.62/52.42 [9016]P1(f332(f332(f334(f852(x90161,x90161)),x90162),f332(f332(f281(x90161,x90161,x90161),x90163),f300(x90161,x90163))))+~P1(f332(f332(f233(a845),f2(a845)),x90164))+~P1(f332(f332(f334(f852(x90161,x90161)),x90162),f332(f332(f173(f852(x90161,x90161),a839),x90164),x90163)))
% 52.62/52.42 [9023]~P38(x90231,x90232)+~P1(f332(f332(f334(f852(x90231,x90231)),f332(f332(f241(x90231,x90231),x90234),x90233)),x90232))+~P1(f332(f332(f334(f852(x90231,x90231)),f332(f332(f241(x90231,x90231),x90233),x90234)),x90232))
% 52.62/52.42 [9024]~P38(x90241,x90242)+~P1(f332(f332(f334(f852(x90241,x90241)),f332(f332(f241(x90241,x90241),x90244),x90243)),x90242))+~P1(f332(f332(f334(f852(x90241,x90241)),f332(f332(f241(x90241,x90241),x90243),x90244)),x90242))
% 52.62/52.42 [9140]~P1(f332(f64(x91401),x91404))+E(f332(f332(f8(x91401,a845),f332(f332(f10(f853(x91402,a839),a845,x91401),f43(x91402)),x91403)),x91404),f332(f43(f852(x91401,x91402)),f332(f332(f248(x91401,x91402),x91404),x91403)))+P1(f332(f332(f334(x91401),f562(x91403,x91402,x91404,x91401)),x91404))
% 52.62/52.42 [9142]~P1(f332(f127(x91421),x91422))+P1(f332(f127(x91421),f332(f332(f148(x91421,x91422),x91423),x91424)))+P1(f332(f332(f334(x91421),x91424),f332(f332(f3(f853(x91421,a839)),f332(f158(x91421),x91422)),f332(f332(f302(x91421),f332(f332(f152(x91421),x91422),x91423)),f180(f853(x91421,a839))))))
% 52.62/52.42 [9151]~P1(f332(f64(x91512),x91513))+~P1(f332(f64(x91511),f332(x91514,f408(x91514,x91511,x91513,x91512))))+P1(f332(f64(x91511),f332(f332(f47(x91512,f853(x91511,a839)),x91513),x91514)))
% 52.62/52.42 [9152]~P1(f332(f64(x91522),x91523))+~P1(f332(f64(x91521),f332(x91524,f608(x91524,x91521,x91523,x91522))))+P1(f332(f64(x91521),f332(f332(f47(x91522,f853(x91521,a839)),x91523),x91524)))
% 52.62/52.42 [9217]~P1(f332(f332(f334(f852(x92171,x92171)),x92172),f332(f332(f281(x92171,x92171,x92171),x92174),f300(x92171,x92174))))+P1(f332(f332(f334(f852(x92171,x92171)),x92172),f332(f332(f281(x92171,x92171,x92171),x92173),f300(x92171,x92173))))+~P1(f332(f332(f232(f853(f852(x92171,x92171),a839)),x92174),x92173))
% 52.62/52.42 [9225]E(f332(f332(f159(x92251),f739(x92254,x92253,x92252,x92251)),x92253),f332(f332(f159(x92251),f739(x92254,x92253,x92252,x92251)),x92252))+~P1(f332(f332(f334(f852(f846(x92251),f846(x92251))),f332(f332(f241(f846(x92251),f846(x92251)),x92252),x92253)),f137(x92251,x92254)))+E(f332(f332(f159(x92251),f332(f181(f846(x92251)),x92252)),x92253),x92252)
% 52.62/52.42 [9241]~P1(f332(f64(x92411),x92414))+E(f332(f332(f8(x92411,a845),f332(f332(f10(f853(x92412,a839),a845,x92411),f43(x92412)),x92413)),x92414),f332(f43(f852(x92411,x92412)),f332(f332(f248(x92411,x92412),x92414),x92413)))+~P1(f332(f64(x92412),f332(x92413,f562(x92413,x92412,x92414,x92411))))
% 52.62/52.42 [9246]~E(f332(f181(f846(x92461)),x92463),f332(f181(f846(x92461)),x92462))+P1(f332(f332(f334(f852(f846(x92461),f846(x92461))),f332(f332(f241(f846(x92461),f846(x92461)),x92462),x92463)),f147(x92461,x92464)))+P1(f332(f332(f334(f852(x92461,x92461)),f716(x92464,x92463,x92462,x92461)),f332(f158(f852(x92461,x92461)),f332(f332(f167(x92461,x92461),x92462),x92463))))
% 52.62/52.42 [9328]~P1(f332(f332(f334(f852(f846(x93281),f846(x93281))),f332(f332(f241(f846(x93281),f846(x93281)),x93282),x93283)),f137(x93281,x93284)))+E(f332(f332(f159(x93281),f332(f181(f846(x93281)),x93282)),x93283),x93282)+P1(f332(f332(f233(a845),f739(x93284,x93283,x93282,x93281)),f332(f332(f236(a845),f332(f181(f846(x93281)),x93282)),f332(f181(f846(x93281)),x93283))))
% 52.62/52.42 [9347]~P1(f332(f332(f334(f852(f846(x93471),f846(x93471))),f332(f332(f241(f846(x93471),f846(x93471)),x93472),x93473)),f137(x93471,x93474)))+P1(f332(f332(f233(a845),f332(f181(f846(x93471)),x93472)),f332(f181(f846(x93471)),x93473)))+P1(f332(f332(f233(a845),f739(x93474,x93473,x93472,x93471)),f332(f332(f236(a845),f332(f181(f846(x93471)),x93472)),f332(f181(f846(x93471)),x93473))))
% 52.62/52.42 [9623]~P1(f332(f332(f332(x96231,f707(x96231,x96234,x96233,x96232)),f710(x96231,x96234,x96233,x96232)),f711(x96231,x96234,x96233,x96232)))+P1(f332(f332(f332(x96231,x96232),x96233),x96234))+~P1(f332(f321(f852(f853(a1,f849(f846(a837))),f852(a1,a1)),a311),f332(f332(f241(f853(a1,f849(f846(a837))),f852(a1,a1)),x96232),f332(f332(f241(a1,a1),x96233),x96234))))
% 52.62/52.42 [9684]P1(f332(f332(f332(x96841,x96842),x96843),x96844))+P1(f332(f321(f852(f853(a1,f849(f846(a837))),f852(a1,a1)),a311),f332(f332(f241(f853(a1,f849(f846(a837))),f852(a1,a1)),f707(x96841,x96844,x96843,x96842)),f332(f332(f241(a1,a1),f710(x96841,x96844,x96843,x96842)),f711(x96841,x96844,x96843,x96842)))))+~P1(f332(f321(f852(f853(a1,f849(f846(a837))),f852(a1,a1)),a311),f332(f332(f241(f853(a1,f849(f846(a837))),f852(a1,a1)),x96842),f332(f332(f241(a1,a1),x96843),x96844))))
% 52.62/52.42 [9723]~P1(f332(f332(f334(f852(f846(x97231),f846(x97231))),f332(f332(f241(f846(x97231),f846(x97231)),x97232),x97233)),f137(x97231,x97234)))+E(f332(f332(f159(x97231),f332(f181(f846(x97231)),x97232)),x97233),x97232)+P1(f332(f332(f334(f852(x97231,x97231)),f332(f332(f241(x97231,x97231),f332(f332(f152(x97231),x97232),f739(x97234,x97233,x97232,x97231))),f332(f332(f152(x97231),x97233),f739(x97234,x97233,x97232,x97231)))),x97234))
% 52.62/52.42 [9726]~P1(f332(f332(f334(f852(f846(x97261),f846(x97261))),f332(f332(f241(f846(x97261),f846(x97261)),x97262),x97263)),f137(x97261,x97264)))+P1(f332(f332(f233(a845),f332(f181(f846(x97261)),x97262)),f332(f181(f846(x97261)),x97263)))+P1(f332(f332(f334(f852(x97261,x97261)),f332(f332(f241(x97261,x97261),f332(f332(f152(x97261),x97262),f739(x97264,x97263,x97262,x97261))),f332(f332(f152(x97261),x97263),f739(x97264,x97263,x97262,x97261)))),x97264))
% 52.62/52.42 [9796]~E(f332(f181(f846(x97961)),x97962),f332(f181(f846(x97961)),x97963))+P1(f332(f332(f334(f852(f846(x97961),f846(x97961))),f332(f332(f241(f846(x97961),f846(x97961)),x97962),x97963)),f147(x97961,x97964)))+~P1(f332(f332(f334(f852(x97961,x97961)),f332(f332(f241(x97961,x97961),f332(f332(f152(x97961),x97962),f733(x97964,x97963,x97962,x97961))),f332(f332(f152(x97961),x97963),f733(x97964,x97963,x97962,x97961)))),x97964))
% 52.62/52.42 [9936]~P4(x99361)+~P1(f332(f64(x99362),x99364))+E(f332(f154(x99361),f332(f332(f143(x99362,x99361),x99363),f92(f846(x99362),f332(f332(f20(f846(x99362),a839,a839),f332(f332(f10(a839,f853(a839,a839),f846(x99362)),a330),f332(f332(f9(f846(x99362),f853(x99362,a839),a839),f332(f332(f10(f853(x99362,a839),f853(f853(x99362,a839),a839),f846(x99362)),a329),f158(x99362))),x99364))),f127(x99362))))),f225(x99362,x99361,x99363,x99364))
% 52.62/52.42 [7327]~P62(x73272)+E(x73271,f2(x73272))+E(f332(f332(f283(x73272),f332(f332(f82(x73272),x73273),f332(f332(f83(x73272),x73274),x73271))),x73271),f332(f332(f82(x73272),x73274),f332(f332(f283(x73272),x73273),x73271)))
% 52.62/52.42 [7328]~P9(x73282)+E(x73281,f2(x73282))+E(f332(f332(f44(x73282),f332(f332(f82(x73282),x73283),f332(f332(f83(x73282),x73284),x73281))),x73281),f332(f332(f82(x73282),x73284),f332(f332(f44(x73282),x73283),x73281)))
% 52.62/52.42 [7329]~P9(x73292)+E(x73291,f2(x73292))+E(f332(f332(f44(x73292),f332(f332(f82(x73292),x73293),f332(f332(f83(x73292),x73291),x73294))),x73291),f332(f332(f82(x73292),x73294),f332(f332(f44(x73292),x73293),x73291)))
% 52.62/52.42 [7570]~P62(x75702)+E(x75701,f2(x75702))+E(f332(f332(f283(x75702),f332(f332(f82(x75702),x75703),f332(f332(f83(x75702),x75704),x75701))),x75701),f332(f332(f82(x75702),f332(f332(f283(x75702),x75703),x75701)),x75704))
% 52.62/52.42 [7571]~P63(x75712)+E(x75711,f2(x75712))+E(f332(f332(f283(x75712),f332(f332(f82(x75712),x75713),f332(f332(f83(x75712),x75711),x75714))),x75711),f332(f332(f82(x75712),f332(f332(f283(x75712),x75713),x75711)),x75714))
% 52.62/52.42 [7572]~P63(x75722)+E(x75721,f2(x75722))+E(f332(f332(f283(x75722),f332(f332(f3(x75722),x75723),f332(f332(f83(x75722),x75721),x75724))),x75721),f332(f332(f3(x75722),f332(f332(f283(x75722),x75723),x75721)),x75724))
% 52.62/52.42 [8623]~E(f332(f332(f281(x86231,x86231,x86231),x86232),x86234),f180(f853(f852(x86231,x86231),a839)))+~E(f332(f332(f281(x86231,x86231,x86231),x86232),x86233),f180(f853(f852(x86231,x86231),a839)))+E(f332(f332(f281(x86231,x86231,x86231),x86232),f332(f332(f103(f853(f852(x86231,x86231),a839)),x86233),x86234)),f180(f853(f852(x86231,x86231),a839)))
% 52.62/52.42 [8734]~P1(f332(f332(f232(f853(x87341,a839)),x87343),x87344))+~P1(f332(f332(f232(f853(x87341,a839)),x87342),x87344))+P1(f332(f332(f232(f853(x87341,a839)),f332(f332(f103(f853(x87341,a839)),x87342),x87343)),x87344))
% 52.62/52.42 [9074]~P1(f332(f64(x90741),x90744))+~P1(f332(f64(x90741),x90743))+E(f332(f332(f3(a845),f332(f332(f82(a845),f332(f332(f8(x90741,a845),x90742),x90743)),f332(f332(f8(x90741,a845),x90742),x90744))),f332(f332(f8(x90741,a845),x90742),f332(f332(f104(f853(x90741,a839)),x90743),x90744))),f332(f332(f8(x90741,a845),x90742),f332(f332(f103(f853(x90741,a839)),x90743),x90744)))
% 52.62/52.42 [9149]~P1(f332(f332(f334(x91491),x91493),x91492))+~P1(f332(f332(f232(f853(x91491,a839)),x91492),f332(f332(f302(x91491),x91493),x91494)))+P1(f332(f332(f232(f853(x91491,a839)),f332(f332(f3(f853(x91491,a839)),x91492),f332(f332(f302(x91491),x91493),f180(f853(x91491,a839))))),x91494))
% 52.62/52.42 [9299]~P1(f332(f332(f334(x92991),x92993),x92992))+P1(f332(f332(f232(f853(x92991,a839)),x92992),f332(f332(f302(x92991),x92993),x92994)))+~P1(f332(f332(f232(f853(x92991,a839)),f332(f332(f3(f853(x92991,a839)),x92992),f332(f332(f302(x92991),x92993),f180(f853(x92991,a839))))),x92994))
% 52.62/52.42 [9300]~P1(f332(f332(f334(x93001),x93003),x93002))+P1(f332(f332(f232(f853(x93001,a839)),x93002),f332(f332(f302(x93001),x93003),x93004)))+~P1(f332(f332(f232(f853(x93001,a839)),f332(f332(f3(f853(x93001,a839)),x93002),f332(f332(f302(x93001),x93003),f180(f853(x93001,a839))))),x93004))
% 52.62/52.42 [9326]~P1(f332(f332(f232(f853(x93261,a839)),x93262),x93264))+P1(f332(f332(f232(f853(x93261,a839)),x93262),f332(f332(f302(x93261),x93263),x93264)))+~P1(f332(f332(f232(f853(x93261,a839)),f332(f332(f3(f853(x93261,a839)),x93262),f332(f332(f302(x93261),x93263),f180(f853(x93261,a839))))),x93264))
% 52.62/52.42 [9385]~P1(f332(f332(f233(a845),x93852),x93854))+~P1(f332(f332(f232(a845),x93851),x93853))+P1(f332(f332(f334(f852(f852(a845,a845),f852(a845,a845))),f332(f332(f241(f852(a845,a845),f852(a845,a845)),f332(f332(f241(a845,a845),x93851),x93852)),f332(f332(f241(a845,a845),x93853),x93854))),a40))
% 52.62/52.42 [9386]~P1(f332(f332(f232(a845),x93862),x93864))+~P1(f332(f332(f232(a845),x93861),x93863))+P1(f332(f332(f334(f852(f852(a845,a845),f852(a845,a845))),f332(f332(f241(f852(a845,a845),f852(a845,a845)),f332(f332(f241(a845,a845),x93861),x93862)),f332(f332(f241(a845,a845),x93863),x93864))),a72))
% 52.62/52.42 [9761]~P31(x97611,f853(f853(x97611,a839),a839),f332(f332(f9(x97611,f853(f852(x97611,x97611),a839),f853(f853(x97611,a839),a839)),f332(f332(f10(f853(x97611,a839),f853(f853(f852(x97611,x97611),a839),f853(f853(x97611,a839),a839)),x97611),f62(x97611)),f332(f332(f9(x97611,f853(x97611,a839),f853(x97611,a839)),f302(x97611)),f180(f853(x97611,a839))))),x97613),x97612)+~P1(f332(f332(f334(x97611),x97614),x97612))+E(f332(f332(f3(f853(f853(x97611,a839),a839)),f332(f332(f62(x97611),x97612),x97613)),f332(f332(f62(x97611),f332(f332(f302(x97611),x97614),f180(f853(x97611,a839)))),x97613)),f332(f332(f62(x97611),f332(f332(f3(f853(x97611,a839)),x97612),f332(f332(f302(x97611),x97614),f180(f853(x97611,a839))))),x97613))
% 52.62/52.42 [9900]~P49(x99001,x99002,x99004)+~P1(f332(f332(f334(f852(x99001,x99001)),x99003),x99004))+P1(f332(f332(f251(x99001,x99001,a839),f332(f332(f9(x99001,f853(x99001,a839),f853(x99001,a839)),f332(f332(f10(f853(a839,a839),f853(f853(x99001,a839),f853(x99001,a839)),x99001),f10(a839,a839,x99001)),f332(f332(f10(a839,f853(a839,a839),x99001),a330),f332(f332(f9(x99001,f853(x99001,a839),a839),f334(x99001)),x99002)))),f332(f332(f9(x99001,f853(x99001,a839),a839),f334(x99001)),x99002))),x99003))
% 52.62/52.42 [9910]P1(f332(f64(x99101),x99102))+~P1(f332(f64(x99103),f332(f303(x99101,x99103,x99104),x99102)))+~P1(f332(f64(x99101),f332(f256(x99101),f332(f332(f20(x99101,a839,a839),f332(f332(f10(a839,f853(a839,a839),x99101),a330),f332(f332(f9(x99101,f853(x99101,a839),a839),f334(x99101)),x99102))),f332(f332(f9(x99101,x99103,a839),f332(f332(f10(x99103,f853(x99103,a839),x99101),a329),x99104)),f332(x99104,f599(x99104,x99103,x99102,x99101)))))))
% 52.62/52.42 [8027]~P63(x80272)+E(x80271,f2(x80272))+E(f332(f332(f283(x80272),f332(f332(f82(x80272),f332(f332(f83(x80272),x80271),x80273)),x80274)),x80271),f332(f332(f82(x80272),x80273),f332(f332(f283(x80272),x80274),x80271)))
% 52.62/52.42 [8028]~P63(x80282)+E(x80281,f2(x80282))+E(f332(f332(f283(x80282),f332(f332(f3(x80282),f332(f332(f83(x80282),x80281),x80283)),x80284)),x80281),f332(f332(f3(x80282),x80283),f332(f332(f283(x80282),x80284),x80281)))
% 52.62/52.42 [8868]~E(f332(f332(f281(x88681,x88681,x88681),x88683),x88684),f180(f853(f852(x88681,x88681),a839)))+~E(f332(f332(f281(x88681,x88681,x88681),x88682),x88684),f180(f853(f852(x88681,x88681),a839)))+E(f332(f332(f281(x88681,x88681,x88681),f332(f332(f103(f853(f852(x88681,x88681),a839)),x88682),x88683)),x88684),f180(f853(f852(x88681,x88681),a839)))
% 52.62/52.42 [9844]~P139(x98441)+~P139(x98442)+E(f332(f332(f310(x98441),f332(f332(f9(x98441,a101,f849(f846(a837))),f332(f332(f10(f853(x98442,f849(f846(a837))),f853(a101,f849(f846(a837))),x98441),f310(x98442)),f332(f332(f10(f853(x98442,f852(x98441,x98442)),f853(x98442,f849(f846(a837))),x98441),f332(f10(f852(x98441,x98442),f849(f846(a837)),x98442),x98443)),f241(x98441,x98442)))),x98444)),x98444),f332(f332(f310(f852(x98441,x98442)),x98443),x98444))
% 52.62/52.42 [9836]P1(f332(x98361,f584(x98362,x98363,x98361,x98364)))+~P1(f332(f64(x98364),f332(f256(x98364),x98361)))+P1(f332(f64(x98363),f332(f256(x98363),f332(f332(f10(f853(x98364,a839),a839,x98363),f89(x98364)),f332(f332(f10(f853(x98364,a839),f853(x98364,a839),x98363),f332(f20(x98364,a839,a839),f332(f332(f10(a839,f853(a839,a839),x98364),a330),x98361))),x98362)))))
% 52.62/52.42 [9857]~P1(f332(f64(x98572),f332(f256(x98572),x98573)))+~P1(f332(f64(x98571),f332(f256(x98571),f332(f332(f9(x98571,x98572,a839),x98574),f584(x98574,x98571,x98573,x98572)))))+P1(f332(f64(x98571),f332(f256(x98571),f332(f332(f10(f853(x98572,a839),a839,x98571),f89(x98572)),f332(f332(f10(f853(x98572,a839),f853(x98572,a839),x98571),f332(f20(x98572,a839,a839),f332(f332(f10(a839,f853(a839,a839),x98572),a330),x98573))),x98574)))))
% 52.62/52.42 [5709]~E(x57095,x57092)+P41(f35(x57091,x57093),x57092,x57094,x57095)+P1(f332(x57091,x57092))
% 52.62/52.42 [6279]E(x62791,x62792)+~P41(f35(x62793,x62794),x62791,x62795,x62792)+P1(f332(x62793,x62791))
% 52.62/52.42 [6280]E(x62801,x62802)+~P41(f35(x62803,x62804),x62801,x62805,x62802)+P1(f332(x62803,x62801))
% 52.62/52.42 [7833]~P41(x78332,x78333,x78334,x78335)+~P41(f35(x78331,x78332),x78335,x78334,x78333)+P41(f35(x78331,x78332),x78333,x78334,x78333)
% 52.62/52.42 [8990]E(x89901,x89902)+~P41(f35(x89905,x89903),x89901,x89904,x89902)+P41(x89903,x89901,x89904,f836(x89902,x89904,x89901,x89903,x89905))
% 52.62/52.42 [8991]E(x89911,x89912)+~P41(f35(x89915,x89913),x89911,x89914,x89912)+P41(x89913,x89911,x89914,f386(x89912,x89914,x89911,x89913,x89915))
% 52.62/52.42 [8993]E(x89931,x89932)+P41(f35(x89933,x89934),f836(x89931,x89935,x89932,x89934,x89933),x89935,x89931)+~P41(f35(x89933,x89934),x89932,x89935,x89931)
% 52.62/52.42 [8994]E(x89941,x89942)+P41(f35(x89943,x89944),f386(x89941,x89945,x89942,x89944,x89943),x89945,x89941)+~P41(f35(x89943,x89944),x89942,x89945,x89941)
% 52.62/52.42 [8996]~P41(f35(x89965,x89961),x89962,x89963,x89964)+P41(x89961,x89962,x89963,f836(x89964,x89963,x89962,x89961,x89965))+~P1(f332(x89965,x89962))
% 52.62/52.42 [8997]~P41(f35(x89975,x89971),x89972,x89973,x89974)+P41(x89971,x89972,x89973,f386(x89974,x89973,x89972,x89971,x89975))+~P1(f332(x89975,x89972))
% 52.62/52.42 [9001]~P41(f35(x90011,x90012),x90015,x90014,x90013)+P41(f35(x90011,x90012),f836(x90013,x90014,x90015,x90012,x90011),x90014,x90013)+~P1(f332(x90011,x90015))
% 52.62/52.42 [9002]~P41(f35(x90021,x90022),x90025,x90024,x90023)+P41(f35(x90021,x90022),f386(x90023,x90024,x90025,x90022,x90021),x90024,x90023)+~P1(f332(x90021,x90025))
% 52.62/52.42 [6429]E(x64291,x64292)+~E(f332(x64293,x64291),f332(x64293,x64292))+~P31(x64294,x64295,x64293,f239(f853(x64294,a839)))
% 52.62/52.42 [6430]E(x64301,x64302)+~E(f332(x64303,x64301),f332(x64303,x64302))+~P31(x64304,x64305,x64303,f239(f853(x64304,a839)))
% 52.62/52.42 [6594]~E(f332(x65943,x65945),f183(x65942))+~E(f332(x65944,x65945),f183(x65942))+E(f332(f170(x65941,x65942,x65943,x65944),x65945),f183(x65942))
% 52.62/52.42 [7368]E(x73681,x73682)+~P31(x73683,x73684,x73685,f239(f853(x73683,a839)))+~E(f332(f303(x73683,x73684,x73685),x73681),f332(f303(x73683,x73684,x73685),x73682))
% 52.62/52.42 [7626]P31(x76262,x76263,f521(x76264,x76263,x76262,x76261),x76261)+~E(f332(f303(x76263,x76262,x76265),x76264),x76261)+E(x76261,f180(f853(x76262,a839)))
% 52.62/52.42 [8157]~P1(f332(f332(x81573,x81572),x81575))+~P1(f332(f332(x81573,x81574),x81572))+P1(f332(f332(f334(x81571),x81572),f282(x81571,x81573,x81574,x81575)))
% 52.62/52.42 [8158]~P1(f332(f332(x81583,x81582),x81585))+~P1(f332(f332(x81583,x81584),x81582))+P1(f332(f332(f334(x81581),x81582),f291(x81581,x81583,x81584,x81585)))
% 52.62/52.42 [8696]~P31(x86961,x86963,x86965,f239(f853(x86961,a839)))+~P31(x86963,x86962,x86964,f239(f853(x86963,a839)))+P31(x86961,x86962,f332(f75(x86963,x86962,x86961,x86964),x86965),f239(f853(x86961,a839)))
% 52.62/52.42 [9195]P1(f332(f332(f334(f852(x91951,x91951)),f332(f332(f241(x91951,x91951),x91952),x91953)),f300(x91951,x91954)))+~P1(f332(f332(f334(f852(x91951,x91951)),f332(f332(f241(x91951,x91951),x91952),x91955)),f300(x91951,x91954)))+~P1(f332(f332(f334(f852(x91951,x91951)),f332(f332(f241(x91951,x91951),x91955),x91953)),f300(x91951,x91954)))
% 52.62/52.42 [9232]~P100(x92322)+~P1(f332(f127(x92321),x92325))+P1(f332(f127(x92321),f139(x92321,x92322,x92323,x92324,x92325)))
% 52.62/52.42 [5241]~E(x52412,f115(x52411))+E(f332(f332(f125(x52411),x52412),x52413),f332(f332(f140(x52411),x52414),x52415))+~E(x52413,f332(f332(f140(x52411),x52414),x52415))
% 52.62/52.42 [5242]~E(x52422,f115(x52421))+E(f332(f332(f125(x52421),x52422),x52423),f332(f332(f140(x52421),x52424),x52425))+~E(f332(f332(f140(x52421),x52424),x52425),x52423)
% 52.62/52.42 [6386]~E(f332(f181(f846(x63861)),x63865),f332(f181(f846(x63862)),x63864))+E(f332(f332(f143(f852(x63861,x63862),x63862),f250(x63861,x63862)),x63863),x63864)+~E(f332(f332(f167(x63861,x63862),x63865),x63864),x63863)
% 52.62/52.42 [6387]~E(f332(f181(f846(x63871)),x63874),f332(f181(f846(x63872)),x63875))+E(f332(f332(f143(f852(x63871,x63872),x63871),f240(x63871,x63872)),x63873),x63874)+~E(f332(f332(f167(x63871,x63872),x63874),x63875),x63873)
% 52.62/52.42 [6883]~P100(x68831)+~P20(x68831,f332(f332(f143(x68832,x68831),x68833),x68835))+P20(x68831,f332(f332(f143(x68832,x68831),x68833),f332(f126(x68832,x68834),x68835)))
% 52.62/52.42 [6929]~P1(f332(x69293,x69295))+~P1(f332(f332(x69292,x69294),x69295))+P1(f332(f332(f94(x69291,x69292,x69293),x69294),x69295))
% 52.62/52.42 [7026]~P100(x70261)+P20(x70261,f332(f332(f143(x70262,x70261),x70263),f151(x70262,x70264,x70265)))+~P20(x70261,f332(f332(f143(x70262,x70261),x70263),x70265))
% 52.62/52.42 [7049]~P55(x70493,x70492,x70495)+~P55(x70491,x70493,x70494)+P55(x70491,x70492,f332(f332(f281(x70491,x70493,x70492),x70494),x70495))
% 52.62/52.42 [7139]E(x71391,x71392)+~P31(x71393,x71394,x71395,f239(f853(x71393,a839)))+~E(f332(f332(f143(x71393,x71394),x71395),x71391),f332(f332(f143(x71393,x71394),x71395),x71392))
% 52.62/52.42 [7140]E(x71401,x71402)+~P31(x71403,x71404,x71405,f239(f853(x71403,a839)))+~E(f332(f332(f143(x71403,x71404),x71405),x71401),f332(f332(f143(x71403,x71404),x71405),x71402))
% 52.62/52.42 [7223]P41(x72231,x72232,x72233,x72234)+~P41(x72231,x72232,x72235,x72234)+~P1(f332(f332(f232(a845),x72235),x72233))
% 52.62/52.42 [7313]~P1(f332(f332(f233(a845),x73131),f332(x73133,x73135)))+P1(f332(f332(f233(a845),x73131),f144(x73132,x73133,x73134)))+~P1(f332(f332(f334(x73132),x73135),f332(f158(x73132),x73134)))
% 52.62/52.42 [7314]~P1(f332(f332(f232(a845),x73141),f332(x73143,x73145)))+P1(f332(f332(f232(a845),x73141),f144(x73142,x73143,x73144)))+~P1(f332(f332(f334(x73142),x73145),f332(f158(x73142),x73144)))
% 52.62/52.42 [7725]~P99(x77251)+P1(f332(f332(f232(f853(x77251,a839)),f295(x77251,x77252,x77253)),f295(x77251,x77254,x77255)))+P1(f332(f332(f232(x77251),x77252),x77253))
% 52.62/52.42 [7752]~P11(x77521)+P1(f332(f332(f232(x77521),f332(f332(f48(x77522,x77521),x77523),x77524)),f332(x77524,x77525)))+~P1(f332(f332(f334(x77522),x77525),x77523))
% 52.62/52.42 [7820]~P31(x78201,x78202,x78204,x78203)+E(f332(f79(x78201,x78202,x78203,x78204),f332(x78204,x78205)),x78205)+~P1(f332(f332(f334(x78201),x78205),x78203))
% 52.62/52.42 [8016]~P1(f332(x80161,x80165))+P1(f332(x80161,f350(x80161,x80162,x80163,x80164)))+~P1(f332(f332(f334(x80164),x80165),x80163))
% 52.62/52.42 [8017]~P1(f332(x80171,x80175))+P1(f332(x80171,f350(x80171,x80172,x80173,x80174)))+~P1(f332(f332(f334(x80174),x80175),x80172))
% 52.62/52.42 [8108]P1(f332(f64(x81081),x81082))+~P1(f332(f64(x81083),x81084))+~P1(f332(f332(f232(f853(x81081,a839)),x81082),f332(f303(x81083,x81081,x81085),x81084)))
% 52.62/52.42 [8118]~P31(x81184,x81181,x81182,f239(f853(x81184,a839)))+~P1(f332(f332(f334(x81184),x81183),x81185))+P1(f332(f332(f334(x81181),f332(x81182,x81183)),f332(f303(x81184,x81181,x81182),x81185)))
% 52.62/52.42 [8268]E(x82681,x82682)+~P31(x82683,x82684,x82685,f332(f332(f103(f853(x82683,a839)),f332(f158(x82683),x82681)),f332(f158(x82683),x82682)))+~E(f332(f332(f143(x82683,x82684),x82685),x82681),f332(f332(f143(x82683,x82684),x82685),x82682))
% 52.62/52.42 [8269]E(x82691,x82692)+~P31(x82693,x82694,x82695,f332(f332(f103(f853(x82693,a839)),f332(f158(x82693),x82691)),f332(f158(x82693),x82692)))+~E(f332(f332(f143(x82693,x82694),x82695),x82691),f332(f332(f143(x82693,x82694),x82695),x82692))
% 52.62/52.42 [8326]~P99(x83261)+~P1(f332(f332(f233(f853(x83261,a839)),f295(x83261,x83264,x83265)),f295(x83261,x83262,x83263)))+P1(f332(f332(f232(x83261),x83262),x83263))
% 52.62/52.42 [8394]~P31(x83941,x83944,x83945,f239(f853(x83941,a839)))+~P1(f332(f332(f334(x83944),f332(x83945,x83942)),f332(f303(x83941,x83944,x83945),x83943)))+P1(f332(f332(f334(x83941),x83942),x83943))
% 52.62/52.42 [8474]P1(f332(x84741,x84742))+~P1(f332(x84741,f354(x84741,x84743,x84744,x84745)))+~P1(f332(f332(f334(x84745),x84742),x84744))
% 52.62/52.42 [8475]P1(f332(x84751,x84752))+~P1(f332(x84751,f354(x84751,x84753,x84754,x84755)))+~P1(f332(f332(f334(x84755),x84752),x84753))
% 52.62/52.42 [8731]~P31(x87312,x87313,x87311,x87314)+E(f332(x87311,f332(f79(x87312,x87313,x87314,x87311),x87315)),x87315)+~P1(f332(f332(f334(x87313),x87315),f332(f303(x87312,x87313,x87311),x87314)))
% 52.62/52.42 [8815]E(x88151,f115(x88152))+E(f332(f332(f140(x88152),x88153),f731(x88154,x88153,x88155,x88151,x88152)),x88151)+~E(f332(f332(f125(x88152),x88151),x88155),f332(f332(f140(x88152),x88153),x88154))
% 52.62/52.42 [8816]E(x88161,f115(x88162))+E(f332(f332(f140(x88162),x88163),f732(x88164,x88161,x88165,x88163,x88162)),x88161)+~E(f332(f332(f125(x88162),x88161),x88164),f332(f332(f140(x88162),x88163),x88165))
% 52.62/52.42 [8831]E(f332(f332(f140(x88312),x88313),f731(x88314,x88313,x88311,x88315,x88312)),x88315)+~E(f332(f332(f125(x88312),x88315),x88311),f332(f332(f140(x88312),x88313),x88314))+E(x88311,f332(f332(f140(x88312),x88313),x88314))
% 52.62/52.42 [8832]E(f332(f332(f140(x88321),x88322),f732(x88324,x88325,x88323,x88322,x88321)),x88325)+~E(f332(f332(f125(x88321),x88325),x88324),f332(f332(f140(x88321),x88322),x88323))+E(f332(f332(f140(x88321),x88322),x88323),x88324)
% 52.62/52.42 [8908]~E(f332(f303(x89083,x89082,x89084),f239(f853(x89083,a839))),f239(f853(x89082,a839)))+~E(f332(f303(x89081,x89083,x89085),f239(f853(x89081,a839))),f239(f853(x89083,a839)))+E(f332(f303(x89081,x89082,f332(f75(x89083,x89082,x89081,x89084),x89085)),f239(f853(x89081,a839))),f239(f853(x89082,a839)))
% 52.62/52.42 [9238]E(x92381,f115(x92382))+~E(f332(f332(f125(x92382),x92381),x92383),f332(f332(f140(x92382),x92385),x92384))+E(f332(f332(f125(x92382),f732(x92383,x92381,x92384,x92385,x92382)),x92383),x92384)
% 52.62/52.42 [9239]E(x92391,f115(x92392))+~E(f332(f332(f125(x92392),x92391),x92395),f332(f332(f140(x92392),x92394),x92393))+E(f332(f332(f125(x92392),f731(x92393,x92394,x92395,x92391,x92392)),x92395),x92393)
% 52.62/52.42 [9247]E(f332(f332(f125(x92472),f731(x92474,x92473,x92471,x92475,x92472)),x92471),x92474)+~E(f332(f332(f125(x92472),x92475),x92471),f332(f332(f140(x92472),x92473),x92474))+E(x92471,f332(f332(f140(x92472),x92473),x92474))
% 52.62/52.42 [9248]~E(f332(f332(f125(x92481),x92485),x92484),f332(f332(f140(x92481),x92482),x92483))+E(f332(f332(f125(x92481),f732(x92484,x92485,x92483,x92482,x92481)),x92484),x92483)+E(f332(f332(f140(x92481),x92482),x92483),x92484)
% 52.62/52.42 [9249]E(f332(f332(f125(x92491),x92495),f735(x92493,x92492,x92494,x92495,x92491)),x92492)+E(f332(f332(f125(x92491),x92492),f734(x92493,x92492,x92494,x92495,x92491)),x92495)+~E(f332(f332(f125(x92491),x92495),x92494),f332(f332(f125(x92491),x92492),x92493))
% 52.62/52.42 [9280]~P100(x92801)+P20(x92801,f332(f332(f143(x92802,x92801),x92803),f139(x92802,x92801,x92803,x92804,x92805)))+~P20(x92801,f332(f332(f143(x92802,x92801),x92803),x92805))
% 52.62/52.42 [9296]~P59(x92965,x92961,x92964,x92963)+P1(f332(f332(x92961,x92962),f538(x92963,x92964,x92961,x92965,x92962)))+~P1(f332(f332(f334(x92965),x92962),x92964))
% 52.62/52.42 [9394]~P1(f332(f332(f334(f852(x93941,x93941)),f332(f332(f241(x93941,x93941),x93945),x93943)),f300(x93941,x93944)))+P1(f332(f332(f334(f852(x93941,x93941)),f332(f332(f241(x93941,x93941),x93942),x93943)),f332(f332(f281(x93941,x93941,x93941),x93944),f300(x93941,x93944))))+~P1(f332(f332(f334(f852(x93941,x93941)),f332(f332(f241(x93941,x93941),x93942),x93945)),f332(f332(f281(x93941,x93941,x93941),x93944),f300(x93941,x93944))))
% 52.62/52.42 [9395]~P1(f332(f332(f334(f852(x93951,x93951)),f332(f332(f241(x93951,x93951),x93952),x93955)),f300(x93951,x93954)))+P1(f332(f332(f334(f852(x93951,x93951)),f332(f332(f241(x93951,x93951),x93952),x93953)),f332(f332(f281(x93951,x93951,x93951),x93954),f300(x93951,x93954))))+~P1(f332(f332(f334(f852(x93951,x93951)),f332(f332(f241(x93951,x93951),x93955),x93953)),f332(f332(f281(x93951,x93951,x93951),x93954),f300(x93951,x93954))))
% 52.62/52.42 [9397]P1(f332(f332(f334(f852(f846(x93971),f846(x93971))),f332(f332(f241(f846(x93971),f846(x93971)),x93972),x93973)),f147(x93971,f300(x93971,x93974))))+~P1(f332(f332(f334(f852(f846(x93971),f846(x93971))),f332(f332(f241(f846(x93971),f846(x93971)),x93972),x93975)),f147(x93971,f300(x93971,x93974))))+~P1(f332(f332(f334(f852(f846(x93971),f846(x93971))),f332(f332(f241(f846(x93971),f846(x93971)),x93975),x93973)),f147(x93971,f300(x93971,x93974))))
% 52.62/52.42 [9401]E(f332(f332(f125(x94011),x94012),f734(x94013,x94012,x94014,x94015,x94011)),x94015)+E(f332(f332(f125(x94011),f735(x94013,x94012,x94014,x94015,x94011)),x94013),x94014)+~E(f332(f332(f125(x94011),x94012),x94013),f332(f332(f125(x94011),x94015),x94014))
% 52.62/52.42 [9402]E(f332(f332(f125(x94021),x94022),f735(x94023,x94024,x94025,x94022,x94021)),x94024)+E(f332(f332(f125(x94021),f734(x94023,x94024,x94025,x94022,x94021)),x94025),x94023)+~E(f332(f332(f125(x94021),x94022),x94025),f332(f332(f125(x94021),x94024),x94023))
% 52.62/52.42 [9459]P1(f332(f332(f334(f852(x94591,x94591)),f332(f332(f241(x94591,x94591),x94592),x94593)),f332(f332(f281(x94591,x94591,x94591),x94594),f300(x94591,x94594))))+~P1(f332(f332(f334(f852(x94591,x94591)),f332(f332(f241(x94591,x94591),x94592),x94595)),f332(f332(f281(x94591,x94591,x94591),x94594),f300(x94591,x94594))))+~P1(f332(f332(f334(f852(x94591,x94591)),f332(f332(f241(x94591,x94591),x94595),x94593)),f332(f332(f281(x94591,x94591,x94591),x94594),f300(x94591,x94594))))
% 52.62/52.42 [9492]E(f332(f332(f125(x94921),f734(x94922,x94923,x94924,x94925,x94921)),x94924),x94922)+~E(f332(f332(f125(x94921),x94923),x94922),f332(f332(f125(x94921),x94925),x94924))+E(f332(f332(f125(x94921),f735(x94922,x94923,x94924,x94925,x94921)),x94922),x94924)
% 52.62/52.42 [9507]~P59(x95071,x95074,x95073,x95072)+~P1(f332(f332(f334(x95071),x95075),x95073))+P1(f332(f332(f334(x95071),f538(x95072,x95073,x95074,x95071,x95075)),x95072))
% 52.62/52.42 [9615]~P1(f332(f332(f334(f852(f853(x96151,a839),f853(x96151,a839))),f332(f332(f241(f853(x96151,a839),f853(x96151,a839)),x96154),x96153)),f325(x96151,x96152)))+~P1(f332(f332(f334(x96151),x96155),x96154))+P1(f332(f332(f334(x96151),f625(x96152,x96153,x96154,x96151,x96155)),x96153))
% 52.62/52.42 [6462]~P23(x64622,x64625,x64621)+~P1(f332(f64(x64622),x64624))+E(f332(x64621,f332(f332(f302(x64622),x64623),x64624)),f332(f332(f67(x64622,x64622,x64625),x64623),x64624))
% 52.62/52.42 [6463]~E(x64633,x64634)+~E(x64632,x64635)+E(f332(f332(f302(x64631),x64632),f332(f332(f302(x64631),x64633),f180(f853(x64631,a839)))),f332(f332(f302(x64631),x64634),f332(f332(f302(x64631),x64635),f180(f853(x64631,a839)))))
% 52.62/52.42 [6475]P1(f332(x64752,x64755))+E(f162(x64751,x64752,f332(f332(f125(x64751),x64753),x64754)),f162(x64751,x64752,x64753))+~P1(f332(f332(f334(x64751),x64755),f332(f158(x64751),x64753)))
% 52.62/52.42 [6510]E(f332(x65101,x65102),f239(f853(x65103,a839)))+~E(f332(f332(f48(x65104,f853(x65103,a839)),x65105),x65101),f239(f853(x65103,a839)))+~P1(f332(f332(f334(x65104),x65102),x65105))
% 52.62/52.42 [6511]E(f332(x65111,x65112),f180(f853(x65113,a839)))+~E(f332(f332(f47(x65114,f853(x65113,a839)),x65115),x65111),f180(f853(x65113,a839)))+~P1(f332(f332(f334(x65114),x65112),x65115))
% 52.62/52.42 [6512]E(f332(x65121,x65122),f239(f853(x65123,a839)))+~E(f332(f332(f48(x65124,f853(x65123,a839)),x65125),x65121),f239(f853(x65123,a839)))+~P1(f332(f332(f334(x65124),x65122),x65125))
% 52.62/52.42 [6513]E(f332(x65131,x65132),f180(f853(x65133,a839)))+~E(f332(f332(f47(x65134,f853(x65133,a839)),x65135),x65131),f180(f853(x65133,a839)))+~P1(f332(f332(f334(x65134),x65132),x65135))
% 52.62/52.42 [6831]~P1(f332(f332(f187(x68311),x68313),x68315))+~P1(f332(f332(f187(x68312),x68315),x68314))+P1(f332(f332(f187(f36(x68311,x68312)),x68313),x68314))
% 52.62/52.42 [6832]~P1(f332(f332(f187(x68321),x68323),x68325))+~P1(f332(f332(f187(x68322),x68325),x68324))+P1(f332(f332(f187(f36(x68321,x68322)),x68323),x68324))
% 52.62/52.42 [7035]~E(x70352,x70354)+~P137(x70351)+E(f332(f332(f82(x70351),f332(f332(f83(x70351),x70352),x70353)),f332(f332(f83(x70351),x70354),x70355)),f332(f332(f82(x70351),f332(f332(f83(x70351),x70352),x70355)),f332(f332(f83(x70351),x70354),x70353)))
% 52.62/52.42 [7036]~E(x70362,x70364)+~P137(x70361)+E(f332(f332(f82(x70361),f332(f332(f83(x70361),x70362),x70363)),f332(f332(f83(x70361),x70364),x70365)),f332(f332(f82(x70361),f332(f332(f83(x70361),x70362),x70365)),f332(f332(f83(x70361),x70364),x70363)))
% 52.62/52.42 [7096]~P11(x70961)+~P1(f332(f332(f334(x70964),x70963),x70965))+P1(f332(f332(f232(x70961),f332(x70962,x70963)),f332(f332(f47(x70964,x70961),x70965),x70962)))
% 52.62/52.42 [7143]~P102(x71431)+P1(f332(f332(f232(x71431),f332(x71432,x71433)),f332(x71434,x71433)))+~P1(f332(f332(f232(f853(x71435,x71431)),x71432),x71434))
% 52.62/52.42 [7144]~P102(x71441)+P1(f332(f332(f232(x71441),f332(x71442,x71443)),f332(x71444,x71443)))+~P1(f332(f332(f232(f853(x71445,x71441)),x71442),x71444))
% 52.62/52.42 [7145]~P102(x71451)+P1(f332(f332(f232(x71451),f332(x71452,x71453)),f332(x71454,x71453)))+~P1(f332(f332(f232(f853(x71455,x71451)),x71452),x71454))
% 52.62/52.42 [7281]E(x72811,x72812)+E(x72813,x72811)+~E(f332(f332(f302(x72814),x72811),f332(f332(f302(x72814),x72815),f180(f853(x72814,a839)))),f332(f332(f302(x72814),x72812),f332(f332(f302(x72814),x72813),f180(f853(x72814,a839)))))
% 52.62/52.42 [7282]E(x72821,x72822)+E(x72823,x72821)+~E(f332(f332(f302(x72824),x72823),f332(f332(f302(x72824),x72822),f180(f853(x72824,a839)))),f332(f332(f302(x72824),x72825),f332(f332(f302(x72824),x72821),f180(f853(x72824,a839)))))
% 52.62/52.42 [7283]E(x72831,x72832)+E(x72831,x72833)+~E(f332(f332(f302(x72834),x72833),f332(f332(f302(x72834),x72832),f180(f853(x72834,a839)))),f332(f332(f302(x72834),x72835),f332(f332(f302(x72834),x72831),f180(f853(x72834,a839)))))
% 52.62/52.42 [7284]E(x72841,x72842)+E(x72841,x72843)+~E(f332(f332(f302(x72844),x72841),f332(f332(f302(x72844),x72845),f180(f853(x72844,a839)))),f332(f332(f302(x72844),x72842),f332(f332(f302(x72844),x72843),f180(f853(x72844,a839)))))
% 52.62/52.42 [7830]P31(x78301,x78302,x78303,x78304)+~P31(x78301,x78302,x78303,x78305)+~P1(f332(f332(f232(f853(x78301,a839)),x78304),x78305))
% 52.62/52.42 [7931]P1(f332(x79311,x79312))+~P1(f332(f332(f187(x79314),x79312),x79315))+P1(f332(f332(f187(f33(x79311,x79313,x79314)),x79312),x79315))
% 52.62/52.42 [7932]P1(f332(x79321,x79322))+~P1(f332(f332(f187(x79324),x79322),x79325))+P1(f332(f332(f187(f33(x79321,x79323,x79324)),x79322),x79325))
% 52.62/52.42 [7933]P1(f332(x79331,x79332))+~P1(f332(f332(f187(x79334),x79332),x79335))+P1(f332(f332(f187(f33(x79331,x79333,x79334)),x79332),x79335))
% 52.62/52.42 [7959]~P1(f332(x79591,x79594))+~P1(f332(f332(f187(x79592),x79594),x79595))+P1(f332(f332(f187(f33(x79591,x79592,x79593)),x79594),x79595))
% 52.62/52.42 [7960]~P1(f332(x79601,x79604))+~P1(f332(f332(f187(x79602),x79604),x79605))+P1(f332(f332(f187(f33(x79601,x79602,x79603)),x79604),x79605))
% 52.62/52.42 [7961]~P1(f332(x79611,x79614))+~P1(f332(f332(f187(x79612),x79614),x79615))+P1(f332(f332(f187(f33(x79611,x79612,x79613)),x79614),x79615))
% 52.62/52.42 [8006]E(x80061,x80062)+~E(f332(f303(x80063,x80064,x80065),x80061),f332(f303(x80063,x80064,x80065),x80062))+~P31(x80063,x80064,x80065,f332(f332(f103(f853(x80063,a839)),x80061),x80062))
% 52.62/52.42 [8106]~P31(x81061,x81062,x81063,x81065)+~P31(x81061,x81062,x81063,x81064)+P31(x81061,x81062,x81063,f332(f332(f104(f853(x81061,a839)),x81064),x81065))
% 52.62/52.42 [8211]~P4(x82111)+E(f332(f332(f82(x82111),f332(x82112,x82113)),f332(f154(x82111),f332(f332(f143(x82114,x82111),x82112),f151(x82114,x82113,x82115)))),f332(f154(x82111),f332(f332(f143(x82114,x82111),x82112),x82115)))+~P1(f332(f332(f334(x82114),x82113),f332(f158(x82114),x82115)))
% 52.62/52.42 [8298]~P100(x82981)+~P20(x82981,f332(f332(f143(x82982,x82981),x82983),x82985))+P20(x82981,f332(f332(f143(x82982,x82981),x82983),f332(f332(f138(x82982,x82981,x82983),x82984),x82985)))
% 52.62/52.42 [8377]P1(f332(x83771,x83772))+P1(f332(f332(f187(x83773),x83772),x83774))+~P1(f332(f332(f187(f33(x83771,x83775,x83773)),x83772),x83774))
% 52.62/52.42 [8378]P1(f332(x83781,x83782))+P1(f332(f332(f187(x83783),x83782),x83784))+~P1(f332(f332(f187(f33(x83781,x83785,x83783)),x83782),x83784))
% 52.62/52.42 [8379]P1(f332(x83791,x83792))+P1(f332(f332(f187(x83793),x83792),x83794))+~P1(f332(f332(f187(f33(x83791,x83795,x83793)),x83792),x83794))
% 52.62/52.42 [8390]~P11(x83901)+P1(f332(f332(f232(x83901),f332(f332(f47(x83902,x83901),x83903),x83904)),f332(f332(f47(x83902,x83901),x83905),x83904)))+~P1(f332(f332(f232(f853(x83902,a839)),x83903),x83905))
% 52.62/52.42 [8391]~P11(x83911)+P1(f332(f332(f232(x83911),f332(f332(f48(x83912,x83911),x83913),x83914)),f332(f332(f48(x83912,x83911),x83915),x83914)))+~P1(f332(f332(f232(f853(x83912,a839)),x83915),x83913))
% 52.62/52.42 [8398]~P1(f332(x83984,x83982))+P1(f332(f332(f187(x83981),x83982),x83983))+~P1(f332(f332(f187(f33(x83984,x83981,x83985)),x83982),x83983))
% 52.62/52.42 [8399]~P1(f332(x83994,x83992))+P1(f332(f332(f187(x83991),x83992),x83993))+~P1(f332(f332(f187(f33(x83994,x83991,x83995)),x83992),x83993))
% 52.62/52.42 [8400]~P1(f332(x84004,x84002))+P1(f332(f332(f187(x84001),x84002),x84003))+~P1(f332(f332(f187(f33(x84004,x84001,x84005)),x84002),x84003))
% 52.62/52.42 [8424]~P100(x84243)+P1(f332(f127(x84241),x84242))+~P1(f332(f127(x84241),f332(f332(f138(x84241,x84243,x84244),x84245),x84242)))
% 52.62/52.42 [8432]P1(f332(f332(f187(x84321),x84322),x84323))+P1(f332(f332(f187(x84324),x84322),x84323))+~P1(f332(f332(f187(f33(x84325,x84321,x84324)),x84322),x84323))
% 52.62/52.42 [8433]P1(f332(f332(f187(x84331),x84332),x84333))+P1(f332(f332(f187(x84334),x84332),x84333))+~P1(f332(f332(f187(f33(x84335,x84331,x84334)),x84332),x84333))
% 52.62/52.42 [8434]P1(f332(f332(f187(x84341),x84342),x84343))+P1(f332(f332(f187(x84344),x84342),x84343))+~P1(f332(f332(f187(f33(x84345,x84341,x84344)),x84342),x84343))
% 52.62/52.42 [8558]~P100(x85581)+~P1(f332(f332(f334(x85582),x85583),f332(f158(x85582),x85584)))+~P1(f332(f127(x85582),f332(f332(f138(x85582,x85581,x85585),x85583),x85584)))
% 52.62/52.42 [8633]~P100(x86331)+P20(x86331,f332(f332(f143(x86332,x86331),x86333),x86334))+~P20(x86331,f332(f332(f143(x86332,x86331),x86333),f332(f332(f138(x86332,x86331,x86333),x86335),x86334)))
% 52.62/52.42 [8718]~P100(x87182)+E(f332(f332(f138(x87181,x87182,x87183),x87184),x87185),f139(x87181,x87182,x87183,x87184,x87185))+P1(f332(f332(f334(x87182),f332(x87183,x87184)),f332(f303(x87181,x87182,x87183),f332(f158(x87181),x87185))))
% 52.62/52.42 [8785]~P100(x87852)+E(f139(x87851,x87852,x87853,x87854,x87855),x87855)+~P1(f332(f332(f334(x87852),f332(x87853,x87854)),f332(f303(x87851,x87852,x87853),f332(f158(x87851),x87855))))
% 52.62/52.42 [8799]~P31(x87992,x87991,x87993,x87995)+P1(f332(f332(f233(f853(x87991,a839)),f332(f303(x87992,x87991,x87993),x87994)),f332(f303(x87992,x87991,x87993),x87995)))+~P1(f332(f332(f233(f853(x87992,a839)),x87994),x87995))
% 52.62/52.42 [8822]~P31(x88222,x88221,x88223,f239(f853(x88222,a839)))+P1(f332(f332(f232(f853(x88221,a839)),f332(f303(x88222,x88221,x88223),x88224)),f332(f303(x88222,x88221,x88223),x88225)))+~P1(f332(f332(f232(f853(x88222,a839)),x88224),x88225))
% 52.62/52.42 [8946]~P31(x89461,x89462,x89463,f239(f853(x89461,a839)))+~P1(f332(f332(f232(f853(x89462,a839)),x89464),f332(f303(x89461,x89462,x89463),x89465)))+P1(f332(f332(f232(f853(x89461,a839)),f332(f305(x89461,x89462,x89463),x89464)),x89465))
% 52.62/52.42 [8965]~E(f332(f303(x89653,x89651,x89654),f239(f853(x89653,a839))),f239(f853(x89651,a839)))+P1(f332(f332(f232(f853(x89651,a839)),x89652),f332(f303(x89653,x89651,x89654),x89655)))+~P1(f332(f332(f232(f853(x89653,a839)),f332(f305(x89653,x89651,x89654),x89652)),x89655))
% 52.62/52.42 [9003]~E(f332(f227(x90032),x90034),f332(f166(x90031,x90032,x90035),x90033))+~P1(f332(f127(x90031),f332(f332(f143(f852(x90031,x90032),x90031),f240(x90031,x90032)),x90035)))+P1(f332(f332(f334(f852(x90031,x90032)),f332(f332(f241(x90031,x90032),x90033),x90034)),f332(f158(f852(x90031,x90032)),x90035)))
% 52.62/52.42 [9004]~E(f332(f166(x90041,x90042,x90045),x90043),f332(f227(x90042),x90044))+~P1(f332(f127(x90041),f332(f332(f143(f852(x90041,x90042),x90041),f240(x90041,x90042)),x90045)))+P1(f332(f332(f334(f852(x90041,x90042)),f332(f332(f241(x90041,x90042),x90043),x90044)),f332(f158(f852(x90041,x90042)),x90045)))
% 52.62/52.42 [9067]~P31(x90671,x90674,x90675,f239(f853(x90671,a839)))+~P1(f332(f332(f232(f853(x90674,a839)),f332(f303(x90671,x90674,x90675),x90672)),f332(f303(x90671,x90674,x90675),x90673)))+P1(f332(f332(f232(f853(x90671,a839)),x90672),x90673))
% 52.62/52.42 [9133]E(f332(f227(x91331),x91332),f332(f166(x91333,x91331,x91334),x91335))+~P1(f332(f127(x91333),f332(f332(f143(f852(x91333,x91331),x91333),f240(x91333,x91331)),x91334)))+~P1(f332(f332(f334(f852(x91333,x91331)),f332(f332(f241(x91333,x91331),x91335),x91332)),f332(f158(f852(x91333,x91331)),x91334)))
% 52.62/52.42 [9134]E(f332(f166(x91341,x91342,x91343),x91344),f332(f227(x91342),x91345))+~P1(f332(f127(x91341),f332(f332(f143(f852(x91341,x91342),x91341),f240(x91341,x91342)),x91343)))+~P1(f332(f332(f334(f852(x91341,x91342)),f332(f332(f241(x91341,x91342),x91344),x91345)),f332(f158(f852(x91341,x91342)),x91343)))
% 52.62/52.42 [9135]E(f332(f166(x91351,x91352,x91353),x91354),f332(f227(x91352),x91355))+~P1(f332(f127(x91351),f332(f332(f143(f852(x91351,x91352),x91351),f240(x91351,x91352)),x91353)))+~P1(f332(f332(f334(f852(x91351,x91352)),f332(f332(f241(x91351,x91352),x91354),x91355)),f332(f158(f852(x91351,x91352)),x91353)))
% 52.62/52.42 [9342]~P22(x93421,x93422,x93423)+~P1(f332(f64(x93421),x93425))+P1(f332(f69(x93421,x93422,x93423,x93424,x93425),f332(f332(f67(x93421,x93422,x93423),x93424),x93425)))
% 52.62/52.42 [9416]P1(f332(x94161,f699(x94162,x94161,x94163,x94164,x94165)))+~P1(f332(f332(f232(f853(x94165,a839)),x94164),x94163))+P1(f332(f332(f232(f853(x94165,a839)),f332(f332(f104(f853(x94165,a839)),x94164),f332(f256(x94165),x94161))),f332(f332(f104(f853(x94165,a839)),x94163),f332(f256(x94165),x94162))))
% 52.62/52.42 [9505]~P11(x95055)+P1(f332(f332(f334(x95051),f665(x95052,x95053,x95051,x95054,x95055)),x95053))+P1(f332(f332(f232(x95055),x95054),f332(f332(f48(x95051,x95055),x95053),x95052)))
% 52.62/52.42 [9517]~P1(f332(x95175,f699(x95175,x95173,x95174,x95172,x95171)))+~P1(f332(f332(f232(f853(x95171,a839)),x95172),x95174))+P1(f332(f332(f232(f853(x95171,a839)),f332(f332(f104(f853(x95171,a839)),x95172),f332(f256(x95171),x95173))),f332(f332(f104(f853(x95171,a839)),x95174),f332(f256(x95171),x95175))))
% 52.62/52.42 [9580]P1(f332(f332(f334(x95801),f699(x95802,x95803,x95804,x95805,x95801)),x95805))+~P1(f332(f332(f232(f853(x95801,a839)),x95805),x95804))+P1(f332(f332(f232(f853(x95801,a839)),f332(f332(f104(f853(x95801,a839)),x95805),f332(f256(x95801),x95803))),f332(f332(f104(f853(x95801,a839)),x95804),f332(f256(x95801),x95802))))
% 52.62/52.42 [9626]~P11(x96261)+~P1(f332(f332(f232(x96261),x96262),f332(x96265,f665(x96265,x96264,x96263,x96262,x96261))))+P1(f332(f332(f232(x96261),x96262),f332(f332(f48(x96263,x96261),x96264),x96265)))
% 52.62/52.42 [9656]~P70(x96561)+~P1(f332(f64(x96562),x96565))+E(f332(f332(f332(f68(x96561,x96562,f83(x96561)),f332(f332(f20(x96562,x96561,x96561),f332(f332(f10(x96561,f853(x96561,x96561),x96562),f83(x96561)),x96563)),x96564)),f80(x96561)),x96565),f332(f332(f83(x96561),f332(f332(f332(f68(x96561,x96562,f83(x96561)),x96563),f80(x96561)),x96565)),f332(f332(f332(f68(x96561,x96562,f83(x96561)),x96564),f80(x96561)),x96565)))
% 52.62/52.42 [9705]~P1(f332(f332(f334(f852(f853(x97051,a839),f853(x97051,a839))),f332(f332(f241(f853(x97051,a839),f853(x97051,a839)),x97055),x97054)),f325(x97051,x97053)))+~P1(f332(f332(f334(x97051),x97052),x97055))+P1(f332(f332(f334(f852(x97051,x97051)),f332(f332(f241(x97051,x97051),x97052),f625(x97053,x97054,x97055,x97051,x97052))),x97053))
% 52.62/52.42 [9854]~P1(f332(f332(f334(f852(f846(x98541),f846(x98541))),f332(f332(f241(f846(x98541),f846(x98541)),f332(f332(f125(x98541),x98545),x98542)),f332(f332(f125(x98541),x98545),x98543))),f137(x98541,x98544)))+P1(f332(f332(f334(f852(f846(x98541),f846(x98541))),f332(f332(f241(f846(x98541),f846(x98541)),x98542),x98543)),f137(x98541,x98544)))+P1(f332(f332(f334(f852(x98541,x98541)),f332(f332(f241(x98541,x98541),f740(x98544,x98543,x98542,x98545,x98541)),f740(x98544,x98543,x98542,x98545,x98541))),x98544))
% 52.62/52.42 [7148]~E(x71483,x71485)+E(f332(f332(f152(x71481),f332(f332(f148(x71481,x71482),x71483),x71484)),x71485),x71484)+~P1(f332(f332(f233(a845),x71483),f332(f181(f846(x71481)),x71482)))
% 52.62/52.42 [7157]~E(f332(f181(f846(x71571)),x71573),f332(f181(f846(x71572)),x71574))+E(f332(f166(x71571,x71572,f332(f332(f167(x71571,x71572),x71573),x71574)),x71575),f183(x71572))+P1(f332(f332(f334(x71571),x71575),f332(f158(x71571),x71573)))
% 52.62/52.42 [7277]~E(f332(f332(f125(x72771),x72772),x72774),f332(f332(f125(x72771),x72773),x72775))+E(f332(f332(f159(x72771),f332(f181(f846(x72771)),x72772)),x72773),x72772)+P1(f332(f332(f232(a845),f332(f181(f846(x72771)),x72773)),f332(f181(f846(x72771)),x72772)))
% 52.62/52.42 [7278]E(x72781,x72782)+E(f332(f332(f152(x72783),f332(f332(f148(x72783,x72784),x72781),x72785)),x72782),f332(f332(f152(x72783),x72784),x72782))+~P1(f332(f332(f233(a845),x72781),f332(f181(f846(x72783)),x72784)))
% 52.62/52.42 [7791]~E(f332(f332(f125(x77911),x77912),x77914),f332(f332(f125(x77911),x77913),x77915))+E(f332(f332(f159(x77911),f332(f181(f846(x77911)),x77912)),x77913),x77912)+~P1(f332(f332(f232(a845),f332(f181(f846(x77911)),x77912)),f332(f181(f846(x77911)),x77913)))
% 52.62/52.42 [7815]~P1(f332(f64(x78151),f332(x78154,x78155)))+~P1(f332(f332(f334(x78152),x78155),x78153))+P1(f332(f64(x78151),f332(f332(f48(x78152,f853(x78151,a839)),x78153),x78154)))
% 52.62/52.42 [7927]~E(f332(f181(f846(x79271)),x79272),f332(f181(f846(x79273)),x79274))+~E(f332(f166(x79271,x79273,f332(f332(f167(x79271,x79273),x79272),x79274)),x79275),f183(x79273))+~P1(f332(f332(f334(x79271),x79275),f332(f158(x79271),x79272)))
% 52.62/52.42 [7993]~P49(x79931,x79933,x79935)+~P49(x79931,x79932,x79934)+P49(x79931,f332(f332(f103(f853(x79931,a839)),x79932),x79933),f332(f332(f103(f853(f852(x79931,x79931),a839)),x79934),x79935))
% 52.62/52.42 [7994]~P49(x79941,x79943,x79945)+~P49(x79941,x79942,x79944)+P49(x79941,f332(f332(f104(f853(x79941,a839)),x79942),x79943),f332(f332(f104(f853(f852(x79941,x79941),a839)),x79944),x79945))
% 52.62/52.42 [8342]E(f332(f332(f241(x83421,x83422),f332(f332(f152(x83421),x83423),x83424)),f332(f332(f152(x83422),x83425),x83424)),f332(f332(f152(f852(x83421,x83422)),f332(f332(f167(x83421,x83422),x83423),x83425)),x83424))+~P1(f332(f332(f233(a845),x83424),f332(f181(f846(x83421)),x83423)))+~P1(f332(f332(f233(a845),x83424),f332(f181(f846(x83422)),x83425)))
% 52.62/52.42 [8502]~P49(x85021,x85023,x85024)+P1(f332(f332(f334(x85021),x85022),x85023))+~P1(f332(f332(f334(f852(x85021,x85021)),f332(f332(f241(x85021,x85021),x85025),x85022)),x85024))
% 52.62/52.42 [8503]~P49(x85031,x85033,x85034)+P1(f332(f332(f334(x85031),x85032),x85033))+~P1(f332(f332(f334(f852(x85031,x85031)),f332(f332(f241(x85031,x85031),x85032),x85035)),x85034))
% 52.62/52.42 [8504]~P14(x85041,x85043,x85044)+P1(f332(f332(f334(x85041),x85042),x85043))+~P1(f332(f332(f334(f852(x85041,x85041)),f332(f332(f241(x85041,x85041),x85045),x85042)),x85044))
% 52.62/52.42 [8505]~P14(x85051,x85053,x85054)+P1(f332(f332(f334(x85051),x85052),x85053))+~P1(f332(f332(f334(f852(x85051,x85051)),f332(f332(f241(x85051,x85051),x85052),x85055)),x85054))
% 52.62/52.42 [8740]~P14(x87401,x87405,x87402)+E(f332(f277(x87401,x87401,x87402),f332(f332(f302(x87401),x87403),f180(f853(x87401,a839)))),f332(f277(x87401,x87401,x87402),f332(f332(f302(x87401),x87404),f180(f853(x87401,a839)))))+~P1(f332(f332(f334(f852(x87401,x87401)),f332(f332(f241(x87401,x87401),x87403),x87404)),x87402))
% 52.62/52.42 [8741]~P14(x87411,x87415,x87412)+E(f332(f277(x87411,x87411,x87412),f332(f332(f302(x87411),x87413),f180(f853(x87411,a839)))),f332(f277(x87411,x87411,x87412),f332(f332(f302(x87411),x87414),f180(f853(x87411,a839)))))+~P1(f332(f332(f334(f852(x87411,x87411)),f332(f332(f241(x87411,x87411),x87413),x87414)),x87412))
% 52.62/52.42 [8905]P1(f332(x89051,x89052))+~P1(f332(f332(f334(x89053),x89052),x89055))+P1(f332(f332(f334(x89053),f354(x89051,x89054,x89055,x89053)),f332(f332(f103(f853(x89053,a839)),x89055),x89054)))
% 52.62/52.42 [8906]P1(f332(x89061,x89062))+~P1(f332(f332(f334(x89063),x89062),x89064))+P1(f332(f332(f334(x89063),f354(x89061,x89064,x89065,x89063)),f332(f332(f103(f853(x89063,a839)),x89065),x89064)))
% 52.62/52.42 [8914]~P1(f332(x89142,x89145))+~P1(f332(f332(f334(x89141),x89145),x89144))+P1(f332(f332(f334(x89141),f350(x89142,x89143,x89144,x89141)),f332(f332(f103(f853(x89141,a839)),x89144),x89143)))
% 52.62/52.42 [8915]~P1(f332(x89152,x89155))+~P1(f332(f332(f334(x89151),x89155),x89153))+P1(f332(f332(f334(x89151),f350(x89152,x89153,x89154,x89151)),f332(f332(f103(f853(x89151,a839)),x89154),x89153)))
% 52.62/52.42 [8928]~P1(f332(f332(f232(f853(x89281,a839)),x89285),x89283))+~P1(f332(f332(f232(f853(x89281,a839)),x89282),x89284))+P1(f332(f332(f232(f853(x89281,a839)),f332(f332(f3(f853(x89281,a839)),x89282),x89283)),f332(f332(f3(f853(x89281,a839)),x89284),x89285)))
% 52.62/52.42 [8929]~P1(f332(f332(f232(f853(x89291,a839)),x89293),x89295))+~P1(f332(f332(f232(f853(x89291,a839)),x89292),x89294))+P1(f332(f332(f232(f853(x89291,a839)),f332(f332(f103(f853(x89291,a839)),x89292),x89293)),f332(f332(f103(f853(x89291,a839)),x89294),x89295)))
% 52.62/52.42 [8930]~P1(f332(f332(f232(f853(x89301,a839)),x89303),x89305))+~P1(f332(f332(f232(f853(x89301,a839)),x89302),x89304))+P1(f332(f332(f232(f853(x89301,a839)),f332(f332(f104(f853(x89301,a839)),x89302),x89303)),f332(f332(f104(f853(x89301,a839)),x89304),x89305)))
% 52.62/52.42 [9019]P1(f332(f332(f334(f852(x90191,x90191)),f332(f332(f241(x90191,x90191),x90192),x90193)),f327(x90191,x90194,x90195)))+~P1(f332(f332(f232(a845),f332(x90194,x90192)),f332(x90194,x90193)))+~P1(f332(f332(f334(f852(x90191,x90191)),f332(f332(f241(x90191,x90191),x90192),x90193)),x90195))
% 52.62/52.42 [9026]~E(f332(f181(f846(x90261)),x90263),f332(f181(f846(x90262)),x90264))+E(f332(f166(x90261,x90262,f332(f332(f167(x90261,x90262),x90263),x90264)),x90265),f332(f227(x90262),f715(x90265,x90264,x90262,x90263,x90261)))+~P1(f332(f332(f334(x90261),x90265),f332(f158(x90261),x90263)))
% 52.62/52.42 [9175]P1(f332(f332(f334(f852(x91751,x91751)),f332(f332(f241(x91751,x91751),x91752),x91753)),f300(x91751,x91754)))+~P1(f332(f332(f334(f852(x91751,x91751)),f332(f332(f241(x91751,x91751),x91752),x91755)),f300(x91751,x91754)))+~P1(f332(f332(f334(f852(x91751,x91751)),f332(f332(f241(x91751,x91751),x91755),x91753)),x91754))
% 52.62/52.42 [9176]P1(f332(f332(f334(f852(x91761,x91761)),f332(f332(f241(x91761,x91761),x91762),x91763)),f300(x91761,x91764)))+~P1(f332(f332(f334(f852(x91761,x91761)),f332(f332(f241(x91761,x91761),x91765),x91763)),f300(x91761,x91764)))+~P1(f332(f332(f334(f852(x91761,x91761)),f332(f332(f241(x91761,x91761),x91762),x91765)),x91764))
% 52.62/52.42 [9270]E(x92701,x92702)+E(f332(a114,f642(x92703,x92704,x92701,x92702,x92705)),x92704)+~P1(f332(f332(f334(f852(x92705,x92705)),f332(f332(f241(x92705,x92705),x92702),x92701)),f332(f332(f173(f852(x92705,x92705),a839),x92704),x92703)))
% 52.62/52.42 [9271]E(x92711,x92712)+E(f332(a114,f644(x92713,x92714,x92711,x92712,x92715)),x92714)+~P1(f332(f332(f334(f852(x92715,x92715)),f332(f332(f241(x92715,x92715),x92712),x92711)),f332(f332(f173(f852(x92715,x92715),a839),x92714),x92713)))
% 52.62/52.42 [9272]E(x92721,f2(a845))+E(f332(a114,f642(x92722,x92721,x92723,x92724,x92725)),x92721)+~P1(f332(f332(f334(f852(x92725,x92725)),f332(f332(f241(x92725,x92725),x92724),x92723)),f332(f332(f173(f852(x92725,x92725),a839),x92721),x92722)))
% 52.62/52.42 [9273]E(x92731,f2(a845))+E(f332(a114,f644(x92732,x92731,x92733,x92734,x92735)),x92731)+~P1(f332(f332(f334(f852(x92735,x92735)),f332(f332(f241(x92735,x92735),x92734),x92733)),f332(f332(f173(f852(x92735,x92735),a839),x92731),x92732)))
% 52.62/52.42 [9292]P1(f332(f332(f334(f852(x92921,x92921)),f332(f332(f241(x92921,x92921),x92922),x92923)),f332(f332(f281(x92921,x92921,x92921),x92924),f300(x92921,x92924))))+~P1(f332(f332(f334(f852(x92921,x92921)),f332(f332(f241(x92921,x92921),x92922),x92925)),x92924))+~P1(f332(f332(f334(f852(x92921,x92921)),f332(f332(f241(x92921,x92921),x92925),x92923)),x92924))
% 52.62/52.42 [9301]~P1(f332(f332(f334(f852(x93011,x93011)),f332(f332(f241(x93011,x93011),x93012),x93015)),f300(x93011,x93014)))+P1(f332(f332(f334(f852(x93011,x93011)),f332(f332(f241(x93011,x93011),x93012),x93013)),f332(f332(f281(x93011,x93011,x93011),x93014),f300(x93011,x93014))))+~P1(f332(f332(f334(f852(x93011,x93011)),f332(f332(f241(x93011,x93011),x93015),x93013)),x93014))
% 52.62/52.42 [9302]~P1(f332(f332(f334(f852(x93021,x93021)),f332(f332(f241(x93021,x93021),x93025),x93023)),f300(x93021,x93024)))+P1(f332(f332(f334(f852(x93021,x93021)),f332(f332(f241(x93021,x93021),x93022),x93023)),f332(f332(f281(x93021,x93021,x93021),x93024),f300(x93021,x93024))))+~P1(f332(f332(f334(f852(x93021,x93021)),f332(f332(f241(x93021,x93021),x93022),x93025)),x93024))
% 52.62/52.42 [9338]~P14(x93381,x93385,x93382)+~P1(f332(f332(f334(f852(x93381,x93381)),f332(f332(f241(x93381,x93381),x93383),x93384)),x93382))+P1(f332(f332(f232(f853(x93381,a839)),f332(f277(x93381,x93381,x93382),f332(f332(f302(x93381),x93383),f180(f853(x93381,a839))))),f332(f277(x93381,x93381,x93382),f332(f332(f302(x93381),x93384),f180(f853(x93381,a839))))))
% 52.62/52.42 [9390]P1(f332(f332(f334(f852(x93901,x93901)),f332(f332(f241(x93901,x93901),x93902),x93903)),f332(f332(f281(x93901,x93901,x93901),x93904),f300(x93901,x93904))))+~P1(f332(f332(f334(f852(x93901,x93901)),f332(f332(f241(x93901,x93901),x93902),x93905)),f332(f332(f281(x93901,x93901,x93901),x93904),f300(x93901,x93904))))+~P1(f332(f332(f334(f852(x93901,x93901)),f332(f332(f241(x93901,x93901),x93905),x93903)),x93904))
% 52.62/52.42 [9391]P1(f332(f332(f334(f852(x93911,x93911)),f332(f332(f241(x93911,x93911),x93912),x93913)),f332(f332(f281(x93911,x93911,x93911),x93914),f300(x93911,x93914))))+~P1(f332(f332(f334(f852(x93911,x93911)),f332(f332(f241(x93911,x93911),x93915),x93913)),f332(f332(f281(x93911,x93911,x93911),x93914),f300(x93911,x93914))))+~P1(f332(f332(f334(f852(x93911,x93911)),f332(f332(f241(x93911,x93911),x93912),x93915)),x93914))
% 52.62/52.42 [9438]~P1(f332(f69(x94381,x94381,x94384,x94382,x94383),x94385))+P1(f332(f332(f334(x94381),x94382),x94383))+P1(f332(f65(x94381,x94384,f332(f332(f302(x94381),x94382),x94383)),x94385))
% 52.62/52.42 [9481]~E(f332(f303(x94813,x94812,x94815),x94814),x94811)+E(x94811,f180(f853(x94812,a839)))+P1(f332(f332(f232(f853(x94813,a839)),f332(f303(x94812,x94813,f521(x94814,x94813,x94812,x94811)),x94811)),x94814))
% 52.62/52.42 [9520]~P11(x95205)+P1(f332(f332(f334(x95201),f394(x95202,x95203,x95204,x95201,x95205)),x95204))+P1(f332(f332(f232(x95205),f332(f332(f47(x95201,x95205),x95204),x95203)),x95202))
% 52.62/52.42 [9682]E(x96821,x96822)+P1(f332(f332(f334(f852(x96823,x96823)),f332(f332(f241(x96823,x96823),x96821),f645(x96824,x96825,x96822,x96821,x96823))),x96824))+~P1(f332(f332(f334(f852(x96823,x96823)),f332(f332(f241(x96823,x96823),x96821),x96822)),f332(f332(f173(f852(x96823,x96823),a839),x96825),x96824)))
% 52.62/52.42 [9683]E(x96831,f2(a845))+P1(f332(f332(f334(f852(x96832,x96832)),f332(f332(f241(x96832,x96832),x96833),f645(x96834,x96831,x96835,x96833,x96832))),x96834))+~P1(f332(f332(f334(f852(x96832,x96832)),f332(f332(f241(x96832,x96832),x96833),x96835)),f332(f332(f173(f852(x96832,x96832),a839),x96831),x96834)))
% 52.62/52.42 [9728]~P11(x97281)+~P1(f332(f332(f232(x97281),f332(x97284,f394(x97285,x97284,x97283,x97282,x97281))),x97285))+P1(f332(f332(f232(x97281),f332(f332(f47(x97282,x97281),x97283),x97284)),x97285))
% 52.62/52.42 [9783]E(x97831,x97832)+P1(f332(f332(f334(f852(x97833,x97833)),f332(f332(f241(x97833,x97833),f643(x97834,x97835,x97831,x97832,x97833)),x97831)),x97834))+~P1(f332(f332(f334(f852(x97833,x97833)),f332(f332(f241(x97833,x97833),x97832),x97831)),f332(f332(f173(f852(x97833,x97833),a839),x97835),x97834)))
% 52.62/52.42 [9784]E(x97841,f2(a845))+P1(f332(f332(f334(f852(x97842,x97842)),f332(f332(f241(x97842,x97842),f643(x97843,x97841,x97844,x97845,x97842)),x97844)),x97843))+~P1(f332(f332(f334(f852(x97842,x97842)),f332(f332(f241(x97842,x97842),x97845),x97844)),f332(f332(f173(f852(x97842,x97842),a839),x97841),x97843)))
% 52.62/52.42 [9788]E(x97881,x97882)+P1(f332(f332(f334(f852(x97883,x97883)),f332(f332(f241(x97883,x97883),x97881),f643(x97884,x97885,x97882,x97881,x97883))),f332(f332(f173(f852(x97883,x97883),a839),f642(x97884,x97885,x97882,x97881,x97883)),x97884)))+~P1(f332(f332(f334(f852(x97883,x97883)),f332(f332(f241(x97883,x97883),x97881),x97882)),f332(f332(f173(f852(x97883,x97883),a839),x97885),x97884)))
% 52.62/52.42 [9789]E(x97891,f2(a845))+P1(f332(f332(f334(f852(x97892,x97892)),f332(f332(f241(x97892,x97892),x97893),f643(x97894,x97891,x97895,x97893,x97892))),f332(f332(f173(f852(x97892,x97892),a839),f642(x97894,x97891,x97895,x97893,x97892)),x97894)))+~P1(f332(f332(f334(f852(x97892,x97892)),f332(f332(f241(x97892,x97892),x97893),x97895)),f332(f332(f173(f852(x97892,x97892),a839),x97891),x97894)))
% 52.62/52.42 [9845]E(x98451,x98452)+P1(f332(f332(f334(f852(x98453,x98453)),f332(f332(f241(x98453,x98453),f645(x98454,x98455,x98451,x98452,x98453)),x98451)),f332(f332(f173(f852(x98453,x98453),a839),f644(x98454,x98455,x98451,x98452,x98453)),x98454)))+~P1(f332(f332(f334(f852(x98453,x98453)),f332(f332(f241(x98453,x98453),x98452),x98451)),f332(f332(f173(f852(x98453,x98453),a839),x98455),x98454)))
% 52.62/52.42 [9846]E(x98461,f2(a845))+P1(f332(f332(f334(f852(x98462,x98462)),f332(f332(f241(x98462,x98462),f645(x98463,x98461,x98464,x98465,x98462)),x98464)),f332(f332(f173(f852(x98462,x98462),a839),f644(x98463,x98461,x98464,x98465,x98462)),x98463)))+~P1(f332(f332(f334(f852(x98462,x98462)),f332(f332(f241(x98462,x98462),x98465),x98464)),f332(f332(f173(f852(x98462,x98462),a839),x98461),x98463)))
% 52.62/52.42 [9879]~P4(x98792)+~P1(f332(f64(x98791),x98795))+E(f332(f332(f8(x98791,x98792),f332(f332(f9(x98791,x98792,x98792),f332(f332(f20(x98791,x98792,f853(x98792,x98792)),f332(f332(f10(a839,f853(x98792,f853(x98792,x98792)),x98791),f98(x98792)),f332(f332(f9(x98791,f853(x98791,a839),a839),f334(x98791)),x98793))),x98794)),f2(x98792))),x98795),f332(f332(f8(x98791,x98792),x98794),f332(f332(f104(f853(x98791,a839)),x98795),x98793)))
% 52.62/52.42 [8556]~P4(x85561)+~P1(f332(f64(x85564),x85565))+E(f332(f332(f82(x85561),f332(x85562,x85563)),f332(f332(f8(x85564,x85561),x85562),f332(f332(f3(f853(x85564,a839)),x85565),f332(f332(f302(x85564),x85563),f180(f853(x85564,a839)))))),f332(f332(f8(x85564,x85561),x85562),f332(f332(f302(x85564),x85563),x85565)))
% 52.62/52.42 [8557]~P70(x85571)+~P1(f332(f64(x85574),x85575))+E(f332(f332(f83(x85571),f332(x85572,x85573)),f332(f332(f11(x85574,x85571),x85572),f332(f332(f3(f853(x85574,a839)),x85575),f332(f332(f302(x85574),x85573),f180(f853(x85574,a839)))))),f332(f332(f11(x85574,x85571),x85572),f332(f332(f302(x85574),x85573),x85575)))
% 52.62/52.42 [8837]~P100(x88372)+~P20(x88372,f332(f142(x88372),f332(f332(f143(x88371,x88372),x88374),x88375)))+E(f332(f126(x88371,f332(f332(f10(x88372,a839,x88371),f332(f233(x88372),x88373)),x88374)),x88375),f162(x88371,f332(f332(f10(x88372,a839,x88371),f332(f233(x88372),x88373)),x88374),x88375))
% 52.62/52.42 [8858]~P4(x88581)+E(f332(f332(f82(x88581),f332(f332(f8(a845,x88581),x88582),f295(a845,x88583,x88584))),f332(f332(f8(a845,x88581),x88582),f295(a845,f332(f332(f82(a845),x88584),f80(a845)),f332(f332(f82(a845),x88584),x88585)))),f332(f332(f8(a845,x88581),x88582),f295(a845,x88583,f332(f332(f82(a845),x88584),x88585))))+~P1(f332(f332(f232(a845),x88583),f332(f332(f82(a845),x88584),f80(a845))))
% 52.62/52.42 [8859]~P1(f332(f332(f334(x88591),x88594),x88595))+~P1(f332(f332(f232(f853(x88591,a839)),f332(f158(x88591),x88592)),x88595))+P1(f332(f332(f232(f853(x88591,a839)),f332(f158(x88591),f332(f332(f148(x88591,x88592),x88593),x88594))),x88595))
% 52.62/52.42 [9076]~P11(x90762)+~P1(f332(f64(x90761),x90765))+E(f332(f332(f67(x90761,x90762,f332(f332(f10(x90762,f853(x90762,x90762),x90761),f103(x90762)),x90763)),x90764),x90765),f332(f332(f103(x90762),x90764),f332(f332(f47(x90761,x90762),x90765),x90763)))
% 52.62/52.42 [9077]~P11(x90772)+~P1(f332(f64(x90771),x90775))+E(f332(f332(f67(x90771,x90772,f332(f332(f10(x90772,f853(x90772,x90772),x90771),f104(x90772)),x90773)),x90774),x90775),f332(f332(f104(x90772),x90774),f332(f332(f48(x90771,x90772),x90775),x90773)))
% 52.62/52.42 [9162]~P31(x91621,x91622,x91623,x91625)+P31(x91621,x91622,x91623,f332(f332(f302(x91621),x91624),x91625))+P1(f332(f332(f334(x91622),f332(x91623,x91624)),f332(f303(x91621,x91622,x91623),f332(f332(f3(f853(x91621,a839)),x91625),f332(f332(f302(x91621),x91624),f180(f853(x91621,a839)))))))
% 52.62/52.42 [9364]~P1(f332(f332(f334(f852(f846(x93641),f846(x93641))),f332(f332(f241(f846(x93641),f846(x93641)),x93642),x93644)),f147(x93641,x93645)))+~P1(f332(f332(f233(a845),x93643),f332(f181(f846(x93641)),x93642)))+P1(f332(f332(f334(f852(x93641,x93641)),f332(f332(f241(x93641,x93641),f332(f332(f152(x93641),x93642),x93643)),f332(f332(f152(x93641),x93644),x93643))),x93645))
% 52.62/52.42 [9590]E(x95901,f2(a1))+~P1(f332(f57(x95903,x95901),f332(f332(f241(a1,a1),x95904),x95905)))+P1(f332(f57(f332(f332(f83(a1),x95902),x95903),x95901),f332(f332(f241(a1,a1),f332(f332(f82(a1),f332(f332(f83(a1),x95902),x95904)),f332(f332(f44(a1),f332(f332(f83(a1),x95902),x95905)),x95901))),f53(a1,f332(f332(f83(a1),x95902),x95905),x95901))))
% 52.62/52.42 [9595]~P1(f332(f332(f233(a845),f2(a845)),x95953))+~P1(f332(f56(x95952,x95953),f332(f332(f241(a845,a845),x95954),x95955)))+P1(f332(f56(f332(f332(f83(a845),x95951),x95952),x95953),f332(f332(f241(a845,a845),f332(f332(f82(a845),f332(f332(f83(a845),x95951),x95954)),f332(f332(f44(a845),f332(f332(f83(a845),x95951),x95955)),x95953))),f53(a845,f332(f332(f83(a845),x95951),x95955),x95953))))
% 52.62/52.42 [9901]~P4(x99012)+~P1(f332(f64(x99011),x99014))+E(f332(f332(f8(x99011,x99012),x99013),f332(f256(x99011),f332(f332(f20(x99011,a839,a839),f332(f332(f10(a839,f853(a839,a839),x99011),a330),f332(f332(f9(x99011,f853(x99011,a839),a839),f334(x99011)),x99014))),f332(f332(f9(x99011,f853(x99011,a839),a839),f334(x99011)),x99015)))),f332(f332(f8(x99011,x99012),f332(f332(f9(x99011,x99012,x99012),f332(f332(f20(x99011,x99012,f853(x99012,x99012)),f332(f332(f10(a839,f853(x99012,f853(x99012,x99012)),x99011),f98(x99012)),f332(f332(f9(x99011,f853(x99011,a839),a839),f334(x99011)),x99015))),x99013)),f2(x99012))),x99014))
% 52.62/52.42 [8194]~E(f332(f332(f125(x81941),x81942),x81945),f332(f332(f125(x81941),x81943),x81944))+E(f332(f332(f125(x81941),f332(f332(f128(x81941),f332(f181(f846(x81941)),x81942)),x81943)),x81944),x81945)+P1(f332(f332(f232(a845),f332(f181(f846(x81941)),x81943)),f332(f181(f846(x81941)),x81942)))
% 52.62/52.42 [8393]~E(f332(f332(f125(x83932),x83933),x83931),f332(f332(f125(x83932),x83934),x83935))+E(x83931,f332(f332(f125(x83932),f332(f332(f128(x83932),f332(f181(f846(x83932)),x83933)),x83934)),x83935))+~P1(f332(f332(f232(a845),f332(f181(f846(x83932)),x83933)),f332(f181(f846(x83932)),x83934)))
% 52.62/52.42 [8485]~E(f332(f332(f82(a845),f332(f332(f83(a845),x84853),x84854)),x84851),f332(f332(f82(a845),f332(f332(f83(a845),x84852),x84854)),x84855))+~P1(f332(f332(f232(a845),x84853),x84852))+E(x84851,f332(f332(f82(a845),f332(f332(f83(a845),f332(f332(f3(a845),x84852),x84853)),x84854)),x84855))
% 52.62/52.42 [8486]~E(f332(f332(f82(a845),f332(f332(f83(a845),x84861),x84863)),x84864),f332(f332(f82(a845),f332(f332(f83(a845),x84862),x84863)),x84865))+~P1(f332(f332(f232(a845),x84862),x84861))+E(f332(f332(f82(a845),f332(f332(f83(a845),f332(f332(f3(a845),x84861),x84862)),x84863)),x84864),x84865)
% 52.62/52.42 [8626]E(f332(f332(f82(a845),f332(f332(f83(a845),x86261),x86262)),x86263),f332(f332(f82(a845),f332(f332(f83(a845),x86264),x86262)),x86265))+~P1(f332(f332(f232(a845),x86264),x86261))+~E(x86265,f332(f332(f82(a845),f332(f332(f83(a845),f332(f332(f3(a845),x86261),x86264)),x86262)),x86263))
% 52.62/52.42 [8627]E(f332(f332(f82(a845),f332(f332(f83(a845),x86271),x86272)),x86273),f332(f332(f82(a845),f332(f332(f83(a845),x86274),x86272)),x86275))+~P1(f332(f332(f232(a845),x86274),x86271))+~E(f332(f332(f82(a845),f332(f332(f83(a845),f332(f332(f3(a845),x86271),x86274)),x86272)),x86273),x86275)
% 52.62/52.42 [8961]~P1(f332(f332(f279(a1),x89611),x89614))+~P1(f332(f332(f279(a1),x89611),f332(f332(f82(a1),x89612),x89615)))+P1(f332(f332(f279(a1),x89611),f332(f332(f82(a1),f332(f332(f82(a1),x89612),f332(f332(f83(a1),x89613),x89614))),x89615)))
% 52.62/52.42 [9163]~P1(f332(f332(f279(a1),x91631),x91634))+P1(f332(f332(f279(a1),x91631),f332(f332(f82(a1),x91632),x91633)))+~P1(f332(f332(f279(a1),x91631),f332(f332(f82(a1),f332(f332(f82(a1),x91632),f332(f332(f83(a1),x91635),x91634))),x91633)))
% 52.62/52.42 [9412]~P4(x94122)+~P1(f332(f64(x94121),x94125))+E(f332(f332(f8(x94121,x94122),f332(f332(f20(x94121,x94122,x94122),f332(f332(f10(x94122,f853(x94122,x94122),x94121),f82(x94122)),x94123)),x94124)),x94125),f332(f332(f82(x94122),f332(f332(f8(x94121,x94122),x94123),x94125)),f332(f332(f8(x94121,x94122),x94124),x94125)))
% 52.62/52.42 [9413]~P70(x94132)+~P1(f332(f64(x94131),x94135))+E(f332(f332(f11(x94131,x94132),f332(f332(f20(x94131,x94132,x94132),f332(f332(f10(x94132,f853(x94132,x94132),x94131),f83(x94132)),x94133)),x94134)),x94135),f332(f332(f83(x94132),f332(f332(f11(x94131,x94132),x94133),x94135)),f332(f332(f11(x94131,x94132),x94134),x94135)))
% 52.62/52.42 [9414]~P62(x94142)+~P1(f332(f64(x94141),x94145))+E(f332(f332(f11(x94141,x94142),f332(f332(f20(x94141,x94142,x94142),f332(f332(f10(x94142,f853(x94142,x94142),x94141),f283(x94142)),x94143)),x94144)),x94145),f332(f332(f283(x94142),f332(f332(f11(x94141,x94142),x94143),x94145)),f332(f332(f11(x94141,x94142),x94144),x94145)))
% 52.62/52.42 [9534]~E(f647(x95345,x95344,x95343,x95342,x95341),f648(x95345,x95344,x95343,x95342,x95341))+P1(f332(f332(f334(f852(x95341,x95341)),f332(f332(f241(x95341,x95341),x95342),x95343)),f300(x95341,x95344)))+~P1(f332(f332(f334(f852(x95341,x95341)),f332(f332(f241(x95341,x95341),x95342),x95343)),f300(x95341,f332(f332(f103(f853(f852(x95341,x95341),a839)),x95344),x95345))))
% 52.62/52.42 [9535]~E(f655(x95355,x95354,x95353,x95352,x95351),f656(x95355,x95354,x95353,x95352,x95351))+P1(f332(f332(f334(f852(x95351,x95351)),f332(f332(f241(x95351,x95351),x95352),x95353)),f300(x95351,x95354)))+~P1(f332(f332(f334(f852(x95351,x95351)),f332(f332(f241(x95351,x95351),x95352),x95353)),f300(x95351,f332(f332(f103(f853(f852(x95351,x95351),a839)),x95354),x95355))))
% 52.62/52.42 [9716]P1(f332(f332(f334(f852(x97161,x97161)),f332(f332(f241(x97161,x97161),x97162),f656(x97165,x97164,x97163,x97162,x97161))),f300(x97161,x97164)))+P1(f332(f332(f334(f852(x97161,x97161)),f332(f332(f241(x97161,x97161),x97162),x97163)),f300(x97161,x97164)))+~P1(f332(f332(f334(f852(x97161,x97161)),f332(f332(f241(x97161,x97161),x97162),x97163)),f300(x97161,f332(f332(f103(f853(f852(x97161,x97161),a839)),x97164),x97165))))
% 52.62/52.42 [9810]P1(f332(f332(f334(f852(x98101,x98101)),f332(f332(f241(x98101,x98101),f648(x98105,x98104,x98103,x98102,x98101)),x98103)),f300(x98101,x98104)))+P1(f332(f332(f334(f852(x98101,x98101)),f332(f332(f241(x98101,x98101),x98102),x98103)),f300(x98101,x98104)))+~P1(f332(f332(f334(f852(x98101,x98101)),f332(f332(f241(x98101,x98101),x98102),x98103)),f300(x98101,f332(f332(f103(f853(f852(x98101,x98101),a839)),x98104),x98105))))
% 52.62/52.42 [9852]P1(f332(f332(f334(f852(x98521,x98521)),f332(f332(f241(x98521,x98521),x98522),x98523)),f300(x98521,x98524)))+P1(f332(f332(f334(f852(x98521,x98521)),f332(f332(f241(x98521,x98521),f647(x98525,x98524,x98523,x98522,x98521)),f648(x98525,x98524,x98523,x98522,x98521))),x98525))+~P1(f332(f332(f334(f852(x98521,x98521)),f332(f332(f241(x98521,x98521),x98522),x98523)),f300(x98521,f332(f332(f103(f853(f852(x98521,x98521),a839)),x98524),x98525))))
% 52.62/52.42 [9853]P1(f332(f332(f334(f852(x98531,x98531)),f332(f332(f241(x98531,x98531),x98532),x98533)),f300(x98531,x98534)))+P1(f332(f332(f334(f852(x98531,x98531)),f332(f332(f241(x98531,x98531),f656(x98535,x98534,x98533,x98532,x98531)),f655(x98535,x98534,x98533,x98532,x98531))),x98535))+~P1(f332(f332(f334(f852(x98531,x98531)),f332(f332(f241(x98531,x98531),x98532),x98533)),f300(x98531,f332(f332(f103(f853(f852(x98531,x98531),a839)),x98534),x98535))))
% 52.62/52.42 [9978]~P1(f332(f332(f334(f852(f846(x99781),f846(x99781))),f332(f332(f241(f846(x99781),f846(x99781)),x99784),x99785)),f147(x99781,x99782)))+~P1(f332(f332(f334(f852(x99781,x99781)),x99783),f332(f158(f852(x99781,x99781)),f332(f332(f167(x99781,x99781),x99784),x99785))))+P1(f332(f332(f251(x99781,x99781,a839),f332(f332(f9(x99781,f853(f852(x99781,x99781),a839),f853(x99781,a839)),f332(f332(f10(f853(x99781,f853(f853(f852(x99781,x99781),a839),a839)),f853(f853(f852(x99781,x99781),a839),f853(x99781,a839)),x99781),f9(x99781,f853(f852(x99781,x99781),a839),a839)),f332(f332(f10(f853(x99781,f852(x99781,x99781)),f853(x99781,f853(f853(f852(x99781,x99781),a839),a839)),x99781),f332(f10(f852(x99781,x99781),f853(f853(f852(x99781,x99781),a839),a839),x99781),f334(f852(x99781,x99781)))),f241(x99781,x99781)))),x99782)),x99783))
% 52.62/52.42 [9442]~P1(f332(f332(f232(a845),x94423),x94422))+~P1(f332(f332(f233(a845),f332(f332(f82(a845),f332(f332(f83(a845),x94423),x94424)),x94421)),f332(f332(f82(a845),f332(f332(f83(a845),x94422),x94424)),x94425)))+P1(f332(f332(f233(a845),x94421),f332(f332(f82(a845),f332(f332(f83(a845),f332(f332(f3(a845),x94422),x94423)),x94424)),x94425)))
% 52.62/52.42 [9443]~P1(f332(f332(f232(a845),x94433),x94432))+~P1(f332(f332(f232(a845),f332(f332(f82(a845),f332(f332(f83(a845),x94433),x94434)),x94431)),f332(f332(f82(a845),f332(f332(f83(a845),x94432),x94434)),x94435)))+P1(f332(f332(f232(a845),x94431),f332(f332(f82(a845),f332(f332(f83(a845),f332(f332(f3(a845),x94432),x94433)),x94434)),x94435)))
% 52.62/52.42 [9463]~P1(f332(f332(f232(a845),x94631),x94634))+P1(f332(f332(f233(a845),f332(f332(f82(a845),f332(f332(f83(a845),x94631),x94632)),x94633)),f332(f332(f82(a845),f332(f332(f83(a845),x94634),x94632)),x94635)))+~P1(f332(f332(f233(a845),x94633),f332(f332(f82(a845),f332(f332(f83(a845),f332(f332(f3(a845),x94634),x94631)),x94632)),x94635)))
% 52.62/52.42 [9464]~P1(f332(f332(f232(a845),x94641),x94644))+P1(f332(f332(f232(a845),f332(f332(f82(a845),f332(f332(f83(a845),x94641),x94642)),x94643)),f332(f332(f82(a845),f332(f332(f83(a845),x94644),x94642)),x94645)))+~P1(f332(f332(f232(a845),x94643),f332(f332(f82(a845),f332(f332(f83(a845),f332(f332(f3(a845),x94644),x94641)),x94642)),x94645)))
% 52.62/52.42 [9570]~P1(f332(f332(f232(a845),x95702),x95701))+~P1(f332(f332(f233(a845),f332(f332(f82(a845),f332(f332(f83(a845),x95701),x95703)),x95704)),f332(f332(f82(a845),f332(f332(f83(a845),x95702),x95703)),x95705)))+P1(f332(f332(f233(a845),f332(f332(f82(a845),f332(f332(f83(a845),f332(f332(f3(a845),x95701),x95702)),x95703)),x95704)),x95705))
% 52.62/52.42 [9571]~P1(f332(f332(f232(a845),x95712),x95711))+~P1(f332(f332(f232(a845),f332(f332(f82(a845),f332(f332(f83(a845),x95711),x95713)),x95714)),f332(f332(f82(a845),f332(f332(f83(a845),x95712),x95713)),x95715)))+P1(f332(f332(f232(a845),f332(f332(f82(a845),f332(f332(f83(a845),f332(f332(f3(a845),x95711),x95712)),x95713)),x95714)),x95715))
% 52.62/52.42 [9612]~P1(f332(f332(f232(a845),x96124),x96121))+P1(f332(f332(f233(a845),f332(f332(f82(a845),f332(f332(f83(a845),x96121),x96122)),x96123)),f332(f332(f82(a845),f332(f332(f83(a845),x96124),x96122)),x96125)))+~P1(f332(f332(f233(a845),f332(f332(f82(a845),f332(f332(f83(a845),f332(f332(f3(a845),x96121),x96124)),x96122)),x96123)),x96125))
% 52.62/52.42 [9613]~P1(f332(f332(f232(a845),x96134),x96131))+P1(f332(f332(f232(a845),f332(f332(f82(a845),f332(f332(f83(a845),x96131),x96132)),x96133)),f332(f332(f82(a845),f332(f332(f83(a845),x96134),x96132)),x96135)))+~P1(f332(f332(f232(a845),f332(f332(f82(a845),f332(f332(f83(a845),f332(f332(f3(a845),x96131),x96134)),x96132)),x96133)),x96135))
% 52.62/52.42 [9837]~P18(x98371,x98372,x98375,x98373)+~P1(f332(f332(f334(f852(x98371,x98371)),x98374),x98375))+P1(f332(f332(f251(x98371,x98371,a839),f332(f332(f9(x98371,f853(x98371,x98372),f853(x98371,a839)),f332(f332(f10(f853(x98372,a839),f853(f853(x98371,x98372),f853(x98371,a839)),x98371),f10(x98372,a839,x98371)),f332(f332(f10(x98372,f853(x98372,a839),x98371),a329),x98373))),x98373)),x98374))
% 52.62/52.42 [7161]~P41(x71614,x71612,x71615,x71616)+P41(f33(x71611,x71613,x71614),x71612,x71615,x71616)+P1(f332(x71611,x71612))
% 52.62/52.42 [7162]~P41(x71624,x71622,x71625,x71626)+P41(f33(x71621,x71623,x71624),x71622,x71625,x71626)+P1(f332(x71621,x71622))
% 52.62/52.42 [7163]~P41(x71634,x71632,x71635,x71636)+P41(f33(x71631,x71633,x71634),x71632,x71635,x71636)+P1(f332(x71631,x71632))
% 52.62/52.42 [7241]~P41(x72412,x72414,x72415,x72416)+P41(f33(x72411,x72412,x72413),x72414,x72415,x72416)+~P1(f332(x72411,x72414))
% 52.62/52.42 [7242]~P41(x72422,x72424,x72425,x72426)+P41(f33(x72421,x72422,x72423),x72424,x72425,x72426)+~P1(f332(x72421,x72424))
% 52.62/52.42 [7243]~P41(x72432,x72434,x72435,x72436)+P41(f33(x72431,x72432,x72433),x72434,x72435,x72436)+~P1(f332(x72431,x72434))
% 52.62/52.42 [7332]P41(x73323,x73322,x73324,x73325)+~P41(f33(x73321,x73326,x73323),x73322,x73324,x73325)+P1(f332(x73321,x73322))
% 52.62/52.42 [7333]P41(x73333,x73332,x73334,x73335)+~P41(f33(x73331,x73336,x73333),x73332,x73334,x73335)+P1(f332(x73331,x73332))
% 52.62/52.42 [7334]P41(x73343,x73342,x73344,x73345)+~P41(f33(x73341,x73346,x73343),x73342,x73344,x73345)+P1(f332(x73341,x73342))
% 52.62/52.42 [7365]P41(x73651,x73652,x73653,x73654)+~P41(f33(x73655,x73651,x73656),x73652,x73653,x73654)+~P1(f332(x73655,x73652))
% 52.62/52.42 [7366]P41(x73661,x73662,x73663,x73664)+~P41(f33(x73665,x73661,x73666),x73662,x73663,x73664)+~P1(f332(x73665,x73662))
% 52.62/52.42 [7367]P41(x73671,x73672,x73673,x73674)+~P41(f33(x73675,x73671,x73676),x73672,x73673,x73674)+~P1(f332(x73675,x73672))
% 52.62/52.42 [7738]~P41(x77381,x77383,x77384,x77386)+~P41(x77382,x77386,x77384,x77385)+P41(f36(x77381,x77382),x77383,x77384,x77385)
% 52.62/52.42 [7739]~P41(x77391,x77393,x77394,x77396)+~P41(x77392,x77396,x77394,x77395)+P41(f36(x77391,x77392),x77393,x77394,x77395)
% 52.62/52.42 [7740]P41(x77401,x77402,x77403,x77404)+P41(x77405,x77402,x77403,x77404)+~P41(f33(x77406,x77401,x77405),x77402,x77403,x77404)
% 52.62/52.42 [7741]P41(x77411,x77412,x77413,x77414)+P41(x77415,x77412,x77413,x77414)+~P41(f33(x77416,x77411,x77415),x77412,x77413,x77414)
% 52.62/52.42 [7742]P41(x77421,x77422,x77423,x77424)+P41(x77425,x77422,x77423,x77424)+~P41(f33(x77426,x77421,x77425),x77422,x77423,x77424)
% 52.62/52.42 [6714]~E(f332(x67144,x67145),f183(x67142))+E(f332(f170(x67141,x67142,x67143,x67144),x67145),f332(f227(x67142),x67146))+~E(f332(x67143,x67145),f332(f227(x67142),x67146))
% 52.62/52.42 [6820]~E(f332(x68203,x68206),f183(x68201))+E(f332(f229(f849(x68201),x68202,f183(x68201),x68203),f332(x68204,x68205)),f183(x68201))+~E(f332(x68204,x68205),f332(f227(x68202),x68206))
% 52.62/52.42 [7424]E(f332(x74241,x74242),f183(x74243))+~E(f332(f170(x74245,x74243,x74246,x74241),x74242),f332(f227(x74243),x74244))+E(f332(x74241,x74242),f332(f227(x74243),x74244))
% 52.62/52.42 [7425]E(f332(x74251,x74252),f183(x74253))+~E(f332(f170(x74255,x74253,x74256,x74251),x74252),f332(f227(x74253),x74254))+E(f332(x74251,x74252),f332(f227(x74253),x74254))
% 52.62/52.42 [7462]~E(f332(f170(x74626,x74623,x74625,x74621),x74622),f332(f227(x74623),x74624))+E(f332(x74621,x74622),f332(f227(x74623),x74624))+E(f332(x74625,x74622),f332(f227(x74623),x74624))
% 52.62/52.42 [7463]~E(f332(f170(x74636,x74633,x74635,x74631),x74632),f332(f227(x74633),x74634))+E(f332(x74631,x74632),f332(f227(x74633),x74634))+E(f332(x74635,x74632),f332(f227(x74633),x74634))
% 52.62/52.42 [8354]~P25(x83546,x83541,x83542,x83544)+E(f332(f75(x83541,x83541,x83541,f332(x83542,x83543)),f332(x83544,x83545)),f332(f75(x83541,x83541,x83541,f332(x83544,x83545)),f332(x83542,x83543)))+~P1(f332(f64(x83546),x83545))
% 52.62/52.42 [8750]~P31(x87501,x87503,x87505,x87506)+~P31(x87503,x87502,x87504,f332(f303(x87501,x87503,x87505),x87506))+P31(x87501,x87502,f332(f75(x87503,x87502,x87501,x87504),x87505),x87506)
% 52.62/52.42 [8751]~P31(x87511,x87513,x87515,x87516)+~P31(x87513,x87512,x87514,f332(f303(x87511,x87513,x87515),x87516))+P31(x87511,x87512,f332(f75(x87513,x87512,x87511,x87514),x87515),x87516)
% 52.62/52.42 [8910]~P31(x89104,x89101,x89105,x89106)+~P31(x89104,x89102,f332(f75(x89101,x89102,x89104,x89103),x89105),x89106)+P31(x89101,x89102,x89103,f332(f303(x89104,x89101,x89105),x89106))
% 52.62/52.42 [9255]~P1(f332(f332(x92554,x92552),x92556))+~P1(f332(f332(x92553,x92555),x92552))+P1(f332(f332(f334(x92551),x92552),f289(x92551,x92553,x92554,x92555,x92556)))
% 52.62/52.42 [9256]~P1(f332(f332(x92563,x92562),x92566))+~P1(f332(f332(x92564,x92565),x92562))+P1(f332(f332(f334(x92561),x92562),f292(x92561,x92563,x92564,x92565,x92566)))
% 52.62/52.42 [9365]E(x93651,x93652)+E(x93653,x93654)+~P1(f332(f332(f334(f852(f846(x93655),f846(x93655))),f332(f332(f241(f846(x93655),f846(x93655)),f332(f332(f140(x93655),x93653),x93651)),f332(f332(f140(x93655),x93654),x93652))),f146(x93655,x93656)))
% 52.62/52.42 [9374]~E(x93742,x93744)+P1(f332(f332(f334(f852(f846(x93741),f846(x93741))),f332(f332(f241(f846(x93741),f846(x93741)),f332(f332(f140(x93741),x93742),x93743)),f332(f332(f140(x93741),x93744),x93745))),f135(x93741,x93746)))+~P1(f332(f332(f334(f852(f846(x93741),f846(x93741))),f332(f332(f241(f846(x93741),f846(x93741)),x93743),x93745)),f135(x93741,x93746)))
% 52.62/52.42 [9375]~E(x93752,x93754)+P1(f332(f332(f334(f852(f846(x93751),f846(x93751))),f332(f332(f241(f846(x93751),f846(x93751)),f332(f332(f140(x93751),x93752),x93753)),f332(f332(f140(x93751),x93754),x93755))),f137(x93751,x93756)))+~P1(f332(f332(f334(f852(f846(x93751),f846(x93751))),f332(f332(f241(f846(x93751),f846(x93751)),x93753),x93755)),f137(x93751,x93756)))
% 52.62/52.42 [9376]~E(x93762,x93764)+P1(f332(f332(f334(f852(f846(x93761),f846(x93761))),f332(f332(f241(f846(x93761),f846(x93761)),f332(f332(f140(x93761),x93762),x93763)),f332(f332(f140(x93761),x93764),x93765))),f146(x93761,x93766)))+~P1(f332(f332(f334(f852(f846(x93761),f846(x93761))),f332(f332(f241(f846(x93761),f846(x93761)),x93763),x93765)),f146(x93761,x93766)))
% 52.62/52.42 [9377]~E(x93772,x93774)+P1(f332(f332(f334(f852(f846(x93771),f846(x93771))),f332(f332(f241(f846(x93771),f846(x93771)),f332(f332(f125(x93771),x93772),x93773)),f332(f332(f125(x93771),x93774),x93775))),f146(x93771,x93776)))+~P1(f332(f332(f334(f852(f846(x93771),f846(x93771))),f332(f332(f241(f846(x93771),f846(x93771)),x93773),x93775)),f146(x93771,x93776)))
% 52.62/52.42 [9378]~E(x93783,x93785)+P1(f332(f332(f334(f852(f846(x93781),f846(x93781))),f332(f332(f241(f846(x93781),f846(x93781)),f332(f332(f125(x93781),x93782),x93783)),f332(f332(f125(x93781),x93784),x93785))),f146(x93781,x93786)))+~P1(f332(f332(f334(f852(f846(x93781),f846(x93781))),f332(f332(f241(f846(x93781),f846(x93781)),x93782),x93784)),f146(x93781,x93786)))
% 52.62/52.42 [9431]E(x94311,x94312)+P1(f332(f332(f334(f852(f846(x94313),f846(x94313))),f332(f332(f241(f846(x94313),f846(x94313)),x94311),x94312)),f146(x94313,x94314)))+~P1(f332(f332(f334(f852(f846(x94313),f846(x94313))),f332(f332(f241(f846(x94313),f846(x94313)),f332(f332(f140(x94313),x94315),x94311)),f332(f332(f140(x94313),x94316),x94312))),f146(x94313,x94314)))
% 52.62/52.42 [9572]~E(x95723,x95725)+P1(f332(f332(f334(f852(f846(x95721),f846(x95721))),f332(f332(f241(f846(x95721),f846(x95721)),f332(f332(f125(x95721),x95722),f332(f332(f140(x95721),x95723),f115(x95721)))),f332(f332(f125(x95721),x95724),f332(f332(f140(x95721),x95725),f115(x95721))))),f146(x95721,x95726)))+~P1(f332(f332(f334(f852(f846(x95721),f846(x95721))),f332(f332(f241(f846(x95721),f846(x95721)),x95722),x95724)),f146(x95721,x95726)))
% 52.62/52.42 [9583]E(f332(x95831,x95832),f183(x95833))+~E(f332(f229(f849(x95836),x95833,f183(x95836),x95834),f332(x95831,x95832)),f183(x95836))+E(f332(x95834,f706(x95832,x95831,x95834,x95835,x95836,x95833)),f183(x95836))
% 52.62/52.42 [9584]E(f332(x95841,x95842),f183(x95843))+~E(f332(f229(f849(x95846),x95843,f183(x95846),x95844),f332(x95841,x95842)),f183(x95846))+E(f332(f227(x95843),f706(x95842,x95841,x95844,x95845,x95846,x95843)),f332(x95841,x95842))
% 52.62/52.42 [9616]E(x96161,x96162)+E(x96163,x96164)+~P1(f332(f332(f334(f852(f846(x96165),f846(x96165))),f332(f332(f241(f846(x96165),f846(x96165)),f332(f332(f125(x96165),x96163),f332(f332(f140(x96165),x96161),f115(x96165)))),f332(f332(f125(x96165),x96164),f332(f332(f140(x96165),x96162),f115(x96165))))),f146(x96165,x96166)))
% 52.62/52.42 [9638]E(x96381,x96382)+~P1(f332(f332(f334(f852(f846(x96383),f846(x96383))),f332(f332(f241(f846(x96383),f846(x96383)),f332(f332(f125(x96383),x96381),f332(f332(f140(x96383),x96385),f115(x96383)))),f332(f332(f125(x96383),x96382),f332(f332(f140(x96383),x96386),f115(x96383))))),f146(x96383,x96384)))+P1(f332(f332(f334(f852(f846(x96383),f846(x96383))),f332(f332(f241(f846(x96383),f846(x96383)),x96381),x96382)),f146(x96383,x96384)))
% 52.62/52.42 [9667]~P1(f332(f332(f334(f852(f853(x96671,a839),f853(x96671,a839))),f332(f332(f241(f853(x96671,a839),f853(x96671,a839)),x96672),x96674)),f325(x96671,x96676)))+~P1(f332(f332(f334(f852(f853(x96671,a839),f853(x96671,a839))),f332(f332(f241(f853(x96671,a839),f853(x96671,a839)),x96673),x96675)),f325(x96671,x96676)))+P1(f332(f332(f334(f852(f853(x96671,a839),f853(x96671,a839))),f332(f332(f241(f853(x96671,a839),f853(x96671,a839)),f332(f332(f103(f853(x96671,a839)),x96672),x96673)),f332(f332(f103(f853(x96671,a839)),x96674),x96675))),f325(x96671,x96676)))
% 52.62/52.42 [5133]~E(f332(x51333,x51336),x51335)+~E(x51334,f332(f227(x51331),x51336))+E(f332(f332(f196(x51331,x51332),x51333),x51334),f332(f227(x51332),x51335))
% 52.62/52.42 [5532]~E(f332(f332(f125(x55321),x55326),x55323),x55325)+E(f332(f332(f125(x55321),x55322),x55323),f332(f332(f140(x55321),x55324),x55325))+~E(x55322,f332(f332(f140(x55321),x55324),x55326))
% 52.62/52.42 [5533]~E(f332(f332(f125(x55331),x55336),x55333),x55335)+E(f332(f332(f125(x55331),x55332),x55333),f332(f332(f125(x55331),x55334),x55335))+~E(x55332,f332(f332(f125(x55331),x55334),x55336))
% 52.62/52.42 [5534]E(f332(f332(f125(x55341),x55342),x55343),f332(f332(f140(x55341),x55344),x55345))+~E(f332(f332(f140(x55341),x55344),x55346),x55342)+~E(x55345,f332(f332(f125(x55341),x55346),x55343))
% 52.62/52.42 [5535]E(f332(f332(f125(x55351),x55352),x55353),f332(f332(f140(x55351),x55354),x55355))+~E(f332(f332(f140(x55351),x55354),x55356),x55352)+~E(x55355,f332(f332(f125(x55351),x55356),x55353))
% 52.62/52.42 [5536]~E(f332(f332(f125(x55361),x55362),x55366),x55364)+E(f332(f332(f125(x55361),x55362),x55363),f332(f332(f125(x55361),x55364),x55365))+~E(x55363,f332(f332(f125(x55361),x55366),x55365))
% 52.62/52.42 [5537]~E(f332(f332(f125(x55371),x55372),x55376),x55374)+E(f332(f332(f125(x55371),x55372),x55373),f332(f332(f125(x55371),x55374),x55375))+~E(x55373,f332(f332(f125(x55371),x55376),x55375))
% 52.62/52.42 [6707]E(f332(x67071,x67072),f332(x67073,x67072))+~E(f332(f332(f143(x67074,x67075),x67071),x67076),f332(f332(f143(x67074,x67075),x67073),x67076))+~P1(f332(f332(f334(x67074),x67072),f332(f158(x67074),x67076)))
% 52.62/52.42 [7099]~P25(x70994,x70995,x70996,x70991)+E(f332(f332(x70991,x70992),x70993),f332(f332(f67(x70994,x70995,x70996),x70993),x70992))+~P1(f332(f64(x70994),x70992))
% 52.62/52.42 [7166]~E(x71662,f332(x71664,x71666))+~P1(f332(f332(f334(x71663),x71666),x71665))+P1(f332(f332(f334(x71661),x71662),f332(f303(x71663,x71661,x71664),x71665)))
% 52.62/52.42 [7167]~E(x71672,f332(x71674,x71676))+~P1(f332(f332(f334(x71673),x71676),x71675))+P1(f332(f332(f334(x71671),x71672),f332(f303(x71673,x71671,x71674),x71675)))
% 52.62/52.42 [7168]~E(x71682,f332(x71684,x71686))+~P1(f332(f332(f334(x71683),x71686),x71685))+P1(f332(f332(f334(x71681),x71682),f332(f303(x71683,x71681,x71684),x71685)))
% 52.62/52.42 [7169]~E(f332(x71694,x71692),x71696)+~P1(f332(f332(f334(x71693),x71696),x71695))+P1(f332(f332(f334(x71691),x71692),f332(f305(x71691,x71693,x71694),x71695)))
% 52.62/52.42 [7644]~P36(x76441,x76442,x76444,x76446)+P36(x76441,x76442,f332(f332(f140(x76441),x76443),x76444),f332(f332(f140(x76441),x76445),x76446))+~P1(f332(f332(x76442,x76443),x76445))
% 52.62/52.42 [7645]~P36(x76451,x76452,x76454,x76456)+P36(x76451,x76452,f332(f332(f140(x76451),x76453),x76454),f332(f332(f140(x76451),x76455),x76456))+~P1(f332(f332(x76452,x76453),x76455))
% 52.62/52.42 [8634]~P57(x86344,x86345,x86341,x86342,x86346)+E(f332(x86341,f332(x86342,x86343)),x86343)+~P1(f332(f332(f334(x86345),x86343),x86346))
% 52.62/52.42 [9367]E(x93671,x93672)+E(f332(f181(f846(x93673)),x93674),f332(f181(f846(x93673)),x93675))+~P1(f332(f332(f334(f852(f846(x93673),f846(x93673))),f332(f332(f241(f846(x93673),f846(x93673)),f332(f332(f140(x93673),x93671),x93674)),f332(f332(f140(x93673),x93672),x93675))),f135(x93673,x93676)))
% 52.62/52.42 [9428]~P22(x94281,x94282,x94283)+E(f332(f332(f67(x94281,x94282,x94283),x94284),x94285),x94286)+~P1(f332(f69(x94281,x94282,x94283,x94284,x94285),x94286))
% 52.62/52.42 [9434]E(f332(f181(f846(x94341)),x94342),f332(f181(f846(x94341)),x94343))+P1(f332(f332(f334(f852(f846(x94341),f846(x94341))),f332(f332(f241(f846(x94341),f846(x94341)),x94342),x94343)),f135(x94341,x94344)))+~P1(f332(f332(f334(f852(f846(x94341),f846(x94341))),f332(f332(f241(f846(x94341),f846(x94341)),f332(f332(f140(x94341),x94345),x94342)),f332(f332(f140(x94341),x94346),x94343))),f135(x94341,x94344)))
% 52.62/52.42 [9455]~P1(f332(f332(f334(f852(x94551,x94551)),f332(f332(f241(x94551,x94551),x94552),x94554)),f300(x94551,x94556)))+P1(f332(f332(f334(f852(f846(x94551),f846(x94551))),f332(f332(f241(f846(x94551),f846(x94551)),f332(f332(f140(x94551),x94552),x94553)),f332(f332(f140(x94551),x94554),x94555))),f300(f846(x94551),f146(x94551,x94556))))+~P1(f332(f332(f334(f852(f846(x94551),f846(x94551))),f332(f332(f241(f846(x94551),f846(x94551)),x94553),x94555)),f300(f846(x94551),f146(x94551,x94556))))
% 52.62/52.42 [9929]~P4(x99292)+E(f332(f332(f8(x99291,x99292),f332(f332(f10(f853(x99293,a839),x99292,x99291),f332(f8(x99293,x99292),x99294)),f332(f332(f10(f853(x99293,a839),f853(x99293,a839),x99291),f256(x99293)),f332(f332(f10(f853(x99293,a839),f853(x99293,a839),x99291),f332(f20(x99293,a839,a839),f332(f332(f10(a839,f853(a839,a839),x99293),a330),f332(f332(f9(x99293,f853(x99293,a839),a839),f334(x99293)),x99295)))),f332(f9(x99293,x99291,a839),f332(f332(f10(x99291,f853(x99291,a839),x99293),a329),x99296)))))),f332(f303(x99293,x99291,x99296),x99295)),f332(f332(f8(x99293,x99292),x99294),x99295))+~P1(f332(f64(x99293),x99295))
% 52.62/52.42 [6767]~P100(x67673)+P1(f332(x67672,x67675))+E(f332(f126(x67671,x67672),f332(f332(f138(x67671,x67673,x67674),x67675),x67676)),f332(f126(x67671,x67672),x67676))
% 52.62/52.42 [6769]P1(f332(x67691,x67692))+~E(f155(x67693,x67691,x67694),f332(f332(f241(f846(x67693),f846(x67693)),x67695),x67696))+~P1(f332(f332(f334(x67693),x67692),f332(f158(x67693),x67695)))
% 52.62/52.42 [6817]~P1(f332(x68172,x68176))+~E(f155(x68171,x68172,x68173),f332(f332(f241(f846(x68171),f846(x68171)),x68174),x68175))+~P1(f332(f332(f334(x68171),x68176),f332(f158(x68171),x68175)))
% 52.62/52.42 [7508]~P21(x75081,x75082,x75083)+~P1(f332(f64(x75081),x75086))+E(f332(f332(f67(x75081,x75082,x75083),x75084),f332(f332(f302(x75081),x75085),x75086)),f332(f332(f67(x75081,x75082,x75083),f332(f332(x75083,x75085),x75084)),x75086))
% 52.62/52.42 [7560]~P100(x75602)+~P1(f332(f332(f232(x75602),f332(x75603,x75604)),f332(x75603,x75605)))+E(f332(f332(f138(x75601,x75602,x75603),x75604),f332(f332(f140(x75601),x75605),x75606)),f332(f332(f140(x75601),x75604),f332(f332(f140(x75601),x75605),x75606)))
% 52.62/52.42 [7676]E(x76761,x76762)+~E(f332(f332(f248(x76763,x76764),x76761),f332(f18(f853(x76764,a839),x76763),x76765)),f332(f332(f248(x76763,x76764),x76762),f332(f18(f853(x76764,a839),x76763),x76765)))+~P1(f332(f332(f334(x76764),x76766),x76765))
% 52.62/52.42 [7744]~P21(x77441,x77442,x77443)+~P1(f332(f64(x77441),x77446))+E(f332(f332(f67(x77441,x77442,x77443),x77444),f332(f332(f302(x77441),x77445),x77446)),f332(f332(x77443,x77445),f332(f332(f67(x77441,x77442,x77443),x77444),x77446)))
% 52.62/52.42 [7860]~P22(x78601,x78602,x78603)+~P1(f332(f64(x78601),x78606))+E(f332(f332(f67(x78601,x78602,x78603),f332(f332(x78603,x78604),x78605)),x78606),f332(f332(x78603,x78604),f332(f332(f67(x78601,x78602,x78603),x78605),x78606)))
% 52.62/52.42 [7928]~P26(x79282,x79285,x79286,x79281)+~P1(f332(f64(x79282),x79284))+E(f332(x79281,f332(f332(f302(x79282),x79283),x79284)),f332(f75(x79285,x79285,x79285,f332(x79281,x79284)),f332(x79286,x79283)))
% 52.62/52.42 [7966]~P100(x79662)+P1(f332(f332(f232(x79662),f332(x79663,x79664)),f332(x79663,x79665)))+E(f332(f332(f138(x79661,x79662,x79663),x79664),f332(f332(f140(x79661),x79665),x79666)),f332(f332(f140(x79661),x79665),f332(f332(f138(x79661,x79662,x79663),x79664),x79666)))
% 52.62/52.42 [8099]~E(f332(f181(f846(x80991)),x80995),f332(f181(f846(x80992)),x80996))+~E(f332(f181(f846(x80991)),x80993),f332(f181(f846(x80992)),x80994))+E(f332(f332(f125(f852(x80991,x80992)),f332(f332(f167(x80991,x80992),x80993),x80994)),f332(f332(f167(x80991,x80992),x80995),x80996)),f332(f332(f167(x80991,x80992),f332(f332(f125(x80991),x80993),x80995)),f332(f332(f125(x80992),x80994),x80996)))
% 52.62/52.42 [8208]~E(x82082,f332(f303(x82083,x82081,x82084),x82086))+P1(f332(f332(f232(f853(x82081,a839)),x82082),f332(f303(x82083,x82081,x82084),x82085)))+~P1(f332(f332(f232(f853(x82083,a839)),x82086),x82085))
% 52.62/52.42 [8310]~P100(x83105)+E(f332(x83101,x83102),f332(x83101,x83103))+E(f332(f332(f138(x83104,x83105,x83101),x83102),f332(f332(f138(x83104,x83105,x83101),x83103),x83106)),f332(f332(f138(x83104,x83105,x83101),x83103),f332(f332(f138(x83104,x83105,x83101),x83102),x83106)))
% 52.62/52.42 [8347]~P31(x83473,x83471,x83474,x83475)+P31(x83473,x83471,f332(f332(f332(f74(x83473,x83471),x83474),x83476),x83472),x83475)+P1(f332(f332(f334(x83471),x83472),f332(f303(x83473,x83471,x83474),x83475)))
% 52.62/52.42 [8493]~P1(f332(f332(f334(x84932),x84934),f332(x84936,x84933)))+~P1(f332(f332(f334(x84931),x84933),x84935))+P1(f332(f332(f334(f852(x84931,x84932)),f332(f332(f241(x84931,x84932),x84933),x84934)),f332(f332(f248(x84931,x84932),x84935),x84936)))
% 52.62/52.42 [8494]~P1(f332(f332(f334(x84942),x84944),f332(x84946,x84943)))+~P1(f332(f332(f334(x84941),x84943),x84945))+P1(f332(f332(f334(f852(x84941,x84942)),f332(f332(f241(x84941,x84942),x84943),x84944)),f332(f332(f248(x84941,x84942),x84945),x84946)))
% 52.62/52.42 [8903]~P4(x89032)+~P31(x89034,x89031,x89035,x89036)+E(f332(f332(f8(x89031,x89032),x89033),f332(f303(x89034,x89031,x89035),x89036)),f332(f332(f8(x89034,x89032),f332(f75(x89031,x89032,x89034,x89033),x89035)),x89036))
% 52.62/52.42 [8904]~P70(x89042)+~P31(x89044,x89041,x89045,x89046)+E(f332(f332(f11(x89041,x89042),x89043),f332(f303(x89044,x89041,x89045),x89046)),f332(f332(f11(x89044,x89042),f332(f75(x89041,x89042,x89044,x89043),x89045)),x89046))
% 52.62/52.42 [9143]~P25(x91433,x91431,x91436,x91432)+~P1(f332(f64(x91433),x91434))+E(f332(f75(x91431,x91431,x91431,f332(x91432,f332(f332(f3(f853(x91433,a839)),x91434),f332(f332(f302(x91433),x91435),f180(f853(x91433,a839)))))),f332(x91436,x91435)),f332(x91432,f332(f332(f302(x91433),x91435),x91434)))
% 52.62/52.42 [9696]~E(f332(f303(x96962,x96964,x96966),f239(f853(x96962,a839))),f239(f853(x96964,a839)))+~E(f332(f303(x96961,x96963,x96965),f239(f853(x96961,a839))),f239(f853(x96963,a839)))+E(f332(f303(f852(x96961,x96962),f852(x96963,x96964),f252(x96961,x96963,x96962,x96964,x96965,x96966)),f239(f853(f852(x96961,x96962),a839))),f239(f853(f852(x96963,x96964),a839)))
% 52.62/52.42 [9759]~P31(x97593,x97594,x97595,f332(x97596,f690(x97596,x97595,x97594,x97593,x97592,x97591)))+P31(x97593,x97594,x97595,f332(f332(f48(x97592,f853(x97593,a839)),x97591),x97596))+E(x97591,f180(f853(x97592,a839)))
% 52.62/52.42 [9816]P31(x98166,x98165,x98164,f332(f332(f48(x98162,f853(x98166,a839)),x98161),x98163))+E(x98161,f180(f853(x98162,a839)))+P1(f332(f332(f334(x98162),f690(x98163,x98164,x98165,x98166,x98162,x98161)),x98161))
% 52.62/52.42 [9823]P1(f332(f332(f334(x98231),f621(x98232,x98233,x98234,x98235,x98236,x98231)),x98236))+P1(f332(f332(f232(f853(f852(x98231,x98234),a839)),f332(f332(f248(x98231,x98234),x98236),x98233)),f332(f332(f248(x98231,x98234),x98235),x98232)))+~P1(f332(f332(f232(f853(x98231,a839)),x98236),x98235))
% 52.62/52.42 [9866]P30(x98666,x98665,f332(f332(f302(f844(x98666)),f332(f332(f332(f93(x98666),x98664),x98663),x98662)),f180(f853(f844(x98666),a839))))+~P30(x98666,x98665,f332(f332(f302(f844(x98666)),f332(f332(f332(f93(x98666),x98664),x98663),x98661)),f180(f853(f844(x98666),a839))))+P1(f332(f332(x98661,f541(x98662,x98661,x98663,x98664,x98665,x98666)),f542(x98662,x98661,x98663,x98664,x98665,x98666)))
% 52.62/52.42 [9867]P30(x98676,x98675,f332(f332(f302(f844(x98676)),f332(f332(f332(f93(x98676),x98671),x98673),x98672)),f180(f853(f844(x98676),a839))))+~P30(x98676,x98675,f332(f332(f302(f844(x98676)),f332(f332(f332(f93(x98676),x98674),x98673),x98672)),f180(f853(f844(x98676),a839))))+P1(f332(f332(x98671,f543(x98671,x98672,x98673,x98674,x98675,x98676)),f544(x98671,x98672,x98673,x98674,x98675,x98676)))
% 52.62/52.42 [9904]~P30(x99041,x99042,f332(f332(f302(f844(x99041)),f332(f332(f332(f93(x99041),x99043),x99044),x99046)),f180(f853(f844(x99041),a839))))+P30(x99041,x99042,f332(f332(f302(f844(x99041)),f332(f332(f332(f93(x99041),x99043),x99044),x99045)),f180(f853(f844(x99041),a839))))+~P1(f332(f332(x99045,f541(x99045,x99046,x99044,x99043,x99042,x99041)),f542(x99045,x99046,x99044,x99043,x99042,x99041)))
% 52.62/52.42 [9905]~P30(x99051,x99052,f332(f332(f302(f844(x99051)),f332(f332(f332(f93(x99051),x99056),x99054),x99055)),f180(f853(f844(x99051),a839))))+P30(x99051,x99052,f332(f332(f302(f844(x99051)),f332(f332(f332(f93(x99051),x99053),x99054),x99055)),f180(f853(f844(x99051),a839))))+~P1(f332(f332(x99056,f543(x99053,x99055,x99054,x99056,x99052,x99051)),f544(x99053,x99055,x99054,x99056,x99052,x99051)))
% 52.62/52.42 [9946]~P1(f332(f332(f232(f853(x99462,a839)),f332(x99464,f621(x99466,x99464,x99462,x99465,x99463,x99461))),f332(x99466,f621(x99466,x99464,x99462,x99465,x99463,x99461))))+~P1(f332(f332(f232(f853(x99461,a839)),x99463),x99465))+P1(f332(f332(f232(f853(f852(x99461,x99462),a839)),f332(f332(f248(x99461,x99462),x99463),x99464)),f332(f332(f248(x99461,x99462),x99465),x99466)))
% 52.62/52.42 [7693]~P1(f332(x76931,x76935))+~P1(f332(x76936,x76934))+P1(f332(x76931,f332(f250(x76932,x76933),f332(f332(f241(x76932,x76933),x76934),x76935))))
% 52.62/52.42 [7694]~P1(f332(x76941,x76944))+~P1(f332(x76946,x76945))+P1(f332(x76941,f332(f240(x76942,x76943),f332(f332(f241(x76942,x76943),x76944),x76945))))
% 52.62/52.42 [7748]~P1(f332(f332(x77484,x77486),x77485))+~P1(f332(f332(f334(x77481),x77486),x77483))+P1(f332(f332(f332(f47(x77481,f853(x77482,a839)),x77483),x77484),x77485))
% 52.62/52.42 [7749]~P1(f332(f332(x77494,x77496),x77495))+~P1(f332(f332(f334(x77491),x77496),x77493))+P1(f332(f332(f332(f47(x77491,f853(x77492,a839)),x77493),x77494),x77495))
% 52.62/52.42 [7782]~E(f332(f181(f846(x77821)),x77823),f332(f181(f846(x77824)),x77825))+~E(f332(f166(x77821,x77824,f332(f332(f167(x77821,x77824),x77823),x77825)),x77822),f332(f227(x77824),x77826))+P1(f332(f332(f334(x77821),x77822),f332(f158(x77821),x77823)))
% 52.62/52.42 [8051]~P1(f332(f332(f334(x80511),x80512),f332(x80515,x80516)))+~P1(f332(f332(f334(x80513),x80516),x80514))+P1(f332(f332(f334(x80511),x80512),f332(f332(f47(x80513,f853(x80511,a839)),x80514),x80515)))
% 52.62/52.42 [8052]~P1(f332(f332(f334(x80521),x80522),f332(x80525,x80526)))+~P1(f332(f332(f334(x80523),x80526),x80524))+P1(f332(f332(f334(x80521),x80522),f332(f332(f47(x80523,f853(x80521,a839)),x80524),x80525)))
% 52.62/52.42 [8091]P1(f332(f332(x80911,x80912),x80913))+~P1(f332(f332(x80914,x80912),x80913))+~P1(f332(f332(f232(f853(x80915,f853(x80916,a839))),x80914),x80911))
% 52.62/52.42 [8092]P1(f332(f332(x80921,x80922),x80923))+~P1(f332(f332(x80924,x80922),x80923))+~P1(f332(f332(f232(f853(x80925,f853(x80926,a839))),x80924),x80921))
% 52.62/52.42 [8230]P1(f332(f332(x82301,x82302),x82303))+~P1(f332(f332(f334(x82304),x82302),x82305))+~P1(f332(f332(f332(f48(x82304,f853(x82306,a839)),x82305),x82301),x82303))
% 52.62/52.42 [8231]P1(f332(f332(x82311,x82312),x82313))+~P1(f332(f332(f334(x82314),x82312),x82315))+~P1(f332(f332(f332(f48(x82314,f853(x82316,a839)),x82315),x82311),x82313))
% 52.62/52.42 [8232]P1(f332(f332(x82321,x82322),x82323))+~P1(f332(f332(f334(x82324),x82322),x82325))+~P1(f332(f332(f332(f48(x82324,f853(x82326,a839)),x82325),x82321),x82323))
% 52.62/52.42 [8368]P1(f332(f332(f334(x83681),x83682),f332(x83683,x83684)))+~P1(f332(f332(f334(x83685),x83684),x83686))+~P1(f332(f332(f334(x83681),x83682),f332(f332(f48(x83685,f853(x83681,a839)),x83686),x83683)))
% 52.62/52.42 [8369]P1(f332(f332(f334(x83691),x83692),f332(x83693,x83694)))+~P1(f332(f332(f334(x83695),x83694),x83696))+~P1(f332(f332(f334(x83691),x83692),f332(f332(f48(x83695,f853(x83691,a839)),x83696),x83693)))
% 52.62/52.42 [8370]P1(f332(f332(f334(x83701),x83702),f332(x83703,x83704)))+~P1(f332(f332(f334(x83705),x83704),x83706))+~P1(f332(f332(f334(x83701),x83702),f332(f332(f48(x83705,f853(x83701,a839)),x83706),x83703)))
% 52.62/52.42 [8616]~P18(x86164,x86165,x86166,x86161)+E(f332(x86161,x86162),f332(x86161,x86163))+~P1(f332(f332(f334(f852(x86164,x86164)),f332(f332(f241(x86164,x86164),x86162),x86163)),x86166))
% 52.62/52.42 [8647]P1(f332(f332(f232(f853(x86471,a839)),x86472),f332(x86473,x86474)))+~P1(f332(f332(f334(x86475),x86474),x86476))+~P1(f332(f332(f232(f853(x86471,a839)),x86472),f332(f332(f48(x86475,f853(x86471,a839)),x86476),x86473)))
% 52.62/52.42 [8672]~P55(x86723,x86724,f332(f278(x86724,x86723),x86725))+E(x86721,f180(f853(x86722,a839)))+E(f332(f332(f48(x86722,f853(x86723,a839)),x86721),f332(f332(f10(f853(x86724,a839),f853(x86723,a839),x86722),f277(x86724,x86723,x86725)),x86726)),f332(f277(x86724,x86723,x86725),f332(f332(f48(x86722,f853(x86724,a839)),x86721),x86726)))
% 52.62/52.42 [8743]P1(f332(f332(f334(x87431),x87432),f332(f277(x87433,x87431,x87434),x87435)))+~P1(f332(f332(f334(x87433),x87436),x87435))+~P1(f332(f332(f334(f852(x87433,x87431)),f332(f332(f241(x87433,x87431),x87436),x87432)),x87434))
% 52.62/52.42 [8744]P1(f332(f332(f334(x87441),x87442),f332(f277(x87443,x87441,x87444),x87445)))+~P1(f332(f332(f334(x87443),x87446),x87445))+~P1(f332(f332(f334(f852(x87443,x87441)),f332(f332(f241(x87443,x87441),x87446),x87442)),x87444))
% 52.62/52.42 [9021]P1(f332(f332(f232(f853(x90211,a839)),f332(f277(x90212,x90211,x90213),x90214)),f332(f277(x90212,x90211,x90215),x90216)))+~P1(f332(f332(f232(f853(x90212,a839)),x90214),x90216))+~P1(f332(f332(f232(f853(f852(x90212,x90211),a839)),x90213),x90215))
% 52.62/52.42 [9177]~P1(f332(f332(f334(x91772),x91776),x91774))+~P1(f332(f332(f232(f853(x91771,a839)),x91773),x91775))+P1(f332(f332(f232(f853(f852(x91771,x91772),a839)),f332(f332(f248(x91771,x91772),x91773),f332(f18(f853(x91772,a839),x91771),x91774))),f332(f332(f248(x91771,x91772),x91775),f332(f18(f853(x91772,a839),x91771),x91774))))
% 52.62/52.42 [9325]~E(x93253,x93255)+P1(f332(f332(f334(f852(f846(x93251),f846(x93251))),f332(f332(f241(f846(x93251),f846(x93251)),f332(f332(f140(x93251),x93252),x93253)),f332(f332(f140(x93251),x93254),x93255))),f146(x93251,x93256)))+~P1(f332(f332(f334(f852(x93251,x93251)),f332(f332(f241(x93251,x93251),x93252),x93254)),x93256))
% 52.62/52.42 [9331]~E(f332(f181(f846(x93311)),x93313),f332(f181(f846(x93311)),x93315))+P1(f332(f332(f334(f852(f846(x93311),f846(x93311))),f332(f332(f241(f846(x93311),f846(x93311)),f332(f332(f140(x93311),x93312),x93313)),f332(f332(f140(x93311),x93314),x93315))),f135(x93311,x93316)))+~P1(f332(f332(f334(f852(x93311,x93311)),f332(f332(f241(x93311,x93311),x93312),x93314)),x93316))
% 52.62/52.42 [9359]P1(f332(f332(f334(f852(x93591,x93591)),f332(f332(f241(x93591,x93591),x93592),x93593)),f332(f332(f173(f852(x93591,x93591),a839),f332(a114,x93594)),x93595)))+~P1(f332(f332(f334(f852(x93591,x93591)),f332(f332(f241(x93591,x93591),x93596),x93593)),x93595))+~P1(f332(f332(f334(f852(x93591,x93591)),f332(f332(f241(x93591,x93591),x93592),x93596)),f332(f332(f173(f852(x93591,x93591),a839),x93594),x93595)))
% 52.62/52.42 [9360]P1(f332(f332(f334(f852(x93601,x93601)),f332(f332(f241(x93601,x93601),x93602),x93603)),f332(f332(f173(f852(x93601,x93601),a839),f332(a114,x93604)),x93605)))+~P1(f332(f332(f334(f852(x93601,x93601)),f332(f332(f241(x93601,x93601),x93602),x93606)),x93605))+~P1(f332(f332(f334(f852(x93601,x93601)),f332(f332(f241(x93601,x93601),x93606),x93603)),f332(f332(f173(f852(x93601,x93601),a839),x93604),x93605)))
% 52.62/52.42 [9363]~P1(f332(f332(f334(x93634),x93635),x93636))+P1(f332(f332(f232(f853(x93631,a839)),x93632),x93633))+~P1(f332(f332(f232(f853(f852(x93631,x93634),a839)),f332(f332(f248(x93631,x93634),x93632),f332(f18(f853(x93634,a839),x93631),x93636))),f332(f332(f248(x93631,x93634),x93633),f332(f18(f853(x93634,a839),x93631),x93636))))
% 52.62/52.42 [9403]E(x94031,x94032)+~P1(f332(f332(f334(f852(f846(x94033),f846(x94033))),f332(f332(f241(f846(x94033),f846(x94033)),f332(f332(f140(x94033),x94031),x94035)),f332(f332(f140(x94033),x94032),x94036))),f135(x94033,x94034)))+P1(f332(f332(f334(f852(x94033,x94033)),f332(f332(f241(x94033,x94033),x94031),x94032)),x94034))
% 52.62/52.42 [9404]E(x94041,x94042)+~P1(f332(f332(f334(f852(f846(x94043),f846(x94043))),f332(f332(f241(f846(x94043),f846(x94043)),f332(f332(f140(x94043),x94041),x94045)),f332(f332(f140(x94043),x94042),x94046))),f137(x94043,x94044)))+P1(f332(f332(f334(f852(x94043,x94043)),f332(f332(f241(x94043,x94043),x94041),x94042)),x94044))
% 52.62/52.42 [9405]E(x94051,x94052)+~P1(f332(f332(f334(f852(f846(x94053),f846(x94053))),f332(f332(f241(f846(x94053),f846(x94053)),f332(f332(f140(x94053),x94051),x94055)),f332(f332(f140(x94053),x94052),x94056))),f146(x94053,x94054)))+P1(f332(f332(f334(f852(x94053,x94053)),f332(f332(f241(x94053,x94053),x94051),x94052)),x94054))
% 52.62/52.42 [9441]P1(f332(f332(f334(f852(f846(x94411),f846(x94411))),f332(f332(f241(f846(x94411),f846(x94411)),f332(f332(f140(x94411),x94412),x94413)),f332(f332(f140(x94411),x94414),x94415))),f147(x94411,x94416)))+~P1(f332(f332(f334(f852(f846(x94411),f846(x94411))),f332(f332(f241(f846(x94411),f846(x94411)),x94413),x94415)),f147(x94411,x94416)))+~P1(f332(f332(f334(f852(x94411,x94411)),f332(f332(f241(x94411,x94411),x94412),x94414)),x94416))
% 52.62/52.42 [9461]P1(f332(x94611,x94612))+~P1(f332(x94611,f391(x94611,x94613,x94614,x94615,x94616)))+~P1(f332(f332(f334(x94616),x94612),f332(f332(f47(x94615,f853(x94616,a839)),x94614),x94613)))
% 52.62/52.42 [9466]~P1(f332(f332(f334(f852(f846(x94661),f846(x94661))),f332(f332(f241(f846(x94661),f846(x94661)),f332(f332(f140(x94661),x94662),x94665)),f332(f332(f140(x94661),x94663),x94666))),f135(x94661,x94664)))+P1(f332(f332(f334(f852(f846(x94661),f846(x94661))),f332(f332(f241(f846(x94661),f846(x94661)),x94665),x94666)),f135(x94661,x94664)))+P1(f332(f332(f334(f852(x94661,x94661)),f332(f332(f241(x94661,x94661),x94662),x94663)),x94664))
% 52.62/52.42 [9467]~P1(f332(f332(f334(f852(f846(x94671),f846(x94671))),f332(f332(f241(f846(x94671),f846(x94671)),f332(f332(f140(x94671),x94672),x94675)),f332(f332(f140(x94671),x94673),x94676))),f137(x94671,x94674)))+P1(f332(f332(f334(f852(f846(x94671),f846(x94671))),f332(f332(f241(f846(x94671),f846(x94671)),x94675),x94676)),f137(x94671,x94674)))+P1(f332(f332(f334(f852(x94671,x94671)),f332(f332(f241(x94671,x94671),x94672),x94673)),x94674))
% 52.62/52.42 [9468]~P1(f332(f332(f334(f852(f846(x94681),f846(x94681))),f332(f332(f241(f846(x94681),f846(x94681)),f332(f332(f140(x94681),x94682),x94685)),f332(f332(f140(x94681),x94683),x94686))),f146(x94681,x94684)))+P1(f332(f332(f334(f852(f846(x94681),f846(x94681))),f332(f332(f241(f846(x94681),f846(x94681)),x94685),x94686)),f146(x94681,x94684)))+P1(f332(f332(f334(f852(x94681,x94681)),f332(f332(f241(x94681,x94681),x94682),x94683)),x94684))
% 52.62/52.42 [9544]P1(f332(x95441,x95442))+P1(f332(f332(f334(x95443),f392(x95441,x95444,x95445,x95443,x95446)),x95445))+~P1(f332(f332(f334(x95446),x95442),f332(f332(f47(x95443,f853(x95446,a839)),x95445),x95444)))
% 52.62/52.42 [9550]~E(x95502,x95504)+P1(f332(f332(f334(f852(f846(x95501),f846(x95501))),f332(f332(f241(f846(x95501),f846(x95501)),f332(f332(f125(x95501),x95502),f332(f332(f140(x95501),x95503),f115(x95501)))),f332(f332(f125(x95501),x95504),f332(f332(f140(x95501),x95505),f115(x95501))))),f146(x95501,x95506)))+~P1(f332(f332(f334(f852(x95501,x95501)),f332(f332(f241(x95501,x95501),x95503),x95505)),x95506))
% 52.62/52.42 [9630]E(x96301,x96302)+~P1(f332(f332(f334(f852(f846(x96303),f846(x96303))),f332(f332(f241(f846(x96303),f846(x96303)),f332(f332(f125(x96303),x96305),f332(f332(f140(x96303),x96301),f115(x96303)))),f332(f332(f125(x96303),x96306),f332(f332(f140(x96303),x96302),f115(x96303))))),f146(x96303,x96304)))+P1(f332(f332(f334(f852(x96303,x96303)),f332(f332(f241(x96303,x96303),x96301),x96302)),x96304))
% 52.62/52.42 [9655]~P1(f332(f332(f334(f852(f846(x96551),f846(x96551))),f332(f332(f241(f846(x96551),f846(x96551)),f332(f332(f125(x96551),x96555),f332(f332(f140(x96551),x96552),f115(x96551)))),f332(f332(f125(x96551),x96556),f332(f332(f140(x96551),x96553),f115(x96551))))),f146(x96551,x96554)))+P1(f332(f332(f334(f852(f846(x96551),f846(x96551))),f332(f332(f241(f846(x96551),f846(x96551)),x96555),x96556)),f146(x96551,x96554)))+P1(f332(f332(f334(f852(x96551,x96551)),f332(f332(f241(x96551,x96551),x96552),x96553)),x96554))
% 52.62/52.42 [9668]P1(f332(x96681,x96682))+P1(f332(f332(f334(x96683),f391(x96681,x96684,x96685,x96686,x96683)),f332(x96684,f392(x96681,x96684,x96685,x96686,x96683))))+~P1(f332(f332(f334(x96683),x96682),f332(f332(f47(x96686,f853(x96683,a839)),x96685),x96684)))
% 52.62/52.42 [8757]~P22(x87573,x87574,x87571)+~P1(f332(f64(x87573),x87576))+E(f332(f332(x87571,x87572),f332(f332(f67(x87573,x87574,x87571),x87575),f332(f332(f3(f853(x87573,a839)),x87576),f332(f332(f302(x87573),x87572),f180(f853(x87573,a839)))))),f332(f332(f67(x87573,x87574,x87571),x87575),f332(f332(f302(x87573),x87572),x87576)))
% 52.62/52.42 [8854]~E(f332(f166(x88541,x88542,x88544),x88545),f332(f227(x88542),x88546))+~P1(f332(f332(x88543,x88545),x88546))+E(f332(f166(x88541,x88542,f332(f126(f852(x88541,x88542),f332(f251(x88541,x88542,a839),x88543)),x88544)),x88545),f332(f227(x88542),x88546))
% 52.62/52.42 [9027]~P1(f332(f332(f334(x90275),x90273),x90276))+P1(f332(f332(f232(f853(x90271,a839)),f332(x90272,x90273)),x90274))+~P1(f332(f332(f232(f853(x90271,a839)),f332(f332(f47(x90275,f853(x90271,a839)),x90276),x90272)),x90274))
% 52.62/52.42 [9605]~P14(x96051,x96055,x96054)+P1(f332(f332(f334(f852(x96051,x96051)),f332(f332(f241(x96051,x96051),x96052),x96053)),x96054))+~P1(f332(f332(f334(x96051),x96056),f332(f332(f104(f853(x96051,a839)),f332(f277(x96051,x96051,x96054),f332(f332(f302(x96051),x96052),f180(f853(x96051,a839))))),f332(f277(x96051,x96051,x96054),f332(f332(f302(x96051),x96053),f180(f853(x96051,a839)))))))
% 52.62/52.42 [8527]~P121(x85272)+~E(f332(f332(f82(x85272),f332(f332(f83(x85272),x85274),x85275)),x85271),f332(f332(f82(x85272),f332(f332(f83(x85272),x85273),x85275)),x85276))+E(x85271,f332(f332(f82(x85272),f332(f332(f83(x85272),f332(f332(f3(x85272),x85273),x85274)),x85275)),x85276))
% 52.62/52.42 [8528]~P121(x85281)+~E(f332(f332(f82(x85281),f332(f332(f83(x85281),x85282),x85284)),x85285),f332(f332(f82(x85281),f332(f332(f83(x85281),x85283),x85284)),x85286))+E(f332(f332(f82(x85281),f332(f332(f83(x85281),f332(f332(f3(x85281),x85282),x85283)),x85284)),x85285),x85286)
% 52.62/52.42 [8675]~P121(x86751)+E(f332(f332(f82(x86751),f332(f332(f83(x86751),x86752),x86753)),x86754),f332(f332(f82(x86751),f332(f332(f83(x86751),x86755),x86753)),x86756))+~E(x86756,f332(f332(f82(x86751),f332(f332(f83(x86751),f332(f332(f3(x86751),x86752),x86755)),x86753)),x86754))
% 52.62/52.42 [8676]~P121(x86761)+E(f332(f332(f82(x86761),f332(f332(f83(x86761),x86762),x86763)),x86764),f332(f332(f82(x86761),f332(f332(f83(x86761),x86765),x86763)),x86766))+~E(f332(f332(f82(x86761),f332(f332(f83(x86761),f332(f332(f3(x86761),x86762),x86765)),x86763)),x86764),x86766)
% 52.62/52.42 [8967]~P1(f332(f332(x89674,x89675),x89676))+~P1(f332(f332(x89673,x89675),x89676))+P1(f332(f332(f332(f332(f104(f853(x89671,f853(x89672,a839))),x89673),x89674),x89675),x89676))
% 52.62/52.42 [9196]P1(f332(f332(x91961,x91962),x91963))+P1(f332(f332(x91964,x91962),x91963))+~P1(f332(f332(f332(f332(f103(f853(x91965,f853(x91966,a839))),x91964),x91961),x91962),x91963))
% 52.62/52.42 [9355]~E(f332(f181(f846(x93551)),x93555),f332(f181(f846(x93552)),x93556))+E(f170(x93551,x93552,f172(x93551,x93552,x93553,f332(f332(f3(f853(x93551,a839)),x93554),f332(f158(x93551),x93555))),f166(x93551,x93552,f332(f142(f852(x93551,x93552)),f332(f332(f167(x93551,x93552),x93555),x93556)))),f172(x93551,x93552,f170(x93551,x93552,x93553,f166(x93551,x93552,f332(f142(f852(x93551,x93552)),f332(f332(f167(x93551,x93552),x93555),x93556)))),x93554))+~P1(f332(f332(f232(f853(x93551,a839)),f332(f158(x93551),x93555)),x93554))
% 52.62/52.42 [9483]~P129(x94831)+~P1(f332(f332(f233(x94831),f332(f332(f82(x94831),f332(f332(f83(x94831),x94834),x94835)),x94832)),f332(f332(f82(x94831),f332(f332(f83(x94831),x94833),x94835)),x94836)))+P1(f332(f332(f233(x94831),x94832),f332(f332(f82(x94831),f332(f332(f83(x94831),f332(f332(f3(x94831),x94833),x94834)),x94835)),x94836)))
% 52.62/52.42 [9484]~P129(x94841)+~P1(f332(f332(f232(x94841),f332(f332(f82(x94841),f332(f332(f83(x94841),x94844),x94845)),x94842)),f332(f332(f82(x94841),f332(f332(f83(x94841),x94843),x94845)),x94846)))+P1(f332(f332(f232(x94841),x94842),f332(f332(f82(x94841),f332(f332(f83(x94841),f332(f332(f3(x94841),x94843),x94844)),x94845)),x94846)))
% 52.62/52.42 [9501]~P129(x95011)+P1(f332(f332(f233(x95011),f332(f332(f82(x95011),f332(f332(f83(x95011),x95012),x95013)),x95014)),f332(f332(f82(x95011),f332(f332(f83(x95011),x95015),x95013)),x95016)))+~P1(f332(f332(f233(x95011),x95014),f332(f332(f82(x95011),f332(f332(f83(x95011),f332(f332(f3(x95011),x95015),x95012)),x95013)),x95016)))
% 52.62/52.42 [9502]~P129(x95021)+P1(f332(f332(f232(x95021),f332(f332(f82(x95021),f332(f332(f83(x95021),x95022),x95023)),x95024)),f332(f332(f82(x95021),f332(f332(f83(x95021),x95025),x95023)),x95026)))+~P1(f332(f332(f232(x95021),x95024),f332(f332(f82(x95021),f332(f332(f83(x95021),f332(f332(f3(x95021),x95025),x95022)),x95023)),x95026)))
% 52.62/52.42 [9598]~P129(x95981)+~P1(f332(f332(f233(x95981),f332(f332(f82(x95981),f332(f332(f83(x95981),x95982),x95984)),x95985)),f332(f332(f82(x95981),f332(f332(f83(x95981),x95983),x95984)),x95986)))+P1(f332(f332(f233(x95981),f332(f332(f82(x95981),f332(f332(f83(x95981),f332(f332(f3(x95981),x95982),x95983)),x95984)),x95985)),x95986))
% 52.62/52.42 [9599]~P129(x95991)+~P1(f332(f332(f232(x95991),f332(f332(f82(x95991),f332(f332(f83(x95991),x95992),x95994)),x95995)),f332(f332(f82(x95991),f332(f332(f83(x95991),x95993),x95994)),x95996)))+P1(f332(f332(f232(x95991),f332(f332(f82(x95991),f332(f332(f83(x95991),f332(f332(f3(x95991),x95992),x95993)),x95994)),x95995)),x95996))
% 52.62/52.42 [9640]~P129(x96401)+P1(f332(f332(f233(x96401),f332(f332(f82(x96401),f332(f332(f83(x96401),x96402),x96403)),x96404)),f332(f332(f82(x96401),f332(f332(f83(x96401),x96405),x96403)),x96406)))+~P1(f332(f332(f233(x96401),f332(f332(f82(x96401),f332(f332(f83(x96401),f332(f332(f3(x96401),x96402),x96405)),x96403)),x96404)),x96406))
% 52.62/52.42 [9641]~P129(x96411)+P1(f332(f332(f232(x96411),f332(f332(f82(x96411),f332(f332(f83(x96411),x96412),x96413)),x96414)),f332(f332(f82(x96411),f332(f332(f83(x96411),x96415),x96413)),x96416)))+~P1(f332(f332(f232(x96411),f332(f332(f82(x96411),f332(f332(f83(x96411),f332(f332(f3(x96411),x96412),x96415)),x96413)),x96414)),x96416))
% 52.62/52.42 [9811]~P4(x98112)+~P1(f332(f64(x98111),x98116))+E(f332(f332(f8(x98111,x98112),f332(f332(f20(x98111,x98112,x98112),f332(f332(f20(x98111,x98112,f853(x98112,x98112)),f332(f332(f10(a839,f853(x98112,f853(x98112,x98112)),x98111),f98(x98112)),x98113)),x98114)),x98115)),x98116),f332(f332(f82(x98112),f332(f332(f8(x98111,x98112),x98114),f332(f332(f104(f853(x98111,a839)),x98116),f332(f256(x98111),x98113)))),f332(f332(f8(x98111,x98112),x98115),f332(f332(f104(f853(x98111,a839)),x98116),f332(f81(f853(x98111,a839)),f332(f256(x98111),x98113))))))
% 52.62/52.42 [9875]P1(f332(f332(f334(x98752),x98754),x98756))+P1(f332(f332(f334(x98752),x98755),x98756))+E(f332(f305(x98751,x98752,f332(f332(f9(x98751,x98752,x98752),f332(f332(f9(x98751,x98752,f853(x98752,x98752)),f332(f332(f10(a839,f853(x98752,f853(x98752,x98752)),x98751),f98(x98752)),f332(f332(f9(x98751,f853(x98751,a839),a839),f334(x98751)),x98753))),x98754)),x98755)),x98756),f180(f853(x98751,a839)))
% 52.62/52.42 [9876]P1(f332(f332(f334(x98762),x98765),x98766))+~P1(f332(f332(f334(x98762),x98764),x98766))+E(f332(f305(x98761,x98762,f332(f332(f9(x98761,x98762,x98762),f332(f332(f9(x98761,x98762,f853(x98762,x98762)),f332(f332(f10(a839,f853(x98762,f853(x98762,x98762)),x98761),f98(x98762)),f332(f332(f9(x98761,f853(x98761,a839),a839),f334(x98761)),x98763))),x98764)),x98765)),x98766),x98763)
% 52.62/52.42 [9877]P1(f332(f332(f334(x98772),x98774),x98776))+~P1(f332(f332(f334(x98772),x98775),x98776))+E(f332(f305(x98771,x98772,f332(f332(f9(x98771,x98772,x98772),f332(f332(f9(x98771,x98772,f853(x98772,x98772)),f332(f332(f10(a839,f853(x98772,f853(x98772,x98772)),x98771),f98(x98772)),f332(f332(f9(x98771,f853(x98771,a839),a839),f334(x98771)),x98773))),x98774)),x98775)),x98776),f332(f81(f853(x98771,a839)),x98773))
% 52.62/52.42 [9878]~P1(f332(f332(f334(x98782),x98784),x98786))+~P1(f332(f332(f334(x98782),x98785),x98786))+E(f332(f305(x98781,x98782,f332(f332(f9(x98781,x98782,x98782),f332(f332(f9(x98781,x98782,f853(x98782,x98782)),f332(f332(f10(a839,f853(x98782,f853(x98782,x98782)),x98781),f98(x98782)),f332(f332(f9(x98781,f853(x98781,a839),a839),f334(x98781)),x98783))),x98784)),x98785)),x98786),f239(f853(x98781,a839)))
% 52.62/52.42 [10010]P30(x100101,x100102,f332(f332(f302(f844(x100101)),f332(f332(f332(f93(x100101),f332(x100103,x100104)),f332(a27,x100104)),f332(x100105,x100104))),f180(f853(f844(x100101),a839))))+~P1(f332(f332(f334(a841),x100104),x100106))+~P30(x100101,f332(f332(f103(f853(f844(x100101),a839)),x100102),f332(f303(a841,f844(x100101),f332(f332(f20(a841,f853(x100101,f853(a842,a839)),f844(x100101)),f332(f332(f20(a841,a840,f853(f853(x100101,f853(a842,a839)),f844(x100101))),f332(f332(f10(f853(x100101,f853(a842,a839)),f853(a840,f853(f853(x100101,f853(a842,a839)),f844(x100101))),a841),f93(x100101)),x100103)),a27)),x100105)),x100106)),f332(f303(a841,f844(x100101),f332(f332(f20(a841,f853(x100101,f853(a842,a839)),f844(x100101)),f332(f332(f20(a841,a840,f853(f853(x100101,f853(a842,a839)),f844(x100101))),f332(f332(f10(f853(x100101,f853(a842,a839)),f853(a840,f853(f853(x100101,f853(a842,a839)),f844(x100101))),a841),f93(x100101)),x100103)),f332(f332(f10(f849(a840),a840,a841),f231(a840)),a30))),x100105)),x100106))
% 52.62/52.42 [8552]E(x85521,x85522)+~P57(x85524,x85525,x85523,x85526,x85527)+~E(f332(x85523,x85521),f332(x85523,x85522))
% 52.62/52.42 [6927]E(f332(f229(f849(x69271),x69272,f183(x69271),x69273),f332(x69274,x69275)),f332(f227(x69271),x69276))+~E(f332(x69274,x69275),f332(f227(x69272),x69277))+~E(f332(x69273,x69277),f332(f227(x69271),x69276))
% 52.62/52.42 [8573]~P17(x85736,x85735,x85737,x85734,x85731)+E(f332(f332(x85731,x85732),x85733),x85734)+P1(f332(f64(x85735),x85733))
% 52.62/52.42 [8574]~P17(x85746,x85745,x85747,x85744,x85741)+E(f332(f332(x85741,x85742),x85743),x85744)+P1(f332(f64(x85745),x85743))
% 52.62/52.42 [9350]P43(x93501,x93502,x93503,x93504,x93505,f332(f332(x93503,x93506),x93507))+~E(f332(f332(x93503,x93506),x93507),x93504)+~E(x93505,f180(f853(x93501,a839)))
% 52.62/52.42 [9521]~P1(f332(x95216,x95213))+~P1(f332(f332(f334(f852(x95212,x95212)),f332(f332(f241(x95212,x95212),x95214),x95215)),f332(x95217,x95213)))+P1(f332(f332(f334(f852(f852(x95211,x95212),f852(x95211,x95212))),f332(f332(f241(f852(x95211,x95212),f852(x95211,x95212)),f332(f332(f241(x95211,x95212),x95213),x95214)),f332(f332(f241(x95211,x95212),x95213),x95215))),f275(x95211,x95212,x95216,x95217)))
% 52.62/52.42 [9694]~P31(x96943,x96941,x96944,f239(f853(x96943,a839)))+E(f332(f166(x96941,x96942,f332(f332(f143(f852(x96943,x96942),f852(x96941,x96942)),f332(f251(x96943,x96942,f852(x96941,x96942)),f332(f332(f10(x96941,f853(x96942,f852(x96941,x96942)),x96943),f241(x96941,x96942)),x96944))),x96945)),f332(x96944,x96946)),f332(f227(x96942),x96947))+~E(f332(f166(x96943,x96942,x96945),x96946),f332(f227(x96942),x96947))
% 52.62/52.42 [9931]~P43(x99312,x99317,x99313,x99316,x99311,f332(f332(x99313,x99315),x99314))+E(f332(f332(x99313,f452(x99314,x99315,x99311,x99316,x99313,x99317,x99312)),f453(x99314,x99315,x99311,x99316,x99313,x99317,x99312)),f332(f332(x99313,x99315),x99314))+E(x99311,f180(f853(x99312,a839)))
% 52.62/52.42 [9932]~P43(x99327,x99326,x99321,x99324,x99325,f332(f332(x99321,x99322),x99323))+E(f332(f332(x99321,f452(x99323,x99322,x99325,x99324,x99321,x99326,x99327)),f453(x99323,x99322,x99325,x99324,x99321,x99326,x99327)),f332(f332(x99321,x99322),x99323))+E(f332(f332(x99321,x99322),x99323),x99324)
% 52.62/52.42 [9586]~P1(f332(f69(x95861,x95864,x95865,x95866,x95863),x95867))+P1(f332(f69(x95861,x95864,x95865,x95866,f332(f332(f302(x95861),x95862),x95863)),f332(f332(x95865,x95862),x95867)))+P1(f332(f332(f334(x95861),x95862),x95863))
% 52.62/52.42 [9956]~P43(x99562,x99567,x99566,x99565,x99561,f332(f332(x99566,x99564),x99563))+E(x99561,f180(f853(x99562,a839)))+P1(f332(f332(f334(x99562),f452(x99563,x99564,x99561,x99565,x99566,x99567,x99562)),x99561))
% 52.62/52.42 [9957]~P43(x99575,x99577,x99571,x99574,x99576,f332(f332(x99571,x99572),x99573))+E(f332(f332(x99571,x99572),x99573),x99574)+P1(f332(f332(f334(x99575),f452(x99573,x99572,x99576,x99574,x99571,x99577,x99575)),x99576))
% 52.62/52.42 [6706]~E(x67065,x67067)+~E(x67066,x67064)+E(f332(f332(f332(f332(f74(x67061,f849(x67062)),x67063),x67064),f332(f227(x67062),x67065)),x67066),f332(f227(x67062),x67067))
% 52.62/52.42 [6841]E(x68411,x68412)+~E(f332(x68415,x68411),f332(f227(x68414),x68417))+E(f332(f332(f332(f332(f74(x68413,f849(x68414)),x68415),x68412),f332(f227(x68414),x68416)),x68411),f332(f227(x68414),x68417))
% 52.62/52.42 [7586]E(x75861,x75862)+~E(x75863,x75864)+~E(f332(f332(f332(f332(f74(x75865,f849(x75866)),x75867),x75864),f332(f227(x75866),x75861)),x75863),f332(f227(x75866),x75862))
% 52.62/52.42 [7651]E(x76511,x76512)+E(f332(x76513,x76514),f332(f227(x76515),x76511))+~E(f332(f332(f332(f332(f74(x76516,f849(x76515)),x76513),x76517),f332(f227(x76515),x76512)),x76514),f332(f227(x76515),x76511))
% 52.62/52.42 [7652]E(x76521,x76522)+E(f332(x76523,x76521),f332(f227(x76524),x76525))+~E(f332(f332(f332(f332(f74(x76526,f849(x76524)),x76523),x76522),f332(f227(x76524),x76527)),x76521),f332(f227(x76524),x76525))
% 52.62/52.42 [8778]~P27(x87784,x87785,x87786,x87787,x87781)+~P1(f332(f64(x87785),x87783))+E(f332(f332(x87781,x87782),x87783),f332(f332(f332(f68(x87784,x87785,x87786),x87782),x87787),x87783))
% 52.62/52.42 [8779]~P17(x87794,x87795,x87796,x87797,x87791)+~P1(f332(f64(x87795),x87793))+E(f332(f332(x87791,x87792),x87793),f332(f332(f332(f68(x87794,x87795,x87796),x87792),x87797),x87793))
% 52.62/52.42 [9318]~P30(x93181,x93182,f332(f332(f302(f844(x93181)),f332(f332(f332(f93(x93181),x93183),x93184),x93187)),f180(f853(f844(x93181),a839))))+P30(x93181,x93182,f332(f332(f302(f844(x93181)),f332(f332(f332(f93(x93181),x93183),f36(x93184,x93185)),x93186)),f180(f853(f844(x93181),a839))))+~P30(x93181,x93182,f332(f332(f302(f844(x93181)),f332(f332(f332(f93(x93181),x93187),x93185),x93186)),f180(f853(f844(x93181),a839))))
% 52.62/52.42 [9496]~P29(x94963,x94964,x94965,x94967,x94966,x94961)+~P1(f332(f64(x94964),x94962))+E(f332(x94961,x94962),f332(f332(f332(f68(x94963,x94964,x94965),x94966),x94967),x94962))
% 52.62/52.42 [9635]P43(x96351,x96352,x96353,x96354,x96355,f332(f332(x96353,x96356),x96357))+~P43(x96351,x96352,x96353,x96354,f332(f332(f3(f853(x96351,a839)),x96355),f332(f332(f302(x96351),x96356),f180(f853(x96351,a839)))),x96357)+~P1(f332(f332(f334(x96351),x96356),x96355))
% 52.62/52.42 [9906]~P30(x99061,x99062,f332(f332(f302(f844(x99061)),f332(f332(f332(f93(x99061),f94(x99061,x99063,x99064)),x99065),x99067)),f180(f853(f844(x99061),a839))))+P30(x99061,x99062,f332(f332(f302(f844(x99061)),f332(f332(f332(f93(x99061),x99063),f33(x99064,x99065,x99066)),x99067)),f180(f853(f844(x99061),a839))))+~P30(x99061,x99062,f332(f332(f302(f844(x99061)),f332(f332(f332(f93(x99061),f94(x99061,x99063,f332(f75(a839,a839,a842,a328),x99064))),x99066),x99067)),f180(f853(f844(x99061),a839))))
% 52.62/52.42 [9974]P1(f332(f332(x99747,f831(x99744,x99745,x99741,x99746,x99743,x99742,x99747)),f832(x99744,x99745,x99741,x99746,x99743,x99742,x99747)))+~P1(f332(f332(x99747,f332(f250(x99742,x99743),x99746)),f332(f240(x99742,x99743),x99746)))+P1(f332(x99741,f332(f332(f251(x99742,x99743,x99744),x99745),x99746)))
% 52.62/52.42 [9983]~P43(x99832,x99833,x99834,x99835,x99831,f332(f332(x99834,x99837),x99836))+P43(x99832,x99833,x99834,x99835,f332(f332(f3(f853(x99832,a839)),x99831),f332(f332(f302(x99832),f452(x99836,x99837,x99831,x99835,x99834,x99833,x99832)),f180(f853(x99832,a839)))),f453(x99836,x99837,x99831,x99835,x99834,x99833,x99832))+E(x99831,f180(f853(x99832,a839)))
% 52.62/52.42 [9984]~P43(x99845,x99846,x99841,x99844,x99847,f332(f332(x99841,x99842),x99843))+P43(x99845,x99846,x99841,x99844,f332(f332(f3(f853(x99845,a839)),x99847),f332(f332(f302(x99845),f452(x99843,x99842,x99847,x99844,x99841,x99846,x99845)),f180(f853(x99845,a839)))),f453(x99843,x99842,x99847,x99844,x99841,x99846,x99845))+E(f332(f332(x99841,x99842),x99843),x99844)
% 52.62/52.42 [10004]~P1(f332(x100041,f332(f332(x100045,f832(x100044,x100045,x100041,x100046,x100043,x100042,x100047)),f831(x100044,x100045,x100041,x100046,x100043,x100042,x100047))))+~P1(f332(f332(x100047,f332(f250(x100042,x100043),x100046)),f332(f240(x100042,x100043),x100046)))+P1(f332(x100041,f332(f332(f251(x100042,x100043,x100044),x100045),x100046)))
% 52.62/52.42 [9339]P1(f332(f332(f232(f853(f852(x93391,x93392),a839)),f332(f332(f281(x93391,x93393,x93392),x93394),x93395)),f332(f332(f281(x93391,x93393,x93392),x93396),x93397)))+~P1(f332(f332(f232(f853(f852(x93393,x93392),a839)),x93395),x93397))+~P1(f332(f332(f232(f853(f852(x93391,x93393),a839)),x93394),x93396))
% 52.62/52.42 [9646]~P1(f332(f332(f334(x96461),x96466),x96465))+P1(f332(f69(x96461,x96462,x96463,x96464,x96465),f332(f332(x96463,x96466),x96467)))+~P1(f332(f69(x96461,x96462,x96463,x96464,f332(f332(f3(f853(x96461,a839)),x96465),f332(f332(f302(x96461),x96466),f180(f853(x96461,a839))))),x96467))
% 52.62/52.42 [9245]E(f170(x92451,x92452,x92453,f166(x92451,x92452,f332(f142(f852(x92451,x92452)),f332(f332(f167(x92451,x92452),x92454),f332(f332(f148(x92452,x92455),x92456),x92457))))),f170(x92451,x92452,x92453,f166(x92451,x92452,f332(f142(f852(x92451,x92452)),f332(f332(f167(x92451,x92452),x92454),x92455)))))+~P1(f332(f332(f233(a845),x92456),f332(f181(f846(x92452)),x92455)))+~P1(f332(f332(f232(a845),f332(f181(f846(x92451)),x92454)),x92456))
% 52.62/52.42 [10035]~P136(x100351)+~P31(f852(x100352,x100353),x100351,f332(f251(x100352,x100353,x100351),f332(f332(f9(x100352,f853(x100353,x100351),f853(x100353,x100351)),f332(f332(f10(f853(x100351,x100351),f853(f853(x100353,x100351),f853(x100353,x100351)),x100352),f10(x100351,x100351,x100353)),f332(f332(f10(x100351,f853(x100351,x100351),x100352),f83(x100351)),x100354))),x100355)),f332(f332(f248(x100352,x100353),x100356),f332(f18(f853(x100353,a839),x100352),x100357)))+E(f332(f332(f8(x100351,x100351),f39(x100351)),f332(f256(x100351),f332(f332(f10(f853(x100352,a839),a839,x100351),f89(x100352)),f332(f332(f10(f853(x100352,f853(x100353,a839)),f853(x100352,a839),x100351),f332(f10(f853(x100353,a839),a839,x100352),f89(x100353))),f332(f332(f9(x100351,f853(x100352,f853(x100353,a839)),f853(x100352,f853(x100353,a839))),f332(f332(f10(f853(x100352,f853(f853(x100353,a839),f853(x100353,a839))),f853(f853(x100352,f853(x100353,a839)),f853(x100352,f853(x100353,a839))),x100351),f20(x100352,f853(x100353,a839),f853(x100353,a839))),f332(f332(f10(f853(x100352,f853(x100353,f853(a839,a839))),f853(x100352,f853(f853(x100353,a839),f853(x100353,a839))),x100351),f332(f10(f853(x100353,f853(a839,a839)),f853(f853(x100353,a839),f853(x100353,a839)),x100352),f20(x100353,a839,a839))),f332(f332(f10(f853(x100352,f853(x100353,a839)),f853(x100352,f853(x100353,f853(a839,a839))),x100351),f332(f10(f853(x100353,a839),f853(x100353,f853(a839,a839)),x100352),f332(f10(a839,f853(a839,a839),x100353),a330))),f332(f332(f9(x100351,f853(x100352,f853(x100353,x100351)),f853(x100352,f853(x100353,a839))),f332(f332(f10(f853(f853(x100353,x100351),f853(x100353,a839)),f853(f853(x100352,f853(x100353,x100351)),f853(x100352,f853(x100353,a839))),x100351),f10(f853(x100353,x100351),f853(x100353,a839),x100352)),f332(f332(f10(f853(x100351,a839),f853(f853(x100353,x100351),f853(x100353,a839)),x100351),f10(x100351,a839,x100353)),a329))),f332(f332(f9(x100352,f853(x100353,x100351),f853(x100353,x100351)),f332(f332(f10(f853(x100351,x100351),f853(f853(x100353,x100351),f853(x100353,x100351)),x100352),f10(x100351,x100351,x100353)),f332(f332(f10(x100351,f853(x100351,x100351),x100352),f83(x100351)),x100354))),x100355)))))),f332(f332(f9(x100352,f853(x100353,a839),f853(x100353,a839)),f332(f332(f10(f853(a839,a839),f853(f853(x100353,a839),f853(x100353,a839)),x100352),f10(a839,a839,x100353)),f332(f332(f10(a839,f853(a839,a839),x100352),a330),f332(f332(f9(x100352,f853(x100352,a839),a839),f334(x100352)),x100356)))),f332(f332(f9(x100353,f853(x100353,a839),a839),f334(x100353)),x100357))))))),f332(f332(f83(x100351),f332(f332(f8(x100352,x100351),x100354),x100356)),f332(f332(f8(x100353,x100351),x100355),x100357)))
% 52.62/52.42 [9724]P53(x97241,x97242,x97243,x97244,x97245,x97246,x97247)+~P1(f332(f332(x97244,x97246),x97248))+~P1(f332(f332(x97245,x97248),x97247))
% 52.62/52.42 [9725]P53(x97251,x97252,x97253,x97254,x97255,x97256,x97257)+~P1(f332(f332(x97254,x97256),x97258))+~P1(f332(f332(x97255,x97258),x97257))
% 52.62/52.42 [9125]~P25(x91258,x91251,x91253,x91255)+~P1(f332(f64(x91258),x91256))+E(f332(f75(x91251,x91251,x91252,f332(x91253,x91254)),f332(f75(x91251,x91251,x91252,f332(x91255,x91256)),x91257)),f332(f75(x91251,x91251,x91252,f332(x91255,x91256)),f332(f75(x91251,x91251,x91252,f332(x91253,x91254)),x91257)))
% 52.62/52.42 [9488]~P28(x94887,x94882,x94885,x94888,x94886,x94881)+~P1(f332(f64(x94882),x94884))+E(f332(x94881,f332(f332(f302(x94882),x94883),x94884)),f332(f332(x94885,f332(x94886,x94883)),f332(x94881,x94884)))
% 52.62/52.42 [9596]~P31(x95962,x95964,x95966,x95968)+~P31(x95961,x95963,x95965,x95967)+P31(f852(x95961,x95962),f852(x95963,x95964),f252(x95961,x95963,x95962,x95964,x95965,x95966),f332(f332(f248(x95961,x95962),x95967),f332(f18(f853(x95962,a839),x95961),x95968)))
% 52.62/52.42 [9281]P1(f332(f332(f334(f852(x92811,x92812)),f332(f332(f241(x92811,x92812),x92813),x92814)),f332(f332(f281(x92811,x92815,x92812),x92816),x92817)))+~P1(f332(f332(f334(f852(x92811,x92815)),f332(f332(f241(x92811,x92815),x92813),x92818)),x92816))+~P1(f332(f332(f334(f852(x92815,x92812)),f332(f332(f241(x92815,x92812),x92818),x92814)),x92817))
% 52.62/52.42 [9471]~P1(f332(f332(f232(f853(f852(x94713,x94712),a839)),x94715),f332(f332(f248(x94713,x94712),x94718),f332(f18(f853(x94712,a839),x94713),x94717))))+~P1(f332(f332(f232(f853(f852(x94711,x94713),a839)),x94714),f332(f332(f248(x94711,x94713),x94716),f332(f18(f853(x94713,a839),x94711),x94718))))+P1(f332(f332(f232(f853(f852(x94711,x94712),a839)),f332(f332(f281(x94711,x94713,x94712),x94714),x94715)),f332(f332(f248(x94711,x94712),x94716),f332(f18(f853(x94712,a839),x94711),x94717))))
% 52.62/52.42 [9516]~E(x95163,x95165)+P1(f332(f332(f334(f852(f852(x95161,x95162),f852(x95161,x95162))),f332(f332(f241(f852(x95161,x95162),f852(x95161,x95162)),f332(f332(f241(x95161,x95162),x95163),x95164)),f332(f332(f241(x95161,x95162),x95165),x95166))),f326(x95161,x95162,x95167,x95168)))+~P1(f332(f332(f334(f852(x95162,x95162)),f332(f332(f241(x95162,x95162),x95164),x95166)),x95168))
% 52.62/52.42 [9614]E(x96141,x96142)+~P1(f332(f332(f334(f852(f852(x96143,x96145),f852(x96143,x96145))),f332(f332(f241(f852(x96143,x96145),f852(x96143,x96145)),f332(f332(f241(x96143,x96145),x96141),x96146)),f332(f332(f241(x96143,x96145),x96142),x96147))),f326(x96143,x96145,x96144,x96148)))+P1(f332(f332(f334(f852(x96143,x96143)),f332(f332(f241(x96143,x96143),x96141),x96142)),x96144))
% 52.62/52.42 [9629]~P1(f332(f332(f334(f852(f852(x96291,x96295),f852(x96291,x96295))),f332(f332(f241(f852(x96291,x96295),f852(x96291,x96295)),f332(f332(f241(x96291,x96295),x96292),x96296)),f332(f332(f241(x96291,x96295),x96293),x96297))),f326(x96291,x96295,x96294,x96298)))+P1(f332(f332(f334(f852(x96291,x96291)),f332(f332(f241(x96291,x96291),x96292),x96293)),x96294))+P1(f332(f332(f334(f852(x96295,x96295)),f332(f332(f241(x96295,x96295),x96296),x96297)),x96298))
% 52.62/52.42 [9545]~P29(x95457,x95455,x95451,x95458,x95452,x95454)+~P1(f332(f64(x95455),x95456))+E(f332(f332(x95451,f332(x95452,x95453)),f332(x95454,f332(f332(f3(f853(x95455,a839)),x95456),f332(f332(f302(x95455),x95453),f180(f853(x95455,a839)))))),f332(x95454,f332(f332(f302(x95455),x95453),x95456)))
% 52.62/52.42 [9083]~P1(f332(f332(f332(x90835,x90838),x90836),x90837))+~P1(f332(f332(f334(x90831),x90838),x90834))+P1(f332(f332(f332(f332(f47(x90831,f853(x90832,f853(x90833,a839))),x90834),x90835),x90836),x90837))
% 52.62/52.42 [9084]~P1(f332(f332(f332(x90845,x90848),x90846),x90847))+~P1(f332(f332(f334(x90841),x90848),x90844))+P1(f332(f332(f332(f332(f47(x90841,f853(x90842,f853(x90843,a839))),x90844),x90845),x90846),x90847))
% 52.62/52.42 [9267]P1(f332(f332(f332(x92671,x92672),x92673),x92674))+~P1(f332(f332(f334(x92675),x92672),x92676))+~P1(f332(f332(f332(f332(f48(x92675,f853(x92677,f853(x92678,a839))),x92676),x92671),x92673),x92674))
% 52.62/52.42 [9268]P1(f332(f332(f332(x92681,x92682),x92683),x92684))+~P1(f332(f332(f334(x92685),x92682),x92686))+~P1(f332(f332(f332(f332(f48(x92685,f853(x92687,f853(x92688,a839))),x92686),x92681),x92683),x92684))
% 52.62/52.42 [9269]P1(f332(f332(f332(x92691,x92692),x92693),x92694))+~P1(f332(f332(f334(x92695),x92692),x92696))+~P1(f332(f332(f332(f332(f48(x92695,f853(x92697,f853(x92698,a839))),x92696),x92691),x92693),x92694))
% 52.62/52.42 [9462]~P27(x94623,x94622,x94624,x94628,x94621)+~P1(f332(f64(x94622),x94627))+E(f332(f332(x94621,f332(f332(f20(x94622,x94623,x94623),f332(f332(f10(x94623,f853(x94623,x94623),x94622),x94624),x94625)),x94626)),x94627),f332(f332(x94624,f332(f332(x94621,x94625),x94627)),f332(f332(x94621,x94626),x94627)))
% 52.62/52.42 [9702]~E(f332(f303(x97022,x97024,x97026),x97028),x970210)+~E(f332(f303(x97021,x97023,x97025),x97027),x97029)+E(f332(f303(f852(x97021,x97022),f852(x97023,x97024),f252(x97021,x97023,x97022,x97024,x97025,x97026)),f332(f332(f248(x97021,x97022),x97027),f332(f18(f853(x97022,a839),x97021),x97028))),f332(f332(f248(x97023,x97024),x97029),f332(f18(f853(x97024,a839),x97023),x970210)))
% 52.62/52.42 [4732]~P100(x47322)+~P20(x47322,x47321)+P20(x47322,f116(x47322,x47321))+E(x47321,f115(x47322))
% 52.62/52.42 [4965]~P11(x49652)+E(f12(x49652,x49651),f46(x49652,x49651))+E(x49651,f180(f853(x49652,a839)))+~P1(f332(f64(x49652),x49651))
% 52.62/52.42 [4966]~P11(x49662)+E(f15(x49662,x49661),f45(x49662,x49661))+E(x49661,f180(f853(x49662,a839)))+~P1(f332(f64(x49662),x49661))
% 52.62/52.42 [5907]~P93(x59072)+E(x59071,f180(f853(x59072,a839)))+P1(f332(f332(f232(x59072),f12(x59072,x59071)),f15(x59072,x59071)))+~P1(f332(f64(x59072),x59071))
% 52.62/52.42 [5921]~P40(x59212)+~P40(x59211)+E(x59211,x59212)+~E(f332(f303(a1,a845,a107),x59211),f332(f303(a1,a845,a107),x59212))
% 52.62/52.42 [8947]~P110(x89471)+~P1(f332(f332(f334(x89471),x89472),f112(x89471)))+P1(f332(f332(f233(x89471),f332(f332(f82(x89471),f332(f332(f82(x89471),f80(x89471)),x89472)),x89472)),f2(x89471)))+~P1(f332(f332(f233(x89471),x89472),f2(x89471)))
% 52.62/52.42 [9166]~P110(x91661)+~P1(f332(f332(f334(x91661),x91662),f112(x91661)))+~P1(f332(f332(f233(x91661),f332(f332(f82(x91661),f332(f332(f82(x91661),f80(x91661)),x91662)),x91662)),f2(x91661)))+P1(f332(f332(f233(x91661),x91662),f2(x91661)))
% 52.62/52.42 [4785]~P105(x47852)+~P136(x47852)+E(x47851,f2(a845))+E(f332(f332(f242(x47852),f2(x47852)),x47851),f2(x47852))
% 52.62/52.42 [4789]~P105(x47891)+~P136(x47891)+~E(x47892,f2(a845))+E(f332(f332(f242(x47891),f2(x47891)),x47892),f80(x47891))
% 52.62/52.42 [4952]~P120(x49522)+E(x49521,f80(x49522))+E(x49521,f332(f81(x49522),f80(x49522)))+~E(f332(f332(f83(x49522),x49521),x49521),f80(x49522))
% 52.62/52.42 [5197]~P83(x51972)+E(x51971,f2(x51972))+E(f84(x51972,x51971),f332(f81(x51972),f80(x51972)))+P1(f332(f332(f233(x51972),f2(x51972)),x51971))
% 52.62/52.42 [5389]~E(x53892,f80(a1))+~E(x53891,f80(a1))+E(f332(f332(f83(a1),x53891),x53892),f80(a1))+~P1(f332(f332(f233(a1),f2(a1)),x53891))
% 52.62/52.42 [5429]~P83(x54292)+E(f84(x54292,x54291),f80(x54292))+E(x54291,f2(x54292))+~P1(f332(f332(f233(x54292),f2(x54292)),x54291))
% 52.62/52.42 [5438]E(x54381,x54382)+~E(f332(f106(a845),x54381),f332(f106(a845),x54382))+P1(f332(a186,f332(f106(a1),x54382)))+P1(f332(a186,f332(f106(a1),x54381)))
% 52.62/52.42 [5485]~P87(x54851)+~E(x54852,f2(x54851))+E(f332(f332(f82(x54851),x54852),x54852),f2(x54851))+~P1(f332(f332(f334(x54851),x54852),f112(x54851)))
% 52.62/52.42 [5521]E(x55211,f2(a1))+~E(f332(f332(f44(a1),x55212),x55211),f2(a1))+P1(f332(f332(f233(a1),x55211),x55212))+P1(f332(f332(f233(a1),x55212),x55211))
% 52.62/52.42 [5550]E(x55501,f2(a1))+~E(f332(f332(f44(a1),x55502),x55501),f2(a1))+P1(f332(f332(f232(a1),x55502),f2(a1)))+P1(f332(f332(f233(a1),x55502),x55501))
% 52.62/52.42 [5582]E(x55821,f2(a1))+~E(f332(f332(f44(a1),x55822),x55821),f2(a1))+P1(f332(f332(f232(a1),f2(a1)),x55822))+P1(f332(f332(f233(a1),x55821),x55822))
% 52.62/52.42 [5618]E(x56181,f2(a1))+~E(f332(f332(f44(a1),x56182),x56181),f2(a1))+P1(f332(f332(f232(a1),x56182),f2(a1)))+P1(f332(f332(f232(a1),f2(a1)),x56182))
% 52.62/52.42 [5619]~P87(x56192)+E(x56191,f2(x56192))+~E(f332(f332(f82(x56192),x56191),x56191),f2(x56192))+~P1(f332(f332(f334(x56192),x56191),f112(x56192)))
% 52.62/52.42 [5686]E(f332(f106(a845),x56861),f332(f106(a845),x56862))+~E(f332(f106(a1),x56862),f2(a1))+P1(f332(a186,f332(f106(a1),x56862)))+~P1(f332(a186,f332(f106(a1),x56861)))
% 52.62/52.42 [5715]~E(f332(f106(a845),x57152),f332(f106(a845),x57151))+E(f332(f106(a1),x57151),f2(a1))+P1(f332(a186,f332(f106(a1),x57151)))+~P1(f332(a186,f332(f106(a1),x57152)))
% 52.62/52.42 [5724]~P100(x57242)+E(x57241,f180(f853(x57242,a839)))+~P1(f332(f64(x57242),x57241))+P1(f332(f332(f334(x57242),f16(x57242,x57241)),x57241))
% 52.62/52.42 [5725]~P100(x57252)+E(x57251,f180(f853(x57252,a839)))+~P1(f332(f64(x57252),x57251))+P1(f332(f332(f334(x57252),f17(x57252,x57251)),x57251))
% 52.62/52.42 [5887]~P110(x58871)+~P88(x58871)+P1(f332(f332(f233(x58871),f2(x58871)),f332(f106(x58871),x58872)))+~P1(f332(f332(f233(a1),a85),x58872))
% 52.62/52.42 [5888]~P110(x58881)+~P88(x58881)+P1(f332(f332(f232(x58881),f2(x58881)),f332(f106(x58881),x58882)))+~P1(f332(f332(f232(a1),a85),x58882))
% 52.62/52.42 [5906]~P110(x59061)+~P88(x59061)+E(f332(f77(x59061),f332(f106(x59061),x59062)),f332(f106(x59061),x59062))+P1(f332(f332(f233(x59061),f332(f106(x59061),x59062)),f2(x59061)))
% 52.62/52.42 [5948]E(x59481,x59482)+~E(f332(a107,x59481),f332(a107,x59482))+~P1(f332(f332(f232(a1),f2(a1)),x59482))+~P1(f332(f332(f232(a1),f2(a1)),x59481))
% 52.62/52.42 [5949]E(x59491,x59492)+~E(f332(a107,x59491),f332(a107,x59492))+~P1(f332(f332(f232(a1),f2(a1)),x59492))+~P1(f332(f332(f232(a1),f2(a1)),x59491))
% 52.62/52.42 [5976]~E(x59761,f2(a1))+E(f54(x59761,x59762),f332(f332(f241(a1,a1),f2(a1)),f2(a1)))+P1(f332(f332(f232(a1),f2(a1)),x59762))+~P1(f332(f332(f232(a1),f2(a1)),x59761))
% 52.62/52.42 [6148]~P88(x61482)+~P110(x61482)+~P1(f332(f332(f233(x61482),f2(x61482)),f332(f106(x61482),x61481)))+P1(f332(f332(f233(a1),a85),x61481))
% 52.62/52.42 [6149]~P88(x61492)+~P110(x61492)+~P1(f332(f332(f232(x61492),f2(x61492)),f332(f106(x61492),x61491)))+P1(f332(f332(f232(a1),a85),x61491))
% 52.62/52.42 [6154]~P110(x61541)+~P88(x61541)+P1(f332(f332(f233(x61541),f332(f106(x61541),x61542)),f2(x61541)))+~P1(f332(f332(f233(a1),x61542),a85))
% 52.62/52.42 [6155]~P110(x61551)+~P88(x61551)+P1(f332(f332(f232(x61551),f332(f106(x61551),x61552)),f2(x61551)))+~P1(f332(f332(f232(a1),x61552),a85))
% 52.62/52.42 [6486]~P88(x64862)+~P110(x64862)+~P1(f332(f332(f233(x64862),f332(f106(x64862),x64861)),f2(x64862)))+P1(f332(f332(f233(a1),x64861),a85))
% 52.62/52.42 [6487]~P88(x64872)+~P110(x64872)+~P1(f332(f332(f232(x64872),f332(f106(x64872),x64871)),f2(x64872)))+P1(f332(f332(f232(a1),x64871),a85))
% 52.62/52.42 [6578]~P110(x65781)+~P88(x65781)+E(f332(f77(x65781),f332(f106(x65781),x65782)),f332(f81(x65781),f332(f106(x65781),x65782)))+~P1(f332(f332(f233(x65781),f332(f106(x65781),x65782)),f2(x65781)))
% 52.62/52.42 [6595]E(f332(f106(a845),x65951),f332(f106(a845),x65952))+~E(f332(f106(a1),x65952),f2(a1))+~P1(f332(f332(f232(a1),f332(f106(a1),x65951)),f2(a1)))+~P1(f332(a186,f332(f106(a1),x65951)))
% 52.62/52.42 [6776]E(x67761,x67762)+~E(f332(a5,x67761),f332(a5,x67762))+~P1(f332(f332(f334(a845),x67762),f239(f853(a845,a839))))+~P1(f332(f332(f334(a845),x67761),f239(f853(a845,a839))))
% 52.62/52.42 [7005]P1(f332(f332(f233(a845),f332(a107,x70051)),f332(a107,x70052)))+~P1(f332(f332(f232(a1),f2(a1)),x70052))+~P1(f332(f332(f232(a1),f2(a1)),x70051))+~P1(f332(f332(f233(a1),x70051),x70052))
% 52.62/52.42 [7006]P1(f332(f332(f232(a845),f332(a107,x70061)),f332(a107,x70062)))+~P1(f332(f332(f232(a1),f2(a1)),x70062))+~P1(f332(f332(f232(a1),f2(a1)),x70061))+~P1(f332(f332(f232(a1),x70061),x70062))
% 52.62/52.42 [7007]P1(f332(f332(f279(a845),f332(a107,x70071)),f332(a107,x70072)))+~P1(f332(f332(f232(a1),f2(a1)),x70072))+~P1(f332(f332(f232(a1),f2(a1)),x70071))+~P1(f332(f332(f279(a1),x70071),x70072))
% 52.62/52.42 [7240]~P12(x72401)+~P40(x72402)+~P1(f332(f332(f334(a1),x72401),x72402))+P1(f332(f332(f334(a845),f332(a107,x72401)),f332(f303(a1,a845,a107),x72402)))
% 52.62/52.42 [7248]~P1(f332(f332(f233(a845),f332(a107,x72481)),f332(a107,x72482)))+~P1(f332(f332(f232(a1),f2(a1)),x72482))+~P1(f332(f332(f232(a1),f2(a1)),x72481))+P1(f332(f332(f233(a1),x72481),x72482))
% 52.62/52.42 [7249]~P1(f332(f332(f232(a845),f332(a107,x72491)),f332(a107,x72492)))+~P1(f332(f332(f232(a1),f2(a1)),x72492))+~P1(f332(f332(f232(a1),f2(a1)),x72491))+P1(f332(f332(f232(a1),x72491),x72492))
% 52.62/52.42 [7250]~P1(f332(f332(f279(a845),f332(a107,x72501)),f332(a107,x72502)))+~P1(f332(f332(f232(a1),f2(a1)),x72502))+~P1(f332(f332(f232(a1),f2(a1)),x72501))+P1(f332(f332(f279(a1),x72501),x72502))
% 52.62/52.42 [7514]~P100(x75142)+E(x75141,f180(f853(x75142,a839)))+~P1(f332(f64(x75142),x75141))+P1(f332(f332(f232(x75142),f14(x75142,f236(x75142),x75141)),f13(x75142,f179(x75142),x75141)))
% 52.62/52.42 [7839]~P12(x78391)+~P40(x78392)+P1(f332(f332(f334(a1),x78391),x78392))+~P1(f332(f332(f334(a845),f332(a107,x78391)),f332(f303(a1,a845,a107),x78392)))
% 52.62/52.42 [5721]~P133(x57212)+E(x57211,f2(a1))+E(f332(f81(x57212),f332(f105(x57212),f332(f81(a1),x57211))),f332(f105(x57212),x57211))+~P1(f332(f332(f233(a1),x57211),f2(a1)))
% 52.62/52.42 [5797]~P87(x57971)+~P88(x57971)+~P35(x57971,f332(f106(x57971),x57972))+P35(x57971,f332(f106(x57971),f332(f332(f82(a1),x57972),x57972)))
% 52.62/52.42 [6138]~P68(x61382)+E(x61381,f180(f853(x61382,a839)))+E(f17(x61382,f332(f303(x61382,x61382,f81(x61382)),x61381)),f332(f81(x61382),f16(x61382,x61381)))+~P1(f332(f64(x61382),x61381))
% 52.62/52.42 [6139]~P68(x61392)+E(x61391,f180(f853(x61392,a839)))+E(f16(x61392,f332(f303(x61392,x61392,f81(x61392)),x61391)),f332(f81(x61392),f17(x61392,x61391)))+~P1(f332(f64(x61392),x61391))
% 52.62/52.42 [6169]~P87(x61691)+~P88(x61691)+P35(x61691,f332(f106(x61691),x61692))+~P35(x61691,f332(f106(x61691),f332(f332(f82(a1),x61692),x61692)))
% 52.62/52.42 [6264]E(x62641,f2(a1))+E(f332(a59,f58(f332(f81(a1),x62641),f332(f81(a1),x62642))),f54(x62641,x62642))+P1(f332(f332(f232(a1),f2(a1)),x62642))+~P1(f332(f332(f232(a1),f2(a1)),x62641))
% 52.62/52.42 [7150]~P1(f332(f332(f233(a1),f2(a1)),x71502))+~P1(f332(f332(f232(a1),f2(a1)),x71501))+~P1(f332(f332(f232(a1),x71502),x71501))+P1(f332(f332(f233(a1),f2(a1)),f332(f332(f44(a1),x71501),x71502)))
% 52.62/52.42 [7591]~E(x75912,f2(a1))+E(f210(x75911,x75912),f332(f332(f241(a1,a1),f2(a1)),f80(a1)))+P1(f332(f332(f233(a1),x75912),f2(a1)))+~P1(f332(f321(f852(a1,a1),a216),f332(f332(f241(a1,a1),x75911),x75912)))
% 52.62/52.42 [7592]~E(x75921,f2(a1))+E(f210(x75921,x75922),f332(f332(f241(a1,a1),f2(a1)),f80(a1)))+P1(f332(f332(f233(a1),x75922),f2(a1)))+~P1(f332(f321(f852(a1,a1),a216),f332(f332(f241(a1,a1),x75921),x75922)))
% 52.62/52.42 [8596]~P40(x85962)+~P40(x85961)+P1(f332(f332(f233(f853(a845,a839)),f332(f303(a1,a845,a107),x85961)),f332(f303(a1,a845,a107),x85962)))+~P1(f332(f332(f233(f853(a1,a839)),x85961),x85962))
% 52.62/52.42 [8597]~P40(x85972)+~P40(x85971)+P1(f332(f332(f232(f853(a845,a839)),f332(f303(a1,a845,a107),x85971)),f332(f303(a1,a845,a107),x85972)))+~P1(f332(f332(f232(f853(a1,a839)),x85971),x85972))
% 52.62/52.42 [8871]~P40(x88712)+~P40(x88711)+~P1(f332(f332(f233(f853(a845,a839)),f332(f303(a1,a845,a107),x88711)),f332(f303(a1,a845,a107),x88712)))+P1(f332(f332(f233(f853(a1,a839)),x88711),x88712))
% 52.62/52.42 [8872]~P40(x88722)+~P40(x88721)+~P1(f332(f332(f232(f853(a845,a839)),f332(f303(a1,a845,a107),x88721)),f332(f303(a1,a845,a107),x88722)))+P1(f332(f332(f232(f853(a1,a839)),x88721),x88722))
% 52.62/52.42 [9310]E(x93101,f2(a1))+E(x93102,f2(a1))+E(f332(f332(f88(a1,f852(a1,a1)),f332(f332(a212,x93102),x93101)),f332(f332(f20(a1,a1,f852(a1,a1)),f332(f332(f10(a1,f853(a1,f852(a1,a1)),a1),f241(a1,a1)),f332(f44(a1),x93102))),f332(f44(a1),x93101))),f210(x93102,x93101))+P1(f332(f332(f233(a1),x93101),f2(a1)))
% 52.62/52.42 [8161]~P88(x81612)+~P110(x81612)+~P1(f332(f332(f233(x81612),f332(f106(x81612),x81611)),f80(x81612)))+P1(f332(f332(f233(a1),x81611),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))
% 52.62/52.42 [8162]~P88(x81622)+~P110(x81622)+~P1(f332(f332(f232(x81622),f332(f106(x81622),x81621)),f80(x81622)))+P1(f332(f332(f232(a1),x81621),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))
% 52.62/52.42 [8436]~P110(x84361)+~P88(x84361)+P1(f332(f332(f233(x84361),f332(f106(x84361),x84362)),f80(x84361)))+~P1(f332(f332(f233(a1),x84362),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))
% 52.62/52.42 [8437]~P110(x84371)+~P88(x84371)+P1(f332(f332(f232(x84371),f332(f106(x84371),x84372)),f80(x84371)))+~P1(f332(f332(f232(a1),x84372),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))
% 52.62/52.42 [8621]~P88(x86212)+~P110(x86212)+~P1(f332(f332(f233(x86212),f80(x86212)),f332(f106(x86212),x86211)))+P1(f332(f332(f233(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),x86211))
% 52.62/52.42 [8622]~P88(x86222)+~P110(x86222)+~P1(f332(f332(f232(x86222),f80(x86222)),f332(f106(x86222),x86221)))+P1(f332(f332(f232(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),x86221))
% 52.62/52.42 [8954]~P110(x89541)+~P88(x89541)+P1(f332(f332(f233(x89541),f80(x89541)),f332(f106(x89541),x89542)))+~P1(f332(f332(f233(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),x89542))
% 52.62/52.42 [8955]~P110(x89551)+~P88(x89551)+P1(f332(f332(f232(x89551),f80(x89551)),f332(f106(x89551),x89552)))+~P1(f332(f332(f232(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),x89552))
% 52.62/52.42 [9433]~P120(x94332)+E(x94331,f80(x94332))+E(x94331,f332(f81(x94332),f80(x94332)))+~E(f332(f332(f242(x94332),x94331),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f80(x94332))
% 52.62/52.42 [9677]~P64(x96771)+~P88(x96771)+~P1(f332(f332(f233(x96771),f2(x96771)),x96772))+P1(f332(f332(f233(x96771),f2(x96771)),f332(f332(f283(x96771),x96772),f332(f106(x96771),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))))
% 52.62/52.42 [9678]~P64(x96781)+~P88(x96781)+~P1(f332(f332(f233(x96781),f2(x96781)),x96782))+P1(f332(f332(f233(x96781),f2(x96781)),f332(f332(f283(x96781),x96782),f332(f106(x96781),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))))
% 52.62/52.42 [9734]~P64(x97341)+~P88(x97341)+P1(f332(f332(f233(x97341),f2(x97341)),x97342))+~P1(f332(f332(f233(x97341),f2(x97341)),f332(f332(f283(x97341),x97342),f332(f106(x97341),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))))
% 52.62/52.42 [10009]~P133(x100092)+E(x100091,f2(a1))+P1(f332(f332(f233(a1),x100091),f2(a1)))+E(f332(f332(f251(a1,a1,x100092),f332(f332(f9(a1,f853(a1,f853(x100092,x100092)),f853(a1,x100092)),f332(f332(f10(f853(f853(x100092,x100092),x100092),f853(f853(a1,f853(x100092,x100092)),f853(a1,x100092)),a1),f10(f853(x100092,x100092),x100092,a1)),f332(f332(f10(x100092,f853(f853(x100092,x100092),x100092),a1),f88(x100092,x100092)),f105(x100092)))),f332(f332(f9(a1,f853(x100092,x100092),f853(x100092,x100092)),f332(f332(f10(f853(x100092,f853(x100092,x100092)),f853(f853(x100092,x100092),f853(x100092,x100092)),a1),f20(x100092,x100092,x100092)),f332(f332(f9(a1,f853(x100092,x100092),f853(x100092,f853(x100092,x100092))),f332(f332(f10(f853(x100092,f853(x100092,x100092)),f853(f853(x100092,x100092),f853(x100092,f853(x100092,x100092))),a1),f10(x100092,f853(x100092,x100092),x100092)),f332(f332(f10(a839,f853(x100092,f853(x100092,x100092)),a1),f98(x100092)),f332(f332(f9(a1,a1,a839),a329),f2(a1))))),f332(f332(f20(x100092,x100092,x100092),f82(x100092)),f7(x100092))))),f332(f332(f9(x100092,x100092,x100092),f332(f332(f10(x100092,f853(x100092,x100092),x100092),f82(x100092)),f332(f332(f20(x100092,x100092,x100092),f82(x100092)),f7(x100092)))),f80(x100092))))),f54(x100091,f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))),f332(f105(x100092),x100091))
% 52.62/52.42 [9781]P1(f332(f332(f232(a1),x97811),f2(a1)))+P1(f332(f332(f233(a1),x97812),x97811))+~P1(f332(f321(f852(a1,a1),a63),f332(f332(f241(a1,a1),x97812),x97811)))+E(f332(f51(x97811),f55(x97812,f332(f332(f83(a1),f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),x97811))),f55(x97812,x97811))
% 52.62/52.42 [9785]P1(f332(f332(f232(a1),x97851),f2(a1)))+~P1(f332(f321(f852(a1,a1),a60),f332(f332(f241(a1,a1),x97852),x97851)))+P1(f332(f332(f232(a1),f2(a1)),f332(f332(f82(a1),x97852),x97851)))+E(f332(f51(x97851),f58(x97852,f332(f332(f83(a1),f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),x97851))),f58(x97852,x97851))
% 52.62/52.42 [4758]~P87(x47583)+~P88(x47583)+E(x47581,x47582)+~E(f332(f106(x47583),x47581),f332(f106(x47583),x47582))
% 52.62/52.42 [5896]~P1(f332(x58961,x58962))+~P1(f332(x58961,x58963))+~P1(f332(f332(f232(a845),x58963),f787(x58962,x58961)))+P1(f332(x58961,f2(a845)))
% 52.62/52.42 [6331]P140(x63312,x63313,x63311)+E(x63311,f2(a1))+P1(f332(f332(f232(a1),f2(a1)),f776(x63311,x63313,x63312)))+P1(f332(f332(f233(a1),x63311),f2(a1)))
% 52.62/52.42 [6332]P141(x63322,x63323,x63321)+E(x63321,f2(a1))+P1(f332(f332(f232(a1),f2(a1)),f781(x63321,x63323,x63322)))+P1(f332(f332(f233(a1),x63321),f2(a1)))
% 52.62/52.42 [6464]P140(x64641,x64642,x64643)+~P1(f332(x64641,x64642))+P1(f332(f332(f232(a1),f2(a1)),f776(x64643,x64642,x64641)))+P1(f332(f332(f233(a1),x64643),f2(a1)))
% 52.62/52.42 [6489]P141(x64891,x64892,x64893)+P1(f332(f332(f232(a1),f2(a1)),f781(x64893,x64892,x64891)))+~P1(f332(x64891,f2(a1)))+P1(f332(f332(f233(a1),x64893),f2(a1)))
% 52.62/52.42 [6521]P140(x65212,x65213,x65211)+E(x65211,f2(a1))+~P1(f332(x65212,f776(x65211,x65213,x65212)))+P1(f332(f332(f233(a1),x65211),f2(a1)))
% 52.62/52.42 [6522]P141(x65222,x65223,x65221)+E(x65221,f2(a1))+~P1(f332(x65222,f779(x65221,x65223,x65222)))+P1(f332(f332(f233(a1),x65221),f2(a1)))
% 52.62/52.42 [6625]~P100(x66251)+~P11(x66251)+~P1(f332(f332(f233(x66251),x66252),f45(x66251,x66253)))+P1(f332(f332(f233(x66251),x66252),f670(x66253,x66252,x66251)))
% 52.62/52.42 [6635]P140(x66351,x66352,x66353)+~P1(f332(x66351,x66352))+~P1(f332(x66351,f776(x66353,x66352,x66351)))+P1(f332(f332(f233(a1),x66353),f2(a1)))
% 52.62/52.42 [6668]P141(x66681,x66682,x66683)+~P1(f332(x66681,f779(x66683,x66682,x66681)))+~P1(f332(x66681,f2(a1)))+P1(f332(f332(f233(a1),x66683),f2(a1)))
% 52.62/52.42 [6930]P140(x69302,x69303,x69301)+E(x69301,f2(a1))+P1(f332(f332(f232(a1),f2(a1)),f776(x69301,x69303,x69302)))+P1(f332(f332(f233(a1),x69301),f775(x69301,x69303,x69302)))
% 52.62/52.42 [6931]P141(x69312,x69313,x69311)+E(x69311,f2(a1))+P1(f332(f332(f232(a1),f2(a1)),f781(x69311,x69313,x69312)))+P1(f332(f332(f233(a1),x69311),f780(x69311,x69313,x69312)))
% 52.62/52.42 [7048]P140(x70481,x70482,x70483)+~P1(f332(x70481,x70482))+P1(f332(f332(f232(a1),f2(a1)),f776(x70483,x70482,x70481)))+P1(f332(f332(f233(a1),x70483),f775(x70483,x70482,x70481)))
% 52.62/52.42 [7069]P141(x70691,x70692,x70693)+P1(f332(f332(f232(a1),f2(a1)),f781(x70693,x70692,x70691)))+P1(f332(f332(f233(a1),x70693),f780(x70693,x70692,x70691)))+~P1(f332(x70691,f2(a1)))
% 52.62/52.42 [7100]P140(x71002,x71003,x71001)+E(x71001,f2(a1))+~P1(f332(x71002,f776(x71001,x71003,x71002)))+P1(f332(f332(f233(a1),x71001),f775(x71001,x71003,x71002)))
% 52.62/52.42 [7101]P141(x71012,x71013,x71011)+E(x71011,f2(a1))+~P1(f332(x71012,f779(x71011,x71013,x71012)))+P1(f332(f332(f233(a1),x71011),f780(x71011,x71013,x71012)))
% 52.62/52.42 [7141]P140(x71412,x71413,x71411)+E(x71411,f2(a1))+P1(f332(f332(f232(a1),f2(a1)),f776(x71411,x71413,x71412)))+~P1(f332(x71412,f775(x71411,x71413,x71412)))
% 52.62/52.42 [7142]P141(x71422,x71423,x71421)+E(x71421,f2(a1))+P1(f332(f332(f232(a1),f2(a1)),f781(x71421,x71423,x71422)))+~P1(f332(x71422,f783(x71421,x71423,x71422)))
% 52.62/52.42 [7247]P140(x72471,x72472,x72473)+~P1(f332(x72471,x72472))+~P1(f332(x72471,f776(x72473,x72472,x72471)))+P1(f332(f332(f233(a1),x72473),f775(x72473,x72472,x72471)))
% 52.62/52.42 [7263]P141(x72631,x72632,x72633)+~P1(f332(x72631,f779(x72633,x72632,x72631)))+P1(f332(f332(f233(a1),x72633),f780(x72633,x72632,x72631)))+~P1(f332(x72631,f2(a1)))
% 52.62/52.42 [7269]P140(x72691,x72692,x72693)+~P1(f332(x72691,x72692))+P1(f332(f332(f232(a1),f2(a1)),f776(x72693,x72692,x72691)))+~P1(f332(x72691,f775(x72693,x72692,x72691)))
% 52.62/52.42 [7287]P141(x72871,x72872,x72873)+P1(f332(f332(f232(a1),f2(a1)),f781(x72873,x72872,x72871)))+~P1(f332(x72871,f783(x72873,x72872,x72871)))+~P1(f332(x72871,f2(a1)))
% 52.62/52.42 [7311]P140(x73112,x73113,x73111)+E(x73111,f2(a1))+~P1(f332(x73112,f776(x73111,x73113,x73112)))+~P1(f332(x73112,f775(x73111,x73113,x73112)))
% 52.62/52.42 [7312]P141(x73122,x73123,x73121)+E(x73121,f2(a1))+~P1(f332(x73122,f779(x73121,x73123,x73122)))+~P1(f332(x73122,f783(x73121,x73123,x73122)))
% 52.62/52.42 [7408]P140(x74081,x74082,x74083)+~P1(f332(x74081,x74082))+~P1(f332(x74081,f776(x74083,x74082,x74081)))+~P1(f332(x74081,f775(x74083,x74082,x74081)))
% 52.62/52.42 [7423]P141(x74231,x74232,x74233)+~P1(f332(x74231,f779(x74233,x74232,x74231)))+~P1(f332(x74231,f783(x74233,x74232,x74231)))+~P1(f332(x74231,f2(a1)))
% 52.62/52.42 [7474]P140(x74742,x74743,x74741)+E(x74741,f2(a1))+P1(f332(f332(f232(a1),f2(a1)),f776(x74741,x74743,x74742)))+P1(f332(f332(f232(a1),f775(x74741,x74743,x74742)),f2(a1)))
% 52.62/52.42 [7475]P141(x74752,x74753,x74751)+E(x74751,f2(a1))+P1(f332(f332(f232(a1),f2(a1)),f781(x74751,x74753,x74752)))+P1(f332(f332(f232(a1),f780(x74751,x74753,x74752)),f2(a1)))
% 52.62/52.42 [7476]~P2(x74761)+~P1(f332(f332(f334(x74761),x74763),f176(x74761)))+~P1(f332(f332(f334(x74761),x74762),f176(x74761)))+P1(f332(f332(f334(x74761),f332(f332(f82(x74761),x74762),x74763)),f176(x74761)))
% 52.62/52.42 [7477]~P133(x74771)+~P1(f332(f332(f334(x74771),x74773),f112(x74771)))+~P1(f332(f332(f334(x74771),x74772),f112(x74771)))+P1(f332(f332(f334(x74771),f332(f332(f82(x74771),x74772),x74773)),f112(x74771)))
% 52.62/52.42 [7478]~P2(x74781)+~P1(f332(f332(f334(x74781),x74783),f176(x74781)))+~P1(f332(f332(f334(x74781),x74782),f176(x74781)))+P1(f332(f332(f334(x74781),f332(f332(f83(x74781),x74782),x74783)),f176(x74781)))
% 52.62/52.42 [7479]~P133(x74791)+~P1(f332(f332(f334(x74791),x74793),f112(x74791)))+~P1(f332(f332(f334(x74791),x74792),f112(x74791)))+P1(f332(f332(f334(x74791),f332(f332(f83(x74791),x74792),x74793)),f112(x74791)))
% 52.62/52.42 [7480]~P133(x74801)+~P1(f332(f332(f334(x74801),x74803),f112(x74801)))+~P1(f332(f332(f334(x74801),x74802),f112(x74801)))+P1(f332(f332(f334(x74801),f332(f332(f3(x74801),x74802),x74803)),f112(x74801)))
% 52.62/52.42 [7481]~P82(x74811)+~P1(f332(f332(f233(x74811),x74813),f2(x74811)))+~P1(f332(f332(f233(x74811),x74812),f2(x74811)))+P1(f332(f332(f233(x74811),f332(f332(f82(x74811),x74812),x74813)),f2(x74811)))
% 52.62/52.42 [7482]~P82(x74821)+~P1(f332(f332(f232(x74821),x74822),f2(x74821)))+~P1(f332(f332(f233(x74821),x74823),f2(x74821)))+P1(f332(f332(f233(x74821),f332(f332(f82(x74821),x74822),x74823)),f2(x74821)))
% 52.62/52.42 [7483]~P82(x74831)+~P1(f332(f332(f232(x74831),x74833),f2(x74831)))+~P1(f332(f332(f233(x74831),x74832),f2(x74831)))+P1(f332(f332(f233(x74831),f332(f332(f82(x74831),x74832),x74833)),f2(x74831)))
% 52.62/52.42 [7484]~P82(x74841)+~P1(f332(f332(f232(x74841),x74843),f2(x74841)))+~P1(f332(f332(f232(x74841),x74842),f2(x74841)))+P1(f332(f332(f232(x74841),f332(f332(f82(x74841),x74842),x74843)),f2(x74841)))
% 52.62/52.42 [7510]P140(x75103,x75102,x75101)+E(x75101,f2(a1))+E(f332(f332(f82(a1),f332(f332(f83(a1),x75101),f777(x75101,x75102,x75103))),f776(x75101,x75102,x75103)),x75102)+P1(f332(f332(f233(a1),x75101),f2(a1)))
% 52.62/52.42 [7511]P141(x75113,x75112,x75111)+E(x75111,f2(a1))+E(f332(f332(f82(a1),f332(f332(f83(a1),x75111),f779(x75111,x75112,x75113))),f781(x75111,x75112,x75113)),x75112)+P1(f332(f332(f233(a1),x75111),f2(a1)))
% 52.62/52.42 [7596]P140(x75961,x75962,x75963)+~P1(f332(x75961,x75962))+P1(f332(f332(f232(a1),f2(a1)),f776(x75963,x75962,x75961)))+P1(f332(f332(f232(a1),f775(x75963,x75962,x75961)),f2(a1)))
% 52.62/52.42 [7627]P141(x76271,x76272,x76273)+P1(f332(f332(f232(a1),f2(a1)),f781(x76273,x76272,x76271)))+~P1(f332(x76271,f2(a1)))+P1(f332(f332(f232(a1),f780(x76273,x76272,x76271)),f2(a1)))
% 52.62/52.42 [7635]P140(x76353,x76352,x76351)+~P1(f332(x76353,x76352))+E(f332(f332(f82(a1),f332(f332(f83(a1),x76351),f777(x76351,x76352,x76353))),f776(x76351,x76352,x76353)),x76352)+P1(f332(f332(f233(a1),x76351),f2(a1)))
% 52.62/52.42 [7640]P140(x76402,x76403,x76401)+E(x76401,f2(a1))+~P1(f332(x76402,f776(x76401,x76403,x76402)))+P1(f332(f332(f232(a1),f775(x76401,x76403,x76402)),f2(a1)))
% 52.62/52.42 [7641]P141(x76412,x76413,x76411)+E(x76411,f2(a1))+~P1(f332(x76412,f779(x76411,x76413,x76412)))+P1(f332(f332(f232(a1),f780(x76411,x76413,x76412)),f2(a1)))
% 52.62/52.42 [7646]P141(x76463,x76462,x76461)+E(f332(f332(f82(a1),f332(f332(f83(a1),x76461),f779(x76461,x76462,x76463))),f781(x76461,x76462,x76463)),x76462)+~P1(f332(x76463,f2(a1)))+P1(f332(f332(f233(a1),x76461),f2(a1)))
% 52.62/52.42 [7699]P140(x76991,x76992,x76993)+~P1(f332(x76991,x76992))+~P1(f332(x76991,f776(x76993,x76992,x76991)))+P1(f332(f332(f232(a1),f775(x76993,x76992,x76991)),f2(a1)))
% 52.62/52.42 [7704]P141(x77041,x77042,x77043)+~P1(f332(x77041,f779(x77043,x77042,x77041)))+~P1(f332(x77041,f2(a1)))+P1(f332(f332(f232(a1),f780(x77043,x77042,x77041)),f2(a1)))
% 52.62/52.42 [7778]~P64(x77781)+~P1(f332(f332(f233(x77781),f332(f332(f283(x77781),x77783),x77782)),f2(x77781)))+P1(f332(f332(f233(x77781),x77782),f2(x77781)))+P1(f332(f332(f233(x77781),x77783),f2(x77781)))
% 52.62/52.42 [7779]~P119(x77791)+~P1(f332(f332(f232(x77791),f332(f332(f83(x77791),x77793),x77792)),f2(x77791)))+P1(f332(f332(f232(x77791),x77792),f2(x77791)))+P1(f332(f332(f232(x77791),x77793),f2(x77791)))
% 52.62/52.42 [7780]~P64(x77801)+~P1(f332(f332(f232(x77801),f332(f332(f283(x77801),x77803),x77802)),f2(x77801)))+P1(f332(f332(f232(x77801),x77802),f2(x77801)))+P1(f332(f332(f232(x77801),x77803),f2(x77801)))
% 52.62/52.42 [7892]P140(x78923,x78922,x78921)+E(x78921,f2(a1))+E(f332(f332(f82(a1),f332(f332(f83(a1),x78921),f777(x78921,x78922,x78923))),f776(x78921,x78922,x78923)),x78922)+P1(f332(f332(f233(a1),x78921),f775(x78921,x78922,x78923)))
% 52.62/52.42 [7893]P141(x78933,x78932,x78931)+E(x78931,f2(a1))+E(f332(f332(f82(a1),f332(f332(f83(a1),x78931),f779(x78931,x78932,x78933))),f781(x78931,x78932,x78933)),x78932)+P1(f332(f332(f233(a1),x78931),f780(x78931,x78932,x78933)))
% 52.62/52.42 [7904]P140(x79043,x79042,x79041)+E(x79041,f2(a1))+E(f332(f332(f82(a1),f332(f332(f83(a1),x79041),f778(x79041,x79042,x79043))),f775(x79041,x79042,x79043)),x79042)+P1(f332(f332(f232(a1),f2(a1)),f776(x79041,x79042,x79043)))
% 52.62/52.42 [7905]P141(x79053,x79052,x79051)+E(x79051,f2(a1))+E(f332(f332(f82(a1),f332(f332(f83(a1),x79051),f783(x79051,x79052,x79053))),f780(x79051,x79052,x79053)),x79052)+P1(f332(f332(f232(a1),f2(a1)),f781(x79051,x79052,x79053)))
% 52.62/52.42 [7952]P140(x79523,x79522,x79521)+~P1(f332(x79523,x79522))+E(f332(f332(f82(a1),f332(f332(f83(a1),x79521),f777(x79521,x79522,x79523))),f776(x79521,x79522,x79523)),x79522)+P1(f332(f332(f233(a1),x79521),f775(x79521,x79522,x79523)))
% 52.62/52.42 [7963]P141(x79633,x79632,x79631)+E(f332(f332(f82(a1),f332(f332(f83(a1),x79631),f779(x79631,x79632,x79633))),f781(x79631,x79632,x79633)),x79632)+P1(f332(f332(f233(a1),x79631),f780(x79631,x79632,x79633)))+~P1(f332(x79633,f2(a1)))
% 52.62/52.42 [7969]P140(x79693,x79692,x79691)+~P1(f332(x79693,x79692))+E(f332(f332(f82(a1),f332(f332(f83(a1),x79691),f778(x79691,x79692,x79693))),f775(x79691,x79692,x79693)),x79692)+P1(f332(f332(f232(a1),f2(a1)),f776(x79691,x79692,x79693)))
% 52.62/52.42 [7976]P141(x79763,x79762,x79761)+E(f332(f332(f82(a1),f332(f332(f83(a1),x79761),f783(x79761,x79762,x79763))),f780(x79761,x79762,x79763)),x79762)+P1(f332(f332(f232(a1),f2(a1)),f781(x79761,x79762,x79763)))+~P1(f332(x79763,f2(a1)))
% 52.62/52.42 [7986]P140(x79863,x79862,x79861)+E(x79861,f2(a1))+E(f332(f332(f82(a1),f332(f332(f83(a1),x79861),f777(x79861,x79862,x79863))),f776(x79861,x79862,x79863)),x79862)+~P1(f332(x79863,f775(x79861,x79862,x79863)))
% 52.62/52.42 [7987]P141(x79873,x79872,x79871)+E(x79871,f2(a1))+E(f332(f332(f82(a1),f332(f332(f83(a1),x79871),f779(x79871,x79872,x79873))),f781(x79871,x79872,x79873)),x79872)+~P1(f332(x79873,f783(x79871,x79872,x79873)))
% 52.62/52.42 [7988]P140(x79883,x79882,x79881)+E(x79881,f2(a1))+E(f332(f332(f82(a1),f332(f332(f83(a1),x79881),f778(x79881,x79882,x79883))),f775(x79881,x79882,x79883)),x79882)+~P1(f332(x79883,f776(x79881,x79882,x79883)))
% 52.62/52.42 [7989]P141(x79893,x79892,x79891)+E(x79891,f2(a1))+E(f332(f332(f82(a1),f332(f332(f83(a1),x79891),f783(x79891,x79892,x79893))),f780(x79891,x79892,x79893)),x79892)+~P1(f332(x79893,f779(x79891,x79892,x79893)))
% 52.62/52.42 [8042]P140(x80423,x80422,x80421)+~P1(f332(x80423,x80422))+E(f332(f332(f82(a1),f332(f332(f83(a1),x80421),f777(x80421,x80422,x80423))),f776(x80421,x80422,x80423)),x80422)+~P1(f332(x80423,f775(x80421,x80422,x80423)))
% 52.62/52.42 [8043]P140(x80433,x80432,x80431)+~P1(f332(x80433,x80432))+E(f332(f332(f82(a1),f332(f332(f83(a1),x80431),f778(x80431,x80432,x80433))),f775(x80431,x80432,x80433)),x80432)+~P1(f332(x80433,f776(x80431,x80432,x80433)))
% 52.62/52.42 [8055]P141(x80553,x80552,x80551)+E(f332(f332(f82(a1),f332(f332(f83(a1),x80551),f779(x80551,x80552,x80553))),f781(x80551,x80552,x80553)),x80552)+~P1(f332(x80553,f783(x80551,x80552,x80553)))+~P1(f332(x80553,f2(a1)))
% 52.62/52.42 [8056]P141(x80563,x80562,x80561)+E(f332(f332(f82(a1),f332(f332(f83(a1),x80561),f783(x80561,x80562,x80563))),f780(x80561,x80562,x80563)),x80562)+~P1(f332(x80563,f779(x80561,x80562,x80563)))+~P1(f332(x80563,f2(a1)))
% 52.62/52.42 [8154]P140(x81543,x81542,x81541)+E(x81541,f2(a1))+E(f332(f332(f82(a1),f332(f332(f83(a1),x81541),f777(x81541,x81542,x81543))),f776(x81541,x81542,x81543)),x81542)+P1(f332(f332(f232(a1),f775(x81541,x81542,x81543)),f2(a1)))
% 52.62/52.42 [8155]P141(x81553,x81552,x81551)+E(x81551,f2(a1))+E(f332(f332(f82(a1),f332(f332(f83(a1),x81551),f779(x81551,x81552,x81553))),f781(x81551,x81552,x81553)),x81552)+P1(f332(f332(f232(a1),f780(x81551,x81552,x81553)),f2(a1)))
% 52.62/52.42 [8193]P140(x81933,x81932,x81931)+~P1(f332(x81933,x81932))+E(f332(f332(f82(a1),f332(f332(f83(a1),x81931),f777(x81931,x81932,x81933))),f776(x81931,x81932,x81933)),x81932)+P1(f332(f332(f232(a1),f775(x81931,x81932,x81933)),f2(a1)))
% 52.62/52.42 [8198]P141(x81983,x81982,x81981)+E(f332(f332(f82(a1),f332(f332(f83(a1),x81981),f779(x81981,x81982,x81983))),f781(x81981,x81982,x81983)),x81982)+~P1(f332(x81983,f2(a1)))+P1(f332(f332(f232(a1),f780(x81981,x81982,x81983)),f2(a1)))
% 52.62/52.42 [8329]P140(x83293,x83292,x83291)+E(x83291,f2(a1))+E(f332(f332(f82(a1),f332(f332(f83(a1),x83291),f778(x83291,x83292,x83293))),f775(x83291,x83292,x83293)),x83292)+E(f332(f332(f82(a1),f332(f332(f83(a1),x83291),f777(x83291,x83292,x83293))),f776(x83291,x83292,x83293)),x83292)
% 52.62/52.42 [8330]P141(x83303,x83302,x83301)+E(x83301,f2(a1))+E(f332(f332(f82(a1),f332(f332(f83(a1),x83301),f783(x83301,x83302,x83303))),f780(x83301,x83302,x83303)),x83302)+E(f332(f332(f82(a1),f332(f332(f83(a1),x83301),f779(x83301,x83302,x83303))),f781(x83301,x83302,x83303)),x83302)
% 52.62/52.42 [8353]P140(x83533,x83532,x83531)+~P1(f332(x83533,x83532))+E(f332(f332(f82(a1),f332(f332(f83(a1),x83531),f778(x83531,x83532,x83533))),f775(x83531,x83532,x83533)),x83532)+E(f332(f332(f82(a1),f332(f332(f83(a1),x83531),f777(x83531,x83532,x83533))),f776(x83531,x83532,x83533)),x83532)
% 52.62/52.42 [8365]P141(x83653,x83652,x83651)+E(f332(f332(f82(a1),f332(f332(f83(a1),x83651),f783(x83651,x83652,x83653))),f780(x83651,x83652,x83653)),x83652)+E(f332(f332(f82(a1),f332(f332(f83(a1),x83651),f779(x83651,x83652,x83653))),f781(x83651,x83652,x83653)),x83652)+~P1(f332(x83653,f2(a1)))
% 52.62/52.42 [8959]~P119(x89591)+~E(x89593,f2(x89591))+~E(x89592,f2(x89591))+P1(f332(f332(f232(x89591),f332(f332(f82(x89591),f332(f332(f83(x89591),x89592),x89592)),f332(f332(f83(x89591),x89593),x89593))),f2(x89591)))
% 52.62/52.42 [9959]~P110(x99591)+~E(x99593,f2(x99591))+~E(x99592,f2(x99591))+P1(f332(f332(f232(x99591),f332(f332(f82(x99591),f332(f332(f242(x99591),x99592),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))),f332(f332(f242(x99591),x99593),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))))),f2(x99591)))
% 52.62/52.42 [4708]~E(x47083,x47081)+~P113(x47082)+E(x47081,f2(x47082))+E(f332(f332(f283(x47082),x47083),x47081),f80(x47082))
% 52.62/52.42 [4759]~P95(x47591)+~E(x47593,f180(x47591))+~E(x47592,f180(x47591))+E(f332(f332(f103(x47591),x47592),x47593),f180(x47591))
% 52.62/52.42 [4760]~P94(x47601)+~E(x47603,f239(x47601))+~E(x47602,f239(x47601))+E(f332(f332(f104(x47601),x47602),x47603),f239(x47601))
% 52.62/52.42 [4846]~P113(x48463)+E(x48461,x48462)+E(x48462,f2(x48463))+~E(f332(f332(f283(x48463),x48461),x48462),f80(x48463))
% 52.62/52.42 [4862]~P134(x48622)+E(x48621,f2(x48622))+E(x48623,f2(x48622))+~E(f332(f332(f83(x48622),x48623),x48621),f2(x48622))
% 52.62/52.42 [4863]~P127(x48632)+E(x48631,f2(x48632))+E(x48633,f2(x48632))+~E(f332(f332(f83(x48632),x48633),x48631),f2(x48632))
% 52.62/52.42 [4864]~P127(x48642)+E(x48641,f2(x48642))+E(x48643,f2(x48642))+~E(f332(f332(f83(x48642),x48643),x48641),f2(x48642))
% 52.62/52.42 [5234]~P111(x52343)+E(x52341,x52342)+E(x52341,f332(f81(x52343),x52342))+~E(f332(f332(f83(x52343),x52341),x52341),f332(f332(f83(x52343),x52342),x52342))
% 52.62/52.42 [5270]~P90(x52701)+E(f332(f81(x52701),x52702),x52703)+~E(f332(f332(f103(x52701),x52702),x52703),f239(x52701))+~E(f332(f332(f104(x52701),x52702),x52703),f180(x52701))
% 52.62/52.42 [5345]~P110(x53453)+E(x53451,x53452)+P1(f332(f332(f233(x53453),x53452),x53451))+P1(f332(f332(f233(x53453),x53451),x53452))
% 52.62/52.42 [5346]~P100(x53463)+E(x53461,x53462)+P1(f332(f332(f233(x53463),x53462),x53461))+P1(f332(f332(f233(x53463),x53461),x53462))
% 52.62/52.42 [5347]~P100(x53473)+E(x53471,x53472)+P1(f332(f332(f233(x53473),x53472),x53471))+P1(f332(f332(f233(x53473),x53471),x53472))
% 52.62/52.42 [5348]~P100(x53483)+E(x53481,x53482)+P1(f332(f332(f233(x53483),x53482),x53481))+P1(f332(f332(f233(x53483),x53481),x53482))
% 52.62/52.42 [5349]~P100(x53493)+E(x53491,x53492)+P1(f332(f332(f233(x53493),x53492),x53491))+P1(f332(f332(f233(x53493),x53491),x53492))
% 52.62/52.42 [5350]~P100(x53503)+E(x53501,x53502)+P1(f332(f332(f233(x53503),x53502),x53501))+P1(f332(f332(f233(x53503),x53501),x53502))
% 52.62/52.42 [5351]~P100(x53513)+E(x53511,x53512)+P1(f332(f332(f233(x53513),x53512),x53511))+P1(f332(f332(f233(x53513),x53511),x53512))
% 52.62/52.42 [5352]~E(x53522,x53523)+~P100(x53521)+P1(f332(f332(f232(x53521),x53522),x53523))+P1(f332(f332(f233(x53521),x53522),x53523))
% 52.62/52.42 [5513]P140(x55132,x55133,x55131)+E(x55131,f2(a1))+P1(f332(f332(f233(a1),x55131),f2(a1)))+P1(f332(f332(f233(a1),f2(a1)),x55131))
% 52.62/52.42 [5514]P141(x55142,x55143,x55141)+E(x55141,f2(a1))+P1(f332(f332(f233(a1),x55141),f2(a1)))+P1(f332(f332(f233(a1),f2(a1)),x55141))
% 52.62/52.42 [5539]E(x55391,x55392)+P1(f332(f332(x55393,x55391),x55392))+P1(f332(f332(f233(a845),x55392),x55391))+P1(f332(f332(f233(a845),x55391),x55392))
% 52.62/52.42 [5598]~P99(x55983)+E(x55981,x55982)+~P1(f332(f332(f232(x55983),x55982),x55981))+P1(f332(f332(f233(x55983),x55982),x55981))
% 52.62/52.42 [5599]~P99(x55993)+E(x55991,x55992)+~P1(f332(f332(f232(x55993),x55991),x55992))+P1(f332(f332(f233(x55993),x55991),x55992))
% 52.62/52.42 [5600]~P99(x56003)+E(x56001,x56002)+~P1(f332(f332(f232(x56003),x56001),x56002))+P1(f332(f332(f233(x56003),x56001),x56002))
% 52.62/52.42 [5601]~P99(x56013)+E(x56011,x56012)+~P1(f332(f332(f232(x56013),x56011),x56012))+P1(f332(f332(f233(x56013),x56011),x56012))
% 52.62/52.42 [5602]~P99(x56023)+E(x56021,x56022)+~P1(f332(f332(f232(x56023),x56021),x56022))+P1(f332(f332(f233(x56023),x56021),x56022))
% 52.62/52.42 [5603]~P99(x56033)+E(x56031,x56032)+~P1(f332(f332(f232(x56033),x56031),x56032))+P1(f332(f332(f233(x56033),x56031),x56032))
% 52.62/52.42 [5604]~P99(x56043)+E(x56041,x56042)+~P1(f332(f332(f232(x56043),x56041),x56042))+P1(f332(f332(f233(x56043),x56041),x56042))
% 52.62/52.42 [5605]~P100(x56053)+E(x56051,x56052)+~P1(f332(f332(f232(x56053),x56051),x56052))+P1(f332(f332(f233(x56053),x56051),x56052))
% 52.62/52.42 [5606]~P100(x56063)+E(x56061,x56062)+~P1(f332(f332(f232(x56063),x56061),x56062))+P1(f332(f332(f233(x56063),x56061),x56062))
% 52.62/52.42 [5718]P140(x57181,x57182,x57183)+~P1(f332(x57181,x57182))+P1(f332(f332(f233(a1),x57183),f2(a1)))+P1(f332(f332(f233(a1),f2(a1)),x57183))
% 52.62/52.42 [5769]P141(x57691,x57692,x57693)+~P1(f332(x57691,f2(a1)))+P1(f332(f332(f233(a1),x57693),f2(a1)))+P1(f332(f332(f233(a1),f2(a1)),x57693))
% 52.62/52.42 [5773]~P93(x57731)+E(f332(f332(f103(x57731),x57732),f12(x57731,x57733)),x57732)+~P1(f332(f64(x57731),x57733))+~P1(f332(f332(f334(x57731),x57732),x57733))
% 52.62/52.42 [5774]~P93(x57741)+E(f332(f332(f104(x57741),x57742),f15(x57741,x57743)),x57742)+~P1(f332(f64(x57741),x57743))+~P1(f332(f332(f334(x57741),x57742),x57743))
% 52.62/52.42 [5807]~P100(x58071)+E(f332(f332(f236(x58071),x58072),f17(x58071,x58073)),f17(x58071,x58073))+~P1(f332(f64(x58071),x58073))+~P1(f332(f332(f334(x58071),x58072),x58073))
% 52.62/52.42 [5808]~P100(x58081)+E(f332(f332(f179(x58081),x58082),f16(x58081,x58083)),f16(x58081,x58083))+~P1(f332(f64(x58081),x58083))+~P1(f332(f332(f334(x58081),x58082),x58083))
% 52.62/52.42 [5809]~P93(x58091)+E(f332(f332(f103(x58091),x58092),f15(x58091,x58093)),f15(x58091,x58093))+~P1(f332(f64(x58091),x58093))+~P1(f332(f332(f334(x58091),x58092),x58093))
% 52.62/52.42 [5810]~P93(x58101)+E(f332(f332(f104(x58101),x58102),f12(x58101,x58103)),f12(x58101,x58103))+~P1(f332(f64(x58101),x58103))+~P1(f332(f332(f334(x58101),x58102),x58103))
% 52.62/52.42 [5847]E(x58471,x58472)+~P99(x58473)+~P1(f332(f332(f232(x58473),x58472),x58471))+~P1(f332(f332(f232(x58473),x58471),x58472))
% 52.62/52.42 [5848]E(x58481,x58482)+~P99(x58483)+~P1(f332(f332(f232(x58483),x58482),x58481))+~P1(f332(f332(f232(x58483),x58481),x58482))
% 52.62/52.42 [5849]E(x58491,x58492)+~P99(x58493)+~P1(f332(f332(f232(x58493),x58492),x58491))+~P1(f332(f332(f232(x58493),x58491),x58492))
% 52.62/52.42 [5850]E(x58501,x58502)+~P99(x58503)+~P1(f332(f332(f232(x58503),x58502),x58501))+~P1(f332(f332(f232(x58503),x58501),x58502))
% 52.62/52.42 [5852]~E(x58521,x58522)+~P100(x58523)+~P1(f332(f332(f233(x58523),x58521),x58522))+~P1(f332(f332(f232(x58523),x58521),x58522))
% 52.62/52.42 [5993]~P103(x59931)+P1(f332(f332(f232(x59931),x59933),x59932))+~P1(f332(f332(f232(x59931),x59932),x59933))+P1(f332(f332(f233(x59931),x59932),x59933))
% 52.62/52.42 [6017]~P100(x60171)+~P1(f332(f64(x60171),x60173))+P1(f332(f332(f232(x60171),x60172),f16(x60171,x60173)))+~P1(f332(f332(f334(x60171),x60172),x60173))
% 52.62/52.42 [6071]~P100(x60711)+E(f332(f332(f236(x60711),x60712),f13(x60711,f179(x60711),x60713)),x60712)+~P1(f332(f64(x60711),x60713))+~P1(f332(f332(f334(x60711),x60712),x60713))
% 52.62/52.42 [6072]~P100(x60721)+E(f332(f332(f179(x60721),x60722),f14(x60721,f236(x60721),x60723)),x60722)+~P1(f332(f64(x60721),x60723))+~P1(f332(f332(f334(x60721),x60722),x60723))
% 52.62/52.42 [6215]E(x62151,x62152)+~E(f332(f332(f3(a845),x62151),x62153),f332(f332(f3(a845),x62152),x62153))+~P1(f332(f332(f232(a845),x62153),x62151))+~P1(f332(f332(f232(a845),x62153),x62152))
% 52.62/52.42 [6243]~P100(x62431)+~P1(f332(f64(x62431),x62432))+~P1(f332(f332(f334(x62431),x62433),x62432))+P1(f332(f332(f232(x62431),f17(x62431,x62432)),x62433))
% 52.62/52.42 [6287]E(x62871,f2(a845))+~P1(f332(f56(x62873,x62871),x62872))+P1(f332(f332(f233(a845),f2(a845)),x62871))+P1(f332(f332(f233(a845),x62871),f332(f250(a845,a845),x62872)))
% 52.62/52.42 [6310]P140(x63102,x63103,x63101)+E(x63101,f2(a1))+P1(f332(f332(f233(a1),x63101),f775(x63101,x63103,x63102)))+P1(f332(f332(f233(a1),f2(a1)),x63101))
% 52.62/52.42 [6311]P141(x63112,x63113,x63111)+E(x63111,f2(a1))+P1(f332(f332(f233(a1),x63111),f780(x63111,x63113,x63112)))+P1(f332(f332(f233(a1),f2(a1)),x63111))
% 52.62/52.42 [6312]~P100(x63121)+E(f332(f332(f236(x63121),x63122),f14(x63121,f236(x63121),x63123)),f14(x63121,f236(x63121),x63123))+~P1(f332(f64(x63121),x63123))+~P1(f332(f332(f334(x63121),x63122),x63123))
% 52.62/52.42 [6313]~P100(x63131)+E(f332(f332(f179(x63131),x63132),f13(x63131,f179(x63131),x63133)),f13(x63131,f179(x63131),x63133))+~P1(f332(f64(x63131),x63133))+~P1(f332(f332(f334(x63131),x63132),x63133))
% 52.62/52.42 [6320]~P1(f332(x63201,x63202))+P1(f332(x63201,f807(x63202,x63201,x63203)))+P1(f332(x63201,f2(a845)))+~P1(f332(f332(f233(a845),x63202),x63203))
% 52.62/52.42 [6358]~P1(f332(f332(f279(a845),x63582),x63581))+~P1(f332(f332(f279(a845),x63581),x63583))+P1(f332(f332(f279(a845),x63581),x63582))+P1(f332(f332(f279(a845),x63582),x63583))
% 52.62/52.42 [6359]~P1(f332(f332(f279(a845),x63593),x63592))+~P1(f332(f332(f279(a845),x63592),x63591))+P1(f332(f332(f279(a845),x63591),x63592))+P1(f332(f332(f279(a845),x63593),x63591))
% 52.62/52.42 [6379]~P1(f332(x63791,x63792))+~P1(f332(f64(x63793),x63792))+P1(f332(x63791,f461(x63791,x63792,x63793)))+P1(f332(x63791,f180(f853(x63793,a839))))
% 52.62/52.42 [6394]~P110(x63941)+~P88(x63941)+P1(f332(f332(f233(x63941),f332(f106(x63941),x63942)),f332(f106(x63941),x63943)))+~P1(f332(f332(f233(a1),x63942),x63943))
% 52.62/52.42 [6395]~P110(x63951)+~P88(x63951)+P1(f332(f332(f232(x63951),f332(f106(x63951),x63952)),f332(f106(x63951),x63953)))+~P1(f332(f332(f232(a1),x63952),x63953))
% 52.62/52.42 [6398]~P1(f332(x63981,x63983))+~P1(f332(f64(x63982),x63983))+P1(f332(f64(x63982),f461(x63981,x63983,x63982)))+P1(f332(x63981,f180(f853(x63982,a839))))
% 52.62/52.42 [6432]P140(x64321,x64322,x64323)+~P1(f332(x64321,x64322))+P1(f332(f332(f233(a1),x64323),f775(x64323,x64322,x64321)))+P1(f332(f332(f233(a1),f2(a1)),x64323))
% 52.62/52.42 [6472]P141(x64721,x64722,x64723)+P1(f332(f332(f233(a1),x64723),f780(x64723,x64722,x64721)))+~P1(f332(x64721,f2(a1)))+P1(f332(f332(f233(a1),f2(a1)),x64723))
% 52.62/52.42 [6500]~P102(x65001)+~P89(x65001)+E(f332(f332(f236(x65001),f332(f106(x65001),x65002)),f332(f106(x65001),x65003)),f332(f106(x65001),x65003))+P1(f332(f332(f232(x65001),f332(f106(x65001),x65002)),f332(f106(x65001),x65003)))
% 52.62/52.42 [6501]~P102(x65011)+~P89(x65011)+E(f332(f332(f179(x65011),f332(f106(x65011),x65012)),f332(f106(x65011),x65013)),f332(f106(x65011),x65012))+P1(f332(f332(f232(x65011),f332(f106(x65011),x65012)),f332(f106(x65011),x65013)))
% 52.62/52.42 [6508]E(x65081,f2(a845))+~P1(f332(f56(x65083,x65081),x65082))+~P1(f332(f332(f233(a845),f2(a845)),x65081))+P1(f332(f332(f232(a845),f2(a845)),f332(f250(a845,a845),x65082)))
% 52.62/52.42 [6514]~P1(f332(f332(f279(a845),x65141),x65143))+~P1(f332(f332(f279(a845),x65142),x65141))+~P1(f332(f332(f279(a845),x65143),x65142))+P1(f332(f332(f279(a845),x65141),x65142))
% 52.62/52.42 [6515]~P1(f332(f332(f279(a845),x65151),x65153))+~P1(f332(f332(f279(a845),x65152),x65151))+P1(f332(f332(f279(a845),x65151),x65152))+~P1(f332(f332(f279(a845),x65153),x65152))
% 52.62/52.42 [6563]P140(x65632,x65633,x65631)+E(x65631,f2(a1))+~P1(f332(x65632,f775(x65631,x65633,x65632)))+P1(f332(f332(f233(a1),f2(a1)),x65631))
% 52.62/52.42 [6564]P141(x65642,x65643,x65641)+E(x65641,f2(a1))+~P1(f332(x65642,f783(x65641,x65643,x65642)))+P1(f332(f332(f233(a1),f2(a1)),x65641))
% 52.62/52.42 [6584]~P9(x65841)+~P89(x65841)+~E(f53(x65841,f332(f106(x65841),x65843),f332(f106(x65841),x65842)),f2(x65841))+P1(f332(f332(f279(x65841),f332(f106(x65841),x65842)),f332(f106(x65841),x65843)))
% 52.62/52.42 [6658]P140(x66581,x66582,x66583)+~P1(f332(x66581,x66582))+~P1(f332(x66581,f775(x66583,x66582,x66581)))+P1(f332(f332(f233(a1),f2(a1)),x66583))
% 52.62/52.42 [6688]P141(x66881,x66882,x66883)+~P1(f332(x66881,f783(x66883,x66882,x66881)))+~P1(f332(x66881,f2(a1)))+P1(f332(f332(f233(a1),f2(a1)),x66883))
% 52.62/52.42 [6699]E(x66991,f2(a845))+~P1(f332(f56(x66993,x66991),x66992))+P1(f332(f332(f232(a845),f332(f250(a845,a845),x66992)),f2(a845)))+P1(f332(f332(f233(a845),f2(a845)),x66991))
% 52.62/52.42 [6804]~P88(x68043)+~P110(x68043)+~P1(f332(f332(f233(x68043),f332(f106(x68043),x68041)),f332(f106(x68043),x68042)))+P1(f332(f332(f233(a1),x68041),x68042))
% 52.62/52.42 [6805]~P88(x68053)+~P110(x68053)+~P1(f332(f332(f232(x68053),f332(f106(x68053),x68051)),f332(f106(x68053),x68052)))+P1(f332(f332(f232(a1),x68051),x68052))
% 52.62/52.42 [6834]~P100(x68341)+~P20(x68341,x68343)+P20(x68341,f332(f332(f140(x68341),x68342),x68343))+~P1(f332(f332(f232(x68341),x68342),f762(x68343,x68342,x68341)))
% 52.62/52.42 [6835]~P100(x68351)+~P20(x68351,x68353)+P20(x68351,f332(f332(f140(x68351),x68352),x68353))+~P1(f332(f332(f232(x68351),x68352),f763(x68353,x68352,x68351)))
% 52.62/52.42 [6908]~P9(x69081)+~P89(x69081)+E(f53(x69081,f332(f106(x69081),x69082),f332(f106(x69081),x69083)),f2(x69081))+~P1(f332(f332(f279(x69081),f332(f106(x69081),x69083)),f332(f106(x69081),x69082)))
% 52.62/52.42 [6922]P140(x69222,x69223,x69221)+E(x69221,f2(a1))+P1(f332(f332(f233(a1),x69221),f2(a1)))+P1(f332(f332(f233(a1),f776(x69221,x69223,x69222)),x69221))
% 52.62/52.42 [6923]P141(x69232,x69233,x69231)+E(x69231,f2(a1))+P1(f332(f332(f233(a1),x69231),f2(a1)))+P1(f332(f332(f233(a1),f781(x69231,x69233,x69232)),x69231))
% 52.62/52.42 [6928]~P100(x69281)+~P89(x69281)+P1(f332(f332(f233(x69281),f332(f106(x69281),x69282)),f332(f106(x69281),x69283)))+P1(f332(f332(f232(x69281),f332(f106(x69281),x69283)),f332(f106(x69281),x69282)))
% 52.62/52.42 [6962]P140(x69622,x69623,x69621)+E(x69621,f2(a1))+P1(f332(f332(f232(a1),f775(x69621,x69623,x69622)),f2(a1)))+P1(f332(f332(f233(a1),f2(a1)),x69621))
% 52.62/52.42 [6963]P141(x69632,x69633,x69631)+E(x69631,f2(a1))+P1(f332(f332(f232(a1),f780(x69631,x69633,x69632)),f2(a1)))+P1(f332(f332(f233(a1),f2(a1)),x69631))
% 52.62/52.42 [6981]~P100(x69811)+~P20(x69811,x69813)+E(f332(f332(f138(x69811,x69811,f7(x69811)),x69812),f151(x69811,x69812,x69813)),x69813)+~P1(f332(f332(f334(x69811),x69812),f332(f158(x69811),x69813)))
% 52.62/52.42 [7031]P140(x70311,x70312,x70313)+~P1(f332(x70311,x70312))+P1(f332(f332(f233(a1),x70313),f2(a1)))+P1(f332(f332(f233(a1),f776(x70313,x70312,x70311)),x70313))
% 52.62/52.42 [7037]~P102(x70371)+~P89(x70371)+E(f332(f332(f236(x70371),f332(f106(x70371),x70372)),f332(f106(x70371),x70373)),f332(f106(x70371),x70372))+~P1(f332(f332(f232(x70371),f332(f106(x70371),x70372)),f332(f106(x70371),x70373)))
% 52.62/52.42 [7038]~P102(x70381)+~P89(x70381)+E(f332(f332(f179(x70381),f332(f106(x70381),x70382)),f332(f106(x70381),x70383)),f332(f106(x70381),x70383))+~P1(f332(f332(f232(x70381),f332(f106(x70381),x70382)),f332(f106(x70381),x70383)))
% 52.62/52.42 [7051]P141(x70511,x70512,x70513)+~P1(f332(x70511,f2(a1)))+P1(f332(f332(f233(a1),x70513),f2(a1)))+P1(f332(f332(f233(a1),f781(x70513,x70512,x70511)),x70513))
% 52.62/52.42 [7061]P140(x70611,x70612,x70613)+~P1(f332(x70611,x70612))+P1(f332(f332(f232(a1),f775(x70613,x70612,x70611)),f2(a1)))+P1(f332(f332(f233(a1),f2(a1)),x70613))
% 52.62/52.42 [7085]P141(x70851,x70852,x70853)+~P1(f332(x70851,f2(a1)))+P1(f332(f332(f232(a1),f780(x70853,x70852,x70851)),f2(a1)))+P1(f332(f332(f233(a1),f2(a1)),x70853))
% 52.62/52.42 [7112]~P1(f332(x71121,x71122))+P1(f332(x71121,f2(a845)))+~P1(f332(f332(f233(a845),x71122),x71123))+P1(f332(f332(f233(a845),f807(x71122,x71121,x71123)),x71123))
% 52.62/52.42 [7129]~P100(x71291)+~P20(x71291,x71293)+P20(x71291,f332(f332(f140(x71291),x71292),x71293))+P1(f332(f332(f334(x71291),f762(x71293,x71292,x71291)),f332(f158(x71291),x71293)))
% 52.62/52.42 [7130]~P100(x71301)+~P20(x71301,x71303)+P20(x71301,f332(f332(f140(x71301),x71302),x71303))+P1(f332(f332(f334(x71301),f763(x71303,x71302,x71301)),f332(f158(x71301),x71303)))
% 52.62/52.42 [7252]~P100(x72521)+~P11(x72521)+~P1(f332(f332(f233(x72521),x72523),f45(x72521,x72522)))+P1(f332(f332(f334(x72521),f670(x72522,x72523,x72521)),x72522))
% 52.62/52.42 [7421]~P100(x74211)+~P11(x74211)+~P1(f332(f332(f233(x74211),f46(x74211,x74213)),x74212))+P1(f332(f332(f334(x74211),f674(x74212,x74213,x74211)),x74213))
% 52.62/52.42 [7422]~P100(x74221)+~P11(x74221)+~P1(f332(f332(f233(x74221),f46(x74221,x74223)),x74222))+P1(f332(f332(f233(x74221),f674(x74222,x74223,x74221)),x74222))
% 52.62/52.42 [7436]P140(x74362,x74363,x74361)+E(x74361,f2(a1))+P1(f332(f332(f233(a1),x74361),f775(x74361,x74363,x74362)))+P1(f332(f332(f233(a1),f776(x74361,x74363,x74362)),x74361))
% 52.62/52.42 [7437]P141(x74372,x74373,x74371)+E(x74371,f2(a1))+P1(f332(f332(f233(a1),x74371),f780(x74371,x74373,x74372)))+P1(f332(f332(f233(a1),f781(x74371,x74373,x74372)),x74371))
% 52.62/52.42 [7533]P140(x75333,x75332,x75331)+E(x75331,f2(a1))+E(f332(f332(f82(a1),f332(f332(f83(a1),x75331),f778(x75331,x75332,x75333))),f775(x75331,x75332,x75333)),x75332)+P1(f332(f332(f233(a1),f2(a1)),x75331))
% 52.62/52.42 [7534]P141(x75343,x75342,x75341)+E(x75341,f2(a1))+E(f332(f332(f82(a1),f332(f332(f83(a1),x75341),f783(x75341,x75342,x75343))),f780(x75341,x75342,x75343)),x75342)+P1(f332(f332(f233(a1),f2(a1)),x75341))
% 52.62/52.42 [7535]~P123(x75351)+~P1(f332(f332(f233(x75351),x75352),f2(x75351)))+P1(f332(f332(f233(x75351),f332(f332(f83(x75351),x75352),x75353)),f2(x75351)))+~P1(f332(f332(f233(x75351),f2(x75351)),x75353))
% 52.62/52.42 [7536]~P123(x75361)+~P1(f332(f332(f233(x75361),x75363),f2(x75361)))+P1(f332(f332(f233(x75361),f332(f332(f83(x75361),x75362),x75363)),f2(x75361)))+~P1(f332(f332(f233(x75361),f2(x75361)),x75362))
% 52.62/52.42 [7537]~P123(x75371)+~P1(f332(f332(f233(x75371),x75372),f2(x75371)))+P1(f332(f332(f233(x75371),f332(f332(f83(x75371),x75372),x75373)),f2(x75371)))+~P1(f332(f332(f233(x75371),f2(x75371)),x75373))
% 52.62/52.42 [7538]~P64(x75381)+~P1(f332(f332(f233(x75381),x75383),f2(x75381)))+P1(f332(f332(f233(x75381),f332(f332(f283(x75381),x75382),x75383)),f2(x75381)))+~P1(f332(f332(f233(x75381),f2(x75381)),x75382))
% 52.62/52.42 [7539]~P64(x75391)+~P1(f332(f332(f233(x75391),x75392),f2(x75391)))+P1(f332(f332(f233(x75391),f332(f332(f283(x75391),x75392),x75393)),f2(x75391)))+~P1(f332(f332(f233(x75391),f2(x75391)),x75393))
% 52.62/52.42 [7540]~P65(x75401)+~P1(f332(f332(f233(x75401),x75403),f2(x75401)))+P1(f332(f332(f233(x75401),f332(f332(f283(x75401),x75402),x75403)),f2(x75401)))+~P1(f332(f332(f233(x75401),f2(x75401)),x75402))
% 52.62/52.42 [7541]~P65(x75411)+~P1(f332(f332(f233(x75411),x75412),f2(x75411)))+P1(f332(f332(f233(x75411),f332(f332(f283(x75411),x75412),x75413)),f2(x75411)))+~P1(f332(f332(f233(x75411),f2(x75411)),x75413))
% 52.62/52.42 [7542]~P128(x75421)+~P1(f332(f332(f232(x75421),x75422),f2(x75421)))+P1(f332(f332(f232(x75421),f332(f332(f83(x75421),x75422),x75423)),f2(x75421)))+~P1(f332(f332(f232(x75421),f2(x75421)),x75423))
% 52.62/52.42 [7543]~P119(x75431)+~P1(f332(f332(f232(x75431),x75433),f2(x75431)))+P1(f332(f332(f232(x75431),f332(f332(f83(x75431),x75432),x75433)),f2(x75431)))+~P1(f332(f332(f232(x75431),f2(x75431)),x75432))
% 52.62/52.42 [7544]~P119(x75441)+~P1(f332(f332(f232(x75441),x75442),f2(x75441)))+P1(f332(f332(f232(x75441),f332(f332(f83(x75441),x75442),x75443)),f2(x75441)))+~P1(f332(f332(f232(x75441),f2(x75441)),x75443))
% 52.62/52.42 [7545]~P128(x75451)+~P1(f332(f332(f232(x75451),x75453),f2(x75451)))+P1(f332(f332(f232(x75451),f332(f332(f83(x75451),x75452),x75453)),f2(x75451)))+~P1(f332(f332(f232(x75451),f2(x75451)),x75452))
% 52.62/52.42 [7546]~P128(x75461)+~P1(f332(f332(f232(x75461),x75463),f2(x75461)))+P1(f332(f332(f232(x75461),f332(f332(f83(x75461),x75462),x75463)),f2(x75461)))+~P1(f332(f332(f232(x75461),f2(x75461)),x75462))
% 52.62/52.42 [7547]~P128(x75471)+~P1(f332(f332(f232(x75471),x75472),f2(x75471)))+P1(f332(f332(f232(x75471),f332(f332(f83(x75471),x75472),x75473)),f2(x75471)))+~P1(f332(f332(f232(x75471),f2(x75471)),x75473))
% 52.62/52.42 [7548]~P128(x75481)+~P1(f332(f332(f232(x75481),x75482),f2(x75481)))+P1(f332(f332(f232(x75481),f332(f332(f83(x75481),x75482),x75483)),f2(x75481)))+~P1(f332(f332(f232(x75481),f2(x75481)),x75483))
% 52.62/52.42 [7549]~P64(x75491)+~P1(f332(f332(f232(x75491),x75493),f2(x75491)))+P1(f332(f332(f232(x75491),f332(f332(f283(x75491),x75492),x75493)),f2(x75491)))+~P1(f332(f332(f232(x75491),f2(x75491)),x75492))
% 52.62/52.42 [7550]~P64(x75501)+~P1(f332(f332(f232(x75501),x75502),f2(x75501)))+P1(f332(f332(f232(x75501),f332(f332(f283(x75501),x75502),x75503)),f2(x75501)))+~P1(f332(f332(f232(x75501),f2(x75501)),x75503))
% 52.62/52.42 [7551]~P65(x75511)+~P1(f332(f332(f233(x75511),x75513),f2(x75511)))+P1(f332(f332(f232(x75511),f332(f332(f283(x75511),x75512),x75513)),f2(x75511)))+~P1(f332(f332(f232(x75511),f2(x75511)),x75512))
% 52.62/52.42 [7552]~P65(x75521)+~P1(f332(f332(f232(x75521),x75522),f2(x75521)))+P1(f332(f332(f232(x75521),f332(f332(f283(x75521),x75522),x75523)),f2(x75521)))+~P1(f332(f332(f233(x75521),f2(x75521)),x75523))
% 52.62/52.42 [7568]P140(x75681,x75682,x75683)+~P1(f332(x75681,x75682))+P1(f332(f332(f233(a1),x75683),f775(x75683,x75682,x75681)))+P1(f332(f332(f233(a1),f776(x75683,x75682,x75681)),x75683))
% 52.62/52.42 [7581]P141(x75811,x75812,x75813)+P1(f332(f332(f233(a1),x75813),f780(x75813,x75812,x75811)))+~P1(f332(x75811,f2(a1)))+P1(f332(f332(f233(a1),f781(x75813,x75812,x75811)),x75813))
% 52.62/52.42 [7633]P140(x76332,x76333,x76331)+E(x76331,f2(a1))+~P1(f332(x76332,f775(x76331,x76333,x76332)))+P1(f332(f332(f233(a1),f776(x76331,x76333,x76332)),x76331))
% 52.62/52.42 [7634]P141(x76342,x76343,x76341)+E(x76341,f2(a1))+~P1(f332(x76342,f783(x76341,x76343,x76342)))+P1(f332(f332(f233(a1),f781(x76341,x76343,x76342)),x76341))
% 52.62/52.42 [7643]P140(x76433,x76432,x76431)+~P1(f332(x76433,x76432))+E(f332(f332(f82(a1),f332(f332(f83(a1),x76431),f778(x76431,x76432,x76433))),f775(x76431,x76432,x76433)),x76432)+P1(f332(f332(f233(a1),f2(a1)),x76431))
% 52.62/52.42 [7661]P141(x76613,x76612,x76611)+E(f332(f332(f82(a1),f332(f332(f83(a1),x76611),f783(x76611,x76612,x76613))),f780(x76611,x76612,x76613)),x76612)+~P1(f332(x76613,f2(a1)))+P1(f332(f332(f233(a1),f2(a1)),x76611))
% 52.62/52.42 [7685]~P1(f332(x76851,x76853))+~P1(f332(f64(x76852),x76853))+P1(f332(f332(f334(x76852),f483(x76851,x76853,x76852)),f461(x76851,x76853,x76852)))+P1(f332(x76851,f180(f853(x76852,a839))))
% 52.62/52.42 [7695]P140(x76951,x76952,x76953)+~P1(f332(x76951,x76952))+~P1(f332(x76951,f775(x76953,x76952,x76951)))+P1(f332(f332(f233(a1),f776(x76953,x76952,x76951)),x76953))
% 52.62/52.42 [7701]P141(x77011,x77012,x77013)+~P1(f332(x77011,f783(x77013,x77012,x77011)))+~P1(f332(x77011,f2(a1)))+P1(f332(f332(f233(a1),f781(x77013,x77012,x77011)),x77013))
% 52.62/52.42 [7773]~P89(x77731)+~P100(x77731)+~P1(f332(f332(f233(x77731),f332(f106(x77731),x77732)),f332(f106(x77731),x77733)))+~P1(f332(f332(f232(x77731),f332(f106(x77731),x77733)),f332(f106(x77731),x77732)))
% 52.62/52.42 [7809]~P64(x78091)+~P1(f332(f332(f233(x78091),f332(f332(f283(x78091),x78093),x78092)),f2(x78091)))+P1(f332(f332(f233(x78091),x78092),f2(x78091)))+P1(f332(f332(f233(x78091),f2(x78091)),x78092))
% 52.62/52.42 [7810]~P64(x78101)+~P1(f332(f332(f233(x78101),f332(f332(f283(x78101),x78102),x78103)),f2(x78101)))+P1(f332(f332(f233(x78101),x78102),f2(x78101)))+P1(f332(f332(f233(x78101),f2(x78101)),x78102))
% 52.62/52.42 [7811]~P119(x78111)+~P1(f332(f332(f232(x78111),f332(f332(f83(x78111),x78113),x78112)),f2(x78111)))+P1(f332(f332(f232(x78111),x78112),f2(x78111)))+P1(f332(f332(f232(x78111),f2(x78111)),x78112))
% 52.62/52.42 [7812]~P119(x78121)+~P1(f332(f332(f232(x78121),f332(f332(f83(x78121),x78122),x78123)),f2(x78121)))+P1(f332(f332(f232(x78121),x78122),f2(x78121)))+P1(f332(f332(f232(x78121),f2(x78121)),x78122))
% 52.62/52.42 [7813]~P64(x78131)+~P1(f332(f332(f232(x78131),f332(f332(f283(x78131),x78133),x78132)),f2(x78131)))+P1(f332(f332(f232(x78131),x78132),f2(x78131)))+P1(f332(f332(f232(x78131),f2(x78131)),x78132))
% 52.62/52.42 [7814]~P64(x78141)+~P1(f332(f332(f232(x78141),f332(f332(f283(x78141),x78142),x78143)),f2(x78141)))+P1(f332(f332(f232(x78141),x78142),f2(x78141)))+P1(f332(f332(f232(x78141),f2(x78141)),x78142))
% 52.62/52.42 [7840]~P64(x78401)+~P1(f332(f332(f233(x78401),f332(f332(f283(x78401),x78402),x78403)),f2(x78401)))+P1(f332(f332(f233(x78401),f2(x78401)),x78402))+P1(f332(f332(f233(x78401),f2(x78401)),x78403))
% 52.62/52.42 [7841]~P119(x78411)+~P1(f332(f332(f232(x78411),f332(f332(f83(x78411),x78412),x78413)),f2(x78411)))+P1(f332(f332(f232(x78411),f2(x78411)),x78412))+P1(f332(f332(f232(x78411),f2(x78411)),x78413))
% 52.62/52.42 [7842]~P64(x78421)+~P1(f332(f332(f232(x78421),f332(f332(f283(x78421),x78422),x78423)),f2(x78421)))+P1(f332(f332(f232(x78421),f2(x78421)),x78422))+P1(f332(f332(f232(x78421),f2(x78421)),x78423))
% 52.62/52.42 [7861]P140(x78612,x78613,x78611)+E(x78611,f2(a1))+P1(f332(f332(f232(a1),f775(x78611,x78613,x78612)),f2(a1)))+P1(f332(f332(f233(a1),f776(x78611,x78613,x78612)),x78611))
% 52.62/52.42 [7862]P141(x78622,x78623,x78621)+E(x78621,f2(a1))+P1(f332(f332(f232(a1),f780(x78621,x78623,x78622)),f2(a1)))+P1(f332(f332(f233(a1),f781(x78621,x78623,x78622)),x78621))
% 52.62/52.42 [7868]~P117(x78681)+~P1(f332(f332(f233(x78681),x78682),f80(x78681)))+P1(f332(f332(f233(x78681),f332(f332(f242(x78681),x78682),f332(a114,x78683))),f80(x78681)))+~P1(f332(f332(f233(x78681),f2(x78681)),x78682))
% 52.62/52.42 [7922]~P100(x79221)+~E(x79223,f115(x79221))+~P20(x79221,f332(f142(x79221),x79223))+E(f332(f132(x79221,x79221,f332(f9(x79221,x79221,x79221),f179(x79221)),x79222),f332(f142(x79221),x79223)),x79222)
% 52.62/52.42 [7924]P140(x79241,x79242,x79243)+~P1(f332(x79241,x79242))+P1(f332(f332(f232(a1),f775(x79243,x79242,x79241)),f2(a1)))+P1(f332(f332(f233(a1),f776(x79243,x79242,x79241)),x79243))
% 52.62/52.42 [7936]P141(x79361,x79362,x79363)+~P1(f332(x79361,f2(a1)))+P1(f332(f332(f232(a1),f780(x79363,x79362,x79361)),f2(a1)))+P1(f332(f332(f233(a1),f781(x79363,x79362,x79361)),x79363))
% 52.62/52.42 [8149]P140(x81493,x81492,x81491)+E(x81491,f2(a1))+E(f332(f332(f82(a1),f332(f332(f83(a1),x81491),f778(x81491,x81492,x81493))),f775(x81491,x81492,x81493)),x81492)+P1(f332(f332(f233(a1),f776(x81491,x81492,x81493)),x81491))
% 52.62/52.42 [8150]P141(x81503,x81502,x81501)+E(x81501,f2(a1))+E(f332(f332(f82(a1),f332(f332(f83(a1),x81501),f783(x81501,x81502,x81503))),f780(x81501,x81502,x81503)),x81502)+P1(f332(f332(f233(a1),f781(x81501,x81502,x81503)),x81501))
% 52.62/52.42 [8185]P140(x81853,x81852,x81851)+~P1(f332(x81853,x81852))+E(f332(f332(f82(a1),f332(f332(f83(a1),x81851),f778(x81851,x81852,x81853))),f775(x81851,x81852,x81853)),x81852)+P1(f332(f332(f233(a1),f776(x81851,x81852,x81853)),x81851))
% 52.62/52.42 [8186]~P4(x81861)+~P70(x81861)+~P40(x81863)+E(f332(f332(f8(a845,x81861),f332(f332(f10(a1,x81861,a845),x81862),f102(a1))),f332(f303(a1,a845,a107),x81863)),f332(f332(f8(a1,x81861),x81862),x81863))
% 52.62/52.42 [8187]~P4(x81871)+~P70(x81871)+~P40(x81873)+E(f332(f332(f11(a845,x81871),f332(f332(f10(a1,x81871,a845),x81872),f102(a1))),f332(f303(a1,a845,a107),x81873)),f332(f332(f11(a1,x81871),x81872),x81873))
% 52.62/52.42 [8195]P141(x81953,x81952,x81951)+E(f332(f332(f82(a1),f332(f332(f83(a1),x81951),f783(x81951,x81952,x81953))),f780(x81951,x81952,x81953)),x81952)+~P1(f332(x81953,f2(a1)))+P1(f332(f332(f233(a1),f781(x81951,x81952,x81953)),x81951))
% 52.62/52.42 [8213]~E(x82132,f2(a845))+~E(f332(f240(a845,a845),x82133),f2(a845))+~E(x82131,f332(f332(f82(a845),f332(f332(f83(a845),f332(f240(a845,a845),x82133)),x82132)),f332(f250(a845,a845),x82133)))+P1(f332(f56(x82131,x82132),x82133))
% 52.62/52.42 [9061]P1(f332(f332(f232(a1),x90611),f2(a1)))+~P1(f332(f332(f233(a1),f332(f332(f82(a1),f332(f332(f83(a1),x90612),x90611)),x90613)),f2(a1)))+~P1(f332(f332(f233(a1),f2(a1)),x90612))+~P1(f332(f332(f232(a1),f2(a1)),x90613))
% 52.62/52.42 [5667]~P93(x56672)+E(x56671,f180(f853(x56672,a839)))+~P1(f332(f64(x56672),x56671))+E(f15(x56672,f332(f332(f302(x56672),x56673),x56671)),f332(f332(f103(x56672),x56673),f15(x56672,x56671)))
% 52.62/52.42 [5668]~P100(x56682)+E(x56681,f180(f853(x56682,a839)))+~P1(f332(f64(x56682),x56681))+E(f16(x56682,f332(f332(f302(x56682),x56683),x56681)),f332(f332(f179(x56682),x56683),f16(x56682,x56681)))
% 52.62/52.42 [5669]~P100(x56692)+E(x56691,f180(f853(x56692,a839)))+~P1(f332(f64(x56692),x56691))+E(f17(x56692,f332(f332(f302(x56692),x56693),x56691)),f332(f332(f236(x56692),x56693),f17(x56692,x56691)))
% 52.62/52.42 [5670]~P93(x56702)+E(x56701,f180(f853(x56702,a839)))+~P1(f332(f64(x56702),x56701))+E(f12(x56702,f332(f332(f302(x56702),x56703),x56701)),f332(f332(f104(x56702),x56703),f12(x56702,x56701)))
% 52.62/52.42 [5990]~P119(x59901)+~E(x59903,f2(x59901))+~E(x59902,f2(x59901))+E(f332(f332(f82(x59901),f332(f332(f83(x59901),x59902),x59902)),f332(f332(f83(x59901),x59903),x59903)),f2(x59901))
% 52.62/52.42 [6065]~P91(x60652)+E(x60651,f180(f853(x60652,a839)))+~P1(f332(f64(x60652),x60651))+E(f332(f66(x60652,f83(x60652)),f332(f332(f302(x60652),x60653),x60651)),f332(f332(f83(x60652),x60653),f332(f66(x60652,f83(x60652)),x60651)))
% 52.62/52.42 [6193]~P100(x61932)+E(x61931,f180(f853(x61932,a839)))+~P1(f332(f64(x61932),x61931))+E(f13(x61932,f179(x61932),f332(f332(f302(x61932),x61933),x61931)),f332(f332(f179(x61932),x61933),f13(x61932,f179(x61932),x61931)))
% 52.62/52.42 [6194]~P100(x61942)+E(x61941,f180(f853(x61942,a839)))+~P1(f332(f64(x61942),x61941))+E(f14(x61942,f236(x61942),f332(f332(f302(x61942),x61943),x61941)),f332(f332(f236(x61942),x61943),f14(x61942,f236(x61942),x61941)))
% 52.62/52.42 [6605]~P93(x66051)+~P1(f332(f64(x66051),x66053))+E(f332(f332(f67(x66051,x66051,f103(x66051)),x66052),x66053),f15(x66051,f332(f332(f302(x66051),x66052),x66053)))+P1(f332(f332(f334(x66051),x66052),x66053))
% 52.62/52.42 [6606]~P100(x66061)+~P1(f332(f64(x66061),x66063))+E(f332(f332(f67(x66061,x66061,f179(x66061)),x66062),x66063),f16(x66061,f332(f332(f302(x66061),x66062),x66063)))+P1(f332(f332(f334(x66061),x66062),x66063))
% 52.62/52.42 [6607]~P100(x66071)+~P1(f332(f64(x66071),x66073))+E(f332(f332(f67(x66071,x66071,f236(x66071)),x66072),x66073),f17(x66071,f332(f332(f302(x66071),x66072),x66073)))+P1(f332(f332(f334(x66071),x66072),x66073))
% 52.62/52.42 [6608]~P93(x66081)+~P1(f332(f64(x66081),x66083))+E(f332(f332(f67(x66081,x66081,f104(x66081)),x66082),x66083),f12(x66081,f332(f332(f302(x66081),x66082),x66083)))+P1(f332(f332(f334(x66081),x66082),x66083))
% 52.62/52.42 [6723]~P66(x67231)+~P1(f332(f64(x67231),x67233))+E(f332(f66(x67231,f83(x67231)),f332(f332(f302(x67231),x67232),x67233)),f332(f332(f67(x67231,x67231,f83(x67231)),x67232),x67233))+P1(f332(f332(f334(x67231),x67232),x67233))
% 52.62/52.42 [6741]~P100(x67411)+~P1(f332(f64(x67411),x67413))+E(f13(x67411,f179(x67411),f332(f332(f302(x67411),x67412),x67413)),f332(f332(f67(x67411,x67411,f179(x67411)),x67412),x67413))+P1(f332(f332(f334(x67411),x67412),x67413))
% 52.62/52.42 [6742]~P100(x67421)+~P1(f332(f64(x67421),x67423))+E(f14(x67421,f236(x67421),f332(f332(f302(x67421),x67422),x67423)),f332(f332(f67(x67421,x67421,f236(x67421)),x67422),x67423))+P1(f332(f332(f334(x67421),x67422),x67423))
% 52.62/52.42 [6809]~E(f332(f332(f82(a1),x68092),f332(f332(f83(a1),x68093),x68091)),x68093)+~P1(f332(f332(f233(a1),f2(a1)),x68093))+P1(f332(f332(f232(a1),f80(a1)),x68091))+~P1(f332(f332(f233(a1),x68092),x68093))
% 52.62/52.42 [6840]~E(f332(f332(f82(a1),x68402),f332(f332(f83(a1),x68403),x68401)),x68403)+P1(f332(f332(f232(a1),x68401),f80(a1)))+~P1(f332(f332(f233(a1),f2(a1)),x68403))+~P1(f332(f332(f232(a1),f2(a1)),x68402))
% 52.62/52.42 [6858]E(x68581,f2(a845))+~P1(f332(f56(x68583,x68581),x68582))+~P1(f332(f332(f233(a845),f2(a845)),x68581))+P1(f332(f332(f233(a845),f332(f250(a845,a845),x68582)),x68581))
% 52.62/52.42 [6887]~P132(x68871)+~P1(f332(f332(f232(x68871),x68872),f2(x68871)))+~P1(f332(f332(f232(x68871),x68873),f2(x68871)))+E(f332(f332(f83(x68871),f332(f77(x68871),x68872)),f332(f77(x68871),x68873)),f332(f77(x68871),f332(f332(f83(x68871),x68872),x68873)))
% 52.62/52.42 [6939]~P132(x69391)+~P1(f332(f332(f232(x69391),x69392),f2(x69391)))+E(f332(f332(f83(x69391),f332(f77(x69391),x69392)),f332(f77(x69391),x69393)),f332(f77(x69391),f332(f332(f83(x69391),x69392),x69393)))+~P1(f332(f332(f232(x69391),f2(x69391)),x69393))
% 52.62/52.42 [6940]~P132(x69401)+~P1(f332(f332(f232(x69401),x69403),f2(x69401)))+E(f332(f332(f83(x69401),f332(f77(x69401),x69402)),f332(f77(x69401),x69403)),f332(f77(x69401),f332(f332(f83(x69401),x69402),x69403)))+~P1(f332(f332(f232(x69401),f2(x69401)),x69402))
% 52.62/52.42 [6990]~P132(x69901)+E(f332(f332(f83(x69901),f332(f77(x69901),x69902)),f332(f77(x69901),x69903)),f332(f77(x69901),f332(f332(f83(x69901),x69902),x69903)))+~P1(f332(f332(f232(x69901),f2(x69901)),x69902))+~P1(f332(f332(f232(x69901),f2(x69901)),x69903))
% 52.62/52.42 [7008]~P119(x70081)+~P1(f332(f332(f233(x70081),x70083),f2(x70081)))+~P1(f332(f332(f233(x70081),x70082),f2(x70081)))+P1(f332(f332(f233(x70081),f2(x70081)),f332(f332(f83(x70081),x70082),x70083)))
% 52.62/52.42 [7009]~P64(x70091)+~P1(f332(f332(f233(x70091),x70093),f2(x70091)))+~P1(f332(f332(f233(x70091),x70092),f2(x70091)))+P1(f332(f332(f233(x70091),f2(x70091)),f332(f332(f283(x70091),x70092),x70093)))
% 52.62/52.42 [7010]~P65(x70101)+~P1(f332(f332(f233(x70101),x70103),f2(x70101)))+~P1(f332(f332(f233(x70101),x70102),f2(x70101)))+P1(f332(f332(f233(x70101),f2(x70101)),f332(f332(f283(x70101),x70102),x70103)))
% 52.62/52.42 [7011]~P119(x70111)+~P1(f332(f332(f232(x70111),x70113),f2(x70111)))+~P1(f332(f332(f232(x70111),x70112),f2(x70111)))+P1(f332(f332(f232(x70111),f2(x70111)),f332(f332(f83(x70111),x70112),x70113)))
% 52.62/52.42 [7012]~P129(x70121)+~P1(f332(f332(f232(x70121),x70123),f2(x70121)))+~P1(f332(f332(f232(x70121),x70122),f2(x70121)))+P1(f332(f332(f232(x70121),f2(x70121)),f332(f332(f83(x70121),x70122),x70123)))
% 52.62/52.42 [7013]~P129(x70131)+~P1(f332(f332(f232(x70131),x70133),f2(x70131)))+~P1(f332(f332(f232(x70131),x70132),f2(x70131)))+P1(f332(f332(f232(x70131),f2(x70131)),f332(f332(f83(x70131),x70132),x70133)))
% 52.62/52.42 [7014]~P64(x70141)+~P1(f332(f332(f232(x70141),x70143),f2(x70141)))+~P1(f332(f332(f232(x70141),x70142),f2(x70141)))+P1(f332(f332(f232(x70141),f2(x70141)),f332(f332(f283(x70141),x70142),x70143)))
% 52.62/52.42 [7015]~P65(x70151)+~P1(f332(f332(f233(x70151),x70153),f2(x70151)))+~P1(f332(f332(f232(x70151),x70152),f2(x70151)))+P1(f332(f332(f232(x70151),f2(x70151)),f332(f332(f283(x70151),x70152),x70153)))
% 52.62/52.42 [7016]~P117(x70161)+~P1(f332(f332(f233(a845),f2(a845)),x70163))+~P1(f332(f332(f233(x70161),f80(x70161)),x70162))+P1(f332(f332(f233(x70161),f80(x70161)),f332(f332(f242(x70161),x70162),x70163)))
% 52.62/52.42 [7113]~P82(x71131)+~P1(f332(f332(f233(x71131),f2(x71131)),x71133))+~P1(f332(f332(f233(x71131),f2(x71131)),x71132))+P1(f332(f332(f233(x71131),f2(x71131)),f332(f332(f82(x71131),x71132),x71133)))
% 52.62/52.42 [7114]~P82(x71141)+~P1(f332(f332(f232(x71141),f2(x71141)),x71142))+~P1(f332(f332(f233(x71141),f2(x71141)),x71143))+P1(f332(f332(f233(x71141),f2(x71141)),f332(f332(f82(x71141),x71142),x71143)))
% 52.62/52.42 [7115]~P82(x71151)+~P1(f332(f332(f232(x71151),f2(x71151)),x71153))+~P1(f332(f332(f233(x71151),f2(x71151)),x71152))+P1(f332(f332(f233(x71151),f2(x71151)),f332(f332(f82(x71151),x71152),x71153)))
% 52.62/52.42 [7116]~P123(x71161)+~P1(f332(f332(f233(x71161),f2(x71161)),x71163))+~P1(f332(f332(f233(x71161),f2(x71161)),x71162))+P1(f332(f332(f233(x71161),f2(x71161)),f332(f332(f83(x71161),x71162),x71163)))
% 52.62/52.42 [7117]~P64(x71171)+~P1(f332(f332(f233(x71171),f2(x71171)),x71173))+~P1(f332(f332(f233(x71171),f2(x71171)),x71172))+P1(f332(f332(f233(x71171),f2(x71171)),f332(f332(f283(x71171),x71172),x71173)))
% 52.62/52.42 [7118]~P65(x71181)+~P1(f332(f332(f233(x71181),f2(x71181)),x71183))+~P1(f332(f332(f233(x71181),f2(x71181)),x71182))+P1(f332(f332(f233(x71181),f2(x71181)),f332(f332(f283(x71181),x71182),x71183)))
% 52.62/52.42 [7119]~P117(x71191)+~P1(f332(f332(f233(x71191),f80(x71191)),x71193))+~P1(f332(f332(f233(x71191),f80(x71191)),x71192))+P1(f332(f332(f233(x71191),f80(x71191)),f332(f332(f83(x71191),x71192),x71193)))
% 52.62/52.42 [7120]~P82(x71201)+~P1(f332(f332(f232(x71201),f2(x71201)),x71203))+~P1(f332(f332(f232(x71201),f2(x71201)),x71202))+P1(f332(f332(f232(x71201),f2(x71201)),f332(f332(f82(x71201),x71202),x71203)))
% 52.62/52.42 [7121]~P119(x71211)+~P1(f332(f332(f232(x71211),f2(x71211)),x71213))+~P1(f332(f332(f232(x71211),f2(x71211)),x71212))+P1(f332(f332(f232(x71211),f2(x71211)),f332(f332(f83(x71211),x71212),x71213)))
% 52.62/52.42 [7122]~P128(x71221)+~P1(f332(f332(f232(x71221),f2(x71221)),x71223))+~P1(f332(f332(f232(x71221),f2(x71221)),x71222))+P1(f332(f332(f232(x71221),f2(x71221)),f332(f332(f83(x71221),x71222),x71223)))
% 52.62/52.42 [7123]~P129(x71231)+~P1(f332(f332(f232(x71231),f2(x71231)),x71233))+~P1(f332(f332(f232(x71231),f2(x71231)),x71232))+P1(f332(f332(f232(x71231),f2(x71231)),f332(f332(f83(x71231),x71232),x71233)))
% 52.62/52.42 [7124]~P64(x71241)+~P1(f332(f332(f232(x71241),f2(x71241)),x71243))+~P1(f332(f332(f232(x71241),f2(x71241)),x71242))+P1(f332(f332(f232(x71241),f2(x71241)),f332(f332(f283(x71241),x71242),x71243)))
% 52.62/52.42 [7125]~P65(x71251)+~P1(f332(f332(f233(x71251),f2(x71251)),x71253))+~P1(f332(f332(f232(x71251),f2(x71251)),x71252))+P1(f332(f332(f232(x71251),f2(x71251)),f332(f332(f283(x71251),x71252),x71253)))
% 52.62/52.42 [7203]~P93(x72031)+~P1(f332(f64(x72031),x72033))+E(f15(x72031,f332(f332(f302(x72031),x72032),x72033)),x72032)+~E(f332(f332(f3(f853(x72031,a839)),x72033),f332(f332(f302(x72031),x72032),f180(f853(x72031,a839)))),f180(f853(x72031,a839)))
% 52.62/52.42 [7204]~P100(x72041)+~P1(f332(f64(x72041),x72043))+E(f16(x72041,f332(f332(f302(x72041),x72042),x72043)),x72042)+~E(f332(f332(f3(f853(x72041,a839)),x72043),f332(f332(f302(x72041),x72042),f180(f853(x72041,a839)))),f180(f853(x72041,a839)))
% 52.62/52.42 [7205]~P100(x72051)+~P1(f332(f64(x72051),x72053))+E(f17(x72051,f332(f332(f302(x72051),x72052),x72053)),x72052)+~E(f332(f332(f3(f853(x72051,a839)),x72053),f332(f332(f302(x72051),x72052),f180(f853(x72051,a839)))),f180(f853(x72051,a839)))
% 52.62/52.42 [7206]~P93(x72061)+~P1(f332(f64(x72061),x72063))+E(f12(x72061,f332(f332(f302(x72061),x72062),x72063)),x72062)+~E(f332(f332(f3(f853(x72061,a839)),x72063),f332(f332(f302(x72061),x72062),f180(f853(x72061,a839)))),f180(f853(x72061,a839)))
% 52.62/52.42 [7207]~P64(x72071)+P1(f332(f332(f233(x72071),x72072),f2(x72071)))+P1(f332(f332(f233(x72071),f2(x72071)),x72073))+~P1(f332(f332(f233(x72071),f2(x72071)),f332(f332(f283(x72071),x72073),x72072)))
% 52.62/52.42 [7208]~P64(x72081)+P1(f332(f332(f233(x72081),x72082),f2(x72081)))+P1(f332(f332(f233(x72081),f2(x72081)),x72083))+~P1(f332(f332(f233(x72081),f2(x72081)),f332(f332(f283(x72081),x72082),x72083)))
% 52.62/52.42 [7209]~P64(x72091)+P1(f332(f332(f233(x72091),x72092),f2(x72091)))+P1(f332(f332(f233(x72091),f2(x72091)),x72092))+~P1(f332(f332(f233(x72091),f2(x72091)),f332(f332(f283(x72091),x72093),x72092)))
% 52.62/52.42 [7210]~P64(x72101)+P1(f332(f332(f233(x72101),x72102),f2(x72101)))+P1(f332(f332(f233(x72101),f2(x72101)),x72102))+~P1(f332(f332(f233(x72101),f2(x72101)),f332(f332(f283(x72101),x72102),x72103)))
% 52.62/52.42 [7211]~P119(x72111)+P1(f332(f332(f232(x72111),x72112),f2(x72111)))+P1(f332(f332(f232(x72111),f2(x72111)),x72113))+~P1(f332(f332(f232(x72111),f2(x72111)),f332(f332(f83(x72111),x72113),x72112)))
% 52.62/52.42 [7212]~P119(x72121)+P1(f332(f332(f232(x72121),x72122),f2(x72121)))+P1(f332(f332(f232(x72121),f2(x72121)),x72123))+~P1(f332(f332(f232(x72121),f2(x72121)),f332(f332(f83(x72121),x72122),x72123)))
% 52.62/52.42 [7213]~P64(x72131)+P1(f332(f332(f232(x72131),x72132),f2(x72131)))+P1(f332(f332(f232(x72131),f2(x72131)),x72133))+~P1(f332(f332(f232(x72131),f2(x72131)),f332(f332(f283(x72131),x72133),x72132)))
% 52.62/52.42 [7214]~P64(x72141)+P1(f332(f332(f232(x72141),x72142),f2(x72141)))+P1(f332(f332(f232(x72141),f2(x72141)),x72143))+~P1(f332(f332(f232(x72141),f2(x72141)),f332(f332(f283(x72141),x72142),x72143)))
% 52.62/52.42 [7215]~P119(x72151)+P1(f332(f332(f232(x72151),x72152),f2(x72151)))+P1(f332(f332(f232(x72151),f2(x72151)),x72152))+~P1(f332(f332(f232(x72151),f2(x72151)),f332(f332(f83(x72151),x72153),x72152)))
% 52.62/52.42 [7216]~P119(x72161)+P1(f332(f332(f232(x72161),x72162),f2(x72161)))+P1(f332(f332(f232(x72161),f2(x72161)),x72162))+~P1(f332(f332(f232(x72161),f2(x72161)),f332(f332(f83(x72161),x72162),x72163)))
% 52.62/52.42 [7217]~P64(x72171)+P1(f332(f332(f232(x72171),x72172),f2(x72171)))+P1(f332(f332(f232(x72171),f2(x72171)),x72172))+~P1(f332(f332(f232(x72171),f2(x72171)),f332(f332(f283(x72171),x72173),x72172)))
% 52.62/52.42 [7218]~P64(x72181)+P1(f332(f332(f232(x72181),x72182),f2(x72181)))+P1(f332(f332(f232(x72181),f2(x72181)),x72182))+~P1(f332(f332(f232(x72181),f2(x72181)),f332(f332(f283(x72181),x72182),x72183)))
% 52.62/52.42 [7303]~P1(f332(f332(f279(a845),x73031),x73033))+P1(f332(f332(f279(a845),x73031),x73032))+~P1(f332(f332(f232(a845),x73032),x73033))+~P1(f332(f332(f279(a845),x73031),f332(f332(f3(a845),x73033),x73032)))
% 52.62/52.42 [7304]~P1(f332(f332(f279(a845),x73041),x73043))+P1(f332(f332(f279(a845),x73041),x73042))+~P1(f332(f332(f232(a845),x73043),x73042))+~P1(f332(f332(f279(a845),x73041),f332(f332(f3(a845),x73042),x73043)))
% 52.62/52.42 [7319]~E(f332(f332(f104(f853(x73191,a839)),f332(f158(x73191),x73192)),f332(f158(x73191),x73193)),f180(f853(x73191,a839)))+~P1(f332(f127(x73191),x73193))+~P1(f332(f127(x73191),x73192))+P1(f332(f127(x73191),f332(f332(f125(x73191),x73192),x73193)))
% 52.62/52.42 [7320]~P100(x73201)+~P1(f332(f64(x73201),x73203))+E(f13(x73201,f179(x73201),f332(f332(f302(x73201),x73202),x73203)),x73202)+~E(f332(f332(f3(f853(x73201,a839)),x73203),f332(f332(f302(x73201),x73202),f180(f853(x73201,a839)))),f180(f853(x73201,a839)))
% 52.62/52.42 [7321]~P100(x73211)+~P1(f332(f64(x73211),x73213))+E(f14(x73211,f236(x73211),f332(f332(f302(x73211),x73212),x73213)),x73212)+~E(f332(f332(f3(f853(x73211,a839)),x73213),f332(f332(f302(x73211),x73212),f180(f853(x73211,a839)))),f180(f853(x73211,a839)))
% 52.62/52.42 [7339]~P110(x73391)+~P1(f332(f332(f233(x73391),x73392),x73393))+~P1(f332(f332(f233(x73391),f332(f81(x73391),x73392)),x73393))+P1(f332(f332(f233(x73391),f332(f77(x73391),x73392)),x73393))
% 52.62/52.42 [7340]~P80(x73401)+~P1(f332(f332(f232(x73401),x73402),x73403))+~P1(f332(f332(f232(x73401),f332(f81(x73401),x73402)),x73403))+P1(f332(f332(f232(x73401),f332(f77(x73401),x73402)),x73403))
% 52.62/52.42 [7341]~P80(x73411)+~P1(f332(f332(f232(x73411),x73412),x73413))+~P1(f332(f332(f232(x73411),f332(f81(x73411),x73412)),x73413))+P1(f332(f332(f232(x73411),f332(f77(x73411),x73412)),x73413))
% 52.62/52.42 [7410]~P123(x74101)+P1(f332(f332(f233(x74101),f2(x74101)),x74102))+~P1(f332(f332(f233(x74101),f2(x74101)),x74103))+~P1(f332(f332(f233(x74101),f2(x74101)),f332(f332(f83(x74101),x74103),x74102)))
% 52.62/52.42 [7411]~P123(x74111)+P1(f332(f332(f233(x74111),f2(x74111)),x74112))+~P1(f332(f332(f233(x74111),f2(x74111)),x74113))+~P1(f332(f332(f233(x74111),f2(x74111)),f332(f332(f83(x74111),x74112),x74113)))
% 52.62/52.42 [7718]E(x77181,x77182)+~P1(f332(f64(x77183),x77181))+~P1(f332(f332(f232(a845),f332(f43(x77183),x77181)),f332(f43(x77183),x77182)))+~P1(f332(f332(f232(f853(x77183,a839)),x77182),x77181))
% 52.62/52.42 [7789]~P1(f332(f332(f232(a845),x77892),x77891))+~P1(f332(f332(f233(a845),x77891),x77893))+~P1(f332(f332(f232(a845),x77892),x77893))+P1(f332(f332(f233(a845),f332(f332(f3(a845),x77891),x77892)),f332(f332(f3(a845),x77893),x77892)))
% 52.62/52.42 [7790]~P1(f332(f332(f232(a845),x77902),x77901))+~P1(f332(f332(f232(a845),x77902),x77903))+~P1(f332(f332(f232(a845),x77901),x77903))+P1(f332(f332(f232(a845),f332(f332(f3(a845),x77901),x77902)),f332(f332(f3(a845),x77903),x77902)))
% 52.62/52.42 [7865]~P1(f332(f332(f233(a1),x78651),f2(a1)))+~P1(f332(f332(f233(a1),f2(a1)),x78652))+~P1(f332(f332(f232(a1),x78652),x78653))+P1(f332(f332(f232(a1),f332(f332(f44(a1),x78651),x78652)),f332(f332(f44(a1),x78651),x78653)))
% 52.62/52.42 [7876]~P1(f332(f332(f233(a1),f2(a1)),x78763))+~P1(f332(f332(f232(a1),f2(a1)),x78761))+~P1(f332(f332(f232(a1),x78763),x78762))+P1(f332(f332(f232(a1),f332(f332(f44(a1),x78761),x78762)),f332(f332(f44(a1),x78761),x78763)))
% 52.62/52.42 [8011]E(f332(x80111,f809(x80112,x80111,x80113)),x80112)+~P1(f332(f332(f232(a1),x80112),f332(x80111,x80113)))+P1(f332(f332(f233(a845),f810(x80112,x80111,x80113)),x80113))+~P1(f332(f332(f232(a1),f332(x80111,f2(a845))),x80112))
% 52.62/52.42 [8012]E(f332(x80121,f811(x80122,x80121,x80123)),x80122)+~P1(f332(f332(f232(a1),x80122),f332(x80121,x80123)))+P1(f332(f332(f233(a845),f812(x80122,x80121,x80123)),x80123))+~P1(f332(f332(f232(a1),f332(x80121,f2(a845))),x80122))
% 52.62/52.42 [8109]~P1(f332(f64(x81091),x81093))+~P1(f332(f332(f233(a845),f332(f43(x81091),x81092)),f332(f43(x81091),x81093)))+~P1(f332(f332(f232(f853(x81091,a839)),x81092),x81093))+P1(f332(f332(f233(f853(x81091,a839)),x81092),x81093))
% 52.62/52.42 [8138]E(f332(f332(f3(a1),f419(x81383,x81381,x81382)),f420(x81383,x81381,x81382)),x81381)+E(f332(f332(f82(a1),x81381),x81382),x81381)+~P1(f332(f332(f233(a1),f2(a1)),x81382))+~P1(f332(f332(f334(a1),f332(f332(f82(a1),x81381),f80(a1))),x81383))
% 52.62/52.42 [8139]E(f332(f332(f82(a1),f421(x81393,x81391,x81392)),f422(x81393,x81391,x81392)),x81391)+E(f332(f332(f3(a1),x81391),x81392),x81391)+~P1(f332(f332(f233(a1),f2(a1)),x81392))+~P1(f332(f332(f334(a1),f332(f332(f3(a1),x81391),f80(a1))),x81393))
% 52.62/52.42 [8191]~P1(f332(f332(f232(a845),x81913),x81911))+P1(f332(f332(f233(a845),x81911),x81912))+~P1(f332(f332(f232(a845),x81913),x81912))+~P1(f332(f332(f233(a845),f332(f332(f3(a845),x81911),x81913)),f332(f332(f3(a845),x81912),x81913)))
% 52.62/52.42 [8192]~P1(f332(f332(f232(a845),x81923),x81921))+P1(f332(f332(f232(a845),x81921),x81922))+~P1(f332(f332(f232(a845),x81923),x81922))+~P1(f332(f332(f232(a845),f332(f332(f3(a845),x81921),x81923)),f332(f332(f3(a845),x81922),x81923)))
% 52.62/52.42 [8206]~P100(x82062)+E(x82061,f115(x82062))+~P20(x82062,f332(f142(x82062),x82061))+E(f332(f132(x82062,x82062,f332(f9(x82062,x82062,x82062),f179(x82062)),x82063),f332(f142(x82062),x82061)),f332(f332(f179(x82062),f332(f332(f152(x82062),x82061),f2(a845))),x82063))
% 52.62/52.42 [8271]E(f332(f332(f82(a1),x82711),x82712),x82711)+~P1(f332(f332(f233(a1),f2(a1)),x82712))+P1(f332(f332(f334(a1),f419(x82713,x82711,x82712)),x82713))+~P1(f332(f332(f334(a1),f332(f332(f82(a1),x82711),f80(a1))),x82713))
% 52.62/52.42 [8272]E(f332(f332(f3(a1),x82721),x82722),x82721)+~P1(f332(f332(f233(a1),f2(a1)),x82722))+P1(f332(f332(f334(a1),f421(x82723,x82721,x82722)),x82723))+~P1(f332(f332(f334(a1),f332(f332(f3(a1),x82721),f80(a1))),x82723))
% 52.62/52.42 [8351]~P1(f332(f332(f232(a1),x83511),f332(x83512,x83513)))+P1(f332(f332(f232(a845),f809(x83511,x83512,x83513)),x83513))+P1(f332(f332(f233(a845),f810(x83511,x83512,x83513)),x83513))+~P1(f332(f332(f232(a1),f332(x83512,f2(a845))),x83511))
% 52.62/52.42 [8352]~P1(f332(f332(f232(a1),x83521),f332(x83522,x83523)))+P1(f332(f332(f232(a845),f811(x83521,x83522,x83523)),x83523))+P1(f332(f332(f233(a845),f812(x83521,x83522,x83523)),x83523))+~P1(f332(f332(f232(a1),f332(x83522,f2(a845))),x83521))
% 52.62/52.42 [8427]E(f332(f332(f82(a1),x84271),x84272),x84271)+~P1(f332(f332(f233(a1),f2(a1)),x84272))+P1(f332(f332(f334(a1),f420(x84273,x84271,x84272)),f295(a1,f80(a1),x84272)))+~P1(f332(f332(f334(a1),f332(f332(f82(a1),x84271),f80(a1))),x84273))
% 52.62/52.42 [8428]E(f332(f332(f3(a1),x84281),x84282),x84281)+~P1(f332(f332(f233(a1),f2(a1)),x84282))+P1(f332(f332(f334(a1),f422(x84283,x84281,x84282)),f295(a1,f80(a1),x84282)))+~P1(f332(f332(f334(a1),f332(f332(f3(a1),x84281),f80(a1))),x84283))
% 52.62/52.42 [8553]~P117(x85531)+~P1(f332(f332(f233(x85531),x85532),f80(x85531)))+~P1(f332(f332(f233(x85531),f2(x85531)),x85532))+P1(f332(f332(f233(x85531),f332(f332(f83(x85531),x85532),f332(f332(f242(x85531),x85532),x85533))),f332(f332(f242(x85531),x85532),x85533)))
% 52.62/52.42 [8628]~P1(f332(x86281,x86282))+P1(f332(x86281,f2(a845)))+~P1(f332(f332(f233(a845),x86282),x86283))+~P1(f332(x86281,f53(a845,f332(a114,f807(x86282,x86281,x86283)),x86283)))
% 52.62/52.42 [8758]E(f830(x87581,x87582,x87583),f2(a845))+P1(f332(f332(x87581,x87583),x87582))+P1(f332(f332(x87581,f830(x87581,x87582,x87583)),f53(a845,f829(x87581,x87582,x87583),f830(x87581,x87582,x87583))))+~P1(f332(f321(f852(a845,a845),a214),f332(f332(f241(a845,a845),x87583),x87582)))
% 52.62/52.42 [8790]~P31(x87901,x87901,x87902,x87903)+E(f332(f303(x87901,x87901,x87902),x87903),x87903)+~P1(f332(f64(x87901),x87903))+~P1(f332(f332(f232(f853(x87901,a839)),f332(f303(x87901,x87901,x87902),x87903)),x87903))
% 52.62/52.42 [9010]P1(f332(f332(x90101,x90102),x90103))+~P1(f332(f332(f233(a1),f828(x90101,x90103,x90102)),f2(a1)))+P1(f332(f332(x90101,f332(f81(a1),f825(x90101,x90103,x90102))),f332(f81(a1),f828(x90101,x90103,x90102))))+~P1(f332(f321(f852(a1,a1),a216),f332(f332(f241(a1,a1),x90102),x90103)))
% 52.62/52.42 [9168]P1(f332(f332(x91681,x91682),x91683))+P1(f332(f332(x91681,f332(f332(f82(a1),f388(x91681,x91683,x91682)),f80(a1))),f396(x91681,x91683,x91682)))+~P1(f332(f332(f232(a1),f388(x91681,x91683,x91682)),f396(x91681,x91683,x91682)))+~P1(f332(f321(f852(a1,a1),a168),f332(f332(f241(a1,a1),x91682),x91683)))
% 52.62/52.42 [9842]E(f332(x98421,f809(x98422,x98421,x98423)),x98422)+~P1(f332(f332(f232(a1),x98422),f332(x98421,x98423)))+~P1(f332(f332(f232(a1),f332(f77(a1),f332(f332(f3(a1),f332(x98421,f332(f332(f82(a845),f810(x98422,x98421,x98423)),f80(a845)))),f332(x98421,f810(x98422,x98421,x98423))))),f80(a1)))+~P1(f332(f332(f232(a1),f332(x98421,f2(a845))),x98422))
% 52.62/52.42 [9843]E(f332(x98431,f811(x98432,x98431,x98433)),x98432)+~P1(f332(f332(f232(a1),x98432),f332(x98431,x98433)))+~P1(f332(f332(f232(a1),f332(f77(a1),f332(f332(f3(a1),f332(x98431,f332(f332(f82(a845),f812(x98432,x98431,x98433)),f80(a845)))),f332(x98431,f812(x98432,x98431,x98433))))),f80(a1)))+~P1(f332(f332(f232(a1),f332(x98431,f2(a845))),x98432))
% 52.62/52.42 [9847]~P1(f332(f332(f232(a1),x98471),f332(x98472,x98473)))+~P1(f332(f332(f232(a1),f332(f77(a1),f332(f332(f3(a1),f332(x98472,f332(f332(f82(a845),f810(x98471,x98472,x98473)),f80(a845)))),f332(x98472,f810(x98471,x98472,x98473))))),f80(a1)))+P1(f332(f332(f232(a845),f809(x98471,x98472,x98473)),x98473))+~P1(f332(f332(f232(a1),f332(x98472,f2(a845))),x98471))
% 52.62/52.42 [9848]~P1(f332(f332(f232(a1),x98481),f332(x98482,x98483)))+~P1(f332(f332(f232(a1),f332(f77(a1),f332(f332(f3(a1),f332(x98482,f332(f332(f82(a845),f812(x98481,x98482,x98483)),f80(a845)))),f332(x98482,f812(x98481,x98482,x98483))))),f80(a1)))+P1(f332(f332(f232(a845),f811(x98481,x98482,x98483)),x98483))+~P1(f332(f332(f232(a1),f332(x98482,f2(a845))),x98481))
% 52.62/52.42 [9902]E(x99021,x99022)+~E(f332(f132(f846(x99023),f846(x99023),f125(x99023),f115(x99023)),x99021),f332(f132(f846(x99023),f846(x99023),f125(x99023),f115(x99023)),x99022))+~E(f332(f181(f846(f846(x99023))),x99021),f332(f181(f846(f846(x99023))),x99022))+~P1(f332(f332(f251(f846(x99023),f846(x99023),a839),f332(f332(f9(f846(x99023),f853(f846(x99023),a845),f853(f846(x99023),a839)),f332(f332(f10(f853(a845,a839),f853(f853(f846(x99023),a845),f853(f846(x99023),a839)),f846(x99023)),f10(a845,a839,f846(x99023))),f332(f332(f10(a845,f853(a845,a839),f846(x99023)),a329),f181(f846(x99023))))),f181(f846(x99023)))),f773(x99021,x99022,x99023)))
% 52.62/52.42 [9903]E(x99031,x99032)+~E(f332(f132(f846(x99033),f846(x99033),f125(x99033),f115(x99033)),x99031),f332(f132(f846(x99033),f846(x99033),f125(x99033),f115(x99033)),x99032))+~E(f332(f181(f846(f846(x99033))),x99031),f332(f181(f846(f846(x99033))),x99032))+~P1(f332(f332(f251(f846(x99033),f846(x99033),a839),f332(f332(f9(f846(x99033),f853(f846(x99033),a845),f853(f846(x99033),a839)),f332(f332(f10(f853(a845,a839),f853(f853(f846(x99033),a845),f853(f846(x99033),a839)),f846(x99033)),f10(a845,a839,f846(x99033))),f332(f332(f10(a845,f853(a845,a839),f846(x99033)),a329),f181(f846(x99033))))),f181(f846(x99033)))),f774(x99032,x99031,x99033)))
% 52.62/52.42 [6712]~E(f80(a845),f2(a845))+~P1(f332(f64(x67121),x67123))+~P1(f332(f64(x67121),x67122))+E(f332(f332(f82(a845),f332(f43(x67121),x67122)),f332(f43(x67121),x67123)),f332(f43(x67121),f332(f332(f103(f853(x67121,a839)),x67122),x67123)))
% 52.62/52.42 [7131]~P100(x71311)+~P1(f332(f64(x71311),x71312))+~P1(f332(f332(f334(x71311),x71313),x71312))+P1(f332(f332(f232(x71311),f332(f66(x71311,f236(x71311)),x71312)),x71313))
% 52.62/52.42 [7132]~P98(x71321)+~P1(f332(f64(x71321),x71322))+~P1(f332(f332(f334(x71321),x71323),x71322))+P1(f332(f332(f232(x71321),f332(f66(x71321,f104(x71321)),x71322)),x71323))
% 52.62/52.42 [7407]~P1(f332(f64(x74071),x74073))+~P1(f332(f64(x74071),x74072))+~E(f332(f332(f104(f853(x74071,a839)),x74072),x74073),f180(f853(x74071,a839)))+E(f332(f332(f82(a845),f332(f43(x74071),x74072)),f332(f43(x74071),x74073)),f332(f43(x74071),f332(f332(f103(f853(x74071,a839)),x74072),x74073)))
% 52.62/52.42 [8196]~P38(x81961,x81963)+~P38(x81961,x81962)+~E(f332(f332(f104(f853(x81961,a839)),f332(f261(x81961,x81961),x81962)),f332(f259(x81961,x81961),x81963)),f180(f853(x81961,a839)))+P38(x81961,f332(f332(f103(f853(f852(x81961,x81961),a839)),x81962),x81963))
% 52.62/52.42 [8284]E(x82841,f332(f332(f44(a845),x82842),x82843))+~P1(f332(f332(f233(a845),f2(a845)),x82843))+~P1(f332(f332(f233(a845),x82842),f332(f332(f83(a845),x82843),f332(a114,x82841))))+~P1(f332(f332(f232(a845),f332(f332(f83(a845),x82843),x82841)),x82842))
% 52.62/52.42 [8425]~P1(f332(f64(x84251),x84252))+~P1(f332(f64(x84251),x84253))+E(f332(f332(f82(a845),f332(f43(x84251),x84252)),f332(f43(x84251),x84253)),f332(f43(x84251),f332(f332(f103(f853(x84251,a839)),x84252),x84253)))+P1(f332(f332(f334(x84251),f506(x84253,x84252,x84251)),f332(f332(f104(f853(x84251,a839)),x84252),x84253)))
% 52.62/52.42 [8769]~P119(x87692)+~E(x87691,f2(x87692))+~E(x87693,f2(x87692))+~P1(f332(f332(f233(x87692),f2(x87692)),f332(f332(f82(x87692),f332(f332(f83(x87692),x87693),x87693)),f332(f332(f83(x87692),x87691),x87691))))
% 52.62/52.42 [9240]~P38(x92401,x92403)+~P38(x92401,x92402)+P38(x92401,f332(f332(f103(f853(f852(x92401,x92401),a839)),x92402),x92403))+~P1(f332(f332(f232(f853(f852(x92401,x92401),a839)),f332(f332(f281(x92401,x92401,x92401),x92402),x92403)),x92402))
% 52.62/52.42 [9366]~P1(f332(x93661,x93663))+~P1(f332(f64(x93662),x93663))+P1(f332(x93661,f180(f853(x93662,a839))))+~P1(f332(x93661,f332(f332(f3(f853(x93662,a839)),f461(x93661,x93663,x93662)),f332(f332(f302(x93662),f483(x93661,x93663,x93662)),f180(f853(x93662,a839))))))
% 52.62/52.42 [8582]~P1(f332(f332(f233(a1),f2(a1)),x85823))+P1(f332(f332(f232(a1),f2(a1)),x85821))+~P1(f332(f332(f233(a1),x85822),x85823))+~P1(f332(f332(f232(a1),f2(a1)),f332(f332(f82(a1),f332(f332(f83(a1),x85823),x85821)),x85822)))
% 52.62/52.42 [8602]~P93(x86021)+~P1(f332(f64(x86021),x86022))+E(f332(f332(f3(f853(x86021,a839)),x86022),f332(f332(f302(x86021),x86023),f180(f853(x86021,a839)))),f180(f853(x86021,a839)))+E(f332(f332(f103(x86021),x86023),f15(x86021,f332(f332(f3(f853(x86021,a839)),x86022),f332(f332(f302(x86021),x86023),f180(f853(x86021,a839)))))),f15(x86021,f332(f332(f302(x86021),x86023),x86022)))
% 52.62/52.42 [8603]~P100(x86031)+~P1(f332(f64(x86031),x86032))+E(f332(f332(f3(f853(x86031,a839)),x86032),f332(f332(f302(x86031),x86033),f180(f853(x86031,a839)))),f180(f853(x86031,a839)))+E(f332(f332(f179(x86031),x86033),f16(x86031,f332(f332(f3(f853(x86031,a839)),x86032),f332(f332(f302(x86031),x86033),f180(f853(x86031,a839)))))),f16(x86031,f332(f332(f302(x86031),x86033),x86032)))
% 52.62/52.42 [8604]~P100(x86041)+~P1(f332(f64(x86041),x86042))+E(f332(f332(f3(f853(x86041,a839)),x86042),f332(f332(f302(x86041),x86043),f180(f853(x86041,a839)))),f180(f853(x86041,a839)))+E(f332(f332(f236(x86041),x86043),f17(x86041,f332(f332(f3(f853(x86041,a839)),x86042),f332(f332(f302(x86041),x86043),f180(f853(x86041,a839)))))),f17(x86041,f332(f332(f302(x86041),x86043),x86042)))
% 52.62/52.42 [8605]~P93(x86051)+~P1(f332(f64(x86051),x86052))+E(f332(f332(f3(f853(x86051,a839)),x86052),f332(f332(f302(x86051),x86053),f180(f853(x86051,a839)))),f180(f853(x86051,a839)))+E(f332(f332(f104(x86051),x86053),f12(x86051,f332(f332(f3(f853(x86051,a839)),x86052),f332(f332(f302(x86051),x86053),f180(f853(x86051,a839)))))),f12(x86051,f332(f332(f302(x86051),x86053),x86052)))
% 52.62/52.42 [8667]~P100(x86671)+~P1(f332(f64(x86671),x86672))+E(f332(f332(f3(f853(x86671,a839)),x86672),f332(f332(f302(x86671),x86673),f180(f853(x86671,a839)))),f180(f853(x86671,a839)))+E(f332(f332(f179(x86671),x86673),f13(x86671,f179(x86671),f332(f332(f3(f853(x86671,a839)),x86672),f332(f332(f302(x86671),x86673),f180(f853(x86671,a839)))))),f13(x86671,f179(x86671),f332(f332(f302(x86671),x86673),x86672)))
% 52.62/52.42 [8668]~P100(x86681)+~P1(f332(f64(x86681),x86682))+E(f332(f332(f3(f853(x86681,a839)),x86682),f332(f332(f302(x86681),x86683),f180(f853(x86681,a839)))),f180(f853(x86681,a839)))+E(f332(f332(f236(x86681),x86683),f14(x86681,f236(x86681),f332(f332(f3(f853(x86681,a839)),x86682),f332(f332(f302(x86681),x86683),f180(f853(x86681,a839)))))),f14(x86681,f236(x86681),f332(f332(f302(x86681),x86683),x86682)))
% 52.62/52.42 [9182]E(x91821,x91822)+~E(f332(f132(f846(x91823),f846(x91823),f125(x91823),f115(x91823)),x91821),f332(f132(f846(x91823),f846(x91823),f125(x91823),f115(x91823)),x91822))+~E(f332(f181(f846(f846(x91823))),x91821),f332(f181(f846(f846(x91823))),x91822))+P1(f332(f332(f334(f852(f846(x91823),f846(x91823))),f773(x91821,x91822,x91823)),f332(f158(f852(f846(x91823),f846(x91823))),f332(f332(f167(f846(x91823),f846(x91823)),x91822),x91821))))
% 52.62/52.42 [9183]E(x91831,x91832)+~E(f332(f132(f846(x91833),f846(x91833),f125(x91833),f115(x91833)),x91831),f332(f132(f846(x91833),f846(x91833),f125(x91833),f115(x91833)),x91832))+~E(f332(f181(f846(f846(x91833))),x91831),f332(f181(f846(f846(x91833))),x91832))+P1(f332(f332(f334(f852(f846(x91833),f846(x91833))),f774(x91832,x91831,x91833)),f332(f158(f852(f846(x91833),f846(x91833))),f332(f332(f167(f846(x91833),f846(x91833)),x91831),x91832))))
% 52.62/52.42 [9993]~P72(x99932)+E(x99931,f180(f853(x99932,a839)))+~P1(f332(f64(x99932),x99931))+E(f16(x99932,f332(f256(x99932),f332(f332(f10(f853(x99932,a839),a839,x99932),f89(x99932)),f332(f332(f9(x99932,f853(x99932,a839),f853(x99932,a839)),f332(f332(f10(f853(x99932,f853(a839,a839)),f853(f853(x99932,a839),f853(x99932,a839)),x99932),f20(x99932,a839,a839)),f332(f332(f10(f853(x99932,a839),f853(x99932,f853(a839,a839)),x99932),f332(f10(a839,f853(a839,a839),x99932),a330)),f332(f332(f9(x99932,f853(x99932,x99932),f853(x99932,a839)),f332(f332(f10(f853(x99932,a839),f853(f853(x99932,x99932),f853(x99932,a839)),x99932),f10(x99932,a839,x99932)),a329)),f332(f82(x99932),x99933))))),f332(f332(f9(x99932,f853(x99932,a839),a839),f334(x99932)),x99931))))),f332(f332(f82(x99932),x99933),f16(x99932,x99931)))
% 52.62/52.42 [9994]~P72(x99942)+E(x99941,f180(f853(x99942,a839)))+~P1(f332(f64(x99942),x99941))+E(f17(x99942,f332(f256(x99942),f332(f332(f10(f853(x99942,a839),a839,x99942),f89(x99942)),f332(f332(f9(x99942,f853(x99942,a839),f853(x99942,a839)),f332(f332(f10(f853(x99942,f853(a839,a839)),f853(f853(x99942,a839),f853(x99942,a839)),x99942),f20(x99942,a839,a839)),f332(f332(f10(f853(x99942,a839),f853(x99942,f853(a839,a839)),x99942),f332(f10(a839,f853(a839,a839),x99942),a330)),f332(f332(f9(x99942,f853(x99942,x99942),f853(x99942,a839)),f332(f332(f10(f853(x99942,a839),f853(f853(x99942,x99942),f853(x99942,a839)),x99942),f10(x99942,a839,x99942)),a329)),f332(f82(x99942),x99943))))),f332(f332(f9(x99942,f853(x99942,a839),a839),f334(x99942)),x99941))))),f332(f332(f82(x99942),x99943),f17(x99942,x99941)))
% 52.62/52.42 [9995]~P97(x99952)+E(x99951,f180(f853(x99952,a839)))+~P1(f332(f64(x99952),x99951))+E(f12(x99952,f332(f256(x99952),f332(f332(f10(f853(x99952,a839),a839,x99952),f89(x99952)),f332(f332(f9(x99952,f853(x99952,a839),f853(x99952,a839)),f332(f332(f10(f853(x99952,f853(a839,a839)),f853(f853(x99952,a839),f853(x99952,a839)),x99952),f20(x99952,a839,a839)),f332(f332(f10(f853(x99952,a839),f853(x99952,f853(a839,a839)),x99952),f332(f10(a839,f853(a839,a839),x99952),a330)),f332(f332(f9(x99952,f853(x99952,x99952),f853(x99952,a839)),f332(f332(f10(f853(x99952,a839),f853(f853(x99952,x99952),f853(x99952,a839)),x99952),f10(x99952,a839,x99952)),a329)),f332(f103(x99952),x99953))))),f332(f332(f9(x99952,f853(x99952,a839),a839),f334(x99952)),x99951))))),f332(f332(f103(x99952),x99953),f12(x99952,x99951)))
% 52.62/52.42 [9996]~P97(x99962)+E(x99961,f180(f853(x99962,a839)))+~P1(f332(f64(x99962),x99961))+E(f15(x99962,f332(f256(x99962),f332(f332(f10(f853(x99962,a839),a839,x99962),f89(x99962)),f332(f332(f9(x99962,f853(x99962,a839),f853(x99962,a839)),f332(f332(f10(f853(x99962,f853(a839,a839)),f853(f853(x99962,a839),f853(x99962,a839)),x99962),f20(x99962,a839,a839)),f332(f332(f10(f853(x99962,a839),f853(x99962,f853(a839,a839)),x99962),f332(f10(a839,f853(a839,a839),x99962),a330)),f332(f332(f9(x99962,f853(x99962,x99962),f853(x99962,a839)),f332(f332(f10(f853(x99962,a839),f853(f853(x99962,x99962),f853(x99962,a839)),x99962),f10(x99962,a839,x99962)),a329)),f332(f104(x99962),x99963))))),f332(f332(f9(x99962,f853(x99962,a839),a839),f334(x99962)),x99961))))),f332(f332(f104(x99962),x99963),f15(x99962,x99961)))
% 52.62/52.42 [9997]~P100(x99972)+E(x99971,f180(f853(x99972,a839)))+~P1(f332(f64(x99972),x99971))+E(f13(x99972,f179(x99972),f332(f256(x99972),f332(f332(f10(f853(x99972,a839),a839,x99972),f89(x99972)),f332(f332(f9(x99972,f853(x99972,a839),f853(x99972,a839)),f332(f332(f10(f853(x99972,f853(a839,a839)),f853(f853(x99972,a839),f853(x99972,a839)),x99972),f20(x99972,a839,a839)),f332(f332(f10(f853(x99972,a839),f853(x99972,f853(a839,a839)),x99972),f332(f10(a839,f853(a839,a839),x99972),a330)),f332(f332(f9(x99972,f853(x99972,x99972),f853(x99972,a839)),f332(f332(f10(f853(x99972,a839),f853(f853(x99972,x99972),f853(x99972,a839)),x99972),f10(x99972,a839,x99972)),a329)),f332(f236(x99972),x99973))))),f332(f332(f9(x99972,f853(x99972,a839),a839),f334(x99972)),x99971))))),f332(f332(f236(x99972),x99973),f13(x99972,f179(x99972),x99971)))
% 52.62/52.42 [9998]~P100(x99982)+E(x99981,f180(f853(x99982,a839)))+~P1(f332(f64(x99982),x99981))+E(f14(x99982,f236(x99982),f332(f256(x99982),f332(f332(f10(f853(x99982,a839),a839,x99982),f89(x99982)),f332(f332(f9(x99982,f853(x99982,a839),f853(x99982,a839)),f332(f332(f10(f853(x99982,f853(a839,a839)),f853(f853(x99982,a839),f853(x99982,a839)),x99982),f20(x99982,a839,a839)),f332(f332(f10(f853(x99982,a839),f853(x99982,f853(a839,a839)),x99982),f332(f10(a839,f853(a839,a839),x99982),a330)),f332(f332(f9(x99982,f853(x99982,x99982),f853(x99982,a839)),f332(f332(f10(f853(x99982,a839),f853(f853(x99982,x99982),f853(x99982,a839)),x99982),f10(x99982,a839,x99982)),a329)),f332(f179(x99982),x99983))))),f332(f332(f9(x99982,f853(x99982,a839),a839),f334(x99982)),x99981))))),f332(f332(f179(x99982),x99983),f14(x99982,f236(x99982),x99981)))
% 52.62/52.42 [9727]~P110(x97271)+~E(x97273,f2(x97271))+~E(x97272,f2(x97271))+E(f332(f332(f82(x97271),f332(f332(f242(x97271),x97272),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))),f332(f332(f242(x97271),x97273),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))),f2(x97271))
% 52.62/52.42 [9886]~P117(x98861)+~P1(f332(f332(f232(x98861),f2(x98861)),x98863))+P1(f332(f332(f233(x98861),x98862),x98863))+~P1(f332(f332(f233(x98861),f332(f332(f242(x98861),x98862),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))),f332(f332(f242(x98861),x98863),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))))
% 52.62/52.42 [9887]~P117(x98871)+~P1(f332(f332(f232(x98871),f2(x98871)),x98873))+P1(f332(f332(f232(x98871),x98872),x98873))+~P1(f332(f332(f232(x98871),f332(f332(f242(x98871),x98872),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))),f332(f332(f242(x98871),x98873),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))))
% 52.62/52.42 [9933]~P110(x99332)+~E(x99331,f2(x99332))+~E(x99333,f2(x99332))+~P1(f332(f332(f233(x99332),f2(x99332)),f332(f332(f82(x99332),f332(f332(f242(x99332),x99333),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99))))),f332(f332(f242(x99332),x99331),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))))))
% 52.62/52.42 [9156]E(x91561,x91562)+~E(f751(x91561,x91562,x91564,x91563),f753(x91561,x91562,x91564,x91563))+P1(f332(f332(f334(f852(f846(x91563),f846(x91563))),f332(f332(f241(f846(x91563),f846(x91563)),x91562),x91561)),f137(x91563,x91564)))+P1(f332(f332(f334(f852(f846(x91563),f846(x91563))),f332(f332(f241(f846(x91563),f846(x91563)),x91561),x91562)),f137(x91563,x91564)))
% 52.62/52.42 [4745]~P62(x47452)+~E(x47454,f2(x47452))+~E(x47451,f2(x47452))+E(x47451,f332(f332(f283(x47452),x47453),x47454))
% 52.62/52.42 [4746]~P62(x47461)+~E(x47463,f2(x47461))+~E(x47464,f2(x47461))+E(f332(f332(f283(x47461),x47462),x47463),x47464)
% 52.62/52.42 [4853]~P62(x48532)+E(x48531,f2(x48532))+~E(x48533,f2(x48532))+~E(x48531,f332(f332(f283(x48532),x48534),x48533))
% 52.62/52.42 [4854]~P62(x48542)+E(x48541,f2(x48542))+~E(x48543,f2(x48542))+~E(f332(f332(f283(x48542),x48544),x48543),x48541)
% 52.62/52.42 [5033]~P113(x50332)+E(x50331,f2(x50332))+~E(f332(f332(f283(x50332),x50333),x50331),x50334)+E(x50333,f332(f332(f83(x50332),x50334),x50331))
% 52.62/52.42 [5034]~P113(x50342)+E(x50341,f2(x50342))+~E(f332(f332(f83(x50342),x50343),x50341),x50344)+E(x50343,f332(f332(f283(x50342),x50344),x50341))
% 52.62/52.42 [5035]~P113(x50352)+E(x50351,f2(x50352))+~E(f332(f332(f83(x50352),x50353),x50351),x50354)+E(x50353,f332(f332(f283(x50352),x50354),x50351))
% 52.62/52.42 [5036]~P62(x50362)+E(x50361,f2(x50362))+~E(f332(f332(f283(x50362),x50363),x50361),x50364)+E(x50363,f332(f332(f83(x50362),x50364),x50361))
% 52.62/52.42 [5037]~P62(x50372)+E(x50371,f2(x50372))+~E(f332(f332(f83(x50372),x50373),x50371),x50374)+E(x50373,f332(f332(f283(x50372),x50374),x50371))
% 52.62/52.42 [5038]~P113(x50382)+E(x50381,f2(x50382))+~E(x50383,f332(f332(f283(x50382),x50384),x50381))+E(f332(f332(f83(x50382),x50383),x50381),x50384)
% 52.62/52.42 [5039]~P113(x50392)+E(x50391,f2(x50392))+~E(x50393,f332(f332(f83(x50392),x50394),x50391))+E(f332(f332(f283(x50392),x50393),x50391),x50394)
% 52.62/52.42 [5040]~P113(x50402)+E(x50401,f2(x50402))+~E(x50403,f332(f332(f83(x50402),x50404),x50401))+E(f332(f332(f283(x50402),x50403),x50401),x50404)
% 52.62/52.42 [5041]~P62(x50412)+E(x50411,f2(x50412))+~E(x50413,f332(f332(f283(x50412),x50414),x50411))+E(f332(f332(f83(x50412),x50413),x50411),x50414)
% 52.62/52.42 [5042]~P62(x50422)+E(x50421,f2(x50422))+~E(x50423,f332(f332(f83(x50422),x50424),x50421))+E(f332(f332(f283(x50422),x50423),x50421),x50424)
% 52.62/52.42 [5075]~P62(x50752)+~E(x50751,f2(x50752))+~E(f332(f332(f83(x50752),x50751),x50754),x50753)+E(x50751,f332(f332(f283(x50752),x50753),x50754))
% 52.62/52.42 [5076]~P62(x50761)+~E(x50764,f2(x50761))+~E(x50762,f332(f332(f83(x50761),x50764),x50763))+E(f332(f332(f283(x50761),x50762),x50763),x50764)
% 52.62/52.42 [5144]~E(x51443,x51444)+~E(x51442,x51443)+~P99(x51441)+E(f295(x51441,x51442,x51443),f332(f332(f302(x51441),x51444),f180(f853(x51441,a839))))
% 52.62/52.42 [5339]~E(f134(x53392,x53391),x53394)+~E(f116(x53392,x53391),x53393)+E(x53391,f115(x53392))+E(f332(f332(f125(x53392),x53393),f332(f332(f140(x53392),x53394),f115(x53392))),x53391)
% 52.62/52.42 [5958]~P117(x59583)+E(x59581,x59582)+~E(f332(f332(f242(x59583),x59584),x59581),f332(f332(f242(x59583),x59584),x59582))+~P1(f332(f332(f233(x59583),f80(x59583)),x59584))
% 52.62/52.42 [5959]E(x59591,x59592)+~E(f332(f332(f302(x59593),x59594),x59591),f332(f332(f302(x59593),x59594),x59592))+P1(f332(f332(f334(x59593),x59594),x59592))+P1(f332(f332(f334(x59593),x59594),x59591))
% 52.62/52.42 [5997]E(f332(x59971,x59972),f2(a845))+~E(f332(f332(f8(x59973,a845),x59971),x59974),f2(a845))+~P1(f332(f64(x59973),x59974))+~P1(f332(f332(f334(x59973),x59972),x59974))
% 52.62/52.42 [5998]E(f332(x59981,x59982),f80(a845))+~E(f332(f332(f11(x59983,a845),x59981),x59984),f80(a845))+~P1(f332(f64(x59983),x59984))+~P1(f332(f332(f334(x59983),x59982),x59984))
% 52.62/52.42 [6225]~P99(x62251)+~P1(f332(f332(f233(x62251),x62254),x62253))+P1(f332(f332(f233(x62251),x62252),x62253))+~P1(f332(f332(f233(x62251),x62252),x62254))
% 52.62/52.42 [6226]~P99(x62261)+~P1(f332(f332(f232(x62261),x62264),x62263))+P1(f332(f332(f233(x62261),x62262),x62263))+~P1(f332(f332(f233(x62261),x62262),x62264))
% 52.62/52.42 [6227]~P99(x62271)+~P1(f332(f332(f232(x62271),x62272),x62274))+P1(f332(f332(f233(x62271),x62272),x62273))+~P1(f332(f332(f233(x62271),x62274),x62273))
% 52.62/52.42 [6228]~P103(x62281)+~P1(f332(f332(f233(x62281),x62282),x62284))+P1(f332(f332(f233(x62281),x62282),x62283))+~P1(f332(f332(f233(x62281),x62284),x62283))
% 52.62/52.42 [6229]~P103(x62291)+~P1(f332(f332(f232(x62291),x62292),x62294))+P1(f332(f332(f233(x62291),x62292),x62293))+~P1(f332(f332(f233(x62291),x62294),x62293))
% 52.62/52.42 [6230]~P103(x62301)+~P1(f332(f332(f232(x62301),x62304),x62303))+P1(f332(f332(f233(x62301),x62302),x62303))+~P1(f332(f332(f233(x62301),x62302),x62304))
% 52.62/52.42 [6231]~P99(x62311)+~P1(f332(f332(f232(x62311),x62314),x62313))+P1(f332(f332(f232(x62311),x62312),x62313))+~P1(f332(f332(f232(x62311),x62312),x62314))
% 52.62/52.42 [6232]~P103(x62321)+~P1(f332(f332(f232(x62321),x62322),x62324))+P1(f332(f332(f232(x62321),x62322),x62323))+~P1(f332(f332(f232(x62321),x62324),x62323))
% 52.62/52.42 [6233]~P73(x62331)+~P1(f332(f332(f279(x62331),x62332),x62334))+P1(f332(f332(f279(x62331),x62332),x62333))+~P1(f332(f332(f279(x62331),x62334),x62333))
% 52.62/52.42 [6478]~P11(x64781)+~P1(f332(f332(f232(x64781),x64782),f46(x64781,x64784)))+P1(f332(f332(f232(x64781),x64782),x64783))+~P1(f332(f332(f334(x64781),x64783),x64784))
% 52.62/52.42 [6627]~P100(x66271)+~P20(x66271,f332(f332(f140(x66271),x66272),x66274))+~P1(f332(f332(f334(x66271),x66273),f332(f158(x66271),x66274)))+P1(f332(f332(f232(x66271),x66272),x66273))
% 52.62/52.42 [6628]~P100(x66281)+~P20(x66281,f332(f332(f140(x66281),x66282),x66284))+~P1(f332(f332(f334(x66281),x66283),f332(f158(x66281),x66284)))+P1(f332(f332(f232(x66281),x66282),x66283))
% 52.62/52.42 [6721]~P11(x67211)+~P1(f332(f332(f232(x67211),f45(x67211,x67214)),x67213))+P1(f332(f332(f232(x67211),x67212),x67213))+~P1(f332(f332(f334(x67211),x67212),x67214))
% 52.62/52.42 [6872]~P9(x68721)+P1(f332(f332(f279(x68721),x68722),f53(x68721,x68723,x68724)))+~P1(f332(f332(f279(x68721),x68722),x68724))+~P1(f332(f332(f279(x68721),x68722),x68723))
% 52.62/52.42 [6873]~P9(x68731)+P1(f332(f332(f279(x68731),x68732),f53(x68731,x68733,x68734)))+~P1(f332(f332(f279(x68731),x68732),x68734))+~P1(f332(f332(f279(x68731),x68732),x68733))
% 52.62/52.42 [7134]~P100(x71341)+E(f332(f332(f103(f853(x71341,a839)),f332(f294(x71341,x71342),x71343)),f332(f294(x71341,x71343),x71344)),f332(f294(x71341,x71342),x71344))+~P1(f332(f332(f232(x71341),x71343),x71344))+~P1(f332(f332(f232(x71341),x71342),x71343))
% 52.62/52.42 [7220]~P9(x72201)+~P1(f332(f332(f279(x72201),x72202),f53(x72201,x72203,x72204)))+P1(f332(f332(f279(x72201),x72202),x72203))+~P1(f332(f332(f279(x72201),x72202),x72204))
% 52.62/52.42 [7221]~P9(x72211)+~P1(f332(f332(f279(x72211),x72212),f53(x72211,x72213,x72214)))+P1(f332(f332(f279(x72211),x72212),x72213))+~P1(f332(f332(f279(x72211),x72212),x72214))
% 52.62/52.42 [7262]~P100(x72621)+E(f332(f332(f103(f853(x72621,a839)),f332(f294(x72621,x72622),x72623)),f295(x72621,x72623,x72624)),f295(x72621,x72622,x72624))+~P1(f332(f332(f232(x72621),x72623),x72624))+~P1(f332(f332(f232(x72621),x72622),x72623))
% 52.62/52.42 [7276]~P99(x72761)+~P52(a845,x72761,f279(a845),x72762)+P1(f332(f332(f232(x72761),f332(x72762,x72763)),f332(x72762,x72764)))+~P1(f332(f332(f279(a845),x72763),x72764))
% 52.62/52.42 [7330]~P100(x73301)+E(f332(f332(f103(f853(x73301,a839)),f298(x73301,x73302,x73303)),f332(f294(x73301,x73303),x73304)),f298(x73301,x73302,x73304))+~P1(f332(f332(f233(x73301),x73302),x73303))+~P1(f332(f332(f232(x73301),x73303),x73304))
% 52.62/52.42 [7353]~P100(x73531)+E(f332(f332(f103(f853(x73531,a839)),f295(x73531,x73532,x73533)),f298(x73531,x73533,x73534)),f332(f294(x73531,x73532),x73534))+~P1(f332(f332(f233(x73531),x73533),x73534))+~P1(f332(f332(f232(x73531),x73532),x73533))
% 52.62/52.42 [7388]~P100(x73881)+E(f332(f332(f103(f853(x73881,a839)),f295(x73881,x73882,x73883)),f297(x73881,x73883,x73884)),f295(x73881,x73882,x73884))+~P1(f332(f332(f232(x73881),x73883),x73884))+~P1(f332(f332(f232(x73881),x73882),x73883))
% 52.62/52.42 [7389]~P100(x73891)+E(f332(f332(f103(f853(x73891,a839)),f297(x73891,x73892,x73893)),f297(x73891,x73893,x73894)),f297(x73891,x73892,x73894))+~P1(f332(f332(f232(x73891),x73893),x73894))+~P1(f332(f332(f232(x73891),x73892),x73893))
% 52.62/52.42 [7390]~P100(x73901)+E(f332(f332(f103(f853(x73901,a839)),f297(x73901,x73902,x73903)),f298(x73901,x73903,x73904)),f298(x73901,x73902,x73904))+~P1(f332(f332(f233(x73901),x73903),x73904))+~P1(f332(f332(f232(x73901),x73902),x73903))
% 52.62/52.42 [7391]~P100(x73911)+E(f332(f332(f103(f853(x73911,a839)),f298(x73911,x73912,x73913)),f295(x73911,x73913,x73914)),f297(x73911,x73912,x73914))+~P1(f332(f332(f233(x73911),x73912),x73913))+~P1(f332(f332(f232(x73911),x73913),x73914))
% 52.62/52.42 [8181]P31(x81811,x81812,f528(x81813,x81812,x81814,x81811),x81814)+~P1(f332(f64(x81812),x81813))+~P1(f332(f64(x81811),x81814))+~P1(f332(f332(f232(a845),f332(f43(x81811),x81814)),f332(f43(x81812),x81813)))
% 52.62/52.42 [8251]~P70(x82511)+~E(f332(x82513,f623(x82513,x82514,x82512,x82511)),f80(x82511))+E(f332(f332(f332(f68(x82511,x82512,f83(x82511)),x82513),f80(x82511)),x82514),f80(x82511))+~P1(f332(f64(x82512),x82514))
% 52.62/52.42 [8525]~P117(x85251)+~P1(f332(f332(f232(x85251),f2(x85251)),x85253))+P1(f332(f332(f232(x85251),x85252),x85253))+~P1(f332(f332(f232(x85251),f332(f332(f242(x85251),x85252),f332(a114,x85254))),f332(f332(f242(x85251),x85253),f332(a114,x85254))))
% 52.62/52.42 [8855]~P70(x88551)+E(f332(f332(f332(f68(x88551,x88552,f83(x88551)),x88553),f80(x88551)),x88554),f80(x88551))+~P1(f332(f64(x88552),x88554))+P1(f332(f332(f334(x88552),f623(x88553,x88554,x88552,x88551)),x88554))
% 52.62/52.42 [9107]~P14(x91072,x91073,x91074)+~P1(f332(f64(x91072),x91073))+~P1(f332(f332(f279(a845),x91071),f332(f43(x91072),f517(x91071,x91074,x91073,x91072))))+P1(f332(f332(f279(a845),x91071),f332(f43(x91072),x91073)))
% 52.62/52.42 [9293]~P1(f332(f332(f279(a845),x92932),x92933))+P1(f332(f332(f279(a845),x92931),x92932))+P1(f332(f332(f279(a845),x92933),x92934))+~P1(f332(f332(f233(f853(a845,a839)),f282(a845,f279(a845),x92932,x92933)),f282(a845,f279(a845),x92931,x92934)))
% 52.62/52.42 [9297]P1(f332(f332(f279(a845),x92971),x92972))+~P1(f332(f332(f279(a845),x92972),x92973))+~P1(f332(f332(f279(a845),x92974),x92973))+~P1(f332(f332(f233(f853(a845,a839)),f282(a845,f279(a845),x92972,x92973)),f282(a845,f279(a845),x92971,x92974)))
% 52.62/52.42 [9298]~P1(f332(f332(f279(a845),x92983),x92981))+P1(f332(f332(f279(a845),x92981),x92982))+~P1(f332(f332(f279(a845),x92983),x92984))+~P1(f332(f332(f233(f853(a845,a839)),f282(a845,f279(a845),x92983,x92981)),f282(a845,f279(a845),x92984,x92982)))
% 52.62/52.42 [9305]~P1(f332(f332(f279(a845),x93051),x93053))+~P1(f332(f332(f279(a845),x93051),x93052))+~P1(f332(f332(f279(a845),x93054),x93053))+~P1(f332(f332(f233(f853(a845,a839)),f282(a845,f279(a845),x93051,x93053)),f282(a845,f279(a845),x93052,x93054)))
% 52.62/52.42 [9311]~P1(f332(f332(f232(a1),x93114),f2(a1)))+P1(f332(f332(f232(a1),f332(f332(f82(a1),f332(f332(f83(a1),x93111),f53(a1,x93112,x93113))),x93114)),f2(a1)))+~P1(f332(f332(f233(a1),f2(a1)),x93113))+~P1(f332(f332(f233(a1),x93111),x93114))
% 52.62/52.42 [9718]~P1(f332(f64(x97181),x97182))+~P1(f332(f332(f334(x97181),x97184),x97182))+~P1(f332(f332(f334(x97181),x97183),x97182))+P1(f332(f332(f233(a845),f332(f43(x97181),f332(f332(f3(f853(x97181,a839)),f332(f332(f3(f853(x97181,a839)),x97182),f332(f332(f302(x97181),x97183),f180(f853(x97181,a839))))),f332(f332(f302(x97181),x97184),f180(f853(x97181,a839)))))),f332(f43(x97181),x97182)))
% 52.62/52.42 [6783]~P136(x67833)+~P112(x67833)+P1(f332(x67831,f833(x67832,x67831,x67833)))+~P1(f332(x67831,f332(f332(f83(x67833),x67832),x67834)))
% 52.62/52.42 [6843]~P100(x68431)+~P1(f332(f332(f233(x68431),x68432),x68434))+~P1(f332(f332(f233(x68431),x68432),x68433))+P1(f332(f332(f233(x68431),x68432),f332(f332(f236(x68431),x68433),x68434)))
% 52.62/52.42 [6844]~P100(x68441)+~P1(f332(f332(f232(x68441),x68442),x68444))+~P1(f332(f332(f232(x68441),x68442),x68443))+P1(f332(f332(f232(x68441),x68442),f332(f332(f236(x68441),x68443),x68444)))
% 52.62/52.42 [6845]~P100(x68451)+~P1(f332(f332(f232(x68451),x68452),x68454))+~P1(f332(f332(f232(x68451),x68452),x68453))+P1(f332(f332(f232(x68451),x68452),f332(f332(f236(x68451),x68453),x68454)))
% 52.62/52.42 [6846]~P100(x68461)+~P1(f332(f332(f232(x68461),x68462),x68464))+~P1(f332(f332(f232(x68461),x68462),x68463))+P1(f332(f332(f232(x68461),x68462),f332(f332(f236(x68461),x68463),x68464)))
% 52.62/52.42 [6847]~P98(x68471)+~P1(f332(f332(f232(x68471),x68472),x68474))+~P1(f332(f332(f232(x68471),x68472),x68473))+P1(f332(f332(f232(x68471),x68472),f332(f332(f104(x68471),x68473),x68474)))
% 52.62/52.42 [6848]~P98(x68481)+~P1(f332(f332(f232(x68481),x68482),x68484))+~P1(f332(f332(f232(x68481),x68482),x68483))+P1(f332(f332(f232(x68481),x68482),f332(f332(f104(x68481),x68483),x68484)))
% 52.62/52.42 [6849]~P98(x68491)+~P1(f332(f332(f232(x68491),x68492),x68494))+~P1(f332(f332(f232(x68491),x68492),x68493))+P1(f332(f332(f232(x68491),x68492),f332(f332(f104(x68491),x68493),x68494)))
% 52.62/52.42 [6850]~P73(x68501)+~P1(f332(f332(f279(x68501),x68502),x68504))+~P1(f332(f332(f279(x68501),x68502),x68503))+P1(f332(f332(f279(x68501),x68502),f332(f332(f82(x68501),x68503),x68504)))
% 52.62/52.42 [6851]~P104(x68511)+~P1(f332(f332(f279(x68511),x68512),x68514))+~P1(f332(f332(f279(x68511),x68512),x68513))+P1(f332(f332(f279(x68511),x68512),f332(f332(f3(x68511),x68513),x68514)))
% 52.62/52.42 [6871]~P63(x68712)+E(x68711,f2(x68712))+E(f332(f332(f283(x68712),f332(f332(f242(x68712),x68711),x68713)),f332(f332(f242(x68712),x68711),x68714)),f332(f332(f242(x68712),x68711),f332(f332(f3(a845),x68713),x68714)))+~P1(f332(f332(f232(a845),x68714),x68713))
% 52.62/52.42 [6915]~P100(x69151)+~P20(x69151,f332(f332(f140(x69151),x69153),x69154))+P20(x69151,f332(f332(f140(x69151),x69152),f332(f332(f140(x69151),x69153),x69154)))+~P1(f332(f332(f232(x69151),x69152),x69153))
% 52.62/52.42 [6916]~P100(x69161)+~P20(x69161,f332(f332(f140(x69161),x69163),x69164))+P20(x69161,f332(f332(f140(x69161),x69162),f332(f332(f140(x69161),x69163),x69164)))+~P1(f332(f332(f232(x69161),x69162),x69163))
% 52.62/52.42 [6956]~P82(x69561)+~P1(f332(f332(f232(x69561),f2(x69561)),x69563))+~P1(f332(f332(f233(x69561),x69562),x69564))+P1(f332(f332(f233(x69561),x69562),f332(f332(f82(x69561),x69563),x69564)))
% 52.62/52.42 [6957]~P82(x69571)+~P1(f332(f332(f232(x69571),x69572),x69574))+~P1(f332(f332(f233(x69571),f2(x69571)),x69573))+P1(f332(f332(f233(x69571),x69572),f332(f332(f82(x69571),x69573),x69574)))
% 52.62/52.42 [6958]~P117(x69581)+~P1(f332(f332(f233(x69581),f2(x69581)),x69583))+~P1(f332(f332(f233(x69581),x69582),x69584))+P1(f332(f332(f233(x69581),x69582),f332(f332(f82(x69581),x69583),x69584)))
% 52.62/52.42 [6959]~P82(x69591)+~P1(f332(f332(f232(x69591),f2(x69591)),x69594))+~P1(f332(f332(f232(x69591),x69592),x69593))+P1(f332(f332(f232(x69591),x69592),f332(f332(f82(x69591),x69593),x69594)))
% 52.62/52.42 [6960]~P82(x69601)+~P1(f332(f332(f232(x69601),f2(x69601)),x69603))+~P1(f332(f332(f232(x69601),x69602),x69604))+P1(f332(f332(f232(x69601),x69602),f332(f332(f82(x69601),x69603),x69604)))
% 52.62/52.42 [6994]~P100(x69941)+P1(f332(f332(f233(x69941),x69942),x69943))+P1(f332(f332(f233(x69941),x69942),x69944))+~P1(f332(f332(f233(x69941),x69942),f332(f332(f179(x69941),x69944),x69943)))
% 52.62/52.42 [6995]~P100(x69951)+P1(f332(f332(f232(x69951),x69952),x69953))+P1(f332(f332(f232(x69951),x69952),x69954))+~P1(f332(f332(f232(x69951),x69952),f332(f332(f179(x69951),x69954),x69953)))
% 52.62/52.42 [7679]~P65(x76791)+~P1(f332(f332(f233(x76791),x76794),f2(x76791)))+~P1(f332(f332(f233(x76791),x76793),f332(f332(f283(x76791),x76792),x76794)))+P1(f332(f332(f233(x76791),x76792),f332(f332(f83(x76791),x76793),x76794)))
% 52.62/52.42 [7680]~P65(x76801)+~P1(f332(f332(f233(x76801),x76804),f2(x76801)))+~P1(f332(f332(f233(x76801),x76803),f332(f332(f83(x76801),x76802),x76804)))+P1(f332(f332(f233(x76801),x76802),f332(f332(f283(x76801),x76803),x76804)))
% 52.62/52.42 [7681]~P65(x76811)+~P1(f332(f332(f233(x76811),x76814),f2(x76811)))+~P1(f332(f332(f232(x76811),x76813),f332(f332(f283(x76811),x76812),x76814)))+P1(f332(f332(f232(x76811),x76812),f332(f332(f83(x76811),x76813),x76814)))
% 52.62/52.42 [7682]~P65(x76821)+~P1(f332(f332(f233(x76821),x76824),f2(x76821)))+~P1(f332(f332(f232(x76821),x76823),f332(f332(f83(x76821),x76822),x76824)))+P1(f332(f332(f232(x76821),x76822),f332(f332(f283(x76821),x76823),x76824)))
% 52.62/52.42 [7792]~P119(x77921)+~P1(f332(f332(f233(x77921),x77922),f2(x77921)))+~P1(f332(f332(f233(x77921),x77924),x77923))+P1(f332(f332(f233(x77921),f332(f332(f83(x77921),x77922),x77923)),f332(f332(f83(x77921),x77922),x77924)))
% 52.62/52.42 [7793]~P119(x77931)+~P1(f332(f332(f233(x77931),x77932),f2(x77931)))+~P1(f332(f332(f233(x77931),x77934),x77933))+P1(f332(f332(f233(x77931),f332(f332(f83(x77931),x77932),x77933)),f332(f332(f83(x77931),x77932),x77934)))
% 52.62/52.42 [7794]~P119(x77941)+~P1(f332(f332(f233(x77941),x77943),f2(x77941)))+~P1(f332(f332(f233(x77941),x77944),x77942))+P1(f332(f332(f233(x77941),f332(f332(f83(x77941),x77942),x77943)),f332(f332(f83(x77941),x77944),x77943)))
% 52.62/52.42 [7795]~P119(x77951)+~P1(f332(f332(f233(x77951),x77953),f2(x77951)))+~P1(f332(f332(f233(x77951),x77954),x77952))+P1(f332(f332(f233(x77951),f332(f332(f83(x77951),x77952),x77953)),f332(f332(f83(x77951),x77954),x77953)))
% 52.62/52.42 [7796]~P119(x77961)+~P1(f332(f332(f233(x77961),x77962),f2(x77961)))+~P1(f332(f332(f233(x77961),x77964),x77963))+P1(f332(f332(f233(x77961),f332(f332(f83(x77961),x77962),x77963)),f332(f332(f83(x77961),x77962),x77964)))
% 52.62/52.42 [7797]~P65(x77971)+~P1(f332(f332(f233(x77971),x77973),f2(x77971)))+~P1(f332(f332(f233(x77971),x77974),x77972))+P1(f332(f332(f233(x77971),f332(f332(f283(x77971),x77972),x77973)),f332(f332(f283(x77971),x77974),x77973)))
% 52.62/52.42 [7798]~P119(x77981)+~P1(f332(f332(f233(x77981),x77982),f2(x77981)))+~P1(f332(f332(f232(x77981),x77984),x77983))+P1(f332(f332(f232(x77981),f332(f332(f83(x77981),x77982),x77983)),f332(f332(f83(x77981),x77982),x77984)))
% 52.62/52.42 [7799]~P129(x77991)+~P1(f332(f332(f232(x77991),x77992),f2(x77991)))+~P1(f332(f332(f232(x77991),x77994),x77993))+P1(f332(f332(f232(x77991),f332(f332(f83(x77991),x77992),x77993)),f332(f332(f83(x77991),x77992),x77994)))
% 52.62/52.42 [7800]~P129(x78001)+~P1(f332(f332(f232(x78001),x78003),f2(x78001)))+~P1(f332(f332(f232(x78001),x78004),x78002))+P1(f332(f332(f232(x78001),f332(f332(f83(x78001),x78002),x78003)),f332(f332(f83(x78001),x78004),x78003)))
% 52.62/52.42 [7801]~P64(x78011)+~P1(f332(f332(f232(x78011),x78013),f2(x78011)))+~P1(f332(f332(f232(x78011),x78014),x78012))+P1(f332(f332(f232(x78011),f332(f332(f283(x78011),x78012),x78013)),f332(f332(f283(x78011),x78014),x78013)))
% 52.62/52.42 [7802]~P117(x78021)+~P1(f332(f332(f233(x78021),f80(x78021)),x78022))+~P1(f332(f332(f233(a845),x78023),x78024))+P1(f332(f332(f233(x78021),f332(f332(f242(x78021),x78022),x78023)),f332(f332(f242(x78021),x78022),x78024)))
% 52.62/52.42 [7803]~P117(x78031)+~P1(f332(f332(f233(x78031),f80(x78031)),x78032))+~P1(f332(f332(f233(a845),x78033),x78034))+P1(f332(f332(f233(x78031),f332(f332(f242(x78031),x78032),x78033)),f332(f332(f242(x78031),x78032),x78034)))
% 52.62/52.42 [7804]~P117(x78041)+~P1(f332(f332(f233(x78041),f80(x78041)),x78042))+~P1(f332(f332(f232(a845),x78043),x78044))+P1(f332(f332(f232(x78041),f332(f332(f242(x78041),x78042),x78043)),f332(f332(f242(x78041),x78042),x78044)))
% 52.62/52.42 [7805]~P117(x78051)+~P1(f332(f332(f232(x78051),f80(x78051)),x78052))+~P1(f332(f332(f232(a845),x78053),x78054))+P1(f332(f332(f232(x78051),f332(f332(f242(x78051),x78052),x78053)),f332(f332(f242(x78051),x78052),x78054)))
% 52.62/52.42 [7832]P1(f332(f332(f233(a845),f2(a845)),f332(x78321,x78322)))+~P1(f332(f64(x78323),x78324))+~P1(f332(f332(f334(x78323),x78322),x78324))+~P1(f332(f332(f233(a845),f2(a845)),f332(f332(f11(x78323,a845),x78321),x78324)))
% 52.62/52.42 [7843]~P119(x78431)+~P1(f332(f332(f233(x78431),x78433),x78434))+~P1(f332(f332(f233(x78431),f2(x78431)),x78432))+P1(f332(f332(f233(x78431),f332(f332(f83(x78431),x78432),x78433)),f332(f332(f83(x78431),x78432),x78434)))
% 52.62/52.42 [7844]~P123(x78441)+~P1(f332(f332(f233(x78441),x78443),x78444))+~P1(f332(f332(f233(x78441),f2(x78441)),x78442))+P1(f332(f332(f233(x78441),f332(f332(f83(x78441),x78442),x78443)),f332(f332(f83(x78441),x78442),x78444)))
% 52.62/52.42 [7845]~P115(x78451)+~P1(f332(f332(f233(x78451),x78453),x78454))+~P1(f332(f332(f233(x78451),f2(x78451)),x78452))+P1(f332(f332(f233(x78451),f332(f332(f83(x78451),x78452),x78453)),f332(f332(f83(x78451),x78452),x78454)))
% 52.62/52.42 [7846]~P119(x78461)+~P1(f332(f332(f233(x78461),x78462),x78464))+~P1(f332(f332(f233(x78461),f2(x78461)),x78463))+P1(f332(f332(f233(x78461),f332(f332(f83(x78461),x78462),x78463)),f332(f332(f83(x78461),x78464),x78463)))
% 52.62/52.42 [7847]~P123(x78471)+~P1(f332(f332(f233(x78471),x78472),x78474))+~P1(f332(f332(f233(x78471),f2(x78471)),x78473))+P1(f332(f332(f233(x78471),f332(f332(f83(x78471),x78472),x78473)),f332(f332(f83(x78471),x78474),x78473)))
% 52.62/52.42 [7848]~P119(x78481)+~P1(f332(f332(f233(x78481),x78483),x78484))+~P1(f332(f332(f233(x78481),f2(x78481)),x78482))+P1(f332(f332(f233(x78481),f332(f332(f83(x78481),x78482),x78483)),f332(f332(f83(x78481),x78482),x78484)))
% 52.62/52.42 [7849]~P65(x78491)+~P1(f332(f332(f233(x78491),x78492),x78494))+~P1(f332(f332(f233(x78491),f2(x78491)),x78493))+P1(f332(f332(f233(x78491),f332(f332(f283(x78491),x78492),x78493)),f332(f332(f283(x78491),x78494),x78493)))
% 52.62/52.42 [7850]~P119(x78501)+~P1(f332(f332(f233(x78501),f2(x78501)),x78502))+~P1(f332(f332(f232(x78501),x78503),x78504))+P1(f332(f332(f232(x78501),f332(f332(f83(x78501),x78502),x78503)),f332(f332(f83(x78501),x78502),x78504)))
% 52.62/52.42 [7851]~P131(x78511)+~P1(f332(f332(f232(x78511),x78513),x78514))+~P1(f332(f332(f232(x78511),f2(x78511)),x78512))+P1(f332(f332(f232(x78511),f332(f332(f83(x78511),x78512),x78513)),f332(f332(f83(x78511),x78512),x78514)))
% 52.62/52.42 [7852]~P130(x78521)+~P1(f332(f332(f232(x78521),x78523),x78524))+~P1(f332(f332(f232(x78521),f2(x78521)),x78522))+P1(f332(f332(f232(x78521),f332(f332(f83(x78521),x78522),x78523)),f332(f332(f83(x78521),x78522),x78524)))
% 52.62/52.42 [7853]~P131(x78531)+~P1(f332(f332(f232(x78531),x78532),x78534))+~P1(f332(f332(f232(x78531),f2(x78531)),x78533))+P1(f332(f332(f232(x78531),f332(f332(f83(x78531),x78532),x78533)),f332(f332(f83(x78531),x78534),x78533)))
% 52.62/52.42 [7854]~P117(x78541)+~P1(f332(f332(f232(x78541),x78542),x78544))+~P1(f332(f332(f232(x78541),f2(x78541)),x78542))+P1(f332(f332(f232(x78541),f332(f332(f242(x78541),x78542),x78543)),f332(f332(f242(x78541),x78544),x78543)))
% 52.62/52.42 [7855]~P64(x78551)+~P1(f332(f332(f232(x78551),x78552),x78554))+~P1(f332(f332(f232(x78551),f2(x78551)),x78553))+P1(f332(f332(f232(x78551),f332(f332(f283(x78551),x78552),x78553)),f332(f332(f283(x78551),x78554),x78553)))
% 52.62/52.42 [7894]~P102(x78942)+P1(f332(f332(f232(f853(x78941,x78942)),x78944),x78943))+~P1(f332(f332(f232(f853(x78941,x78942)),x78943),x78944))+P1(f332(f332(f233(f853(x78941,x78942)),x78943),x78944))
% 52.62/52.42 [7938]P1(f332(f332(f334(x79381),x79382),x79383))+P1(f332(f332(f334(x79381),x79382),x79384))+~P1(f332(f332(f232(f853(x79381,a839)),x79384),x79383))+P1(f332(f332(f233(f853(x79381,a839)),x79384),f332(f332(f302(x79381),x79382),x79383)))
% 52.62/52.42 [8045]~P111(x80452)+E(x80451,f2(x80452))+P1(f332(f332(f279(x80452),x80453),x80454))+~P1(f332(f332(f279(x80452),f332(f332(f83(x80452),x80453),x80451)),f332(f332(f83(x80452),x80454),x80451)))
% 52.62/52.42 [8046]~P111(x80462)+E(x80461,f2(x80462))+P1(f332(f332(f279(x80462),x80463),x80464))+~P1(f332(f332(f279(x80462),f332(f332(f83(x80462),x80461),x80463)),f332(f332(f83(x80462),x80461),x80464)))
% 52.62/52.42 [8090]P1(f332(f332(f334(x80901),x80902),x80903))+P1(f332(f332(f334(x80901),x80902),x80904))+~P1(f332(f332(f233(f853(x80901,a839)),x80904),f332(f332(f302(x80901),x80902),x80903)))+P1(f332(f332(f232(f853(x80901,a839)),x80904),x80903))
% 52.62/52.42 [8159]~P119(x81591)+P1(f332(f332(f233(x81591),x81593),x81592))+P1(f332(f332(f233(x81591),x81592),x81593))+~P1(f332(f332(f233(x81591),f332(f332(f83(x81591),x81594),x81592)),f332(f332(f83(x81591),x81594),x81593)))
% 52.62/52.42 [8160]~P119(x81601)+P1(f332(f332(f233(x81601),x81603),x81602))+P1(f332(f332(f233(x81601),x81602),x81603))+~P1(f332(f332(f233(x81601),f332(f332(f83(x81601),x81602),x81604)),f332(f332(f83(x81601),x81603),x81604)))
% 52.62/52.42 [8171]~P119(x81711)+P1(f332(f332(f233(x81711),x81714),f2(x81711)))+P1(f332(f332(f233(x81711),x81712),x81713))+~P1(f332(f332(f233(x81711),f332(f332(f83(x81711),x81712),x81714)),f332(f332(f83(x81711),x81713),x81714)))
% 52.62/52.42 [8172]~P119(x81721)+P1(f332(f332(f233(x81721),x81724),f2(x81721)))+P1(f332(f332(f233(x81721),x81722),x81723))+~P1(f332(f332(f233(x81721),f332(f332(f83(x81721),x81724),x81722)),f332(f332(f83(x81721),x81724),x81723)))
% 52.62/52.42 [8175]~P119(x81751)+P1(f332(f332(f233(x81751),x81752),x81753))+P1(f332(f332(f233(x81751),f2(x81751)),x81754))+~P1(f332(f332(f233(x81751),f332(f332(f83(x81751),x81754),x81753)),f332(f332(f83(x81751),x81754),x81752)))
% 52.62/52.42 [8176]~P119(x81761)+P1(f332(f332(f233(x81761),x81762),x81763))+P1(f332(f332(f233(x81761),f2(x81761)),x81764))+~P1(f332(f332(f233(x81761),f332(f332(f83(x81761),x81763),x81764)),f332(f332(f83(x81761),x81762),x81764)))
% 52.62/52.42 [8189]~P119(x81891)+P1(f332(f332(f233(x81891),x81892),f2(x81891)))+P1(f332(f332(f233(x81891),f2(x81891)),x81892))+~P1(f332(f332(f233(x81891),f332(f332(f83(x81891),x81893),x81892)),f332(f332(f83(x81891),x81894),x81892)))
% 52.62/52.42 [8190]~P119(x81901)+P1(f332(f332(f233(x81901),x81902),f2(x81901)))+P1(f332(f332(f233(x81901),f2(x81901)),x81902))+~P1(f332(f332(f233(x81901),f332(f332(f83(x81901),x81902),x81903)),f332(f332(f83(x81901),x81902),x81904)))
% 52.62/52.42 [8214]~P119(x82141)+~P1(f332(f332(f233(x82141),x82144),f2(x82141)))+P1(f332(f332(f233(x82141),x82142),x82143))+~P1(f332(f332(f233(x82141),f332(f332(f83(x82141),x82144),x82143)),f332(f332(f83(x82141),x82144),x82142)))
% 52.62/52.42 [8215]~P119(x82151)+~P1(f332(f332(f233(x82151),x82154),f2(x82151)))+P1(f332(f332(f232(x82151),x82152),x82153))+~P1(f332(f332(f232(x82151),f332(f332(f83(x82151),x82154),x82153)),f332(f332(f83(x82151),x82154),x82152)))
% 52.62/52.42 [8226]~P117(x82263)+~P1(f332(f332(f233(x82263),f80(x82263)),x82264))+P1(f332(f332(f233(a845),x82261),x82262))+~P1(f332(f332(f233(x82263),f332(f332(f242(x82263),x82264),x82261)),f332(f332(f242(x82263),x82264),x82262)))
% 52.62/52.42 [8227]~P117(x82273)+~P1(f332(f332(f233(x82273),f80(x82273)),x82274))+P1(f332(f332(f233(a845),x82271),x82272))+~P1(f332(f332(f233(x82273),f332(f332(f242(x82273),x82274),x82271)),f332(f332(f242(x82273),x82274),x82272)))
% 52.62/52.42 [8228]~P117(x82283)+~P1(f332(f332(f233(x82283),f80(x82283)),x82284))+P1(f332(f332(f232(a845),x82281),x82282))+~P1(f332(f332(f232(x82283),f332(f332(f242(x82283),x82284),x82281)),f332(f332(f242(x82283),x82284),x82282)))
% 52.62/52.42 [8229]~P117(x82293)+~P1(f332(f332(f233(x82293),f80(x82293)),x82294))+P1(f332(f332(f232(a845),x82291),x82292))+~P1(f332(f332(f232(x82293),f332(f332(f242(x82293),x82294),x82291)),f332(f332(f242(x82293),x82294),x82292)))
% 52.62/52.42 [8239]~P119(x82391)+P1(f332(f332(f233(x82391),x82392),x82393))+~P1(f332(f332(f233(x82391),f2(x82391)),x82394))+~P1(f332(f332(f233(x82391),f332(f332(f83(x82391),x82394),x82392)),f332(f332(f83(x82391),x82394),x82393)))
% 52.62/52.42 [8240]~P123(x82401)+P1(f332(f332(f233(x82401),x82402),x82403))+~P1(f332(f332(f232(x82401),f2(x82401)),x82404))+~P1(f332(f332(f233(x82401),f332(f332(f83(x82401),x82404),x82402)),f332(f332(f83(x82401),x82404),x82403)))
% 52.62/52.42 [8241]~P125(x82411)+P1(f332(f332(f233(x82411),x82412),x82413))+~P1(f332(f332(f232(x82411),f2(x82411)),x82414))+~P1(f332(f332(f233(x82411),f332(f332(f83(x82411),x82414),x82412)),f332(f332(f83(x82411),x82414),x82413)))
% 52.62/52.42 [8242]~P117(x82421)+~P1(f332(f332(f232(x82421),f2(x82421)),x82423))+P1(f332(f332(f233(x82421),x82422),x82423))+~P1(f332(f332(f233(x82421),f332(f332(f242(x82421),x82422),x82424)),f332(f332(f242(x82421),x82423),x82424)))
% 52.62/52.42 [8243]~P123(x82431)+P1(f332(f332(f233(x82431),x82432),x82433))+~P1(f332(f332(f232(x82431),f2(x82431)),x82434))+~P1(f332(f332(f233(x82431),f332(f332(f83(x82431),x82432),x82434)),f332(f332(f83(x82431),x82433),x82434)))
% 52.62/52.42 [8244]~P125(x82441)+P1(f332(f332(f233(x82441),x82442),x82443))+~P1(f332(f332(f232(x82441),f2(x82441)),x82444))+~P1(f332(f332(f233(x82441),f332(f332(f83(x82441),x82442),x82444)),f332(f332(f83(x82441),x82443),x82444)))
% 52.62/52.42 [8245]~P119(x82451)+P1(f332(f332(f232(x82451),x82452),x82453))+~P1(f332(f332(f233(x82451),f2(x82451)),x82454))+~P1(f332(f332(f232(x82451),f332(f332(f83(x82451),x82454),x82452)),f332(f332(f83(x82451),x82454),x82453)))
% 52.62/52.42 [8246]~P123(x82461)+P1(f332(f332(f232(x82461),x82462),x82463))+~P1(f332(f332(f233(x82461),f2(x82461)),x82464))+~P1(f332(f332(f232(x82461),f332(f332(f83(x82461),x82464),x82462)),f332(f332(f83(x82461),x82464),x82463)))
% 52.62/52.42 [8247]~P123(x82471)+P1(f332(f332(f232(x82471),x82472),x82473))+~P1(f332(f332(f233(x82471),f2(x82471)),x82474))+~P1(f332(f332(f232(x82471),f332(f332(f83(x82471),x82472),x82474)),f332(f332(f83(x82471),x82473),x82474)))
% 52.62/52.42 [8287]P1(f332(f332(f334(x82871),x82872),x82873))+~P1(f332(f332(f232(f853(x82871,a839)),x82873),x82874))+~P1(f332(f332(f233(f853(x82871,a839)),x82873),x82874))+P1(f332(f332(f233(f853(x82871,a839)),x82873),f332(f332(f302(x82871),x82872),x82874)))
% 52.62/52.42 [8322]~P136(x83221)+~P112(x83221)+P1(f332(f332(f279(x83221),x83222),f332(f332(f82(x83221),f833(x83222,x83223,x83221)),f2(x83221))))+~P1(f332(x83223,f332(f332(f83(x83221),x83222),x83224)))
% 52.62/52.42 [8648]E(f332(f332(f3(a1),f346(x86481,x86482,x86483,x86484)),f347(x86481,x86482,x86483,x86484)),x86484)+~P1(f332(f332(f233(a1),f2(a1)),x86483))+~P1(f332(f332(f232(a1),x86481),x86484))+P1(f332(f332(f232(a1),x86481),f332(f332(f82(a1),x86484),x86483)))
% 52.62/52.42 [8649]E(f332(f332(f3(a1),f356(x86491,x86492,x86493,x86494)),f357(x86491,x86492,x86493,x86494)),x86494)+~P1(f332(f332(f233(a1),f2(a1)),x86493))+~P1(f332(f332(f233(a1),x86491),x86494))+P1(f332(f332(f233(a1),x86491),f332(f332(f82(a1),x86494),x86493)))
% 52.62/52.42 [8775]~E(f332(f332(f152(x87751),x87753),f756(x87754,x87753,x87751,x87752)),f332(f332(f152(x87751),x87754),f756(x87754,x87753,x87751,x87752)))+E(f332(f332(f159(x87751),x87752),x87753),f332(f332(f159(x87751),x87752),x87754))+~P1(f332(f332(f232(a845),x87752),f332(f181(f846(x87751)),x87753)))+~P1(f332(f332(f232(a845),x87752),f332(f181(f846(x87751)),x87754)))
% 52.62/52.42 [8826]~P1(f332(f332(f233(a1),f2(a1)),x88263))+~P1(f332(f332(f232(a1),x88261),x88264))+P1(f332(f332(f334(a1),f346(x88261,x88262,x88263,x88264)),x88262))+P1(f332(f332(f232(a1),x88261),f332(f332(f82(a1),x88264),x88263)))
% 52.62/52.42 [8827]~P1(f332(f332(f233(a1),f2(a1)),x88273))+~P1(f332(f332(f233(a1),x88271),x88274))+P1(f332(f332(f334(a1),f356(x88271,x88272,x88273,x88274)),x88272))+P1(f332(f332(f233(a1),x88271),f332(f332(f82(a1),x88274),x88273)))
% 52.62/52.42 [8864]~P100(x88641)+~P1(f332(f64(x88641),x88643))+~P1(f332(f332(f334(x88641),x88644),x88643))+P1(f332(f332(f232(x88641),f332(f332(f67(x88641,x88641,f236(x88641)),x88642),x88643)),f332(f332(f236(x88641),x88644),x88642)))
% 52.62/52.42 [8865]~P98(x88651)+~P1(f332(f64(x88651),x88653))+~P1(f332(f332(f334(x88651),x88654),x88653))+P1(f332(f332(f232(x88651),f332(f332(f67(x88651,x88651,f104(x88651)),x88652),x88653)),f332(f332(f104(x88651),x88654),x88652)))
% 52.62/52.42 [8874]~P14(x88742,x88743,x88744)+~P1(f332(f64(x88742),x88743))+P1(f332(f332(f279(a845),x88741),f332(f43(x88742),x88743)))+P1(f332(f332(f334(f853(x88742,a839)),f517(x88741,x88744,x88743,x88742)),f332(f332(f62(x88742),x88743),x88744)))
% 52.62/52.42 [8913]E(f332(f332(f159(x89131),x89132),x89133),f332(f332(f159(x89131),x89132),x89134))+P1(f332(f332(f233(a845),f756(x89133,x89134,x89131,x89132)),x89132))+~P1(f332(f332(f232(a845),x89132),f332(f181(f846(x89131)),x89133)))+~P1(f332(f332(f232(a845),x89132),f332(f181(f846(x89131)),x89134)))
% 52.62/52.42 [8918]~P1(f332(f332(f233(a1),f2(a1)),x89183))+~P1(f332(f332(f233(a1),x89181),x89182))+P1(f332(f332(f334(a1),f357(x89181,x89184,x89183,x89182)),f295(a1,f80(a1),x89183)))+P1(f332(f332(f233(a1),x89181),f332(f332(f82(a1),x89182),x89183)))
% 52.62/52.42 [8919]~P1(f332(f332(f233(a1),f2(a1)),x89193))+~P1(f332(f332(f232(a1),x89191),x89192))+P1(f332(f332(f334(a1),f347(x89191,x89194,x89193,x89192)),f295(a1,f80(a1),x89193)))+P1(f332(f332(f232(a1),x89191),f332(f332(f82(a1),x89192),x89193)))
% 52.62/52.42 [9082]~E(f166(x90821,x90822,x90823),f166(x90821,x90822,x90824))+E(f332(f158(f852(x90821,x90822)),x90823),f332(f158(f852(x90821,x90822)),x90824))+~P1(f332(f127(x90821),f332(f332(f143(f852(x90821,x90822),x90821),f240(x90821,x90822)),x90824)))+~P1(f332(f127(x90821),f332(f332(f143(f852(x90821,x90822),x90821),f240(x90821,x90822)),x90823)))
% 52.62/52.42 [9085]E(f166(x90851,x90852,x90853),f166(x90851,x90852,x90854))+~E(f332(f158(f852(x90851,x90852)),x90853),f332(f158(f852(x90851,x90852)),x90854))+~P1(f332(f127(x90851),f332(f332(f143(f852(x90851,x90852),x90851),f240(x90851,x90852)),x90854)))+~P1(f332(f127(x90851),f332(f332(f143(f852(x90851,x90852),x90851),f240(x90851,x90852)),x90853)))
% 52.62/52.42 [9202]~P100(x92021)+~P1(f332(f64(x92021),x92024))+P1(f332(f332(f334(x92021),f689(x92022,x92023,x92024,x92021)),x92024))+P1(f332(f332(f232(x92021),f332(f332(f67(x92021,x92021,f179(x92021)),x92022),x92024)),f332(f332(f179(x92021),x92023),x92022)))
% 52.62/52.42 [9203]~P92(x92031)+~P1(f332(f64(x92031),x92034))+P1(f332(f332(f334(x92031),f693(x92032,x92033,x92034,x92031)),x92034))+P1(f332(f332(f232(x92031),f332(f332(f67(x92031,x92031,f103(x92031)),x92032),x92034)),f332(f332(f103(x92031),x92033),x92032)))
% 52.62/52.42 [9329]~P100(x93291)+~P1(f332(f64(x93291),x93293))+~P1(f332(f332(f232(x93291),f689(x93292,x93294,x93293,x93291)),x93294))+P1(f332(f332(f232(x93291),f332(f332(f67(x93291,x93291,f179(x93291)),x93292),x93293)),f332(f332(f179(x93291),x93294),x93292)))
% 52.62/52.42 [9330]~P92(x93301)+~P1(f332(f64(x93301),x93303))+~P1(f332(f332(f232(x93301),f693(x93302,x93304,x93303,x93301)),x93304))+P1(f332(f332(f232(x93301),f332(f332(f67(x93301,x93301,f103(x93301)),x93302),x93303)),f332(f332(f103(x93301),x93304),x93302)))
% 52.62/52.42 [9332]~P1(f332(f332(f233(a1),f2(a1)),x93323))+~P1(f332(f332(f232(a1),f2(a1)),x93324))+~P1(f332(f332(f233(a1),x93324),x93321))+P1(f332(f332(f233(a1),f332(f332(f82(a1),f332(f332(f83(a1),x93321),f53(a1,x93322,x93323))),x93324)),f332(f332(f83(a1),x93321),x93323)))
% 52.62/52.42 [9592]~P99(x95921)+P1(f332(f332(f233(x95921),f332(x95922,x95923)),f332(x95922,x95924)))+~P1(f332(f332(f233(a845),x95923),x95924))+~P1(f332(f332(f233(x95921),f332(x95922,f649(x95924,x95923,x95922,x95921))),f332(x95922,f332(a114,f649(x95924,x95923,x95922,x95921)))))
% 52.62/52.42 [9593]~P99(x95931)+P1(f332(f332(f233(x95931),f332(x95932,x95933)),f332(x95932,x95934)))+~P1(f332(f332(f233(a845),x95933),x95934))+~P1(f332(f332(f233(x95931),f332(x95932,f662(x95934,x95933,x95932,x95931))),f332(x95932,f332(a114,f662(x95934,x95933,x95932,x95931)))))
% 52.62/52.42 [9594]~P99(x95943)+~P1(f332(f332(f233(x95943),f332(x95944,x95941)),f332(x95944,x95942)))+P1(f332(f332(f233(a845),x95941),x95942))+~P1(f332(f332(f233(x95943),f332(x95944,f649(x95942,x95941,x95944,x95943))),f332(x95944,f332(a114,f649(x95942,x95941,x95944,x95943)))))
% 52.62/52.42 [9687]E(x96871,x96872)+P1(f332(f332(f334(f852(f846(x96873),f846(x96873))),f332(f332(f241(f846(x96873),f846(x96873)),x96872),x96871)),f137(x96873,x96874)))+P1(f332(f332(f334(f852(f846(x96873),f846(x96873))),f332(f332(f241(f846(x96873),f846(x96873)),x96871),x96872)),f137(x96873,x96874)))+~P1(f332(f332(f334(f852(x96873,x96873)),f332(f332(f241(x96873,x96873),f751(x96871,x96872,x96874,x96873)),f753(x96871,x96872,x96874,x96873))),x96874))
% 52.62/52.42 [9688]E(x96881,x96882)+P1(f332(f332(f334(f852(f846(x96883),f846(x96883))),f332(f332(f241(f846(x96883),f846(x96883)),x96882),x96881)),f137(x96883,x96884)))+P1(f332(f332(f334(f852(f846(x96883),f846(x96883))),f332(f332(f241(f846(x96883),f846(x96883)),x96881),x96882)),f137(x96883,x96884)))+~P1(f332(f332(f334(f852(x96883,x96883)),f332(f332(f241(x96883,x96883),f753(x96881,x96882,x96884,x96883)),f751(x96881,x96882,x96884,x96883))),x96884))
% 52.62/52.42 [7377]~P100(x73771)+~P1(f332(f332(f233(x73771),x73773),x73774))+~P1(f332(f332(f233(x73771),x73772),x73774))+P1(f332(f332(f233(x73771),f332(f332(f179(x73771),x73772),x73773)),x73774))
% 52.62/52.42 [7378]~P100(x73781)+~P1(f332(f332(f232(x73781),x73783),x73784))+~P1(f332(f332(f232(x73781),x73782),x73784))+P1(f332(f332(f232(x73781),f332(f332(f179(x73781),x73782),x73783)),x73784))
% 52.62/52.42 [7379]~P100(x73791)+~P1(f332(f332(f232(x73791),x73793),x73794))+~P1(f332(f332(f232(x73791),x73792),x73794))+P1(f332(f332(f232(x73791),f332(f332(f179(x73791),x73792),x73793)),x73794))
% 52.62/52.42 [7380]~P100(x73801)+~P1(f332(f332(f232(x73801),x73803),x73804))+~P1(f332(f332(f232(x73801),x73802),x73804))+P1(f332(f332(f232(x73801),f332(f332(f179(x73801),x73802),x73803)),x73804))
% 52.62/52.42 [7381]~P92(x73811)+~P1(f332(f332(f232(x73811),x73813),x73814))+~P1(f332(f332(f232(x73811),x73812),x73814))+P1(f332(f332(f232(x73811),f332(f332(f103(x73811),x73812),x73813)),x73814))
% 52.62/52.42 [7382]~P92(x73821)+~P1(f332(f332(f232(x73821),x73823),x73824))+~P1(f332(f332(f232(x73821),x73822),x73824))+P1(f332(f332(f232(x73821),f332(f332(f103(x73821),x73822),x73823)),x73824))
% 52.62/52.42 [7383]~P92(x73831)+~P1(f332(f332(f232(x73831),x73833),x73834))+~P1(f332(f332(f232(x73831),x73832),x73834))+P1(f332(f332(f232(x73831),f332(f332(f103(x73831),x73832),x73833)),x73834))
% 52.62/52.42 [7624]~P9(x76241)+E(f332(f332(f82(x76241),f332(f332(f44(x76241),x76242),x76243)),f332(f332(f44(x76241),x76244),x76243)),f332(f332(f44(x76241),f332(f332(f82(x76241),x76242),x76244)),x76243))+~P1(f332(f332(f279(x76241),x76243),x76244))+~P1(f332(f332(f279(x76241),x76243),x76242))
% 52.62/52.42 [7702]~E(x77021,x77023)+E(f130(a845,f332(f294(a845,x77021),x77022)),f332(f332(f140(a845),x77023),x77024))+~E(f130(a845,f332(f294(a845,f332(f332(f82(a845),x77021),f80(a845))),x77022)),x77024)+~P1(f332(f332(f233(a845),x77021),x77022))
% 52.62/52.42 [7713]~P100(x77131)+P1(f332(f332(f233(x77131),x77132),x77133))+P1(f332(f332(f233(x77131),x77134),x77133))+~P1(f332(f332(f233(x77131),f332(f332(f236(x77131),x77134),x77132)),x77133))
% 52.62/52.42 [7714]~P100(x77141)+P1(f332(f332(f232(x77141),x77142),x77143))+P1(f332(f332(f232(x77141),x77144),x77143))+~P1(f332(f332(f232(x77141),f332(f332(f236(x77141),x77144),x77142)),x77143))
% 52.62/52.42 [7995]~P64(x79951)+~P1(f332(f332(f233(x79951),f2(x79951)),x79953))+~P1(f332(f332(f233(x79951),x79952),f332(f332(f283(x79951),x79954),x79953)))+P1(f332(f332(f233(x79951),f332(f332(f83(x79951),x79952),x79953)),x79954))
% 52.62/52.42 [7996]~P65(x79961)+~P1(f332(f332(f233(x79961),f2(x79961)),x79963))+~P1(f332(f332(f233(x79961),x79962),f332(f332(f283(x79961),x79964),x79963)))+P1(f332(f332(f233(x79961),f332(f332(f83(x79961),x79962),x79963)),x79964))
% 52.62/52.42 [7997]~P64(x79971)+~P1(f332(f332(f233(x79971),f2(x79971)),x79973))+~P1(f332(f332(f233(x79971),x79972),f332(f332(f83(x79971),x79974),x79973)))+P1(f332(f332(f233(x79971),f332(f332(f283(x79971),x79972),x79973)),x79974))
% 52.62/52.42 [7998]~P65(x79981)+~P1(f332(f332(f233(x79981),f2(x79981)),x79983))+~P1(f332(f332(f233(x79981),x79982),f332(f332(f83(x79981),x79984),x79983)))+P1(f332(f332(f233(x79981),f332(f332(f283(x79981),x79982),x79983)),x79984))
% 52.62/52.42 [7999]~P65(x79991)+~P1(f332(f332(f233(x79991),f2(x79991)),x79993))+~P1(f332(f332(f233(x79991),x79992),f332(f332(f83(x79991),x79994),x79993)))+P1(f332(f332(f233(x79991),f332(f332(f283(x79991),x79992),x79993)),x79994))
% 52.62/52.42 [8000]~P64(x80001)+~P1(f332(f332(f233(x80001),f2(x80001)),x80003))+~P1(f332(f332(f232(x80001),x80002),f332(f332(f283(x80001),x80004),x80003)))+P1(f332(f332(f232(x80001),f332(f332(f83(x80001),x80002),x80003)),x80004))
% 52.62/52.42 [8001]~P65(x80011)+~P1(f332(f332(f233(x80011),f2(x80011)),x80013))+~P1(f332(f332(f232(x80011),x80012),f332(f332(f283(x80011),x80014),x80013)))+P1(f332(f332(f232(x80011),f332(f332(f83(x80011),x80012),x80013)),x80014))
% 52.62/52.42 [8002]~P64(x80021)+~P1(f332(f332(f233(x80021),f2(x80021)),x80023))+~P1(f332(f332(f232(x80021),x80022),f332(f332(f83(x80021),x80024),x80023)))+P1(f332(f332(f232(x80021),f332(f332(f283(x80021),x80022),x80023)),x80024))
% 52.62/52.42 [8003]~P65(x80031)+~P1(f332(f332(f233(x80031),f2(x80031)),x80033))+~P1(f332(f332(f232(x80031),x80032),f332(f332(f83(x80031),x80034),x80033)))+P1(f332(f332(f232(x80031),f332(f332(f283(x80031),x80032),x80033)),x80034))
% 52.62/52.42 [8004]~P65(x80041)+~P1(f332(f332(f233(x80041),f2(x80041)),x80043))+~P1(f332(f332(f232(x80041),x80042),f332(f332(f83(x80041),x80044),x80043)))+P1(f332(f332(f232(x80041),f332(f332(f283(x80041),x80042),x80043)),x80044))
% 52.62/52.42 [8128]~P64(x81281)+~P1(f332(f332(f233(x81281),f2(x81281)),x81284))+P1(f332(f332(f233(x81281),x81282),f332(f332(f83(x81281),x81283),x81284)))+~P1(f332(f332(f233(x81281),f332(f332(f283(x81281),x81282),x81284)),x81283))
% 52.62/52.42 [8129]~P64(x81291)+~P1(f332(f332(f233(x81291),f2(x81291)),x81294))+P1(f332(f332(f233(x81291),x81292),f332(f332(f283(x81291),x81293),x81294)))+~P1(f332(f332(f233(x81291),f332(f332(f83(x81291),x81292),x81294)),x81293))
% 52.62/52.42 [8130]~P65(x81301)+~P1(f332(f332(f233(x81301),f2(x81301)),x81304))+P1(f332(f332(f233(x81301),x81302),f332(f332(f283(x81301),x81303),x81304)))+~P1(f332(f332(f233(x81301),f332(f332(f83(x81301),x81302),x81304)),x81303))
% 52.62/52.42 [8131]~P65(x81311)+~P1(f332(f332(f233(x81311),f2(x81311)),x81314))+P1(f332(f332(f233(x81311),x81312),f332(f332(f83(x81311),x81313),x81314)))+~P1(f332(f332(f233(x81311),f332(f332(f283(x81311),x81312),x81314)),x81313))
% 52.62/52.42 [8132]~P65(x81321)+~P1(f332(f332(f233(x81321),f2(x81321)),x81324))+P1(f332(f332(f233(x81321),x81322),f332(f332(f283(x81321),x81323),x81324)))+~P1(f332(f332(f233(x81321),f332(f332(f83(x81321),x81322),x81324)),x81323))
% 52.62/52.42 [8133]~P64(x81331)+~P1(f332(f332(f233(x81331),f2(x81331)),x81334))+P1(f332(f332(f232(x81331),x81332),f332(f332(f83(x81331),x81333),x81334)))+~P1(f332(f332(f232(x81331),f332(f332(f283(x81331),x81332),x81334)),x81333))
% 52.62/52.42 [8134]~P64(x81341)+~P1(f332(f332(f233(x81341),f2(x81341)),x81344))+P1(f332(f332(f232(x81341),x81342),f332(f332(f283(x81341),x81343),x81344)))+~P1(f332(f332(f232(x81341),f332(f332(f83(x81341),x81342),x81344)),x81343))
% 52.62/52.42 [8135]~P65(x81351)+~P1(f332(f332(f233(x81351),f2(x81351)),x81354))+P1(f332(f332(f232(x81351),x81352),f332(f332(f283(x81351),x81353),x81354)))+~P1(f332(f332(f232(x81351),f332(f332(f83(x81351),x81352),x81354)),x81353))
% 52.62/52.42 [8136]~P65(x81361)+~P1(f332(f332(f233(x81361),f2(x81361)),x81364))+P1(f332(f332(f232(x81361),x81362),f332(f332(f83(x81361),x81363),x81364)))+~P1(f332(f332(f232(x81361),f332(f332(f283(x81361),x81362),x81364)),x81363))
% 52.62/52.42 [8137]~P65(x81371)+~P1(f332(f332(f233(x81371),f2(x81371)),x81374))+P1(f332(f332(f232(x81371),x81372),f332(f332(f283(x81371),x81373),x81374)))+~P1(f332(f332(f232(x81371),f332(f332(f83(x81371),x81372),x81374)),x81373))
% 52.62/52.42 [8292]~P65(x82921)+~P1(f332(f332(f233(x82921),x82923),f2(x82921)))+~P1(f332(f332(f233(x82921),f332(f332(f283(x82921),x82924),x82923)),x82922))+P1(f332(f332(f233(x82921),f332(f332(f83(x82921),x82922),x82923)),x82924))
% 52.62/52.42 [8293]~P65(x82931)+~P1(f332(f332(f233(x82931),x82933),f2(x82931)))+~P1(f332(f332(f233(x82931),f332(f332(f83(x82931),x82934),x82933)),x82932))+P1(f332(f332(f233(x82931),f332(f332(f283(x82931),x82932),x82933)),x82934))
% 52.62/52.42 [8294]~P65(x82941)+~P1(f332(f332(f233(x82941),x82943),f2(x82941)))+~P1(f332(f332(f232(x82941),f332(f332(f283(x82941),x82944),x82943)),x82942))+P1(f332(f332(f232(x82941),f332(f332(f83(x82941),x82942),x82943)),x82944))
% 52.62/52.42 [8295]~P65(x82951)+~P1(f332(f332(f233(x82951),x82953),f2(x82951)))+~P1(f332(f332(f232(x82951),f332(f332(f83(x82951),x82954),x82953)),x82952))+P1(f332(f332(f232(x82951),f332(f332(f283(x82951),x82952),x82953)),x82954))
% 52.62/52.42 [8308]~P1(f332(x83081,x83084))+~P1(f332(f332(f233(a845),x83082),f332(f332(f83(a845),x83083),f332(a114,x83084))))+P1(f332(x83081,f332(f332(f44(a845),x83082),x83083)))+~P1(f332(f332(f232(a845),f332(f332(f83(a845),x83083),x83084)),x83082))
% 52.62/52.42 [8523]~P100(x85231)+~P1(f332(f64(x85231),x85234))+~P1(f332(f332(f334(x85231),x85232),x85234))+P1(f332(f332(f232(x85231),f332(f332(f179(x85231),x85232),x85233)),f332(f332(f67(x85231,x85231,f179(x85231)),x85233),x85234)))
% 52.62/52.42 [8524]~P92(x85241)+~P1(f332(f64(x85241),x85244))+~P1(f332(f332(f334(x85241),x85242),x85244))+P1(f332(f332(f232(x85241),f332(f332(f103(x85241),x85242),x85243)),f332(f332(f67(x85241,x85241,f103(x85241)),x85243),x85244)))
% 52.62/52.42 [8650]~P1(f332(f64(x86501),x86502))+E(f332(f43(x86501),f332(f332(f3(f853(x86501,a839)),x86502),f332(f332(f302(x86501),x86503),x86504))),f332(f332(f3(a845),f332(f43(x86501),f332(f332(f3(f853(x86501,a839)),x86502),x86504))),f80(a845)))+P1(f332(f332(f334(x86501),x86503),x86504))+~P1(f332(f332(f334(x86501),x86503),x86502))
% 52.62/52.42 [8714]E(f332(f332(f82(a1),f348(x87141,x87142,x87143,x87144)),f349(x87141,x87142,x87143,x87144)),x87144)+~P1(f332(f332(f233(a1),f2(a1)),x87143))+~P1(f332(f332(f232(a1),x87144),x87141))+P1(f332(f332(f232(a1),f332(f332(f3(a1),x87144),x87143)),x87141))
% 52.62/52.42 [8715]E(f332(f332(f82(a1),f359(x87151,x87152,x87153,x87154)),f360(x87151,x87152,x87153,x87154)),x87154)+~P1(f332(f332(f233(a1),f2(a1)),x87153))+~P1(f332(f332(f233(a1),x87154),x87151))+P1(f332(f332(f233(a1),f332(f332(f3(a1),x87154),x87153)),x87151))
% 52.62/52.42 [8898]~P1(f332(f332(f233(a1),f2(a1)),x88983))+~P1(f332(f332(f232(a1),x88984),x88981))+P1(f332(f332(f334(a1),f348(x88981,x88982,x88983,x88984)),x88982))+P1(f332(f332(f232(a1),f332(f332(f3(a1),x88984),x88983)),x88981))
% 52.62/52.42 [8899]~P1(f332(f332(f233(a1),f2(a1)),x88993))+~P1(f332(f332(f233(a1),x88994),x88991))+P1(f332(f332(f334(a1),f359(x88991,x88992,x88993,x88994)),x88992))+P1(f332(f332(f233(a1),f332(f332(f3(a1),x88994),x88993)),x88991))
% 52.62/52.42 [8978]~P1(f332(f332(f233(a1),f2(a1)),x89782))+~P1(f332(f332(f233(a1),x89781),x89783))+P1(f332(f332(f334(a1),f360(x89783,x89784,x89782,x89781)),f295(a1,f80(a1),x89782)))+P1(f332(f332(f233(a1),f332(f332(f3(a1),x89781),x89782)),x89783))
% 52.62/52.42 [8979]~P1(f332(f332(f233(a1),f2(a1)),x89792))+~P1(f332(f332(f232(a1),x89791),x89793))+P1(f332(f332(f334(a1),f349(x89793,x89794,x89792,x89791)),f295(a1,f80(a1),x89792)))+P1(f332(f332(f232(a1),f332(f332(f3(a1),x89791),x89792)),x89793))
% 52.62/52.42 [9000]~P1(f332(f332(f233(a1),f2(a1)),x90003))+~P1(f332(f332(f232(a1),f2(a1)),x90004))+~P1(f332(f332(f233(a1),x90004),x90001))+P1(f332(f332(f232(a1),f2(a1)),f332(f332(f82(a1),f332(f332(f83(a1),x90001),f53(a1,x90002,x90003))),x90004)))
% 52.62/52.42 [9058]~P100(x90581)+~P1(f332(f64(x90581),x90584))+~P1(f332(f332(f232(x90581),x90582),f688(x90583,x90582,x90584,x90581)))+P1(f332(f332(f232(x90581),f332(f332(f236(x90581),x90582),x90583)),f332(f332(f67(x90581,x90581,f236(x90581)),x90583),x90584)))
% 52.62/52.42 [9059]~P98(x90591)+~P1(f332(f64(x90591),x90594))+~P1(f332(f332(f232(x90591),x90592),f692(x90593,x90592,x90594,x90591)))+P1(f332(f332(f232(x90591),f332(f332(f104(x90591),x90592),x90593)),f332(f332(f67(x90591,x90591,f104(x90591)),x90593),x90594)))
% 52.62/52.42 [9072]~P1(f332(f332(f232(a1),x90724),f2(a1)))+~P1(f332(f332(f233(a1),f2(a1)),x90722))+~P1(f332(f332(f233(a1),x90721),x90724))+P1(f332(f332(f233(a1),f332(f332(f83(a1),x90721),x90722)),f332(f332(f82(a1),f332(f332(f83(a1),x90721),f53(a1,x90723,x90722))),x90724)))
% 52.62/52.42 [9094]P1(f332(f64(x90941),x90942))+~P1(f332(f64(x90941),x90943))+~P1(f332(f332(f334(f853(x90941,a839)),x90942),f332(f332(f62(x90941),x90943),x90944)))+~P1(f332(f332(f232(f853(f852(x90941,x90941),a839)),x90944),f332(f332(f248(x90941,x90941),x90943),f332(f18(f853(x90941,a839),x90941),x90943))))
% 52.62/52.42 [9117]~P100(x91171)+~P1(f332(f64(x91171),x91174))+P1(f332(f332(f334(x91171),f688(x91172,x91173,x91174,x91171)),x91174))+P1(f332(f332(f232(x91171),f332(f332(f236(x91171),x91173),x91172)),f332(f332(f67(x91171,x91171,f236(x91171)),x91172),x91174)))
% 52.62/52.42 [9118]~P98(x91181)+~P1(f332(f64(x91181),x91184))+P1(f332(f332(f334(x91181),f692(x91182,x91183,x91184,x91181)),x91184))+P1(f332(f332(f232(x91181),f332(f332(f104(x91181),x91183),x91182)),f332(f332(f67(x91181,x91181,f104(x91181)),x91182),x91184)))
% 52.62/52.42 [9490]~P1(f332(f64(x94902),x94904))+~P1(f332(f64(x94901),x94903))+~P1(f332(f332(f232(a845),f332(f43(x94902),x94904)),f332(f43(x94901),x94903)))+P1(f332(f332(f232(f853(x94901,a839)),f332(f303(x94902,x94901,f528(x94903,x94901,x94904,x94902)),x94904)),x94903))
% 52.62/52.42 [9155]~P1(f332(f332(f334(x91551),x91552),x91554))+P1(f332(f332(f334(x91551),x91552),x91553))+~P1(f332(f332(f233(f853(x91551,a839)),x91554),f332(f332(f302(x91551),x91552),x91553)))+P1(f332(f332(f233(f853(x91551,a839)),f332(f332(f3(f853(x91551,a839)),x91554),f332(f332(f302(x91551),x91552),f180(f853(x91551,a839))))),x91553))
% 52.62/52.42 [9307]~P1(f332(f332(f334(x93071),x93072),x93074))+P1(f332(f332(f334(x93071),x93072),x93073))+P1(f332(f332(f233(f853(x93071,a839)),x93074),f332(f332(f302(x93071),x93072),x93073)))+~P1(f332(f332(f233(f853(x93071,a839)),f332(f332(f3(f853(x93071,a839)),x93074),f332(f332(f302(x93071),x93072),f180(f853(x93071,a839))))),x93073))
% 52.62/52.42 [9335]P1(f332(f332(f334(x93351),x93352),x93353))+~P1(f332(f332(f232(f853(x93351,a839)),x93354),x93353))+P1(f332(f332(f233(f853(x93351,a839)),x93354),f332(f332(f302(x93351),x93352),x93353)))+~P1(f332(f332(f233(f853(x93351,a839)),f332(f332(f3(f853(x93351,a839)),x93354),f332(f332(f302(x93351),x93352),f180(f853(x93351,a839))))),x93353))
% 52.62/52.42 [9340]~P1(f332(f332(f334(x93401),x93403),x93402))+~P1(f332(f332(f233(f853(x93401,a839)),x93402),x93404))+P1(f332(f332(f233(f853(x93401,a839)),x93402),f332(f332(f302(x93401),x93403),x93404)))+~P1(f332(f332(f233(f853(x93401,a839)),f332(f332(f3(f853(x93401,a839)),x93402),f332(f332(f302(x93401),x93403),f180(f853(x93401,a839))))),x93404))
% 52.62/52.42 [9352]~P1(f332(f332(f232(f853(x93521,a839)),x93522),x93524))+~P1(f332(f332(f233(f853(x93521,a839)),x93522),x93524))+P1(f332(f332(f233(f853(x93521,a839)),x93522),f332(f332(f302(x93521),x93523),x93524)))+~P1(f332(f332(f233(f853(x93521,a839)),f332(f332(f3(f853(x93521,a839)),x93522),f332(f332(f302(x93521),x93523),f180(f853(x93521,a839))))),x93524))
% 52.62/52.42 [9679]E(f332(f332(f152(x96791),f332(f332(f152(f846(x96791)),f164(x96791,x96792)),x96793)),x96794),f332(f332(f152(x96791),f332(f332(f152(f846(x96791)),x96792),x96794)),x96793))+~P1(f332(f332(f233(a845),x96793),f332(f181(f846(f846(x96791))),f164(x96791,x96792))))+~P20(a845,f332(f142(a845),f332(f332(f143(f846(x96791),a845),f181(f846(x96791))),x96792)))+~P1(f332(f332(f233(a845),x96794),f332(f181(f846(f846(x96791))),f332(f126(f846(x96791),f332(f332(f10(a845,a839,f846(x96791)),f332(f233(a845),x96793)),f181(f846(x96791)))),x96792))))
% 52.62/52.42 [9700]~P1(f332(f332(f334(f852(a845,a845)),x97004),x97001))+~P1(f332(f332(f334(f852(f852(a845,a845),f852(a845,a845))),f332(f332(f241(f852(a845,a845),f852(a845,a845)),x97004),x97002)),a40))+~P1(f332(f332(f334(f852(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839))),f332(f332(f241(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839)),x97001),x97003)),a41))+P1(f332(f332(f334(f852(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839))),f332(f332(f241(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839)),x97001),f332(f332(f302(f852(a845,a845)),x97002),x97003))),a41))
% 52.62/52.42 [9701]~P1(f332(f332(f334(f852(a845,a845)),x97014),x97011))+~P1(f332(f332(f334(f852(f852(a845,a845),f852(a845,a845))),f332(f332(f241(f852(a845,a845),f852(a845,a845)),x97014),x97012)),a72))+~P1(f332(f332(f334(f852(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839))),f332(f332(f241(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839)),x97011),x97013)),a73))+P1(f332(f332(f334(f852(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839))),f332(f332(f241(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839)),x97011),f332(f332(f302(f852(a845,a845)),x97012),x97013))),a73))
% 52.62/52.42 [9714]~P1(f332(f332(f334(f852(a845,a845)),x97144),x97143))+~P1(f332(f332(f334(f852(f852(a845,a845),f852(a845,a845))),f332(f332(f241(f852(a845,a845),f852(a845,a845)),x97141),x97144)),a40))+~P1(f332(f332(f334(f852(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839))),f332(f332(f241(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839)),x97142),x97143)),a42))+P1(f332(f332(f334(f852(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839))),f332(f332(f241(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839)),f332(f332(f302(f852(a845,a845)),x97141),x97142)),x97143)),a42))
% 52.62/52.42 [9715]~P1(f332(f332(f334(f852(a845,a845)),x97154),x97153))+~P1(f332(f332(f334(f852(f852(a845,a845),f852(a845,a845))),f332(f332(f241(f852(a845,a845),f852(a845,a845)),x97151),x97154)),a72))+~P1(f332(f332(f334(f852(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839))),f332(f332(f241(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839)),x97152),x97153)),a71))+P1(f332(f332(f334(f852(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839))),f332(f332(f241(f853(f852(a845,a845),a839),f853(f852(a845,a845),a839)),f332(f332(f302(f852(a845,a845)),x97151),x97152)),x97153)),a71))
% 52.62/52.42 [5905]~P13(x59054,x59051)+~P1(f332(f332(x59051,x59052),x59055))+P1(f332(f332(x59051,x59052),x59053))+~P1(f332(f332(x59051,x59055),x59053))
% 52.62/52.42 [5171]~P8(x51715)+E(x51711,x51712)+~E(x51713,x51714)+~E(f332(f332(f3(x51715),x51713),x51714),f332(f332(f3(x51715),x51711),x51712))
% 52.62/52.42 [5172]~P8(x51725)+E(x51721,x51722)+~E(x51723,x51724)+~E(f332(f332(f3(x51725),x51723),x51724),f332(f332(f3(x51725),x51721),x51722))
% 52.62/52.42 [6018]~P23(x60185,x60181,x60183)+E(f332(f332(x60181,x60182),f332(x60183,x60184)),f332(x60183,x60184))+~P1(f332(f64(x60185),x60184))+~P1(f332(f332(f334(x60185),x60182),x60184))
% 52.62/52.42 [6216]~P78(x62161)+~E(f332(f332(f3(x62161),x62164),x62165),f332(f332(f3(x62161),x62162),x62163))+~P1(f332(f332(f233(x62161),x62164),x62165))+P1(f332(f332(f233(x62161),x62162),x62163))
% 52.62/52.42 [6217]~P78(x62171)+~E(f332(f332(f3(x62171),x62174),x62175),f332(f332(f3(x62171),x62172),x62173))+~P1(f332(f332(f233(x62171),x62174),x62175))+P1(f332(f332(f233(x62171),x62172),x62173))
% 52.62/52.42 [6218]~P78(x62181)+~E(f332(f332(f3(x62181),x62184),x62185),f332(f332(f3(x62181),x62182),x62183))+~P1(f332(f332(f232(x62181),x62184),x62185))+P1(f332(f332(f232(x62181),x62182),x62183))
% 52.62/52.42 [6219]~P78(x62191)+~E(f332(f332(f3(x62191),x62194),x62195),f332(f332(f3(x62191),x62192),x62193))+~P1(f332(f332(f232(x62191),x62194),x62195))+P1(f332(f332(f232(x62191),x62192),x62193))
% 52.62/52.42 [7222]~E(x72222,f332(f332(f140(x72221),x72224),x72225))+P1(f332(f332(f334(f846(x72221)),x72222),f149(x72221,x72223)))+~P1(f332(f332(f334(f846(x72221)),x72225),f149(x72221,x72223)))+~P1(f332(f332(f334(x72221),x72224),x72223))
% 52.62/52.42 [7656]~E(f332(f181(f846(x76561)),x76563),f332(f181(f846(x76562)),x76564))+~E(f332(f332(f143(f852(x76561,x76562),x76562),f250(x76561,x76562)),x76565),x76564)+~E(f332(f332(f143(f852(x76561,x76562),x76561),f240(x76561,x76562)),x76565),x76563)+E(f332(f332(f167(x76561,x76562),x76563),x76564),x76565)
% 52.62/52.42 [7992]~P99(x79921)+P1(f332(f332(f233(f853(x79921,a839)),f295(x79921,x79922,x79923)),f295(x79921,x79924,x79925)))+~P1(f332(f332(f232(x79921),x79924),x79925))+P1(f332(f332(f232(x79921),x79922),x79923))
% 52.62/52.42 [8084]~P99(x80841)+P1(f332(f332(f232(f853(x80841,a839)),f295(x80841,x80842,x80843)),f295(x80841,x80844,x80845)))+~P1(f332(f332(f232(x80841),x80843),x80845))+~P1(f332(f332(f232(x80841),x80844),x80842))
% 52.62/52.42 [8202]~P100(x82021)+P1(f332(f332(f232(x82021),x82022),x82023))+P1(f332(f332(f232(x82021),x82024),x82023))+~P1(f332(f332(f232(f853(x82021,a839)),f332(f294(x82021,x82023),x82022)),f332(f294(x82021,x82024),x82025)))
% 52.62/52.42 [8203]~P100(x82031)+P1(f332(f332(f232(x82031),x82032),x82033))+P1(f332(f332(f232(x82031),x82032),x82034))+~P1(f332(f332(f232(f853(x82031,a839)),f332(f294(x82031,x82033),x82032)),f332(f294(x82031,x82035),x82034)))
% 52.62/52.42 [8443]~P99(x84431)+~P1(f332(f332(f233(f853(x84431,a839)),f295(x84431,x84434,x84432)),f295(x84431,x84435,x84433)))+P1(f332(f332(f232(x84431),x84432),x84433))+~P1(f332(f332(f232(x84431),x84434),x84432))
% 52.62/52.42 [8444]~P99(x84441)+~P1(f332(f332(f232(f853(x84441,a839)),f295(x84441,x84444,x84442)),f295(x84441,x84445,x84443)))+P1(f332(f332(f232(x84441),x84442),x84443))+~P1(f332(f332(f232(x84441),x84444),x84442))
% 52.62/52.42 [8445]~P99(x84451)+~P1(f332(f332(f233(f853(x84451,a839)),f295(x84451,x84453,x84454)),f295(x84451,x84452,x84455)))+P1(f332(f332(f232(x84451),x84452),x84453))+~P1(f332(f332(f232(x84451),x84453),x84454))
% 52.62/52.42 [8446]~P99(x84461)+~P1(f332(f332(f232(f853(x84461,a839)),f295(x84461,x84463,x84464)),f295(x84461,x84462,x84465)))+P1(f332(f332(f232(x84461),x84462),x84463))+~P1(f332(f332(f232(x84461),x84463),x84464))
% 52.62/52.42 [5904]~P23(x59042,x59045,x59043)+E(x59041,f180(f853(x59042,a839)))+~P1(f332(f64(x59042),x59041))+E(f332(x59043,f332(f332(f302(x59042),x59044),x59041)),f332(f332(x59045,x59044),f332(x59043,x59041)))
% 52.62/52.42 [6710]~E(x67101,x67102)+~E(f332(f332(f104(f853(x67103,a839)),x67104),x67105),f180(f853(x67103,a839)))+~P1(f332(f332(f334(x67103),x67102),x67105))+~P1(f332(f332(f334(x67103),x67101),x67104))
% 52.62/52.42 [6796]~P24(x67962,x67965,x67961)+~P1(f332(f64(x67962),x67964))+E(f332(x67961,f332(f332(f302(x67962),x67963),x67964)),f332(f332(f67(x67962,x67962,x67965),x67963),x67964))+P1(f332(f332(f334(x67962),x67963),x67964))
% 52.62/52.42 [6866]~P4(x68662)+~P1(f332(f64(x68661),x68665))+E(f332(f332(f8(x68661,x68662),x68663),f332(f332(f302(x68661),x68664),x68665)),f332(f332(f82(x68662),f332(x68663,x68664)),f332(f332(f8(x68661,x68662),x68663),x68665)))+P1(f332(f332(f334(x68661),x68664),x68665))
% 52.62/52.42 [6867]~P4(x68672)+~P1(f332(f64(x68671),x68675))+E(f332(f332(f8(x68671,x68672),x68673),f332(f332(f302(x68671),x68674),x68675)),f332(f332(f82(x68672),f332(x68673,x68674)),f332(f332(f8(x68671,x68672),x68673),x68675)))+P1(f332(f332(f334(x68671),x68674),x68675))
% 52.62/52.42 [6868]~P70(x68682)+~P1(f332(f64(x68681),x68685))+E(f332(f332(f11(x68681,x68682),x68683),f332(f332(f302(x68681),x68684),x68685)),f332(f332(f83(x68682),f332(x68683,x68684)),f332(f332(f11(x68681,x68682),x68683),x68685)))+P1(f332(f332(f334(x68681),x68684),x68685))
% 52.62/52.42 [6869]~P70(x68692)+~P1(f332(f64(x68691),x68695))+E(f332(f332(f11(x68691,x68692),x68693),f332(f332(f302(x68691),x68694),x68695)),f332(f332(f83(x68692),f332(x68693,x68694)),f332(f332(f11(x68691,x68692),x68693),x68695)))+P1(f332(f332(f334(x68691),x68694),x68695))
% 52.62/52.42 [7280]~P73(x72801)+~P1(f332(f64(x72804),x72805))+~P1(f332(f332(f334(x72804),x72803),x72805))+P1(f332(f332(f279(x72801),f332(x72802,x72803)),f332(f332(f11(x72804,x72801),x72802),x72805)))
% 52.62/52.42 [7393]~P24(x73932,x73935,x73931)+~P1(f332(f64(x73932),x73934))+E(f332(x73931,f332(f332(f302(x73932),x73933),x73934)),x73933)+~E(f332(f332(f3(f853(x73932,a839)),x73934),f332(f332(f302(x73932),x73933),f180(f853(x73932,a839)))),f180(f853(x73932,a839)))
% 52.62/52.42 [7705]~P1(f332(x77051,x77053))+~P1(f332(f332(f187(x77052),x77053),x77055))+~P1(f332(f332(f187(f35(x77051,x77052)),x77055),x77054))+P1(f332(f332(f187(f35(x77051,x77052)),x77053),x77054))
% 52.62/52.42 [7706]~P1(f332(x77061,x77063))+~P1(f332(f332(f187(x77062),x77063),x77065))+~P1(f332(f332(f187(f35(x77061,x77062)),x77065),x77064))+P1(f332(f332(f187(f35(x77061,x77062)),x77063),x77064))
% 52.62/52.42 [7724]~P73(x77241)+~P1(f332(f332(f279(x77241),x77242),x77244))+~P1(f332(f332(f232(a845),x77243),x77245))+P1(f332(f332(f279(x77241),f332(f332(f242(x77241),x77242),x77243)),f332(f332(f242(x77241),x77244),x77245)))
% 52.62/52.42 [7758]~P9(x77581)+E(f332(f332(f44(x77581),f332(f332(f83(x77581),x77582),x77583)),f332(f332(f83(x77581),x77584),x77585)),f332(f332(f83(x77581),f332(f332(f44(x77581),x77582),x77584)),f332(f332(f44(x77581),x77583),x77585)))+~P1(f332(f332(f279(x77581),x77585),x77583))+~P1(f332(f332(f279(x77581),x77584),x77582))
% 52.62/52.42 [7762]~P81(x77621)+~P1(f332(f332(f233(x77621),x77623),x77625))+~P1(f332(f332(f233(x77621),x77622),x77624))+P1(f332(f332(f233(x77621),f332(f332(f82(x77621),x77622),x77623)),f332(f332(f82(x77621),x77624),x77625)))
% 52.62/52.42 [7763]~P81(x77631)+~P1(f332(f332(f232(x77631),x77632),x77634))+~P1(f332(f332(f233(x77631),x77633),x77635))+P1(f332(f332(f233(x77631),f332(f332(f82(x77631),x77632),x77633)),f332(f332(f82(x77631),x77634),x77635)))
% 52.62/52.42 [7764]~P81(x77641)+~P1(f332(f332(f232(x77641),x77643),x77645))+~P1(f332(f332(f233(x77641),x77642),x77644))+P1(f332(f332(f233(x77641),f332(f332(f82(x77641),x77642),x77643)),f332(f332(f82(x77641),x77644),x77645)))
% 52.62/52.42 [7765]~P79(x77651)+~P1(f332(f332(f232(x77651),x77653),x77655))+~P1(f332(f332(f232(x77651),x77652),x77654))+P1(f332(f332(f232(x77651),f332(f332(f82(x77651),x77652),x77653)),f332(f332(f82(x77651),x77654),x77655)))
% 52.62/52.42 [7766]~P100(x77661)+~P1(f332(f332(f232(x77661),x77663),x77665))+~P1(f332(f332(f232(x77661),x77662),x77664))+P1(f332(f332(f232(x77661),f332(f332(f236(x77661),x77662),x77663)),f332(f332(f236(x77661),x77664),x77665)))
% 52.62/52.42 [7767]~P100(x77671)+~P1(f332(f332(f232(x77671),x77673),x77675))+~P1(f332(f332(f232(x77671),x77672),x77674))+P1(f332(f332(f232(x77671),f332(f332(f179(x77671),x77672),x77673)),f332(f332(f179(x77671),x77674),x77675)))
% 52.62/52.42 [7768]~P92(x77681)+~P1(f332(f332(f232(x77681),x77683),x77685))+~P1(f332(f332(f232(x77681),x77682),x77684))+P1(f332(f332(f232(x77681),f332(f332(f103(x77681),x77682),x77683)),f332(f332(f103(x77681),x77684),x77685)))
% 52.62/52.42 [7769]~P98(x77691)+~P1(f332(f332(f232(x77691),x77693),x77695))+~P1(f332(f332(f232(x77691),x77692),x77694))+P1(f332(f332(f232(x77691),f332(f332(f104(x77691),x77692),x77693)),f332(f332(f104(x77691),x77694),x77695)))
% 52.62/52.42 [7770]~P73(x77701)+~P1(f332(f332(f279(x77701),x77703),x77705))+~P1(f332(f332(f279(x77701),x77702),x77704))+P1(f332(f332(f279(x77701),f332(f332(f83(x77701),x77702),x77703)),f332(f332(f83(x77701),x77704),x77705)))
% 52.62/52.42 [7902]~P137(x79025)+E(x79021,x79022)+E(x79023,x79024)+~E(f332(f332(f82(x79025),f332(f332(f83(x79025),x79023),x79021)),f332(f332(f83(x79025),x79024),x79022)),f332(f332(f82(x79025),f332(f332(f83(x79025),x79023),x79022)),f332(f332(f83(x79025),x79024),x79021)))
% 52.62/52.42 [7903]~P137(x79035)+E(x79031,x79032)+E(x79033,x79034)+~E(f332(f332(f82(x79035),f332(f332(f83(x79035),x79033),x79031)),f332(f332(f83(x79035),x79034),x79032)),f332(f332(f82(x79035),f332(f332(f83(x79035),x79033),x79032)),f332(f332(f83(x79035),x79034),x79031)))
% 52.62/52.42 [8041]P33(x80411,x80412,x80413)+~P34(x80411,x80414,x80415)+~P33(x80411,x80412,f793(x80415,x80414,x80411,x80412))+~P1(f332(f332(f334(f844(x80411)),x80413),x80415))
% 52.62/52.42 [8104]~P100(x81044)+~P1(f332(f127(x81041),x81043))+P1(f332(f332(f334(x81041),x81042),f332(f158(x81041),x81043)))+P1(f332(f127(x81041),f332(f332(f138(x81041,x81044,x81045),x81042),x81043)))
% 52.62/52.42 [8248]~P4(x82481)+E(f332(f332(f82(x82481),f332(f332(f8(a845,x82481),x82482),f332(f294(a845,x82483),x82484))),f332(f332(f8(a845,x82481),x82482),f332(f294(a845,x82484),x82485))),f332(f332(f8(a845,x82481),x82482),f332(f294(a845,x82483),x82485)))+~P1(f332(f332(f232(a845),x82484),x82485))+~P1(f332(f332(f232(a845),x82483),x82484))
% 52.62/52.42 [8249]~P8(x82491)+E(f332(f332(f3(x82491),f332(f332(f8(a845,x82491),x82492),f332(f294(a845,x82493),x82494))),f332(f332(f8(a845,x82491),x82492),f332(f294(a845,x82493),x82495))),f332(f332(f8(a845,x82491),x82492),f332(f294(a845,x82495),x82494)))+~P1(f332(f332(f232(a845),x82495),x82494))+~P1(f332(f332(f232(a845),x82493),x82495))
% 52.62/52.42 [8568]~P63(x85682)+E(x85681,f2(x85682))+E(x85683,f2(x85682))+E(f332(f332(f283(x85682),f332(f332(f82(x85682),f332(f332(f83(x85682),x85684),x85681)),f332(f332(f83(x85682),x85685),x85683))),f332(f332(f83(x85682),x85683),x85681)),f332(f332(f82(x85682),f332(f332(f283(x85682),x85684),x85683)),f332(f332(f283(x85682),x85685),x85681)))
% 52.62/52.42 [8569]~P63(x85692)+E(x85691,f2(x85692))+E(x85693,f2(x85692))+E(f332(f332(f283(x85692),f332(f332(f3(x85692),f332(f332(f83(x85692),x85694),x85691)),f332(f332(f83(x85692),x85695),x85693))),f332(f332(f83(x85692),x85693),x85691)),f332(f332(f3(x85692),f332(f332(f283(x85692),x85694),x85693)),f332(f332(f283(x85692),x85695),x85691)))
% 52.62/52.42 [8578]~E(x85782,f332(x85783,x85781))+E(x85781,f522(x85782,x85783,x85784,x85785))+~P31(x85785,x85784,x85783,f239(f853(x85785,a839)))+~P1(f332(f332(f334(x85784),x85782),f332(f303(x85785,x85784,x85783),f239(f853(x85785,a839)))))
% 52.62/52.42 [8762]~P110(x87621)+~P1(f332(f332(f233(x87621),f332(f77(x87621),x87622)),x87624))+P1(f332(f332(f233(x87621),f332(f332(f83(x87621),f332(f77(x87621),x87622)),f332(f77(x87621),x87623))),f332(f332(f83(x87621),x87624),x87625)))+~P1(f332(f332(f233(x87621),f332(f77(x87621),x87623)),x87625))
% 52.62/52.42 [8776]~P34(x87761,x87765,x87764)+P33(x87761,x87762,x87763)+P1(f332(f332(f334(f844(x87761)),f793(x87764,x87765,x87761,x87762)),x87765))+~P1(f332(f332(f334(f844(x87761)),x87763),x87764))
% 52.62/52.42 [8856]~P31(x88561,x88563,x88565,x88562)+~P1(f332(f64(x88563),x88564))+P1(f332(f332(f232(a845),f332(f43(x88561),x88562)),f332(f43(x88563),x88564)))+~P1(f332(f332(f232(f853(x88563,a839)),f332(f303(x88561,x88563,x88565),x88562)),x88564))
% 52.62/52.42 [8925]~P4(x89252)+~P31(x89251,x89251,x89254,x89255)+~P1(f332(f64(x89251),x89255))+E(f332(f332(f8(x89251,x89252),f332(f75(x89251,x89252,x89251,x89253),x89254)),x89255),f332(f332(f8(x89251,x89252),x89253),f332(f303(x89251,x89251,x89254),x89255)))
% 52.62/52.42 [8926]~P70(x89262)+~P31(x89261,x89261,x89264,x89265)+~P1(f332(f64(x89261),x89265))+E(f332(f332(f11(x89261,x89262),f332(f75(x89261,x89262,x89261,x89263),x89264)),x89265),f332(f332(f11(x89261,x89262),x89263),f332(f303(x89261,x89261,x89264),x89265)))
% 52.62/52.42 [9007]~E(f523(x90072,x90074,x90071,x90073,x90075),x90075)+~E(x90072,f332(x90074,x90075))+~P31(x90073,x90071,x90074,f239(f853(x90073,a839)))+P1(f332(f332(f334(x90071),x90072),f332(f303(x90073,x90071,x90074),f239(f853(x90073,a839)))))
% 52.62/52.42 [9038]~P38(x90381,x90382)+~P1(f332(f332(f334(x90381),x90383),x90384))+~P1(f332(f332(f334(x90381),x90385),x90384))+~P1(f332(f332(f334(f852(x90381,x90381)),f332(f332(f241(x90381,x90381),x90385),f694(x90382,x90381,x90384))),x90382))
% 52.62/52.42 [9071]~P31(x90712,x90713,x90715,x90711)+E(x90711,f180(f853(x90712,a839)))+E(f332(f303(x90713,x90712,f524(x90714,x90713,x90712,x90711)),x90714),x90711)+~P1(f332(f332(f232(f853(x90713,a839)),f332(f303(x90712,x90713,x90715),x90711)),x90714))
% 52.62/52.42 [9110]~E(x91102,f332(x91101,x91105))+~P31(x91104,x91103,x91101,f239(f853(x91104,a839)))+E(f332(x91101,f523(x91102,x91101,x91103,x91104,x91105)),x91102)+P1(f332(f332(f334(x91103),x91102),f332(f303(x91104,x91103,x91101),f239(f853(x91104,a839)))))
% 52.62/52.42 [9513]~P100(x95135)+~P11(x95135)+P1(f332(f332(f334(x95131),f393(x95132,x95133,x95131,x95134,x95135)),x95133))+~P1(f332(f332(f233(x95135),x95134),f332(f332(f47(x95131,x95135),x95133),x95132)))
% 52.62/52.42 [9518]~P100(x95181)+~P11(x95181)+P1(f332(f332(f233(x95181),x95182),f332(x95183,f393(x95183,x95184,x95185,x95182,x95181))))+~P1(f332(f332(f233(x95181),x95182),f332(f332(f47(x95185,x95181),x95184),x95183)))
% 52.62/52.42 [9587]~P66(x95871)+~P1(f332(f69(x95871,x95871,f83(x95871),x95872,x95873),x95875))+P1(f332(f332(f334(x95871),x95872),x95873))+P1(f332(f69(x95871,x95871,f83(x95871),x95874,f332(f332(f302(x95871),x95872),x95873)),f332(f332(f83(x95871),x95874),x95875)))
% 52.62/52.42 [9797]~P4(x97972)+~P1(f332(f64(x97971),x97975))+E(f332(f332(f8(x97971,x97972),f332(f332(f9(x97971,x97972,x97972),f332(f332(f20(x97971,x97972,f853(x97972,x97972)),f332(f332(f10(a839,f853(x97972,f853(x97972,x97972)),x97971),f98(x97972)),f332(a329,x97973))),x97974)),f2(x97972))),x97975),f2(x97972))+P1(f332(f332(f334(x97971),x97973),x97975))
% 52.62/52.42 [9798]~P70(x97982)+~P1(f332(f64(x97981),x97985))+E(f332(f332(f11(x97981,x97982),f332(f332(f9(x97981,x97982,x97982),f332(f332(f20(x97981,x97982,f853(x97982,x97982)),f332(f332(f10(a839,f853(x97982,f853(x97982,x97982)),x97981),f98(x97982)),f332(a329,x97983))),x97984)),f80(x97982))),x97985),f80(x97982))+P1(f332(f332(f334(x97981),x97983),x97985))
% 52.62/52.42 [9799]~P4(x97992)+~P1(f332(f64(x97991),x97995))+E(f332(f332(f8(x97991,x97992),f332(f332(f9(x97991,x97992,x97992),f332(f332(f20(x97991,x97992,f853(x97992,x97992)),f332(f332(f10(a839,f853(x97992,f853(x97992,x97992)),x97991),f98(x97992)),f332(a329,x97993))),x97994)),f2(x97992))),x97995),f332(x97994,x97993))+~P1(f332(f332(f334(x97991),x97993),x97995))
% 52.62/52.42 [9800]~P70(x98002)+~P1(f332(f64(x98001),x98005))+E(f332(f332(f11(x98001,x98002),f332(f332(f9(x98001,x98002,x98002),f332(f332(f20(x98001,x98002,f853(x98002,x98002)),f332(f332(f10(a839,f853(x98002,f853(x98002,x98002)),x98001),f98(x98002)),f332(a329,x98003))),x98004)),f80(x98002))),x98005),f332(x98004,x98003))+~P1(f332(f332(f334(x98001),x98003),x98005))
% 52.62/52.42 [9861]~P4(x98612)+~P1(f332(f64(x98611),x98615))+E(f332(f332(f8(x98611,x98612),f332(f332(f9(x98611,x98612,x98612),f332(f332(f20(x98611,x98612,f853(x98612,x98612)),f332(f332(f10(a839,f853(x98612,f853(x98612,x98612)),x98611),f98(x98612)),f332(f332(f9(x98611,x98611,a839),a329),x98613))),x98614)),f2(x98612))),x98615),f2(x98612))+P1(f332(f332(f334(x98611),x98613),x98615))
% 52.62/52.42 [9862]~P70(x98622)+~P1(f332(f64(x98621),x98625))+E(f332(f332(f11(x98621,x98622),f332(f332(f9(x98621,x98622,x98622),f332(f332(f20(x98621,x98622,f853(x98622,x98622)),f332(f332(f10(a839,f853(x98622,f853(x98622,x98622)),x98621),f98(x98622)),f332(f332(f9(x98621,x98621,a839),a329),x98623))),x98624)),f80(x98622))),x98625),f80(x98622))+P1(f332(f332(f334(x98621),x98623),x98625))
% 52.62/52.42 [9864]~P4(x98642)+~P1(f332(f64(x98641),x98645))+E(f332(f332(f8(x98641,x98642),f332(f332(f9(x98641,x98642,x98642),f332(f332(f20(x98641,x98642,f853(x98642,x98642)),f332(f332(f10(a839,f853(x98642,f853(x98642,x98642)),x98641),f98(x98642)),f332(f332(f9(x98641,x98641,a839),a329),x98643))),x98644)),f2(x98642))),x98645),f332(x98644,x98643))+~P1(f332(f332(f334(x98641),x98643),x98645))
% 52.62/52.42 [9865]~P70(x98652)+~P1(f332(f64(x98651),x98655))+E(f332(f332(f11(x98651,x98652),f332(f332(f9(x98651,x98652,x98652),f332(f332(f20(x98651,x98652,f853(x98652,x98652)),f332(f332(f10(a839,f853(x98652,f853(x98652,x98652)),x98651),f98(x98652)),f332(f332(f9(x98651,x98651,a839),a329),x98653))),x98654)),f80(x98652))),x98655),f332(x98654,x98653))+~P1(f332(f332(f334(x98651),x98653),x98655))
% 52.62/52.42 [7761]~P8(x77612)+~P1(f332(f64(x77611),x77614))+E(f332(f332(f8(x77611,x77612),x77613),f332(f332(f3(f853(x77611,a839)),x77614),f332(f332(f302(x77611),x77615),f180(f853(x77611,a839))))),f332(f332(f8(x77611,x77612),x77613),x77614))+P1(f332(f332(f334(x77611),x77615),x77614))
% 52.62/52.42 [8254]~P121(x82542)+~P1(f332(f64(x82541),x82544))+E(f332(f332(f8(x82541,x82542),x82543),f332(f332(f3(f853(x82541,a839)),x82544),f332(f332(f302(x82541),x82545),f180(f853(x82541,a839))))),f332(f332(f3(x82542),f332(f332(f8(x82541,x82542),x82543),x82544)),f332(x82543,x82545)))+~P1(f332(f332(f334(x82541),x82545),x82544))
% 52.62/52.42 [8255]~P8(x82552)+~P1(f332(f64(x82551),x82554))+E(f332(f332(f8(x82551,x82552),x82553),f332(f332(f3(f853(x82551,a839)),x82554),f332(f332(f302(x82551),x82555),f180(f853(x82551,a839))))),f332(f332(f3(x82552),f332(f332(f8(x82551,x82552),x82553),x82554)),f332(x82553,x82555)))+~P1(f332(f332(f334(x82551),x82555),x82554))
% 52.62/52.42 [8266]~P73(x82661)+~P1(f332(f332(f232(a845),x82663),x82665))+~P1(f332(f332(f279(x82661),f332(f332(f242(x82661),x82662),x82665)),x82664))+P1(f332(f332(f279(x82661),f332(f332(f242(x82661),x82662),x82663)),x82664))
% 52.62/52.42 [8283]~P8(x82831)+~P1(f332(f64(x82832),x82834))+E(f332(f332(f3(x82831),f332(f332(f8(x82832,x82831),x82833),x82834)),f332(f332(f8(x82832,x82831),x82833),x82835)),f332(f332(f8(x82832,x82831),x82833),f332(f332(f3(f853(x82832,a839)),x82834),x82835)))+~P1(f332(f332(f232(f853(x82832,a839)),x82835),x82834))
% 52.62/52.42 [8304]P1(f332(f64(x83041),f332(x83042,x83043)))+~P1(f332(f64(x83044),x83045))+~P1(f332(f332(f334(x83044),x83043),x83045))+~P1(f332(f64(x83041),f332(f332(f47(x83044,f853(x83041,a839)),x83045),x83042)))
% 52.62/52.42 [8727]~P14(x87271,x87275,x87274)+~E(f332(f277(x87271,x87271,x87274),f332(f332(f302(x87271),x87272),f180(f853(x87271,a839)))),f332(f277(x87271,x87271,x87274),f332(f332(f302(x87271),x87273),f180(f853(x87271,a839)))))+~P1(f332(f332(f334(x87271),x87273),x87275))+P1(f332(f332(f334(f852(x87271,x87271)),f332(f332(f241(x87271,x87271),x87272),x87273)),x87274))
% 52.62/52.42 [8998]~P1(f332(x89981,x89985))+P1(f332(x89981,f378(x89981,x89982,x89983,x89984)))+P1(f332(x89981,f375(x89981,x89982,x89983,x89984)))+~P1(f332(f332(f334(x89984),x89985),f332(f332(f103(f853(x89984,a839)),x89983),x89982)))
% 52.62/52.42 [9159]~P1(f332(x91591,x91595))+P1(f332(x91591,f375(x91591,x91592,x91593,x91594)))+P1(f332(f332(f334(x91594),f378(x91591,x91592,x91593,x91594)),x91592))+~P1(f332(f332(f334(x91594),x91595),f332(f332(f103(f853(x91594,a839)),x91593),x91592)))
% 52.62/52.42 [9160]~P1(f332(x91601,x91605))+P1(f332(x91601,f378(x91601,x91602,x91603,x91604)))+P1(f332(f332(f334(x91604),f375(x91601,x91602,x91603,x91604)),x91603))+~P1(f332(f332(f334(x91604),x91605),f332(f332(f103(f853(x91604,a839)),x91603),x91602)))
% 52.62/52.42 [9164]P1(f332(x91641,x91642))+~P1(f332(x91641,f377(x91641,x91643,x91644,x91645)))+~P1(f332(x91641,f376(x91641,x91643,x91644,x91645)))+~P1(f332(f332(f334(x91645),x91642),f332(f332(f103(f853(x91645,a839)),x91644),x91643)))
% 52.62/52.42 [9197]E(x91971,x91972)+~P1(f332(f332(f334(f852(x91973,x91973)),f332(f332(f241(x91973,x91973),x91971),x91972)),f300(x91973,x91975)))+P1(f332(f332(f334(x91973),x91971),x91974))+~P1(f332(f332(f232(f853(f852(x91973,x91973),a839)),x91975),f332(f332(f248(x91973,x91973),x91974),f332(f18(f853(x91973,a839),x91973),x91974))))
% 52.62/52.42 [9214]P1(f332(x92141,x92142))+~P1(f332(x92141,f376(x92141,x92144,x92145,x92143)))+P1(f332(f332(f334(x92143),f377(x92141,x92144,x92145,x92143)),x92144))+~P1(f332(f332(f334(x92143),x92142),f332(f332(f103(f853(x92143,a839)),x92145),x92144)))
% 52.62/52.42 [9215]P1(f332(x92151,x92152))+~P1(f332(x92151,f377(x92151,x92154,x92155,x92153)))+P1(f332(f332(f334(x92153),f376(x92151,x92154,x92155,x92153)),x92155))+~P1(f332(f332(f334(x92153),x92152),f332(f332(f103(f853(x92153,a839)),x92155),x92154)))
% 52.62/52.42 [9277]P1(f332(x92771,x92772))+P1(f332(f332(f334(x92773),f377(x92771,x92774,x92775,x92773)),x92774))+P1(f332(f332(f334(x92773),f376(x92771,x92774,x92775,x92773)),x92775))+~P1(f332(f332(f334(x92773),x92772),f332(f332(f103(f853(x92773,a839)),x92775),x92774)))
% 52.62/52.42 [9279]~P1(f332(x92792,x92795))+P1(f332(f332(f334(x92791),f378(x92792,x92793,x92794,x92791)),x92793))+P1(f332(f332(f334(x92791),f375(x92792,x92793,x92794,x92791)),x92794))+~P1(f332(f332(f334(x92791),x92795),f332(f332(f103(f853(x92791,a839)),x92794),x92793)))
% 52.62/52.42 [9426]~P14(x94261,x94265,x94264)+~P1(f332(f332(f334(x94261),x94263),x94265))+P1(f332(f332(f334(f852(x94261,x94261)),f332(f332(f241(x94261,x94261),x94262),x94263)),x94264))+~P1(f332(f332(f232(f853(x94261,a839)),f332(f277(x94261,x94261,x94264),f332(f332(f302(x94261),x94263),f180(f853(x94261,a839))))),f332(f277(x94261,x94261,x94264),f332(f332(f302(x94261),x94262),f180(f853(x94261,a839))))))
% 52.62/52.42 [9542]~P100(x95425)+~P11(x95425)+P1(f332(f332(f334(x95421),f661(x95422,x95423,x95424,x95421,x95425)),x95424))+~P1(f332(f332(f233(x95425),f332(f332(f48(x95421,x95425),x95424),x95423)),x95422))
% 52.62/52.42 [9574]~P3(x95745)+~P79(x95745)+P1(f332(f332(f334(x95741),f752(x95742,x95743,x95744,x95741,x95745)),f332(f158(x95741),x95744)))+P1(f332(f332(f232(x95745),f332(f154(x95745),f332(f332(f143(x95741,x95745),x95743),x95744))),f332(f154(x95745),f332(f332(f143(x95741,x95745),x95742),x95744))))
% 52.62/52.42 [9669]~P100(x96691)+~P11(x96691)+P1(f332(f332(f233(x96691),f332(x96692,f661(x96693,x96692,x96694,x96695,x96691))),x96693))+~P1(f332(f332(f233(x96691),f332(f332(f48(x96695,x96691),x96694),x96692)),x96693))
% 52.62/52.42 [9814]~P3(x98141)+~P79(x98141)+~P1(f332(f332(f232(x98141),f332(x98143,f752(x98145,x98143,x98144,x98142,x98141))),f332(x98145,f752(x98145,x98143,x98144,x98142,x98141))))+P1(f332(f332(f232(x98141),f332(f154(x98141),f332(f332(f143(x98142,x98141),x98143),x98144))),f332(f154(x98141),f332(f332(f143(x98142,x98141),x98145),x98144))))
% 52.62/52.42 [8585]~P4(x85851)+~P1(f332(f64(x85854),x85855))+~P1(f332(f332(f334(x85854),x85853),x85855))+E(f332(f332(f82(x85851),f332(x85852,x85853)),f332(f332(f8(x85854,x85851),x85852),f332(f332(f3(f853(x85854,a839)),x85855),f332(f332(f302(x85854),x85853),f180(f853(x85854,a839)))))),f332(f332(f8(x85854,x85851),x85852),x85855))
% 52.62/52.42 [8586]~P4(x85861)+~P1(f332(f64(x85864),x85865))+~P1(f332(f332(f334(x85864),x85863),x85865))+E(f332(f332(f82(x85861),f332(x85862,x85863)),f332(f332(f8(x85864,x85861),x85862),f332(f332(f3(f853(x85864,a839)),x85865),f332(f332(f302(x85864),x85863),f180(f853(x85864,a839)))))),f332(f332(f8(x85864,x85861),x85862),x85865))
% 52.62/52.42 [8587]~P70(x85871)+~P1(f332(f64(x85874),x85875))+~P1(f332(f332(f334(x85874),x85873),x85875))+E(f332(f332(f83(x85871),f332(x85872,x85873)),f332(f332(f11(x85874,x85871),x85872),f332(f332(f3(f853(x85874,a839)),x85875),f332(f332(f302(x85874),x85873),f180(f853(x85874,a839)))))),f332(f332(f11(x85874,x85871),x85872),x85875))
% 52.62/52.42 [8640]~P24(x86401,x86404,x86405)+~P1(f332(f64(x86401),x86402))+E(f332(f332(f3(f853(x86401,a839)),x86402),f332(f332(f302(x86401),x86403),f180(f853(x86401,a839)))),f180(f853(x86401,a839)))+E(f332(f332(x86404,x86403),f332(x86405,f332(f332(f3(f853(x86401,a839)),x86402),f332(f332(f302(x86401),x86403),f180(f853(x86401,a839)))))),f332(x86405,f332(f332(f302(x86401),x86403),x86402)))
% 52.62/52.42 [8973]~P4(x89731)+~P1(f332(f64(x89732),x89735))+~P1(f332(f64(x89732),x89734))+E(f332(f332(f82(x89731),f332(f332(f8(x89732,x89731),x89733),f332(f332(f103(f853(x89732,a839)),x89734),x89735))),f332(f332(f8(x89732,x89731),x89733),f332(f332(f104(f853(x89732,a839)),x89734),x89735))),f332(f332(f82(x89731),f332(f332(f8(x89732,x89731),x89733),x89734)),f332(f332(f8(x89732,x89731),x89733),x89735)))
% 52.62/52.42 [8974]~P70(x89741)+~P1(f332(f64(x89742),x89745))+~P1(f332(f64(x89742),x89744))+E(f332(f332(f83(x89741),f332(f332(f11(x89742,x89741),x89743),f332(f332(f103(f853(x89742,a839)),x89744),x89745))),f332(f332(f11(x89742,x89741),x89743),f332(f332(f104(f853(x89742,a839)),x89744),x89745))),f332(f332(f83(x89741),f332(f332(f11(x89742,x89741),x89743),x89744)),f332(f332(f11(x89742,x89741),x89743),x89745)))
% 52.62/52.42 [8975]~P70(x89751)+~P1(f332(f64(x89752),x89755))+~P1(f332(f64(x89752),x89754))+E(f332(f332(f83(x89751),f332(f332(f11(x89752,x89751),x89753),f332(f332(f103(f853(x89752,a839)),x89754),x89755))),f332(f332(f11(x89752,x89751),x89753),f332(f332(f104(f853(x89752,a839)),x89754),x89755))),f332(f332(f83(x89751),f332(f332(f11(x89752,x89751),x89753),x89754)),f332(f332(f11(x89752,x89751),x89753),x89755)))
% 52.62/52.42 [9109]~P8(x91091)+~P1(f332(f64(x91092),x91095))+~P1(f332(f64(x91092),x91094))+E(f332(f332(f3(x91091),f332(f332(f82(x91091),f332(f332(f8(x91092,x91091),x91093),x91094)),f332(f332(f8(x91092,x91091),x91093),x91095))),f332(f332(f8(x91092,x91091),x91093),f332(f332(f104(f853(x91092,a839)),x91094),x91095))),f332(f332(f8(x91092,x91091),x91093),f332(f332(f103(f853(x91092,a839)),x91094),x91095)))
% 52.62/52.42 [9291]~P31(x92911,x92912,x92913,x92915)+~P31(x92911,x92912,x92913,x92914)+P31(x92911,x92912,x92913,f332(f332(f103(f853(x92911,a839)),x92914),x92915))+~E(f332(f332(f104(f853(x92912,a839)),f332(f303(x92911,x92912,x92913),f332(f332(f3(f853(x92911,a839)),x92914),x92915))),f332(f303(x92911,x92912,x92913),f332(f332(f3(f853(x92911,a839)),x92915),x92914))),f180(f853(x92912,a839)))
% 52.62/52.42 [9398]E(x93981,f2(a1))+~P1(f332(f332(f233(a1),f2(a1)),x93983))+~P1(f332(f57(x93982,x93981),f332(f332(f241(a1,a1),x93984),x93985)))+P1(f332(f57(x93982,f332(f332(f83(a1),x93981),x93983)),f332(f332(f241(a1,a1),f332(f332(f44(a1),x93984),x93983)),f332(f332(f82(a1),f332(f332(f83(a1),x93981),f53(a1,x93984,x93983))),x93985))))
% 52.62/52.42 [9406]~P1(f332(f332(f233(a845),f2(a845)),x94063))+~P1(f332(f332(f233(a845),f2(a845)),x94062))+~P1(f332(f56(x94061,x94062),f332(f332(f241(a845,a845),x94064),x94065)))+P1(f332(f56(x94061,f332(f332(f83(a845),x94062),x94063)),f332(f332(f241(a845,a845),f332(f332(f44(a845),x94064),x94063)),f332(f332(f82(a845),f332(f332(f83(a845),x94062),f53(a845,x94064,x94063))),x94065))))
% 52.62/52.42 [9456]E(f332(f332(f82(a1),f365(x94561,x94562,x94563,x94564,x94565)),f366(x94561,x94562,x94563,x94564,x94565)),x94565)+~P1(f332(f332(f279(a1),x94564),x94563))+~P1(f332(f332(f279(a1),x94564),f332(f332(f82(a1),x94565),x94561)))+P1(f332(f332(f279(a1),x94564),f332(f332(f82(a1),f332(f332(f3(a1),x94565),x94563)),x94561)))
% 52.62/52.42 [9457]E(f332(f332(f3(a1),f367(x94571,x94572,x94573,x94574,x94575)),f368(x94571,x94572,x94573,x94574,x94575)),x94575)+~P1(f332(f332(f279(a1),x94574),x94573))+~P1(f332(f332(f279(a1),x94574),f332(f332(f82(a1),x94575),x94571)))+P1(f332(f332(f279(a1),x94574),f332(f332(f82(a1),f332(f332(f82(a1),x94575),x94573)),x94571)))
% 52.62/52.42 [9458]~P70(x94581)+~P1(f332(f64(x94582),x94585))+~P1(f332(f64(x94582),x94584))+E(f332(f332(f83(x94581),f332(f332(f332(f68(x94581,x94582,f83(x94581)),x94583),f80(x94581)),f332(f332(f103(f853(x94582,a839)),x94584),x94585))),f332(f332(f332(f68(x94581,x94582,f83(x94581)),x94583),f80(x94581)),f332(f332(f104(f853(x94582,a839)),x94584),x94585))),f332(f332(f83(x94581),f332(f332(f332(f68(x94581,x94582,f83(x94581)),x94583),f80(x94581)),x94584)),f332(f332(f332(f68(x94581,x94582,f83(x94581)),x94583),f80(x94581)),x94585)))
% 52.62/52.42 [9460]~E(f332(f332(f159(x94601),x94605),x94602),f332(f332(f159(x94601),x94605),x94603))+P1(f332(f332(f334(f852(f846(x94601),f846(x94601))),f332(f332(f241(f846(x94601),f846(x94601)),x94602),x94603)),f137(x94601,x94604)))+~P1(f332(f332(f233(a845),x94605),f332(f332(f236(a845),f332(f181(f846(x94601)),x94602)),f332(f181(f846(x94601)),x94603))))+~P1(f332(f332(f334(f852(x94601,x94601)),f332(f332(f241(x94601,x94601),f332(f332(f152(x94601),x94602),x94605)),f332(f332(f152(x94601),x94603),x94605))),x94604))
% 52.62/52.42 [9469]E(f332(f332(f82(a1),f369(x94691,x94692,x94693,x94694,x94695)),f370(x94691,x94692,x94693,x94694,x94695)),x94695)+~P1(f332(f332(f279(a1),x94694),x94693))+P1(f332(f332(f279(a1),x94694),f332(f332(f82(a1),x94695),x94691)))+~P1(f332(f332(f279(a1),x94694),f332(f332(f82(a1),f332(f332(f3(a1),x94695),x94693)),x94691)))
% 52.62/52.42 [9470]E(f332(f332(f3(a1),f362(x94701,x94702,x94703,x94704,x94705)),f363(x94701,x94702,x94703,x94704,x94705)),x94705)+~P1(f332(f332(f279(a1),x94704),x94703))+P1(f332(f332(f279(a1),x94704),f332(f332(f82(a1),x94705),x94701)))+~P1(f332(f332(f279(a1),x94704),f332(f332(f82(a1),f332(f332(f82(a1),x94705),x94703)),x94701)))
% 52.62/52.42 [9551]~P1(f332(f332(f279(a1),x95514),x95513))+P1(f332(f332(f334(a1),f367(x95511,x95512,x95513,x95514,x95515)),x95512))+~P1(f332(f332(f279(a1),x95514),f332(f332(f82(a1),x95515),x95511)))+P1(f332(f332(f279(a1),x95514),f332(f332(f82(a1),f332(f332(f82(a1),x95515),x95513)),x95511)))
% 52.62/52.42 [9552]~P1(f332(f332(f279(a1),x95524),x95523))+P1(f332(f332(f334(a1),f365(x95521,x95522,x95523,x95524,x95525)),x95522))+~P1(f332(f332(f279(a1),x95524),f332(f332(f82(a1),x95525),x95521)))+P1(f332(f332(f279(a1),x95524),f332(f332(f82(a1),f332(f332(f3(a1),x95525),x95523)),x95521)))
% 52.62/52.42 [9559]~P1(f332(f332(f279(a1),x95594),x95593))+P1(f332(f332(f334(a1),f368(x95591,x95592,x95593,x95594,x95595)),f295(a1,f80(a1),x95593)))+~P1(f332(f332(f279(a1),x95594),f332(f332(f82(a1),x95595),x95591)))+P1(f332(f332(f279(a1),x95594),f332(f332(f82(a1),f332(f332(f82(a1),x95595),x95593)),x95591)))
% 52.62/52.42 [9560]~P1(f332(f332(f279(a1),x95604),x95603))+P1(f332(f332(f334(a1),f366(x95601,x95602,x95603,x95604,x95605)),f295(a1,f80(a1),x95603)))+~P1(f332(f332(f279(a1),x95604),f332(f332(f82(a1),x95605),x95601)))+P1(f332(f332(f279(a1),x95604),f332(f332(f82(a1),f332(f332(f3(a1),x95605),x95603)),x95601)))
% 52.62/52.42 [9561]~P2(x95615)+~P79(x95615)+P1(f332(f332(f334(x95611),f440(x95612,x95613,x95614,x95611,x95615)),x95614))+P1(f332(f332(f232(x95615),f332(f332(f8(x95611,x95615),x95613),x95614)),f332(f332(f83(x95615),f332(f102(x95615),f332(f43(x95611),x95614))),x95612)))
% 52.62/52.42 [9562]~P1(f332(f332(f279(a1),x95624),x95623))+P1(f332(f332(f334(a1),f362(x95621,x95622,x95623,x95624,x95625)),x95622))+P1(f332(f332(f279(a1),x95624),f332(f332(f82(a1),x95625),x95621)))+~P1(f332(f332(f279(a1),x95624),f332(f332(f82(a1),f332(f332(f82(a1),x95625),x95623)),x95621)))
% 52.62/52.42 [9563]~P1(f332(f332(f279(a1),x95634),x95633))+P1(f332(f332(f334(a1),f369(x95631,x95632,x95633,x95634,x95635)),x95632))+P1(f332(f332(f279(a1),x95634),f332(f332(f82(a1),x95635),x95631)))+~P1(f332(f332(f279(a1),x95634),f332(f332(f82(a1),f332(f332(f3(a1),x95635),x95633)),x95631)))
% 52.62/52.42 [9564]~P1(f332(f332(f279(a1),x95641),x95645))+P1(f332(f332(f334(a1),f363(x95643,x95644,x95645,x95641,x95642)),f295(a1,f80(a1),x95645)))+P1(f332(f332(f279(a1),x95641),f332(f332(f82(a1),x95642),x95643)))+~P1(f332(f332(f279(a1),x95641),f332(f332(f82(a1),f332(f332(f82(a1),x95642),x95645)),x95643)))
% 52.62/52.42 [9565]~P1(f332(f332(f279(a1),x95651),x95655))+P1(f332(f332(f334(a1),f370(x95653,x95654,x95655,x95651,x95652)),f295(a1,f80(a1),x95655)))+P1(f332(f332(f279(a1),x95651),f332(f332(f82(a1),x95652),x95653)))+~P1(f332(f332(f279(a1),x95651),f332(f332(f82(a1),f332(f332(f3(a1),x95652),x95655)),x95653)))
% 52.62/52.42 [9730]~P2(x97301)+~P79(x97301)+~P1(f332(f332(f232(x97301),f332(x97303,f440(x97305,x97303,x97304,x97302,x97301))),x97305))+P1(f332(f332(f232(x97301),f332(f332(f8(x97302,x97301),x97303),x97304)),f332(f332(f83(x97301),f332(f102(x97301),f332(f43(x97302),x97304))),x97305)))
% 52.62/52.42 [8612]E(f332(f332(f125(x86121),x86122),x86123),f332(f332(f125(x86121),x86124),x86125))+~E(f332(f332(f159(x86121),f332(f181(f846(x86121)),x86122)),x86124),x86122)+~E(f332(f332(f125(x86121),f332(f332(f128(x86121),f332(f181(f846(x86121)),x86122)),x86124)),x86125),x86123)+P1(f332(f332(f232(a845),f332(f181(f846(x86121)),x86124)),f332(f181(f846(x86121)),x86122)))
% 52.62/52.42 [8725]E(f332(f332(f125(x87251),x87252),x87253),f332(f332(f125(x87251),x87254),x87255))+~E(f332(f332(f159(x87251),f332(f181(f846(x87251)),x87252)),x87254),x87252)+~E(x87253,f332(f332(f125(x87251),f332(f332(f128(x87251),f332(f181(f846(x87251)),x87252)),x87254)),x87255))+~P1(f332(f332(f232(a845),f332(f181(f846(x87251)),x87252)),f332(f181(f846(x87251)),x87254)))
% 52.62/52.42 [9882]~P1(f332(x98825,x98824))+~P1(f332(f64(x98822),f332(f256(x98822),x98825)))+P1(f332(f64(x98821),f332(f256(x98821),f332(f332(f9(x98821,x98822,a839),x98823),x98824))))+~P1(f332(f64(x98821),f332(f256(x98821),f332(f332(f10(f853(x98822,a839),a839,x98821),f89(x98822)),f332(f332(f10(f853(x98822,a839),f853(x98822,a839),x98821),f332(f20(x98822,a839,a839),f332(f332(f10(a839,f853(a839,a839),x98822),a330),x98825))),x98823)))))
% 52.62/52.42 [7906]~P41(x79062,x79063,x79064,x79066)+~P41(f35(x79061,x79062),x79066,x79064,x79065)+P41(f35(x79061,x79062),x79063,x79064,x79065)+~P1(f332(x79061,x79063))
% 52.62/52.42 [7907]~P41(x79072,x79073,x79074,x79076)+~P41(f35(x79071,x79072),x79076,x79074,x79075)+P41(f35(x79071,x79072),x79073,x79074,x79075)+~P1(f332(x79071,x79073))
% 52.62/52.42 [8419]~P25(x84195,x84191,x84196,x84192)+E(f332(f75(x84191,x84191,x84191,f332(x84192,x84193)),f332(x84192,x84194)),f332(f75(x84191,x84191,x84191,f332(x84192,x84194)),f332(x84192,x84193)))+~P1(f332(f64(x84195),x84194))+~P1(f332(f64(x84195),x84193))
% 52.62/52.42 [7817]~P31(x78171,x78172,x78174,x78173)+~E(f332(x78174,x78176),x78175)+E(f332(f79(x78171,x78172,x78173,x78174),x78175),x78176)+~P1(f332(f332(f334(x78171),x78176),x78173))
% 52.62/52.42 [8010]~P26(x80106,x80101,x80104,x80102)+E(f332(f75(x80101,x80101,x80101,f332(x80102,x80103)),f332(x80104,x80105)),f332(x80102,x80103))+~P1(f332(f64(x80106),x80103))+~P1(f332(f332(f334(x80106),x80105),x80103))
% 52.62/52.42 [9147]~P25(x91473,x91471,x91476,x91472)+E(f332(f75(x91471,x91471,x91471,f332(x91472,f332(f332(f3(f853(x91473,a839)),x91474),f332(f332(f302(x91473),x91475),f180(f853(x91473,a839)))))),f332(x91476,x91475)),f332(x91472,x91474))+~P1(f332(f64(x91473),x91474))+~P1(f332(f332(f334(x91473),x91475),x91474))
% 52.62/52.42 [6874]~P9(x68741)+~E(f53(x68741,x68743,x68744),f53(x68741,x68746,x68744))+~E(f53(x68741,x68742,x68744),f53(x68741,x68745,x68744))+E(f53(x68741,f332(f332(f82(x68741),x68742),x68743),x68744),f53(x68741,f332(f332(f82(x68741),x68745),x68746),x68744))
% 52.62/52.42 [6875]~P9(x68751)+~E(f53(x68751,x68753,x68754),f53(x68751,x68756,x68754))+~E(f53(x68751,x68752,x68754),f53(x68751,x68755,x68754))+E(f53(x68751,f332(f332(f83(x68751),x68752),x68753),x68754),f53(x68751,f332(f332(f83(x68751),x68755),x68756),x68754))
% 52.62/52.42 [6876]~P10(x68761)+~E(f53(x68761,x68763,x68764),f53(x68761,x68766,x68764))+~E(f53(x68761,x68762,x68764),f53(x68761,x68765,x68764))+E(f53(x68761,f332(f332(f3(x68761),x68762),x68763),x68764),f53(x68761,f332(f332(f3(x68761),x68765),x68766),x68764))
% 52.62/52.42 [7708]~P22(x77081,x77082,x77083)+~P1(f332(f64(x77081),x77086))+E(f332(f332(f67(x77081,x77082,x77083),x77084),f332(f332(f302(x77081),x77085),x77086)),f332(f332(f67(x77081,x77082,x77083),f332(f332(x77083,x77085),x77084)),x77086))+P1(f332(f332(f334(x77081),x77085),x77086))
% 52.62/52.42 [7775]~P11(x77751)+P1(f332(f332(f232(x77751),x77752),f332(x77753,x77754)))+~P1(f332(f332(f334(x77755),x77754),x77756))+~P1(f332(f332(f232(x77751),x77752),f332(f332(f48(x77755,x77751),x77756),x77753)))
% 52.62/52.42 [7935]~P22(x79351,x79352,x79353)+~P1(f332(f64(x79351),x79356))+E(f332(f332(f67(x79351,x79352,x79353),x79354),f332(f332(f302(x79351),x79355),x79356)),f332(f332(x79353,x79355),f332(f332(f67(x79351,x79352,x79353),x79354),x79356)))+P1(f332(f332(f334(x79351),x79355),x79356))
% 52.62/52.42 [8026]~P100(x80263)+~P1(f332(x80262,x80265))+~P20(x80263,f332(f332(f143(x80261,x80263),x80264),x80266))+E(f332(f126(x80261,x80262),f332(f332(f138(x80261,x80263,x80264),x80265),x80266)),f332(f332(f138(x80261,x80263,x80264),x80265),f332(f126(x80261,x80262),x80266)))
% 52.62/52.42 [8049]E(x80491,x80492)+E(x80493,f2(a1))+~P1(f332(f57(x80494,x80493),f332(f332(f241(a1,a1),x80495),x80492)))+~P1(f332(f57(x80494,x80493),f332(f332(f241(a1,a1),x80496),x80491)))
% 52.62/52.42 [8050]E(x80501,x80502)+E(x80503,f2(a1))+~P1(f332(f57(x80504,x80503),f332(f332(f241(a1,a1),x80502),x80505)))+~P1(f332(f57(x80504,x80503),f332(f332(f241(a1,a1),x80501),x80506)))
% 52.62/52.42 [8072]~P25(x80722,x80725,x80726,x80721)+~P1(f332(f64(x80722),x80724))+E(f332(x80721,f332(f332(f302(x80722),x80723),x80724)),f332(f75(x80725,x80725,x80725,f332(x80721,x80724)),f332(x80726,x80723)))+P1(f332(f332(f334(x80722),x80723),x80724))
% 52.62/52.42 [8286]~P26(x82865,x82861,x82866,x82862)+E(f332(f75(x82861,x82861,x82861,f332(x82862,x82863)),f332(x82862,x82864)),f332(x82862,x82863))+~P1(f332(f64(x82865),x82863))+~P1(f332(f332(f232(f853(x82865,a839)),x82864),x82863))
% 52.62/52.42 [9337]~P31(x93371,x93372,x93374,x93373)+~P1(f332(f332(f334(x93372),x93375),f332(f303(x93371,x93372,x93374),x93373)))+P1(f332(f332(f334(x93371),f332(f79(x93371,x93372,x93373,x93374),x93375)),x93376))+~P1(f332(f332(f232(f853(x93371,a839)),x93373),x93376))
% 52.62/52.42 [9680]~P4(x96802)+~E(f496(x96801,x96803,x96805,x96806,x96804,x96802),f497(x96801,x96803,x96805,x96806,x96804,x96802))+~P1(f332(f64(x96804),x96806))+E(f332(f332(f8(x96801,x96802),x96803),f332(f303(x96804,x96801,x96805),x96806)),f332(f332(f8(x96804,x96802),f332(f75(x96801,x96802,x96804,x96803),x96805)),x96806))
% 52.62/52.42 [9710]~P4(x97106)+E(f332(x97101,f496(x97102,x97103,x97101,x97104,x97105,x97106)),f332(x97101,f497(x97102,x97103,x97101,x97104,x97105,x97106)))+E(f332(f332(f8(x97102,x97106),x97103),f332(f303(x97105,x97102,x97101),x97104)),f332(f332(f8(x97105,x97106),f332(f75(x97102,x97106,x97105,x97103),x97101)),x97104))+~P1(f332(f64(x97105),x97104))
% 52.62/52.42 [9764]~P4(x97642)+~E(f332(x97643,f332(x97645,f497(x97641,x97643,x97645,x97646,x97644,x97642))),f2(x97642))+~P1(f332(f64(x97644),x97646))+E(f332(f332(f8(x97641,x97642),x97643),f332(f303(x97644,x97641,x97645),x97646)),f332(f332(f8(x97644,x97642),f332(f75(x97641,x97642,x97644,x97643),x97645)),x97646))
% 52.62/52.42 [9824]~P4(x98242)+~P1(f332(f64(x98244),x98246))+E(f332(f332(f8(x98241,x98242),x98243),f332(f303(x98244,x98241,x98245),x98246)),f332(f332(f8(x98244,x98242),f332(f75(x98241,x98242,x98244,x98243),x98245)),x98246))+P1(f332(f332(f334(x98244),f497(x98241,x98243,x98245,x98246,x98244,x98242)),x98246))
% 52.62/52.42 [9825]~P4(x98252)+~P1(f332(f64(x98254),x98256))+E(f332(f332(f8(x98251,x98252),x98253),f332(f303(x98254,x98251,x98255),x98256)),f332(f332(f8(x98254,x98252),f332(f75(x98251,x98252,x98254,x98253),x98255)),x98256))+P1(f332(f332(f334(x98254),f496(x98251,x98253,x98255,x98256,x98254,x98252)),x98256))
% 52.62/52.42 [9947]~P70(x99471)+~P1(f332(f64(x99472),x99476))+E(f332(f332(f332(f68(x99471,x99472,f83(x99471)),f332(f332(f20(x99472,f853(x99473,a839),x99471),f332(f332(f9(x99472,x99471,f853(f853(x99473,a839),x99471)),f332(f332(f10(f853(x99473,x99471),f853(x99471,f853(f853(x99473,a839),x99471)),x99472),f68(x99471,x99473,f83(x99471))),x99474)),f80(x99471))),x99475)),f80(x99471)),x99476),f332(f332(f332(f68(x99471,f852(x99472,x99473),f83(x99471)),f332(f251(x99472,x99473,x99471),x99474)),f80(x99471)),f332(f332(f248(x99472,x99473),x99476),x99475)))+P1(f332(f332(f334(x99472),f564(x99474,x99475,x99473,x99476,x99472,x99471)),x99476))
% 52.62/52.42 [9963]~P70(x99631)+~P1(f332(f64(x99632),x99636))+E(f332(f332(f332(f68(x99631,x99632,f83(x99631)),f332(f332(f20(x99632,f853(x99633,a839),x99631),f332(f332(f9(x99632,x99631,f853(f853(x99633,a839),x99631)),f332(f332(f10(f853(x99633,x99631),f853(x99631,f853(f853(x99633,a839),x99631)),x99632),f68(x99631,x99633,f83(x99631))),x99634)),f80(x99631))),x99635)),f80(x99631)),x99636),f332(f332(f332(f68(x99631,f852(x99632,x99633),f83(x99631)),f332(f251(x99632,x99633,x99631),x99634)),f80(x99631)),f332(f332(f248(x99632,x99633),x99636),x99635)))+~P1(f332(f64(x99633),f332(x99635,f564(x99634,x99635,x99633,x99636,x99632,x99631))))
% 52.62/52.42 [8201]~P26(x82012,x82015,x82016,x82011)+~P1(f332(f64(x82012),x82014))+~P1(f332(f64(x82012),x82013))+E(f332(x82011,f332(f332(f103(f853(x82012,a839)),x82013),x82014)),f332(f75(x82015,x82015,x82015,f332(x82011,x82013)),f332(x82011,x82014)))
% 52.62/52.42 [8421]~P11(x84211)+P1(f332(f332(f232(x84211),f332(x84212,x84213)),x84214))+~P1(f332(f332(f334(x84215),x84213),x84216))+~P1(f332(f332(f232(x84211),f332(f332(f47(x84215,x84211),x84216),x84212)),x84214))
% 52.62/52.42 [8795]~P31(x87952,x87951,x87953,x87956)+E(f332(f332(f3(f853(x87951,a839)),f332(f303(x87952,x87951,x87953),x87954)),f332(f303(x87952,x87951,x87953),x87955)),f332(f303(x87952,x87951,x87953),f332(f332(f3(f853(x87952,a839)),x87954),x87955)))+~P1(f332(f332(f232(f853(x87952,a839)),x87955),x87956))+~P1(f332(f332(f232(f853(x87952,a839)),x87954),x87956))
% 52.62/52.42 [8796]~P31(x87962,x87961,x87963,x87966)+E(f332(f332(f104(f853(x87961,a839)),f332(f303(x87962,x87961,x87963),x87964)),f332(f303(x87962,x87961,x87963),x87965)),f332(f303(x87962,x87961,x87963),f332(f332(f104(f853(x87962,a839)),x87964),x87965)))+~P1(f332(f332(f232(f853(x87962,a839)),x87965),x87966))+~P1(f332(f332(f232(f853(x87962,a839)),x87964),x87966))
% 52.62/52.42 [9039]E(x90391,x90392)+~P55(x90393,x90394,x90395)+~P1(f332(f332(f334(f852(x90393,x90394)),f332(f332(f241(x90393,x90394),x90396),x90392)),x90395))+~P1(f332(f332(f334(f852(x90393,x90394)),f332(f332(f241(x90393,x90394),x90396),x90391)),x90395))
% 52.62/52.42 [9040]E(x90401,x90402)+~P55(x90403,x90404,x90405)+~P1(f332(f332(f334(f852(x90403,x90404)),f332(f332(f241(x90403,x90404),x90406),x90402)),x90405))+~P1(f332(f332(f334(f852(x90403,x90404)),f332(f332(f241(x90403,x90404),x90406),x90401)),x90405))
% 52.62/52.42 [9620]~P4(x96201)+~P1(f332(f64(x96203),x96206))+~P1(f332(f64(x96202),x96205))+E(f332(f332(f82(x96201),f332(f332(f8(x96202,x96201),f332(f75(f854(x96202,x96203),x96201,x96202,x96204),f304(x96202,x96203))),x96205)),f332(f332(f8(x96203,x96201),f332(f75(f854(x96202,x96203),x96201,x96203,x96204),f313(x96203,x96202))),x96206)),f332(f332(f8(f854(x96202,x96203),x96201),x96204),f314(x96202,x96203,x96205,x96206)))
% 52.62/52.42 [9760]~P66(x97601)+~E(f332(x97603,f627(x97604,x97606,x97603,x97605,x97602,x97601)),f332(x97606,f627(x97604,x97606,x97603,x97605,x97602,x97601)))+~P1(f332(f64(x97602),x97605))+E(f332(f332(f332(f68(x97601,x97602,f83(x97601)),x97603),x97604),x97605),f332(f332(f332(f68(x97601,x97602,f83(x97601)),x97606),x97604),x97605))
% 52.62/52.42 [9821]~P66(x98211)+~P1(f332(f64(x98212),x98215))+E(f332(f332(f332(f68(x98211,x98212,f83(x98211)),x98213),x98214),x98215),f332(f332(f332(f68(x98211,x98212,f83(x98211)),x98216),x98214),x98215))+P1(f332(f332(f334(x98212),f627(x98214,x98213,x98216,x98215,x98212,x98211)),x98215))
% 52.62/52.42 [8625]~P66(x86251)+~P1(f332(f64(x86252),x86256))+P1(f332(f332(f334(x86252),x86255),x86256))+E(f332(f332(f332(f68(x86251,x86252,f83(x86251)),x86253),x86254),f332(f332(f302(x86252),x86255),x86256)),f332(f332(f83(x86251),f332(x86253,x86255)),f332(f332(f332(f68(x86251,x86252,f83(x86251)),x86253),x86254),x86256)))
% 52.62/52.42 [8669]~P14(x86691,x86696,x86693)+~P18(x86691,f853(x86692,a839),x86693,x86695)+~P1(f332(f332(f334(x86691),x86694),x86696))+E(f332(f332(f47(x86691,f853(x86692,a839)),f332(f277(x86691,x86691,x86693),f332(f332(f302(x86691),x86694),f180(f853(x86691,a839))))),x86695),f332(x86695,x86694))
% 52.62/52.42 [8777]~P22(x87773,x87774,x87771)+~P1(f332(f64(x87773),x87776))+~P1(f332(f332(f334(x87773),x87772),x87776))+E(f332(f332(x87771,x87772),f332(f332(f67(x87773,x87774,x87771),x87775),f332(f332(f3(f853(x87773,a839)),x87776),f332(f332(f302(x87773),x87772),f180(f853(x87773,a839)))))),f332(f332(f67(x87773,x87774,x87771),x87775),x87776))
% 52.62/52.42 [9050]~P25(x90503,x90501,x90506,x90502)+~P1(f332(f64(x90503),x90505))+~P1(f332(f64(x90503),x90504))+E(f332(f75(x90501,x90501,x90501,f332(x90502,f332(f332(f103(f853(x90503,a839)),x90504),x90505))),f332(x90502,f332(f332(f104(f853(x90503,a839)),x90504),x90505))),f332(f75(x90501,x90501,x90501,f332(x90502,x90504)),f332(x90502,x90505)))
% 52.62/52.42 [9357]~E(x93573,f332(f332(f148(x93571,x93572),x93575),x93576))+P1(f332(f332(f334(f852(f846(x93571),f846(x93571))),f332(f332(f241(f846(x93571),f846(x93571)),x93572),x93573)),f146(x93571,x93574)))+~P1(f332(f332(f233(a845),x93575),f332(f181(f846(x93571)),x93572)))+~P1(f332(f332(f334(f852(x93571,x93571)),f332(f332(f241(x93571,x93571),f332(f332(f152(x93571),x93572),x93575)),x93576)),x93574))
% 52.62/52.42 [9840]~P4(x98402)+~P1(f332(f64(x98401),x98406))+P1(f332(f332(f334(x98401),f563(x98404,x98405,x98403,x98406,x98401,x98402)),x98406))+E(f332(f332(f8(x98401,x98402),f332(f332(f20(x98401,f853(x98403,a839),x98402),f332(f332(f10(f853(x98403,x98402),f853(f853(x98403,a839),x98402),x98401),f8(x98403,x98402)),x98404)),x98405)),x98406),f332(f332(f8(f852(x98401,x98403),x98402),f332(f251(x98401,x98403,x98402),x98404)),f332(f332(f248(x98401,x98403),x98406),x98405)))
% 52.62/52.42 [9841]~P70(x98412)+~P1(f332(f64(x98411),x98416))+P1(f332(f332(f334(x98411),f559(x98414,x98415,x98413,x98416,x98411,x98412)),x98416))+E(f332(f332(f11(x98411,x98412),f332(f332(f20(x98411,f853(x98413,a839),x98412),f332(f332(f10(f853(x98413,x98412),f853(f853(x98413,a839),x98412),x98411),f11(x98413,x98412)),x98414)),x98415)),x98416),f332(f332(f11(f852(x98411,x98413),x98412),f332(f251(x98411,x98413,x98412),x98414)),f332(f332(f248(x98411,x98413),x98416),x98415)))
% 52.62/52.42 [9880]~P4(x98802)+~P1(f332(f64(x98801),x98806))+~P1(f332(f64(x98803),f332(x98805,f563(x98804,x98805,x98803,x98806,x98801,x98802))))+E(f332(f332(f8(x98801,x98802),f332(f332(f20(x98801,f853(x98803,a839),x98802),f332(f332(f10(f853(x98803,x98802),f853(f853(x98803,a839),x98802),x98801),f8(x98803,x98802)),x98804)),x98805)),x98806),f332(f332(f8(f852(x98801,x98803),x98802),f332(f251(x98801,x98803,x98802),x98804)),f332(f332(f248(x98801,x98803),x98806),x98805)))
% 52.62/52.42 [9881]~P70(x98812)+~P1(f332(f64(x98811),x98816))+~P1(f332(f64(x98813),f332(x98815,f559(x98814,x98815,x98813,x98816,x98811,x98812))))+E(f332(f332(f11(x98811,x98812),f332(f332(f20(x98811,f853(x98813,a839),x98812),f332(f332(f10(f853(x98813,x98812),f853(f853(x98813,a839),x98812),x98811),f11(x98813,x98812)),x98814)),x98815)),x98816),f332(f332(f11(f852(x98811,x98813),x98812),f332(f251(x98811,x98813,x98812),x98814)),f332(f332(f248(x98811,x98813),x98816),x98815)))
% 52.62/52.42 [9863]~P70(x98632)+~P1(f332(f64(x98631),x98636))+P1(f332(f332(f334(x98631),x98633),x98636))+E(f332(f332(f11(x98631,x98632),f332(f332(f9(x98631,x98632,x98632),f332(f332(f20(x98631,x98632,f853(x98632,x98632)),f332(f332(f10(a839,f853(x98632,f853(x98632,x98632)),x98631),f98(x98632)),f332(f332(f9(x98631,x98631,a839),a329),x98633))),x98634)),x98635)),x98636),f332(f332(f242(x98632),x98635),f332(f43(x98631),x98636)))
% 52.62/52.42 [9868]~P70(x98682)+~P1(f332(f64(x98681),x98686))+~P1(f332(f332(f334(x98681),x98683),x98686))+E(f332(f332(f11(x98681,x98682),f332(f332(f9(x98681,x98682,x98682),f332(f332(f20(x98681,x98682,f853(x98682,x98682)),f332(f332(f10(a839,f853(x98682,f853(x98682,x98682)),x98681),f98(x98682)),f332(f332(f9(x98681,x98681,a839),a329),x98683))),x98684)),x98685)),x98686),f332(f332(f83(x98682),f332(x98684,x98683)),f332(f332(f242(x98682),x98685),f332(f332(f3(a845),f332(f43(x98681),x98686)),f80(a845)))))
% 52.62/52.42 [9934]~P1(f332(f64(x99341),x99345))+~P1(f332(f64(x99342),x99343))+P1(f332(f332(f334(x99342),f585(x99346,x99344,x99343,x99342,x99345,x99341)),x99343))+E(f332(f332(f8(x99341,a845),f332(f332(f10(f853(x99342,a839),a845,x99341),f43(x99342)),f332(f332(f10(f853(x99342,a839),f853(x99342,a839),x99341),f256(x99342)),f332(f332(f10(f853(x99342,a839),f853(x99342,a839),x99341),f332(f20(x99342,a839,a839),f332(f332(f10(a839,f853(a839,a839),x99342),a330),f332(f332(f9(x99342,f853(x99342,a839),a839),f334(x99342)),x99343)))),x99344)))),x99345),f332(f332(f83(a845),x99346),f332(f43(x99342),x99343)))
% 52.62/52.42 [9935]~P1(f332(f64(x99351),x99355))+~P1(f332(f64(x99352),x99353))+P1(f332(f332(f334(x99352),f586(x99356,x99354,x99353,x99352,x99355,x99351)),x99353))+E(f332(f332(f8(x99351,a845),f332(f332(f10(f853(x99352,a839),a845,x99351),f43(x99352)),f332(f332(f10(f853(x99352,a839),f853(x99352,a839),x99351),f256(x99352)),f332(f332(f10(f853(x99352,a839),f853(x99352,a839),x99351),f332(f20(x99352,a839,a839),f332(f332(f10(a839,f853(a839,a839),x99352),a330),f332(f332(f9(x99352,f853(x99352,a839),a839),f334(x99352)),x99353)))),x99354)))),x99355),f332(f332(f8(x99352,a845),x99356),x99353))
% 52.62/52.42 [9969]~P1(f332(f64(x99692),x99693))+~P1(f332(f64(x99691),x99695))+~E(f332(f43(x99691),f332(f256(x99691),f332(f332(f20(x99691,a839,a839),f332(f332(f10(a839,f853(a839,a839),x99691),a330),f332(f332(f9(x99691,f853(x99691,a839),a839),f334(x99691)),x99695))),f332(f332(f9(x99691,x99692,a839),x99694),f585(x99696,x99694,x99693,x99692,x99695,x99691))))),x99696)+E(f332(f332(f8(x99691,a845),f332(f332(f10(f853(x99692,a839),a845,x99691),f43(x99692)),f332(f332(f10(f853(x99692,a839),f853(x99692,a839),x99691),f256(x99692)),f332(f332(f10(f853(x99692,a839),f853(x99692,a839),x99691),f332(f20(x99692,a839,a839),f332(f332(f10(a839,f853(a839,a839),x99692),a330),f332(f332(f9(x99692,f853(x99692,a839),a839),f334(x99692)),x99693)))),x99694)))),x99695),f332(f332(f83(a845),x99696),f332(f43(x99692),x99693)))
% 52.62/52.42 [9971]~P1(f332(f64(x99712),x99713))+~P1(f332(f64(x99711),x99715))+~E(f332(f43(x99711),f332(f256(x99711),f332(f332(f20(x99711,a839,a839),f332(f332(f10(a839,f853(a839,a839),x99711),a330),f332(f332(f9(x99711,f853(x99711,a839),a839),f334(x99711)),x99715))),f332(f332(f9(x99711,x99712,a839),x99714),f586(x99716,x99714,x99713,x99712,x99715,x99711))))),f332(x99716,f586(x99716,x99714,x99713,x99712,x99715,x99711)))+E(f332(f332(f8(x99711,a845),f332(f332(f10(f853(x99712,a839),a845,x99711),f43(x99712)),f332(f332(f10(f853(x99712,a839),f853(x99712,a839),x99711),f256(x99712)),f332(f332(f10(f853(x99712,a839),f853(x99712,a839),x99711),f332(f20(x99712,a839,a839),f332(f332(f10(a839,f853(a839,a839),x99712),a330),f332(f332(f9(x99712,f853(x99712,a839),a839),f334(x99712)),x99713)))),x99714)))),x99715),f332(f332(f8(x99712,a845),x99716),x99713))
% 52.62/52.42 [9619]E(x96191,x96192)+~P22(x96193,x96194,x96195)+~P1(f332(f69(x96193,x96194,x96195,x96196,x96197),x96192))+~P1(f332(f69(x96193,x96194,x96195,x96196,x96197),x96191))
% 52.62/52.42 [9429]P1(f332(x94291,x94292))+~P1(f332(f332(f334(x94297),x94292),f332(x94296,x94294)))+~P1(f332(x94291,f389(x94291,x94296,x94295,x94293,x94297)))+~P1(f332(f332(f334(x94293),x94294),x94295))
% 52.62/52.42 [9855]~P22(x98557,x98556,x98551)+E(f332(f332(x98551,x98552),f663(x98552,x98553,x98554,x98555,x98551,x98556,x98557)),x98553)+~P1(f332(f69(x98557,x98556,x98551,x98555,x98554),x98553))+~P1(f332(f332(f334(x98557),x98552),x98554))
% 52.62/52.42 [9919]~P22(x99191,x99192,x99193)+~P1(f332(f69(x99191,x99192,x99193,x99194,x99195),x99197))+P1(f332(f69(x99191,x99192,x99193,x99194,f332(f332(f3(f853(x99191,a839)),x99195),f332(f332(f302(x99191),x99196),f180(f853(x99191,a839))))),f663(x99196,x99197,x99195,x99194,x99193,x99192,x99191)))+~P1(f332(f332(f334(x99191),x99196),x99195))
% 52.62/52.42 [9333]~P66(x93331)+~P31(x93335,x93332,x93336,x93337)+~P1(f332(f64(x93335),x93337))+E(f332(f332(f332(f68(x93331,x93332,f83(x93331)),x93333),x93334),f332(f303(x93335,x93332,x93336),x93337)),f332(f332(f332(f68(x93331,x93335,f83(x93331)),f332(f75(x93332,x93331,x93335,x93333),x93336)),x93334),x93337))
% 52.62/52.42 [9451]~E(f332(f332(f302(x94511),x94515),x94516),f332(f332(f302(x94511),x94512),x94513))+~P1(f332(f69(x94511,x94511,x94514,x94512,x94513),x94517))+P1(f332(f332(f334(x94511),x94512),x94513))+P1(f332(f65(x94511,x94514,f332(f332(f302(x94511),x94515),x94516)),x94517))
% 52.62/52.42 [9530]P1(f332(x95301,x95302))+~P1(f332(f332(f334(x95303),x95302),f332(x95304,x95307)))+~P1(f332(f332(f334(x95306),x95307),x95305))+P1(f332(f332(f334(x95303),f389(x95301,x95304,x95305,x95306,x95303)),f332(f332(f47(x95306,f853(x95303,a839)),x95305),x95304)))
% 52.62/52.42 [9543]~P31(x95432,x95431,x95435,x95434)+~P31(x95431,x95433,x95436,f332(f303(x95432,x95431,x95435),x95434))+E(f332(f332(f75(x95431,x95432,x95433,f79(x95432,x95431,x95434,x95435)),f79(x95431,x95433,f332(f303(x95432,x95431,x95435),x95434),x95436)),x95437),f332(f79(x95432,x95433,x95434,f332(f75(x95431,x95433,x95432,x95436),x95435)),x95437))+~P1(f332(f332(f334(x95433),x95437),f332(f303(x95431,x95433,x95436),f332(f303(x95432,x95431,x95435),x95434))))
% 52.62/52.42 [9856]~P22(x98567,x98566,x98561)+E(f332(f332(x98561,x98562),f691(x98563,x98564,x98562,x98565,x98561,x98566,x98567)),x98563)+P1(f332(f332(f334(x98567),x98562),x98564))+~P1(f332(f69(x98567,x98566,x98561,x98565,f332(f332(f302(x98567),x98562),x98564)),x98563))
% 52.62/52.42 [9918]~P22(x99181,x99184,x99185)+P1(f332(f69(x99181,x99184,x99185,x99186,x99183),f691(x99187,x99183,x99182,x99186,x99185,x99184,x99181)))+P1(f332(f332(f334(x99181),x99182),x99183))+~P1(f332(f69(x99181,x99184,x99185,x99186,f332(f332(f302(x99181),x99182),x99183)),x99187))
% 52.62/52.42 [9602]E(x96021,f2(a1))+~P1(f332(f57(x96023,x96021),f332(f332(f241(a1,a1),x96025),x96027)))+~P1(f332(f57(x96022,x96021),f332(f332(f241(a1,a1),x96024),x96026)))+P1(f332(f57(f332(f332(f82(a1),x96022),x96023),x96021),f332(f332(f241(a1,a1),f332(f332(f82(a1),f332(f332(f82(a1),x96024),x96025)),f332(f332(f44(a1),f332(f332(f82(a1),x96026),x96027)),x96021))),f53(a1,f332(f332(f82(a1),x96026),x96027),x96021))))
% 52.62/52.42 [9604]~P1(f332(f332(f233(a845),f2(a845)),x96043))+~P1(f332(f56(x96042,x96043),f332(f332(f241(a845,a845),x96045),x96047)))+~P1(f332(f56(x96041,x96043),f332(f332(f241(a845,a845),x96044),x96046)))+P1(f332(f56(f332(f332(f82(a845),x96041),x96042),x96043),f332(f332(f241(a845,a845),f332(f332(f82(a845),f332(f332(f82(a845),x96044),x96045)),f332(f332(f44(a845),f332(f332(f82(a845),x96046),x96047)),x96043))),f53(a845,f332(f332(f82(a845),x96046),x96047),x96043))))
% 52.62/52.42 [9968]~P4(x99682)+~P1(f332(f64(x99683),x99685))+~P1(f332(f64(x99681),x99687))+E(f332(f332(f8(x99681,x99682),f332(f332(f20(x99681,f853(x99683,a839),x99682),f332(f332(f10(f853(x99683,x99682),f853(f853(x99683,a839),x99682),x99681),f8(x99683,x99682)),x99684)),f332(f332(f10(f853(x99683,a839),f853(x99683,a839),x99681),f256(x99683)),f332(f332(f10(f853(x99683,a839),f853(x99683,a839),x99681),f332(f20(x99683,a839,a839),f332(f332(f10(a839,f853(a839,a839),x99683),a330),f332(f332(f9(x99683,f853(x99683,a839),a839),f334(x99683)),x99685)))),x99686)))),x99687),f332(f332(f8(x99683,x99682),f332(f332(f20(x99683,f853(x99681,a839),x99682),f332(f332(f10(f853(x99681,x99682),f853(f853(x99681,a839),x99682),x99683),f8(x99681,x99682)),f332(f9(x99681,x99683,x99682),x99684))),f332(f332(f10(f853(x99681,a839),f853(x99681,a839),x99683),f256(x99681)),f332(f332(f10(f853(x99681,a839),f853(x99681,a839),x99683),f332(f20(x99681,a839,a839),f332(f332(f10(a839,f853(a839,a839),x99681),a330),f332(f332(f9(x99681,f853(x99681,a839),a839),f334(x99681)),x99687)))),f332(f9(x99681,x99683,a839),x99686))))),x99685))
% 52.62/52.42 [9489]~P28(x94897,x94896,x94891,x94898,x94892,x94894)+E(f332(f332(x94891,f332(x94892,x94893)),f332(x94894,x94895)),f332(x94894,x94895))+~P1(f332(f64(x94896),x94895))+~P1(f332(f332(f334(x94896),x94893),x94895))
% 52.62/52.42 [9493]~P19(x94936,x94931,x94932,x94938,x94933,x94934)+~P14(x94936,x94937,x94938)+P18(x94931,x94932,x94933,f332(x94934,x94935))+~P1(f332(f332(f334(x94936),x94935),x94937))
% 52.62/52.42 [7735]~P41(x77354,x77355,x77356,x77353)+~P33(x77358,x77356,f332(f332(f332(f93(x77358),x77357),x77354),x77351))+P1(f332(f332(x77351,x77352),x77353))+~P1(f332(f332(x77357,x77352),x77355))
% 52.62/52.42 [9137]~P25(x91377,x91371,x91378,x91373)+~P1(f332(f64(x91377),x91375))+~P1(f332(f64(x91377),x91374))+E(f332(f75(x91371,x91371,x91372,f332(x91373,x91374)),f332(f75(x91371,x91371,x91372,f332(x91373,x91375)),x91376)),f332(f75(x91371,x91371,x91372,f332(x91373,x91375)),f332(f75(x91371,x91371,x91372,f332(x91373,x91374)),x91376)))
% 52.62/52.42 [9204]~P31(x92042,x92042,x92045,x92046)+~P27(x92043,x92042,x92047,x92048,x92041)+~P1(f332(f64(x92042),x92046))+E(f332(f332(x92041,f332(f75(x92042,x92043,x92042,x92044),x92045)),x92046),f332(f332(x92041,x92044),f332(f303(x92042,x92042,x92045),x92046)))
% 52.62/52.42 [9491]~P29(x94917,x94912,x94915,x94918,x94916,x94911)+~P1(f332(f64(x94912),x94914))+E(f332(x94911,f332(f332(f302(x94912),x94913),x94914)),f332(f332(x94915,f332(x94916,x94913)),f332(x94911,x94914)))+P1(f332(f332(f334(x94912),x94913),x94914))
% 52.62/52.42 [9498]~P28(x94986,x94985,x94981,x94987,x94988,x94982)+E(f332(f332(x94981,f332(x94982,x94983)),f332(x94982,x94984)),f332(x94982,x94984))+~P1(f332(f64(x94985),x94984))+~P1(f332(f332(f232(f853(x94985,a839)),x94983),x94984))
% 52.62/52.42 [9124]P1(f332(f332(f334(f852(f846(x91241),f846(x91241))),f332(f332(f241(f846(x91241),f846(x91241)),x91242),x91243)),f146(x91241,x91244)))+~E(x91243,f332(f332(f125(x91241),x91245),f332(f332(f140(x91241),x91246),x91247)))+~E(x91242,f332(f332(f125(x91241),x91245),f332(f332(f140(x91241),x91248),x91247)))+~P1(f332(f332(f334(f852(x91241,x91241)),f332(f332(f241(x91241,x91241),x91248),x91246)),x91244))
% 52.62/52.42 [9494]~P28(x94946,x94942,x94945,x94947,x94948,x94941)+~P1(f332(f64(x94942),x94944))+~P1(f332(f64(x94942),x94943))+E(f332(x94941,f332(f332(f103(f853(x94942,a839)),x94943),x94944)),f332(f332(x94945,f332(x94941,x94943)),f332(x94941,x94944)))
% 52.62/52.42 [10008]~P31(x100084,x100082,x100085,x100088)+E(f332(f332(f48(x100081,f853(x100082,a839)),x100083),f332(f332(f10(f853(x100084,a839),f853(x100082,a839),x100081),f303(x100084,x100082,x100085)),x100086)),f332(f303(x100084,x100082,x100085),f332(f332(f48(x100081,f853(x100084,a839)),x100083),x100086)))+~P1(f332(f332(f334(x100081),x100087),x100083))+P1(f332(f332(f334(x100081),f678(x100087,x100086,x100083,x100081,x100088,x100085,x100082,x100084)),x100083))
% 52.62/52.42 [10027]~P31(x100274,x100272,x100275,x100277)+E(f332(f332(f48(x100271,f853(x100272,a839)),x100273),f332(f332(f10(f853(x100274,a839),f853(x100272,a839),x100271),f303(x100274,x100272,x100275)),x100276)),f332(f303(x100274,x100272,x100275),f332(f332(f48(x100271,f853(x100274,a839)),x100273),x100276)))+~P1(f332(f332(f334(x100271),x100278),x100273))+~P1(f332(f332(f232(f853(x100274,a839)),f332(x100276,f678(x100278,x100276,x100273,x100271,x100277,x100275,x100272,x100274))),x100277))
% 52.62/52.42 [9548]~P29(x95487,x95485,x95481,x95488,x95482,x95484)+~P1(f332(f64(x95485),x95486))+~P1(f332(f332(f334(x95485),x95483),x95486))+E(f332(f332(x95481,f332(x95482,x95483)),f332(x95484,f332(f332(f3(f853(x95485,a839)),x95486),f332(f332(f302(x95485),x95483),f180(f853(x95485,a839)))))),f332(x95484,x95486))
% 52.62/52.42 [9557]~P29(x95576,x95573,x95571,x95577,x95578,x95572)+~P1(f332(f64(x95573),x95575))+~P1(f332(f64(x95573),x95574))+E(f332(f332(x95571,f332(x95572,f332(f332(f103(f853(x95573,a839)),x95574),x95575))),f332(x95572,f332(f332(f104(f853(x95573,a839)),x95574),x95575))),f332(f332(x95571,f332(x95572,x95574)),f332(x95572,x95575)))
% 52.62/52.42 [9639]P43(x96391,x96392,x96393,x96394,x96395,f332(f332(x96393,x96396),x96397))+~P43(x96391,x96392,x96393,x96394,f332(f332(f3(f853(x96391,a839)),x96395),f332(f332(f302(x96391),x96398),f180(f853(x96391,a839)))),x96399)+~E(f332(f332(x96393,x96396),x96397),f332(f332(x96393,x96398),x96399))+~P1(f332(f332(f334(x96391),x96398),x96395))
% 52.62/52.42 [10038]P30(x100381,x100382,f332(f332(f302(f844(x100381)),f332(f332(f332(f93(x100381),f332(x100383,f439(x100384,x100385,x100386,x100387,x100383,x100382,x100381,x100388,x100389))),f332(x100387,f439(x100384,x100385,x100386,x100387,x100383,x100382,x100381,x100388,x100389))),f332(x100386,f439(x100384,x100385,x100386,x100387,x100383,x100382,x100381,x100388,x100389)))),f180(f853(f844(x100381),a839))))+~P1(f332(f64(x100389),x100388))+~P30(x100381,x100382,f332(f303(x100389,f844(x100381),f332(f332(f20(x100389,f853(x100381,f853(a842,a839)),f844(x100381)),f332(f332(f20(x100389,a840,f853(f853(x100381,f853(a842,a839)),f844(x100381))),f332(f332(f10(f853(x100381,f853(a842,a839)),f853(a840,f853(f853(x100381,f853(a842,a839)),f844(x100381))),x100389),f93(x100381)),x100383)),x100387)),x100386)),x100388))+P30(x100381,x100382,f332(f303(x100389,f844(x100381),f332(f332(f20(x100389,f853(x100381,f853(a842,a839)),f844(x100381)),f332(f332(f20(x100389,a840,f853(f853(x100381,f853(a842,a839)),f844(x100381))),f332(f332(f10(f853(x100381,f853(a842,a839)),f853(a840,f853(f853(x100381,f853(a842,a839)),f844(x100381))),x100389),f93(x100381)),x100385)),x100387)),x100384)),x100388))
% 52.62/52.42 [10039]~P30(x100391,x100392,f332(f332(f302(f844(x100391)),f332(f332(f332(f93(x100391),f332(x100394,f439(x100396,x100394,x100398,x100395,x100399,x100392,x100391,x100397,x100393))),f332(x100395,f439(x100396,x100394,x100398,x100395,x100399,x100392,x100391,x100397,x100393))),f332(x100396,f439(x100396,x100394,x100398,x100395,x100399,x100392,x100391,x100397,x100393)))),f180(f853(f844(x100391),a839))))+~P1(f332(f64(x100393),x100397))+~P30(x100391,x100392,f332(f303(x100393,f844(x100391),f332(f332(f20(x100393,f853(x100391,f853(a842,a839)),f844(x100391)),f332(f332(f20(x100393,a840,f853(f853(x100391,f853(a842,a839)),f844(x100391))),f332(f332(f10(f853(x100391,f853(a842,a839)),f853(a840,f853(f853(x100391,f853(a842,a839)),f844(x100391))),x100393),f93(x100391)),x100399)),x100395)),x100398)),x100397))+P30(x100391,x100392,f332(f303(x100393,f844(x100391),f332(f332(f20(x100393,f853(x100391,f853(a842,a839)),f844(x100391)),f332(f332(f20(x100393,a840,f853(f853(x100391,f853(a842,a839)),f844(x100391))),f332(f332(f10(f853(x100391,f853(a842,a839)),f853(a840,f853(f853(x100391,f853(a842,a839)),f844(x100391))),x100393),f93(x100391)),x100394)),x100395)),x100396)),x100397))
% 52.62/52.42 [9581]~P19(x95816,x95817,x95818,x95819,x958110,x95811)+E(f332(f332(x95811,x95812),x95813),f332(f332(x95811,x95814),x95815))+~P1(f332(f332(f334(f852(x95817,x95817)),f332(f332(f241(x95817,x95817),x95813),x95815)),x958110))+~P1(f332(f332(f334(f852(x95816,x95816)),f332(f332(f241(x95816,x95816),x95812),x95814)),x95819))
% 52.62/52.42 [6803]E(x68031,x68032)+~P1(f332(f332(f232(a1),f2(a1)),x68032))+~P1(f332(f332(f232(a1),f2(a1)),x68031))+~P1(f332(f332(f279(a1),x68032),x68031))+~P1(f332(f332(f279(a1),x68031),x68032))
% 52.62/52.42 [9356]E(x93561,f2(a1))+E(x93562,f2(a1))+E(f332(f332(f88(a1,f852(a1,a1)),f332(f332(a212,x93562),x93561)),f332(f332(f20(a1,a1,f852(a1,a1)),f332(f332(f10(a1,f853(a1,f852(a1,a1)),a1),f241(a1,a1)),f332(f44(a1),x93562))),f332(f44(a1),x93561))),f210(x93562,x93561))+P1(f332(f332(f233(a1),x93561),f2(a1)))+~P1(f332(f321(f852(a1,a1),a216),f332(f332(f241(a1,a1),x93562),x93561)))
% 52.62/52.42 [9206]~P93(x92062)+E(x92061,f180(f853(x92062,a839)))+~P1(f332(f64(x92062),x92061))+P1(f332(f332(f334(x92062),f15(x92062,x92061)),x92061))+~P1(f332(f332(f334(x92062),f332(f332(f103(x92062),f442(x92061,x92062)),f446(x92061,x92062))),f332(f332(f302(x92062),f442(x92061,x92062)),f332(f332(f302(x92062),f446(x92061,x92062)),f180(f853(x92062,a839))))))
% 52.62/52.42 [9207]~P100(x92072)+E(x92071,f180(f853(x92072,a839)))+~P1(f332(f64(x92072),x92071))+P1(f332(f332(f334(x92072),f16(x92072,x92071)),x92071))+~P1(f332(f332(f334(x92072),f332(f332(f179(x92072),f443(x92071,x92072)),f445(x92071,x92072))),f332(f332(f302(x92072),f443(x92071,x92072)),f332(f332(f302(x92072),f445(x92071,x92072)),f180(f853(x92072,a839))))))
% 52.62/52.42 [9208]~P100(x92082)+E(x92081,f180(f853(x92082,a839)))+~P1(f332(f64(x92082),x92081))+P1(f332(f332(f334(x92082),f17(x92082,x92081)),x92081))+~P1(f332(f332(f334(x92082),f332(f332(f236(x92082),f447(x92081,x92082)),f448(x92081,x92082))),f332(f332(f302(x92082),f447(x92081,x92082)),f332(f332(f302(x92082),f448(x92081,x92082)),f180(f853(x92082,a839))))))
% 52.62/52.42 [9209]~P93(x92092)+E(x92091,f180(f853(x92092,a839)))+~P1(f332(f64(x92092),x92091))+P1(f332(f332(f334(x92092),f12(x92092,x92091)),x92091))+~P1(f332(f332(f334(x92092),f332(f332(f104(x92092),f513(x92091,x92092)),f518(x92091,x92092))),f332(f332(f302(x92092),f513(x92091,x92092)),f332(f332(f302(x92092),f518(x92091,x92092)),f180(f853(x92092,a839))))))
% 52.62/52.42 [9237]~P66(x92372)+E(x92371,f180(f853(x92372,a839)))+~P1(f332(f64(x92372),x92371))+P1(f332(f332(f334(x92372),f332(f66(x92372,f83(x92372)),x92371)),x92371))+~P1(f332(f332(f334(x92372),f332(f332(f83(x92372),f565(x92371,x92372)),f566(x92371,x92372))),f332(f332(f302(x92372),f565(x92371,x92372)),f332(f332(f302(x92372),f566(x92371,x92372)),f180(f853(x92372,a839))))))
% 52.62/52.42 [9243]~P100(x92432)+E(x92431,f180(f853(x92432,a839)))+~P1(f332(f64(x92432),x92431))+P1(f332(f332(f334(x92432),f13(x92432,f179(x92432),x92431)),x92431))+~P1(f332(f332(f334(x92432),f332(f332(f179(x92432),f451(x92431,x92432)),f454(x92431,x92432))),f332(f332(f302(x92432),f451(x92431,x92432)),f332(f332(f302(x92432),f454(x92431,x92432)),f180(f853(x92432,a839))))))
% 52.62/52.42 [9244]~P100(x92442)+E(x92441,f180(f853(x92442,a839)))+~P1(f332(f64(x92442),x92441))+P1(f332(f332(f334(x92442),f14(x92442,f236(x92442),x92441)),x92441))+~P1(f332(f332(f334(x92442),f332(f332(f236(x92442),f455(x92441,x92442)),f456(x92441,x92442))),f332(f332(f302(x92442),f455(x92441,x92442)),f332(f332(f302(x92442),f456(x92441,x92442)),f180(f853(x92442,a839))))))
% 52.62/52.42 [6417]~P82(x64172)+E(x64171,f2(x64172))+~E(f332(f332(f82(x64172),x64173),x64171),f2(x64172))+~P1(f332(f332(f232(x64172),f2(x64172)),x64173))+~P1(f332(f332(f232(x64172),f2(x64172)),x64171))
% 52.62/52.42 [6418]~P82(x64182)+E(x64181,f2(x64182))+~E(f332(f332(f82(x64182),x64181),x64183),f2(x64182))+~P1(f332(f332(f232(x64182),f2(x64182)),x64183))+~P1(f332(f332(f232(x64182),f2(x64182)),x64181))
% 52.62/52.42 [6620]~P1(f332(f332(f279(a845),x66202),x66201))+~P1(f332(f332(f279(a845),x66201),x66203))+P1(f332(f332(f279(a845),x66202),x66203))+P1(f332(f332(f279(a845),x66201),x66202))+P1(f332(f332(f279(a845),x66203),x66201))
% 52.62/52.42 [6802]~P1(f332(f332(f279(a845),x68021),x68023))+~P1(f332(f332(f279(a845),x68023),x68022))+~P1(f332(f332(f279(a845),x68022),x68021))+P1(f332(f332(f279(a845),x68021),x68022))+P1(f332(f332(f279(a845),x68023),x68021))
% 52.62/52.42 [7136]~P100(x71361)+E(f17(x71361,x71362),x71363)+~P1(f332(f64(x71361),x71362))+~P1(f332(f332(f232(x71361),x71363),f626(x71363,x71362,x71361)))+~P1(f332(f332(f334(x71361),x71363),x71362))
% 52.62/52.42 [7171]~P100(x71711)+~P20(x71711,x71712)+~P20(x71711,x71713)+P20(x71711,f332(f332(f125(x71711),x71712),x71713))+P1(f332(f332(f334(x71711),f764(x71713,x71712,x71711)),f332(f158(x71711),x71712)))
% 52.62/52.42 [7172]~P100(x71721)+~P20(x71721,x71722)+~P20(x71721,x71723)+P20(x71721,f332(f332(f125(x71721),x71722),x71723))+P1(f332(f332(f334(x71721),f765(x71723,x71722,x71721)),f332(f158(x71721),x71723)))
% 52.62/52.42 [7238]~P100(x72381)+E(f16(x72381,x72382),x72383)+~P1(f332(f64(x72381),x72382))+P1(f332(f332(f334(x72381),f629(x72383,x72382,x72381)),x72382))+~P1(f332(f332(f334(x72381),x72383),x72382))
% 52.62/52.42 [7239]~P100(x72391)+E(f17(x72391,x72392),x72393)+~P1(f332(f64(x72391),x72392))+P1(f332(f332(f334(x72391),f626(x72393,x72392,x72391)),x72392))+~P1(f332(f332(f334(x72391),x72393),x72392))
% 52.62/52.42 [7838]~P100(x78381)+E(f16(x78381,x78382),x78383)+~P1(f332(f64(x78381),x78382))+~P1(f332(f332(f334(x78381),x78383),x78382))+~P1(f332(f332(f232(x78381),f629(x78383,x78382,x78381)),x78383))
% 52.62/52.42 [8152]~P100(x81521)+~P20(x81521,x81522)+~P20(x81521,x81523)+P20(x81521,f332(f332(f125(x81521),x81522),x81523))+~P1(f332(f332(f232(x81521),f764(x81523,x81522,x81521)),f765(x81523,x81522,x81521)))
% 52.62/52.42 [8881]~P93(x88812)+E(x88811,f180(f853(x88812,a839)))+~E(f332(f332(f103(x88812),f332(x88813,f477(x88811,x88813,x88812))),f332(x88813,f478(x88811,x88813,x88812))),f332(x88813,f332(f332(f103(x88812),f477(x88811,x88813,x88812)),f478(x88811,x88813,x88812))))+E(f15(x88812,f332(f303(x88812,x88812,x88813),x88811)),f332(x88813,f15(x88812,x88811)))+~P1(f332(f64(x88812),x88811))
% 52.62/52.42 [8882]~P100(x88822)+E(x88821,f180(f853(x88822,a839)))+~E(f332(f332(f179(x88822),f332(x88823,f467(x88821,x88823,x88822))),f332(x88823,f473(x88821,x88823,x88822))),f332(x88823,f332(f332(f179(x88822),f467(x88821,x88823,x88822)),f473(x88821,x88823,x88822))))+E(f16(x88822,f332(f303(x88822,x88822,x88823),x88821)),f332(x88823,f16(x88822,x88821)))+~P1(f332(f64(x88822),x88821))
% 52.62/52.42 [8883]~P100(x88832)+E(x88831,f180(f853(x88832,a839)))+~E(f332(f332(f236(x88832),f332(x88833,f475(x88831,x88833,x88832))),f332(x88833,f476(x88831,x88833,x88832))),f332(x88833,f332(f332(f236(x88832),f475(x88831,x88833,x88832)),f476(x88831,x88833,x88832))))+E(f17(x88832,f332(f303(x88832,x88832,x88833),x88831)),f332(x88833,f17(x88832,x88831)))+~P1(f332(f64(x88832),x88831))
% 52.62/52.42 [8884]~P93(x88842)+E(x88841,f180(f853(x88842,a839)))+~E(f332(f332(f104(x88842),f332(x88843,f530(x88841,x88843,x88842))),f332(x88843,f532(x88841,x88843,x88842))),f332(x88843,f332(f332(f104(x88842),f530(x88841,x88843,x88842)),f532(x88841,x88843,x88842))))+E(f12(x88842,f332(f303(x88842,x88842,x88843),x88841)),f332(x88843,f12(x88842,x88841)))+~P1(f332(f64(x88842),x88841))
% 52.62/52.42 [8948]~P100(x89482)+E(x89481,f180(f853(x89482,a839)))+~E(f332(f332(f179(x89482),f332(x89483,f468(x89481,x89483,x89482))),f332(x89483,f470(x89481,x89483,x89482))),f332(x89483,f332(f332(f179(x89482),f468(x89481,x89483,x89482)),f470(x89481,x89483,x89482))))+E(f13(x89482,f179(x89482),f332(f303(x89482,x89482,x89483),x89481)),f332(x89483,f13(x89482,f179(x89482),x89481)))+~P1(f332(f64(x89482),x89481))
% 52.62/52.42 [8949]~P100(x89492)+E(x89491,f180(f853(x89492,a839)))+~E(f332(f332(f236(x89492),f332(x89493,f471(x89491,x89493,x89492))),f332(x89493,f472(x89491,x89493,x89492))),f332(x89493,f332(f332(f236(x89492),f471(x89491,x89493,x89492)),f472(x89491,x89493,x89492))))+E(f14(x89492,f236(x89492),f332(f303(x89492,x89492,x89493),x89491)),f332(x89493,f14(x89492,f236(x89492),x89491)))+~P1(f332(f64(x89492),x89491))
% 52.62/52.42 [6032]~P93(x60322)+E(x60321,f180(f853(x60322,a839)))+~P1(f332(f64(x60322),x60321))+E(f15(x60322,f332(f332(f302(x60322),x60323),x60321)),f332(f332(f103(x60322),x60323),f15(x60322,x60321)))+P1(f332(f332(f334(x60322),x60323),x60321))
% 52.62/52.42 [6033]~P100(x60332)+E(x60331,f180(f853(x60332,a839)))+~P1(f332(f64(x60332),x60331))+E(f16(x60332,f332(f332(f302(x60332),x60333),x60331)),f332(f332(f179(x60332),x60333),f16(x60332,x60331)))+P1(f332(f332(f334(x60332),x60333),x60331))
% 52.62/52.42 [6034]~P100(x60342)+E(x60341,f180(f853(x60342,a839)))+~P1(f332(f64(x60342),x60341))+E(f17(x60342,f332(f332(f302(x60342),x60343),x60341)),f332(f332(f236(x60342),x60343),f17(x60342,x60341)))+P1(f332(f332(f334(x60342),x60343),x60341))
% 52.62/52.42 [6035]~P93(x60352)+E(x60351,f180(f853(x60352,a839)))+~P1(f332(f64(x60352),x60351))+E(f12(x60352,f332(f332(f302(x60352),x60353),x60351)),f332(f332(f104(x60352),x60353),f12(x60352,x60351)))+P1(f332(f332(f334(x60352),x60353),x60351))
% 52.62/52.42 [6434]~P66(x64342)+E(x64341,f180(f853(x64342,a839)))+~P1(f332(f64(x64342),x64341))+E(f332(f66(x64342,f83(x64342)),f332(f332(f302(x64342),x64343),x64341)),f332(f332(f83(x64342),x64343),f332(f66(x64342,f83(x64342)),x64341)))+P1(f332(f332(f334(x64342),x64343),x64341))
% 52.62/52.42 [6524]~P100(x65242)+E(x65241,f180(f853(x65242,a839)))+~P1(f332(f64(x65242),x65241))+E(f13(x65242,f179(x65242),f332(f332(f302(x65242),x65243),x65241)),f332(f332(f179(x65242),x65243),f13(x65242,f179(x65242),x65241)))+P1(f332(f332(f334(x65242),x65243),x65241))
% 52.62/52.42 [6525]~P100(x65252)+E(x65251,f180(f853(x65252,a839)))+~P1(f332(f64(x65252),x65251))+E(f14(x65252,f236(x65252),f332(f332(f302(x65252),x65253),x65251)),f332(f332(f236(x65252),x65253),f14(x65252,f236(x65252),x65251)))+P1(f332(f332(f334(x65252),x65253),x65251))
% 52.62/52.42 [6974]~P100(x69742)+E(f332(f332(f236(x69742),f17(x69742,x69741)),f17(x69742,x69743)),f17(x69742,x69743))+E(x69741,f180(f853(x69742,a839)))+~P1(f332(f64(x69742),x69743))+~P1(f332(f332(f232(f853(x69742,a839)),x69741),x69743))
% 52.62/52.42 [6975]~P100(x69752)+E(f332(f332(f179(x69752),f16(x69752,x69751)),f16(x69752,x69753)),f16(x69752,x69753))+E(x69751,f180(f853(x69752,a839)))+~P1(f332(f64(x69752),x69753))+~P1(f332(f332(f232(f853(x69752,a839)),x69751),x69753))
% 52.62/52.42 [6976]~P93(x69762)+E(f332(f332(f103(x69762),f15(x69762,x69761)),f15(x69762,x69763)),f15(x69762,x69763))+E(x69761,f180(f853(x69762,a839)))+~P1(f332(f64(x69762),x69763))+~P1(f332(f332(f232(f853(x69762,a839)),x69761),x69763))
% 52.62/52.42 [6977]~P93(x69772)+E(f332(f332(f104(x69772),f12(x69772,x69771)),f12(x69772,x69773)),f12(x69772,x69773))+E(x69771,f180(f853(x69772,a839)))+~P1(f332(f64(x69772),x69773))+~P1(f332(f332(f232(f853(x69772,a839)),x69771),x69773))
% 52.62/52.42 [7294]~P100(x72942)+E(x72941,f180(f853(x72942,a839)))+~P1(f332(f64(x72942),x72943))+P1(f332(f332(f232(x72942),f16(x72942,x72941)),f16(x72942,x72943)))+~P1(f332(f332(f232(f853(x72942,a839)),x72941),x72943))
% 52.62/52.42 [7295]~P100(x72952)+E(x72951,f180(f853(x72952,a839)))+~P1(f332(f64(x72952),x72953))+P1(f332(f332(f232(x72952),f17(x72952,x72953)),f17(x72952,x72951)))+~P1(f332(f332(f232(f853(x72952,a839)),x72951),x72953))
% 52.62/52.42 [7357]~P93(x73571)+E(f15(x73571,x73572),x73573)+~P1(f332(f64(x73571),x73572))+~E(f332(f332(f3(f853(x73571,a839)),x73572),f332(f332(f302(x73571),x73573),f180(f853(x73571,a839)))),f180(f853(x73571,a839)))+~P1(f332(f332(f334(x73571),x73573),x73572))
% 52.62/52.42 [7358]~P100(x73581)+E(f16(x73581,x73582),x73583)+~P1(f332(f64(x73581),x73582))+~E(f332(f332(f3(f853(x73581,a839)),x73582),f332(f332(f302(x73581),x73583),f180(f853(x73581,a839)))),f180(f853(x73581,a839)))+~P1(f332(f332(f334(x73581),x73583),x73582))
% 52.62/52.42 [7359]~P100(x73591)+E(f17(x73591,x73592),x73593)+~P1(f332(f64(x73591),x73592))+~E(f332(f332(f3(f853(x73591,a839)),x73592),f332(f332(f302(x73591),x73593),f180(f853(x73591,a839)))),f180(f853(x73591,a839)))+~P1(f332(f332(f334(x73591),x73593),x73592))
% 52.62/52.42 [7360]~P93(x73601)+E(f12(x73601,x73602),x73603)+~P1(f332(f64(x73601),x73602))+~E(f332(f332(f3(f853(x73601,a839)),x73602),f332(f332(f302(x73601),x73603),f180(f853(x73601,a839)))),f180(f853(x73601,a839)))+~P1(f332(f332(f334(x73601),x73603),x73602))
% 52.62/52.42 [7460]~P100(x74601)+E(f13(x74601,f179(x74601),x74602),x74603)+~P1(f332(f64(x74601),x74602))+~E(f332(f332(f3(f853(x74601,a839)),x74602),f332(f332(f302(x74601),x74603),f180(f853(x74601,a839)))),f180(f853(x74601,a839)))+~P1(f332(f332(f334(x74601),x74603),x74602))
% 52.62/52.42 [7461]~P100(x74611)+E(f14(x74611,f236(x74611),x74612),x74613)+~P1(f332(f64(x74611),x74612))+~E(f332(f332(f3(f853(x74611,a839)),x74612),f332(f332(f302(x74611),x74613),f180(f853(x74611,a839)))),f180(f853(x74611,a839)))+~P1(f332(f332(f334(x74611),x74613),x74612))
% 52.62/52.42 [7498]~P100(x74982)+E(x74981,f180(f853(x74982,a839)))+~P1(f332(f64(x74982),x74981))+~P1(f332(f332(f233(x74982),x74983),f547(x74983,x74981,x74982)))+P1(f332(f332(f233(x74982),x74983),f332(f66(x74982,f236(x74982)),x74981)))
% 52.62/52.42 [7499]~P100(x74992)+E(x74991,f180(f853(x74992,a839)))+~P1(f332(f64(x74992),x74991))+~P1(f332(f332(f232(x74992),x74993),f548(x74993,x74991,x74992)))+P1(f332(f332(f232(x74992),x74993),f332(f66(x74992,f236(x74992)),x74991)))
% 52.62/52.42 [7500]~P98(x75002)+E(x75001,f180(f853(x75002,a839)))+~P1(f332(f64(x75002),x75001))+~P1(f332(f332(f232(x75002),x75003),f549(x75003,x75001,x75002)))+P1(f332(f332(f232(x75002),x75003),f332(f66(x75002,f104(x75002)),x75001)))
% 52.62/52.42 [7588]~P98(x75882)+E(x75881,f180(f853(x75882,a839)))+~P1(f332(f64(x75882),x75881))+P1(f332(f332(f334(x75882),f549(x75883,x75881,x75882)),x75881))+P1(f332(f332(f232(x75882),x75883),f332(f66(x75882,f104(x75882)),x75881)))
% 52.62/52.42 [7589]~P100(x75892)+E(x75891,f180(f853(x75892,a839)))+~P1(f332(f64(x75892),x75891))+P1(f332(f332(f334(x75892),f548(x75893,x75891,x75892)),x75891))+P1(f332(f332(f232(x75892),x75893),f332(f66(x75892,f236(x75892)),x75891)))
% 52.62/52.42 [7590]~P100(x75902)+E(x75901,f180(f853(x75902,a839)))+~P1(f332(f64(x75902),x75901))+P1(f332(f332(f334(x75902),f547(x75903,x75901,x75902)),x75901))+P1(f332(f332(f233(x75902),x75903),f332(f66(x75902,f236(x75902)),x75901)))
% 52.62/52.42 [7710]~P100(x77102)+E(x77101,f180(f853(x77102,a839)))+E(f332(f332(f236(x77102),f14(x77102,f236(x77102),x77101)),f14(x77102,f236(x77102),x77103)),f14(x77102,f236(x77102),x77103))+~P1(f332(f64(x77102),x77103))+~P1(f332(f332(f232(f853(x77102,a839)),x77101),x77103))
% 52.62/52.42 [7711]~P100(x77112)+E(x77111,f180(f853(x77112,a839)))+E(f332(f332(f179(x77112),f13(x77112,f179(x77112),x77111)),f13(x77112,f179(x77112),x77113)),f13(x77112,f179(x77112),x77113))+~P1(f332(f64(x77112),x77113))+~P1(f332(f332(f232(f853(x77112,a839)),x77111),x77113))
% 52.62/52.42 [7913]~E(f675(x79131,x79133,x79132),f676(x79131,x79133,x79132))+~E(f332(f43(x79132),f677(x79131,x79133,x79132)),x79131)+E(f332(f332(f83(a845),x79131),f332(f43(f853(x79132,a839)),x79133)),f332(f43(x79132),f45(f853(x79132,a839),x79133)))+~P1(f332(f64(x79132),f45(f853(x79132,a839),x79133)))+~P1(f332(f64(f853(x79132,a839)),x79133))
% 52.62/52.42 [8088]~P100(x80882)+E(x80881,f180(f853(x80882,a839)))+~P1(f332(f64(x80882),x80883))+P1(f332(f332(f232(x80882),f332(f66(x80882,f236(x80882)),x80883)),f332(f66(x80882,f236(x80882)),x80881)))+~P1(f332(f332(f232(f853(x80882,a839)),x80881),x80883))
% 52.62/52.42 [8392]~E(f675(x83921,x83923,x83922),f676(x83921,x83923,x83922))+E(f332(f332(f83(a845),x83921),f332(f43(f853(x83922,a839)),x83923)),f332(f43(x83922),f45(f853(x83922,a839),x83923)))+P1(f332(f332(f334(f853(x83922,a839)),f677(x83921,x83923,x83922)),x83923))+~P1(f332(f64(x83922),f45(f853(x83922,a839),x83923)))+~P1(f332(f64(f853(x83922,a839)),x83923))
% 52.62/52.42 [8416]~E(f332(f43(x84162),f677(x84161,x84163,x84162)),x84161)+E(f332(f332(f83(a845),x84161),f332(f43(f853(x84162,a839)),x84163)),f332(f43(x84162),f45(f853(x84162,a839),x84163)))+P1(f332(f332(f334(f853(x84162,a839)),f676(x84161,x84163,x84162)),x84163))+~P1(f332(f64(x84162),f45(f853(x84162,a839),x84163)))+~P1(f332(f64(f853(x84162,a839)),x84163))
% 52.62/52.42 [8417]~E(f332(f43(x84172),f677(x84171,x84173,x84172)),x84171)+E(f332(f332(f83(a845),x84171),f332(f43(f853(x84172,a839)),x84173)),f332(f43(x84172),f45(f853(x84172,a839),x84173)))+P1(f332(f332(f334(f853(x84172,a839)),f675(x84171,x84173,x84172)),x84173))+~P1(f332(f64(x84172),f45(f853(x84172,a839),x84173)))+~P1(f332(f64(f853(x84172,a839)),x84173))
% 52.62/52.42 [8447]~E(f332(f43(x84472),f677(x84471,x84473,x84472)),x84471)+~E(f332(f332(f104(f853(x84472,a839)),f676(x84471,x84473,x84472)),f675(x84471,x84473,x84472)),f180(f853(x84472,a839)))+E(f332(f332(f83(a845),x84471),f332(f43(f853(x84472,a839)),x84473)),f332(f43(x84472),f45(f853(x84472,a839),x84473)))+~P1(f332(f64(f853(x84472,a839)),x84473))+~P1(f332(f64(x84472),f45(f853(x84472,a839),x84473)))
% 52.62/52.42 [8673]E(f332(f332(f83(a845),x86731),f332(f43(f853(x86732,a839)),x86733)),f332(f43(x86732),f45(f853(x86732,a839),x86733)))+P1(f332(f332(f334(f853(x86732,a839)),f677(x86731,x86733,x86732)),x86733))+P1(f332(f332(f334(f853(x86732,a839)),f676(x86731,x86733,x86732)),x86733))+~P1(f332(f64(f853(x86732,a839)),x86733))+~P1(f332(f64(x86732),f45(f853(x86732,a839),x86733)))
% 52.62/52.42 [8674]E(f332(f332(f83(a845),x86741),f332(f43(f853(x86742,a839)),x86743)),f332(f43(x86742),f45(f853(x86742,a839),x86743)))+P1(f332(f332(f334(f853(x86742,a839)),f677(x86741,x86743,x86742)),x86743))+P1(f332(f332(f334(f853(x86742,a839)),f675(x86741,x86743,x86742)),x86743))+~P1(f332(f64(f853(x86742,a839)),x86743))+~P1(f332(f64(x86742),f45(f853(x86742,a839),x86743)))
% 52.62/52.42 [8699]~E(f332(f332(f104(f853(x86992,a839)),f676(x86991,x86993,x86992)),f675(x86991,x86993,x86992)),f180(f853(x86992,a839)))+E(f332(f332(f83(a845),x86991),f332(f43(f853(x86992,a839)),x86993)),f332(f43(x86992),f45(f853(x86992,a839),x86993)))+~P1(f332(f64(f853(x86992,a839)),x86993))+P1(f332(f332(f334(f853(x86992,a839)),f677(x86991,x86993,x86992)),x86993))+~P1(f332(f64(x86992),f45(f853(x86992,a839),x86993)))
% 52.62/52.42 [8927]~P91(x89272)+E(x89271,f180(f853(x89272,a839)))+~E(f332(f332(f83(x89272),f332(x89273,f567(x89271,x89273,x89272))),f332(x89273,f568(x89271,x89273,x89272))),f332(x89273,f332(f332(f83(x89272),f567(x89271,x89273,x89272)),f568(x89271,x89273,x89272))))+~P1(f332(f64(x89272),x89271))+E(f332(f66(x89272,f83(x89272)),f332(f303(x89272,x89272,x89273),x89271)),f332(x89273,f332(f66(x89272,f83(x89272)),x89271)))
% 52.62/52.42 [9795]P1(f332(f332(x97951,x97952),x97953))+P1(f332(f332(f233(a1),f823(x97951,x97953,x97952)),f824(x97951,x97953,x97952)))+P1(f332(f332(f232(a1),f824(x97951,x97953,x97952)),f2(a1)))+P1(f332(f332(x97951,f823(x97951,x97953,x97952)),f332(f332(f83(a1),f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f824(x97951,x97953,x97952))))+~P1(f332(f321(f852(a1,a1),a63),f332(f332(f241(a1,a1),x97952),x97953)))
% 52.62/52.42 [9801]P1(f332(f332(x98011,x98012),x98013))+P1(f332(f332(f232(a1),f822(x98011,x98013,x98012)),f2(a1)))+P1(f332(f332(x98011,f821(x98011,x98013,x98012)),f332(f332(f83(a1),f332(f106(a1),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f822(x98011,x98013,x98012))))+P1(f332(f332(f232(a1),f2(a1)),f332(f332(f82(a1),f821(x98011,x98013,x98012)),f822(x98011,x98013,x98012))))+~P1(f332(f321(f852(a1,a1),a60),f332(f332(f241(a1,a1),x98012),x98013)))
% 52.62/52.42 [7883]~P110(x78831)+~P1(f332(f332(f232(x78831),x78832),f80(x78831)))+~P1(f332(f332(f232(x78831),f2(x78831)),x78832))+~P1(f332(f332(f232(x78831),f2(x78831)),x78833))+P1(f332(f332(f232(x78831),f332(f332(f83(x78831),x78832),x78833)),x78833))
% 52.62/52.42 [7884]~P110(x78841)+~P1(f332(f332(f232(x78841),x78843),f80(x78841)))+~P1(f332(f332(f232(x78841),f2(x78841)),x78843))+~P1(f332(f332(f232(x78841),f2(x78841)),x78842))+P1(f332(f332(f232(x78841),f332(f332(f83(x78841),x78842),x78843)),x78842))
% 52.62/52.42 [8233]~P100(x82332)+E(x82331,f180(f853(x82332,a839)))+~P1(f332(f64(x82332),x82331))+P1(f332(f332(f334(x82332),f552(x82333,x82331,x82332)),x82331))+~P1(f332(f332(f232(x82332),f332(f66(x82332,f236(x82332)),x82331)),x82333))
% 52.62/52.42 [8234]~P100(x82342)+E(x82341,f180(f853(x82342,a839)))+~P1(f332(f64(x82342),x82341))+P1(f332(f332(f334(x82342),f553(x82343,x82341,x82342)),x82341))+~P1(f332(f332(f233(x82342),f332(f66(x82342,f236(x82342)),x82341)),x82343))
% 52.62/52.42 [8235]~P100(x82352)+E(x82351,f180(f853(x82352,a839)))+~P1(f332(f64(x82352),x82351))+P1(f332(f332(f233(x82352),f553(x82353,x82351,x82352)),x82353))+~P1(f332(f332(f233(x82352),f332(f66(x82352,f236(x82352)),x82351)),x82353))
% 52.62/52.42 [8236]~P100(x82362)+E(x82361,f180(f853(x82362,a839)))+~P1(f332(f64(x82362),x82361))+P1(f332(f332(f232(x82362),f552(x82363,x82361,x82362)),x82363))+~P1(f332(f332(f232(x82362),f332(f66(x82362,f236(x82362)),x82361)),x82363))
% 52.62/52.42 [8321]~P1(f332(x83211,x83213))+P1(f332(x83211,f352(x83211,x83212)))+P1(f332(x83211,f351(x83211,x83212)))+~P1(f332(f332(f233(a1),f2(a1)),x83212))+P1(f332(x83211,f332(f332(f3(a1),f351(x83211,x83212)),f332(f332(f83(a1),f353(x83211,x83212)),x83212))))
% 52.62/52.42 [8539]~P1(f332(x85391,x85393))+P1(f332(x85391,f351(x85391,x85392)))+~P1(f332(f332(f233(a1),f2(a1)),x85392))+P1(f332(f332(f334(a1),f352(x85391,x85392)),f295(a1,f80(a1),x85392)))+P1(f332(x85391,f332(f332(f3(a1),f351(x85391,x85392)),f332(f332(f83(a1),f353(x85391,x85392)),x85392))))
% 52.62/52.42 [8717]~P1(f332(x87171,x87173))+~P1(f332(x87171,f351(x87171,x87172)))+P1(f332(x87171,f352(x87171,x87172)))+~P1(f332(f332(f233(a1),f2(a1)),x87172))+~P1(f332(x87171,f332(f332(f3(a1),f351(x87171,x87172)),f332(f332(f83(a1),f353(x87171,x87172)),x87172))))
% 52.62/52.42 [8820]~P1(f332(x88201,x88203))+~P1(f332(x88201,f351(x88201,x88202)))+~P1(f332(f332(f233(a1),f2(a1)),x88202))+P1(f332(f332(f334(a1),f352(x88201,x88202)),f295(a1,f80(a1),x88202)))+~P1(f332(x88201,f332(f332(f3(a1),f351(x88201,x88202)),f332(f332(f83(a1),f353(x88201,x88202)),x88202))))
% 52.62/52.42 [8636]~P93(x86361)+~P1(f332(f64(x86361),x86362))+E(f332(f332(f3(f853(x86361,a839)),x86362),f332(f332(f302(x86361),x86363),f180(f853(x86361,a839)))),f180(f853(x86361,a839)))+~P1(f332(f332(f334(x86361),x86363),x86362))+E(f332(f332(f103(x86361),x86363),f15(x86361,f332(f332(f3(f853(x86361,a839)),x86362),f332(f332(f302(x86361),x86363),f180(f853(x86361,a839)))))),f15(x86361,x86362))
% 52.62/52.42 [8637]~P100(x86371)+~P1(f332(f64(x86371),x86372))+E(f332(f332(f3(f853(x86371,a839)),x86372),f332(f332(f302(x86371),x86373),f180(f853(x86371,a839)))),f180(f853(x86371,a839)))+~P1(f332(f332(f334(x86371),x86373),x86372))+E(f332(f332(f179(x86371),x86373),f16(x86371,f332(f332(f3(f853(x86371,a839)),x86372),f332(f332(f302(x86371),x86373),f180(f853(x86371,a839)))))),f16(x86371,x86372))
% 52.62/52.42 [8638]~P100(x86381)+~P1(f332(f64(x86381),x86382))+E(f332(f332(f3(f853(x86381,a839)),x86382),f332(f332(f302(x86381),x86383),f180(f853(x86381,a839)))),f180(f853(x86381,a839)))+~P1(f332(f332(f334(x86381),x86383),x86382))+E(f332(f332(f236(x86381),x86383),f17(x86381,f332(f332(f3(f853(x86381,a839)),x86382),f332(f332(f302(x86381),x86383),f180(f853(x86381,a839)))))),f17(x86381,x86382))
% 52.62/52.42 [8639]~P93(x86391)+~P1(f332(f64(x86391),x86392))+E(f332(f332(f3(f853(x86391,a839)),x86392),f332(f332(f302(x86391),x86393),f180(f853(x86391,a839)))),f180(f853(x86391,a839)))+~P1(f332(f332(f334(x86391),x86393),x86392))+E(f332(f332(f104(x86391),x86393),f12(x86391,f332(f332(f3(f853(x86391,a839)),x86392),f332(f332(f302(x86391),x86393),f180(f853(x86391,a839)))))),f12(x86391,x86392))
% 52.62/52.42 [8694]~P100(x86941)+~P1(f332(f64(x86941),x86942))+E(f332(f332(f3(f853(x86941,a839)),x86942),f332(f332(f302(x86941),x86943),f180(f853(x86941,a839)))),f180(f853(x86941,a839)))+~P1(f332(f332(f334(x86941),x86943),x86942))+E(f332(f332(f179(x86941),x86943),f13(x86941,f179(x86941),f332(f332(f3(f853(x86941,a839)),x86942),f332(f332(f302(x86941),x86943),f180(f853(x86941,a839)))))),f13(x86941,f179(x86941),x86942))
% 52.62/52.42 [8695]~P100(x86951)+~P1(f332(f64(x86951),x86952))+E(f332(f332(f3(f853(x86951,a839)),x86952),f332(f332(f302(x86951),x86953),f180(f853(x86951,a839)))),f180(f853(x86951,a839)))+~P1(f332(f332(f334(x86951),x86953),x86952))+E(f332(f332(f236(x86951),x86953),f14(x86951,f236(x86951),f332(f332(f3(f853(x86951,a839)),x86952),f332(f332(f302(x86951),x86953),f180(f853(x86951,a839)))))),f14(x86951,f236(x86951),x86952))
% 52.62/52.42 [8705]~P100(x87051)+~P1(f332(f64(x87051),x87053))+~P1(f332(f64(x87051),x87052))+E(f332(f332(f104(f853(x87051,a839)),x87052),x87053),f180(f853(x87051,a839)))+E(f332(f332(f236(x87051),f17(x87051,f332(f332(f103(f853(x87051,a839)),x87052),x87053))),f17(x87051,f332(f332(f104(f853(x87051,a839)),x87052),x87053))),f332(f332(f236(x87051),f17(x87051,x87052)),f17(x87051,x87053)))
% 52.62/52.42 [8706]~P100(x87061)+~P1(f332(f64(x87061),x87063))+~P1(f332(f64(x87061),x87062))+E(f332(f332(f104(f853(x87061,a839)),x87062),x87063),f180(f853(x87061,a839)))+E(f332(f332(f179(x87061),f16(x87061,f332(f332(f103(f853(x87061,a839)),x87062),x87063))),f16(x87061,f332(f332(f104(f853(x87061,a839)),x87062),x87063))),f332(f332(f179(x87061),f16(x87061,x87062)),f16(x87061,x87063)))
% 52.62/52.42 [8707]~P93(x87071)+~P1(f332(f64(x87071),x87073))+~P1(f332(f64(x87071),x87072))+E(f332(f332(f104(f853(x87071,a839)),x87072),x87073),f180(f853(x87071,a839)))+E(f332(f332(f103(x87071),f15(x87071,f332(f332(f103(f853(x87071,a839)),x87072),x87073))),f15(x87071,f332(f332(f104(f853(x87071,a839)),x87072),x87073))),f332(f332(f103(x87071),f15(x87071,x87072)),f15(x87071,x87073)))
% 52.62/52.42 [8708]~P93(x87081)+~P1(f332(f64(x87081),x87083))+~P1(f332(f64(x87081),x87082))+E(f332(f332(f104(f853(x87081,a839)),x87082),x87083),f180(f853(x87081,a839)))+E(f332(f332(f104(x87081),f12(x87081,f332(f332(f103(f853(x87081,a839)),x87082),x87083))),f12(x87081,f332(f332(f104(f853(x87081,a839)),x87082),x87083))),f332(f332(f104(x87081),f12(x87081,x87082)),f12(x87081,x87083)))
% 52.62/52.42 [8901]~P100(x89011)+~P1(f332(f64(x89011),x89013))+~P1(f332(f64(x89011),x89012))+E(f332(f332(f104(f853(x89011,a839)),x89012),x89013),f180(f853(x89011,a839)))+E(f332(f332(f236(x89011),f14(x89011,f236(x89011),f332(f332(f103(f853(x89011,a839)),x89012),x89013))),f14(x89011,f236(x89011),f332(f332(f104(f853(x89011,a839)),x89012),x89013))),f332(f332(f236(x89011),f14(x89011,f236(x89011),x89012)),f14(x89011,f236(x89011),x89013)))
% 52.62/52.42 [8902]~P100(x89021)+~P1(f332(f64(x89021),x89023))+~P1(f332(f64(x89021),x89022))+E(f332(f332(f104(f853(x89021,a839)),x89022),x89023),f180(f853(x89021,a839)))+E(f332(f332(f179(x89021),f13(x89021,f179(x89021),f332(f332(f103(f853(x89021,a839)),x89022),x89023))),f13(x89021,f179(x89021),f332(f332(f104(f853(x89021,a839)),x89022),x89023))),f332(f332(f179(x89021),f13(x89021,f179(x89021),x89022)),f13(x89021,f179(x89021),x89023)))
% 52.62/52.42 [9636]~P117(x96363)+E(x96361,x96362)+~P1(f332(f332(f232(x96363),f2(x96363)),x96362))+~P1(f332(f332(f232(x96363),f2(x96363)),x96361))+~E(f332(f332(f242(x96363),x96361),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))),f332(f332(f242(x96363),x96362),f332(f106(a845),f332(f332(f82(a1),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)),f332(f332(f3(a1),f332(f332(f82(a1),a85),a85)),a99)))))
% 52.62/52.42 [4976]~P89(x49761)+~P62(x49761)+~E(x49764,f2(x49761))+~E(f332(f106(x49761),x49762),f2(x49761))+E(f332(f106(x49761),x49762),f332(f332(f283(x49761),x49763),x49764))
% 52.62/52.42 [4977]~P89(x49771)+~P62(x49771)+~E(x49773,f2(x49771))+~E(f332(f106(x49771),x49774),f2(x49771))+E(f332(f332(f283(x49771),x49772),x49773),f332(f106(x49771),x49774))
% 52.62/52.42 [5072]~P89(x50722)+~P62(x50722)+~E(x50721,f2(x50722))+~E(f332(f106(x50722),x50724),f2(x50722))+E(x50721,f332(f332(f283(x50722),x50723),f332(f106(x50722),x50724)))
% 52.62/52.42 [5073]~P89(x50731)+~P62(x50731)+~E(x50734,f2(x50731))+~E(f332(f106(x50731),x50733),f2(x50731))+E(f332(f332(f283(x50731),x50732),f332(f106(x50731),x50733)),x50734)
% 52.62/52.42 [5097]~P89(x50971)+~P62(x50971)+~E(x50973,f2(x50971))+E(f332(f106(x50971),x50972),f2(x50971))+~E(f332(f106(x50971),x50972),f332(f332(f283(x50971),x50974),x50973))
% 52.62/52.42 [5098]~P89(x50981)+~P62(x50981)+~E(x50983,f2(x50981))+E(f332(f106(x50981),x50982),f2(x50981))+~E(f332(f332(f283(x50981),x50984),x50983),f332(f106(x50981),x50982))
% 52.62/52.42 [5259]~P89(x52592)+~P62(x52592)+E(x52591,f2(x52592))+~E(f332(f106(x52592),x52593),f2(x52592))+~E(x52591,f332(f332(f283(x52592),x52594),f332(f106(x52592),x52593)))
% 52.62/52.42 [5260]~P89(x52602)+~P62(x52602)+E(x52601,f2(x52602))+~E(f332(f106(x52602),x52603),f2(x52602))+~E(f332(f332(f283(x52602),x52604),f332(f106(x52602),x52603)),x52601)
% 52.62/52.42 [5480]~P89(x54802)+~P62(x54802)+~E(x54801,f2(x54802))+E(x54801,f332(f332(f283(x54802),x54803),f332(f106(x54802),x54804)))+~E(f332(f332(f83(x54802),x54801),f332(f106(x54802),x54804)),x54803)
% 52.62/52.42 [5481]~P89(x54811)+~P62(x54811)+~E(x54814,f2(x54811))+~E(x54812,f332(f332(f83(x54811),x54814),f332(f106(x54811),x54813)))+E(f332(f332(f283(x54811),x54812),f332(f106(x54811),x54813)),x54814)
% 52.62/52.42 [5542]~P89(x55421)+~P62(x55421)+E(f332(f106(x55421),x55422),f2(x55421))+~E(f332(f332(f283(x55421),x55423),f332(f106(x55421),x55422)),x55424)+E(x55423,f332(f332(f83(x55421),x55424),f332(f106(x55421),x55422)))
% 52.62/52.42 [5543]~P89(x55431)+~P62(x55431)+E(f332(f106(x55431),x55432),f2(x55431))+~E(f332(f332(f83(x55431),x55433),f332(f106(x55431),x55432)),x55434)+E(x55433,f332(f332(f283(x55431),x55434),f332(f106(x55431),x55432)))
% 52.62/52.42 [5544]~P89(x55441)+~P62(x55441)+E(f332(f106(x55441),x55442),f2(x55441))+~E(x55443,f332(f332(f283(x55441),x55444),f332(f106(x55441),x55442)))+E(f332(f332(f83(x55441),x55443),f332(f106(x55441),x55442)),x55444)
% 52.62/52.42 [5545]~P89(x55451)+~P62(x55451)+E(f332(f106(x55451),x55452),f2(x55451))+~E(x55453,f332(f332(f83(x55451),x55454),f332(f106(x55451),x55452)))+E(f332(f332(f283(x55451),x55453),f332(f106(x55451),x55452)),x55454)
% 52.62/52.42 [5753]~P9(x57532)+E(x57531,f2(x57532))+~E(f332(f332(f44(x57532),x57533),x57531),x57534)+E(x57533,f332(f332(f83(x57532),x57534),x57531))+~P1(f332(f332(f279(x57532),x57531),x57533))
% 52.62/52.42 [5754]~P9(x57542)+E(x57541,f2(x57542))+~E(x57543,f332(f332(f83(x57542),x57544),x57541))+E(f332(f332(f44(x57542),x57543),x57541),x57544)+~P1(f332(f332(f279(x57542),x57541),x57543))
% 52.62/52.42 [6221]E(f412(x62211,x62212,x62213),x62214)+E(f332(x62211,x62214),f2(a845))+~E(f332(f332(f8(x62213,a845),x62211),x62212),f80(a845))+~P1(f332(f64(x62213),x62212))+~P1(f332(f332(f334(x62213),x62214),x62212))
% 52.62/52.42 [6289]E(f414(x62891,x62892,x62893),x62894)+E(f332(x62891,x62894),f2(a845))+~E(f332(f332(f8(x62893,a845),x62891),x62892),f332(a114,f2(a845)))+~P1(f332(f64(x62893),x62892))+~P1(f332(f332(f334(x62893),x62894),x62892))
% 52.62/52.42 [6403]~P100(x64031)+~P11(x64031)+P1(f332(f332(f233(x64031),x64032),f45(x64031,x64033)))+~P1(f332(f332(f233(x64031),x64032),x64034))+~P1(f332(f332(f334(x64031),x64034),x64033))
% 52.62/52.42 [6581]~P100(x65811)+~P11(x65811)+~P1(f332(f332(f233(x65811),x65814),x65813))+P1(f332(f332(f233(x65811),f46(x65811,x65812)),x65813))+~P1(f332(f332(f334(x65811),x65814),x65812))
% 52.62/52.42 [6857]~P117(x68573)+E(x68571,x68572)+~E(f332(f332(f242(x68573),x68571),f332(a114,x68574)),f332(f332(f242(x68573),x68572),f332(a114,x68574)))+~P1(f332(f332(f232(x68573),f2(x68573)),x68572))+~P1(f332(f332(f232(x68573),f2(x68573)),x68571))
% 52.62/52.42 [7068]~E(f417(x70682,x70683,x70681,x70684),x70684)+~E(f332(x70682,x70684),f80(a845))+E(f332(f332(f8(x70681,a845),x70682),x70683),f80(a845))+~P1(f332(f64(x70681),x70683))+~P1(f332(f332(f334(x70681),x70684),x70683))
% 52.62/52.42 [7075]~P73(x70754)+~P127(x70754)+E(f332(x70751,f450(x70751,x70752,x70753,x70754)),f2(x70754))+~E(f332(f332(f11(x70753,x70754),x70751),x70752),f2(x70754))+~P1(f332(f64(x70753),x70752))
% 52.62/52.42 [7158]~E(f415(x71582,x71583,x71581,x71584),x71584)+~E(f332(x71582,x71584),f332(a114,f2(a845)))+E(f332(f332(f8(x71581,a845),x71582),x71583),f332(a114,f2(a845)))+~P1(f332(f64(x71581),x71583))+~P1(f332(f332(f334(x71581),x71584),x71583))
% 52.62/52.42 [7923]~E(f332(x79232,x79234),f80(a845))+~E(f332(x79232,f417(x79232,x79233,x79231,x79234)),f2(a845))+E(f332(f332(f8(x79231,a845),x79232),x79233),f80(a845))+~P1(f332(f64(x79231),x79233))+~P1(f332(f332(f334(x79231),x79234),x79233))
% 52.62/52.42 [7968]~E(f332(x79682,x79684),f332(a114,f2(a845)))+~E(f332(x79682,f415(x79682,x79683,x79681,x79684)),f2(a845))+E(f332(f332(f8(x79681,a845),x79682),x79683),f332(a114,f2(a845)))+~P1(f332(f64(x79681),x79683))+~P1(f332(f332(f334(x79681),x79684),x79683))
% 52.62/52.42 [8047]~P136(x80472)+~P112(x80472)+~P1(f332(x80471,x80474))+~P1(f332(f332(f279(x80472),x80473),f332(f332(f82(x80472),x80474),f2(x80472))))+P1(f332(x80471,f332(f332(f83(x80472),x80473),f835(x80473,x80471,x80472))))
% 52.62/52.42 [8542]E(x85421,x85422)+E(f332(f332(f82(a1),f424(x85423,x85422,x85424,x85421)),f425(x85423,x85422,x85424,x85421)),x85421)+~E(f332(f332(f3(a1),x85421),x85424),x85422)+~P1(f332(f332(f233(a1),f2(a1)),x85424))+~P1(f332(f332(f334(a1),x85422),x85423))
% 52.62/52.42 [8543]E(x85431,x85432)+E(f332(f332(f3(a1),f426(x85433,x85432,x85434,x85431)),f427(x85433,x85432,x85434,x85431)),x85431)+~E(f332(f332(f82(a1),x85431),x85434),x85432)+~P1(f332(f332(f233(a1),f2(a1)),x85434))+~P1(f332(f332(f334(a1),x85432),x85433))
% 52.62/52.42 [8704]E(f332(x87041,f813(x87042,x87041,x87043,x87044)),x87042)+P1(f332(f332(f232(a845),x87044),f814(x87042,x87041,x87043,x87044)))+~P1(f332(f332(f232(a1),x87042),f332(x87041,x87043)))+~P1(f332(f332(f233(a845),x87044),x87043))+~P1(f332(f332(f232(a1),f332(x87041,x87044)),x87042))
% 52.62/52.42 [8721]~P73(x87214)+~P127(x87214)+~E(f332(f332(f11(x87211,x87214),x87212),x87213),f2(x87214))+~P1(f332(f64(x87211),x87213))+P1(f332(f332(f334(x87211),f450(x87212,x87213,x87211,x87214)),x87213))
% 52.62/52.42 [8754]~E(f332(x87542,x87544),f80(a845))+E(f332(f332(f8(x87541,a845),x87542),x87543),f80(a845))+~P1(f332(f64(x87541),x87543))+~P1(f332(f332(f334(x87541),x87544),x87543))+P1(f332(f332(f334(x87541),f417(x87542,x87543,x87541,x87544)),x87543))
% 52.62/52.42 [8763]E(x87631,x87632)+~E(f332(f332(f82(a1),x87632),x87634),x87631)+~P1(f332(f332(f233(a1),f2(a1)),x87634))+~P1(f332(f332(f334(a1),x87631),x87633))+P1(f332(f332(f334(a1),f426(x87633,x87631,x87634,x87632)),x87633))
% 52.62/52.42 [8764]E(x87641,x87642)+~E(f332(f332(f3(a1),x87642),x87644),x87641)+~P1(f332(f332(f233(a1),f2(a1)),x87644))+~P1(f332(f332(f334(a1),x87641),x87643))+P1(f332(f332(f334(a1),f424(x87643,x87641,x87644,x87642)),x87643))
% 52.62/52.42 [8766]~E(f332(x87662,x87664),f332(a114,f2(a845)))+E(f332(f332(f8(x87661,a845),x87662),x87663),f332(a114,f2(a845)))+~P1(f332(f64(x87661),x87663))+~P1(f332(f332(f334(x87661),x87664),x87663))+P1(f332(f332(f334(x87661),f415(x87662,x87663,x87661,x87664)),x87663))
% 52.62/52.42 [8770]P59(x87702,x87703,x87704,x87701)+E(x87701,f180(f853(x87702,a839)))+~P1(f332(f64(x87702),x87704))+~P1(f332(f64(x87702),x87701))+P1(f332(f332(f334(x87702),f537(x87701,x87704,x87703,x87702)),x87704))
% 52.62/52.42 [8833]E(x88331,x88332)+~E(f332(f332(f82(a1),x88332),x88334),x88331)+~P1(f332(f332(f233(a1),f2(a1)),x88334))+~P1(f332(f332(f334(a1),x88331),x88333))+P1(f332(f332(f334(a1),f427(x88333,x88331,x88334,x88332)),f295(a1,f80(a1),x88334)))
% 52.62/52.42 [8834]E(x88341,x88342)+~E(f332(f332(f3(a1),x88342),x88344),x88341)+~P1(f332(f332(f233(a1),f2(a1)),x88344))+~P1(f332(f332(f334(a1),x88341),x88343))+P1(f332(f332(f334(a1),f425(x88343,x88341,x88344,x88342)),f295(a1,f80(a1),x88344)))
% 52.62/52.42 [8907]P1(f332(f332(f232(a845),x89071),f813(x89072,x89073,x89074,x89071)))+~P1(f332(f332(f232(a1),x89072),f332(x89073,x89074)))+P1(f332(f332(f232(a845),x89071),f814(x89072,x89073,x89074,x89071)))+~P1(f332(f332(f233(a845),x89071),x89074))+~P1(f332(f332(f232(a1),f332(x89073,x89071)),x89072))
% 52.62/52.42 [9014]E(f332(x90141,f813(x90142,x90141,x90143,x90144)),x90142)+~P1(f332(f332(f232(a1),x90142),f332(x90141,x90143)))+P1(f332(f332(f233(a845),f814(x90142,x90141,x90143,x90144)),x90143))+~P1(f332(f332(f233(a845),x90144),x90143))+~P1(f332(f332(f232(a1),f332(x90141,x90144)),x90142))
% 52.62/52.42 [9119]~P1(f332(f332(f279(a845),x91194),x91191))+~P1(f332(f332(f279(a845),x91194),x91193))+~P1(f332(f332(f279(a845),x91192),x91191))+P1(f332(f332(f279(a845),x91191),x91192))+P1(f332(f332(f233(f853(a845,a839)),f282(a845,f279(a845),x91193,x91192)),f282(a845,f279(a845),x91194,x91191)))
% 52.62/52.42 [9120]~P1(f332(f332(f279(a845),x91202),x91201))+~P1(f332(f332(f279(a845),x91203),x91204))+~P1(f332(f332(f279(a845),x91202),x91204))+P1(f332(f332(f279(a845),x91201),x91202))+P1(f332(f332(f233(f853(a845,a839)),f282(a845,f279(a845),x91201,x91203)),f282(a845,f279(a845),x91202,x91204)))
% 52.62/52.42 [9131]~P1(f332(f332(f232(a1),x91312),f332(x91313,x91314)))+P1(f332(f332(f232(a845),x91311),f814(x91312,x91313,x91314,x91311)))+P1(f332(f332(f232(a845),f813(x91312,x91313,x91314,x91311)),x91314))+~P1(f332(f332(f233(a845),x91311),x91314))+~P1(f332(f332(f232(a1),f332(x91313,x91311)),x91312))
% 52.62/52.42 [9132]~P1(f332(f332(f232(a1),x91322),f332(x91323,x91324)))+P1(f332(f332(f232(a845),x91321),f813(x91322,x91323,x91324,x91321)))+P1(f332(f332(f233(a845),f814(x91322,x91323,x91324,x91321)),x91324))+~P1(f332(f332(f233(a845),x91321),x91324))+~P1(f332(f332(f232(a1),f332(x91323,x91321)),x91322))
% 52.62/52.42 [9219]~P1(f332(f332(f232(a1),x92191),f332(x92192,x92193)))+P1(f332(f332(f232(a845),f813(x92191,x92192,x92193,x92194)),x92193))+~P1(f332(f332(f233(a845),x92194),x92193))+~P1(f332(f332(f232(a1),f332(x92192,x92194)),x92191))+P1(f332(f332(f233(a845),f814(x92191,x92192,x92193,x92194)),x92193))
% 52.62/52.42 [9303]E(x93031,f180(f853(x93032,a839)))+~P1(f332(f64(x93032),x93034))+~P1(f332(f64(x93032),x93031))+P1(f332(f332(f334(f852(f853(x93032,a839),f853(x93032,a839))),f332(f332(f241(f853(x93032,a839),f853(x93032,a839)),x93034),x93031)),f325(x93032,x93033)))+P1(f332(f332(f334(x93032),f539(x93033,x93031,x93034,x93032)),x93034))
% 52.62/52.42 [9304]E(x93041,f180(f853(x93042,a839)))+~P1(f332(f64(x93042),x93044))+~P1(f332(f64(x93042),x93041))+P1(f332(f332(f334(f852(f853(x93042,a839),f853(x93042,a839))),f332(f332(f241(f853(x93042,a839),f853(x93042,a839)),x93044),x93041)),f325(x93042,x93043)))+P1(f332(f332(f334(x93042),f624(x93043,x93041,x93044,x93042)),x93044))
% 52.62/52.42 [9948]E(f332(x99481,f813(x99482,x99481,x99483,x99484)),x99482)+~P1(f332(f332(f232(a1),x99482),f332(x99481,x99483)))+~P1(f332(f332(f232(a1),f332(f77(a1),f332(f332(f3(a1),f332(x99481,f332(f332(f82(a845),f814(x99482,x99481,x99483,x99484)),f80(a845)))),f332(x99481,f814(x99482,x99481,x99483,x99484))))),f80(a1)))+~P1(f332(f332(f233(a845),x99484),x99483))+~P1(f332(f332(f232(a1),f332(x99481,x99484)),x99482))
% 52.62/52.42 [9949]~P1(f332(f332(f232(a1),x99492),f332(x99493,x99494)))+P1(f332(f332(f232(a845),x99491),f813(x99492,x99493,x99494,x99491)))+~P1(f332(f332(f232(a1),f332(f77(a1),f332(f332(f3(a1),f332(x99493,f332(f332(f82(a845),f814(x99492,x99493,x99494,x99491)),f80(a845)))),f332(x99493,f814(x99492,x99493,x99494,x99491))))),f80(a1)))+~P1(f332(f332(f233(a845),x99491),x99494))+~P1(f332(f332(f232(a1),f332(x99493,x99491)),x99492))
% 52.62/52.42 [9950]~P1(f332(f332(f232(a1),x99501),f332(x99502,x99503)))+~P1(f332(f332(f232(a1),f332(f77(a1),f332(f332(f3(a1),f332(x99502,f332(f332(f82(a845),f814(x99501,x99502,x99503,x99504)),f80(a845)))),f332(x99502,f814(x99501,x99502,x99503,x99504))))),f80(a1)))+~P1(f332(f332(f233(a845),x99504),x99503))+~P1(f332(f332(f232(a1),f332(x99502,x99504)),x99501))+P1(f332(f332(f232(a845),f813(x99501,x99502,x99503,x99504)),x99503))
% 52.62/52.42 [5502]~P89(x55022)+~P62(x55022)+E(x55021,f2(x55022))+~E(f332(f332(f283(x55022),x55023),x55021),f332(f106(x55022),x55024))+E(x55023,f332(f332(f83(x55022),f332(f106(x55022),x55024)),x55021))
% 52.62/52.42 [5503]~P89(x55032)+~P62(x55032)+E(x55031,f2(x55032))+~E(f332(f106(x55032),x55033),f332(f332(f283(x55032),x55034),x55031))+E(f332(f332(f83(x55032),f332(f106(x55032),x55033)),x55031),x55034)
% 52.62/52.42 [5653]~P89(x56532)+~P62(x56532)+E(x56531,f2(x56532))+E(f332(f106(x56532),x56533),f332(f332(f283(x56532),x56534),x56531))+~E(f332(f332(f83(x56532),f332(f106(x56532),x56533)),x56531),x56534)
% 52.62/52.42 [5654]~P89(x56542)+~P62(x56542)+E(x56541,f2(x56542))+E(f332(f332(f283(x56542),x56543),x56541),f332(f106(x56542),x56544))+~E(x56543,f332(f332(f83(x56542),f332(f106(x56542),x56544)),x56541))
% 52.62/52.42 [5791]~P89(x57911)+~P62(x57911)+~E(f332(f106(x57911),x57912),f2(x57911))+E(f332(f106(x57911),x57912),f332(f332(f283(x57911),x57913),x57914))+~E(f332(f332(f83(x57911),f332(f106(x57911),x57912)),x57914),x57913)
% 52.62/52.42 [5792]~P89(x57921)+~P62(x57921)+~E(f332(f106(x57921),x57924),f2(x57921))+E(f332(f332(f283(x57921),x57922),x57923),f332(f106(x57921),x57924))+~E(x57922,f332(f332(f83(x57921),f332(f106(x57921),x57924)),x57923))
% 52.62/52.42 [7126]~P64(x71261)+P1(f332(f332(f233(x71261),x71262),f2(x71261)))+~P1(f332(f332(f233(x71261),x71263),f2(x71261)))+P1(f332(f332(f233(x71261),f2(x71261)),x71262))+P1(f332(f332(f233(x71261),x71263),f332(f332(f283(x71261),x71264),x71262)))
% 52.62/52.42 [7127]~P64(x71271)+P1(f332(f332(f233(x71271),x71272),f2(x71271)))+~P1(f332(f332(f232(x71271),x71273),f2(x71271)))+P1(f332(f332(f233(x71271),f2(x71271)),x71272))+P1(f332(f332(f232(x71271),x71273),f332(f332(f283(x71271),x71274),x71272)))
% 52.62/52.42 [7398]~P64(x73981)+P1(f332(f332(f233(x73981),x73982),f2(x73981)))+P1(f332(f332(f233(x73981),x73983),f2(x73981)))+P1(f332(f332(f233(x73981),f2(x73981)),x73983))+~P1(f332(f332(f233(x73981),x73982),f332(f332(f283(x73981),x73984),x73983)))
% 52.62/52.42 [7399]~P64(x73991)+P1(f332(f332(f233(x73991),x73992),f2(x73991)))+P1(f332(f332(f232(x73991),x73993),f2(x73991)))+P1(f332(f332(f233(x73991),f2(x73991)),x73992))+~P1(f332(f332(f232(x73991),x73993),f332(f332(f283(x73991),x73994),x73992)))
% 52.62/52.42 [7517]E(x75171,x75172)+~E(f332(f332(f152(x75173),x75174),x75171),f332(f332(f152(x75173),x75174),x75172))+~P1(f332(f127(x75173),x75174))+~P1(f332(f332(f233(a845),x75172),f332(f181(f846(x75173)),x75174)))+~P1(f332(f332(f233(a845),x75171),f332(f181(f846(x75173)),x75174)))
% 52.62/52.42 [7518]E(x75181,x75182)+~E(f332(f332(f152(x75183),x75184),x75181),f332(f332(f152(x75183),x75184),x75182))+~P1(f332(f127(x75183),x75184))+~P1(f332(f332(f233(a845),x75182),f332(f181(f846(x75183)),x75184)))+~P1(f332(f332(f233(a845),x75181),f332(f181(f846(x75183)),x75184)))
% 52.62/52.42 [7885]~P64(x78851)+~P1(f332(f332(f233(x78851),x78853),f2(x78851)))+P1(f332(f332(f233(x78851),f2(x78851)),x78852))+~P1(f332(f332(f233(x78851),x78854),f332(f332(f83(x78851),x78853),x78852)))+P1(f332(f332(f233(x78851),x78853),f332(f332(f283(x78851),x78854),x78852)))
% 52.62/52.42 [7886]~P64(x78861)+~P1(f332(f332(f232(x78861),x78863),f2(x78861)))+P1(f332(f332(f233(x78861),f2(x78861)),x78862))+~P1(f332(f332(f232(x78861),x78864),f332(f332(f83(x78861),x78863),x78862)))+P1(f332(f332(f232(x78861),x78863),f332(f332(f283(x78861),x78864),x78862)))
% 52.62/52.42 [7887]~P64(x78871)+~P1(f332(f332(f233(x78871),x78872),f2(x78871)))+P1(f332(f332(f233(x78871),f2(x78871)),x78872))+~P1(f332(f332(f233(x78871),x78874),f332(f332(f83(x78871),x78873),x78872)))+P1(f332(f332(f233(x78871),x78873),f332(f332(f283(x78871),x78874),x78872)))
% 52.62/52.42 [7888]~P64(x78881)+~P1(f332(f332(f233(x78881),x78882),f2(x78881)))+P1(f332(f332(f233(x78881),f2(x78881)),x78882))+~P1(f332(f332(f233(x78881),x78884),f332(f332(f283(x78881),x78883),x78882)))+P1(f332(f332(f233(x78881),x78883),f332(f332(f83(x78881),x78884),x78882)))
% 52.62/52.42 [7889]~P64(x78891)+~P1(f332(f332(f233(x78891),x78892),f2(x78891)))+P1(f332(f332(f233(x78891),f2(x78891)),x78892))+~P1(f332(f332(f232(x78891),x78894),f332(f332(f83(x78891),x78893),x78892)))+P1(f332(f332(f232(x78891),x78893),f332(f332(f283(x78891),x78894),x78892)))
% 52.62/52.42 [7890]~P64(x78901)+~P1(f332(f332(f233(x78901),x78902),f2(x78901)))+P1(f332(f332(f233(x78901),f2(x78901)),x78902))+~P1(f332(f332(f232(x78901),x78904),f332(f332(f283(x78901),x78903),x78902)))+P1(f332(f332(f232(x78901),x78903),f332(f332(f83(x78901),x78904),x78902)))
% 52.62/52.42 [8015]~P9(x80151)+~P1(f332(f332(f279(x80151),x80153),x80154))+~P1(f332(f332(f279(x80151),x80153),x80152))+~P1(f332(f332(f279(x80151),x80152),x80154))+P1(f332(f332(f279(x80151),f332(f332(f44(x80151),x80152),x80153)),f332(f332(f44(x80151),x80154),x80153)))
% 52.62/52.42 [8029]~P100(x80291)+~P20(x80291,x80292)+~P1(f332(f332(f232(a845),x80293),x80294))+P1(f332(f332(f232(x80291),f332(f332(f152(x80291),x80292),x80293)),f332(f332(f152(x80291),x80292),x80294)))+~P1(f332(f332(f233(a845),x80294),f332(f181(f846(x80291)),x80292)))
% 52.62/52.42 [8030]~P100(x80301)+~P20(x80301,x80302)+~P1(f332(f332(f232(a845),x80303),x80304))+P1(f332(f332(f232(x80301),f332(f332(f152(x80301),x80302),x80303)),f332(f332(f152(x80301),x80302),x80304)))+~P1(f332(f332(f233(a845),x80304),f332(f181(f846(x80301)),x80302)))
% 52.62/52.42 [8080]~P117(x80801)+~P1(f332(f332(f233(x80801),x80802),f80(x80801)))+~P1(f332(f332(f233(x80801),f2(x80801)),x80802))+~P1(f332(f332(f233(a845),x80804),x80803))+P1(f332(f332(f233(x80801),f332(f332(f242(x80801),x80802),x80803)),f332(f332(f242(x80801),x80802),x80804)))
% 52.62/52.42 [8081]~P117(x80811)+~P1(f332(f332(f232(x80811),x80812),f80(x80811)))+~P1(f332(f332(f232(x80811),f2(x80811)),x80812))+~P1(f332(f332(f232(a845),x80814),x80813))+P1(f332(f332(f232(x80811),f332(f332(f242(x80811),x80812),x80813)),f332(f332(f242(x80811),x80812),x80814)))
% 52.62/52.42 [8082]~P117(x80821)+~P1(f332(f332(f232(x80821),f2(x80821)),x80822))+~P1(f332(f332(f233(a845),f2(a845)),x80823))+~P1(f332(f332(f233(x80821),x80822),x80824))+P1(f332(f332(f233(x80821),f332(f332(f242(x80821),x80822),x80823)),f332(f332(f242(x80821),x80824),x80823)))
% 52.62/52.42 [8100]~P100(x81001)+~P20(x81001,f332(f142(x81001),x81002))+~P1(f332(f332(f232(a845),x81004),x81003))+P1(f332(f332(f232(x81001),f332(f332(f152(x81001),x81002),x81003)),f332(f332(f152(x81001),x81002),x81004)))+~P1(f332(f332(f233(a845),x81003),f332(f181(f846(x81001)),x81002)))
% 52.62/52.42 [8328]~P9(x83281)+P1(f332(f332(f279(x83281),x83282),x83283))+~P1(f332(f332(f279(x83281),x83284),x83283))+~P1(f332(f332(f279(x83281),x83284),x83282))+~P1(f332(f332(f279(x83281),f332(f332(f44(x83281),x83282),x83284)),f332(f332(f44(x83281),x83283),x83284)))
% 52.62/52.42 [8345]~P65(x83451)+~P1(f332(f332(f233(x83451),x83452),f2(x83451)))+~P1(f332(f332(f233(x83451),x83453),x83454))+~P1(f332(f332(f233(x83451),f2(x83451)),f332(f332(f83(x83451),x83453),x83454)))+P1(f332(f332(f233(x83451),f332(f332(f283(x83451),x83452),x83453)),f332(f332(f283(x83451),x83452),x83454)))
% 52.62/52.42 [8346]~P64(x83461)+~P1(f332(f332(f232(x83461),x83462),f2(x83461)))+~P1(f332(f332(f232(x83461),x83463),x83464))+~P1(f332(f332(f233(x83461),f2(x83461)),f332(f332(f83(x83461),x83463),x83464)))+P1(f332(f332(f232(x83461),f332(f332(f283(x83461),x83462),x83463)),f332(f332(f283(x83461),x83462),x83464)))
% 52.62/52.42 [8356]~P65(x83561)+~P1(f332(f332(f233(x83561),x83564),x83563))+~P1(f332(f332(f233(x83561),f2(x83561)),x83562))+~P1(f332(f332(f233(x83561),f2(x83561)),f332(f332(f83(x83561),x83563),x83564)))+P1(f332(f332(f233(x83561),f332(f332(f283(x83561),x83562),x83563)),f332(f332(f283(x83561),x83562),x83564)))
% 52.62/52.42 [8357]~P65(x83571)+~P1(f332(f332(f232(x83571),x83574),x83573))+~P1(f332(f332(f232(x83571),f2(x83571)),x83572))+~P1(f332(f332(f233(x83571),f2(x83571)),f332(f332(f83(x83571),x83573),x83574)))+P1(f332(f332(f232(x83571),f332(f332(f283(x83571),x83572),x83573)),f332(f332(f283(x83571),x83572),x83574)))
% 52.62/52.42 [8465]P1(f332(x84651,x84652))+~P1(f332(f64(x84654),x84652))+P1(f332(x84651,f484(x84651,x84653,x84652,x84654)))+~P1(f332(x84651,f180(f853(x84654,a839))))+~P1(f332(f332(f232(f853(x84654,a839)),x84652),x84653))
% 52.62/52.42 [8473]P1(f332(x84731,x84732))+P1(f332(f64(x84733),f484(x84731,x84734,x84732,x84733)))+~P1(f332(f64(x84733),x84732))+~P1(f332(x84731,f180(f853(x84733,a839))))+~P1(f332(f332(f232(f853(x84733,a839)),x84732),x84734))
% 52.62/52.42 [8701]E(f332(f332(f82(a1),f434(x87011,x87012,x87013,x87014)),f435(x87011,x87012,x87013,x87014)),x87014)+~P1(f332(f332(f233(a1),f2(a1)),x87013))+~P1(f332(f332(f233(a1),x87012),x87014))+~P1(f332(f332(f334(a1),x87012),x87011))+P1(f332(f332(f233(a1),x87012),f332(f332(f3(a1),x87014),x87013)))
% 52.62/52.42 [8887]~P1(f332(f332(f233(a1),f2(a1)),x88873))+~P1(f332(f332(f233(a1),x88872),x88874))+~P1(f332(f332(f334(a1),x88872),x88871))+P1(f332(f332(f334(a1),f434(x88871,x88872,x88873,x88874)),x88871))+P1(f332(f332(f233(a1),x88872),f332(f332(f3(a1),x88874),x88873)))
% 52.62/52.42 [8900]P1(f332(x89001,x89002))+~P1(f332(f64(x89003),x89002))+P1(f332(f332(f334(x89003),f485(x89001,x89004,x89002,x89003)),x89004))+~P1(f332(x89001,f180(f853(x89003,a839))))+~P1(f332(f332(f232(f853(x89003,a839)),x89002),x89004))
% 52.62/52.42 [8917]E(f332(f332(f82(a1),f429(x89171,x89172,x89173,x89174)),f430(x89171,x89172,x89173,x89174)),x89174)+~P1(f332(f332(f233(a1),f2(a1)),x89173))+~P1(f332(f332(f232(a1),x89172),x89174))+P1(f332(f332(f232(a1),x89172),f332(f332(f3(a1),x89174),x89173)))+~P1(f332(f332(f334(a1),f332(f332(f3(a1),x89172),f80(a1))),x89171))
% 52.62/52.42 [8964]~P1(f332(f332(f233(a1),f2(a1)),x89643))+~P1(f332(f332(f233(a1),x89641),x89642))+~P1(f332(f332(f334(a1),x89641),x89644))+P1(f332(f332(f334(a1),f435(x89644,x89641,x89643,x89642)),f295(a1,f80(a1),x89643)))+P1(f332(f332(f233(a1),x89641),f332(f332(f3(a1),x89642),x89643)))
% 52.62/52.42 [9057]~P1(f332(f332(f233(a1),f2(a1)),x90573))+~P1(f332(f332(f232(a1),x90572),x90574))+P1(f332(f332(f334(a1),f429(x90571,x90572,x90573,x90574)),x90571))+P1(f332(f332(f232(a1),x90572),f332(f332(f3(a1),x90574),x90573)))+~P1(f332(f332(f334(a1),f332(f332(f3(a1),x90572),f80(a1))),x90571))
% 52.62/52.42 [9095]~P1(f332(f332(f233(a1),f2(a1)),x90953))+~P1(f332(f332(f232(a1),x90951),x90952))+P1(f332(f332(f334(a1),f430(x90954,x90951,x90953,x90952)),f295(a1,f80(a1),x90953)))+P1(f332(f332(f232(a1),x90951),f332(f332(f3(a1),x90952),x90953)))+~P1(f332(f332(f334(a1),f332(f332(f3(a1),x90951),f80(a1))),x90954))
% 52.62/52.42 [9306]P1(f332(x93061,x93062))+~P1(f332(f332(f334(x93063),f485(x93061,x93064,x93062,x93063)),f484(x93061,x93064,x93062,x93063)))+~P1(f332(f64(x93063),x93062))+~P1(f332(x93061,f180(f853(x93063,a839))))+~P1(f332(f332(f232(f853(x93063,a839)),x93062),x93064))
% 52.62/52.42 [9510]P1(f332(x95101,x95102))+~P1(f332(f64(x95103),x95102))+~P1(f332(x95101,f332(f332(f302(x95103),f485(x95101,x95104,x95102,x95103)),f484(x95101,x95104,x95102,x95103))))+~P1(f332(x95101,f180(f853(x95103,a839))))+~P1(f332(f332(f232(f853(x95103,a839)),x95102),x95104))
% 52.62/52.42 [9830]~P99(x98303)+~P54(a845,x98303,f332(f332(f20(a845,f853(a845,a839),f853(a845,a839)),f332(f332(f10(f853(a845,f853(a839,a839)),f853(f853(a845,a839),f853(a845,a839)),a845),f20(a845,a839,a839)),f332(f332(f10(f853(a845,a839),f853(a845,f853(a839,a839)),a845),f332(f10(a839,f853(a839,a839),a845),a330)),f279(a845)))),f332(f332(f10(f853(a845,a839),f853(a845,a839),a845),f332(f10(a839,a839,a845),a328)),f332(f9(a845,a845,a839),f279(a845)))),x98304)+P1(f332(f332(f233(x98303),f332(x98304,x98302)),f332(x98304,x98301)))+~P1(f332(f332(f279(a845),x98302),x98301))+P1(f332(f332(f279(a845),x98301),x98302))
% 52.62/52.42 [7657]~P64(x76571)+P1(f332(f332(f233(x76571),x76572),f2(x76571)))+P1(f332(f332(f233(x76571),f2(x76571)),x76572))+~P1(f332(f332(f233(x76571),f2(x76571)),x76574))+P1(f332(f332(f233(x76571),f332(f332(f283(x76571),x76573),x76572)),x76574))
% 52.62/52.42 [7658]~P64(x76581)+P1(f332(f332(f233(x76581),x76582),f2(x76581)))+~P1(f332(f332(f232(x76581),f2(x76581)),x76584))+P1(f332(f332(f233(x76581),f2(x76581)),x76582))+P1(f332(f332(f232(x76581),f332(f332(f283(x76581),x76583),x76582)),x76584))
% 52.62/52.42 [7941]~P1(f332(f332(f232(a1),x79414),f2(a1)))+~E(x79412,f332(f332(f82(a1),f332(f332(f83(a1),x79411),x79413)),x79414))+P1(f332(f332(f233(a1),f2(a1)),x79411))+~P1(f332(f332(f233(a1),x79411),x79414))+P1(f332(f57(x79412,x79411),f332(f332(f241(a1,a1),x79413),x79414)))
% 52.62/52.42 [7978]~P1(f332(x79781,x79784))+P1(f332(x79781,f802(x79782,x79781,x79783)))+~P1(f332(f332(f233(a1),f2(a1)),x79783))+~P1(f332(f332(f232(a1),f2(a1)),x79782))+P1(f332(x79781,f332(f332(f82(a1),x79784),f332(f332(f83(a1),x79782),x79783))))
% 52.62/52.42 [7979]~P1(f332(x79791,x79794))+P1(f332(x79791,f806(x79792,x79791,x79793)))+~P1(f332(f332(f233(a1),f2(a1)),x79793))+~P1(f332(f332(f232(a1),f2(a1)),x79792))+P1(f332(x79791,f332(f332(f3(a1),x79794),f332(f332(f83(a1),x79792),x79793))))
% 52.62/52.42 [7980]~P64(x79801)+P1(f332(f332(f233(x79801),x79802),f2(x79801)))+P1(f332(f332(f233(x79801),f2(x79801)),x79802))+P1(f332(f332(f233(x79801),f2(x79801)),x79803))+~P1(f332(f332(f233(x79801),f332(f332(f283(x79801),x79804),x79802)),x79803))
% 52.62/52.42 [7981]~P64(x79811)+P1(f332(f332(f233(x79811),x79812),f2(x79811)))+P1(f332(f332(f233(x79811),f2(x79811)),x79812))+P1(f332(f332(f232(x79811),f2(x79811)),x79813))+~P1(f332(f332(f232(x79811),f332(f332(f283(x79811),x79814),x79812)),x79813))
% 52.62/52.42 [8025]~E(x80251,f332(f332(f82(a1),f332(f332(f83(a1),x80252),x80253)),x80254))+~P1(f332(f332(f233(a1),f2(a1)),x80252))+~P1(f332(f332(f232(a1),f2(a1)),x80254))+~P1(f332(f332(f233(a1),x80254),x80252))+P1(f332(f57(x80251,x80252),f332(f332(f241(a1,a1),x80253),x80254)))
% 52.62/52.42 [8142]~P64(x81421)+P1(f332(f332(f233(x81421),x81422),f2(x81421)))+~P1(f332(f332(f233(x81421),f2(x81421)),x81424))+~P1(f332(f332(f233(x81421),x81423),f332(f332(f83(x81421),x81424),x81422)))+P1(f332(f332(f233(x81421),f332(f332(f283(x81421),x81423),x81422)),x81424))
% 52.62/52.42 [8143]~P64(x81431)+P1(f332(f332(f233(x81431),x81432),f2(x81431)))+~P1(f332(f332(f232(x81431),f2(x81431)),x81434))+~P1(f332(f332(f232(x81431),x81433),f332(f332(f83(x81431),x81434),x81432)))+P1(f332(f332(f232(x81431),f332(f332(f283(x81431),x81433),x81432)),x81434))
% 52.62/52.42 [8221]~P64(x82211)+P1(f332(f332(f233(x82211),x82212),f2(x82211)))+~P1(f332(f332(f233(x82211),x82213),f2(x82211)))+P1(f332(f332(f233(x82211),x82213),f332(f332(f283(x82211),x82214),x82212)))+~P1(f332(f332(f233(x82211),f332(f332(f83(x82211),x82213),x82212)),x82214))
% 52.62/52.42 [8222]~P64(x82221)+P1(f332(f332(f233(x82221),x82222),f2(x82221)))+~P1(f332(f332(f232(x82221),x82223),f2(x82221)))+P1(f332(f332(f232(x82221),x82223),f332(f332(f283(x82221),x82224),x82222)))+~P1(f332(f332(f232(x82221),f332(f332(f83(x82221),x82223),x82222)),x82224))
% 52.62/52.42 [8381]~P64(x83811)+~P1(f332(f332(f233(x83811),x83812),f2(x83811)))+P1(f332(f332(f233(x83811),f2(x83811)),x83812))+~P1(f332(f332(f233(x83811),f332(f332(f283(x83811),x83814),x83812)),x83813))+P1(f332(f332(f233(x83811),f332(f332(f83(x83811),x83813),x83812)),x83814))
% 52.62/52.42 [8382]~P64(x83821)+~P1(f332(f332(f233(x83821),x83822),f2(x83821)))+P1(f332(f332(f233(x83821),f2(x83821)),x83822))+~P1(f332(f332(f233(x83821),f332(f332(f83(x83821),x83824),x83822)),x83823))+P1(f332(f332(f233(x83821),f332(f332(f283(x83821),x83823),x83822)),x83824))
% 52.62/52.42 [8383]~P64(x83831)+~P1(f332(f332(f233(x83831),x83832),f2(x83831)))+P1(f332(f332(f233(x83831),f2(x83831)),x83832))+~P1(f332(f332(f232(x83831),f332(f332(f283(x83831),x83834),x83832)),x83833))+P1(f332(f332(f232(x83831),f332(f332(f83(x83831),x83833),x83832)),x83834))
% 52.62/52.42 [8384]~P64(x83841)+~P1(f332(f332(f233(x83841),x83842),f2(x83841)))+P1(f332(f332(f233(x83841),f2(x83841)),x83842))+~P1(f332(f332(f232(x83841),f332(f332(f83(x83841),x83844),x83842)),x83843))+P1(f332(f332(f232(x83841),f332(f332(f283(x83841),x83843),x83842)),x83844))
% 52.62/52.42 [8403]~P64(x84031)+~P1(f332(f332(f233(x84031),f2(x84031)),x84034))+P1(f332(f332(f233(x84031),f2(x84031)),x84032))+~P1(f332(f332(f233(x84031),f332(f332(f83(x84031),x84034),x84032)),x84033))+P1(f332(f332(f233(x84031),f332(f332(f283(x84031),x84033),x84032)),x84034))
% 52.62/52.42 [8404]~P64(x84041)+~P1(f332(f332(f232(x84041),f2(x84041)),x84044))+P1(f332(f332(f233(x84041),f2(x84041)),x84042))+~P1(f332(f332(f232(x84041),f332(f332(f83(x84041),x84044),x84042)),x84043))+P1(f332(f332(f232(x84041),f332(f332(f283(x84041),x84043),x84042)),x84044))
% 52.62/52.42 [8456]~P64(x84561)+~P89(x84561)+~P1(f332(f332(f233(x84561),f2(x84561)),x84564))+~P1(f332(f332(f233(x84561),f332(f332(f283(x84561),x84562),x84564)),f332(f106(x84561),x84563)))+P1(f332(f332(f233(x84561),x84562),f332(f332(f83(x84561),f332(f106(x84561),x84563)),x84564)))
% 52.62/52.42 [8457]~P64(x84571)+~P89(x84571)+~P1(f332(f332(f233(x84571),f2(x84571)),x84574))+~P1(f332(f332(f232(x84571),f332(f332(f283(x84571),x84572),x84574)),f332(f106(x84571),x84573)))+P1(f332(f332(f232(x84571),x84572),f332(f332(f83(x84571),f332(f106(x84571),x84573)),x84574)))
% 52.62/52.42 [8466]~P64(x84661)+~P89(x84661)+~P1(f332(f332(f233(x84661),f2(x84661)),x84663))+P1(f332(f332(f233(x84661),f332(f332(f283(x84661),x84662),x84663)),f332(f106(x84661),x84664)))+~P1(f332(f332(f233(x84661),x84662),f332(f332(f83(x84661),f332(f106(x84661),x84664)),x84663)))
% 52.62/52.42 [8467]~P64(x84671)+~P89(x84671)+~P1(f332(f332(f233(x84671),f2(x84671)),x84673))+P1(f332(f332(f232(x84671),f332(f332(f283(x84671),x84672),x84673)),f332(f106(x84671),x84674)))+~P1(f332(f332(f232(x84671),x84672),f332(f332(f83(x84671),f332(f106(x84671),x84674)),x84673)))
% 52.62/52.42 [8481]~P64(x84811)+~P1(f332(f332(f233(x84811),x84814),f2(x84811)))+~P1(f332(f332(f233(x84811),x84813),f332(f332(f83(x84811),x84812),x84814)))+P1(f332(f332(f233(x84811),x84812),f332(f332(f283(x84811),x84813),x84814)))+~P1(f332(f332(f233(x84811),f332(f332(f83(x84811),x84812),x84814)),x84813))
% 52.62/52.42 [8482]~P64(x84821)+~P1(f332(f332(f233(x84821),x84822),f2(x84821)))+~P1(f332(f332(f233(x84821),x84823),f332(f332(f83(x84821),x84822),x84824)))+P1(f332(f332(f233(x84821),x84822),f332(f332(f283(x84821),x84823),x84824)))+~P1(f332(f332(f233(x84821),f332(f332(f83(x84821),x84822),x84824)),x84823))
% 52.62/52.42 [8483]~P64(x84831)+~P1(f332(f332(f233(x84831),x84834),f2(x84831)))+~P1(f332(f332(f232(x84831),x84833),f332(f332(f83(x84831),x84832),x84834)))+P1(f332(f332(f232(x84831),x84832),f332(f332(f283(x84831),x84833),x84834)))+~P1(f332(f332(f232(x84831),f332(f332(f83(x84831),x84832),x84834)),x84833))
% 52.62/52.42 [8484]~P64(x84841)+~P1(f332(f332(f232(x84841),x84842),f2(x84841)))+~P1(f332(f332(f232(x84841),x84843),f332(f332(f83(x84841),x84842),x84844)))+P1(f332(f332(f232(x84841),x84842),f332(f332(f283(x84841),x84843),x84844)))+~P1(f332(f332(f232(x84841),f332(f332(f83(x84841),x84842),x84844)),x84843))
% 52.62/52.42 [8529]~P64(x85291)+~P89(x85291)+~P1(f332(f332(f233(x85291),f2(x85291)),f332(f106(x85291),x85293)))+~P1(f332(f332(f233(x85291),x85292),f332(f332(f283(x85291),x85294),f332(f106(x85291),x85293))))+P1(f332(f332(f233(x85291),f332(f332(f83(x85291),x85292),f332(f106(x85291),x85293))),x85294))
% 52.62/52.42 [8530]~P64(x85301)+~P89(x85301)+~P1(f332(f332(f233(x85301),f2(x85301)),f332(f106(x85301),x85303)))+~P1(f332(f332(f233(x85301),x85302),f332(f332(f83(x85301),x85304),f332(f106(x85301),x85303))))+P1(f332(f332(f233(x85301),f332(f332(f283(x85301),x85302),f332(f106(x85301),x85303))),x85304))
% 52.62/52.42 [8531]~P64(x85311)+~P89(x85311)+~P1(f332(f332(f233(x85311),f2(x85311)),f332(f106(x85311),x85313)))+~P1(f332(f332(f232(x85311),x85312),f332(f332(f283(x85311),x85314),f332(f106(x85311),x85313))))+P1(f332(f332(f232(x85311),f332(f332(f83(x85311),x85312),f332(f106(x85311),x85313))),x85314))
% 52.62/52.42 [8532]~P64(x85321)+~P89(x85321)+~P1(f332(f332(f233(x85321),f2(x85321)),f332(f106(x85321),x85323)))+~P1(f332(f332(f232(x85321),x85322),f332(f332(f83(x85321),x85324),f332(f106(x85321),x85323))))+P1(f332(f332(f232(x85321),f332(f332(f283(x85321),x85322),f332(f106(x85321),x85323))),x85324))
% 52.62/52.42 [8583]~P64(x85831)+~P1(f332(f332(f233(x85831),x85833),f2(x85831)))+~P1(f332(f332(f233(x85831),x85832),f332(f332(f83(x85831),x85834),x85833)))+~P1(f332(f332(f233(x85831),f332(f332(f83(x85831),x85834),x85833)),x85832))+P1(f332(f332(f233(x85831),f332(f332(f283(x85831),x85832),x85833)),x85834))
% 52.62/52.42 [8584]~P64(x85841)+~P1(f332(f332(f233(x85841),x85843),f2(x85841)))+~P1(f332(f332(f232(x85841),x85842),f332(f332(f83(x85841),x85844),x85843)))+~P1(f332(f332(f232(x85841),f332(f332(f83(x85841),x85844),x85843)),x85842))+P1(f332(f332(f232(x85841),f332(f332(f283(x85841),x85842),x85843)),x85844))
% 52.62/52.42 [8598]~P64(x85981)+~P1(f332(f332(f233(x85981),f2(x85981)),x85984))+~P1(f332(f332(f233(x85981),x85982),f332(f332(f83(x85981),x85984),x85983)))+~P1(f332(f332(f233(x85981),f332(f332(f83(x85981),x85984),x85983)),x85982))+P1(f332(f332(f233(x85981),f332(f332(f283(x85981),x85982),x85983)),x85984))
% 52.62/52.42 [8599]~P64(x85991)+~P1(f332(f332(f232(x85991),f2(x85991)),x85994))+~P1(f332(f332(f232(x85991),x85992),f332(f332(f83(x85991),x85994),x85993)))+~P1(f332(f332(f232(x85991),f332(f332(f83(x85991),x85994),x85993)),x85992))+P1(f332(f332(f232(x85991),f332(f332(f283(x85991),x85992),x85993)),x85994))
% 52.62/52.42 [8629]~P64(x86291)+~P89(x86291)+~P1(f332(f332(f233(x86291),f2(x86291)),f332(f106(x86291),x86294)))+P1(f332(f332(f233(x86291),x86292),f332(f332(f83(x86291),x86293),f332(f106(x86291),x86294))))+~P1(f332(f332(f233(x86291),f332(f332(f283(x86291),x86292),f332(f106(x86291),x86294))),x86293))
% 52.62/52.42 [8630]~P64(x86301)+~P89(x86301)+~P1(f332(f332(f233(x86301),f2(x86301)),f332(f106(x86301),x86304)))+P1(f332(f332(f233(x86301),x86302),f332(f332(f283(x86301),x86303),f332(f106(x86301),x86304))))+~P1(f332(f332(f233(x86301),f332(f332(f83(x86301),x86302),f332(f106(x86301),x86304))),x86303))
% 52.62/52.42 [8631]~P64(x86311)+~P89(x86311)+~P1(f332(f332(f233(x86311),f2(x86311)),f332(f106(x86311),x86314)))+P1(f332(f332(f232(x86311),x86312),f332(f332(f83(x86311),x86313),f332(f106(x86311),x86314))))+~P1(f332(f332(f232(x86311),f332(f332(f283(x86311),x86312),f332(f106(x86311),x86314))),x86313))
% 52.62/52.42 [8632]~P64(x86321)+~P89(x86321)+~P1(f332(f332(f233(x86321),f2(x86321)),f332(f106(x86321),x86324)))+P1(f332(f332(f232(x86321),x86322),f332(f332(f283(x86321),x86323),f332(f106(x86321),x86324))))+~P1(f332(f332(f232(x86321),f332(f332(f83(x86321),x86322),f332(f106(x86321),x86324))),x86323))
% 52.62/52.42 [8756]E(f332(f332(f3(a1),f436(x87561,x87562,x87563,x87564)),f437(x87561,x87562,x87563,x87564)),x87564)+~P1(f332(f332(f233(a1),f2(a1)),x87563))+~P1(f332(f332(f334(a1),x87562),x87561))+~P1(f332(f332(f233(a1),x87564),x87562))+P1(f332(f332(f233(a1),f332(f332(f82(a1),x87564),x87563)),x87562))
% 52.62/52.42 [8817]~P1(f332(x88171,x88172))+~P1(f332(f332(f233(a1),f2(a1)),x88174))+~P1(f332(f332(f232(a1),f2(a1)),x88173))+~P1(f332(x88171,f332(f332(f82(a1),f802(x88173,x88171,x88174)),x88174)))+P1(f332(x88171,f332(f332(f82(a1),x88172),f332(f332(f83(a1),x88173),x88174))))
% 52.62/52.42 [8818]~P1(f332(x88181,x88182))+~P1(f332(f332(f233(a1),f2(a1)),x88184))+~P1(f332(f332(f232(a1),f2(a1)),x88183))+~P1(f332(x88181,f332(f332(f3(a1),f806(x88183,x88181,x88184)),x88184)))+P1(f332(x88181,f332(f332(f3(a1),x88182),f332(f332(f83(a1),x88183),x88184))))
% 52.62/52.42 [8957]~P1(f332(f332(f233(a1),f2(a1)),x89573))+~P1(f332(f332(f334(a1),x89572),x89571))+~P1(f332(f332(f233(a1),x89574),x89572))+P1(f332(f332(f334(a1),f436(x89571,x89572,x89573,x89574)),x89571))+P1(f332(f332(f233(a1),f332(f332(f82(a1),x89574),x89573)),x89572))
% 52.62/52.42 [8977]E(f332(f332(f3(a1),f431(x89771,x89772,x89773,x89774)),f432(x89771,x89772,x89773,x89774)),x89774)+~P1(f332(f332(f233(a1),f2(a1)),x89773))+~P1(f332(f332(f232(a1),x89774),x89772))+~P1(f332(f332(f334(a1),f332(f332(f82(a1),x89772),f80(a1))),x89771))+P1(f332(f332(f232(a1),f332(f332(f82(a1),x89774),x89773)),x89772))
% 52.62/52.42 [9009]~P1(f332(f332(f233(a1),f2(a1)),x90092))+~P1(f332(f332(f334(a1),x90093),x90094))+~P1(f332(f332(f233(a1),x90091),x90093))+P1(f332(f332(f334(a1),f437(x90094,x90093,x90092,x90091)),f295(a1,f80(a1),x90092)))+P1(f332(f332(f233(a1),f332(f332(f82(a1),x90091),x90092)),x90093))
% 52.62/52.42 [9088]~P1(f332(f332(f233(a1),f2(a1)),x90883))+~P1(f332(f332(f232(a1),x90884),x90882))+P1(f332(f332(f334(a1),f431(x90881,x90882,x90883,x90884)),x90881))+~P1(f332(f332(f334(a1),f332(f332(f82(a1),x90882),f80(a1))),x90881))+P1(f332(f332(f232(a1),f332(f332(f82(a1),x90884),x90883)),x90882))
% 52.62/52.42 [9127]~P1(f332(f332(f233(a1),f2(a1)),x91272))+~P1(f332(f332(f232(a1),x91271),x91273))+P1(f332(f332(f334(a1),f432(x91274,x91273,x91272,x91271)),f295(a1,f80(a1),x91272)))+~P1(f332(f332(f334(a1),f332(f332(f82(a1),x91273),f80(a1))),x91274))+P1(f332(f332(f232(a1),f332(f332(f82(a1),x91271),x91272)),x91273))
% 52.62/52.42 [9393]~P38(x93931,x93933)+~P32(x93931,x93934)+P38(x93931,f332(f332(f103(f853(f852(x93931,x93931),a839)),x93932),x93933))+~P1(f332(f332(f232(f853(f852(x93931,x93931),a839)),x93932),f332(f240(f853(f852(x93931,x93931),a839),f853(f852(x93931,x93931),a839)),x93934)))+~P1(f332(f332(f232(f853(f852(x93931,x93931),a839)),x93933),f332(f250(f853(f852(x93931,x93931),a839),f853(f852(x93931,x93931),a839)),x93934)))
% 52.62/52.42 [9661]~E(f332(f707(x96611,x96614,x96613,x96612),f711(x96611,x96614,x96613,x96612)),f183(f846(a837)))+P1(f332(f332(f233(a1),f710(x96611,x96614,x96613,x96612)),f711(x96611,x96614,x96613,x96612)))+P1(f332(f332(f332(x96611,x96612),x96613),x96614))+P1(f332(f332(f332(x96611,f707(x96611,x96614,x96613,x96612)),f710(x96611,x96614,x96613,x96612)),f332(f332(f82(a1),f711(x96611,x96614,x96613,x96612)),f80(a1))))+~P1(f332(f321(f852(f853(a1,f849(f846(a837))),f852(a1,a1)),a311),f332(f332(f241(f853(a1,f849(f846(a837))),f852(a1,a1)),x96612),f332(f332(f241(a1,a1),x96613),x96614))))
% 52.62/52.42 [9763]~P24(x97632,x97634,x97633)+E(x97631,f180(f853(x97632,a839)))+~P1(f332(f64(x97632),x97631))+P1(f332(f332(f334(x97632),f332(x97633,x97631)),x97631))+~P1(f332(f332(f334(x97632),f332(f332(x97634,f458(x97631,x97633,x97634,x97632)),f459(x97631,x97633,x97634,x97632))),f332(f332(f302(x97632),f458(x97631,x97633,x97634,x97632)),f332(f332(f302(x97632),f459(x97631,x97633,x97634,x97632)),f180(f853(x97632,a839))))))
% 52.62/52.42 [8619]~P64(x86191)+~P89(x86191)+~P1(f332(f332(f233(x86191),f2(x86191)),x86193))+~P1(f332(f332(f233(x86191),f332(f106(x86191),x86192)),f332(f332(f283(x86191),x86194),x86193)))+P1(f332(f332(f233(x86191),f332(f332(f83(x86191),f332(f106(x86191),x86192)),x86193)),x86194))
% 52.62/52.42 [8620]~P64(x86201)+~P89(x86201)+~P1(f332(f332(f233(x86201),f2(x86201)),x86203))+~P1(f332(f332(f232(x86201),f332(f106(x86201),x86202)),f332(f332(f283(x86201),x86204),x86203)))+P1(f332(f332(f232(x86201),f332(f332(f83(x86201),f332(f106(x86201),x86202)),x86203)),x86204))
% 52.62/52.42 [8759]~P64(x87591)+~P89(x87591)+~P1(f332(f332(f233(x87591),f2(x87591)),x87594))+P1(f332(f332(f233(x87591),f332(f106(x87591),x87592)),f332(f332(f283(x87591),x87593),x87594)))+~P1(f332(f332(f233(x87591),f332(f332(f83(x87591),f332(f106(x87591),x87592)),x87594)),x87593))
% 52.62/52.42 [8760]~P64(x87601)+~P89(x87601)+~P1(f332(f332(f233(x87601),f2(x87601)),x87604))+P1(f332(f332(f232(x87601),f332(f106(x87601),x87602)),f332(f332(f283(x87601),x87603),x87604)))+~P1(f332(f332(f232(x87601),f332(f332(f83(x87601),f332(f106(x87601),x87602)),x87604)),x87603))
% 52.62/52.42 [9313]~P55(x93131,x93131,x93134)+P1(f332(f332(f334(f852(x93131,x93131)),f332(f332(f241(x93131,x93131),x93132),x93133)),f300(x93131,x93134)))+P1(f332(f332(f334(f852(x93131,x93131)),f332(f332(f241(x93131,x93131),x93133),x93132)),f300(x93131,x93134)))+~P1(f332(f332(f334(f852(x93131,x93131)),f332(f332(f241(x93131,x93131),x93135),x93132)),f300(x93131,x93134)))+~P1(f332(f332(f334(f852(x93131,x93131)),f332(f332(f241(x93131,x93131),x93135),x93133)),f300(x93131,x93134)))
% 52.62/52.42 [5492]E(x54921,f2(a845))+~E(f332(f43(x54922),x54925),x54921)+E(f332(f43(x54922),x54923),f332(a114,x54921))+~E(x54923,f332(f332(f302(x54922),x54924),x54925))+P1(f332(f332(f334(x54922),x54924),x54925))
% 52.62/52.42 [5613]~P63(x56132)+E(x56131,f2(x56132))+E(x56133,f2(x56132))+~E(f332(f332(f283(x56132),x56134),x56133),f332(f332(f283(x56132),x56135),x56131))+E(f332(f332(f83(x56132),x56134),x56131),f332(f332(f83(x56132),x56135),x56133))
% 52.62/52.42 [5614]~P63(x56142)+E(x56141,f2(x56142))+E(x56143,f2(x56142))+~E(f332(f332(f83(x56142),x56144),x56143),f332(f332(f83(x56142),x56145),x56141))+E(f332(f332(f283(x56142),x56144),x56141),f332(f332(f283(x56142),x56145),x56143))
% 52.62/52.42 [5687]~E(f332(f43(x56871),x56875),x56873)+~E(x56875,f180(f853(x56871,a839)))+E(f332(f43(x56871),x56872),f332(a114,x56873))+~E(x56872,f332(f332(f302(x56871),x56874),x56875))+P1(f332(f332(f334(x56871),x56874),x56875))
% 52.62/52.42 [5914]~P73(x59142)+~E(f332(x59143,x59145),f2(x59142))+E(f332(f332(f11(x59141,x59142),x59143),x59144),f2(x59142))+~P1(f332(f64(x59141),x59144))+~P1(f332(f332(f334(x59141),x59145),x59144))
% 52.62/52.42 [6300]~P100(x63003)+E(x63001,x63002)+~E(f332(f294(x63003,x63004),x63001),f332(f294(x63003,x63005),x63002))+~P1(f332(f332(f233(x63003),x63005),x63002))+~P1(f332(f332(f233(x63003),x63004),x63001))
% 52.62/52.42 [6301]~P100(x63013)+E(x63011,x63012)+~E(f332(f294(x63013,x63011),x63014),f332(f294(x63013,x63012),x63015))+~P1(f332(f332(f233(x63013),x63012),x63015))+~P1(f332(f332(f233(x63013),x63011),x63014))
% 52.62/52.42 [6302]~P100(x63023)+E(x63021,x63022)+~E(f332(f294(x63023,x63024),x63021),f332(f294(x63023,x63025),x63022))+~P1(f332(f332(f233(x63023),x63025),x63022))+~P1(f332(f332(f233(x63023),x63024),x63021))
% 52.62/52.42 [6303]~P100(x63033)+E(x63031,x63032)+~E(f332(f294(x63033,x63031),x63034),f332(f294(x63033,x63032),x63035))+~P1(f332(f332(f233(x63033),x63032),x63035))+~P1(f332(f332(f233(x63033),x63031),x63034))
% 52.62/52.42 [7412]~P100(x74121)+~P20(x74121,f332(f332(f125(x74121),x74124),x74125))+~P1(f332(f332(f334(x74121),x74123),f332(f158(x74121),x74125)))+~P1(f332(f332(f334(x74121),x74122),f332(f158(x74121),x74124)))+P1(f332(f332(f232(x74121),x74122),x74123))
% 52.62/52.42 [8515]~P99(x85151)+~P1(f332(f332(f233(f853(x85151,a839)),f295(x85151,x85155,x85152)),f295(x85151,x85154,x85153)))+~P1(f332(f332(f232(x85151),x85155),x85152))+P1(f332(f332(f233(x85151),x85152),x85153))+P1(f332(f332(f233(x85151),x85154),x85155))
% 52.62/52.42 [9807]~P23(x98072,x98075,x98073)+E(x98071,f180(f853(x98072,a839)))+~E(f332(f332(x98075,f332(x98074,f576(x98071,x98074,x98073,x98075,x98072))),f332(x98074,f577(x98071,x98074,x98073,x98075,x98072))),f332(x98074,f332(f332(x98075,f576(x98071,x98074,x98073,x98075,x98072)),f577(x98071,x98074,x98073,x98075,x98072))))+E(f332(x98073,f332(f303(x98072,x98072,x98074),x98071)),f332(x98074,f332(x98073,x98071)))+~P1(f332(f64(x98072),x98071))
% 52.62/52.42 [6299]~P24(x62992,x62995,x62993)+E(x62991,f180(f853(x62992,a839)))+~P1(f332(f64(x62992),x62991))+E(f332(x62993,f332(f332(f302(x62992),x62994),x62991)),f332(f332(x62995,x62994),f332(x62993,x62991)))+P1(f332(f332(f334(x62992),x62994),x62991))
% 52.62/52.42 [7149]~P23(x71492,x71493,x71494)+E(f332(f332(x71493,f332(x71494,x71491)),f332(x71494,x71495)),f332(x71494,x71495))+E(x71491,f180(f853(x71492,a839)))+~P1(f332(f64(x71492),x71495))+~P1(f332(f332(f232(f853(x71492,a839)),x71491),x71495))
% 52.62/52.42 [7553]~P24(x75534,x75535,x75531)+E(f332(x75531,x75532),x75533)+~P1(f332(f64(x75534),x75532))+~E(f332(f332(f3(f853(x75534,a839)),x75532),f332(f332(f302(x75534),x75533),f180(f853(x75534,a839)))),f180(f853(x75534,a839)))+~P1(f332(f332(f334(x75534),x75533),x75532))
% 52.62/52.42 [7700]E(x77001,x77002)+~E(f332(f181(f846(x77003)),x77002),f332(f181(f846(x77004)),x77005))+~E(f332(f181(f846(x77003)),x77001),f332(f181(f846(x77004)),x77005))+~E(f166(x77004,x77003,f332(f332(f167(x77004,x77003),x77005),x77001)),f166(x77004,x77003,f332(f332(f167(x77004,x77003),x77005),x77002)))+~P1(f332(f127(x77004),x77005))
% 52.62/52.42 [8438]~P70(x84381)+~P112(x84381)+~P1(f332(f64(x84382),x84385))+P1(f332(f332(f279(x84381),f332(f332(f11(x84382,x84381),x84383),x84384)),f332(f332(f11(x84382,x84381),x84383),x84385)))+~P1(f332(f332(f232(f853(x84382,a839)),x84384),x84385))
% 52.62/52.42 [8488]E(x84881,x84882)+~P14(x84883,x84884,x84885)+E(f332(f332(f104(f853(x84883,a839)),x84881),x84882),f180(f853(x84883,a839)))+~P1(f332(f332(f334(f853(x84883,a839)),x84882),f332(f332(f62(x84883),x84884),x84885)))+~P1(f332(f332(f334(f853(x84883,a839)),x84881),f332(f332(f62(x84883),x84884),x84885)))
% 52.62/52.42 [8889]~P31(x88891,x88893,x88895,x88892)+~P1(f332(f64(x88893),x88894))+~P1(f332(f64(x88891),x88892))+P1(f332(f332(f232(a845),f332(f43(x88891),x88892)),f332(f43(x88893),x88894)))+~P1(f332(f332(f232(f853(x88893,a839)),f332(f303(x88891,x88893,x88895),x88892)),x88894))
% 52.62/52.42 [9191]~P4(x91912)+~E(f332(x91913,f479(x91913,x91914,x91915,x91911,x91912)),f2(x91912))+E(f332(f332(f8(x91911,x91912),x91913),x91914),f332(f332(f8(x91911,x91912),x91913),x91915))+~P1(f332(f64(x91911),x91915))+~P1(f332(f332(f232(f853(x91911,a839)),x91914),x91915))
% 52.62/52.42 [9192]~P4(x91922)+~E(f332(x91923,f482(x91923,x91924,x91925,x91921,x91922)),f2(x91922))+E(f332(f332(f8(x91921,x91922),x91923),x91924),f332(f332(f8(x91921,x91922),x91923),x91925))+~P1(f332(f64(x91921),x91925))+~P1(f332(f332(f232(f853(x91921,a839)),x91924),x91925))
% 52.62/52.42 [9193]~P70(x91932)+~E(f332(x91933,f480(x91933,x91934,x91935,x91931,x91932)),f80(x91932))+E(f332(f332(f11(x91931,x91932),x91933),x91934),f332(f332(f11(x91931,x91932),x91933),x91935))+~P1(f332(f64(x91931),x91935))+~P1(f332(f332(f232(f853(x91931,a839)),x91934),x91935))
% 52.62/52.42 [9194]~P70(x91942)+~E(f332(x91943,f481(x91943,x91944,x91945,x91941,x91942)),f80(x91942))+E(f332(f332(f11(x91941,x91942),x91943),x91944),f332(f332(f11(x91941,x91942),x91943),x91945))+~P1(f332(f64(x91941),x91945))+~P1(f332(f332(f232(f853(x91941,a839)),x91944),x91945))
% 52.62/52.42 [9644]~P82(x96441)+~P1(f332(f64(x96442),x96445))+~P1(f332(f332(f232(x96441),f2(x96441)),f332(x96443,f438(x96443,x96444,x96445,x96442,x96441))))+P1(f332(f332(f232(x96441),f332(f332(f8(x96442,x96441),x96443),x96444)),f332(f332(f8(x96442,x96441),x96443),x96445)))+~P1(f332(f332(f232(f853(x96442,a839)),x96444),x96445))
% 52.62/52.42 [7409]E(x74091,f2(a845))+P1(f332(x74092,x74093))+~E(x74094,f332(f332(f82(a845),f332(f332(f83(a845),x74091),x74093)),x74095))+~P1(f332(f332(f233(a845),x74095),x74091))+~P1(f332(x74092,f332(f332(f44(a845),x74094),x74091)))
% 52.62/52.42 [7492]E(x74921,f2(a845))+P1(f332(x74922,x74923))+~P1(f332(x74922,f53(a845,x74924,x74921)))+~E(x74924,f332(f332(f82(a845),f332(f332(f83(a845),x74921),x74925)),x74923))+~P1(f332(f332(f233(a845),x74923),x74921))
% 52.62/52.42 [7788]~P63(x77883)+E(f332(x77881,x77882),f2(x77883))+~P1(f332(f64(x77884),x77885))+E(f332(f332(f11(x77884,x77883),x77881),f332(f332(f3(f853(x77884,a839)),x77885),f332(f332(f302(x77884),x77882),f180(f853(x77884,a839))))),f332(f332(f11(x77884,x77883),x77881),x77885))+P1(f332(f332(f334(x77884),x77882),x77885))
% 52.62/52.42 [8182]~P4(x81821)+~P1(f332(f64(x81822),x81825))+~P1(f332(f64(x81822),x81824))+~E(f332(f332(f104(f853(x81822,a839)),x81824),x81825),f180(f853(x81822,a839)))+E(f332(f332(f82(x81821),f332(f332(f8(x81822,x81821),x81823),x81824)),f332(f332(f8(x81822,x81821),x81823),x81825)),f332(f332(f8(x81822,x81821),x81823),f332(f332(f103(f853(x81822,a839)),x81824),x81825)))
% 52.62/52.42 [8183]~P70(x81831)+~P1(f332(f64(x81832),x81835))+~P1(f332(f64(x81832),x81834))+~E(f332(f332(f104(f853(x81832,a839)),x81834),x81835),f180(f853(x81832,a839)))+E(f332(f332(f83(x81831),f332(f332(f11(x81832,x81831),x81833),x81834)),f332(f332(f11(x81832,x81831),x81833),x81835)),f332(f332(f11(x81832,x81831),x81833),f332(f332(f103(f853(x81832,a839)),x81834),x81835)))
% 52.62/52.42 [8184]~P70(x81841)+~P1(f332(f64(x81842),x81845))+~P1(f332(f64(x81842),x81844))+~E(f332(f332(f104(f853(x81842,a839)),x81844),x81845),f180(f853(x81842,a839)))+E(f332(f332(f83(x81841),f332(f332(f11(x81842,x81841),x81843),x81844)),f332(f332(f11(x81842,x81841),x81843),x81845)),f332(f332(f11(x81842,x81841),x81843),f332(f332(f103(f853(x81842,a839)),x81844),x81845)))
% 52.62/52.42 [8274]~P63(x82743)+E(f332(x82741,x82742),f2(x82743))+~P1(f332(f64(x82744),x82745))+E(f332(f332(f11(x82744,x82743),x82741),f332(f332(f3(f853(x82744,a839)),x82745),f332(f332(f302(x82744),x82742),f180(f853(x82744,a839))))),f332(f332(f283(x82743),f332(f332(f11(x82744,x82743),x82741),x82745)),f332(x82741,x82742)))+~P1(f332(f332(f334(x82744),x82742),x82745))
% 52.62/52.42 [8771]~P14(x87711,x87715,x87714)+~E(f332(f277(x87711,x87711,x87714),f332(f332(f302(x87711),x87712),f180(f853(x87711,a839)))),f332(f277(x87711,x87711,x87714),f332(f332(f302(x87711),x87713),f180(f853(x87711,a839)))))+~P1(f332(f332(f334(x87711),x87713),x87715))+~P1(f332(f332(f334(x87711),x87712),x87715))+P1(f332(f332(f334(f852(x87711,x87711)),f332(f332(f241(x87711,x87711),x87712),x87713)),x87714))
% 52.62/52.42 [8772]~P14(x87721,x87725,x87724)+~E(f332(f277(x87721,x87721,x87724),f332(f332(f302(x87721),x87722),f180(f853(x87721,a839)))),f332(f277(x87721,x87721,x87724),f332(f332(f302(x87721),x87723),f180(f853(x87721,a839)))))+~P1(f332(f332(f334(x87721),x87723),x87725))+~P1(f332(f332(f334(x87721),x87722),x87725))+P1(f332(f332(f334(f852(x87721,x87721)),f332(f332(f241(x87721,x87721),x87722),x87723)),x87724))
% 52.62/52.42 [8850]~P14(x88501,x88505,x88502)+E(f332(f277(x88501,x88501,x88502),f332(f332(f302(x88501),x88503),f180(f853(x88501,a839)))),f332(f277(x88501,x88501,x88502),f332(f332(f302(x88501),x88504),f180(f853(x88501,a839)))))+~P1(f332(f332(f334(x88501),x88504),x88505))+~P1(f332(f332(f334(x88501),x88503),x88505))+~P1(f332(f332(f334(f852(x88501,x88501)),f332(f332(f241(x88501,x88501),x88503),x88504)),x88502))
% 52.62/52.42 [8939]~P14(x89391,x89395,x89394)+~E(f332(f332(f62(x89391),f332(f332(f302(x89391),x89392),f180(f853(x89391,a839)))),x89394),f332(f332(f62(x89391),f332(f332(f302(x89391),x89393),f180(f853(x89391,a839)))),x89394))+~P1(f332(f332(f334(x89391),x89393),x89395))+~P1(f332(f332(f334(x89391),x89392),x89395))+P1(f332(f332(f334(f852(x89391,x89391)),f332(f332(f241(x89391,x89391),x89392),x89393)),x89394))
% 52.62/52.42 [8956]~P14(x89561,x89565,x89563)+E(f332(f332(f62(x89561),f332(f332(f302(x89561),x89562),f180(f853(x89561,a839)))),x89563),f332(f332(f62(x89561),f332(f332(f302(x89561),x89564),f180(f853(x89561,a839)))),x89563))+~P1(f332(f332(f334(x89561),x89564),x89565))+~P1(f332(f332(f334(x89561),x89562),x89565))+~P1(f332(f332(f334(f852(x89561,x89561)),f332(f332(f241(x89561,x89561),x89562),x89564)),x89563))
% 52.62/52.42 [9218]~P70(x92181)+~P1(f332(f64(x92182),x92185))+~P1(f332(f64(x92182),x92184))+~E(f332(f332(f104(f853(x92182,a839)),x92184),x92185),f180(f853(x92182,a839)))+E(f332(f332(f83(x92181),f332(f332(f332(f68(x92181,x92182,f83(x92181)),x92183),f80(x92181)),x92184)),f332(f332(f332(f68(x92181,x92182,f83(x92181)),x92183),f80(x92181)),x92185)),f332(f332(f332(f68(x92181,x92182,f83(x92181)),x92183),f80(x92181)),f332(f332(f103(f853(x92182,a839)),x92184),x92185)))
% 52.62/52.42 [9228]~P4(x92281)+~E(f332(x92283,f508(x92283,x92285,x92284,x92282,x92281)),f2(x92281))+~P1(f332(f64(x92282),x92284))+~P1(f332(f64(x92282),x92285))+E(f332(f332(f82(x92281),f332(f332(f8(x92282,x92281),x92283),x92284)),f332(f332(f8(x92282,x92281),x92283),x92285)),f332(f332(f8(x92282,x92281),x92283),f332(f332(f103(f853(x92282,a839)),x92284),x92285)))
% 52.62/52.42 [9229]~P4(x92291)+~E(f332(x92293,f512(x92293,x92295,x92294,x92292,x92291)),f2(x92291))+~P1(f332(f64(x92292),x92294))+~P1(f332(f64(x92292),x92295))+E(f332(f332(f82(x92291),f332(f332(f8(x92292,x92291),x92293),x92294)),f332(f332(f8(x92292,x92291),x92293),x92295)),f332(f332(f8(x92292,x92291),x92293),f332(f332(f103(f853(x92292,a839)),x92294),x92295)))
% 52.62/52.42 [9230]~P70(x92301)+~E(f332(x92303,f509(x92303,x92305,x92304,x92302,x92301)),f80(x92301))+~P1(f332(f64(x92302),x92304))+~P1(f332(f64(x92302),x92305))+E(f332(f332(f83(x92301),f332(f332(f11(x92302,x92301),x92303),x92304)),f332(f332(f11(x92302,x92301),x92303),x92305)),f332(f332(f11(x92302,x92301),x92303),f332(f332(f103(f853(x92302,a839)),x92304),x92305)))
% 52.62/52.42 [9231]~P70(x92311)+~E(f332(x92313,f511(x92313,x92315,x92314,x92312,x92311)),f80(x92311))+~P1(f332(f64(x92312),x92314))+~P1(f332(f64(x92312),x92315))+E(f332(f332(f83(x92311),f332(f332(f11(x92312,x92311),x92313),x92314)),f332(f332(f11(x92312,x92311),x92313),x92315)),f332(f332(f11(x92312,x92311),x92313),f332(f332(f103(f853(x92312,a839)),x92314),x92315)))
% 52.62/52.42 [9435]~P70(x94351)+~E(f332(x94353,f531(x94353,x94355,x94354,x94352,x94351)),f80(x94351))+~P1(f332(f64(x94352),x94354))+~P1(f332(f64(x94352),x94355))+E(f332(f332(f83(x94351),f332(f332(f332(f68(x94351,x94352,f83(x94351)),x94353),f80(x94351)),x94354)),f332(f332(f332(f68(x94351,x94352,f83(x94351)),x94353),f80(x94351)),x94355)),f332(f332(f332(f68(x94351,x94352,f83(x94351)),x94353),f80(x94351)),f332(f332(f103(f853(x94352,a839)),x94354),x94355)))
% 52.62/52.42 [9536]~P4(x95362)+E(f332(f332(f8(x95361,x95362),x95363),x95364),f332(f332(f8(x95361,x95362),x95363),x95365))+~P1(f332(f64(x95361),x95365))+~P1(f332(f332(f232(f853(x95361,a839)),x95364),x95365))+P1(f332(f332(f334(x95361),f479(x95363,x95364,x95365,x95361,x95362)),f332(f332(f3(f853(x95361,a839)),x95365),x95364)))
% 52.62/52.42 [9537]~P4(x95372)+E(f332(f332(f8(x95371,x95372),x95373),x95374),f332(f332(f8(x95371,x95372),x95373),x95375))+~P1(f332(f64(x95371),x95375))+~P1(f332(f332(f232(f853(x95371,a839)),x95374),x95375))+P1(f332(f332(f334(x95371),f482(x95373,x95374,x95375,x95371,x95372)),f332(f332(f3(f853(x95371,a839)),x95375),x95374)))
% 52.62/52.42 [9538]~P70(x95382)+E(f332(f332(f11(x95381,x95382),x95383),x95384),f332(f332(f11(x95381,x95382),x95383),x95385))+~P1(f332(f64(x95381),x95385))+~P1(f332(f332(f232(f853(x95381,a839)),x95384),x95385))+P1(f332(f332(f334(x95381),f480(x95383,x95384,x95385,x95381,x95382)),f332(f332(f3(f853(x95381,a839)),x95385),x95384)))
% 52.62/52.42 [9539]~P70(x95392)+E(f332(f332(f11(x95391,x95392),x95393),x95394),f332(f332(f11(x95391,x95392),x95393),x95395))+~P1(f332(f64(x95391),x95395))+~P1(f332(f332(f232(f853(x95391,a839)),x95394),x95395))+P1(f332(f332(f334(x95391),f481(x95393,x95394,x95395,x95391,x95392)),f332(f332(f3(f853(x95391,a839)),x95395),x95394)))
% 52.62/52.42 [9553]~P4(x95531)+~P1(f332(f64(x95532),x95534))+~P1(f332(f64(x95532),x95535))+E(f332(f332(f82(x95531),f332(f332(f8(x95532,x95531),x95533),x95534)),f332(f332(f8(x95532,x95531),x95533),x95535)),f332(f332(f8(x95532,x95531),x95533),f332(f332(f103(f853(x95532,a839)),x95534),x95535)))+P1(f332(f332(f334(x95532),f508(x95533,x95535,x95534,x95532,x95531)),f332(f332(f104(f853(x95532,a839)),x95534),x95535)))
% 52.62/52.42 [9554]~P4(x95541)+~P1(f332(f64(x95542),x95544))+~P1(f332(f64(x95542),x95545))+E(f332(f332(f82(x95541),f332(f332(f8(x95542,x95541),x95543),x95544)),f332(f332(f8(x95542,x95541),x95543),x95545)),f332(f332(f8(x95542,x95541),x95543),f332(f332(f103(f853(x95542,a839)),x95544),x95545)))+P1(f332(f332(f334(x95542),f512(x95543,x95545,x95544,x95542,x95541)),f332(f332(f104(f853(x95542,a839)),x95544),x95545)))
% 52.62/52.42 [9555]~P70(x95551)+~P1(f332(f64(x95552),x95554))+~P1(f332(f64(x95552),x95555))+E(f332(f332(f83(x95551),f332(f332(f11(x95552,x95551),x95553),x95554)),f332(f332(f11(x95552,x95551),x95553),x95555)),f332(f332(f11(x95552,x95551),x95553),f332(f332(f103(f853(x95552,a839)),x95554),x95555)))+P1(f332(f332(f334(x95552),f509(x95553,x95555,x95554,x95552,x95551)),f332(f332(f104(f853(x95552,a839)),x95554),x95555)))
% 52.62/52.42 [9556]~P70(x95561)+~P1(f332(f64(x95562),x95564))+~P1(f332(f64(x95562),x95565))+E(f332(f332(f83(x95561),f332(f332(f11(x95562,x95561),x95563),x95564)),f332(f332(f11(x95562,x95561),x95563),x95565)),f332(f332(f11(x95562,x95561),x95563),f332(f332(f103(f853(x95562,a839)),x95564),x95565)))+P1(f332(f332(f334(x95562),f511(x95563,x95565,x95564,x95562,x95561)),f332(f332(f104(f853(x95562,a839)),x95564),x95565)))
% 52.62/52.42 [9568]~P82(x95685)+~P1(f332(f64(x95681),x95684))+P1(f332(f332(f232(x95685),f332(f332(f8(x95681,x95685),x95682),x95683)),f332(f332(f8(x95681,x95685),x95682),x95684)))+~P1(f332(f332(f232(f853(x95681,a839)),x95683),x95684))+P1(f332(f332(f334(x95681),f438(x95682,x95683,x95684,x95681,x95685)),f332(f332(f3(f853(x95681,a839)),x95684),x95683)))
% 52.62/52.42 [9610]~P70(x96101)+~P1(f332(f64(x96102),x96104))+~P1(f332(f64(x96102),x96105))+E(f332(f332(f83(x96101),f332(f332(f332(f68(x96101,x96102,f83(x96101)),x96103),f80(x96101)),x96104)),f332(f332(f332(f68(x96101,x96102,f83(x96101)),x96103),f80(x96101)),x96105)),f332(f332(f332(f68(x96101,x96102,f83(x96101)),x96103),f80(x96101)),f332(f332(f103(f853(x96102,a839)),x96104),x96105)))+P1(f332(f332(f334(x96102),f531(x96103,x96105,x96104,x96102,x96101)),f332(f332(f104(f853(x96102,a839)),x96104),x96105)))
% 52.62/52.42 [8665]~P24(x86651,x86654,x86655)+~P1(f332(f64(x86651),x86652))+E(f332(f332(f3(f853(x86651,a839)),x86652),f332(f332(f302(x86651),x86653),f180(f853(x86651,a839)))),f180(f853(x86651,a839)))+~P1(f332(f332(f334(x86651),x86653),x86652))+E(f332(f332(x86654,x86653),f332(x86655,f332(f332(f3(f853(x86651,a839)),x86652),f332(f332(f302(x86651),x86653),f180(f853(x86651,a839)))))),f332(x86655,x86652))
% 52.62/52.42 [8732]~P24(x87321,x87324,x87325)+~P1(f332(f64(x87321),x87323))+~P1(f332(f64(x87321),x87322))+E(f332(f332(f104(f853(x87321,a839)),x87322),x87323),f180(f853(x87321,a839)))+E(f332(f332(x87324,f332(x87325,f332(f332(f103(f853(x87321,a839)),x87322),x87323))),f332(x87325,f332(f332(f104(f853(x87321,a839)),x87322),x87323))),f332(f332(x87324,f332(x87325,x87322)),f332(x87325,x87323)))
% 52.62/52.42 [9233]~P1(f332(f332(f232(a1),x92334),f2(a1)))+~P1(f332(f332(f233(a1),x92333),x92335))+P1(f332(f332(f232(a1),x92331),x92332))+~P1(f332(f332(f233(a1),x92333),x92334))+~P1(f332(f332(f232(a1),f332(f332(f82(a1),f332(f332(f83(a1),x92333),x92332)),x92335)),f332(f332(f82(a1),f332(f332(f83(a1),x92333),x92331)),x92334)))
% 52.62/52.42 [9235]~P1(f332(f332(f232(a1),f2(a1)),x92355))+P1(f332(f332(f232(a1),x92351),x92352))+~P1(f332(f332(f233(a1),x92353),x92354))+~P1(f332(f332(f233(a1),x92355),x92354))+~P1(f332(f332(f232(a1),f332(f332(f82(a1),f332(f332(f83(a1),x92354),x92351)),x92355)),f332(f332(f82(a1),f332(f332(f83(a1),x92354),x92352)),x92353)))
% 52.62/52.42 [9348]~P63(x93485)+E(f332(x93481,f510(x93481,x93482,x93483,x93484,x93485)),f2(x93485))+~P1(f332(f64(x93484),x93483))+~P1(f332(f64(x93484),x93482))+E(f332(f332(f283(x93485),f332(f332(f83(x93485),f332(f332(f11(x93484,x93485),x93481),x93483)),f332(f332(f11(x93484,x93485),x93481),x93482))),f332(f332(f11(x93484,x93485),x93481),f332(f332(f104(f853(x93484,a839)),x93483),x93482))),f332(f332(f11(x93484,x93485),x93481),f332(f332(f103(f853(x93484,a839)),x93483),x93482)))
% 52.62/52.42 [9603]~P63(x96031)+~P1(f332(f64(x96032),x96034))+~P1(f332(f64(x96032),x96035))+E(f332(f332(f283(x96031),f332(f332(f83(x96031),f332(f332(f11(x96032,x96031),x96033),x96034)),f332(f332(f11(x96032,x96031),x96033),x96035))),f332(f332(f11(x96032,x96031),x96033),f332(f332(f104(f853(x96032,a839)),x96034),x96035))),f332(f332(f11(x96032,x96031),x96033),f332(f332(f103(f853(x96032,a839)),x96034),x96035)))+P1(f332(f332(f334(x96032),f510(x96033,x96035,x96034,x96032,x96031)),f332(f332(f104(f853(x96032,a839)),x96034),x96035)))
% 52.62/52.42 [8976]E(f332(f332(f125(x89761),x89762),x89763),f332(f332(f125(x89761),x89764),x89765))+~E(f332(f332(f159(x89761),f332(f181(f846(x89761)),x89764)),x89762),x89764)+~E(f332(f332(f159(x89761),f332(f181(f846(x89761)),x89762)),x89764),x89762)+~E(x89765,f332(f332(f125(x89761),f332(f332(f128(x89761),f332(f181(f846(x89761)),x89764)),x89762)),x89763))+~E(f332(f332(f125(x89761),f332(f332(f128(x89761),f332(f181(f846(x89761)),x89762)),x89764)),x89765),x89763)
% 52.62/52.42 [9346]~P100(x93462)+E(f332(f332(f138(x93461,x93462,x93463),x93464),f151(x93461,x93464,x93465)),x93465)+~P20(x93462,f332(f332(f143(x93461,x93462),x93463),x93465))+~P1(f332(f332(f334(x93461),x93464),f332(f158(x93461),x93465)))+~E(f332(f131(x93461),f332(f126(x93461,f332(f332(f10(x93462,a839,x93461),f332(a329,f332(x93463,x93464))),x93463)),x93465)),x93464)
% 52.62/52.42 [9658]~P66(x96581)+~P1(f332(f69(x96581,x96581,f83(x96581),x96582,x96583),x96585))+~P1(f332(f332(f334(x96581),x96584),x96583))+P1(f332(f332(f334(x96581),x96582),x96583))+P1(f332(f69(x96581,x96581,f83(x96581),x96584,f332(f332(f302(x96581),x96582),f332(f332(f3(f853(x96581,a839)),x96583),f332(f332(f302(x96581),x96584),f180(f853(x96581,a839)))))),x96585))
% 52.62/52.42 [7153]E(x71531,x71532)+~P31(x71534,x71535,x71533,x71536)+~E(f332(x71533,x71531),f332(x71533,x71532))+~P1(f332(f332(f334(x71534),x71532),x71536))+~P1(f332(f332(f334(x71534),x71531),x71536))
% 52.62/52.42 [7154]E(x71541,x71542)+~P31(x71544,x71545,x71543,x71546)+~E(f332(x71543,x71541),f332(x71543,x71542))+~P1(f332(f332(f334(x71544),x71542),x71546))+~P1(f332(f332(f334(x71544),x71541),x71546))
% 52.62/52.42 [7155]E(x71551,x71552)+~P31(x71554,x71555,x71553,x71556)+~E(f332(x71553,x71551),f332(x71553,x71552))+~P1(f332(f332(f334(x71554),x71552),x71556))+~P1(f332(f332(f334(x71554),x71551),x71556))
% 52.62/52.42 [7156]E(x71561,x71562)+~P31(x71564,x71565,x71563,x71566)+~E(f332(x71563,x71561),f332(x71563,x71562))+~P1(f332(f332(f334(x71564),x71562),x71566))+~P1(f332(f332(f334(x71564),x71561),x71566))
% 52.62/52.42 [6397]~P137(x63974)+E(x63971,x63972)+~E(x63975,x63976)+E(x63973,f2(x63974))+~E(f332(f332(f82(x63974),x63975),f332(f332(f83(x63974),x63973),x63971)),f332(f332(f82(x63974),x63976),f332(f332(f83(x63974),x63973),x63972)))
% 52.62/52.42 [7472]~P100(x74721)+~P11(x74721)+~P1(f332(f332(f233(x74721),x74722),f332(x74725,x74726)))+~P1(f332(f332(f334(x74723),x74726),x74724))+P1(f332(f332(f233(x74721),x74722),f332(f332(f47(x74723,x74721),x74724),x74725)))
% 52.62/52.42 [9822]~P73(x98226)+~P1(f332(f64(x98221),x98225))+P1(f332(f332(f334(x98221),f628(x98222,x98223,x98224,x98225,x98221,x98226)),x98224))+P1(f332(f332(f279(x98226),f332(f332(f11(x98221,x98226),x98223),x98224)),f332(f332(f11(x98221,x98226),x98222),x98225)))+~P1(f332(f332(f232(f853(x98221,a839)),x98224),x98225))
% 52.62/52.42 [9945]~P73(x99451)+~P1(f332(f64(x99452),x99456))+~P1(f332(f332(f279(x99451),f332(x99453,f628(x99455,x99453,x99454,x99456,x99452,x99451))),f332(x99455,f628(x99455,x99453,x99454,x99456,x99452,x99451))))+P1(f332(f332(f279(x99451),f332(f332(f11(x99452,x99451),x99453),x99454)),f332(f332(f11(x99452,x99451),x99455),x99456)))+~P1(f332(f332(f232(f853(x99452,a839)),x99454),x99456))
% 52.62/52.42 [8153]~P100(x81531)+~P11(x81531)+~P1(f332(f332(f233(x81531),f332(x81534,x81536)),x81535))+~P1(f332(f332(f334(x81532),x81536),x81533))+P1(f332(f332(f233(x81531),f332(f332(f48(x81532,x81531),x81533),x81534)),x81535))
% 52.62/52.42 [8410]~P25(x84102,x84105,x84106,x84101)+~P1(f332(f64(x84102),x84104))+~P1(f332(f64(x84102),x84103))+~E(f332(f332(f104(f853(x84102,a839)),x84103),x84104),f180(f853(x84102,a839)))+E(f332(x84101,f332(f332(f103(f853(x84102,a839)),x84103),x84104)),f332(f75(x84105,x84105,x84105,f332(x84101,x84103)),f332(x84101,x84104)))
% 52.62/52.42 [9062]~P112(x90621)+~P108(x90621)+~P1(f332(f332(f279(x90621),x90622),x90625))+~P1(f332(f332(f279(x90621),x90622),f332(f332(f82(x90621),x90623),x90626)))+P1(f332(f332(f279(x90621),x90622),f332(f332(f82(x90621),f332(f332(f3(x90621),x90623),f332(f332(f83(x90621),x90624),x90625))),x90626)))
% 52.62/52.42 [9063]~P112(x90631)+~P108(x90631)+~P1(f332(f332(f279(x90631),x90632),x90635))+~P1(f332(f332(f279(x90631),x90632),f332(f332(f82(x90631),x90633),x90636)))+P1(f332(f332(f279(x90631),x90632),f332(f332(f82(x90631),f332(f332(f3(x90631),x90633),f332(f332(f83(x90631),x90634),x90635))),x90636)))
% 52.62/52.42 [9222]~P112(x92221)+~P108(x92221)+~P1(f332(f332(f279(x92221),x92222),x92225))+P1(f332(f332(f279(x92221),x92222),f332(f332(f82(x92221),x92223),x92224)))+~P1(f332(f332(f279(x92221),x92222),f332(f332(f82(x92221),f332(f332(f3(x92221),x92223),f332(f332(f83(x92221),x92226),x92225))),x92224)))
% 52.62/52.42 [9223]~P112(x92231)+~P108(x92231)+~P1(f332(f332(f279(x92231),x92232),x92235))+P1(f332(f332(f279(x92231),x92232),f332(f332(f82(x92231),x92233),x92234)))+~P1(f332(f332(f279(x92231),x92232),f332(f332(f82(x92231),f332(f332(f3(x92231),x92233),f332(f332(f83(x92231),x92236),x92235))),x92234)))
% 52.62/52.42 [8703]E(x87031,x87032)+~P57(x87034,x87035,x87036,x87033,x87037)+~E(f332(x87033,x87031),f332(x87033,x87032))+~P1(f332(f332(f334(x87035),x87032),x87037))+~P1(f332(f332(f334(x87035),x87031),x87037))
% 52.62/52.42 [9953]~P14(x99531,x99537,x99536)+~P18(x99531,f853(x99535,a839),x99536,x99534)+P1(f332(f332(f334(x99531),f507(x99532,x99533,x99534,x99535,x99536,x99537,x99531)),x99537))+~P1(f332(f332(f334(f853(x99531,a839)),x99533),f332(f332(f62(x99531),x99537),x99536)))+P1(f332(f332(f334(f853(x99535,a839)),f332(f332(f47(x99531,f853(x99535,a839)),x99533),x99534)),x99532))
% 52.62/52.42 [10000]~P14(x100002,x100006,x100007)+~P18(x100002,f853(x100001,a839),x100007,x100004)+~P1(f332(f332(f334(f853(x100002,a839)),x100003),f332(f332(f62(x100002),x100006),x100007)))+~P1(f332(f332(f334(f853(x100001,a839)),f332(x100004,f507(x100005,x100003,x100004,x100001,x100007,x100006,x100002))),x100005))+P1(f332(f332(f334(f853(x100001,a839)),f332(f332(f47(x100002,f853(x100001,a839)),x100003),x100004)),x100005))
% 52.62/52.42 [8320]~P70(x83202)+~P31(x83201,x83205,x83208,x83204)+~E(x83203,f332(f75(x83205,x83202,x83201,x83206),x83208))+~E(x83207,f332(f303(x83201,x83205,x83208),x83204))+E(f332(f332(f11(x83201,x83202),x83203),x83204),f332(f332(f11(x83205,x83202),x83206),x83207))
% 52.62/52.42 [10003]~P70(x100032)+~P31(x100035,x100031,x100038,x100037)+~E(f332(x100036,f535(x100033,x100036,x100034,x100037,x100038,x100031,x100035,x100032)),f332(f332(f75(x100031,x100032,x100035,x100033),x100038),f535(x100033,x100036,x100034,x100037,x100038,x100031,x100035,x100032)))+~E(x100034,f332(f303(x100035,x100031,x100038),x100037))+E(f332(f332(f11(x100031,x100032),x100033),x100034),f332(f332(f11(x100035,x100032),x100036),x100037))
% 52.62/52.42 [10006]~P4(x100062)+~P31(x100061,x100065,x100068,x100064)+~E(x100067,f332(f303(x100061,x100065,x100068),x100064))+E(f332(f332(f8(x100061,x100062),x100063),x100064),f332(f332(f8(x100065,x100062),x100066),x100067))+P1(f332(f332(f334(x100061),f633(x100066,x100063,x100067,x100064,x100068,x100065,x100061,x100062)),x100064))
% 52.62/52.42 [10007]~P70(x100072)+~P31(x100071,x100075,x100078,x100074)+~E(x100077,f332(f303(x100071,x100075,x100078),x100074))+E(f332(f332(f11(x100071,x100072),x100073),x100074),f332(f332(f11(x100075,x100072),x100076),x100077))+P1(f332(f332(f334(x100071),f535(x100076,x100073,x100077,x100074,x100078,x100075,x100071,x100072)),x100074))
% 52.62/52.42 [10011]~P4(x100112)+~P31(x100115,x100111,x100118,x100117)+~E(x100114,f332(f303(x100115,x100111,x100118),x100117))+~E(f332(x100116,f633(x100113,x100116,x100114,x100117,x100118,x100111,x100115,x100112)),f332(x100113,f332(x100118,f633(x100113,x100116,x100114,x100117,x100118,x100111,x100115,x100112))))+E(f332(f332(f8(x100111,x100112),x100113),x100114),f332(f332(f8(x100115,x100112),x100116),x100117))
% 52.62/52.42 [9411]~E(f332(f181(f846(x94112)),x94115),f332(f181(f846(x94111)),x94113))+~E(f332(f181(f846(x94112)),x94114),f332(f181(f846(x94111)),x94113))+~E(f332(f332(f332(f74(x94111,f849(x94112)),f166(x94111,x94112,f332(f332(f167(x94111,x94112),x94113),x94114))),x94116),f332(f227(x94112),x94117)),f332(f332(f332(f74(x94111,f849(x94112)),f166(x94111,x94112,f332(f332(f167(x94111,x94112),x94113),x94115))),x94116),f332(f227(x94112),x94118)))+E(f166(x94111,x94112,f332(f332(f167(x94111,x94112),x94113),x94114)),f166(x94111,x94112,f332(f332(f167(x94111,x94112),x94113),x94115)))+P1(f332(f332(f334(x94111),x94116),f332(f158(x94111),x94113)))
% 52.62/52.42 [9506]~P29(x95066,x95062,x95065,x95067,x95068,x95061)+~P1(f332(f64(x95062),x95064))+~P1(f332(f64(x95062),x95063))+~E(f332(f332(f104(f853(x95062,a839)),x95063),x95064),f180(f853(x95062,a839)))+E(f332(x95061,f332(f332(f103(f853(x95062,a839)),x95063),x95064)),f332(f332(x95065,f332(x95061,x95063)),f332(x95061,x95064)))
% 52.62/52.42 [9897]~P29(x98978,x98972,x98975,x98977,x98976,x98971)+~E(f332(x98976,f578(x98974,x98973,x98971,x98976,x98977,x98975,x98972)),x98977)+~P1(f332(f64(x98972),x98973))+~P1(f332(f64(x98972),x98974))+E(f332(x98971,f332(f332(f103(f853(x98972,a839)),x98973),x98974)),f332(f332(x98975,f332(x98971,x98973)),f332(x98971,x98974)))
% 52.62/52.42 [9958]~P29(x99588,x99582,x99585,x99587,x99586,x99581)+~P1(f332(f64(x99582),x99583))+~P1(f332(f64(x99582),x99584))+E(f332(x99581,f332(f332(f103(f853(x99582,a839)),x99583),x99584)),f332(f332(x99585,f332(x99581,x99583)),f332(x99581,x99584)))+P1(f332(f332(f334(x99582),f578(x99584,x99583,x99581,x99586,x99587,x99585,x99582)),f332(f332(f104(f853(x99582,a839)),x99583),x99584)))
% 52.62/52.42 [9649]~P14(x96494,x96498,x96495)+~P14(x96491,x96499,x96493)+~P19(x96491,x96494,f853(x96492,a839),x96493,x96495,x96497)+P18(x96491,f853(x96492,a839),x96493,f332(f332(f10(f853(x96494,f853(x96492,a839)),f853(x96492,a839),x96491),f332(f47(x96494,f853(x96492,a839)),f332(f277(x96494,x96494,x96495),f332(f332(f302(x96494),x96496),f180(f853(x96494,a839)))))),x96497))+~P1(f332(f332(f334(x96494),x96496),x96498))
% 52.62/52.42 [4932]~P122(x49322)+~P127(x49322)+~P138(x49322)+~P105(x49322)+E(x49321,f2(x49322))+~E(f332(f332(f242(x49322),x49321),x49323),f2(x49322))
% 52.62/52.42 [4933]~P122(x49332)+~P127(x49332)+~P138(x49332)+~P105(x49332)+~E(x49331,f2(a845))+~E(f332(f332(f242(x49332),x49333),x49331),f2(x49332))
% 52.62/52.42 [6377]~P82(x63771)+~E(x63773,f2(x63771))+~E(x63772,f2(x63771))+E(f332(f332(f82(x63771),x63772),x63773),f2(x63771))+~P1(f332(f332(f232(x63771),f2(x63771)),x63773))+~P1(f332(f332(f232(x63771),f2(x63771)),x63772))
% 52.62/52.42 [8749]E(x87491,f2(a845))+~E(x87492,f332(f332(f82(a845),f332(f332(f83(a845),f332(f240(a845,a845),x87493)),x87491)),f332(f250(a845,a845),x87493)))+P1(f332(f56(x87492,x87491),x87493))+~P1(f332(f332(f232(a845),f332(f250(a845,a845),x87493)),f2(a845)))+P1(f332(f332(f233(a845),f2(a845)),x87491))+~P1(f332(f332(f233(a845),x87491),f332(f250(a845,a845),x87493)))
% 52.62/52.42 [8761]~E(f332(f240(a845,a845),x87613),f2(a845))+~E(x87611,f332(f332(f82(a845),f332(f332(f83(a845),f332(f240(a845,a845),x87613)),x87612)),f332(f250(a845,a845),x87613)))+P1(f332(f56(x87611,x87612),x87613))+~P1(f332(f332(f232(a845),f332(f250(a845,a845),x87613)),f2(a845)))+P1(f332(f332(f233(a845),f2(a845)),x87612))+~P1(f332(f332(f233(a845),x87612),f332(f250(a845,a845),x87613)))
% 52.62/52.42 [8768]E(x87681,f2(a845))+~E(x87682,f332(f332(f82(a845),f332(f332(f83(a845),f332(f240(a845,a845),x87683)),x87681)),f332(f250(a845,a845),x87683)))+P1(f332(f56(x87682,x87681),x87683))+~P1(f332(f332(f233(a845),f2(a845)),x87681))+~P1(f332(f332(f232(a845),f2(a845)),f332(f250(a845,a845),x87683)))+~P1(f332(f332(f233(a845),f332(f250(a845,a845),x87683)),x87681))
% 52.62/52.42 [8782]~E(f332(f240(a845,a845),x87823),f2(a845))+~E(x87821,f332(f332(f82(a845),f332(f332(f83(a845),f332(f240(a845,a845),x87823)),x87822)),f332(f250(a845,a845),x87823)))+P1(f332(f56(x87821,x87822),x87823))+~P1(f332(f332(f233(a845),f2(a845)),x87822))+~P1(f332(f332(f232(a845),f2(a845)),f332(f250(a845,a845),x87823)))+~P1(f332(f332(f233(a845),f332(f250(a845,a845),x87823)),x87822))
% 52.62/52.42 [6777]~P93(x67772)+E(x67771,f180(f853(x67772,a839)))+E(x67773,f180(f853(x67772,a839)))+~P1(f332(f64(x67772),x67771))+~P1(f332(f64(x67772),x67773))+E(f15(x67772,f332(f332(f103(f853(x67772,a839)),x67773),x67771)),f332(f332(f103(x67772),f15(x67772,x67773)),f15(x67772,x67771)))
% 52.62/52.42 [6778]~P100(x67782)+E(x67781,f180(f853(x67782,a839)))+E(x67783,f180(f853(x67782,a839)))+~P1(f332(f64(x67782),x67781))+~P1(f332(f64(x67782),x67783))+E(f16(x67782,f332(f332(f103(f853(x67782,a839)),x67783),x67781)),f332(f332(f179(x67782),f16(x67782,x67783)),f16(x67782,x67781)))
% 52.62/52.42 [6779]~P100(x67792)+E(x67791,f180(f853(x67792,a839)))+E(x67793,f180(f853(x67792,a839)))+~P1(f332(f64(x67792),x67791))+~P1(f332(f64(x67792),x67793))+E(f17(x67792,f332(f332(f103(f853(x67792,a839)),x67793),x67791)),f332(f332(f236(x67792),f17(x67792,x67793)),f17(x67792,x67791)))
% 52.62/52.42 [6780]~P93(x67802)+E(x67801,f180(f853(x67802,a839)))+E(x67803,f180(f853(x67802,a839)))+~P1(f332(f64(x67802),x67801))+~P1(f332(f64(x67802),x67803))+E(f12(x67802,f332(f332(f103(f853(x67802,a839)),x67803),x67801)),f332(f332(f104(x67802),f12(x67802,x67803)),f12(x67802,x67801)))
% 52.62/52.42 [7444]~P91(x74442)+E(x74441,f180(f853(x74442,a839)))+E(x74443,f180(f853(x74442,a839)))+~P1(f332(f64(x74442),x74441))+~P1(f332(f64(x74442),x74443))+E(f332(f332(f83(x74442),f332(f66(x74442,f83(x74442)),x74443)),f332(f66(x74442,f83(x74442)),x74441)),f332(f66(x74442,f83(x74442)),f332(f332(f103(f853(x74442,a839)),x74443),x74441)))
% 52.62/52.42 [7609]~P100(x76092)+E(x76091,f180(f853(x76092,a839)))+E(x76093,f180(f853(x76092,a839)))+~P1(f332(f64(x76092),x76091))+~P1(f332(f64(x76092),x76093))+E(f332(f332(f179(x76092),f13(x76092,f179(x76092),x76093)),f13(x76092,f179(x76092),x76091)),f13(x76092,f179(x76092),f332(f332(f103(f853(x76092,a839)),x76093),x76091)))
% 52.62/52.42 [7610]~P100(x76102)+E(x76101,f180(f853(x76102,a839)))+E(x76103,f180(f853(x76102,a839)))+~P1(f332(f64(x76102),x76101))+~P1(f332(f64(x76102),x76103))+E(f332(f332(f236(x76102),f14(x76102,f236(x76102),x76103)),f14(x76102,f236(x76102),x76101)),f14(x76102,f236(x76102),f332(f332(f103(f853(x76102,a839)),x76103),x76101)))
% 52.62/52.42 [8618]~P1(f332(x86181,x86183))+P1(f332(x86181,f355(x86181,x86182)))+P1(f332(x86181,f351(x86181,x86182)))+~P1(f332(f332(f233(a1),f2(a1)),x86182))+~P1(f332(f332(f334(a1),x86183),f295(a1,f80(a1),x86182)))+P1(f332(x86181,f332(f332(f3(a1),f351(x86181,x86182)),f332(f332(f83(a1),f353(x86181,x86182)),x86182))))
% 52.62/52.42 [8880]~P1(f332(x88801,x88803))+~P1(f332(x88801,f351(x88801,x88802)))+P1(f332(x88801,f355(x88801,x88802)))+~P1(f332(f332(f233(a1),f2(a1)),x88802))+~P1(f332(f332(f334(a1),x88803),f295(a1,f80(a1),x88802)))+~P1(f332(x88801,f332(f332(f3(a1),f351(x88801,x88802)),f332(f332(f83(a1),f353(x88801,x88802)),x88802))))
% 52.62/52.42 [10031]~P97(x100312)+E(x100311,f180(f853(x100312,a839)))+E(x100313,f180(f853(x100312,a839)))+~P1(f332(f64(x100312),x100311))+~P1(f332(f64(x100312),x100313))+E(f12(x100312,f332(f256(x100312),f332(f332(f10(f853(x100312,a839),a839,x100312),f89(x100312)),f332(f332(f10(f853(x100312,f853(x100312,a839)),f853(x100312,a839),x100312),f332(f10(f853(x100312,a839),a839,x100312),f89(x100312))),f332(f332(f9(x100312,f853(x100312,f853(x100312,a839)),f853(x100312,f853(x100312,a839))),f332(f332(f10(f853(x100312,f853(f853(x100312,a839),f853(x100312,a839))),f853(f853(x100312,f853(x100312,a839)),f853(x100312,f853(x100312,a839))),x100312),f20(x100312,f853(x100312,a839),f853(x100312,a839))),f332(f332(f10(f853(x100312,f853(x100312,f853(a839,a839))),f853(x100312,f853(f853(x100312,a839),f853(x100312,a839))),x100312),f332(f10(f853(x100312,f853(a839,a839)),f853(f853(x100312,a839),f853(x100312,a839)),x100312),f20(x100312,a839,a839))),f332(f332(f10(f853(x100312,f853(x100312,a839)),f853(x100312,f853(x100312,f853(a839,a839))),x100312),f332(f10(f853(x100312,a839),f853(x100312,f853(a839,a839)),x100312),f332(f10(a839,f853(a839,a839),x100312),a330))),f332(f332(f9(x100312,f853(x100312,f853(x100312,x100312)),f853(x100312,f853(x100312,a839))),f332(f332(f10(f853(f853(x100312,x100312),f853(x100312,a839)),f853(f853(x100312,f853(x100312,x100312)),f853(x100312,f853(x100312,a839))),x100312),f10(f853(x100312,x100312),f853(x100312,a839),x100312)),f332(f332(f10(f853(x100312,a839),f853(f853(x100312,x100312),f853(x100312,a839)),x100312),f10(x100312,a839,x100312)),a329))),f103(x100312)))))),f332(f332(f9(x100312,f853(x100312,a839),f853(x100312,a839)),f332(f332(f10(f853(a839,a839),f853(f853(x100312,a839),f853(x100312,a839)),x100312),f10(a839,a839,x100312)),f332(f332(f10(a839,f853(a839,a839),x100312),a330),f332(f332(f9(x100312,f853(x100312,a839),a839),f334(x100312)),x100313)))),f332(f332(f9(x100312,f853(x100312,a839),a839),f334(x100312)),x100311))))))),f332(f332(f103(x100312),f12(x100312,x100313)),f12(x100312,x100311)))
% 52.62/52.42 [10032]~P97(x100322)+E(x100321,f180(f853(x100322,a839)))+E(x100323,f180(f853(x100322,a839)))+~P1(f332(f64(x100322),x100321))+~P1(f332(f64(x100322),x100323))+E(f15(x100322,f332(f256(x100322),f332(f332(f10(f853(x100322,a839),a839,x100322),f89(x100322)),f332(f332(f10(f853(x100322,f853(x100322,a839)),f853(x100322,a839),x100322),f332(f10(f853(x100322,a839),a839,x100322),f89(x100322))),f332(f332(f9(x100322,f853(x100322,f853(x100322,a839)),f853(x100322,f853(x100322,a839))),f332(f332(f10(f853(x100322,f853(f853(x100322,a839),f853(x100322,a839))),f853(f853(x100322,f853(x100322,a839)),f853(x100322,f853(x100322,a839))),x100322),f20(x100322,f853(x100322,a839),f853(x100322,a839))),f332(f332(f10(f853(x100322,f853(x100322,f853(a839,a839))),f853(x100322,f853(f853(x100322,a839),f853(x100322,a839))),x100322),f332(f10(f853(x100322,f853(a839,a839)),f853(f853(x100322,a839),f853(x100322,a839)),x100322),f20(x100322,a839,a839))),f332(f332(f10(f853(x100322,f853(x100322,a839)),f853(x100322,f853(x100322,f853(a839,a839))),x100322),f332(f10(f853(x100322,a839),f853(x100322,f853(a839,a839)),x100322),f332(f10(a839,f853(a839,a839),x100322),a330))),f332(f332(f9(x100322,f853(x100322,f853(x100322,x100322)),f853(x100322,f853(x100322,a839))),f332(f332(f10(f853(f853(x100322,x100322),f853(x100322,a839)),f853(f853(x100322,f853(x100322,x100322)),f853(x100322,f853(x100322,a839))),x100322),f10(f853(x100322,x100322),f853(x100322,a839),x100322)),f332(f332(f10(f853(x100322,a839),f853(f853(x100322,x100322),f853(x100322,a839)),x100322),f10(x100322,a839,x100322)),a329))),f104(x100322)))))),f332(f332(f9(x100322,f853(x100322,a839),f853(x100322,a839)),f332(f332(f10(f853(a839,a839),f853(f853(x100322,a839),f853(x100322,a839)),x100322),f10(a839,a839,x100322)),f332(f332(f10(a839,f853(a839,a839),x100322),a330),f332(f332(f9(x100322,f853(x100322,a839),a839),f334(x100322)),x100323)))),f332(f332(f9(x100322,f853(x100322,a839),a839),f334(x100322)),x100321))))))),f332(f332(f104(x100322),f15(x100322,x100323)),f15(x100322,x100321)))
% 52.62/52.42 [10033]~P100(x100332)+E(x100331,f180(f853(x100332,a839)))+E(x100333,f180(f853(x100332,a839)))+~P1(f332(f64(x100332),x100331))+~P1(f332(f64(x100332),x100333))+E(f13(x100332,f179(x100332),f332(f256(x100332),f332(f332(f10(f853(x100332,a839),a839,x100332),f89(x100332)),f332(f332(f10(f853(x100332,f853(x100332,a839)),f853(x100332,a839),x100332),f332(f10(f853(x100332,a839),a839,x100332),f89(x100332))),f332(f332(f9(x100332,f853(x100332,f853(x100332,a839)),f853(x100332,f853(x100332,a839))),f332(f332(f10(f853(x100332,f853(f853(x100332,a839),f853(x100332,a839))),f853(f853(x100332,f853(x100332,a839)),f853(x100332,f853(x100332,a839))),x100332),f20(x100332,f853(x100332,a839),f853(x100332,a839))),f332(f332(f10(f853(x100332,f853(x100332,f853(a839,a839))),f853(x100332,f853(f853(x100332,a839),f853(x100332,a839))),x100332),f332(f10(f853(x100332,f853(a839,a839)),f853(f853(x100332,a839),f853(x100332,a839)),x100332),f20(x100332,a839,a839))),f332(f332(f10(f853(x100332,f853(x100332,a839)),f853(x100332,f853(x100332,f853(a839,a839))),x100332),f332(f10(f853(x100332,a839),f853(x100332,f853(a839,a839)),x100332),f332(f10(a839,f853(a839,a839),x100332),a330))),f332(f332(f9(x100332,f853(x100332,f853(x100332,x100332)),f853(x100332,f853(x100332,a839))),f332(f332(f10(f853(f853(x100332,x100332),f853(x100332,a839)),f853(f853(x100332,f853(x100332,x100332)),f853(x100332,f853(x100332,a839))),x100332),f10(f853(x100332,x100332),f853(x100332,a839),x100332)),f332(f332(f10(f853(x100332,a839),f853(f853(x100332,x100332),f853(x100332,a839)),x100332),f10(x100332,a839,x100332)),a329))),f236(x100332)))))),f332(f332(f9(x100332,f853(x100332,a839),f853(x100332,a839)),f332(f332(f10(f853(a839,a839),f853(f853(x100332,a839),f853(x100332,a839)),x100332),f10(a839,a839,x100332)),f332(f332(f10(a839,f853(a839,a839),x100332),a330),f332(f332(f9(x100332,f853(x100332,a839),a839),f334(x100332)),x100333)))),f332(f332(f9(x100332,f853(x100332,a839),a839),f334(x100332)),x100331))))))),f332(f332(f236(x100332),f13(x100332,f179(x100332),x100333)),f13(x100332,f179(x100332),x100331)))
% 52.62/52.42 [10034]~P100(x100342)+E(x100341,f180(f853(x100342,a839)))+E(x100343,f180(f853(x100342,a839)))+~P1(f332(f64(x100342),x100341))+~P1(f332(f64(x100342),x100343))+E(f14(x100342,f236(x100342),f332(f256(x100342),f332(f332(f10(f853(x100342,a839),a839,x100342),f89(x100342)),f332(f332(f10(f853(x100342,f853(x100342,a839)),f853(x100342,a839),x100342),f332(f10(f853(x100342,a839),a839,x100342),f89(x100342))),f332(f332(f9(x100342,f853(x100342,f853(x100342,a839)),f853(x100342,f853(x100342,a839))),f332(f332(f10(f853(x100342,f853(f853(x100342,a839),f853(x100342,a839))),f853(f853(x100342,f853(x100342,a839)),f853(x100342,f853(x100342,a839))),x100342),f20(x100342,f853(x100342,a839),f853(x100342,a839))),f332(f332(f10(f853(x100342,f853(x100342,f853(a839,a839))),f853(x100342,f853(f853(x100342,a839),f853(x100342,a839))),x100342),f332(f10(f853(x100342,f853(a839,a839)),f853(f853(x100342,a839),f853(x100342,a839)),x100342),f20(x100342,a839,a839))),f332(f332(f10(f853(x100342,f853(x100342,a839)),f853(x100342,f853(x100342,f853(a839,a839))),x100342),f332(f10(f853(x100342,a839),f853(x100342,f853(a839,a839)),x100342),f332(f10(a839,f853(a839,a839),x100342),a330))),f332(f332(f9(x100342,f853(x100342,f853(x100342,x100342)),f853(x100342,f853(x100342,a839))),f332(f332(f10(f853(f853(x100342,x100342),f853(x100342,a839)),f853(f853(x100342,f853(x100342,x100342)),f853(x100342,f853(x100342,a839))),x100342),f10(f853(x100342,x100342),f853(x100342,a839),x100342)),f332(f332(f10(f853(x100342,a839),f853(f853(x100342,x100342),f853(x100342,a839)),x100342),f10(x100342,a839,x100342)),a329))),f179(x100342)))))),f332(f332(f9(x100342,f853(x100342,a839),f853(x100342,a839)),f332(f332(f10(f853(a839,a839),f853(f853(x100342,a839),f853(x100342,a839)),x100342),f10(a839,a839,x100342)),f332(f332(f10(a839,f853(a839,a839),x100342),a330),f332(f332(f9(x100342,f853(x100342,a839),a839),f334(x100342)),x100343)))),f332(f332(f9(x100342,f853(x100342,a839),a839),f334(x100342)),x100341))))))),f332(f332(f179(x100342),f14(x100342,f236(x100342),x100343)),f14(x100342,f236(x100342),x100341)))
% 52.62/52.42 [7109]~P117(x71093)+E(x71091,x71092)+~E(f332(f332(f242(x71093),x71091),x71094),f332(f332(f242(x71093),x71092),x71094))+~P1(f332(f332(f232(x71093),f2(x71093)),x71092))+~P1(f332(f332(f232(x71093),f2(x71093)),x71091))+~P1(f332(f332(f233(a845),f2(a845)),x71094))
% 52.62/52.42 [7964]~P64(x79641)+~P89(x79641)+P1(f332(f332(f233(x79641),x79642),f2(x79641)))+P1(f332(f332(f233(x79641),f2(x79641)),x79642))+P1(f332(f332(f233(x79641),f332(f332(f283(x79641),x79643),x79642)),f332(f106(x79641),x79644)))+~P1(f332(f332(f233(x79641),f2(x79641)),f332(f106(x79641),x79644)))
% 52.62/52.42 [7965]~P64(x79651)+~P89(x79651)+P1(f332(f332(f233(x79651),x79652),f2(x79651)))+P1(f332(f332(f233(x79651),f2(x79651)),x79652))+P1(f332(f332(f232(x79651),f332(f332(f283(x79651),x79653),x79652)),f332(f106(x79651),x79654)))+~P1(f332(f332(f232(x79651),f2(x79651)),f332(f106(x79651),x79654)))
% 52.62/52.42 [8199]~P64(x81991)+~P89(x81991)+P1(f332(f332(f233(x81991),x81992),f2(x81991)))+P1(f332(f332(f233(x81991),f2(x81991)),x81992))+~P1(f332(f332(f233(x81991),f332(f332(f283(x81991),x81994),x81992)),f332(f106(x81991),x81993)))+P1(f332(f332(f233(x81991),f2(x81991)),f332(f106(x81991),x81993)))
% 52.62/52.42 [8200]~P64(x82001)+~P89(x82001)+P1(f332(f332(f233(x82001),x82002),f2(x82001)))+P1(f332(f332(f233(x82001),f2(x82001)),x82002))+~P1(f332(f332(f232(x82001),f332(f332(f283(x82001),x82004),x82002)),f332(f106(x82001),x82003)))+P1(f332(f332(f232(x82001),f2(x82001)),f332(f106(x82001),x82003)))
% 52.62/52.42 [7404]~P100(x74042)+E(x74041,f180(f853(x74042,a839)))+~P1(f332(f64(x74042),x74041))+~P1(f332(f332(f334(x74042),x74044),x74041))+P1(f332(f332(f233(x74042),x74043),x74044))+~P1(f332(f332(f233(x74042),x74043),f332(f66(x74042,f236(x74042)),x74041)))
% 52.62/52.42 [7405]~P100(x74052)+E(x74051,f180(f853(x74052,a839)))+~P1(f332(f64(x74052),x74051))+~P1(f332(f332(f334(x74052),x74054),x74051))+P1(f332(f332(f232(x74052),x74053),x74054))+~P1(f332(f332(f232(x74052),x74053),f332(f66(x74052,f236(x74052)),x74051)))
% 52.62/52.42 [7406]~P98(x74062)+E(x74061,f180(f853(x74062,a839)))+~P1(f332(f64(x74062),x74061))+~P1(f332(f332(f334(x74062),x74064),x74061))+P1(f332(f332(f232(x74062),x74063),x74064))+~P1(f332(f332(f232(x74062),x74063),f332(f66(x74062,f104(x74062)),x74061)))
% 52.62/52.42 [7914]~P64(x79141)+~P89(x79141)+P1(f332(f332(f233(x79141),f332(f106(x79141),x79142)),f2(x79141)))+~P1(f332(f332(f233(x79141),x79143),f2(x79141)))+P1(f332(f332(f233(x79141),f2(x79141)),f332(f106(x79141),x79142)))+P1(f332(f332(f233(x79141),x79143),f332(f332(f283(x79141),x79144),f332(f106(x79141),x79142))))
% 52.62/52.42 [7915]~P64(x79151)+~P89(x79151)+P1(f332(f332(f233(x79151),f332(f106(x79151),x79152)),f2(x79151)))+~P1(f332(f332(f232(x79151),x79153),f2(x79151)))+P1(f332(f332(f233(x79151),f2(x79151)),f332(f106(x79151),x79152)))+P1(f332(f332(f232(x79151),x79153),f332(f332(f283(x79151),x79154),f332(f106(x79151),x79152))))
% 52.62/52.42 [7925]~P64(x79251)+~P89(x79251)+P1(f332(f332(f233(x79251),x79252),f2(x79251)))+~P1(f332(f332(f233(x79251),f332(f106(x79251),x79253)),f2(x79251)))+P1(f332(f332(f233(x79251),f2(x79251)),x79252))+P1(f332(f332(f233(x79251),f332(f106(x79251),x79253)),f332(f332(f283(x79251),x79254),x79252)))
% 52.62/52.42 [7926]~P64(x79261)+~P89(x79261)+P1(f332(f332(f233(x79261),x79262),f2(x79261)))+~P1(f332(f332(f232(x79261),f332(f106(x79261),x79263)),f2(x79261)))+P1(f332(f332(f233(x79261),f2(x79261)),x79262))+P1(f332(f332(f232(x79261),f332(f106(x79261),x79263)),f332(f332(f283(x79261),x79264),x79262)))
% 52.62/52.42 [8073]~P64(x80731)+~P89(x80731)+P1(f332(f332(f233(x80731),x80732),f2(x80731)))+P1(f332(f332(f233(x80731),f332(f106(x80731),x80733)),f2(x80731)))+P1(f332(f332(f233(x80731),f2(x80731)),x80732))+~P1(f332(f332(f233(x80731),f332(f106(x80731),x80733)),f332(f332(f283(x80731),x80734),x80732)))
% 52.62/52.42 [8074]~P64(x80741)+~P89(x80741)+P1(f332(f332(f233(x80741),x80742),f2(x80741)))+P1(f332(f332(f232(x80741),f332(f106(x80741),x80743)),f2(x80741)))+P1(f332(f332(f233(x80741),f2(x80741)),x80742))+~P1(f332(f332(f232(x80741),f332(f106(x80741),x80743)),f332(f332(f283(x80741),x80744),x80742)))
% 52.62/52.42 [8147]~P64(x81471)+~P89(x81471)+P1(f332(f332(f233(x81471),x81472),f2(x81471)))+P1(f332(f332(f233(x81471),f332(f106(x81471),x81473)),f2(x81471)))+P1(f332(f332(f233(x81471),f2(x81471)),f332(f106(x81471),x81473)))+~P1(f332(f332(f233(x81471),x81472),f332(f332(f283(x81471),x81474),f332(f106(x81471),x81473))))
% 52.62/52.42 [8148]~P64(x81481)+~P89(x81481)+P1(f332(f332(f232(x81481),x81482),f2(x81481)))+P1(f332(f332(f233(x81481),f332(f106(x81481),x81483)),f2(x81481)))+P1(f332(f332(f233(x81481),f2(x81481)),f332(f106(x81481),x81483)))+~P1(f332(f332(f232(x81481),x81482),f332(f332(f283(x81481),x81484),f332(f106(x81481),x81483))))
% 52.62/52.42 [8339]~P64(x83391)+~P89(x83391)+~P1(f332(f332(f233(x83391),x83393),f2(x83391)))+P1(f332(f332(f233(x83391),f2(x83391)),f332(f106(x83391),x83392)))+~P1(f332(f332(f233(x83391),x83394),f332(f332(f83(x83391),x83393),f332(f106(x83391),x83392))))+P1(f332(f332(f233(x83391),x83393),f332(f332(f283(x83391),x83394),f332(f106(x83391),x83392))))
% 52.62/52.42 [8340]~P64(x83401)+~P89(x83401)+~P1(f332(f332(f232(x83401),x83403),f2(x83401)))+P1(f332(f332(f233(x83401),f2(x83401)),f332(f106(x83401),x83402)))+~P1(f332(f332(f232(x83401),x83404),f332(f332(f83(x83401),x83403),f332(f106(x83401),x83402))))+P1(f332(f332(f232(x83401),x83403),f332(f332(f283(x83401),x83404),f332(f106(x83401),x83402))))
% 52.62/52.42 [8509]~P64(x85091)+~P89(x85091)+~P1(f332(f332(f233(x85091),f332(f106(x85091),x85092)),f2(x85091)))+P1(f332(f332(f233(x85091),f2(x85091)),f332(f106(x85091),x85092)))+~P1(f332(f332(f233(x85091),x85094),f332(f332(f83(x85091),x85093),f332(f106(x85091),x85092))))+P1(f332(f332(f233(x85091),x85093),f332(f332(f283(x85091),x85094),f332(f106(x85091),x85092))))
% 52.62/52.42 [8510]~P64(x85101)+~P89(x85101)+~P1(f332(f332(f233(x85101),f332(f106(x85101),x85102)),f2(x85101)))+P1(f332(f332(f233(x85101),f2(x85101)),f332(f106(x85101),x85102)))+~P1(f332(f332(f233(x85101),x85104),f332(f332(f283(x85101),x85103),f332(f106(x85101),x85102))))+P1(f332(f332(f233(x85101),x85103),f332(f332(f83(x85101),x85104),f332(f106(x85101),x85102))))
% 52.62/52.42 [8511]~P64(x85111)+~P89(x85111)+~P1(f332(f332(f233(x85111),f332(f106(x85111),x85112)),f2(x85111)))+P1(f332(f332(f233(x85111),f2(x85111)),f332(f106(x85111),x85112)))+~P1(f332(f332(f232(x85111),x85114),f332(f332(f83(x85111),x85113),f332(f106(x85111),x85112))))+P1(f332(f332(f232(x85111),x85113),f332(f332(f283(x85111),x85114),f332(f106(x85111),x85112))))
% 52.62/52.42 [8512]~P64(x85121)+~P89(x85121)+~P1(f332(f332(f233(x85121),f332(f106(x85121),x85122)),f2(x85121)))+P1(f332(f332(f233(x85121),f2(x85121)),f332(f106(x85121),x85122)))+~P1(f332(f332(f232(x85121),x85124),f332(f332(f283(x85121),x85123),f332(f106(x85121),x85122))))+P1(f332(f332(f232(x85121),x85123),f332(f332(f83(x85121),x85124),f332(f106(x85121),x85122))))
% 52.62/52.42 [7300]E(x73001,f2(a1))+E(f332(f332(f44(a1),x73002),x73001),x73003)+~P1(f332(f332(f232(a1),x73004),f2(a1)))+~E(x73002,f332(f332(f82(a1),f332(f332(f83(a1),x73001),x73003)),x73004))+P1(f332(f332(f233(a1),f2(a1)),x73001))+~P1(f332(f332(f233(a1),x73001),x73004))
% 52.62/52.42 [7316]E(f53(a1,x73162,x73161),x73163)+E(x73161,f2(a1))+~P1(f332(f332(f232(a1),x73163),f2(a1)))+~E(x73162,f332(f332(f82(a1),f332(f332(f83(a1),x73161),x73164)),x73163))+P1(f332(f332(f233(a1),f2(a1)),x73161))+~P1(f332(f332(f233(a1),x73161),x73163))
% 52.62/52.42 [7443]E(x74431,f2(a1))+E(f332(f332(f44(a1),x74432),x74431),x74433)+~E(x74432,f332(f332(f82(a1),f332(f332(f83(a1),x74431),x74433)),x74434))+~P1(f332(f332(f233(a1),f2(a1)),x74431))+~P1(f332(f332(f232(a1),f2(a1)),x74434))+~P1(f332(f332(f233(a1),x74434),x74431))
% 52.62/52.42 [7468]E(f53(a1,x74682,x74681),x74683)+E(x74681,f2(a1))+~E(x74682,f332(f332(f82(a1),f332(f332(f83(a1),x74681),x74684)),x74683))+~P1(f332(f332(f233(a1),f2(a1)),x74681))+~P1(f332(f332(f232(a1),f2(a1)),x74683))+~P1(f332(f332(f233(a1),x74683),x74681))
% 52.62/52.42 [7613]~P100(x76132)+E(x76131,f180(f853(x76132,a839)))+~P1(f332(f64(x76132),x76131))+~P1(f332(f332(f233(x76132),x76134),x76133))+~P1(f332(f332(f334(x76132),x76134),x76131))+P1(f332(f332(f233(x76132),f332(f66(x76132,f236(x76132)),x76131)),x76133))
% 52.62/52.42 [7614]~P100(x76142)+E(x76141,f180(f853(x76142,a839)))+~P1(f332(f64(x76142),x76141))+~P1(f332(f332(f232(x76142),x76144),x76143))+~P1(f332(f332(f334(x76142),x76144),x76141))+P1(f332(f332(f232(x76142),f332(f66(x76142,f236(x76142)),x76141)),x76143))
% 52.62/52.42 [8177]~P1(f332(f332(f232(a1),x81774),f2(a1)))+~E(x81771,f332(f332(f82(a1),f332(f332(f83(a1),x81772),x81773)),x81774))+~P1(f332(f332(f232(a1),f2(a1)),x81774))+~P1(f332(f332(f233(a1),x81774),x81772))+~P1(f332(f332(f233(a1),x81772),x81774))+P1(f332(f57(x81771,x81772),f332(f332(f241(a1,a1),x81773),x81774)))
% 52.62/52.42 [8296]~P64(x82961)+~P89(x82961)+P1(f332(f332(f233(x82961),f332(f106(x82961),x82962)),f2(x82961)))+~P1(f332(f332(f233(x82961),f2(x82961)),x82964))+P1(f332(f332(f233(x82961),f2(x82961)),f332(f106(x82961),x82962)))+P1(f332(f332(f233(x82961),f332(f332(f283(x82961),x82963),f332(f106(x82961),x82962))),x82964))
% 52.62/52.42 [8297]~P64(x82971)+~P89(x82971)+P1(f332(f332(f233(x82971),f332(f106(x82971),x82972)),f2(x82971)))+~P1(f332(f332(f232(x82971),f2(x82971)),x82974))+P1(f332(f332(f233(x82971),f2(x82971)),f332(f106(x82971),x82972)))+P1(f332(f332(f232(x82971),f332(f332(f283(x82971),x82973),f332(f106(x82971),x82972))),x82974))
% 52.62/52.42 [8413]~P64(x84131)+~P89(x84131)+~P1(f332(f332(f233(x84131),x84132),f2(x84131)))+P1(f332(f332(f233(x84131),f2(x84131)),x84132))+~P1(f332(f332(f233(x84131),f332(f106(x84131),x84134)),f332(f332(f283(x84131),x84133),x84132)))+P1(f332(f332(f233(x84131),x84133),f332(f332(f83(x84131),f332(f106(x84131),x84134)),x84132)))
% 52.62/52.42 [8414]~P64(x84141)+~P89(x84141)+~P1(f332(f332(f233(x84141),x84142),f2(x84141)))+P1(f332(f332(f233(x84141),f2(x84141)),x84142))+~P1(f332(f332(f232(x84141),f332(f106(x84141),x84144)),f332(f332(f283(x84141),x84143),x84142)))+P1(f332(f332(f232(x84141),x84143),f332(f332(f83(x84141),f332(f106(x84141),x84144)),x84142)))
% 52.62/52.42 [8454]~P64(x84541)+~P89(x84541)+~P1(f332(f332(f233(x84541),x84542),f2(x84541)))+P1(f332(f332(f233(x84541),f2(x84541)),x84542))+P1(f332(f332(f233(x84541),f332(f106(x84541),x84543)),f332(f332(f283(x84541),x84544),x84542)))+~P1(f332(f332(f233(x84541),x84544),f332(f332(f83(x84541),f332(f106(x84541),x84543)),x84542)))
% 52.62/52.42 [8455]~P64(x84551)+~P89(x84551)+~P1(f332(f332(f233(x84551),x84552),f2(x84551)))+P1(f332(f332(f233(x84551),f2(x84551)),x84552))+P1(f332(f332(f232(x84551),f332(f106(x84551),x84553)),f332(f332(f283(x84551),x84554),x84552)))+~P1(f332(f332(f232(x84551),x84554),f332(f332(f83(x84551),f332(f106(x84551),x84553)),x84552)))
% 52.62/52.42 [8540]~P64(x85401)+~P89(x85401)+P1(f332(f332(f233(x85401),f332(f106(x85401),x85403)),f2(x85401)))+P1(f332(f332(f233(x85401),f2(x85401)),x85402))+P1(f332(f332(f233(x85401),f2(x85401)),f332(f106(x85401),x85403)))+~P1(f332(f332(f233(x85401),f332(f332(f283(x85401),x85404),f332(f106(x85401),x85403))),x85402))
% 52.62/52.42 [8541]~P64(x85411)+~P89(x85411)+P1(f332(f332(f233(x85411),f332(f106(x85411),x85413)),f2(x85411)))+P1(f332(f332(f232(x85411),f2(x85411)),x85412))+P1(f332(f332(f233(x85411),f2(x85411)),f332(f106(x85411),x85413)))+~P1(f332(f332(f232(x85411),f332(f332(f283(x85411),x85414),f332(f106(x85411),x85413))),x85412))
% 52.62/52.42 [8580]~P64(x85801)+~P89(x85801)+~P1(f332(f332(f233(x85801),f332(f106(x85801),x85803)),f2(x85801)))+P1(f332(f332(f233(x85801),f2(x85801)),x85802))+P1(f332(f332(f233(x85801),f332(f106(x85801),x85803)),f332(f332(f283(x85801),x85804),x85802)))+~P1(f332(f332(f233(x85801),x85804),f332(f332(f83(x85801),f332(f106(x85801),x85803)),x85802)))
% 52.62/52.42 [8581]~P64(x85811)+~P89(x85811)+~P1(f332(f332(f232(x85811),f332(f106(x85811),x85813)),f2(x85811)))+P1(f332(f332(f233(x85811),f2(x85811)),x85812))+P1(f332(f332(f232(x85811),f332(f106(x85811),x85813)),f332(f332(f283(x85811),x85814),x85812)))+~P1(f332(f332(f232(x85811),x85814),f332(f332(f83(x85811),f332(f106(x85811),x85813)),x85812)))
% 52.62/52.42 [8588]~P64(x85881)+~P89(x85881)+P1(f332(f332(f233(x85881),x85882),f2(x85881)))+P1(f332(f332(f233(x85881),f332(f332(f283(x85881),x85883),x85882)),f332(f106(x85881),x85884)))+~P1(f332(f332(f233(x85881),f2(x85881)),f332(f106(x85881),x85884)))+~P1(f332(f332(f233(x85881),x85883),f332(f332(f83(x85881),f332(f106(x85881),x85884)),x85882)))
% 52.62/52.42 [8589]~P64(x85891)+~P89(x85891)+P1(f332(f332(f233(x85891),x85892),f2(x85891)))+P1(f332(f332(f232(x85891),f332(f332(f283(x85891),x85893),x85892)),f332(f106(x85891),x85894)))+~P1(f332(f332(f232(x85891),f2(x85891)),f332(f106(x85891),x85894)))+~P1(f332(f332(f232(x85891),x85893),f332(f332(f83(x85891),f332(f106(x85891),x85894)),x85892)))
% 52.62/52.42 [8606]~P64(x86061)+~P89(x86061)+P1(f332(f332(f233(x86061),f332(f106(x86061),x86062)),f2(x86061)))+~P1(f332(f332(f233(x86061),f2(x86061)),x86064))+~P1(f332(f332(f233(x86061),x86063),f332(f332(f83(x86061),x86064),f332(f106(x86061),x86062))))+P1(f332(f332(f233(x86061),f332(f332(f283(x86061),x86063),f332(f106(x86061),x86062))),x86064))
% 52.62/52.42 [8607]~P64(x86071)+~P89(x86071)+P1(f332(f332(f233(x86071),f332(f106(x86071),x86072)),f2(x86071)))+~P1(f332(f332(f232(x86071),f2(x86071)),x86074))+~P1(f332(f332(f232(x86071),x86073),f332(f332(f83(x86071),x86074),f332(f106(x86071),x86072))))+P1(f332(f332(f232(x86071),f332(f332(f283(x86071),x86073),f332(f106(x86071),x86072))),x86074))
% 52.62/52.42 [8688]~P64(x86881)+~P89(x86881)+P1(f332(f332(f233(x86881),f332(f106(x86881),x86882)),f2(x86881)))+~P1(f332(f332(f233(x86881),x86883),f2(x86881)))+P1(f332(f332(f233(x86881),x86883),f332(f332(f283(x86881),x86884),f332(f106(x86881),x86882))))+~P1(f332(f332(f233(x86881),f332(f332(f83(x86881),x86883),f332(f106(x86881),x86882))),x86884))
% 52.62/52.42 [8689]~P64(x86891)+~P89(x86891)+P1(f332(f332(f233(x86891),f332(f106(x86891),x86892)),f2(x86891)))+~P1(f332(f332(f232(x86891),x86893),f2(x86891)))+P1(f332(f332(f232(x86891),x86893),f332(f332(f283(x86891),x86894),f332(f106(x86891),x86892))))+~P1(f332(f332(f232(x86891),f332(f332(f83(x86891),x86893),f332(f106(x86891),x86892))),x86894))
% 52.62/52.42 [8786]~P64(x87861)+~P89(x87861)+~P1(f332(f332(f233(x87861),f2(x87861)),x87864))+P1(f332(f332(f233(x87861),f2(x87861)),f332(f106(x87861),x87862)))+~P1(f332(f332(f233(x87861),f332(f332(f83(x87861),x87864),f332(f106(x87861),x87862))),x87863))+P1(f332(f332(f233(x87861),f332(f332(f283(x87861),x87863),f332(f106(x87861),x87862))),x87864))
% 52.62/52.42 [8787]~P64(x87871)+~P89(x87871)+~P1(f332(f332(f232(x87871),f2(x87871)),x87874))+P1(f332(f332(f233(x87871),f2(x87871)),f332(f106(x87871),x87872)))+~P1(f332(f332(f232(x87871),f332(f332(f83(x87871),x87874),f332(f106(x87871),x87872))),x87873))+P1(f332(f332(f232(x87871),f332(f332(f283(x87871),x87873),f332(f106(x87871),x87872))),x87874))
% 52.62/52.42 [8835]~P64(x88351)+~P89(x88351)+~P1(f332(f332(f233(x88351),x88352),f2(x88351)))+P1(f332(f332(f233(x88351),x88352),f332(f332(f283(x88351),x88353),f332(f106(x88351),x88354))))+~P1(f332(f332(f233(x88351),x88353),f332(f332(f83(x88351),x88352),f332(f106(x88351),x88354))))+~P1(f332(f332(f233(x88351),f332(f332(f83(x88351),x88352),f332(f106(x88351),x88354))),x88353))
% 52.62/52.42 [8836]~P64(x88361)+~P89(x88361)+~P1(f332(f332(f232(x88361),x88362),f2(x88361)))+P1(f332(f332(f232(x88361),x88362),f332(f332(f283(x88361),x88363),f332(f106(x88361),x88364))))+~P1(f332(f332(f232(x88361),x88363),f332(f332(f83(x88361),x88362),f332(f106(x88361),x88364))))+~P1(f332(f332(f232(x88361),f332(f332(f83(x88361),x88362),f332(f106(x88361),x88364))),x88363))
% 52.62/52.42 [8860]~P64(x88601)+~P89(x88601)+~P1(f332(f332(f233(x88601),f332(f106(x88601),x88602)),f2(x88601)))+P1(f332(f332(f233(x88601),f2(x88601)),f332(f106(x88601),x88602)))+~P1(f332(f332(f233(x88601),f332(f332(f283(x88601),x88604),f332(f106(x88601),x88602))),x88603))+P1(f332(f332(f233(x88601),f332(f332(f83(x88601),x88603),f332(f106(x88601),x88602))),x88604))
% 52.62/52.42 [8861]~P64(x88611)+~P89(x88611)+~P1(f332(f332(f233(x88611),f332(f106(x88611),x88612)),f2(x88611)))+P1(f332(f332(f233(x88611),f2(x88611)),f332(f106(x88611),x88612)))+~P1(f332(f332(f233(x88611),f332(f332(f83(x88611),x88614),f332(f106(x88611),x88612))),x88613))+P1(f332(f332(f233(x88611),f332(f332(f283(x88611),x88613),f332(f106(x88611),x88612))),x88614))
% 52.62/52.42 [8862]~P64(x88621)+~P89(x88621)+~P1(f332(f332(f233(x88621),f332(f106(x88621),x88622)),f2(x88621)))+P1(f332(f332(f233(x88621),f2(x88621)),f332(f106(x88621),x88622)))+~P1(f332(f332(f232(x88621),f332(f332(f283(x88621),x88624),f332(f106(x88621),x88622))),x88623))+P1(f332(f332(f232(x88621),f332(f332(f83(x88621),x88623),f332(f106(x88621),x88622))),x88624))
% 52.62/52.42 [8863]~P64(x88631)+~P89(x88631)+~P1(f332(f332(f233(x88631),f332(f106(x88631),x88632)),f2(x88631)))+P1(f332(f332(f233(x88631),f2(x88631)),f332(f106(x88631),x88632)))+~P1(f332(f332(f232(x88631),f332(f332(f83(x88631),x88634),f332(f106(x88631),x88632))),x88633))+P1(f332(f332(f232(x88631),f332(f332(f283(x88631),x88633),f332(f106(x88631),x88632))),x88634))
% 52.62/52.42 [8940]~P64(x89401)+~P89(x89401)+~P1(f332(f332(f233(x89401),f332(f106(x89401),x89404)),f2(x89401)))+P1(f332(f332(f233(x89401),x89402),f332(f332(f283(x89401),x89403),f332(f106(x89401),x89404))))+~P1(f332(f332(f233(x89401),x89403),f332(f332(f83(x89401),x89402),f332(f106(x89401),x89404))))+~P1(f332(f332(f233(x89401),f332(f332(f83(x89401),x89402),f332(f106(x89401),x89404))),x89403))
% 52.62/52.42 [8941]~P64(x89411)+~P89(x89411)+~P1(f332(f332(f233(x89411),f332(f106(x89411),x89414)),f2(x89411)))+P1(f332(f332(f232(x89411),x89412),f332(f332(f283(x89411),x89413),f332(f106(x89411),x89414))))+~P1(f332(f332(f232(x89411),x89413),f332(f332(f83(x89411),x89412),f332(f106(x89411),x89414))))+~P1(f332(f332(f232(x89411),f332(f332(f83(x89411),x89412),f332(f106(x89411),x89414))),x89413))
% 52.62/52.42 [8980]~P64(x89801)+~P89(x89801)+~P1(f332(f332(f233(x89801),f2(x89801)),x89804))+~P1(f332(f332(f233(x89801),x89802),f332(f332(f83(x89801),x89804),f332(f106(x89801),x89803))))+~P1(f332(f332(f233(x89801),f332(f332(f83(x89801),x89804),f332(f106(x89801),x89803))),x89802))+P1(f332(f332(f233(x89801),f332(f332(f283(x89801),x89802),f332(f106(x89801),x89803))),x89804))
% 52.62/52.42 [8981]~P64(x89811)+~P89(x89811)+~P1(f332(f332(f232(x89811),f2(x89811)),x89814))+~P1(f332(f332(f232(x89811),x89812),f332(f332(f83(x89811),x89814),f332(f106(x89811),x89813))))+~P1(f332(f332(f232(x89811),f332(f332(f83(x89811),x89814),f332(f106(x89811),x89813))),x89812))+P1(f332(f332(f232(x89811),f332(f332(f283(x89811),x89812),f332(f106(x89811),x89813))),x89814))
% 52.62/52.42 [9017]~P64(x90171)+~P89(x90171)+~P1(f332(f332(f233(x90171),f332(f106(x90171),x90173)),f2(x90171)))+~P1(f332(f332(f233(x90171),x90172),f332(f332(f83(x90171),x90174),f332(f106(x90171),x90173))))+~P1(f332(f332(f233(x90171),f332(f332(f83(x90171),x90174),f332(f106(x90171),x90173))),x90172))+P1(f332(f332(f233(x90171),f332(f332(f283(x90171),x90172),f332(f106(x90171),x90173))),x90174))
% 52.62/52.42 [9018]~P64(x90181)+~P89(x90181)+~P1(f332(f332(f233(x90181),f332(f106(x90181),x90183)),f2(x90181)))+~P1(f332(f332(f232(x90181),x90182),f332(f332(f83(x90181),x90184),f332(f106(x90181),x90183))))+~P1(f332(f332(f232(x90181),f332(f332(f83(x90181),x90184),f332(f106(x90181),x90183))),x90182))+P1(f332(f332(f232(x90181),f332(f332(f283(x90181),x90182),f332(f106(x90181),x90183))),x90184))
% 52.62/52.42 [8745]~P64(x87451)+~P89(x87451)+~P1(f332(f332(f233(x87451),x87452),f2(x87451)))+~P1(f332(f332(f233(x87451),f332(f332(f283(x87451),x87454),x87452)),f332(f106(x87451),x87453)))+P1(f332(f332(f233(x87451),f2(x87451)),x87452))+P1(f332(f332(f233(x87451),f332(f332(f83(x87451),f332(f106(x87451),x87453)),x87452)),x87454))
% 52.62/52.42 [8746]~P64(x87461)+~P89(x87461)+~P1(f332(f332(f233(x87461),x87462),f2(x87461)))+~P1(f332(f332(f232(x87461),f332(f332(f283(x87461),x87464),x87462)),f332(f106(x87461),x87463)))+P1(f332(f332(f233(x87461),f2(x87461)),x87462))+P1(f332(f332(f232(x87461),f332(f332(f83(x87461),f332(f106(x87461),x87463)),x87462)),x87464))
% 52.62/52.42 [8838]~P64(x88381)+~P89(x88381)+~P1(f332(f332(f233(x88381),x88382),f2(x88381)))+P1(f332(f332(f233(x88381),f2(x88381)),x88382))+P1(f332(f332(f233(x88381),f332(f332(f283(x88381),x88383),x88382)),f332(f106(x88381),x88384)))+~P1(f332(f332(f233(x88381),f332(f332(f83(x88381),f332(f106(x88381),x88384)),x88382)),x88383))
% 52.62/52.42 [8839]~P64(x88391)+~P89(x88391)+~P1(f332(f332(f233(x88391),x88392),f2(x88391)))+P1(f332(f332(f233(x88391),f2(x88391)),x88392))+P1(f332(f332(f232(x88391),f332(f332(f283(x88391),x88393),x88392)),f332(f106(x88391),x88394)))+~P1(f332(f332(f232(x88391),f332(f332(f83(x88391),f332(f106(x88391),x88394)),x88392)),x88393))
% 52.62/52.42 [8877]~P64(x88771)+~P89(x88771)+P1(f332(f332(f233(x88771),x88772),f2(x88771)))+~P1(f332(f332(f233(x88771),f332(f106(x88771),x88773)),f2(x88771)))+P1(f332(f332(f233(x88771),f332(f106(x88771),x88773)),f332(f332(f283(x88771),x88774),x88772)))+~P1(f332(f332(f233(x88771),f332(f332(f83(x88771),f332(f106(x88771),x88773)),x88772)),x88774))
% 52.62/52.42 [8878]~P64(x88781)+~P89(x88781)+P1(f332(f332(f233(x88781),x88782),f2(x88781)))+~P1(f332(f332(f232(x88781),f332(f106(x88781),x88783)),f2(x88781)))+P1(f332(f332(f232(x88781),f332(f106(x88781),x88783)),f332(f332(f283(x88781),x88784),x88782)))+~P1(f332(f332(f232(x88781),f332(f332(f83(x88781),f332(f106(x88781),x88783)),x88782)),x88784))
% 52.62/52.42 [8894]~P64(x88941)+~P89(x88941)+P1(f332(f332(f233(x88941),f2(x88941)),x88942))+P1(f332(f332(f233(x88941),f332(f332(f283(x88941),x88943),x88942)),f332(f106(x88941),x88944)))+~P1(f332(f332(f233(x88941),f2(x88941)),f332(f106(x88941),x88944)))+~P1(f332(f332(f233(x88941),f332(f332(f83(x88941),f332(f106(x88941),x88944)),x88942)),x88943))
% 52.62/52.42 [8895]~P64(x88951)+~P89(x88951)+P1(f332(f332(f233(x88951),f2(x88951)),x88952))+P1(f332(f332(f232(x88951),f332(f332(f283(x88951),x88953),x88952)),f332(f106(x88951),x88954)))+~P1(f332(f332(f232(x88951),f2(x88951)),f332(f106(x88951),x88954)))+~P1(f332(f332(f232(x88951),f332(f332(f83(x88951),f332(f106(x88951),x88954)),x88952)),x88953))
% 52.62/52.42 [9048]~P64(x90481)+~P89(x90481)+~P1(f332(f332(f233(x90481),x90484),f2(x90481)))+P1(f332(f332(f233(x90481),f332(f106(x90481),x90482)),f332(f332(f283(x90481),x90483),x90484)))+~P1(f332(f332(f233(x90481),x90483),f332(f332(f83(x90481),f332(f106(x90481),x90482)),x90484)))+~P1(f332(f332(f233(x90481),f332(f332(f83(x90481),f332(f106(x90481),x90482)),x90484)),x90483))
% 52.62/52.42 [9049]~P64(x90491)+~P89(x90491)+~P1(f332(f332(f233(x90491),x90494),f2(x90491)))+P1(f332(f332(f232(x90491),f332(f106(x90491),x90492)),f332(f332(f283(x90491),x90493),x90494)))+~P1(f332(f332(f232(x90491),x90493),f332(f332(f83(x90491),f332(f106(x90491),x90492)),x90494)))+~P1(f332(f332(f232(x90491),f332(f332(f83(x90491),f332(f106(x90491),x90492)),x90494)),x90493))
% 52.62/52.42 [9078]~P64(x90781)+~P89(x90781)+~P1(f332(f332(f233(x90781),x90783),f2(x90781)))+P1(f332(f332(f233(x90781),f332(f332(f283(x90781),x90782),x90783)),f332(f106(x90781),x90784)))+~P1(f332(f332(f233(x90781),x90782),f332(f332(f83(x90781),f332(f106(x90781),x90784)),x90783)))+~P1(f332(f332(f233(x90781),f332(f332(f83(x90781),f332(f106(x90781),x90784)),x90783)),x90782))
% 52.62/52.42 [9079]~P64(x90791)+~P89(x90791)+~P1(f332(f332(f233(x90791),x90793),f2(x90791)))+P1(f332(f332(f232(x90791),f332(f332(f283(x90791),x90792),x90793)),f332(f106(x90791),x90794)))+~P1(f332(f332(f232(x90791),x90792),f332(f332(f83(x90791),f332(f106(x90791),x90794)),x90793)))+~P1(f332(f332(f232(x90791),f332(f332(f83(x90791),f332(f106(x90791),x90794)),x90793)),x90792))
% 52.62/52.42 [9097]~P64(x90971)+~P89(x90971)+~P1(f332(f332(f233(x90971),f332(f106(x90971),x90972)),f2(x90971)))+P1(f332(f332(f233(x90971),f332(f106(x90971),x90972)),f332(f332(f283(x90971),x90973),x90974)))+~P1(f332(f332(f233(x90971),x90973),f332(f332(f83(x90971),f332(f106(x90971),x90972)),x90974)))+~P1(f332(f332(f233(x90971),f332(f332(f83(x90971),f332(f106(x90971),x90972)),x90974)),x90973))
% 52.62/52.42 [9098]~P64(x90981)+~P89(x90981)+~P1(f332(f332(f232(x90981),f332(f106(x90981),x90982)),f2(x90981)))+P1(f332(f332(f232(x90981),f332(f106(x90981),x90982)),f332(f332(f283(x90981),x90983),x90984)))+~P1(f332(f332(f232(x90981),x90983),f332(f332(f83(x90981),f332(f106(x90981),x90982)),x90984)))+~P1(f332(f332(f232(x90981),f332(f332(f83(x90981),f332(f106(x90981),x90982)),x90984)),x90983))
% 52.62/52.42 [9103]~P64(x91031)+~P89(x91031)+P1(f332(f332(f233(x91031),f332(f332(f283(x91031),x91032),x91033)),f332(f106(x91031),x91034)))+~P1(f332(f332(f233(x91031),f2(x91031)),f332(f106(x91031),x91034)))+~P1(f332(f332(f233(x91031),x91032),f332(f332(f83(x91031),f332(f106(x91031),x91034)),x91033)))+~P1(f332(f332(f233(x91031),f332(f332(f83(x91031),f332(f106(x91031),x91034)),x91033)),x91032))
% 52.62/52.42 [9104]~P64(x91041)+~P89(x91041)+P1(f332(f332(f232(x91041),f332(f332(f283(x91041),x91042),x91043)),f332(f106(x91041),x91044)))+~P1(f332(f332(f232(x91041),f2(x91041)),f332(f106(x91041),x91044)))+~P1(f332(f332(f232(x91041),x91042),f332(f332(f83(x91041),f332(f106(x91041),x91044)),x91043)))+~P1(f332(f332(f232(x91041),f332(f332(f83(x91041),f332(f106(x91041),x91044)),x91043)),x91042))
% 52.62/52.42 [5938]~P73(x59382)+~P127(x59382)+~E(f332(x59383,x59385),f2(x59382))+E(f332(f332(f11(x59381,x59382),x59383),x59384),f2(x59382))+~P1(f332(f64(x59381),x59384))+~P1(f332(f332(f334(x59381),x59385),x59384))
% 52.62/52.42 [8343]~P99(x83431)+P1(f332(f332(f233(f853(x83431,a839)),f295(x83431,x83432,x83433)),f295(x83431,x83434,x83435)))+~P1(f332(f332(f233(x83431),x83433),x83435))+~P1(f332(f332(f232(x83431),x83434),x83432))+~P1(f332(f332(f232(x83431),x83434),x83435))+~P1(f332(f332(f232(x83431),x83433),x83435))
% 52.62/52.42 [8344]~P99(x83441)+P1(f332(f332(f233(f853(x83441,a839)),f295(x83441,x83442,x83443)),f295(x83441,x83444,x83445)))+~P1(f332(f332(f233(x83441),x83444),x83442))+~P1(f332(f332(f232(x83441),x83443),x83445))+~P1(f332(f332(f232(x83441),x83444),x83445))+~P1(f332(f332(f232(x83441),x83444),x83442))
% 52.62/52.42 [9126]P59(x91262,x91263,x91264,x91261)+E(x91261,f180(f853(x91262,a839)))+~P1(f332(f64(x91262),x91264))+~P1(f332(f64(x91262),x91261))+~P1(f332(f332(x91263,f537(x91261,x91264,x91263,x91262)),x91265))+~P1(f332(f332(f334(x91262),x91265),x91261))
% 52.62/52.42 [9252]~E(x92523,x92525)+~P4(x92521)+~P70(x92521)+~P40(x92523)+E(f332(f332(f8(a1,x92521),x92522),x92523),f332(f332(f8(a1,x92521),x92524),x92525))+P1(f332(f332(f232(a1),f2(a1)),f384(x92522,x92524,x92523,x92525,x92521)))
% 52.62/52.42 [9253]~E(x92533,x92535)+~P4(x92531)+~P70(x92531)+~P40(x92533)+E(f332(f332(f11(a1,x92531),x92532),x92533),f332(f332(f11(a1,x92531),x92534),x92535))+P1(f332(f332(f232(a1),f2(a1)),f533(x92532,x92534,x92533,x92535,x92531)))
% 52.62/52.42 [9418]~E(x94185,x94183)+~P4(x94181)+~P70(x94181)+~P40(x94185)+~E(f332(x94182,f384(x94184,x94182,x94185,x94183,x94181)),f332(x94184,f384(x94184,x94182,x94185,x94183,x94181)))+E(f332(f332(f8(a1,x94181),x94182),x94183),f332(f332(f8(a1,x94181),x94184),x94185))
% 52.62/52.42 [9419]~E(x94195,x94193)+~P4(x94191)+~P70(x94191)+~P40(x94195)+~E(f332(x94192,f533(x94194,x94192,x94195,x94193,x94191)),f332(x94194,f533(x94194,x94192,x94195,x94193,x94191)))+E(f332(f332(f11(a1,x94191),x94192),x94193),f332(f332(f11(a1,x94191),x94194),x94195))
% 52.62/52.42 [9503]~P78(x95033)+E(f332(x95031,x95032),f2(x95033))+~E(f332(f332(f8(x95034,x95033),x95031),x95035),f2(x95033))+~P1(f332(f64(x95034),x95035))+P1(f332(f332(f334(x95034),f457(x95032,x95031,x95035,x95034,x95033)),x95035))+~P1(f332(f332(f334(x95034),x95032),x95035))
% 52.62/52.42 [9625]~P78(x96253)+E(f332(x96251,x96252),f2(x96253))+~E(f332(f332(f8(x96254,x96253),x96251),x96255),f2(x96253))+~P1(f332(f64(x96254),x96255))+~P1(f332(f332(f334(x96254),x96252),x96255))+~P1(f332(f332(f232(x96253),f2(x96253)),f332(x96251,f457(x96252,x96251,x96255,x96254,x96253))))
% 52.62/52.42 [8256]~P123(x82561)+~P1(f332(f332(f232(x82561),f2(x82561)),x82563))+~P1(f332(f332(f233(x82561),x82563),x82565))+~P1(f332(f332(f233(x82561),x82562),x82564))+~P1(f332(f332(f233(x82561),f2(x82561)),x82564))+P1(f332(f332(f233(x82561),f332(f332(f83(x82561),x82562),x82563)),f332(f332(f83(x82561),x82564),x82565)))
% 52.62/52.42 [8257]~P123(x82571)+~P1(f332(f332(f232(x82571),f2(x82571)),x82573))+~P1(f332(f332(f232(x82571),f2(x82571)),x82572))+~P1(f332(f332(f233(x82571),x82573),x82575))+~P1(f332(f332(f233(x82571),x82572),x82574))+P1(f332(f332(f233(x82571),f332(f332(f83(x82571),x82572),x82573)),f332(f332(f83(x82571),x82574),x82575)))
% 52.62/52.42 [8258]~P123(x82581)+~P1(f332(f332(f232(x82581),x82582),x82584))+~P1(f332(f332(f232(x82581),f2(x82581)),x82583))+~P1(f332(f332(f233(x82581),x82583),x82585))+~P1(f332(f332(f233(x82581),f2(x82581)),x82582))+P1(f332(f332(f233(x82581),f332(f332(f83(x82581),x82582),x82583)),f332(f332(f83(x82581),x82584),x82585)))
% 52.62/52.42 [8259]~P123(x82591)+~P1(f332(f332(f232(x82591),x82593),x82595))+~P1(f332(f332(f232(x82591),f2(x82591)),x82592))+~P1(f332(f332(f233(x82591),x82592),x82594))+~P1(f332(f332(f233(x82591),f2(x82591)),x82593))+P1(f332(f332(f233(x82591),f332(f332(f83(x82591),x82592),x82593)),f332(f332(f83(x82591),x82594),x82595)))
% 52.62/52.42 [8260]~P65(x82601)+~P1(f332(f332(f232(x82601),x82602),x82604))+~P1(f332(f332(f233(x82601),x82605),x82603))+~P1(f332(f332(f233(x82601),f2(x82601)),x82605))+~P1(f332(f332(f233(x82601),f2(x82601)),x82602))+P1(f332(f332(f233(x82601),f332(f332(f283(x82601),x82602),x82603)),f332(f332(f283(x82601),x82604),x82605)))
% 52.62/52.42 [8261]~P65(x82611)+~P1(f332(f332(f232(x82611),x82615),x82613))+~P1(f332(f332(f232(x82611),f2(x82611)),x82612))+~P1(f332(f332(f233(x82611),x82612),x82614))+~P1(f332(f332(f233(x82611),f2(x82611)),x82615))+P1(f332(f332(f233(x82611),f332(f332(f283(x82611),x82612),x82613)),f332(f332(f283(x82611),x82614),x82615)))
% 52.62/52.42 [8262]~P131(x82621)+~P1(f332(f332(f232(x82621),x82623),x82625))+~P1(f332(f332(f232(x82621),x82622),x82624))+~P1(f332(f332(f232(x82621),f2(x82621)),x82623))+~P1(f332(f332(f232(x82621),f2(x82621)),x82624))+P1(f332(f332(f232(x82621),f332(f332(f83(x82621),x82622),x82623)),f332(f332(f83(x82621),x82624),x82625)))
% 52.62/52.42 [8263]~P131(x82631)+~P1(f332(f332(f232(x82631),x82633),x82635))+~P1(f332(f332(f232(x82631),x82632),x82634))+~P1(f332(f332(f232(x82631),f2(x82631)),x82633))+~P1(f332(f332(f232(x82631),f2(x82631)),x82632))+P1(f332(f332(f232(x82631),f332(f332(f83(x82631),x82632),x82633)),f332(f332(f83(x82631),x82634),x82635)))
% 52.62/52.42 [8264]~P65(x82641)+~P1(f332(f332(f233(x82641),f2(x82641)),x82645))+~P1(f332(f332(f232(x82641),x82645),x82643))+~P1(f332(f332(f232(x82641),x82642),x82644))+~P1(f332(f332(f232(x82641),f2(x82641)),x82642))+P1(f332(f332(f232(x82641),f332(f332(f283(x82641),x82642),x82643)),f332(f332(f283(x82641),x82644),x82645)))
% 52.62/52.42 [9540]~P4(x95405)+~P81(x95405)+E(x95401,f180(f853(x95402,a839)))+~P1(f332(f64(x95402),x95401))+P1(f332(f332(f334(x95402),f489(x95403,x95404,x95401,x95402,x95405)),x95401))+P1(f332(f332(f233(x95405),f332(f332(f8(x95402,x95405),x95404),x95401)),f332(f332(f8(x95402,x95405),x95403),x95401)))
% 52.62/52.42 [9645]~P4(x96451)+~P79(x96451)+~P1(f332(f64(x96452),x96455))+~P1(f332(f332(f232(x96451),f2(x96451)),f332(x96453,f444(x96453,x96454,x96455,x96452,x96451))))+P1(f332(f332(f232(x96451),f332(f332(f8(x96452,x96451),x96453),x96454)),f332(f332(f8(x96452,x96451),x96453),x96455)))+~P1(f332(f332(f232(f853(x96452,a839)),x96454),x96455))
% 52.62/52.42 [9812]~P4(x98123)+~P81(x98123)+E(x98121,f180(f853(x98122,a839)))+~P1(f332(f64(x98122),x98121))+~P1(f332(f332(f233(x98123),f332(x98124,f489(x98125,x98124,x98121,x98122,x98123))),f332(x98125,f489(x98125,x98124,x98121,x98122,x98123))))+P1(f332(f332(f233(x98123),f332(f332(f8(x98122,x98123),x98124),x98121)),f332(f332(f8(x98122,x98123),x98125),x98121)))
% 52.62/52.42 [6969]~P23(x69692,x69695,x69694)+E(x69691,f180(f853(x69692,a839)))+E(x69693,f180(f853(x69692,a839)))+~P1(f332(f64(x69692),x69691))+~P1(f332(f64(x69692),x69693))+E(f332(x69694,f332(f332(f103(f853(x69692,a839)),x69693),x69691)),f332(f332(x69695,f332(x69694,x69693)),f332(x69694,x69691)))
% 52.62/52.42 [7578]~P141(x75781,x75783,x75784)+P1(f332(x75781,x75782))+~P1(f332(f332(f233(a1),x75784),f2(a1)))+~P1(f332(f332(f232(a1),x75785),f2(a1)))+~E(x75783,f332(f332(f82(a1),f332(f332(f83(a1),x75784),x75782)),x75785))+~P1(f332(f332(f233(a1),x75784),x75785))
% 52.62/52.42 [7579]~P140(x75791,x75793,x75794)+P1(f332(x75791,x75792))+~P1(f332(f332(f233(a1),x75794),f2(a1)))+~P1(f332(f332(f232(a1),x75792),f2(a1)))+~E(x75793,f332(f332(f82(a1),f332(f332(f83(a1),x75794),x75795)),x75792))+~P1(f332(f332(f233(a1),x75794),x75792))
% 52.62/52.42 [7622]~P141(x76221,x76223,x76224)+P1(f332(x76221,x76222))+~E(x76223,f332(f332(f82(a1),f332(f332(f83(a1),x76224),x76222)),x76225))+~P1(f332(f332(f233(a1),f2(a1)),x76224))+~P1(f332(f332(f232(a1),f2(a1)),x76225))+~P1(f332(f332(f233(a1),x76225),x76224))
% 52.62/52.42 [7623]~P140(x76231,x76233,x76234)+P1(f332(x76231,x76232))+~E(x76233,f332(f332(f82(a1),f332(f332(f83(a1),x76234),x76235)),x76232))+~P1(f332(f332(f233(a1),f2(a1)),x76234))+~P1(f332(f332(f232(a1),f2(a1)),x76232))+~P1(f332(f332(f233(a1),x76232),x76234))
% 52.62/52.42 [8548]P1(f332(f332(x85481,x85482),x85483))+~P1(f332(f332(x85481,f332(f332(f44(a1),x85484),x85485)),f53(a1,x85484,x85485)))+~P1(f332(f332(f233(a1),x85485),f2(a1)))+~P1(f332(f332(f232(a1),x85483),f2(a1)))+~E(x85484,f332(f332(f82(a1),f332(f332(f83(a1),x85485),x85482)),x85483))+~P1(f332(f332(f233(a1),x85485),x85483))
% 52.62/52.42 [8555]P1(f332(f332(x85551,x85552),x85553))+~P1(f332(f332(x85551,f332(f332(f44(a1),x85554),x85555)),f53(a1,x85554,x85555)))+~E(x85554,f332(f332(f82(a1),f332(f332(f83(a1),x85555),x85552)),x85553))+~P1(f332(f332(f233(a1),f2(a1)),x85555))+~P1(f332(f332(f232(a1),f2(a1)),x85553))+~P1(f332(f332(f233(a1),x85553),x85555))
% 52.62/52.42 [8774]E(x87741,x87742)+~P56(x87743,x87745,x87744)+~P1(f332(f332(f334(x87743),x87742),x87745))+~P1(f332(f332(f334(x87743),x87741),x87745))+P1(f332(f332(f334(f852(x87743,x87743)),f332(f332(f241(x87743,x87743),x87741),x87742)),x87744))+P1(f332(f332(f334(f852(x87743,x87743)),f332(f332(f241(x87743,x87743),x87742),x87741)),x87744))
% 52.62/52.42 [9569]~P4(x95695)+~P79(x95695)+~P1(f332(f64(x95691),x95694))+P1(f332(f332(f232(x95695),f332(f332(f8(x95691,x95695),x95692),x95693)),f332(f332(f8(x95691,x95695),x95692),x95694)))+~P1(f332(f332(f232(f853(x95691,a839)),x95693),x95694))+P1(f332(f332(f334(x95691),f444(x95692,x95693,x95694,x95691,x95695)),f332(f332(f3(f853(x95691,a839)),x95694),x95693)))
% 52.62/52.42 [9652]E(x96521,f180(f853(x96522,a839)))+~P1(f332(f64(x96522),x96523))+~P1(f332(f64(x96522),x96521))+P1(f332(f332(f334(f852(f853(x96522,a839),f853(x96522,a839))),f332(f332(f241(f853(x96522,a839),f853(x96522,a839)),x96523),x96521)),f325(x96522,x96524)))+~P1(f332(f332(f334(x96522),x96525),x96521))+~P1(f332(f332(f334(f852(x96522,x96522)),f332(f332(f241(x96522,x96522),f539(x96524,x96521,x96523,x96522)),x96525)),x96524))
% 52.62/52.42 [9653]E(x96531,f180(f853(x96532,a839)))+~P1(f332(f64(x96532),x96533))+~P1(f332(f64(x96532),x96531))+P1(f332(f332(f334(f852(f853(x96532,a839),f853(x96532,a839))),f332(f332(f241(f853(x96532,a839),f853(x96532,a839)),x96533),x96531)),f325(x96532,x96534)))+~P1(f332(f332(f334(x96532),x96535),x96531))+~P1(f332(f332(f334(f852(x96532,x96532)),f332(f332(f241(x96532,x96532),f624(x96534,x96531,x96533,x96532)),x96535)),x96534))
% 52.62/52.42 [9815]~P78(x98151)+~E(f332(f332(f8(x98155,x98151),x98152),x98156),x98154)+~P1(f332(f64(x98155),x98156))+P1(f332(f332(f334(x98155),f469(x98153,x98154,x98152,x98156,x98155,x98151)),x98156))+P1(f332(f332(f232(x98151),f332(x98152,x98153)),x98154))+~P1(f332(f332(f334(x98155),x98153),x98156))
% 52.62/52.42 [9869]~P78(x98691)+~E(f332(f332(f8(x98695,x98691),x98692),x98696),x98694)+~P1(f332(f64(x98695),x98696))+~P1(f332(f332(f334(x98695),x98693),x98696))+~P1(f332(f332(f232(x98691),f2(x98691)),f332(x98692,f469(x98693,x98694,x98692,x98696,x98695,x98691))))+P1(f332(f332(f232(x98691),f332(x98692,x98693)),x98694))
% 52.62/52.42 [9986]~E(x99865,x99868)+~E(x99864,x99867)+~P4(x99862)+~P102(x99861)+E(f332(f332(f8(x99861,x99862),x99863),f332(f294(x99861,x99864),x99865)),f332(f332(f8(x99861,x99862),x99866),f332(f294(x99861,x99867),x99868)))+P1(f332(f332(f232(x99861),x99864),f374(x99863,x99866,x99865,x99868,x99864,x99867,x99861,x99862)))
% 52.62/52.42 [10002]~E(x100027,x100024)+~E(x100028,x100025)+~P4(x100022)+~P102(x100021)+~E(f332(x100023,f374(x100026,x100023,x100028,x100025,x100027,x100024,x100021,x100022)),f332(x100026,f374(x100026,x100023,x100028,x100025,x100027,x100024,x100021,x100022)))+E(f332(f332(f8(x100021,x100022),x100023),f332(f294(x100021,x100024),x100025)),f332(f332(f8(x100021,x100022),x100026),f332(f294(x100021,x100027),x100028)))
% 52.62/52.42 [10005]~E(x100054,x100057)+~E(x100055,x100058)+~P4(x100052)+~P102(x100051)+E(f332(f332(f8(x100051,x100052),x100053),f332(f294(x100051,x100054),x100055)),f332(f332(f8(x100051,x100052),x100056),f332(f294(x100051,x100057),x100058)))+P1(f332(f332(f233(x100051),f374(x100053,x100056,x100055,x100058,x100054,x100057,x100051,x100052)),x100055))
% 52.62/52.42 [9657]~P14(x96575,x96579,x96576)+~P14(x96571,x965710,x96573)+~P19(x96571,x96575,f853(x96572,a839),x96573,x96576,x96578)+~P1(f332(f332(f334(x96575),x96577),x96579))+~P1(f332(f332(f334(x96571),x96574),x965710))+E(f332(f332(f47(x96571,f853(x96572,a839)),f332(f277(x96571,x96571,x96573),f332(f332(f302(x96571),x96574),f180(f853(x96571,a839))))),f332(f332(f10(f853(x96575,f853(x96572,a839)),f853(x96572,a839),x96571),f332(f47(x96575,f853(x96572,a839)),f332(f277(x96575,x96575,x96576),f332(f332(f302(x96575),x96577),f180(f853(x96575,a839)))))),x96578)),f332(f332(x96578,x96574),x96577))
% 52.62/52.42 [5463]~P100(x54633)+~P20(x54633,x54632)+~P20(x54633,x54631)+E(x54631,x54632)+~E(f332(f158(x54633),x54631),f332(f158(x54633),x54632))+~P1(f332(f127(x54633),x54632))+~P1(f332(f127(x54633),x54631))
% 52.62/52.42 [4816]~P122(x48162)+~P127(x48162)+~P138(x48162)+~P105(x48162)+~E(x48163,f2(x48162))+E(x48161,f2(a845))+E(f332(f332(f242(x48162),x48163),x48161),f2(x48162))
% 52.62/52.42 [9012]E(x90121,f2(a845))+~E(x90122,f332(f332(f82(a845),f332(f332(f83(a845),f332(f240(a845,a845),x90123)),x90121)),f332(f250(a845,a845),x90123)))+P1(f332(f56(x90122,x90121),x90123))+~P1(f332(f332(f232(a845),f332(f250(a845,a845),x90123)),f2(a845)))+~P1(f332(f332(f232(a845),f2(a845)),f332(f250(a845,a845),x90123)))+~P1(f332(f332(f233(a845),x90121),f332(f250(a845,a845),x90123)))+~P1(f332(f332(f233(a845),f332(f250(a845,a845),x90123)),x90121))
% 52.62/52.42 [9020]~E(f332(f240(a845,a845),x90203),f2(a845))+~E(x90201,f332(f332(f82(a845),f332(f332(f83(a845),f332(f240(a845,a845),x90203)),x90202)),f332(f250(a845,a845),x90203)))+P1(f332(f56(x90201,x90202),x90203))+~P1(f332(f332(f232(a845),f332(f250(a845,a845),x90203)),f2(a845)))+~P1(f332(f332(f232(a845),f2(a845)),f332(f250(a845,a845),x90203)))+~P1(f332(f332(f233(a845),x90202),f332(f250(a845,a845),x90203)))+~P1(f332(f332(f233(a845),f332(f250(a845,a845),x90203)),x90202))
% 52.62/52.42 [7456]~P93(x74562)+E(x74561,f180(f853(x74562,a839)))+E(x74563,f180(f853(x74562,a839)))+~P1(f332(f64(x74562),x74561))+~P1(f332(f64(x74562),x74563))+~E(f332(f332(f104(f853(x74562,a839)),x74563),x74561),f180(f853(x74562,a839)))+E(f15(x74562,f332(f332(f103(f853(x74562,a839)),x74563),x74561)),f332(f332(f103(x74562),f15(x74562,x74563)),f15(x74562,x74561)))
% 52.62/52.42 [7457]~P100(x74572)+E(x74571,f180(f853(x74572,a839)))+E(x74573,f180(f853(x74572,a839)))+~P1(f332(f64(x74572),x74571))+~P1(f332(f64(x74572),x74573))+~E(f332(f332(f104(f853(x74572,a839)),x74573),x74571),f180(f853(x74572,a839)))+E(f16(x74572,f332(f332(f103(f853(x74572,a839)),x74573),x74571)),f332(f332(f179(x74572),f16(x74572,x74573)),f16(x74572,x74571)))
% 52.62/52.42 [7458]~P100(x74582)+E(x74581,f180(f853(x74582,a839)))+E(x74583,f180(f853(x74582,a839)))+~P1(f332(f64(x74582),x74581))+~P1(f332(f64(x74582),x74583))+~E(f332(f332(f104(f853(x74582,a839)),x74583),x74581),f180(f853(x74582,a839)))+E(f17(x74582,f332(f332(f103(f853(x74582,a839)),x74583),x74581)),f332(f332(f236(x74582),f17(x74582,x74583)),f17(x74582,x74581)))
% 52.62/52.42 [7459]~P93(x74592)+E(x74591,f180(f853(x74592,a839)))+E(x74593,f180(f853(x74592,a839)))+~P1(f332(f64(x74592),x74591))+~P1(f332(f64(x74592),x74593))+~E(f332(f332(f104(f853(x74592,a839)),x74593),x74591),f180(f853(x74592,a839)))+E(f12(x74592,f332(f332(f103(f853(x74592,a839)),x74593),x74591)),f332(f332(f104(x74592),f12(x74592,x74593)),f12(x74592,x74591)))
% 52.62/52.42 [7937]~P66(x79372)+E(x79371,f180(f853(x79372,a839)))+E(x79373,f180(f853(x79372,a839)))+~P1(f332(f64(x79372),x79371))+~P1(f332(f64(x79372),x79373))+~E(f332(f332(f104(f853(x79372,a839)),x79373),x79371),f180(f853(x79372,a839)))+E(f332(f332(f83(x79372),f332(f66(x79372,f83(x79372)),x79373)),f332(f66(x79372,f83(x79372)),x79371)),f332(f66(x79372,f83(x79372)),f332(f332(f103(f853(x79372,a839)),x79373),x79371)))
% 52.62/52.42 [8007]~P100(x80072)+E(x80071,f180(f853(x80072,a839)))+E(x80073,f180(f853(x80072,a839)))+~P1(f332(f64(x80072),x80071))+~P1(f332(f64(x80072),x80073))+~E(f332(f332(f104(f853(x80072,a839)),x80073),x80071),f180(f853(x80072,a839)))+E(f332(f332(f179(x80072),f13(x80072,f179(x80072),x80073)),f13(x80072,f179(x80072),x80071)),f13(x80072,f179(x80072),f332(f332(f103(f853(x80072,a839)),x80073),x80071)))
% 52.62/52.42 [8008]~P100(x80082)+E(x80081,f180(f853(x80082,a839)))+E(x80083,f180(f853(x80082,a839)))+~P1(f332(f64(x80082),x80081))+~P1(f332(f64(x80082),x80083))+~E(f332(f332(f104(f853(x80082,a839)),x80083),x80081),f180(f853(x80082,a839)))+E(f332(f332(f236(x80082),f14(x80082,f236(x80082),x80083)),f14(x80082,f236(x80082),x80081)),f14(x80082,f236(x80082),f332(f332(f103(f853(x80082,a839)),x80083),x80081)))
% 52.62/52.42 [7716]E(x77161,f2(a1))+E(f332(f332(f44(a1),x77162),x77161),x77163)+~P1(f332(f332(f232(a1),x77164),f2(a1)))+~E(x77162,f332(f332(f82(a1),f332(f332(f83(a1),x77161),x77163)),x77164))+~P1(f332(f332(f232(a1),f2(a1)),x77164))+~P1(f332(f332(f233(a1),x77164),x77161))+~P1(f332(f332(f233(a1),x77161),x77164))
% 52.62/52.42 [7722]E(f53(a1,x77222,x77221),x77223)+E(x77221,f2(a1))+~P1(f332(f332(f232(a1),x77223),f2(a1)))+~E(x77222,f332(f332(f82(a1),f332(f332(f83(a1),x77221),x77224)),x77223))+~P1(f332(f332(f232(a1),f2(a1)),x77223))+~P1(f332(f332(f233(a1),x77223),x77221))+~P1(f332(f332(f233(a1),x77221),x77223))
% 52.62/52.42 [6743]~P9(x67432)+E(x67431,f2(x67432))+E(x67433,f2(x67432))+~E(f332(f332(f44(x67432),x67434),x67433),f332(f332(f44(x67432),x67435),x67431))+E(f332(f332(f83(x67432),x67434),x67431),f332(f332(f83(x67432),x67433),x67435))+~P1(f332(f332(f279(x67432),x67431),x67435))+~P1(f332(f332(f279(x67432),x67433),x67434))
% 52.62/52.42 [6744]~P9(x67442)+E(x67441,f2(x67442))+E(x67443,f2(x67442))+~E(f332(f332(f83(x67442),x67444),x67443),f332(f332(f83(x67442),x67441),x67445))+E(f332(f332(f44(x67442),x67444),x67441),f332(f332(f44(x67442),x67445),x67443))+~P1(f332(f332(f279(x67442),x67441),x67444))+~P1(f332(f332(f279(x67442),x67443),x67445))
% 52.62/52.42 [7631]~P24(x76312,x76315,x76314)+E(x76311,f180(f853(x76312,a839)))+E(x76313,f180(f853(x76312,a839)))+~P1(f332(f64(x76312),x76311))+~P1(f332(f64(x76312),x76313))+~E(f332(f332(f104(f853(x76312,a839)),x76313),x76311),f180(f853(x76312,a839)))+E(f332(x76314,f332(f332(f103(f853(x76312,a839)),x76313),x76311)),f332(f332(x76315,f332(x76314,x76313)),f332(x76314,x76311)))
% 52.62/52.42 [9224]~P31(x92243,x92241,x92245,x92244)+~P31(x92241,x92243,x92246,x92242)+E(f332(f43(x92241),x92242),f332(f43(x92243),x92244))+~P1(f332(f64(x92243),x92244))+~P1(f332(f64(x92241),x92242))+~P1(f332(f332(f232(f853(x92243,a839)),f332(f303(x92241,x92243,x92246),x92242)),x92244))+~P1(f332(f332(f232(f853(x92241,a839)),f332(f303(x92243,x92241,x92245),x92244)),x92242))
% 52.62/52.42 [9172]~P1(f332(f332(f233(a1),f332(f332(f82(a1),f332(f332(f83(a1),x91725),x91721)),x91726)),f2(a1)))+~E(f332(f332(f82(a1),f332(f332(f83(a1),x91723),x91722)),x91724),f332(f332(f82(a1),f332(f332(f83(a1),x91725),x91721)),x91726))+~P1(f332(f332(f233(a1),f2(a1)),x91725))+~P1(f332(f332(f232(a1),f2(a1)),x91726))+~P1(f332(f332(f233(a1),x91724),x91723))+~P1(f332(f332(f232(a1),x91725),x91723))+P1(f332(f332(f232(a1),x91721),x91722))
% 52.62/52.42 [8963]~E(f332(f332(f82(a1),f332(f332(f83(a1),x89633),x89631)),x89634),f332(f332(f82(a1),f332(f332(f83(a1),x89635),x89632)),x89636))+~P1(f332(f332(f233(a1),f2(a1)),x89635))+~P1(f332(f332(f232(a1),f2(a1)),x89634))+~P1(f332(f332(f233(a1),x89636),x89635))+~P1(f332(f332(f232(a1),x89635),x89633))+P1(f332(f332(f232(a1),x89631),x89632))+~P1(f332(f332(f232(a1),f2(a1)),f332(f332(f82(a1),f332(f332(f83(a1),x89635),x89632)),x89636)))
% 52.62/52.42 [9128]~P124(x91281)+~E(f332(f332(f82(x91281),x91282),x91284),f80(x91281))+~P1(f332(f332(f232(x91281),f2(x91281)),x91284))+~P1(f332(f332(f232(x91281),f2(x91281)),x91282))+~P1(f332(f332(f233(x91281),x91285),x91286))+~P1(f332(f332(f233(x91281),x91283),x91286))+P1(f332(f332(f233(x91281),f332(f332(f82(x91281),f332(f332(f83(x91281),x91282),x91283)),f332(f332(f83(x91281),x91284),x91285))),x91286))
% 52.62/52.42 [9129]~P126(x91291)+~E(f332(f332(f82(x91291),x91292),x91294),f80(x91291))+~P1(f332(f332(f232(x91291),x91295),x91296))+~P1(f332(f332(f232(x91291),x91293),x91296))+~P1(f332(f332(f232(x91291),f2(x91291)),x91294))+~P1(f332(f332(f232(x91291),f2(x91291)),x91292))+P1(f332(f332(f232(x91291),f332(f332(f82(x91291),f332(f332(f83(x91291),x91292),x91293)),f332(f332(f83(x91291),x91294),x91295))),x91296))
% 52.62/52.42 [9911]~P14(x99117,x99116,x99115)+E(x99111,x99112)+~P18(x99117,f853(x99114,a839),x99115,x99113)+E(f332(x99113,f500(x99111,x99112,x99113,x99114,x99115,x99116,x99117)),f332(x99113,f501(x99111,x99112,x99113,x99114,x99115,x99116,x99117)))+~E(f332(f332(f47(x99117,f853(x99114,a839)),x99111),x99113),f332(f332(f47(x99117,f853(x99114,a839)),x99112),x99113))+~P1(f332(f332(f334(f853(x99117,a839)),x99112),f332(f332(f62(x99117),x99116),x99115)))+~P1(f332(f332(f334(f853(x99117,a839)),x99111),f332(f332(f62(x99117),x99116),x99115)))
% 52.62/52.42 [9951]~P14(x99513,x99517,x99516)+E(x99511,x99512)+~P18(x99513,f853(x99515,a839),x99516,x99514)+~E(f332(f332(f47(x99513,f853(x99515,a839)),x99511),x99514),f332(f332(f47(x99513,f853(x99515,a839)),x99512),x99514))+P1(f332(f332(f334(x99513),f501(x99511,x99512,x99514,x99515,x99516,x99517,x99513)),x99517))+~P1(f332(f332(f334(f853(x99513,a839)),x99512),f332(f332(f62(x99513),x99517),x99516)))+~P1(f332(f332(f334(f853(x99513,a839)),x99511),f332(f332(f62(x99513),x99517),x99516)))
% 52.62/52.42 [9952]~P14(x99523,x99527,x99526)+E(x99521,x99522)+~P18(x99523,f853(x99525,a839),x99526,x99524)+~E(f332(f332(f47(x99523,f853(x99525,a839)),x99521),x99524),f332(f332(f47(x99523,f853(x99525,a839)),x99522),x99524))+P1(f332(f332(f334(x99523),f500(x99521,x99522,x99524,x99525,x99526,x99527,x99523)),x99527))+~P1(f332(f332(f334(f853(x99523,a839)),x99522),f332(f332(f62(x99523),x99527),x99526)))+~P1(f332(f332(f334(f853(x99523,a839)),x99521),f332(f332(f62(x99523),x99527),x99526)))
% 52.62/52.42 [10019]E(x100191,x100192)+~P14(x100193,x100196,x100197)+~P18(x100193,f853(x100194,a839),x100197,x100195)+~E(f332(f332(f47(x100193,f853(x100194,a839)),x100191),x100195),f332(f332(f47(x100193,f853(x100194,a839)),x100192),x100195))+~P1(f332(f332(f334(f852(x100193,x100193)),f332(f332(f241(x100193,x100193),f501(x100191,x100192,x100195,x100194,x100197,x100196,x100193)),f500(x100191,x100192,x100195,x100194,x100197,x100196,x100193))),x100197))+~P1(f332(f332(f334(f853(x100193,a839)),x100192),f332(f332(f62(x100193),x100196),x100197)))+~P1(f332(f332(f334(f853(x100193,a839)),x100191),f332(f332(f62(x100193),x100196),x100197)))
% 52.62/52.42 [8962]~P14(x89621,x89627,x89624)+~E(x89625,x89626)+~P1(f332(f332(f334(x89621),x89623),x89626))+~P1(f332(f332(f334(x89621),x89622),x89625))+~P1(f332(f332(f334(f853(x89621,a839)),x89626),f332(f332(f62(x89621),x89627),x89624)))+~P1(f332(f332(f334(f853(x89621,a839)),x89625),f332(f332(f62(x89621),x89627),x89624)))+P1(f332(f332(f334(f852(x89621,x89621)),f332(f332(f241(x89621,x89621),x89622),x89623)),x89624))
% 52.62/52.42 [9092]E(x90921,x90922)+~P14(x90923,x90924,x90925)+~P1(f332(f332(f334(x90923),x90926),x90922))+~P1(f332(f332(f334(x90923),x90927),x90921))+~P1(f332(f332(f334(f853(x90923,a839)),x90922),f332(f332(f62(x90923),x90924),x90925)))+~P1(f332(f332(f334(f853(x90923,a839)),x90921),f332(f332(f62(x90923),x90924),x90925)))+~P1(f332(f332(f334(f852(x90923,x90923)),f332(f332(f241(x90923,x90923),x90927),x90926)),x90925))
% 52.62/52.42 [9093]E(x90931,x90932)+~P14(x90933,x90934,x90935)+~P1(f332(f332(f334(x90933),x90936),x90932))+~P1(f332(f332(f334(x90933),x90937),x90931))+~P1(f332(f332(f334(f853(x90933,a839)),x90932),f332(f332(f62(x90933),x90934),x90935)))+~P1(f332(f332(f334(f853(x90933,a839)),x90931),f332(f332(f62(x90933),x90934),x90935)))+~P1(f332(f332(f334(f852(x90933,x90933)),f332(f332(f241(x90933,x90933),x90937),x90936)),x90935))
% 52.62/52.42 [10036]~P14(x100369,x100368,x100367)+~P14(x100361,x1003611,x1003610)+~P19(x100361,x100369,f853(x100366,a839),x1003610,x100367,x100365)+P1(f332(f332(f334(x100361),f502(x100362,x100363,x100364,x100365,x100366,x100367,x100368,x100369,x1003610,x1003611,x100361)),x1003611))+~P1(f332(f332(f334(f853(x100369,a839)),x100363),f332(f332(f62(x100369),x100368),x100367)))+~P1(f332(f332(f334(f853(x100361,a839)),x100364),f332(f332(f62(x100361),x1003611),x1003610)))+P1(f332(f332(f334(f853(x100366,a839)),f332(f332(f47(x100361,f853(x100366,a839)),x100364),f332(f332(f10(f853(x100369,f853(x100366,a839)),f853(x100366,a839),x100361),f332(f47(x100369,f853(x100366,a839)),x100363)),x100365))),x100362))
% 52.62/52.42 [10037]~P14(x1003711,x1003710,x100379)+~P14(x100371,x100378,x100377)+~P19(x1003711,x100371,f853(x100376,a839),x100379,x100377,x100375)+P1(f332(f332(f334(x100371),f503(x100372,x100373,x100374,x100375,x100376,x100377,x100378,x100371,x100379,x1003710,x1003711)),x100378))+~P1(f332(f332(f334(f853(x1003711,a839)),x100374),f332(f332(f62(x1003711),x1003710),x100379)))+~P1(f332(f332(f334(f853(x100371,a839)),x100373),f332(f332(f62(x100371),x100378),x100377)))+P1(f332(f332(f334(f853(x100376,a839)),f332(f332(f47(x1003711,f853(x100376,a839)),x100374),f332(f332(f10(f853(x100371,f853(x100376,a839)),f853(x100376,a839),x1003711),f332(f47(x100371,f853(x100376,a839)),x100373)),x100375))),x100372))
% 52.62/52.42 [10040]~P14(x100402,x100408,x100409)+~P14(x100404,x1004010,x1004011)+~P19(x100402,x100404,f853(x100401,a839),x100409,x1004011,x100406)+~P1(f332(f332(f334(f853(x100402,a839)),x100403),f332(f332(f62(x100402),x100408),x100409)))+~P1(f332(f332(f334(f853(x100404,a839)),x100405),f332(f332(f62(x100404),x1004010),x1004011)))+~P1(f332(f332(f334(f853(x100401,a839)),f332(f332(x100406,f502(x100407,x100405,x100403,x100406,x100401,x1004011,x1004010,x100404,x100409,x100408,x100402)),f503(x100407,x100405,x100403,x100406,x100401,x1004011,x1004010,x100404,x100409,x100408,x100402))),x100407))+P1(f332(f332(f334(f853(x100401,a839)),f332(f332(f47(x100402,f853(x100401,a839)),x100403),f332(f332(f10(f853(x100404,f853(x100401,a839)),f853(x100401,a839),x100402),f332(f47(x100404,f853(x100401,a839)),x100405)),x100406))),x100407))
% 52.62/52.42 [9005]E(x90051,x90052)+~P100(x90054)+~P31(x90053,x90054,x90055,f332(f332(f103(f853(x90053,a839)),f332(f158(x90053),x90051)),f332(f158(x90053),x90052)))+~E(f332(f158(x90053),x90051),f332(f158(x90053),x90052))+~P20(x90054,f332(f332(f143(x90053,x90054),x90055),x90052))+~P20(x90054,f332(f332(f143(x90053,x90054),x90055),x90051))+~P1(f332(f127(x90054),f332(f332(f143(x90053,x90054),x90055),x90052)))+~P1(f332(f127(x90054),f332(f332(f143(x90053,x90054),x90055),x90051)))
% 52.62/52.42 %EqnAxiom
% 52.62/52.42 [1]E(x11,x11)
% 52.62/52.42 [2]E(x22,x21)+~E(x21,x22)
% 52.62/52.42 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 52.62/52.42 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 52.62/52.42 [5]~E(x51,x52)+E(f3(x51),f3(x52))
% 52.62/52.42 [6]~E(x61,x62)+E(f102(x61),f102(x62))
% 52.62/52.42 [7]~E(x71,x72)+E(f34(x71),f34(x72))
% 52.62/52.42 [8]~E(x81,x82)+E(f332(x81,x83),f332(x82,x83))
% 52.62/52.42 [9]~E(x91,x92)+E(f332(x93,x91),f332(x93,x92))
% 52.62/52.42 [10]~E(x101,x102)+E(f86(x101),f86(x102))
% 52.62/52.42 [11]~E(x111,x112)+E(f586(x111,x113,x114,x115,x116,x117),f586(x112,x113,x114,x115,x116,x117))
% 52.62/52.42 [12]~E(x121,x122)+E(f586(x123,x121,x124,x125,x126,x127),f586(x123,x122,x124,x125,x126,x127))
% 52.62/52.42 [13]~E(x131,x132)+E(f586(x133,x134,x131,x135,x136,x137),f586(x133,x134,x132,x135,x136,x137))
% 52.62/52.42 [14]~E(x141,x142)+E(f586(x143,x144,x145,x141,x146,x147),f586(x143,x144,x145,x142,x146,x147))
% 52.62/52.42 [15]~E(x151,x152)+E(f586(x153,x154,x155,x156,x151,x157),f586(x153,x154,x155,x156,x152,x157))
% 52.62/52.42 [16]~E(x161,x162)+E(f586(x163,x164,x165,x166,x167,x161),f586(x163,x164,x165,x166,x167,x162))
% 52.62/52.42 [17]~E(x171,x172)+E(f233(x171),f233(x172))
% 52.62/52.42 [18]~E(x181,x182)+E(f9(x181,x183,x184),f9(x182,x183,x184))
% 52.62/52.42 [19]~E(x191,x192)+E(f9(x193,x191,x194),f9(x193,x192,x194))
% 52.62/52.42 [20]~E(x201,x202)+E(f9(x203,x204,x201),f9(x203,x204,x202))
% 52.62/52.42 [21]~E(x211,x212)+E(f179(x211),f179(x212))
% 52.62/52.42 [22]~E(x221,x222)+E(f103(x221),f103(x222))
% 52.62/52.42 [23]~E(x231,x232)+E(f180(x231),f180(x232))
% 52.62/52.42 [24]~E(x241,x242)+E(f503(x241,x243,x244,x245,x246,x247,x248,x249,x2410,x2411,x2412),f503(x242,x243,x244,x245,x246,x247,x248,x249,x2410,x2411,x2412))
% 52.62/52.42 [25]~E(x251,x252)+E(f503(x253,x251,x254,x255,x256,x257,x258,x259,x2510,x2511,x2512),f503(x253,x252,x254,x255,x256,x257,x258,x259,x2510,x2511,x2512))
% 52.62/52.42 [26]~E(x261,x262)+E(f503(x263,x264,x261,x265,x266,x267,x268,x269,x2610,x2611,x2612),f503(x263,x264,x262,x265,x266,x267,x268,x269,x2610,x2611,x2612))
% 52.62/52.42 [27]~E(x271,x272)+E(f503(x273,x274,x275,x271,x276,x277,x278,x279,x2710,x2711,x2712),f503(x273,x274,x275,x272,x276,x277,x278,x279,x2710,x2711,x2712))
% 52.62/52.42 [28]~E(x281,x282)+E(f503(x283,x284,x285,x286,x281,x287,x288,x289,x2810,x2811,x2812),f503(x283,x284,x285,x286,x282,x287,x288,x289,x2810,x2811,x2812))
% 52.62/52.42 [29]~E(x291,x292)+E(f503(x293,x294,x295,x296,x297,x291,x298,x299,x2910,x2911,x2912),f503(x293,x294,x295,x296,x297,x292,x298,x299,x2910,x2911,x2912))
% 52.62/52.42 [30]~E(x301,x302)+E(f503(x303,x304,x305,x306,x307,x308,x301,x309,x3010,x3011,x3012),f503(x303,x304,x305,x306,x307,x308,x302,x309,x3010,x3011,x3012))
% 52.62/52.42 [31]~E(x311,x312)+E(f503(x313,x314,x315,x316,x317,x318,x319,x311,x3110,x3111,x3112),f503(x313,x314,x315,x316,x317,x318,x319,x312,x3110,x3111,x3112))
% 52.62/52.42 [32]~E(x321,x322)+E(f503(x323,x324,x325,x326,x327,x328,x329,x3210,x321,x3211,x3212),f503(x323,x324,x325,x326,x327,x328,x329,x3210,x322,x3211,x3212))
% 52.62/52.42 [33]~E(x331,x332)+E(f503(x333,x334,x335,x336,x337,x338,x339,x3310,x3311,x331,x3312),f503(x333,x334,x335,x336,x337,x338,x339,x3310,x3311,x332,x3312))
% 52.62/52.42 [34]~E(x341,x342)+E(f503(x343,x344,x345,x346,x347,x348,x349,x3410,x3411,x3412,x341),f503(x343,x344,x345,x346,x347,x348,x349,x3410,x3411,x3412,x342))
% 52.62/52.42 [35]~E(x351,x352)+E(f236(x351),f236(x352))
% 52.62/52.42 [36]~E(x361,x362)+E(f104(x361),f104(x362))
% 52.62/52.42 [37]~E(x371,x372)+E(f105(x371),f105(x372))
% 52.62/52.42 [38]~E(x381,x382)+E(f39(x381),f39(x382))
% 52.62/52.42 [39]~E(x391,x392)+E(f334(x391),f334(x392))
% 52.62/52.42 [40]~E(x401,x402)+E(f80(x401),f80(x402))
% 52.62/52.42 [41]~E(x411,x412)+E(f502(x411,x413,x414,x415,x416,x417,x418,x419,x4110,x4111,x4112),f502(x412,x413,x414,x415,x416,x417,x418,x419,x4110,x4111,x4112))
% 52.62/52.42 [42]~E(x421,x422)+E(f502(x423,x421,x424,x425,x426,x427,x428,x429,x4210,x4211,x4212),f502(x423,x422,x424,x425,x426,x427,x428,x429,x4210,x4211,x4212))
% 52.62/52.42 [43]~E(x431,x432)+E(f502(x433,x434,x431,x435,x436,x437,x438,x439,x4310,x4311,x4312),f502(x433,x434,x432,x435,x436,x437,x438,x439,x4310,x4311,x4312))
% 52.62/52.42 [44]~E(x441,x442)+E(f502(x443,x444,x445,x441,x446,x447,x448,x449,x4410,x4411,x4412),f502(x443,x444,x445,x442,x446,x447,x448,x449,x4410,x4411,x4412))
% 52.62/52.42 [45]~E(x451,x452)+E(f502(x453,x454,x455,x456,x451,x457,x458,x459,x4510,x4511,x4512),f502(x453,x454,x455,x456,x452,x457,x458,x459,x4510,x4511,x4512))
% 52.62/52.42 [46]~E(x461,x462)+E(f502(x463,x464,x465,x466,x467,x461,x468,x469,x4610,x4611,x4612),f502(x463,x464,x465,x466,x467,x462,x468,x469,x4610,x4611,x4612))
% 52.62/52.42 [47]~E(x471,x472)+E(f502(x473,x474,x475,x476,x477,x478,x471,x479,x4710,x4711,x4712),f502(x473,x474,x475,x476,x477,x478,x472,x479,x4710,x4711,x4712))
% 52.62/52.42 [48]~E(x481,x482)+E(f502(x483,x484,x485,x486,x487,x488,x489,x481,x4810,x4811,x4812),f502(x483,x484,x485,x486,x487,x488,x489,x482,x4810,x4811,x4812))
% 52.62/52.42 [49]~E(x491,x492)+E(f502(x493,x494,x495,x496,x497,x498,x499,x4910,x491,x4911,x4912),f502(x493,x494,x495,x496,x497,x498,x499,x4910,x492,x4911,x4912))
% 52.62/52.42 [50]~E(x501,x502)+E(f502(x503,x504,x505,x506,x507,x508,x509,x5010,x5011,x501,x5012),f502(x503,x504,x505,x506,x507,x508,x509,x5010,x5011,x502,x5012))
% 52.62/52.42 [51]~E(x511,x512)+E(f502(x513,x514,x515,x516,x517,x518,x519,x5110,x5111,x5112,x511),f502(x513,x514,x515,x516,x517,x518,x519,x5110,x5111,x5112,x512))
% 52.62/52.42 [52]~E(x521,x522)+E(f113(x521),f113(x522))
% 52.62/52.42 [53]~E(x531,x532)+E(f187(x531),f187(x532))
% 52.62/52.42 [54]~E(x541,x542)+E(f853(x541,x543),f853(x542,x543))
% 52.62/52.42 [55]~E(x551,x552)+E(f853(x553,x551),f853(x553,x552))
% 52.62/52.42 [56]~E(x561,x562)+E(f6(x561),f6(x562))
% 52.62/52.42 [57]~E(x571,x572)+E(f83(x571),f83(x572))
% 52.62/52.42 [58]~E(x581,x582)+E(f81(x581),f81(x582))
% 52.62/52.42 [59]~E(x591,x592)+E(f232(x591),f232(x592))
% 52.62/52.42 [60]~E(x601,x602)+E(f181(x601),f181(x602))
% 52.62/52.42 [61]~E(x611,x612)+E(f10(x611,x613,x614),f10(x612,x613,x614))
% 52.62/52.42 [62]~E(x621,x622)+E(f10(x623,x621,x624),f10(x623,x622,x624))
% 52.62/52.42 [63]~E(x631,x632)+E(f10(x633,x634,x631),f10(x633,x634,x632))
% 52.62/52.42 [64]~E(x641,x642)+E(f106(x641),f106(x642))
% 52.62/52.42 [65]~E(x651,x652)+E(f849(x651),f849(x652))
% 52.62/52.42 [66]~E(x661,x662)+E(f20(x661,x663,x664),f20(x662,x663,x664))
% 52.62/52.42 [67]~E(x671,x672)+E(f20(x673,x671,x674),f20(x673,x672,x674))
% 52.62/52.42 [68]~E(x681,x682)+E(f20(x683,x684,x681),f20(x683,x684,x682))
% 52.62/52.42 [69]~E(x691,x692)+E(f256(x691),f256(x692))
% 52.62/52.42 [70]~E(x701,x702)+E(f43(x701),f43(x702))
% 52.62/52.42 [71]~E(x711,x712)+E(f62(x711),f62(x712))
% 52.62/52.42 [72]~E(x721,x722)+E(f8(x721,x723),f8(x722,x723))
% 52.62/52.42 [73]~E(x731,x732)+E(f8(x733,x731),f8(x733,x732))
% 52.62/52.42 [74]~E(x741,x742)+E(f158(x741),f158(x742))
% 52.62/52.42 [75]~E(x751,x752)+E(f302(x751),f302(x752))
% 52.62/52.42 [76]~E(x761,x762)+E(f140(x761),f140(x762))
% 52.62/52.42 [77]~E(x771,x772)+E(f82(x771),f82(x772))
% 52.62/52.42 [78]~E(x781,x782)+E(f74(x781,x783),f74(x782,x783))
% 52.62/52.42 [79]~E(x791,x792)+E(f74(x793,x791),f74(x793,x792))
% 52.62/52.42 [80]~E(x801,x802)+E(f852(x801,x803),f852(x802,x803))
% 52.62/52.42 [81]~E(x811,x812)+E(f852(x813,x811),f852(x813,x812))
% 52.62/52.42 [82]~E(x821,x822)+E(f125(x821),f125(x822))
% 52.62/52.42 [83]~E(x831,x832)+E(f530(x831,x833,x834),f530(x832,x833,x834))
% 52.62/52.42 [84]~E(x841,x842)+E(f530(x843,x841,x844),f530(x843,x842,x844))
% 52.62/52.42 [85]~E(x851,x852)+E(f530(x853,x854,x851),f530(x853,x854,x852))
% 52.62/52.42 [86]~E(x861,x862)+E(f241(x861,x863),f241(x862,x863))
% 52.62/52.42 [87]~E(x871,x872)+E(f241(x873,x871),f241(x873,x872))
% 52.62/52.42 [88]~E(x881,x882)+E(f169(x881,x883,x884),f169(x882,x883,x884))
% 52.62/52.42 [89]~E(x891,x892)+E(f169(x893,x891,x894),f169(x893,x892,x894))
% 52.62/52.42 [90]~E(x901,x902)+E(f169(x903,x904,x901),f169(x903,x904,x902))
% 52.62/52.42 [91]~E(x911,x912)+E(f53(x911,x913,x914),f53(x912,x913,x914))
% 52.62/52.42 [92]~E(x921,x922)+E(f53(x923,x921,x924),f53(x923,x922,x924))
% 52.62/52.42 [93]~E(x931,x932)+E(f53(x933,x934,x931),f53(x933,x934,x932))
% 52.62/52.42 [94]~E(x941,x942)+E(f44(x941),f44(x942))
% 52.62/52.42 [95]~E(x951,x952)+E(f844(x951),f844(x952))
% 52.62/52.42 [96]~E(x961,x962)+E(f148(x961,x963),f148(x962,x963))
% 52.62/52.42 [97]~E(x971,x972)+E(f148(x973,x971),f148(x973,x972))
% 52.62/52.42 [98]~E(x981,x982)+E(f283(x981),f283(x982))
% 52.62/52.42 [99]~E(x991,x992)+E(f242(x991),f242(x992))
% 52.62/52.42 [100]~E(x1001,x1002)+E(f737(x1001,x1003,x1004,x1005),f737(x1002,x1003,x1004,x1005))
% 52.62/52.42 [101]~E(x1011,x1012)+E(f737(x1013,x1011,x1014,x1015),f737(x1013,x1012,x1014,x1015))
% 52.62/52.42 [102]~E(x1021,x1022)+E(f737(x1023,x1024,x1021,x1025),f737(x1023,x1024,x1022,x1025))
% 52.62/52.42 [103]~E(x1031,x1032)+E(f737(x1033,x1034,x1035,x1031),f737(x1033,x1034,x1035,x1032))
% 52.62/52.42 [104]~E(x1041,x1042)+E(f830(x1041,x1043,x1044),f830(x1042,x1043,x1044))
% 52.62/52.42 [105]~E(x1051,x1052)+E(f830(x1053,x1051,x1054),f830(x1053,x1052,x1054))
% 52.62/52.42 [106]~E(x1061,x1062)+E(f830(x1063,x1064,x1061),f830(x1063,x1064,x1062))
% 52.62/52.42 [107]~E(x1071,x1072)+E(f829(x1071,x1073,x1074),f829(x1072,x1073,x1074))
% 52.62/52.42 [108]~E(x1081,x1082)+E(f829(x1083,x1081,x1084),f829(x1083,x1082,x1084))
% 52.62/52.42 [109]~E(x1091,x1092)+E(f829(x1093,x1094,x1091),f829(x1093,x1094,x1092))
% 52.62/52.42 [110]~E(x1101,x1102)+E(f64(x1101),f64(x1102))
% 52.62/52.42 [111]~E(x1111,x1112)+E(f67(x1111,x1113,x1114),f67(x1112,x1113,x1114))
% 52.62/52.42 [112]~E(x1121,x1122)+E(f67(x1123,x1121,x1124),f67(x1123,x1122,x1124))
% 52.62/52.42 [113]~E(x1131,x1132)+E(f67(x1133,x1134,x1131),f67(x1133,x1134,x1132))
% 52.62/52.42 [114]~E(x1141,x1142)+E(f138(x1141,x1143,x1144),f138(x1142,x1143,x1144))
% 52.62/52.42 [115]~E(x1151,x1152)+E(f138(x1153,x1151,x1154),f138(x1153,x1152,x1154))
% 52.62/52.42 [116]~E(x1161,x1162)+E(f138(x1163,x1164,x1161),f138(x1163,x1164,x1162))
% 52.62/52.42 [117]~E(x1171,x1172)+E(f145(x1171,x1173,x1174,x1175),f145(x1172,x1173,x1174,x1175))
% 52.62/52.42 [118]~E(x1181,x1182)+E(f145(x1183,x1181,x1184,x1185),f145(x1183,x1182,x1184,x1185))
% 52.62/52.42 [119]~E(x1191,x1192)+E(f145(x1193,x1194,x1191,x1195),f145(x1193,x1194,x1192,x1195))
% 52.62/52.42 [120]~E(x1201,x1202)+E(f145(x1203,x1204,x1205,x1201),f145(x1203,x1204,x1205,x1202))
% 52.62/52.42 [121]~E(x1211,x1212)+E(f151(x1211,x1213,x1214),f151(x1212,x1213,x1214))
% 52.62/52.42 [122]~E(x1221,x1222)+E(f151(x1223,x1221,x1224),f151(x1223,x1222,x1224))
% 52.62/52.42 [123]~E(x1231,x1232)+E(f151(x1233,x1234,x1231),f151(x1233,x1234,x1232))
% 52.62/52.42 [124]~E(x1241,x1242)+E(f128(x1241),f128(x1242))
% 52.62/52.42 [125]~E(x1251,x1252)+E(f688(x1251,x1253,x1254,x1255),f688(x1252,x1253,x1254,x1255))
% 52.62/52.42 [126]~E(x1261,x1262)+E(f688(x1263,x1261,x1264,x1265),f688(x1263,x1262,x1264,x1265))
% 52.62/52.42 [127]~E(x1271,x1272)+E(f688(x1273,x1274,x1271,x1275),f688(x1273,x1274,x1272,x1275))
% 52.62/52.42 [128]~E(x1281,x1282)+E(f688(x1283,x1284,x1285,x1281),f688(x1283,x1284,x1285,x1282))
% 52.62/52.42 [129]~E(x1291,x1292)+E(f767(x1291),f767(x1292))
% 52.62/52.42 [130]~E(x1301,x1302)+E(f33(x1301,x1303,x1304),f33(x1302,x1303,x1304))
% 52.62/52.42 [131]~E(x1311,x1312)+E(f33(x1313,x1311,x1314),f33(x1313,x1312,x1314))
% 52.62/52.42 [132]~E(x1321,x1322)+E(f33(x1323,x1324,x1321),f33(x1323,x1324,x1322))
% 52.62/52.42 [133]~E(x1331,x1332)+E(f282(x1331,x1333,x1334,x1335),f282(x1332,x1333,x1334,x1335))
% 52.62/52.42 [134]~E(x1341,x1342)+E(f282(x1343,x1341,x1344,x1345),f282(x1343,x1342,x1344,x1345))
% 52.62/52.42 [135]~E(x1351,x1352)+E(f282(x1353,x1354,x1351,x1355),f282(x1353,x1354,x1352,x1355))
% 52.62/52.42 [136]~E(x1361,x1362)+E(f282(x1363,x1364,x1365,x1361),f282(x1363,x1364,x1365,x1362))
% 52.62/52.42 [137]~E(x1371,x1372)+E(f131(x1371),f131(x1372))
% 52.62/52.42 [138]~E(x1381,x1382)+E(f48(x1381,x1383),f48(x1382,x1383))
% 52.62/52.42 [139]~E(x1391,x1392)+E(f48(x1393,x1391),f48(x1393,x1392))
% 52.62/52.42 [140]~E(x1401,x1402)+E(f616(x1401,x1403),f616(x1402,x1403))
% 52.62/52.42 [141]~E(x1411,x1412)+E(f616(x1413,x1411),f616(x1413,x1412))
% 52.62/52.42 [142]~E(x1421,x1422)+E(f57(x1421,x1423),f57(x1422,x1423))
% 52.62/52.42 [143]~E(x1431,x1432)+E(f57(x1433,x1431),f57(x1433,x1432))
% 52.62/52.42 [144]~E(x1441,x1442)+E(f200(x1441,x1443,x1444,x1445),f200(x1442,x1443,x1444,x1445))
% 52.62/52.42 [145]~E(x1451,x1452)+E(f200(x1453,x1451,x1454,x1455),f200(x1453,x1452,x1454,x1455))
% 52.62/52.42 [146]~E(x1461,x1462)+E(f200(x1463,x1464,x1461,x1465),f200(x1463,x1464,x1462,x1465))
% 52.62/52.42 [147]~E(x1471,x1472)+E(f200(x1473,x1474,x1475,x1471),f200(x1473,x1474,x1475,x1472))
% 52.62/52.42 [148]~E(x1481,x1482)+E(f108(x1481),f108(x1482))
% 52.62/52.42 [149]~E(x1491,x1492)+E(f109(x1491),f109(x1492))
% 52.62/52.42 [150]~E(x1501,x1502)+E(f333(x1501),f333(x1502))
% 52.62/52.42 [151]~E(x1511,x1512)+E(f115(x1511),f115(x1512))
% 52.62/52.42 [152]~E(x1521,x1522)+E(f675(x1521,x1523,x1524),f675(x1522,x1523,x1524))
% 52.62/52.42 [153]~E(x1531,x1532)+E(f675(x1533,x1531,x1534),f675(x1533,x1532,x1534))
% 52.62/52.42 [154]~E(x1541,x1542)+E(f675(x1543,x1544,x1541),f675(x1543,x1544,x1542))
% 52.62/52.42 [155]~E(x1551,x1552)+E(f238(x1551,x1553),f238(x1552,x1553))
% 52.62/52.42 [156]~E(x1561,x1562)+E(f238(x1563,x1561),f238(x1563,x1562))
% 52.62/52.42 [157]~E(x1571,x1572)+E(f532(x1571,x1573,x1574),f532(x1572,x1573,x1574))
% 52.62/52.42 [158]~E(x1581,x1582)+E(f532(x1583,x1581,x1584),f532(x1583,x1582,x1584))
% 52.62/52.42 [159]~E(x1591,x1592)+E(f532(x1593,x1594,x1591),f532(x1593,x1594,x1592))
% 52.62/52.42 [160]~E(x1601,x1602)+E(f183(x1601),f183(x1602))
% 52.62/52.42 [161]~E(x1611,x1612)+E(f846(x1611),f846(x1612))
% 52.62/52.42 [162]~E(x1621,x1622)+E(f190(x1621,x1623,x1624,x1625),f190(x1622,x1623,x1624,x1625))
% 52.62/52.42 [163]~E(x1631,x1632)+E(f190(x1633,x1631,x1634,x1635),f190(x1633,x1632,x1634,x1635))
% 52.62/52.42 [164]~E(x1641,x1642)+E(f190(x1643,x1644,x1641,x1645),f190(x1643,x1644,x1642,x1645))
% 52.62/52.42 [165]~E(x1651,x1652)+E(f190(x1653,x1654,x1655,x1651),f190(x1653,x1654,x1655,x1652))
% 52.62/52.42 [166]~E(x1661,x1662)+E(f535(x1661,x1663,x1664,x1665,x1666,x1667,x1668,x1669),f535(x1662,x1663,x1664,x1665,x1666,x1667,x1668,x1669))
% 52.62/52.42 [167]~E(x1671,x1672)+E(f535(x1673,x1671,x1674,x1675,x1676,x1677,x1678,x1679),f535(x1673,x1672,x1674,x1675,x1676,x1677,x1678,x1679))
% 52.62/52.42 [168]~E(x1681,x1682)+E(f535(x1683,x1684,x1681,x1685,x1686,x1687,x1688,x1689),f535(x1683,x1684,x1682,x1685,x1686,x1687,x1688,x1689))
% 52.62/52.42 [169]~E(x1691,x1692)+E(f535(x1693,x1694,x1695,x1691,x1696,x1697,x1698,x1699),f535(x1693,x1694,x1695,x1692,x1696,x1697,x1698,x1699))
% 52.62/52.42 [170]~E(x1701,x1702)+E(f535(x1703,x1704,x1705,x1706,x1701,x1707,x1708,x1709),f535(x1703,x1704,x1705,x1706,x1702,x1707,x1708,x1709))
% 52.62/52.42 [171]~E(x1711,x1712)+E(f535(x1713,x1714,x1715,x1716,x1717,x1711,x1718,x1719),f535(x1713,x1714,x1715,x1716,x1717,x1712,x1718,x1719))
% 52.62/52.42 [172]~E(x1721,x1722)+E(f535(x1723,x1724,x1725,x1726,x1727,x1728,x1721,x1729),f535(x1723,x1724,x1725,x1726,x1727,x1728,x1722,x1729))
% 52.62/52.42 [173]~E(x1731,x1732)+E(f535(x1733,x1734,x1735,x1736,x1737,x1738,x1739,x1731),f535(x1733,x1734,x1735,x1736,x1737,x1738,x1739,x1732))
% 52.62/52.42 [174]~E(x1741,x1742)+E(f7(x1741),f7(x1742))
% 52.62/52.42 [175]~E(x1751,x1752)+E(f18(x1751,x1753),f18(x1752,x1753))
% 52.62/52.42 [176]~E(x1761,x1762)+E(f18(x1763,x1761),f18(x1763,x1762))
% 52.62/52.42 [177]~E(x1771,x1772)+E(f735(x1771,x1773,x1774,x1775,x1776),f735(x1772,x1773,x1774,x1775,x1776))
% 52.62/52.42 [178]~E(x1781,x1782)+E(f735(x1783,x1781,x1784,x1785,x1786),f735(x1783,x1782,x1784,x1785,x1786))
% 52.62/52.42 [179]~E(x1791,x1792)+E(f735(x1793,x1794,x1791,x1795,x1796),f735(x1793,x1794,x1792,x1795,x1796))
% 52.62/52.42 [180]~E(x1801,x1802)+E(f735(x1803,x1804,x1805,x1801,x1806),f735(x1803,x1804,x1805,x1802,x1806))
% 52.62/52.42 [181]~E(x1811,x1812)+E(f735(x1813,x1814,x1815,x1816,x1811),f735(x1813,x1814,x1815,x1816,x1812))
% 52.62/52.42 [182]~E(x1821,x1822)+E(f825(x1821,x1823,x1824),f825(x1822,x1823,x1824))
% 52.62/52.42 [183]~E(x1831,x1832)+E(f825(x1833,x1831,x1834),f825(x1833,x1832,x1834))
% 52.62/52.42 [184]~E(x1841,x1842)+E(f825(x1843,x1844,x1841),f825(x1843,x1844,x1842))
% 52.62/52.42 [185]~E(x1851,x1852)+E(f142(x1851),f142(x1852))
% 52.62/52.42 [186]~E(x1861,x1862)+E(f12(x1861,x1863),f12(x1862,x1863))
% 52.62/52.42 [187]~E(x1871,x1872)+E(f12(x1873,x1871),f12(x1873,x1872))
% 52.62/52.42 [188]~E(x1881,x1882)+E(f574(x1881,x1883,x1884,x1885,x1886,x1887,x1888,x1889),f574(x1882,x1883,x1884,x1885,x1886,x1887,x1888,x1889))
% 52.62/52.42 [189]~E(x1891,x1892)+E(f574(x1893,x1891,x1894,x1895,x1896,x1897,x1898,x1899),f574(x1893,x1892,x1894,x1895,x1896,x1897,x1898,x1899))
% 52.62/52.42 [190]~E(x1901,x1902)+E(f574(x1903,x1904,x1901,x1905,x1906,x1907,x1908,x1909),f574(x1903,x1904,x1902,x1905,x1906,x1907,x1908,x1909))
% 52.62/52.42 [191]~E(x1911,x1912)+E(f574(x1913,x1914,x1915,x1911,x1916,x1917,x1918,x1919),f574(x1913,x1914,x1915,x1912,x1916,x1917,x1918,x1919))
% 52.62/52.42 [192]~E(x1921,x1922)+E(f574(x1923,x1924,x1925,x1926,x1921,x1927,x1928,x1929),f574(x1923,x1924,x1925,x1926,x1922,x1927,x1928,x1929))
% 52.62/52.42 [193]~E(x1931,x1932)+E(f574(x1933,x1934,x1935,x1936,x1937,x1931,x1938,x1939),f574(x1933,x1934,x1935,x1936,x1937,x1932,x1938,x1939))
% 52.62/52.42 [194]~E(x1941,x1942)+E(f574(x1943,x1944,x1945,x1946,x1947,x1948,x1941,x1949),f574(x1943,x1944,x1945,x1946,x1947,x1948,x1942,x1949))
% 52.62/52.42 [195]~E(x1951,x1952)+E(f574(x1953,x1954,x1955,x1956,x1957,x1958,x1959,x1951),f574(x1953,x1954,x1955,x1956,x1957,x1958,x1959,x1952))
% 52.62/52.42 [196]~E(x1961,x1962)+E(f126(x1961,x1963),f126(x1962,x1963))
% 52.62/52.42 [197]~E(x1971,x1972)+E(f126(x1973,x1971),f126(x1973,x1972))
% 52.62/52.42 [198]~E(x1981,x1982)+E(f45(x1981,x1983),f45(x1982,x1983))
% 52.62/52.42 [199]~E(x1991,x1992)+E(f45(x1993,x1991),f45(x1993,x1992))
% 52.62/52.42 [200]~E(x2001,x2002)+E(f738(x2001,x2003,x2004,x2005),f738(x2002,x2003,x2004,x2005))
% 52.62/52.42 [201]~E(x2011,x2012)+E(f738(x2013,x2011,x2014,x2015),f738(x2013,x2012,x2014,x2015))
% 52.62/52.42 [202]~E(x2021,x2022)+E(f738(x2023,x2024,x2021,x2025),f738(x2023,x2024,x2022,x2025))
% 52.62/52.42 [203]~E(x2031,x2032)+E(f738(x2033,x2034,x2035,x2031),f738(x2033,x2034,x2035,x2032))
% 52.62/52.42 [204]~E(x2041,x2042)+E(f143(x2041,x2043),f143(x2042,x2043))
% 52.62/52.42 [205]~E(x2051,x2052)+E(f143(x2053,x2051),f143(x2053,x2052))
% 52.62/52.42 [206]~E(x2061,x2062)+E(f112(x2061),f112(x2062))
% 52.62/52.42 [207]~E(x2071,x2072)+E(f300(x2071,x2073),f300(x2072,x2073))
% 52.62/52.42 [208]~E(x2081,x2082)+E(f300(x2083,x2081),f300(x2083,x2082))
% 52.62/52.42 [209]~E(x2091,x2092)+E(f75(x2091,x2093,x2094,x2095),f75(x2092,x2093,x2094,x2095))
% 52.62/52.42 [210]~E(x2101,x2102)+E(f75(x2103,x2101,x2104,x2105),f75(x2103,x2102,x2104,x2105))
% 52.62/52.42 [211]~E(x2111,x2112)+E(f75(x2113,x2114,x2111,x2115),f75(x2113,x2114,x2112,x2115))
% 52.62/52.42 [212]~E(x2121,x2122)+E(f75(x2123,x2124,x2125,x2121),f75(x2123,x2124,x2125,x2122))
% 52.62/52.42 [213]~E(x2131,x2132)+E(f251(x2131,x2133,x2134),f251(x2132,x2133,x2134))
% 52.62/52.42 [214]~E(x2141,x2142)+E(f251(x2143,x2141,x2144),f251(x2143,x2142,x2144))
% 52.62/52.42 [215]~E(x2151,x2152)+E(f251(x2153,x2154,x2151),f251(x2153,x2154,x2152))
% 52.62/52.42 [216]~E(x2161,x2162)+E(f252(x2161,x2163,x2164,x2165,x2166,x2167),f252(x2162,x2163,x2164,x2165,x2166,x2167))
% 52.62/52.42 [217]~E(x2171,x2172)+E(f252(x2173,x2171,x2174,x2175,x2176,x2177),f252(x2173,x2172,x2174,x2175,x2176,x2177))
% 52.62/52.42 [218]~E(x2181,x2182)+E(f252(x2183,x2184,x2181,x2185,x2186,x2187),f252(x2183,x2184,x2182,x2185,x2186,x2187))
% 52.62/52.42 [219]~E(x2191,x2192)+E(f252(x2193,x2194,x2195,x2191,x2196,x2197),f252(x2193,x2194,x2195,x2192,x2196,x2197))
% 52.62/52.42 [220]~E(x2201,x2202)+E(f252(x2203,x2204,x2205,x2206,x2201,x2207),f252(x2203,x2204,x2205,x2206,x2202,x2207))
% 52.62/52.42 [221]~E(x2211,x2212)+E(f252(x2213,x2214,x2215,x2216,x2217,x2211),f252(x2213,x2214,x2215,x2216,x2217,x2212))
% 52.62/52.42 [222]~E(x2221,x2222)+E(f279(x2221),f279(x2222))
% 52.62/52.42 [223]~E(x2231,x2232)+E(f152(x2231),f152(x2232))
% 52.62/52.42 [224]~E(x2241,x2242)+E(f298(x2241,x2243,x2244),f298(x2242,x2243,x2244))
% 52.62/52.42 [225]~E(x2251,x2252)+E(f298(x2253,x2251,x2254),f298(x2253,x2252,x2254))
% 52.62/52.42 [226]~E(x2261,x2262)+E(f298(x2263,x2264,x2261),f298(x2263,x2264,x2262))
% 52.62/52.42 [227]~E(x2271,x2272)+E(f585(x2271,x2273,x2274,x2275,x2276,x2277),f585(x2272,x2273,x2274,x2275,x2276,x2277))
% 52.62/52.42 [228]~E(x2281,x2282)+E(f585(x2283,x2281,x2284,x2285,x2286,x2287),f585(x2283,x2282,x2284,x2285,x2286,x2287))
% 52.62/52.42 [229]~E(x2291,x2292)+E(f585(x2293,x2294,x2291,x2295,x2296,x2297),f585(x2293,x2294,x2292,x2295,x2296,x2297))
% 52.62/52.42 [230]~E(x2301,x2302)+E(f585(x2303,x2304,x2305,x2301,x2306,x2307),f585(x2303,x2304,x2305,x2302,x2306,x2307))
% 52.62/52.42 [231]~E(x2311,x2312)+E(f585(x2313,x2314,x2315,x2316,x2311,x2317),f585(x2313,x2314,x2315,x2316,x2312,x2317))
% 52.62/52.42 [232]~E(x2321,x2322)+E(f585(x2323,x2324,x2325,x2326,x2327,x2321),f585(x2323,x2324,x2325,x2326,x2327,x2322))
% 52.62/52.42 [233]~E(x2331,x2332)+E(f281(x2331,x2333,x2334),f281(x2332,x2333,x2334))
% 52.62/52.42 [234]~E(x2341,x2342)+E(f281(x2343,x2341,x2344),f281(x2343,x2342,x2344))
% 52.62/52.42 [235]~E(x2351,x2352)+E(f281(x2353,x2354,x2351),f281(x2353,x2354,x2352))
% 52.62/52.42 [236]~E(x2361,x2362)+E(f47(x2361,x2363),f47(x2362,x2363))
% 52.62/52.42 [237]~E(x2371,x2372)+E(f47(x2373,x2371),f47(x2373,x2372))
% 52.62/52.42 [238]~E(x2381,x2382)+E(f321(x2381,x2383),f321(x2382,x2383))
% 52.62/52.42 [239]~E(x2391,x2392)+E(f321(x2393,x2391),f321(x2393,x2392))
% 52.62/52.42 [240]~E(x2401,x2402)+E(f248(x2401,x2403),f248(x2402,x2403))
% 52.62/52.42 [241]~E(x2411,x2412)+E(f248(x2413,x2411),f248(x2413,x2412))
% 52.62/52.42 [242]~E(x2421,x2422)+E(f813(x2421,x2423,x2424,x2425),f813(x2422,x2423,x2424,x2425))
% 52.62/52.42 [243]~E(x2431,x2432)+E(f813(x2433,x2431,x2434,x2435),f813(x2433,x2432,x2434,x2435))
% 52.62/52.42 [244]~E(x2441,x2442)+E(f813(x2443,x2444,x2441,x2445),f813(x2443,x2444,x2442,x2445))
% 52.62/52.42 [245]~E(x2451,x2452)+E(f813(x2453,x2454,x2455,x2451),f813(x2453,x2454,x2455,x2452))
% 52.62/52.42 [246]~E(x2461,x2462)+E(f239(x2461),f239(x2462))
% 52.62/52.42 [247]~E(x2471,x2472)+E(f134(x2471,x2473),f134(x2472,x2473))
% 52.62/52.42 [248]~E(x2481,x2482)+E(f134(x2483,x2481),f134(x2483,x2482))
% 52.62/52.42 [249]~E(x2491,x2492)+E(f728(x2491),f728(x2492))
% 52.62/52.42 [250]~E(x2501,x2502)+E(f77(x2501),f77(x2502))
% 52.62/52.42 [251]~E(x2511,x2512)+E(f305(x2511,x2513,x2514),f305(x2512,x2513,x2514))
% 52.62/52.42 [252]~E(x2521,x2522)+E(f305(x2523,x2521,x2524),f305(x2523,x2522,x2524))
% 52.62/52.42 [253]~E(x2531,x2532)+E(f305(x2533,x2534,x2531),f305(x2533,x2534,x2532))
% 52.62/52.42 [254]~E(x2541,x2542)+E(f734(x2541,x2543,x2544,x2545,x2546),f734(x2542,x2543,x2544,x2545,x2546))
% 52.62/52.42 [255]~E(x2551,x2552)+E(f734(x2553,x2551,x2554,x2555,x2556),f734(x2553,x2552,x2554,x2555,x2556))
% 52.62/52.42 [256]~E(x2561,x2562)+E(f734(x2563,x2564,x2561,x2565,x2566),f734(x2563,x2564,x2562,x2565,x2566))
% 52.62/52.42 [257]~E(x2571,x2572)+E(f734(x2573,x2574,x2575,x2571,x2576),f734(x2573,x2574,x2575,x2572,x2576))
% 52.62/52.42 [258]~E(x2581,x2582)+E(f734(x2583,x2584,x2585,x2586,x2581),f734(x2583,x2584,x2585,x2586,x2582))
% 52.62/52.42 [259]~E(x2591,x2592)+E(f146(x2591,x2593),f146(x2592,x2593))
% 52.62/52.42 [260]~E(x2601,x2602)+E(f146(x2603,x2601),f146(x2603,x2602))
% 52.62/52.42 [261]~E(x2611,x2612)+E(f116(x2611,x2613),f116(x2612,x2613))
% 52.62/52.42 [262]~E(x2621,x2622)+E(f116(x2623,x2621),f116(x2623,x2622))
% 52.62/52.42 [263]~E(x2631,x2632)+E(f227(x2631),f227(x2632))
% 52.62/52.42 [264]~E(x2641,x2642)+E(f28(x2641,x2643),f28(x2642,x2643))
% 52.62/52.42 [265]~E(x2651,x2652)+E(f28(x2653,x2651),f28(x2653,x2652))
% 52.62/52.42 [266]~E(x2661,x2662)+E(f167(x2661,x2663),f167(x2662,x2663))
% 52.62/52.42 [267]~E(x2671,x2672)+E(f167(x2673,x2671),f167(x2673,x2672))
% 52.62/52.42 [268]~E(x2681,x2682)+E(f207(x2681),f207(x2682))
% 52.62/52.42 [269]~E(x2691,x2692)+E(f759(x2691),f759(x2692))
% 52.62/52.42 [270]~E(x2701,x2702)+E(f221(x2701,x2703),f221(x2702,x2703))
% 52.62/52.42 [271]~E(x2711,x2712)+E(f221(x2713,x2711),f221(x2713,x2712))
% 52.62/52.42 [272]~E(x2721,x2722)+E(f184(x2721),f184(x2722))
% 52.62/52.42 [273]~E(x2731,x2732)+E(f526(x2731,x2733),f526(x2732,x2733))
% 52.62/52.42 [274]~E(x2741,x2742)+E(f526(x2743,x2741),f526(x2743,x2742))
% 52.62/52.42 [275]~E(x2751,x2752)+E(f117(x2751),f117(x2752))
% 52.62/52.42 [276]~E(x2761,x2762)+E(f277(x2761,x2763,x2764),f277(x2762,x2763,x2764))
% 52.62/52.42 [277]~E(x2771,x2772)+E(f277(x2773,x2771,x2774),f277(x2773,x2772,x2774))
% 52.62/52.42 [278]~E(x2781,x2782)+E(f277(x2783,x2784,x2781),f277(x2783,x2784,x2782))
% 52.62/52.42 [279]~E(x2791,x2792)+E(f780(x2791,x2793,x2794),f780(x2792,x2793,x2794))
% 52.62/52.42 [280]~E(x2801,x2802)+E(f780(x2803,x2801,x2804),f780(x2803,x2802,x2804))
% 52.62/52.42 [281]~E(x2811,x2812)+E(f780(x2813,x2814,x2811),f780(x2813,x2814,x2812))
% 52.62/52.42 [282]~E(x2821,x2822)+E(f13(x2821,x2823,x2824),f13(x2822,x2823,x2824))
% 52.62/52.42 [283]~E(x2831,x2832)+E(f13(x2833,x2831,x2834),f13(x2833,x2832,x2834))
% 52.62/52.42 [284]~E(x2841,x2842)+E(f13(x2843,x2844,x2841),f13(x2843,x2844,x2842))
% 52.62/52.42 [285]~E(x2851,x2852)+E(f46(x2851,x2853),f46(x2852,x2853))
% 52.62/52.42 [286]~E(x2861,x2862)+E(f46(x2863,x2861),f46(x2863,x2862))
% 52.62/52.42 [287]~E(x2871,x2872)+E(f732(x2871,x2873,x2874,x2875,x2876),f732(x2872,x2873,x2874,x2875,x2876))
% 52.62/52.42 [288]~E(x2881,x2882)+E(f732(x2883,x2881,x2884,x2885,x2886),f732(x2883,x2882,x2884,x2885,x2886))
% 52.62/52.42 [289]~E(x2891,x2892)+E(f732(x2893,x2894,x2891,x2895,x2896),f732(x2893,x2894,x2892,x2895,x2896))
% 52.62/52.42 [290]~E(x2901,x2902)+E(f732(x2903,x2904,x2905,x2901,x2906),f732(x2903,x2904,x2905,x2902,x2906))
% 52.62/52.42 [291]~E(x2911,x2912)+E(f732(x2913,x2914,x2915,x2916,x2911),f732(x2913,x2914,x2915,x2916,x2912))
% 52.62/52.42 [292]~E(x2921,x2922)+E(f141(x2921),f141(x2922))
% 52.62/52.42 [293]~E(x2931,x2932)+E(f224(x2931,x2933,x2934),f224(x2932,x2933,x2934))
% 52.62/52.42 [294]~E(x2941,x2942)+E(f224(x2943,x2941,x2944),f224(x2943,x2942,x2944))
% 52.62/52.42 [295]~E(x2951,x2952)+E(f224(x2953,x2954,x2951),f224(x2953,x2954,x2952))
% 52.62/52.42 [296]~E(x2961,x2962)+E(f149(x2961,x2963),f149(x2962,x2963))
% 52.62/52.42 [297]~E(x2971,x2972)+E(f149(x2973,x2971),f149(x2973,x2972))
% 52.62/52.42 [298]~E(x2981,x2982)+E(f303(x2981,x2983,x2984),f303(x2982,x2983,x2984))
% 52.62/52.42 [299]~E(x2991,x2992)+E(f303(x2993,x2991,x2994),f303(x2993,x2992,x2994))
% 52.62/52.42 [300]~E(x3001,x3002)+E(f303(x3003,x3004,x3001),f303(x3003,x3004,x3002))
% 52.62/52.42 [301]~E(x3011,x3012)+E(f157(x3011),f157(x3012))
% 52.62/52.42 [302]~E(x3021,x3022)+E(f731(x3021,x3023,x3024,x3025,x3026),f731(x3022,x3023,x3024,x3025,x3026))
% 52.62/52.42 [303]~E(x3031,x3032)+E(f731(x3033,x3031,x3034,x3035,x3036),f731(x3033,x3032,x3034,x3035,x3036))
% 52.62/52.42 [304]~E(x3041,x3042)+E(f731(x3043,x3044,x3041,x3045,x3046),f731(x3043,x3044,x3042,x3045,x3046))
% 52.62/52.42 [305]~E(x3051,x3052)+E(f731(x3053,x3054,x3055,x3051,x3056),f731(x3053,x3054,x3055,x3052,x3056))
% 52.62/52.42 [306]~E(x3061,x3062)+E(f731(x3063,x3064,x3065,x3066,x3061),f731(x3063,x3064,x3065,x3066,x3062))
% 52.62/52.42 [307]~E(x3071,x3072)+E(f132(x3071,x3073,x3074,x3075),f132(x3072,x3073,x3074,x3075))
% 52.62/52.42 [308]~E(x3081,x3082)+E(f132(x3083,x3081,x3084,x3085),f132(x3083,x3082,x3084,x3085))
% 52.62/52.42 [309]~E(x3091,x3092)+E(f132(x3093,x3094,x3091,x3095),f132(x3093,x3094,x3092,x3095))
% 52.62/52.42 [310]~E(x3101,x3102)+E(f132(x3103,x3104,x3105,x3101),f132(x3103,x3104,x3105,x3102))
% 52.62/52.42 [311]~E(x3111,x3112)+E(f380(x3111,x3113,x3114),f380(x3112,x3113,x3114))
% 52.62/52.42 [312]~E(x3121,x3122)+E(f380(x3123,x3121,x3124),f380(x3123,x3122,x3124))
% 52.62/52.42 [313]~E(x3131,x3132)+E(f380(x3133,x3134,x3131),f380(x3133,x3134,x3132))
% 52.62/52.42 [314]~E(x3141,x3142)+E(f775(x3141,x3143,x3144),f775(x3142,x3143,x3144))
% 52.62/52.42 [315]~E(x3151,x3152)+E(f775(x3153,x3151,x3154),f775(x3153,x3152,x3154))
% 52.62/52.42 [316]~E(x3161,x3162)+E(f775(x3163,x3164,x3161),f775(x3163,x3164,x3162))
% 52.62/52.42 [317]~E(x3171,x3172)+E(f250(x3171,x3173),f250(x3172,x3173))
% 52.62/52.42 [318]~E(x3181,x3182)+E(f250(x3183,x3181),f250(x3183,x3182))
% 52.62/52.42 [319]~E(x3191,x3192)+E(f278(x3191,x3193),f278(x3192,x3193))
% 52.62/52.42 [320]~E(x3201,x3202)+E(f278(x3203,x3201),f278(x3203,x3202))
% 52.62/52.42 [321]~E(x3211,x3212)+E(f259(x3211,x3213),f259(x3212,x3213))
% 52.62/52.42 [322]~E(x3221,x3222)+E(f259(x3223,x3221),f259(x3223,x3222))
% 52.62/52.42 [323]~E(x3231,x3232)+E(f677(x3231,x3233,x3234),f677(x3232,x3233,x3234))
% 52.62/52.42 [324]~E(x3241,x3242)+E(f677(x3243,x3241,x3244),f677(x3243,x3242,x3244))
% 52.62/52.42 [325]~E(x3251,x3252)+E(f677(x3253,x3254,x3251),f677(x3253,x3254,x3252))
% 52.62/52.42 [326]~E(x3261,x3262)+E(f58(x3261,x3263),f58(x3262,x3263))
% 52.62/52.42 [327]~E(x3271,x3272)+E(f58(x3273,x3271),f58(x3273,x3272))
% 52.62/52.42 [328]~E(x3281,x3282)+E(f545(x3281,x3283,x3284,x3285,x3286),f545(x3282,x3283,x3284,x3285,x3286))
% 52.62/52.42 [329]~E(x3291,x3292)+E(f545(x3293,x3291,x3294,x3295,x3296),f545(x3293,x3292,x3294,x3295,x3296))
% 52.62/52.42 [330]~E(x3301,x3302)+E(f545(x3303,x3304,x3301,x3305,x3306),f545(x3303,x3304,x3302,x3305,x3306))
% 52.62/52.42 [331]~E(x3311,x3312)+E(f545(x3313,x3314,x3315,x3311,x3316),f545(x3313,x3314,x3315,x3312,x3316))
% 52.62/52.42 [332]~E(x3321,x3322)+E(f545(x3323,x3324,x3325,x3326,x3321),f545(x3323,x3324,x3325,x3326,x3322))
% 52.62/52.42 [333]~E(x3331,x3332)+E(f783(x3331,x3333,x3334),f783(x3332,x3333,x3334))
% 52.62/52.42 [334]~E(x3341,x3342)+E(f783(x3343,x3341,x3344),f783(x3343,x3342,x3344))
% 52.62/52.42 [335]~E(x3351,x3352)+E(f783(x3353,x3354,x3351),f783(x3353,x3354,x3352))
% 52.62/52.42 [336]~E(x3361,x3362)+E(f154(x3361),f154(x3362))
% 52.62/52.42 [337]~E(x3371,x3372)+E(f512(x3371,x3373,x3374,x3375,x3376),f512(x3372,x3373,x3374,x3375,x3376))
% 52.62/52.42 [338]~E(x3381,x3382)+E(f512(x3383,x3381,x3384,x3385,x3386),f512(x3383,x3382,x3384,x3385,x3386))
% 52.62/52.42 [339]~E(x3391,x3392)+E(f512(x3393,x3394,x3391,x3395,x3396),f512(x3393,x3394,x3392,x3395,x3396))
% 52.62/52.42 [340]~E(x3401,x3402)+E(f512(x3403,x3404,x3405,x3401,x3406),f512(x3403,x3404,x3405,x3402,x3406))
% 52.62/52.42 [341]~E(x3411,x3412)+E(f512(x3413,x3414,x3415,x3416,x3411),f512(x3413,x3414,x3415,x3416,x3412))
% 52.62/52.42 [342]~E(x3421,x3422)+E(f162(x3421,x3423,x3424),f162(x3422,x3423,x3424))
% 52.62/52.42 [343]~E(x3431,x3432)+E(f162(x3433,x3431,x3434),f162(x3433,x3432,x3434))
% 52.62/52.42 [344]~E(x3441,x3442)+E(f162(x3443,x3444,x3441),f162(x3443,x3444,x3442))
% 52.62/52.42 [345]~E(x3451,x3452)+E(f257(x3451),f257(x3452))
% 52.62/52.42 [346]~E(x3461,x3462)+E(f324(x3461,x3463),f324(x3462,x3463))
% 52.62/52.42 [347]~E(x3471,x3472)+E(f324(x3473,x3471),f324(x3473,x3472))
% 52.62/52.42 [348]~E(x3481,x3482)+E(f89(x3481),f89(x3482))
% 52.62/52.42 [349]~E(x3491,x3492)+E(f325(x3491,x3493),f325(x3492,x3493))
% 52.62/52.42 [350]~E(x3501,x3502)+E(f325(x3503,x3501),f325(x3503,x3502))
% 52.62/52.42 [351]~E(x3511,x3512)+E(f226(x3511,x3513),f226(x3512,x3513))
% 52.62/52.42 [352]~E(x3521,x3522)+E(f226(x3523,x3521),f226(x3523,x3522))
% 52.62/52.42 [353]~E(x3531,x3532)+E(f265(x3531,x3533),f265(x3532,x3533))
% 52.62/52.42 [354]~E(x3541,x3542)+E(f265(x3543,x3541),f265(x3543,x3542))
% 52.62/52.42 [355]~E(x3551,x3552)+E(f280(x3551,x3553),f280(x3552,x3553))
% 52.62/52.42 [356]~E(x3561,x3562)+E(f280(x3563,x3561),f280(x3563,x3562))
% 52.62/52.42 [357]~E(x3571,x3572)+E(f173(x3571,x3573),f173(x3572,x3573))
% 52.62/52.42 [358]~E(x3581,x3582)+E(f173(x3583,x3581),f173(x3583,x3582))
% 52.62/52.42 [359]~E(x3591,x3592)+E(f170(x3591,x3593,x3594,x3595),f170(x3592,x3593,x3594,x3595))
% 52.62/52.42 [360]~E(x3601,x3602)+E(f170(x3603,x3601,x3604,x3605),f170(x3603,x3602,x3604,x3605))
% 52.62/52.42 [361]~E(x3611,x3612)+E(f170(x3613,x3614,x3611,x3615),f170(x3613,x3614,x3612,x3615))
% 52.62/52.42 [362]~E(x3621,x3622)+E(f170(x3623,x3624,x3625,x3621),f170(x3623,x3624,x3625,x3622))
% 52.62/52.42 [363]~E(x3631,x3632)+E(f135(x3631,x3633),f135(x3632,x3633))
% 52.62/52.42 [364]~E(x3641,x3642)+E(f135(x3643,x3641),f135(x3643,x3642))
% 52.62/52.42 [365]~E(x3651,x3652)+E(f776(x3651,x3653,x3654),f776(x3652,x3653,x3654))
% 52.62/52.42 [366]~E(x3661,x3662)+E(f776(x3663,x3661,x3664),f776(x3663,x3662,x3664))
% 52.62/52.42 [367]~E(x3671,x3672)+E(f776(x3673,x3674,x3671),f776(x3673,x3674,x3672))
% 52.62/52.42 [368]~E(x3681,x3682)+E(f378(x3681,x3683,x3684,x3685),f378(x3682,x3683,x3684,x3685))
% 52.62/52.42 [369]~E(x3691,x3692)+E(f378(x3693,x3691,x3694,x3695),f378(x3693,x3692,x3694,x3695))
% 52.62/52.42 [370]~E(x3701,x3702)+E(f378(x3703,x3704,x3701,x3705),f378(x3703,x3704,x3702,x3705))
% 52.62/52.42 [371]~E(x3711,x3712)+E(f378(x3713,x3714,x3715,x3711),f378(x3713,x3714,x3715,x3712))
% 52.62/52.42 [372]~E(x3721,x3722)+E(f448(x3721,x3723),f448(x3722,x3723))
% 52.62/52.42 [373]~E(x3731,x3732)+E(f448(x3733,x3731),f448(x3733,x3732))
% 52.62/52.42 [374]~E(x3741,x3742)+E(f191(x3741,x3743,x3744,x3745),f191(x3742,x3743,x3744,x3745))
% 52.62/52.42 [375]~E(x3751,x3752)+E(f191(x3753,x3751,x3754,x3755),f191(x3753,x3752,x3754,x3755))
% 52.62/52.42 [376]~E(x3761,x3762)+E(f191(x3763,x3764,x3761,x3765),f191(x3763,x3764,x3762,x3765))
% 52.62/52.42 [377]~E(x3771,x3772)+E(f191(x3773,x3774,x3775,x3771),f191(x3773,x3774,x3775,x3772))
% 52.62/52.42 [378]~E(x3781,x3782)+E(f136(x3781,x3783),f136(x3782,x3783))
% 52.62/52.42 [379]~E(x3791,x3792)+E(f136(x3793,x3791),f136(x3793,x3792))
% 52.62/52.42 [380]~E(x3801,x3802)+E(f35(x3801,x3803),f35(x3802,x3803))
% 52.62/52.42 [381]~E(x3811,x3812)+E(f35(x3813,x3811),f35(x3813,x3812))
% 52.62/52.42 [382]~E(x3821,x3822)+E(f130(x3821,x3823),f130(x3822,x3823))
% 52.62/52.42 [383]~E(x3831,x3832)+E(f130(x3833,x3831),f130(x3833,x3832))
% 52.62/52.42 [384]~E(x3841,x3842)+E(f172(x3841,x3843,x3844,x3845),f172(x3842,x3843,x3844,x3845))
% 52.62/52.42 [385]~E(x3851,x3852)+E(f172(x3853,x3851,x3854,x3855),f172(x3853,x3852,x3854,x3855))
% 52.62/52.42 [386]~E(x3861,x3862)+E(f172(x3863,x3864,x3861,x3865),f172(x3863,x3864,x3862,x3865))
% 52.62/52.42 [387]~E(x3871,x3872)+E(f172(x3873,x3874,x3875,x3871),f172(x3873,x3874,x3875,x3872))
% 52.62/52.42 [388]~E(x3881,x3882)+E(f316(x3881,x3883,x3884,x3885),f316(x3882,x3883,x3884,x3885))
% 52.62/52.42 [389]~E(x3891,x3892)+E(f316(x3893,x3891,x3894,x3895),f316(x3893,x3892,x3894,x3895))
% 52.62/52.42 [390]~E(x3901,x3902)+E(f316(x3903,x3904,x3901,x3905),f316(x3903,x3904,x3902,x3905))
% 52.62/52.42 [391]~E(x3911,x3912)+E(f316(x3913,x3914,x3915,x3911),f316(x3913,x3914,x3915,x3912))
% 52.62/52.42 [392]~E(x3921,x3922)+E(f779(x3921,x3923,x3924),f779(x3922,x3923,x3924))
% 52.62/52.42 [393]~E(x3931,x3932)+E(f779(x3933,x3931,x3934),f779(x3933,x3932,x3934))
% 52.62/52.42 [394]~E(x3941,x3942)+E(f779(x3943,x3944,x3941),f779(x3943,x3944,x3942))
% 52.62/52.42 [395]~E(x3951,x3952)+E(f87(x3951,x3953),f87(x3952,x3953))
% 52.62/52.42 [396]~E(x3961,x3962)+E(f87(x3963,x3961),f87(x3963,x3962))
% 52.62/52.42 [397]~E(x3971,x3972)+E(f291(x3971,x3973,x3974,x3975),f291(x3972,x3973,x3974,x3975))
% 52.62/52.42 [398]~E(x3981,x3982)+E(f291(x3983,x3981,x3984,x3985),f291(x3983,x3982,x3984,x3985))
% 52.62/52.42 [399]~E(x3991,x3992)+E(f291(x3993,x3994,x3991,x3995),f291(x3993,x3994,x3992,x3995))
% 52.62/52.42 [400]~E(x4001,x4002)+E(f291(x4003,x4004,x4005,x4001),f291(x4003,x4004,x4005,x4002))
% 52.62/52.42 [401]~E(x4011,x4012)+E(f92(x4011,x4013),f92(x4012,x4013))
% 52.62/52.42 [402]~E(x4021,x4022)+E(f92(x4023,x4021),f92(x4023,x4022))
% 52.62/52.42 [403]~E(x4031,x4032)+E(f163(x4031,x4033),f163(x4032,x4033))
% 52.62/52.42 [404]~E(x4041,x4042)+E(f163(x4043,x4041),f163(x4043,x4042))
% 52.62/52.42 [405]~E(x4051,x4052)+E(f171(x4051,x4053,x4054),f171(x4052,x4053,x4054))
% 52.62/52.42 [406]~E(x4061,x4062)+E(f171(x4063,x4061,x4064),f171(x4063,x4062,x4064))
% 52.62/52.42 [407]~E(x4071,x4072)+E(f171(x4073,x4074,x4071),f171(x4073,x4074,x4072))
% 52.62/52.42 [408]~E(x4081,x4082)+E(f15(x4081,x4083),f15(x4082,x4083))
% 52.62/52.42 [409]~E(x4091,x4092)+E(f15(x4093,x4091),f15(x4093,x4092))
% 52.62/52.42 [410]~E(x4101,x4102)+E(f127(x4101),f127(x4102))
% 52.62/52.42 [411]~E(x4111,x4112)+E(f16(x4111,x4113),f16(x4112,x4113))
% 52.62/52.42 [412]~E(x4121,x4122)+E(f16(x4123,x4121),f16(x4123,x4122))
% 52.62/52.42 [413]~E(x4131,x4132)+E(f431(x4131,x4133,x4134,x4135),f431(x4132,x4133,x4134,x4135))
% 52.62/52.42 [414]~E(x4141,x4142)+E(f431(x4143,x4141,x4144,x4145),f431(x4143,x4142,x4144,x4145))
% 52.62/52.42 [415]~E(x4151,x4152)+E(f431(x4153,x4154,x4151,x4155),f431(x4153,x4154,x4152,x4155))
% 52.62/52.42 [416]~E(x4161,x4162)+E(f431(x4163,x4164,x4165,x4161),f431(x4163,x4164,x4165,x4162))
% 52.62/52.42 [417]~E(x4171,x4172)+E(f295(x4171,x4173,x4174),f295(x4172,x4173,x4174))
% 52.62/52.42 [418]~E(x4181,x4182)+E(f295(x4183,x4181,x4184),f295(x4183,x4182,x4184))
% 52.62/52.42 [419]~E(x4191,x4192)+E(f295(x4193,x4194,x4191),f295(x4193,x4194,x4192))
% 52.62/52.42 [420]~E(x4201,x4202)+E(f707(x4201,x4203,x4204,x4205),f707(x4202,x4203,x4204,x4205))
% 52.62/52.42 [421]~E(x4211,x4212)+E(f707(x4213,x4211,x4214,x4215),f707(x4213,x4212,x4214,x4215))
% 52.62/52.42 [422]~E(x4221,x4222)+E(f707(x4223,x4224,x4221,x4225),f707(x4223,x4224,x4222,x4225))
% 52.62/52.42 [423]~E(x4231,x4232)+E(f707(x4233,x4234,x4235,x4231),f707(x4233,x4234,x4235,x4232))
% 52.62/52.42 [424]~E(x4241,x4242)+E(f450(x4241,x4243,x4244,x4245),f450(x4242,x4243,x4244,x4245))
% 52.62/52.42 [425]~E(x4251,x4252)+E(f450(x4253,x4251,x4254,x4255),f450(x4253,x4252,x4254,x4255))
% 52.62/52.42 [426]~E(x4261,x4262)+E(f450(x4263,x4264,x4261,x4265),f450(x4263,x4264,x4262,x4265))
% 52.62/52.42 [427]~E(x4271,x4272)+E(f450(x4273,x4274,x4275,x4271),f450(x4273,x4274,x4275,x4272))
% 52.62/52.42 [428]~E(x4281,x4282)+E(f225(x4281,x4283,x4284,x4285),f225(x4282,x4283,x4284,x4285))
% 52.62/52.42 [429]~E(x4291,x4292)+E(f225(x4293,x4291,x4294,x4295),f225(x4293,x4292,x4294,x4295))
% 52.62/52.42 [430]~E(x4301,x4302)+E(f225(x4303,x4304,x4301,x4305),f225(x4303,x4304,x4302,x4305))
% 52.62/52.42 [431]~E(x4311,x4312)+E(f225(x4313,x4314,x4315,x4311),f225(x4313,x4314,x4315,x4312))
% 52.62/52.42 [432]~E(x4321,x4322)+E(f11(x4321,x4323),f11(x4322,x4323))
% 52.62/52.42 [433]~E(x4331,x4332)+E(f11(x4333,x4331),f11(x4333,x4332))
% 52.62/52.42 [434]~E(x4341,x4342)+E(f65(x4341,x4343,x4344),f65(x4342,x4343,x4344))
% 52.62/52.42 [435]~E(x4351,x4352)+E(f65(x4353,x4351,x4354),f65(x4353,x4352,x4354))
% 52.62/52.42 [436]~E(x4361,x4362)+E(f65(x4363,x4364,x4361),f65(x4363,x4364,x4362))
% 52.62/52.42 [437]~E(x4371,x4372)+E(f269(x4371,x4373,x4374),f269(x4372,x4373,x4374))
% 52.62/52.42 [438]~E(x4381,x4382)+E(f269(x4383,x4381,x4384),f269(x4383,x4382,x4384))
% 52.62/52.42 [439]~E(x4391,x4392)+E(f269(x4393,x4394,x4391),f269(x4393,x4394,x4392))
% 52.62/52.42 [440]~E(x4401,x4402)+E(f31(x4401,x4403,x4404),f31(x4402,x4403,x4404))
% 52.62/52.42 [441]~E(x4411,x4412)+E(f31(x4413,x4411,x4414),f31(x4413,x4412,x4414))
% 52.62/52.42 [442]~E(x4421,x4422)+E(f31(x4423,x4424,x4421),f31(x4423,x4424,x4422))
% 52.62/52.42 [443]~E(x4431,x4432)+E(f550(x4431,x4433,x4434),f550(x4432,x4433,x4434))
% 52.62/52.42 [444]~E(x4441,x4442)+E(f550(x4443,x4441,x4444),f550(x4443,x4442,x4444))
% 52.62/52.42 [445]~E(x4451,x4452)+E(f550(x4453,x4454,x4451),f550(x4453,x4454,x4452))
% 52.62/52.42 [446]~E(x4461,x4462)+E(f345(x4461,x4463,x4464,x4465),f345(x4462,x4463,x4464,x4465))
% 52.62/52.42 [447]~E(x4471,x4472)+E(f345(x4473,x4471,x4474,x4475),f345(x4473,x4472,x4474,x4475))
% 52.62/52.42 [448]~E(x4481,x4482)+E(f345(x4483,x4484,x4481,x4485),f345(x4483,x4484,x4482,x4485))
% 52.62/52.42 [449]~E(x4491,x4492)+E(f345(x4493,x4494,x4495,x4491),f345(x4493,x4494,x4495,x4492))
% 52.62/52.42 [450]~E(x4501,x4502)+E(f93(x4501),f93(x4502))
% 52.62/52.42 [451]~E(x4511,x4512)+E(f32(x4511,x4513,x4514),f32(x4512,x4513,x4514))
% 52.62/52.42 [452]~E(x4521,x4522)+E(f32(x4523,x4521,x4524),f32(x4523,x4522,x4524))
% 52.62/52.42 [453]~E(x4531,x4532)+E(f32(x4533,x4534,x4531),f32(x4533,x4534,x4532))
% 52.62/52.42 [454]~E(x4541,x4542)+E(f698(x4541,x4543),f698(x4542,x4543))
% 52.62/52.42 [455]~E(x4551,x4552)+E(f698(x4553,x4551),f698(x4553,x4552))
% 52.62/52.42 [456]~E(x4561,x4562)+E(f175(x4561,x4563,x4564,x4565),f175(x4562,x4563,x4564,x4565))
% 52.62/52.42 [457]~E(x4571,x4572)+E(f175(x4573,x4571,x4574,x4575),f175(x4573,x4572,x4574,x4575))
% 52.62/52.42 [458]~E(x4581,x4582)+E(f175(x4583,x4584,x4581,x4585),f175(x4583,x4584,x4582,x4585))
% 52.62/52.42 [459]~E(x4591,x4592)+E(f175(x4593,x4594,x4595,x4591),f175(x4593,x4594,x4595,x4592))
% 52.62/52.42 [460]~E(x4601,x4602)+E(f778(x4601,x4603,x4604),f778(x4602,x4603,x4604))
% 52.62/52.42 [461]~E(x4611,x4612)+E(f778(x4613,x4611,x4614),f778(x4613,x4612,x4614))
% 52.62/52.42 [462]~E(x4621,x4622)+E(f778(x4623,x4624,x4621),f778(x4623,x4624,x4622))
% 52.62/52.42 [463]~E(x4631,x4632)+E(f823(x4631,x4633,x4634),f823(x4632,x4633,x4634))
% 52.62/52.42 [464]~E(x4641,x4642)+E(f823(x4643,x4641,x4644),f823(x4643,x4642,x4644))
% 52.62/52.42 [465]~E(x4651,x4652)+E(f823(x4653,x4654,x4651),f823(x4653,x4654,x4652))
% 52.62/52.42 [466]~E(x4661,x4662)+E(f164(x4661,x4663),f164(x4662,x4663))
% 52.62/52.42 [467]~E(x4671,x4672)+E(f164(x4673,x4671),f164(x4673,x4672))
% 52.62/52.42 [468]~E(x4681,x4682)+E(f229(x4681,x4683,x4684,x4685),f229(x4682,x4683,x4684,x4685))
% 52.62/52.42 [469]~E(x4691,x4692)+E(f229(x4693,x4691,x4694,x4695),f229(x4693,x4692,x4694,x4695))
% 52.62/52.42 [470]~E(x4701,x4702)+E(f229(x4703,x4704,x4701,x4705),f229(x4703,x4704,x4702,x4705))
% 52.62/52.42 [471]~E(x4711,x4712)+E(f229(x4713,x4714,x4715,x4711),f229(x4713,x4714,x4715,x4712))
% 52.62/52.42 [472]~E(x4721,x4722)+E(f486(x4721,x4723,x4724,x4725,x4726),f486(x4722,x4723,x4724,x4725,x4726))
% 52.62/52.42 [473]~E(x4731,x4732)+E(f486(x4733,x4731,x4734,x4735,x4736),f486(x4733,x4732,x4734,x4735,x4736))
% 52.62/52.42 [474]~E(x4741,x4742)+E(f486(x4743,x4744,x4741,x4745,x4746),f486(x4743,x4744,x4742,x4745,x4746))
% 52.62/52.42 [475]~E(x4751,x4752)+E(f486(x4753,x4754,x4755,x4751,x4756),f486(x4753,x4754,x4755,x4752,x4756))
% 52.62/52.42 [476]~E(x4761,x4762)+E(f486(x4763,x4764,x4765,x4766,x4761),f486(x4763,x4764,x4765,x4766,x4762))
% 52.62/52.42 [477]~E(x4771,x4772)+E(f260(x4771,x4773),f260(x4772,x4773))
% 52.62/52.42 [478]~E(x4781,x4782)+E(f260(x4783,x4781),f260(x4783,x4782))
% 52.62/52.42 [479]~E(x4791,x4792)+E(f14(x4791,x4793,x4794),f14(x4792,x4793,x4794))
% 52.62/52.42 [480]~E(x4801,x4802)+E(f14(x4803,x4801,x4804),f14(x4803,x4802,x4804))
% 52.62/52.42 [481]~E(x4811,x4812)+E(f14(x4813,x4814,x4811),f14(x4813,x4814,x4812))
% 52.62/52.42 [482]~E(x4821,x4822)+E(f847(x4821),f847(x4822))
% 52.62/52.42 [483]~E(x4831,x4832)+E(f174(x4831,x4833,x4834),f174(x4832,x4833,x4834))
% 52.62/52.42 [484]~E(x4841,x4842)+E(f174(x4843,x4841,x4844),f174(x4843,x4842,x4844))
% 52.62/52.42 [485]~E(x4851,x4852)+E(f174(x4853,x4854,x4851),f174(x4853,x4854,x4852))
% 52.62/52.42 [486]~E(x4861,x4862)+E(f307(x4861,x4863,x4864),f307(x4862,x4863,x4864))
% 52.62/52.42 [487]~E(x4871,x4872)+E(f307(x4873,x4871,x4874),f307(x4873,x4872,x4874))
% 52.62/52.42 [488]~E(x4881,x4882)+E(f307(x4883,x4884,x4881),f307(x4883,x4884,x4882))
% 52.62/52.42 [489]~E(x4891,x4892)+E(f299(x4891),f299(x4892))
% 52.62/52.42 [490]~E(x4901,x4902)+E(f294(x4901,x4903),f294(x4902,x4903))
% 52.62/52.42 [491]~E(x4911,x4912)+E(f294(x4913,x4911),f294(x4913,x4912))
% 52.62/52.42 [492]~E(x4921,x4922)+E(f133(x4921,x4923),f133(x4922,x4923))
% 52.62/52.42 [493]~E(x4931,x4932)+E(f133(x4933,x4931),f133(x4933,x4932))
% 52.62/52.42 [494]~E(x4941,x4942)+E(f516(x4941,x4943,x4944,x4945),f516(x4942,x4943,x4944,x4945))
% 52.62/52.42 [495]~E(x4951,x4952)+E(f516(x4953,x4951,x4954,x4955),f516(x4953,x4952,x4954,x4955))
% 52.62/52.42 [496]~E(x4961,x4962)+E(f516(x4963,x4964,x4961,x4965),f516(x4963,x4964,x4962,x4965))
% 52.62/52.42 [497]~E(x4971,x4972)+E(f516(x4973,x4974,x4975,x4971),f516(x4973,x4974,x4975,x4972))
% 52.62/52.42 [498]~E(x4981,x4982)+E(f166(x4981,x4983,x4984),f166(x4982,x4983,x4984))
% 52.62/52.42 [499]~E(x4991,x4992)+E(f166(x4993,x4991,x4994),f166(x4993,x4992,x4994))
% 52.62/52.42 [500]~E(x5001,x5002)+E(f166(x5003,x5004,x5001),f166(x5003,x5004,x5002))
% 52.62/52.42 [501]~E(x5011,x5012)+E(f659(x5011,x5013,x5014,x5015,x5016),f659(x5012,x5013,x5014,x5015,x5016))
% 52.62/52.42 [502]~E(x5021,x5022)+E(f659(x5023,x5021,x5024,x5025,x5026),f659(x5023,x5022,x5024,x5025,x5026))
% 52.62/52.42 [503]~E(x5031,x5032)+E(f659(x5033,x5034,x5031,x5035,x5036),f659(x5033,x5034,x5032,x5035,x5036))
% 52.62/52.42 [504]~E(x5041,x5042)+E(f659(x5043,x5044,x5045,x5041,x5046),f659(x5043,x5044,x5045,x5042,x5046))
% 52.62/52.42 [505]~E(x5051,x5052)+E(f659(x5053,x5054,x5055,x5056,x5051),f659(x5053,x5054,x5055,x5056,x5052))
% 52.62/52.42 [506]~E(x5061,x5062)+E(f549(x5061,x5063,x5064),f549(x5062,x5063,x5064))
% 52.62/52.42 [507]~E(x5071,x5072)+E(f549(x5073,x5071,x5074),f549(x5073,x5072,x5074))
% 52.62/52.42 [508]~E(x5081,x5082)+E(f549(x5083,x5084,x5081),f549(x5083,x5084,x5082))
% 52.62/52.42 [509]~E(x5091,x5092)+E(f38(x5091,x5093,x5094,x5095,x5096,x5097,x5098,x5099,x50910,x50911),f38(x5092,x5093,x5094,x5095,x5096,x5097,x5098,x5099,x50910,x50911))
% 52.62/52.42 [510]~E(x5101,x5102)+E(f38(x5103,x5101,x5104,x5105,x5106,x5107,x5108,x5109,x51010,x51011),f38(x5103,x5102,x5104,x5105,x5106,x5107,x5108,x5109,x51010,x51011))
% 52.62/52.42 [511]~E(x5111,x5112)+E(f38(x5113,x5114,x5111,x5115,x5116,x5117,x5118,x5119,x51110,x51111),f38(x5113,x5114,x5112,x5115,x5116,x5117,x5118,x5119,x51110,x51111))
% 52.62/52.42 [512]~E(x5121,x5122)+E(f38(x5123,x5124,x5125,x5121,x5126,x5127,x5128,x5129,x51210,x51211),f38(x5123,x5124,x5125,x5122,x5126,x5127,x5128,x5129,x51210,x51211))
% 52.62/52.42 [513]~E(x5131,x5132)+E(f38(x5133,x5134,x5135,x5136,x5131,x5137,x5138,x5139,x51310,x51311),f38(x5133,x5134,x5135,x5136,x5132,x5137,x5138,x5139,x51310,x51311))
% 52.62/52.42 [514]~E(x5141,x5142)+E(f38(x5143,x5144,x5145,x5146,x5147,x5141,x5148,x5149,x51410,x51411),f38(x5143,x5144,x5145,x5146,x5147,x5142,x5148,x5149,x51410,x51411))
% 52.62/52.42 [515]~E(x5151,x5152)+E(f38(x5153,x5154,x5155,x5156,x5157,x5158,x5151,x5159,x51510,x51511),f38(x5153,x5154,x5155,x5156,x5157,x5158,x5152,x5159,x51510,x51511))
% 52.62/52.42 [516]~E(x5161,x5162)+E(f38(x5163,x5164,x5165,x5166,x5167,x5168,x5169,x5161,x51610,x51611),f38(x5163,x5164,x5165,x5166,x5167,x5168,x5169,x5162,x51610,x51611))
% 52.62/52.42 [517]~E(x5171,x5172)+E(f38(x5173,x5174,x5175,x5176,x5177,x5178,x5179,x51710,x5171,x51711),f38(x5173,x5174,x5175,x5176,x5177,x5178,x5179,x51710,x5172,x51711))
% 52.62/52.42 [518]~E(x5181,x5182)+E(f38(x5183,x5184,x5185,x5186,x5187,x5188,x5189,x51810,x51811,x5181),f38(x5183,x5184,x5185,x5186,x5187,x5188,x5189,x51810,x51811,x5182))
% 52.62/52.42 [519]~E(x5191,x5192)+E(f322(x5191,x5193),f322(x5192,x5193))
% 52.62/52.42 [520]~E(x5201,x5202)+E(f322(x5203,x5201),f322(x5203,x5202))
% 52.62/52.42 [521]~E(x5211,x5212)+E(f240(x5211,x5213),f240(x5212,x5213))
% 52.62/52.42 [522]~E(x5221,x5222)+E(f240(x5223,x5221),f240(x5223,x5222))
% 52.62/52.42 [523]~E(x5231,x5232)+E(f528(x5231,x5233,x5234,x5235),f528(x5232,x5233,x5234,x5235))
% 52.62/52.42 [524]~E(x5241,x5242)+E(f528(x5243,x5241,x5244,x5245),f528(x5243,x5242,x5244,x5245))
% 52.62/52.42 [525]~E(x5251,x5252)+E(f528(x5253,x5254,x5251,x5255),f528(x5253,x5254,x5252,x5255))
% 52.62/52.42 [526]~E(x5261,x5262)+E(f528(x5263,x5264,x5265,x5261),f528(x5263,x5264,x5265,x5262))
% 52.62/52.42 [527]~E(x5271,x5272)+E(f137(x5271,x5273),f137(x5272,x5273))
% 52.62/52.42 [528]~E(x5281,x5282)+E(f137(x5283,x5281),f137(x5283,x5282))
% 52.62/52.42 [529]~E(x5291,x5292)+E(f258(x5291),f258(x5292))
% 52.62/52.42 [530]~E(x5301,x5302)+E(f792(x5301,x5303,x5304),f792(x5302,x5303,x5304))
% 52.62/52.42 [531]~E(x5311,x5312)+E(f792(x5313,x5311,x5314),f792(x5313,x5312,x5314))
% 52.62/52.42 [532]~E(x5321,x5322)+E(f792(x5323,x5324,x5321),f792(x5323,x5324,x5322))
% 52.62/52.42 [533]~E(x5331,x5332)+E(f159(x5331),f159(x5332))
% 52.62/52.42 [534]~E(x5341,x5342)+E(f739(x5341,x5343,x5344,x5345),f739(x5342,x5343,x5344,x5345))
% 52.62/52.42 [535]~E(x5351,x5352)+E(f739(x5353,x5351,x5354,x5355),f739(x5353,x5352,x5354,x5355))
% 52.62/52.42 [536]~E(x5361,x5362)+E(f739(x5363,x5364,x5361,x5365),f739(x5363,x5364,x5362,x5365))
% 52.62/52.42 [537]~E(x5371,x5372)+E(f739(x5373,x5374,x5375,x5371),f739(x5373,x5374,x5375,x5372))
% 52.62/52.42 [538]~E(x5381,x5382)+E(f468(x5381,x5383,x5384),f468(x5382,x5383,x5384))
% 52.62/52.42 [539]~E(x5391,x5392)+E(f468(x5393,x5391,x5394),f468(x5393,x5392,x5394))
% 52.62/52.42 [540]~E(x5401,x5402)+E(f468(x5403,x5404,x5401),f468(x5403,x5404,x5402))
% 52.62/52.42 [541]~E(x5411,x5412)+E(f609(x5411,x5413,x5414),f609(x5412,x5413,x5414))
% 52.62/52.42 [542]~E(x5421,x5422)+E(f609(x5423,x5421,x5424),f609(x5423,x5422,x5424))
% 52.62/52.42 [543]~E(x5431,x5432)+E(f609(x5433,x5434,x5431),f609(x5433,x5434,x5432))
% 52.62/52.42 [544]~E(x5441,x5442)+E(f821(x5441,x5443,x5444),f821(x5442,x5443,x5444))
% 52.62/52.42 [545]~E(x5451,x5452)+E(f821(x5453,x5451,x5454),f821(x5453,x5452,x5454))
% 52.62/52.42 [546]~E(x5461,x5462)+E(f821(x5463,x5464,x5461),f821(x5463,x5464,x5462))
% 52.62/52.42 [547]~E(x5471,x5472)+E(f68(x5471,x5473,x5474),f68(x5472,x5473,x5474))
% 52.62/52.42 [548]~E(x5481,x5482)+E(f68(x5483,x5481,x5484),f68(x5483,x5482,x5484))
% 52.62/52.42 [549]~E(x5491,x5492)+E(f68(x5493,x5494,x5491),f68(x5493,x5494,x5492))
% 52.62/52.42 [550]~E(x5501,x5502)+E(f296(x5501),f296(x5502))
% 52.62/52.42 [551]~E(x5511,x5512)+E(f98(x5511),f98(x5512))
% 52.62/52.42 [552]~E(x5521,x5522)+E(f176(x5521),f176(x5522))
% 52.62/52.42 [553]~E(x5531,x5532)+E(f286(x5531,x5533,x5534),f286(x5532,x5533,x5534))
% 52.62/52.42 [554]~E(x5541,x5542)+E(f286(x5543,x5541,x5544),f286(x5543,x5542,x5544))
% 52.62/52.42 [555]~E(x5551,x5552)+E(f286(x5553,x5554,x5551),f286(x5553,x5554,x5552))
% 52.62/52.42 [556]~E(x5561,x5562)+E(f463(x5561,x5563,x5564),f463(x5562,x5563,x5564))
% 52.62/52.42 [557]~E(x5571,x5572)+E(f463(x5573,x5571,x5574),f463(x5573,x5572,x5574))
% 52.62/52.42 [558]~E(x5581,x5582)+E(f463(x5583,x5584,x5581),f463(x5583,x5584,x5582))
% 52.62/52.42 [559]~E(x5591,x5592)+E(f741(x5591,x5593,x5594,x5595),f741(x5592,x5593,x5594,x5595))
% 52.62/52.42 [560]~E(x5601,x5602)+E(f741(x5603,x5601,x5604,x5605),f741(x5603,x5602,x5604,x5605))
% 52.62/52.42 [561]~E(x5611,x5612)+E(f741(x5613,x5614,x5611,x5615),f741(x5613,x5614,x5612,x5615))
% 52.62/52.42 [562]~E(x5621,x5622)+E(f741(x5623,x5624,x5625,x5621),f741(x5623,x5624,x5625,x5622))
% 52.62/52.42 [563]~E(x5631,x5632)+E(f790(x5631,x5633,x5634),f790(x5632,x5633,x5634))
% 52.62/52.42 [564]~E(x5641,x5642)+E(f790(x5643,x5641,x5644),f790(x5643,x5642,x5644))
% 52.62/52.42 [565]~E(x5651,x5652)+E(f790(x5653,x5654,x5651),f790(x5653,x5654,x5652))
% 52.62/52.42 [566]~E(x5661,x5662)+E(f293(x5661),f293(x5662))
% 52.62/52.42 [567]~E(x5671,x5672)+E(f521(x5671,x5673,x5674,x5675),f521(x5672,x5673,x5674,x5675))
% 52.62/52.42 [568]~E(x5681,x5682)+E(f521(x5683,x5681,x5684,x5685),f521(x5683,x5682,x5684,x5685))
% 52.62/52.42 [569]~E(x5691,x5692)+E(f521(x5693,x5694,x5691,x5695),f521(x5693,x5694,x5692,x5695))
% 52.62/52.42 [570]~E(x5701,x5702)+E(f521(x5703,x5704,x5705,x5701),f521(x5703,x5704,x5705,x5702))
% 52.62/52.42 [571]~E(x5711,x5712)+E(f88(x5711,x5713),f88(x5712,x5713))
% 52.62/52.42 [572]~E(x5721,x5722)+E(f88(x5723,x5721),f88(x5723,x5722))
% 52.62/52.42 [573]~E(x5731,x5732)+E(f297(x5731,x5733,x5734),f297(x5732,x5733,x5734))
% 52.62/52.42 [574]~E(x5741,x5742)+E(f297(x5743,x5741,x5744),f297(x5743,x5742,x5744))
% 52.62/52.42 [575]~E(x5751,x5752)+E(f297(x5753,x5754,x5751),f297(x5753,x5754,x5752))
% 52.62/52.42 [576]~E(x5761,x5762)+E(f351(x5761,x5763),f351(x5762,x5763))
% 52.62/52.42 [577]~E(x5771,x5772)+E(f351(x5773,x5771),f351(x5773,x5772))
% 52.62/52.42 [578]~E(x5781,x5782)+E(f219(x5781,x5783,x5784,x5785,x5786),f219(x5782,x5783,x5784,x5785,x5786))
% 52.62/52.42 [579]~E(x5791,x5792)+E(f219(x5793,x5791,x5794,x5795,x5796),f219(x5793,x5792,x5794,x5795,x5796))
% 52.62/52.42 [580]~E(x5801,x5802)+E(f219(x5803,x5804,x5801,x5805,x5806),f219(x5803,x5804,x5802,x5805,x5806))
% 52.62/52.42 [581]~E(x5811,x5812)+E(f219(x5813,x5814,x5815,x5811,x5816),f219(x5813,x5814,x5815,x5812,x5816))
% 52.62/52.42 [582]~E(x5821,x5822)+E(f219(x5823,x5824,x5825,x5826,x5821),f219(x5823,x5824,x5825,x5826,x5822))
% 52.62/52.42 [583]~E(x5831,x5832)+E(f627(x5831,x5833,x5834,x5835,x5836,x5837),f627(x5832,x5833,x5834,x5835,x5836,x5837))
% 52.62/52.42 [584]~E(x5841,x5842)+E(f627(x5843,x5841,x5844,x5845,x5846,x5847),f627(x5843,x5842,x5844,x5845,x5846,x5847))
% 52.62/52.42 [585]~E(x5851,x5852)+E(f627(x5853,x5854,x5851,x5855,x5856,x5857),f627(x5853,x5854,x5852,x5855,x5856,x5857))
% 52.62/52.42 [586]~E(x5861,x5862)+E(f627(x5863,x5864,x5865,x5861,x5866,x5867),f627(x5863,x5864,x5865,x5862,x5866,x5867))
% 52.62/52.42 [587]~E(x5871,x5872)+E(f627(x5873,x5874,x5875,x5876,x5871,x5877),f627(x5873,x5874,x5875,x5876,x5872,x5877))
% 52.62/52.42 [588]~E(x5881,x5882)+E(f627(x5883,x5884,x5885,x5886,x5887,x5881),f627(x5883,x5884,x5885,x5886,x5887,x5882))
% 52.62/52.42 [589]~E(x5891,x5892)+E(f253(x5891,x5893,x5894,x5895),f253(x5892,x5893,x5894,x5895))
% 52.62/52.42 [590]~E(x5901,x5902)+E(f253(x5903,x5901,x5904,x5905),f253(x5903,x5902,x5904,x5905))
% 52.62/52.42 [591]~E(x5911,x5912)+E(f253(x5913,x5914,x5911,x5915),f253(x5913,x5914,x5912,x5915))
% 52.62/52.42 [592]~E(x5921,x5922)+E(f253(x5923,x5924,x5925,x5921),f253(x5923,x5924,x5925,x5922))
% 52.62/52.42 [593]~E(x5931,x5932)+E(f452(x5931,x5933,x5934,x5935,x5936,x5937,x5938),f452(x5932,x5933,x5934,x5935,x5936,x5937,x5938))
% 52.62/52.42 [594]~E(x5941,x5942)+E(f452(x5943,x5941,x5944,x5945,x5946,x5947,x5948),f452(x5943,x5942,x5944,x5945,x5946,x5947,x5948))
% 52.62/52.42 [595]~E(x5951,x5952)+E(f452(x5953,x5954,x5951,x5955,x5956,x5957,x5958),f452(x5953,x5954,x5952,x5955,x5956,x5957,x5958))
% 52.62/52.42 [596]~E(x5961,x5962)+E(f452(x5963,x5964,x5965,x5961,x5966,x5967,x5968),f452(x5963,x5964,x5965,x5962,x5966,x5967,x5968))
% 52.62/52.42 [597]~E(x5971,x5972)+E(f452(x5973,x5974,x5975,x5976,x5971,x5977,x5978),f452(x5973,x5974,x5975,x5976,x5972,x5977,x5978))
% 52.62/52.42 [598]~E(x5981,x5982)+E(f452(x5983,x5984,x5985,x5986,x5987,x5981,x5988),f452(x5983,x5984,x5985,x5986,x5987,x5982,x5988))
% 52.62/52.42 [599]~E(x5991,x5992)+E(f452(x5993,x5994,x5995,x5996,x5997,x5998,x5991),f452(x5993,x5994,x5995,x5996,x5997,x5998,x5992))
% 52.62/52.42 [600]~E(x6001,x6002)+E(f626(x6001,x6003,x6004),f626(x6002,x6003,x6004))
% 52.62/52.42 [601]~E(x6011,x6012)+E(f626(x6013,x6011,x6014),f626(x6013,x6012,x6014))
% 52.62/52.42 [602]~E(x6021,x6022)+E(f626(x6023,x6024,x6021),f626(x6023,x6024,x6022))
% 52.62/52.42 [603]~E(x6031,x6032)+E(f17(x6031,x6033),f17(x6032,x6033))
% 52.62/52.42 [604]~E(x6041,x6042)+E(f17(x6043,x6041),f17(x6043,x6042))
% 52.62/52.42 [605]~E(x6051,x6052)+E(f78(x6051,x6053,x6054,x6055,x6056),f78(x6052,x6053,x6054,x6055,x6056))
% 52.62/52.42 [606]~E(x6061,x6062)+E(f78(x6063,x6061,x6064,x6065,x6066),f78(x6063,x6062,x6064,x6065,x6066))
% 52.62/52.42 [607]~E(x6071,x6072)+E(f78(x6073,x6074,x6071,x6075,x6076),f78(x6073,x6074,x6072,x6075,x6076))
% 52.62/52.42 [608]~E(x6081,x6082)+E(f78(x6083,x6084,x6085,x6081,x6086),f78(x6083,x6084,x6085,x6082,x6086))
% 52.62/52.42 [609]~E(x6091,x6092)+E(f78(x6093,x6094,x6095,x6096,x6091),f78(x6093,x6094,x6095,x6096,x6092))
% 52.62/52.42 [610]~E(x6101,x6102)+E(f457(x6101,x6103,x6104,x6105,x6106),f457(x6102,x6103,x6104,x6105,x6106))
% 52.62/52.42 [611]~E(x6111,x6112)+E(f457(x6113,x6111,x6114,x6115,x6116),f457(x6113,x6112,x6114,x6115,x6116))
% 52.62/52.42 [612]~E(x6121,x6122)+E(f457(x6123,x6124,x6121,x6125,x6126),f457(x6123,x6124,x6122,x6125,x6126))
% 52.62/52.42 [613]~E(x6131,x6132)+E(f457(x6133,x6134,x6135,x6131,x6136),f457(x6133,x6134,x6135,x6132,x6136))
% 52.62/52.42 [614]~E(x6141,x6142)+E(f457(x6143,x6144,x6145,x6146,x6141),f457(x6143,x6144,x6145,x6146,x6142))
% 52.62/52.42 [615]~E(x6151,x6152)+E(f540(x6151,x6153,x6154,x6155,x6156),f540(x6152,x6153,x6154,x6155,x6156))
% 52.62/52.42 [616]~E(x6161,x6162)+E(f540(x6163,x6161,x6164,x6165,x6166),f540(x6163,x6162,x6164,x6165,x6166))
% 52.62/52.42 [617]~E(x6171,x6172)+E(f540(x6173,x6174,x6171,x6175,x6176),f540(x6173,x6174,x6172,x6175,x6176))
% 52.62/52.42 [618]~E(x6181,x6182)+E(f540(x6183,x6184,x6185,x6181,x6186),f540(x6183,x6184,x6185,x6182,x6186))
% 52.62/52.42 [619]~E(x6191,x6192)+E(f540(x6193,x6194,x6195,x6196,x6191),f540(x6193,x6194,x6195,x6196,x6192))
% 52.62/52.42 [620]~E(x6201,x6202)+E(f494(x6201,x6203,x6204,x6205),f494(x6202,x6203,x6204,x6205))
% 52.62/52.42 [621]~E(x6211,x6212)+E(f494(x6213,x6211,x6214,x6215),f494(x6213,x6212,x6214,x6215))
% 52.62/52.42 [622]~E(x6221,x6222)+E(f494(x6223,x6224,x6221,x6225),f494(x6223,x6224,x6222,x6225))
% 52.62/52.42 [623]~E(x6231,x6232)+E(f494(x6233,x6234,x6235,x6231),f494(x6233,x6234,x6235,x6232))
% 52.62/52.42 [624]~E(x6241,x6242)+E(f816(x6241,x6243,x6244),f816(x6242,x6243,x6244))
% 52.62/52.42 [625]~E(x6251,x6252)+E(f816(x6253,x6251,x6254),f816(x6253,x6252,x6254))
% 52.62/52.42 [626]~E(x6261,x6262)+E(f816(x6263,x6264,x6261),f816(x6263,x6264,x6262))
% 52.62/52.42 [627]~E(x6271,x6272)+E(f582(x6271,x6273),f582(x6272,x6273))
% 52.62/52.42 [628]~E(x6281,x6282)+E(f582(x6283,x6281),f582(x6283,x6282))
% 52.62/52.42 [629]~E(x6291,x6292)+E(f84(x6291,x6293),f84(x6292,x6293))
% 52.62/52.42 [630]~E(x6301,x6302)+E(f84(x6303,x6301),f84(x6303,x6302))
% 52.62/52.42 [631]~E(x6311,x6312)+E(f854(x6311,x6313),f854(x6312,x6313))
% 52.62/52.42 [632]~E(x6321,x6322)+E(f854(x6323,x6321),f854(x6323,x6322))
% 52.62/52.42 [633]~E(x6331,x6332)+E(f422(x6331,x6333,x6334),f422(x6332,x6333,x6334))
% 52.62/52.42 [634]~E(x6341,x6342)+E(f422(x6343,x6341,x6344),f422(x6343,x6342,x6344))
% 52.62/52.42 [635]~E(x6351,x6352)+E(f422(x6353,x6354,x6351),f422(x6353,x6354,x6352))
% 52.62/52.42 [636]~E(x6361,x6362)+E(f292(x6361,x6363,x6364,x6365,x6366),f292(x6362,x6363,x6364,x6365,x6366))
% 52.62/52.42 [637]~E(x6371,x6372)+E(f292(x6373,x6371,x6374,x6375,x6376),f292(x6373,x6372,x6374,x6375,x6376))
% 52.62/52.42 [638]~E(x6381,x6382)+E(f292(x6383,x6384,x6381,x6385,x6386),f292(x6383,x6384,x6382,x6385,x6386))
% 52.62/52.42 [639]~E(x6391,x6392)+E(f292(x6393,x6394,x6395,x6391,x6396),f292(x6393,x6394,x6395,x6392,x6396))
% 52.62/52.42 [640]~E(x6401,x6402)+E(f292(x6403,x6404,x6405,x6406,x6401),f292(x6403,x6404,x6405,x6406,x6402))
% 52.62/52.42 [641]~E(x6411,x6412)+E(f544(x6411,x6413,x6414,x6415,x6416,x6417),f544(x6412,x6413,x6414,x6415,x6416,x6417))
% 52.62/52.42 [642]~E(x6421,x6422)+E(f544(x6423,x6421,x6424,x6425,x6426,x6427),f544(x6423,x6422,x6424,x6425,x6426,x6427))
% 52.62/52.42 [643]~E(x6431,x6432)+E(f544(x6433,x6434,x6431,x6435,x6436,x6437),f544(x6433,x6434,x6432,x6435,x6436,x6437))
% 52.62/52.42 [644]~E(x6441,x6442)+E(f544(x6443,x6444,x6445,x6441,x6446,x6447),f544(x6443,x6444,x6445,x6442,x6446,x6447))
% 52.62/52.42 [645]~E(x6451,x6452)+E(f544(x6453,x6454,x6455,x6456,x6451,x6457),f544(x6453,x6454,x6455,x6456,x6452,x6457))
% 52.62/52.42 [646]~E(x6461,x6462)+E(f544(x6463,x6464,x6465,x6466,x6467,x6461),f544(x6463,x6464,x6465,x6466,x6467,x6462))
% 52.62/52.42 [647]~E(x6471,x6472)+E(f262(x6471,x6473,x6474),f262(x6472,x6473,x6474))
% 52.62/52.42 [648]~E(x6481,x6482)+E(f262(x6483,x6481,x6484),f262(x6483,x6482,x6484))
% 52.62/52.42 [649]~E(x6491,x6492)+E(f262(x6493,x6494,x6491),f262(x6493,x6494,x6492))
% 52.62/52.42 [650]~E(x6501,x6502)+E(f76(x6501,x6503),f76(x6502,x6503))
% 52.62/52.42 [651]~E(x6511,x6512)+E(f76(x6513,x6511),f76(x6513,x6512))
% 52.62/52.42 [652]~E(x6521,x6522)+E(f268(x6521,x6523,x6524,x6525),f268(x6522,x6523,x6524,x6525))
% 52.62/52.42 [653]~E(x6531,x6532)+E(f268(x6533,x6531,x6534,x6535),f268(x6533,x6532,x6534,x6535))
% 52.62/52.42 [654]~E(x6541,x6542)+E(f268(x6543,x6544,x6541,x6545),f268(x6543,x6544,x6542,x6545))
% 52.62/52.42 [655]~E(x6551,x6552)+E(f268(x6553,x6554,x6555,x6551),f268(x6553,x6554,x6555,x6552))
% 52.62/52.42 [656]~E(x6561,x6562)+E(f656(x6561,x6563,x6564,x6565,x6566),f656(x6562,x6563,x6564,x6565,x6566))
% 52.62/52.42 [657]~E(x6571,x6572)+E(f656(x6573,x6571,x6574,x6575,x6576),f656(x6573,x6572,x6574,x6575,x6576))
% 52.62/52.42 [658]~E(x6581,x6582)+E(f656(x6583,x6584,x6581,x6585,x6586),f656(x6583,x6584,x6582,x6585,x6586))
% 52.62/52.42 [659]~E(x6591,x6592)+E(f656(x6593,x6594,x6595,x6591,x6596),f656(x6593,x6594,x6595,x6592,x6596))
% 52.62/52.42 [660]~E(x6601,x6602)+E(f656(x6603,x6604,x6605,x6606,x6601),f656(x6603,x6604,x6605,x6606,x6602))
% 52.62/52.42 [661]~E(x6611,x6612)+E(f55(x6611,x6613),f55(x6612,x6613))
% 52.62/52.42 [662]~E(x6621,x6622)+E(f55(x6623,x6621),f55(x6623,x6622))
% 52.62/52.42 [663]~E(x6631,x6632)+E(f161(x6631,x6633,x6634),f161(x6632,x6633,x6634))
% 52.62/52.42 [664]~E(x6641,x6642)+E(f161(x6643,x6641,x6644),f161(x6643,x6642,x6644))
% 52.62/52.42 [665]~E(x6651,x6652)+E(f161(x6653,x6654,x6651),f161(x6653,x6654,x6652))
% 52.62/52.42 [666]~E(x6661,x6662)+E(f691(x6661,x6663,x6664,x6665,x6666,x6667,x6668),f691(x6662,x6663,x6664,x6665,x6666,x6667,x6668))
% 52.62/52.42 [667]~E(x6671,x6672)+E(f691(x6673,x6671,x6674,x6675,x6676,x6677,x6678),f691(x6673,x6672,x6674,x6675,x6676,x6677,x6678))
% 52.62/52.42 [668]~E(x6681,x6682)+E(f691(x6683,x6684,x6681,x6685,x6686,x6687,x6688),f691(x6683,x6684,x6682,x6685,x6686,x6687,x6688))
% 52.62/52.42 [669]~E(x6691,x6692)+E(f691(x6693,x6694,x6695,x6691,x6696,x6697,x6698),f691(x6693,x6694,x6695,x6692,x6696,x6697,x6698))
% 52.62/52.42 [670]~E(x6701,x6702)+E(f691(x6703,x6704,x6705,x6706,x6701,x6707,x6708),f691(x6703,x6704,x6705,x6706,x6702,x6707,x6708))
% 52.62/52.42 [671]~E(x6711,x6712)+E(f691(x6713,x6714,x6715,x6716,x6717,x6711,x6718),f691(x6713,x6714,x6715,x6716,x6717,x6712,x6718))
% 52.62/52.42 [672]~E(x6721,x6722)+E(f691(x6723,x6724,x6725,x6726,x6727,x6728,x6721),f691(x6723,x6724,x6725,x6726,x6727,x6728,x6722))
% 52.62/52.42 [673]~E(x6731,x6732)+E(f492(x6731),f492(x6732))
% 52.62/52.42 [674]~E(x6741,x6742)+E(f390(x6741,x6743,x6744,x6745,x6746),f390(x6742,x6743,x6744,x6745,x6746))
% 52.62/52.42 [675]~E(x6751,x6752)+E(f390(x6753,x6751,x6754,x6755,x6756),f390(x6753,x6752,x6754,x6755,x6756))
% 52.62/52.42 [676]~E(x6761,x6762)+E(f390(x6763,x6764,x6761,x6765,x6766),f390(x6763,x6764,x6762,x6765,x6766))
% 52.62/52.42 [677]~E(x6771,x6772)+E(f390(x6773,x6774,x6775,x6771,x6776),f390(x6773,x6774,x6775,x6772,x6776))
% 52.62/52.42 [678]~E(x6781,x6782)+E(f390(x6783,x6784,x6785,x6786,x6781),f390(x6783,x6784,x6785,x6786,x6782))
% 52.62/52.42 [679]~E(x6791,x6792)+E(f408(x6791,x6793,x6794,x6795),f408(x6792,x6793,x6794,x6795))
% 52.62/52.42 [680]~E(x6801,x6802)+E(f408(x6803,x6801,x6804,x6805),f408(x6803,x6802,x6804,x6805))
% 52.62/52.42 [681]~E(x6811,x6812)+E(f408(x6813,x6814,x6811,x6815),f408(x6813,x6814,x6812,x6815))
% 52.62/52.42 [682]~E(x6821,x6822)+E(f408(x6823,x6824,x6825,x6821),f408(x6823,x6824,x6825,x6822))
% 52.62/52.42 [683]~E(x6831,x6832)+E(f215(x6831,x6833,x6834,x6835),f215(x6832,x6833,x6834,x6835))
% 52.62/52.42 [684]~E(x6841,x6842)+E(f215(x6843,x6841,x6844,x6845),f215(x6843,x6842,x6844,x6845))
% 52.62/52.42 [685]~E(x6851,x6852)+E(f215(x6853,x6854,x6851,x6855),f215(x6853,x6854,x6852,x6855))
% 52.62/52.42 [686]~E(x6861,x6862)+E(f215(x6863,x6864,x6865,x6861),f215(x6863,x6864,x6865,x6862))
% 52.62/52.42 [687]~E(x6871,x6872)+E(f414(x6871,x6873,x6874),f414(x6872,x6873,x6874))
% 52.62/52.42 [688]~E(x6881,x6882)+E(f414(x6883,x6881,x6884),f414(x6883,x6882,x6884))
% 52.62/52.42 [689]~E(x6891,x6892)+E(f414(x6893,x6894,x6891),f414(x6893,x6894,x6892))
% 52.62/52.42 [690]~E(x6901,x6902)+E(f54(x6901,x6903),f54(x6902,x6903))
% 52.62/52.42 [691]~E(x6911,x6912)+E(f54(x6913,x6911),f54(x6913,x6912))
% 52.62/52.42 [692]~E(x6921,x6922)+E(f793(x6921,x6923,x6924,x6925),f793(x6922,x6923,x6924,x6925))
% 52.62/52.42 [693]~E(x6931,x6932)+E(f793(x6933,x6931,x6934,x6935),f793(x6933,x6932,x6934,x6935))
% 52.62/52.42 [694]~E(x6941,x6942)+E(f793(x6943,x6944,x6941,x6945),f793(x6943,x6944,x6942,x6945))
% 52.62/52.42 [695]~E(x6951,x6952)+E(f793(x6953,x6954,x6955,x6951),f793(x6953,x6954,x6955,x6952))
% 52.62/52.42 [696]~E(x6961,x6962)+E(f554(x6961,x6963),f554(x6962,x6963))
% 52.62/52.42 [697]~E(x6971,x6972)+E(f554(x6973,x6971),f554(x6973,x6972))
% 52.62/52.42 [698]~E(x6981,x6982)+E(f678(x6981,x6983,x6984,x6985,x6986,x6987,x6988,x6989),f678(x6982,x6983,x6984,x6985,x6986,x6987,x6988,x6989))
% 52.62/52.42 [699]~E(x6991,x6992)+E(f678(x6993,x6991,x6994,x6995,x6996,x6997,x6998,x6999),f678(x6993,x6992,x6994,x6995,x6996,x6997,x6998,x6999))
% 52.62/52.42 [700]~E(x7001,x7002)+E(f678(x7003,x7004,x7001,x7005,x7006,x7007,x7008,x7009),f678(x7003,x7004,x7002,x7005,x7006,x7007,x7008,x7009))
% 52.62/52.42 [701]~E(x7011,x7012)+E(f678(x7013,x7014,x7015,x7011,x7016,x7017,x7018,x7019),f678(x7013,x7014,x7015,x7012,x7016,x7017,x7018,x7019))
% 52.62/52.42 [702]~E(x7021,x7022)+E(f678(x7023,x7024,x7025,x7026,x7021,x7027,x7028,x7029),f678(x7023,x7024,x7025,x7026,x7022,x7027,x7028,x7029))
% 52.62/52.42 [703]~E(x7031,x7032)+E(f678(x7033,x7034,x7035,x7036,x7037,x7031,x7038,x7039),f678(x7033,x7034,x7035,x7036,x7037,x7032,x7038,x7039))
% 52.62/52.42 [704]~E(x7041,x7042)+E(f678(x7043,x7044,x7045,x7046,x7047,x7048,x7041,x7049),f678(x7043,x7044,x7045,x7046,x7047,x7048,x7042,x7049))
% 52.62/52.42 [705]~E(x7051,x7052)+E(f678(x7053,x7054,x7055,x7056,x7057,x7058,x7059,x7051),f678(x7053,x7054,x7055,x7056,x7057,x7058,x7059,x7052))
% 52.62/52.42 [706]~E(x7061,x7062)+E(f376(x7061,x7063,x7064,x7065),f376(x7062,x7063,x7064,x7065))
% 52.62/52.42 [707]~E(x7071,x7072)+E(f376(x7073,x7071,x7074,x7075),f376(x7073,x7072,x7074,x7075))
% 52.62/52.42 [708]~E(x7081,x7082)+E(f376(x7083,x7084,x7081,x7085),f376(x7083,x7084,x7082,x7085))
% 52.62/52.42 [709]~E(x7091,x7092)+E(f376(x7093,x7094,x7095,x7091),f376(x7093,x7094,x7095,x7092))
% 52.62/52.42 [710]~E(x7101,x7102)+E(f642(x7101,x7103,x7104,x7105,x7106),f642(x7102,x7103,x7104,x7105,x7106))
% 52.62/52.42 [711]~E(x7111,x7112)+E(f642(x7113,x7111,x7114,x7115,x7116),f642(x7113,x7112,x7114,x7115,x7116))
% 52.62/52.42 [712]~E(x7121,x7122)+E(f642(x7123,x7124,x7121,x7125,x7126),f642(x7123,x7124,x7122,x7125,x7126))
% 52.62/52.42 [713]~E(x7131,x7132)+E(f642(x7133,x7134,x7135,x7131,x7136),f642(x7133,x7134,x7135,x7132,x7136))
% 52.62/52.42 [714]~E(x7141,x7142)+E(f642(x7143,x7144,x7145,x7146,x7141),f642(x7143,x7144,x7145,x7146,x7142))
% 52.62/52.42 [715]~E(x7151,x7152)+E(f477(x7151,x7153,x7154),f477(x7152,x7153,x7154))
% 52.62/52.42 [716]~E(x7161,x7162)+E(f477(x7163,x7161,x7164),f477(x7163,x7162,x7164))
% 52.62/52.42 [717]~E(x7171,x7172)+E(f477(x7173,x7174,x7171),f477(x7173,x7174,x7172))
% 52.62/52.42 [718]~E(x7181,x7182)+E(f598(x7181,x7183,x7184,x7185),f598(x7182,x7183,x7184,x7185))
% 52.62/52.42 [719]~E(x7191,x7192)+E(f598(x7193,x7191,x7194,x7195),f598(x7193,x7192,x7194,x7195))
% 52.62/52.42 [720]~E(x7201,x7202)+E(f598(x7203,x7204,x7201,x7205),f598(x7203,x7204,x7202,x7205))
% 52.62/52.42 [721]~E(x7211,x7212)+E(f598(x7213,x7214,x7215,x7211),f598(x7213,x7214,x7215,x7212))
% 52.62/52.42 [722]~E(x7221,x7222)+E(f634(x7221,x7223,x7224,x7225,x7226),f634(x7222,x7223,x7224,x7225,x7226))
% 52.62/52.42 [723]~E(x7231,x7232)+E(f634(x7233,x7231,x7234,x7235,x7236),f634(x7233,x7232,x7234,x7235,x7236))
% 52.62/52.42 [724]~E(x7241,x7242)+E(f634(x7243,x7244,x7241,x7245,x7246),f634(x7243,x7244,x7242,x7245,x7246))
% 52.62/52.42 [725]~E(x7251,x7252)+E(f634(x7253,x7254,x7255,x7251,x7256),f634(x7253,x7254,x7255,x7252,x7256))
% 52.62/52.42 [726]~E(x7261,x7262)+E(f634(x7263,x7264,x7265,x7266,x7261),f634(x7263,x7264,x7265,x7266,x7262))
% 52.62/52.42 [727]~E(x7271,x7272)+E(f326(x7271,x7273,x7274,x7275),f326(x7272,x7273,x7274,x7275))
% 52.62/52.42 [728]~E(x7281,x7282)+E(f326(x7283,x7281,x7284,x7285),f326(x7283,x7282,x7284,x7285))
% 52.62/52.42 [729]~E(x7291,x7292)+E(f326(x7293,x7294,x7291,x7295),f326(x7293,x7294,x7292,x7295))
% 52.62/52.42 [730]~E(x7301,x7302)+E(f326(x7303,x7304,x7305,x7301),f326(x7303,x7304,x7305,x7302))
% 52.62/52.42 [731]~E(x7311,x7312)+E(f203(x7311),f203(x7312))
% 52.62/52.42 [732]~E(x7321,x7322)+E(f536(x7321,x7323,x7324,x7325,x7326),f536(x7322,x7323,x7324,x7325,x7326))
% 52.62/52.42 [733]~E(x7331,x7332)+E(f536(x7333,x7331,x7334,x7335,x7336),f536(x7333,x7332,x7334,x7335,x7336))
% 52.62/52.42 [734]~E(x7341,x7342)+E(f536(x7343,x7344,x7341,x7345,x7346),f536(x7343,x7344,x7342,x7345,x7346))
% 52.62/52.42 [735]~E(x7351,x7352)+E(f536(x7353,x7354,x7355,x7351,x7356),f536(x7353,x7354,x7355,x7352,x7356))
% 52.62/52.42 [736]~E(x7361,x7362)+E(f536(x7363,x7364,x7365,x7366,x7361),f536(x7363,x7364,x7365,x7366,x7362))
% 52.62/52.42 [737]~E(x7371,x7372)+E(f729(x7371,x7373,x7374),f729(x7372,x7373,x7374))
% 52.62/52.42 [738]~E(x7381,x7382)+E(f729(x7383,x7381,x7384),f729(x7383,x7382,x7384))
% 52.62/52.42 [739]~E(x7391,x7392)+E(f729(x7393,x7394,x7391),f729(x7393,x7394,x7392))
% 52.62/52.42 [740]~E(x7401,x7402)+E(f606(x7401,x7403,x7404),f606(x7402,x7403,x7404))
% 52.62/52.42 [741]~E(x7411,x7412)+E(f606(x7413,x7411,x7414),f606(x7413,x7412,x7414))
% 52.62/52.42 [742]~E(x7421,x7422)+E(f606(x7423,x7424,x7421),f606(x7423,x7424,x7422))
% 52.62/52.42 [743]~E(x7431,x7432)+E(f716(x7431,x7433,x7434,x7435),f716(x7432,x7433,x7434,x7435))
% 52.62/52.42 [744]~E(x7441,x7442)+E(f716(x7443,x7441,x7444,x7445),f716(x7443,x7442,x7444,x7445))
% 52.62/52.42 [745]~E(x7451,x7452)+E(f716(x7453,x7454,x7451,x7455),f716(x7453,x7454,x7452,x7455))
% 52.62/52.42 [746]~E(x7461,x7462)+E(f716(x7463,x7464,x7465,x7461),f716(x7463,x7464,x7465,x7462))
% 52.62/52.42 [747]~E(x7471,x7472)+E(f210(x7471,x7473),f210(x7472,x7473))
% 52.62/52.42 [748]~E(x7481,x7482)+E(f210(x7483,x7481),f210(x7483,x7482))
% 52.62/52.42 [749]~E(x7491,x7492)+E(f686(x7491,x7493,x7494),f686(x7492,x7493,x7494))
% 52.62/52.42 [750]~E(x7501,x7502)+E(f686(x7503,x7501,x7504),f686(x7503,x7502,x7504))
% 52.62/52.42 [751]~E(x7511,x7512)+E(f686(x7513,x7514,x7511),f686(x7513,x7514,x7512))
% 52.62/52.42 [752]~E(x7521,x7522)+E(f372(x7521,x7523),f372(x7522,x7523))
% 52.62/52.42 [753]~E(x7531,x7532)+E(f372(x7533,x7531),f372(x7533,x7532))
% 52.62/52.42 [754]~E(x7541,x7542)+E(f371(x7541,x7543),f371(x7542,x7543))
% 52.62/52.42 [755]~E(x7551,x7552)+E(f371(x7553,x7551),f371(x7553,x7552))
% 52.62/52.42 [756]~E(x7561,x7562)+E(f231(x7561),f231(x7562))
% 52.62/52.42 [757]~E(x7571,x7572)+E(f338(x7571),f338(x7572))
% 52.62/52.42 [758]~E(x7581,x7582)+E(f817(x7581,x7583,x7584),f817(x7582,x7583,x7584))
% 52.62/52.42 [759]~E(x7591,x7592)+E(f817(x7593,x7591,x7594),f817(x7593,x7592,x7594))
% 52.62/52.42 [760]~E(x7601,x7602)+E(f817(x7603,x7604,x7601),f817(x7603,x7604,x7602))
% 52.62/52.42 [761]~E(x7611,x7612)+E(f736(x7611,x7613),f736(x7612,x7613))
% 52.62/52.42 [762]~E(x7621,x7622)+E(f736(x7623,x7621),f736(x7623,x7622))
% 52.62/52.42 [763]~E(x7631,x7632)+E(f147(x7631,x7633),f147(x7632,x7633))
% 52.62/52.42 [764]~E(x7641,x7642)+E(f147(x7643,x7641),f147(x7643,x7642))
% 52.62/52.42 [765]~E(x7651,x7652)+E(f350(x7651,x7653,x7654,x7655),f350(x7652,x7653,x7654,x7655))
% 52.62/52.42 [766]~E(x7661,x7662)+E(f350(x7663,x7661,x7664,x7665),f350(x7663,x7662,x7664,x7665))
% 52.62/52.42 [767]~E(x7671,x7672)+E(f350(x7673,x7674,x7671,x7675),f350(x7673,x7674,x7672,x7675))
% 52.62/52.42 [768]~E(x7681,x7682)+E(f350(x7683,x7684,x7685,x7681),f350(x7683,x7684,x7685,x7682))
% 52.62/52.42 [769]~E(x7691,x7692)+E(f314(x7691,x7693,x7694,x7695),f314(x7692,x7693,x7694,x7695))
% 52.62/52.42 [770]~E(x7701,x7702)+E(f314(x7703,x7701,x7704,x7705),f314(x7703,x7702,x7704,x7705))
% 52.62/52.42 [771]~E(x7711,x7712)+E(f314(x7713,x7714,x7711,x7715),f314(x7713,x7714,x7712,x7715))
% 52.62/52.42 [772]~E(x7721,x7722)+E(f314(x7723,x7724,x7725,x7721),f314(x7723,x7724,x7725,x7722))
% 52.62/52.42 [773]~E(x7731,x7732)+E(f789(x7731,x7733,x7734),f789(x7732,x7733,x7734))
% 52.62/52.42 [774]~E(x7741,x7742)+E(f789(x7743,x7741,x7744),f789(x7743,x7742,x7744))
% 52.62/52.42 [775]~E(x7751,x7752)+E(f789(x7753,x7754,x7751),f789(x7753,x7754,x7752))
% 52.62/52.42 [776]~E(x7761,x7762)+E(f402(x7761,x7763),f402(x7762,x7763))
% 52.62/52.42 [777]~E(x7771,x7772)+E(f402(x7773,x7771),f402(x7773,x7772))
% 52.62/52.42 [778]~E(x7781,x7782)+E(f56(x7781,x7783),f56(x7782,x7783))
% 52.62/52.42 [779]~E(x7791,x7792)+E(f56(x7793,x7791),f56(x7793,x7792))
% 52.62/52.42 [780]~E(x7801,x7802)+E(f497(x7801,x7803,x7804,x7805,x7806,x7807),f497(x7802,x7803,x7804,x7805,x7806,x7807))
% 52.62/52.42 [781]~E(x7811,x7812)+E(f497(x7813,x7811,x7814,x7815,x7816,x7817),f497(x7813,x7812,x7814,x7815,x7816,x7817))
% 52.62/52.42 [782]~E(x7821,x7822)+E(f497(x7823,x7824,x7821,x7825,x7826,x7827),f497(x7823,x7824,x7822,x7825,x7826,x7827))
% 52.62/52.42 [783]~E(x7831,x7832)+E(f497(x7833,x7834,x7835,x7831,x7836,x7837),f497(x7833,x7834,x7835,x7832,x7836,x7837))
% 52.62/52.42 [784]~E(x7841,x7842)+E(f497(x7843,x7844,x7845,x7846,x7841,x7847),f497(x7843,x7844,x7845,x7846,x7842,x7847))
% 52.62/52.42 [785]~E(x7851,x7852)+E(f497(x7853,x7854,x7855,x7856,x7857,x7851),f497(x7853,x7854,x7855,x7856,x7857,x7852))
% 52.62/52.42 [786]~E(x7861,x7862)+E(f577(x7861,x7863,x7864,x7865,x7866),f577(x7862,x7863,x7864,x7865,x7866))
% 52.62/52.42 [787]~E(x7871,x7872)+E(f577(x7873,x7871,x7874,x7875,x7876),f577(x7873,x7872,x7874,x7875,x7876))
% 52.62/52.42 [788]~E(x7881,x7882)+E(f577(x7883,x7884,x7881,x7885,x7886),f577(x7883,x7884,x7882,x7885,x7886))
% 52.62/52.42 [789]~E(x7891,x7892)+E(f577(x7893,x7894,x7895,x7891,x7896),f577(x7893,x7894,x7895,x7892,x7896))
% 52.62/52.42 [790]~E(x7901,x7902)+E(f577(x7903,x7904,x7905,x7906,x7901),f577(x7903,x7904,x7905,x7906,x7902))
% 52.62/52.42 [791]~E(x7911,x7912)+E(f584(x7911,x7913,x7914,x7915),f584(x7912,x7913,x7914,x7915))
% 52.62/52.42 [792]~E(x7921,x7922)+E(f584(x7923,x7921,x7924,x7925),f584(x7923,x7922,x7924,x7925))
% 52.62/52.42 [793]~E(x7931,x7932)+E(f584(x7933,x7934,x7931,x7935),f584(x7933,x7934,x7932,x7935))
% 52.62/52.42 [794]~E(x7941,x7942)+E(f584(x7943,x7944,x7945,x7941),f584(x7943,x7944,x7945,x7942))
% 52.62/52.42 [795]~E(x7951,x7952)+E(f760(x7951,x7953),f760(x7952,x7953))
% 52.62/52.42 [796]~E(x7961,x7962)+E(f760(x7963,x7961),f760(x7963,x7962))
% 52.62/52.42 [797]~E(x7971,x7972)+E(f412(x7971,x7973,x7974),f412(x7972,x7973,x7974))
% 52.62/52.42 [798]~E(x7981,x7982)+E(f412(x7983,x7981,x7984),f412(x7983,x7982,x7984))
% 52.62/52.42 [799]~E(x7991,x7992)+E(f412(x7993,x7994,x7991),f412(x7993,x7994,x7992))
% 52.62/52.42 [800]~E(x8001,x8002)+E(f708(x8001,x8003,x8004,x8005,x8006,x8007),f708(x8002,x8003,x8004,x8005,x8006,x8007))
% 52.62/52.42 [801]~E(x8011,x8012)+E(f708(x8013,x8011,x8014,x8015,x8016,x8017),f708(x8013,x8012,x8014,x8015,x8016,x8017))
% 52.62/52.42 [802]~E(x8021,x8022)+E(f708(x8023,x8024,x8021,x8025,x8026,x8027),f708(x8023,x8024,x8022,x8025,x8026,x8027))
% 52.62/52.42 [803]~E(x8031,x8032)+E(f708(x8033,x8034,x8035,x8031,x8036,x8037),f708(x8033,x8034,x8035,x8032,x8036,x8037))
% 52.62/52.42 [804]~E(x8041,x8042)+E(f708(x8043,x8044,x8045,x8046,x8041,x8047),f708(x8043,x8044,x8045,x8046,x8042,x8047))
% 52.62/52.42 [805]~E(x8051,x8052)+E(f708(x8053,x8054,x8055,x8056,x8057,x8051),f708(x8053,x8054,x8055,x8056,x8057,x8052))
% 52.62/52.42 [806]~E(x8061,x8062)+E(f690(x8061,x8063,x8064,x8065,x8066,x8067),f690(x8062,x8063,x8064,x8065,x8066,x8067))
% 52.62/52.42 [807]~E(x8071,x8072)+E(f690(x8073,x8071,x8074,x8075,x8076,x8077),f690(x8073,x8072,x8074,x8075,x8076,x8077))
% 52.62/52.42 [808]~E(x8081,x8082)+E(f690(x8083,x8084,x8081,x8085,x8086,x8087),f690(x8083,x8084,x8082,x8085,x8086,x8087))
% 52.62/52.43 [809]~E(x8091,x8092)+E(f690(x8093,x8094,x8095,x8091,x8096,x8097),f690(x8093,x8094,x8095,x8092,x8096,x8097))
% 52.62/52.43 [810]~E(x8101,x8102)+E(f690(x8103,x8104,x8105,x8106,x8101,x8107),f690(x8103,x8104,x8105,x8106,x8102,x8107))
% 52.62/52.43 [811]~E(x8111,x8112)+E(f690(x8113,x8114,x8115,x8116,x8117,x8111),f690(x8113,x8114,x8115,x8116,x8117,x8112))
% 52.62/52.43 [812]~E(x8121,x8122)+E(f684(x8121,x8123,x8124),f684(x8122,x8123,x8124))
% 52.62/52.43 [813]~E(x8131,x8132)+E(f684(x8133,x8131,x8134),f684(x8133,x8132,x8134))
% 52.62/52.43 [814]~E(x8141,x8142)+E(f684(x8143,x8144,x8141),f684(x8143,x8144,x8142))
% 52.62/52.43 [815]~E(x8151,x8152)+E(f310(x8151),f310(x8152))
% 52.62/52.43 [816]~E(x8161,x8162)+E(f709(x8161,x8163,x8164,x8165,x8166,x8167),f709(x8162,x8163,x8164,x8165,x8166,x8167))
% 52.62/52.43 [817]~E(x8171,x8172)+E(f709(x8173,x8171,x8174,x8175,x8176,x8177),f709(x8173,x8172,x8174,x8175,x8176,x8177))
% 52.62/52.43 [818]~E(x8181,x8182)+E(f709(x8183,x8184,x8181,x8185,x8186,x8187),f709(x8183,x8184,x8182,x8185,x8186,x8187))
% 52.62/52.43 [819]~E(x8191,x8192)+E(f709(x8193,x8194,x8195,x8191,x8196,x8197),f709(x8193,x8194,x8195,x8192,x8196,x8197))
% 52.62/52.43 [820]~E(x8201,x8202)+E(f709(x8203,x8204,x8205,x8206,x8201,x8207),f709(x8203,x8204,x8205,x8206,x8202,x8207))
% 52.62/52.43 [821]~E(x8211,x8212)+E(f709(x8213,x8214,x8215,x8216,x8217,x8211),f709(x8213,x8214,x8215,x8216,x8217,x8212))
% 52.62/52.43 [822]~E(x8221,x8222)+E(f261(x8221,x8223),f261(x8222,x8223))
% 52.62/52.43 [823]~E(x8231,x8232)+E(f261(x8233,x8231),f261(x8233,x8232))
% 52.62/52.43 [824]~E(x8241,x8242)+E(f69(x8241,x8243,x8244,x8245,x8246),f69(x8242,x8243,x8244,x8245,x8246))
% 52.62/52.43 [825]~E(x8251,x8252)+E(f69(x8253,x8251,x8254,x8255,x8256),f69(x8253,x8252,x8254,x8255,x8256))
% 52.62/52.43 [826]~E(x8261,x8262)+E(f69(x8263,x8264,x8261,x8265,x8266),f69(x8263,x8264,x8262,x8265,x8266))
% 52.62/52.43 [827]~E(x8271,x8272)+E(f69(x8273,x8274,x8275,x8271,x8276),f69(x8273,x8274,x8275,x8272,x8276))
% 52.62/52.43 [828]~E(x8281,x8282)+E(f69(x8283,x8284,x8285,x8286,x8281),f69(x8283,x8284,x8285,x8286,x8282))
% 52.62/52.43 [829]~E(x8291,x8292)+E(f487(x8291,x8293,x8294,x8295,x8296),f487(x8292,x8293,x8294,x8295,x8296))
% 52.62/52.43 [830]~E(x8301,x8302)+E(f487(x8303,x8301,x8304,x8305,x8306),f487(x8303,x8302,x8304,x8305,x8306))
% 52.62/52.43 [831]~E(x8311,x8312)+E(f487(x8313,x8314,x8311,x8315,x8316),f487(x8313,x8314,x8312,x8315,x8316))
% 52.62/52.43 [832]~E(x8321,x8322)+E(f487(x8323,x8324,x8325,x8321,x8326),f487(x8323,x8324,x8325,x8322,x8326))
% 52.62/52.43 [833]~E(x8331,x8332)+E(f487(x8333,x8334,x8335,x8336,x8331),f487(x8333,x8334,x8335,x8336,x8332))
% 52.62/52.43 [834]~E(x8341,x8342)+E(f822(x8341,x8343,x8344),f822(x8342,x8343,x8344))
% 52.62/52.43 [835]~E(x8351,x8352)+E(f822(x8353,x8351,x8354),f822(x8353,x8352,x8354))
% 52.62/52.43 [836]~E(x8361,x8362)+E(f822(x8363,x8364,x8361),f822(x8363,x8364,x8362))
% 52.62/52.43 [837]~E(x8371,x8372)+E(f51(x8371),f51(x8372))
% 52.62/52.43 [838]~E(x8381,x8382)+E(f144(x8381,x8383,x8384),f144(x8382,x8383,x8384))
% 52.62/52.43 [839]~E(x8391,x8392)+E(f144(x8393,x8391,x8394),f144(x8393,x8392,x8394))
% 52.62/52.43 [840]~E(x8401,x8402)+E(f144(x8403,x8404,x8401),f144(x8403,x8404,x8402))
% 52.62/52.43 [841]~E(x8411,x8412)+E(f655(x8411,x8413,x8414,x8415,x8416),f655(x8412,x8413,x8414,x8415,x8416))
% 52.62/52.43 [842]~E(x8421,x8422)+E(f655(x8423,x8421,x8424,x8425,x8426),f655(x8423,x8422,x8424,x8425,x8426))
% 52.62/52.43 [843]~E(x8431,x8432)+E(f655(x8433,x8434,x8431,x8435,x8436),f655(x8433,x8434,x8432,x8435,x8436))
% 52.62/52.43 [844]~E(x8441,x8442)+E(f655(x8443,x8444,x8445,x8441,x8446),f655(x8443,x8444,x8445,x8442,x8446))
% 52.62/52.43 [845]~E(x8451,x8452)+E(f655(x8453,x8454,x8455,x8456,x8451),f655(x8453,x8454,x8455,x8456,x8452))
% 52.62/52.43 [846]~E(x8461,x8462)+E(f742(x8461,x8463,x8464,x8465),f742(x8462,x8463,x8464,x8465))
% 52.62/52.43 [847]~E(x8471,x8472)+E(f742(x8473,x8471,x8474,x8475),f742(x8473,x8472,x8474,x8475))
% 52.62/52.43 [848]~E(x8481,x8482)+E(f742(x8483,x8484,x8481,x8485),f742(x8483,x8484,x8482,x8485))
% 52.62/52.43 [849]~E(x8491,x8492)+E(f742(x8493,x8494,x8495,x8491),f742(x8493,x8494,x8495,x8492))
% 52.62/52.43 [850]~E(x8501,x8502)+E(f36(x8501,x8503),f36(x8502,x8503))
% 52.62/52.43 [851]~E(x8511,x8512)+E(f36(x8513,x8511),f36(x8513,x8512))
% 52.62/52.43 [852]~E(x8521,x8522)+E(f275(x8521,x8523,x8524,x8525),f275(x8522,x8523,x8524,x8525))
% 52.62/52.43 [853]~E(x8531,x8532)+E(f275(x8533,x8531,x8534,x8535),f275(x8533,x8532,x8534,x8535))
% 52.62/52.43 [854]~E(x8541,x8542)+E(f275(x8543,x8544,x8541,x8545),f275(x8543,x8544,x8542,x8545))
% 52.62/52.43 [855]~E(x8551,x8552)+E(f275(x8553,x8554,x8555,x8551),f275(x8553,x8554,x8555,x8552))
% 52.62/52.43 [856]~E(x8561,x8562)+E(f811(x8561,x8563,x8564),f811(x8562,x8563,x8564))
% 52.62/52.43 [857]~E(x8571,x8572)+E(f811(x8573,x8571,x8574),f811(x8573,x8572,x8574))
% 52.62/52.43 [858]~E(x8581,x8582)+E(f811(x8583,x8584,x8581),f811(x8583,x8584,x8582))
% 52.62/52.43 [859]~E(x8591,x8592)+E(f591(x8591,x8593),f591(x8592,x8593))
% 52.62/52.43 [860]~E(x8601,x8602)+E(f591(x8603,x8601),f591(x8603,x8602))
% 52.62/52.43 [861]~E(x8611,x8612)+E(f94(x8611,x8613,x8614),f94(x8612,x8613,x8614))
% 52.62/52.43 [862]~E(x8621,x8622)+E(f94(x8623,x8621,x8624),f94(x8623,x8622,x8624))
% 52.62/52.43 [863]~E(x8631,x8632)+E(f94(x8633,x8634,x8631),f94(x8633,x8634,x8632))
% 52.62/52.43 [864]~E(x8641,x8642)+E(f383(x8641,x8643),f383(x8642,x8643))
% 52.62/52.43 [865]~E(x8651,x8652)+E(f383(x8653,x8651),f383(x8653,x8652))
% 52.62/52.43 [866]~E(x8661,x8662)+E(f211(x8661,x8663),f211(x8662,x8663))
% 52.62/52.43 [867]~E(x8671,x8672)+E(f211(x8673,x8671),f211(x8673,x8672))
% 52.62/52.43 [868]~E(x8681,x8682)+E(f705(x8681,x8683,x8684,x8685,x8686,x8687),f705(x8682,x8683,x8684,x8685,x8686,x8687))
% 52.62/52.43 [869]~E(x8691,x8692)+E(f705(x8693,x8691,x8694,x8695,x8696,x8697),f705(x8693,x8692,x8694,x8695,x8696,x8697))
% 52.62/52.43 [870]~E(x8701,x8702)+E(f705(x8703,x8704,x8701,x8705,x8706,x8707),f705(x8703,x8704,x8702,x8705,x8706,x8707))
% 52.62/52.43 [871]~E(x8711,x8712)+E(f705(x8713,x8714,x8715,x8711,x8716,x8717),f705(x8713,x8714,x8715,x8712,x8716,x8717))
% 52.62/52.43 [872]~E(x8721,x8722)+E(f705(x8723,x8724,x8725,x8726,x8721,x8727),f705(x8723,x8724,x8725,x8726,x8722,x8727))
% 52.62/52.43 [873]~E(x8731,x8732)+E(f705(x8733,x8734,x8735,x8736,x8737,x8731),f705(x8733,x8734,x8735,x8736,x8737,x8732))
% 52.62/52.43 [874]~E(x8741,x8742)+E(f810(x8741,x8743,x8744),f810(x8742,x8743,x8744))
% 52.62/52.43 [875]~E(x8751,x8752)+E(f810(x8753,x8751,x8754),f810(x8753,x8752,x8754))
% 52.62/52.43 [876]~E(x8761,x8762)+E(f810(x8763,x8764,x8761),f810(x8763,x8764,x8762))
% 52.62/52.43 [877]~E(x8771,x8772)+E(f342(x8771,x8773),f342(x8772,x8773))
% 52.62/52.43 [878]~E(x8781,x8782)+E(f342(x8783,x8781),f342(x8783,x8782))
% 52.62/52.43 [879]~E(x8791,x8792)+E(f360(x8791,x8793,x8794,x8795),f360(x8792,x8793,x8794,x8795))
% 52.62/52.43 [880]~E(x8801,x8802)+E(f360(x8803,x8801,x8804,x8805),f360(x8803,x8802,x8804,x8805))
% 52.62/52.43 [881]~E(x8811,x8812)+E(f360(x8813,x8814,x8811,x8815),f360(x8813,x8814,x8812,x8815))
% 52.62/52.43 [882]~E(x8821,x8822)+E(f360(x8823,x8824,x8825,x8821),f360(x8823,x8824,x8825,x8822))
% 52.62/52.43 [883]~E(x8831,x8832)+E(f235(x8831,x8833),f235(x8832,x8833))
% 52.62/52.43 [884]~E(x8841,x8842)+E(f235(x8843,x8841),f235(x8843,x8842))
% 52.62/52.43 [885]~E(x8851,x8852)+E(f836(x8851,x8853,x8854,x8855,x8856),f836(x8852,x8853,x8854,x8855,x8856))
% 52.62/52.43 [886]~E(x8861,x8862)+E(f836(x8863,x8861,x8864,x8865,x8866),f836(x8863,x8862,x8864,x8865,x8866))
% 52.62/52.43 [887]~E(x8871,x8872)+E(f836(x8873,x8874,x8871,x8875,x8876),f836(x8873,x8874,x8872,x8875,x8876))
% 52.62/52.43 [888]~E(x8881,x8882)+E(f836(x8883,x8884,x8885,x8881,x8886),f836(x8883,x8884,x8885,x8882,x8886))
% 52.62/52.43 [889]~E(x8891,x8892)+E(f836(x8893,x8894,x8895,x8896,x8891),f836(x8893,x8894,x8895,x8896,x8892))
% 52.62/52.43 [890]~E(x8901,x8902)+E(f653(x8901,x8903,x8904,x8905),f653(x8902,x8903,x8904,x8905))
% 52.62/52.43 [891]~E(x8911,x8912)+E(f653(x8913,x8911,x8914,x8915),f653(x8913,x8912,x8914,x8915))
% 52.62/52.43 [892]~E(x8921,x8922)+E(f653(x8923,x8924,x8921,x8925),f653(x8923,x8924,x8922,x8925))
% 52.62/52.43 [893]~E(x8931,x8932)+E(f653(x8933,x8934,x8935,x8931),f653(x8933,x8934,x8935,x8932))
% 52.62/52.43 [894]~E(x8941,x8942)+E(f650(x8941,x8943,x8944),f650(x8942,x8943,x8944))
% 52.62/52.43 [895]~E(x8951,x8952)+E(f650(x8953,x8951,x8954),f650(x8953,x8952,x8954))
% 52.62/52.43 [896]~E(x8961,x8962)+E(f650(x8963,x8964,x8961),f650(x8963,x8964,x8962))
% 52.62/52.43 [897]~E(x8971,x8972)+E(f603(x8971,x8973),f603(x8972,x8973))
% 52.62/52.43 [898]~E(x8981,x8982)+E(f603(x8983,x8981),f603(x8983,x8982))
% 52.62/52.43 [899]~E(x8991,x8992)+E(f122(x8991),f122(x8992))
% 52.62/52.43 [900]~E(x9001,x9002)+E(f185(x9001,x9003),f185(x9002,x9003))
% 52.62/52.43 [901]~E(x9011,x9012)+E(f185(x9013,x9011),f185(x9013,x9012))
% 52.62/52.43 [902]~E(x9021,x9022)+E(f395(x9021,x9023,x9024,x9025,x9026),f395(x9022,x9023,x9024,x9025,x9026))
% 52.62/52.43 [903]~E(x9031,x9032)+E(f395(x9033,x9031,x9034,x9035,x9036),f395(x9033,x9032,x9034,x9035,x9036))
% 52.62/52.43 [904]~E(x9041,x9042)+E(f395(x9043,x9044,x9041,x9045,x9046),f395(x9043,x9044,x9042,x9045,x9046))
% 52.62/52.43 [905]~E(x9051,x9052)+E(f395(x9053,x9054,x9055,x9051,x9056),f395(x9053,x9054,x9055,x9052,x9056))
% 52.62/52.43 [906]~E(x9061,x9062)+E(f395(x9063,x9064,x9065,x9066,x9061),f395(x9063,x9064,x9065,x9066,x9062))
% 52.62/52.43 [907]~E(x9071,x9072)+E(f120(x9071,x9073),f120(x9072,x9073))
% 52.62/52.43 [908]~E(x9081,x9082)+E(f120(x9083,x9081),f120(x9083,x9082))
% 52.62/52.43 [909]~E(x9091,x9092)+E(f194(x9091,x9093),f194(x9092,x9093))
% 52.62/52.43 [910]~E(x9101,x9102)+E(f194(x9103,x9101),f194(x9103,x9102))
% 52.62/52.43 [911]~E(x9111,x9112)+E(f781(x9111,x9113,x9114),f781(x9112,x9113,x9114))
% 52.62/52.43 [912]~E(x9121,x9122)+E(f781(x9123,x9121,x9124),f781(x9123,x9122,x9124))
% 52.62/52.43 [913]~E(x9131,x9132)+E(f781(x9133,x9134,x9131),f781(x9133,x9134,x9132))
% 52.62/52.43 [914]~E(x9141,x9142)+E(f123(x9141,x9143),f123(x9142,x9143))
% 52.62/52.43 [915]~E(x9151,x9152)+E(f123(x9153,x9151),f123(x9153,x9152))
% 52.62/52.43 [916]~E(x9161,x9162)+E(f37(x9161,x9163,x9164,x9165,x9166,x9167,x9168,x9169,x91610,x91611),f37(x9162,x9163,x9164,x9165,x9166,x9167,x9168,x9169,x91610,x91611))
% 52.62/52.43 [917]~E(x9171,x9172)+E(f37(x9173,x9171,x9174,x9175,x9176,x9177,x9178,x9179,x91710,x91711),f37(x9173,x9172,x9174,x9175,x9176,x9177,x9178,x9179,x91710,x91711))
% 52.62/52.43 [918]~E(x9181,x9182)+E(f37(x9183,x9184,x9181,x9185,x9186,x9187,x9188,x9189,x91810,x91811),f37(x9183,x9184,x9182,x9185,x9186,x9187,x9188,x9189,x91810,x91811))
% 52.62/52.43 [919]~E(x9191,x9192)+E(f37(x9193,x9194,x9195,x9191,x9196,x9197,x9198,x9199,x91910,x91911),f37(x9193,x9194,x9195,x9192,x9196,x9197,x9198,x9199,x91910,x91911))
% 52.62/52.43 [920]~E(x9201,x9202)+E(f37(x9203,x9204,x9205,x9206,x9201,x9207,x9208,x9209,x92010,x92011),f37(x9203,x9204,x9205,x9206,x9202,x9207,x9208,x9209,x92010,x92011))
% 52.62/52.43 [921]~E(x9211,x9212)+E(f37(x9213,x9214,x9215,x9216,x9217,x9211,x9218,x9219,x92110,x92111),f37(x9213,x9214,x9215,x9216,x9217,x9212,x9218,x9219,x92110,x92111))
% 52.62/52.43 [922]~E(x9221,x9222)+E(f37(x9223,x9224,x9225,x9226,x9227,x9228,x9221,x9229,x92210,x92211),f37(x9223,x9224,x9225,x9226,x9227,x9228,x9222,x9229,x92210,x92211))
% 52.62/52.43 [923]~E(x9231,x9232)+E(f37(x9233,x9234,x9235,x9236,x9237,x9238,x9239,x9231,x92310,x92311),f37(x9233,x9234,x9235,x9236,x9237,x9238,x9239,x9232,x92310,x92311))
% 52.62/52.43 [924]~E(x9241,x9242)+E(f37(x9243,x9244,x9245,x9246,x9247,x9248,x9249,x92410,x9241,x92411),f37(x9243,x9244,x9245,x9246,x9247,x9248,x9249,x92410,x9242,x92411))
% 52.62/52.43 [925]~E(x9251,x9252)+E(f37(x9253,x9254,x9255,x9256,x9257,x9258,x9259,x92510,x92511,x9251),f37(x9253,x9254,x9255,x9256,x9257,x9258,x9259,x92510,x92511,x9252))
% 52.62/52.43 [926]~E(x9261,x9262)+E(f474(x9261,x9263),f474(x9262,x9263))
% 52.62/52.43 [927]~E(x9271,x9272)+E(f474(x9273,x9271),f474(x9273,x9272))
% 52.62/52.43 [928]~E(x9281,x9282)+E(f377(x9281,x9283,x9284,x9285),f377(x9282,x9283,x9284,x9285))
% 52.62/52.43 [929]~E(x9291,x9292)+E(f377(x9293,x9291,x9294,x9295),f377(x9293,x9292,x9294,x9295))
% 52.62/52.43 [930]~E(x9301,x9302)+E(f377(x9303,x9304,x9301,x9305),f377(x9303,x9304,x9302,x9305))
% 52.62/52.43 [931]~E(x9311,x9312)+E(f377(x9313,x9314,x9315,x9311),f377(x9313,x9314,x9315,x9312))
% 52.62/52.43 [932]~E(x9321,x9322)+E(f787(x9321,x9323),f787(x9322,x9323))
% 52.62/52.43 [933]~E(x9331,x9332)+E(f787(x9333,x9331),f787(x9333,x9332))
% 52.62/52.43 [934]~E(x9341,x9342)+E(f195(x9341),f195(x9342))
% 52.62/52.43 [935]~E(x9351,x9352)+E(f505(x9351,x9353,x9354),f505(x9352,x9353,x9354))
% 52.62/52.43 [936]~E(x9361,x9362)+E(f505(x9363,x9361,x9364),f505(x9363,x9362,x9364))
% 52.62/52.43 [937]~E(x9371,x9372)+E(f505(x9373,x9374,x9371),f505(x9373,x9374,x9372))
% 52.62/52.43 [938]~E(x9381,x9382)+E(f359(x9381,x9383,x9384,x9385),f359(x9382,x9383,x9384,x9385))
% 52.62/52.43 [939]~E(x9391,x9392)+E(f359(x9393,x9391,x9394,x9395),f359(x9393,x9392,x9394,x9395))
% 52.62/52.43 [940]~E(x9401,x9402)+E(f359(x9403,x9404,x9401,x9405),f359(x9403,x9404,x9402,x9405))
% 52.62/52.43 [941]~E(x9411,x9412)+E(f359(x9413,x9414,x9415,x9411),f359(x9413,x9414,x9415,x9412))
% 52.62/52.43 [942]~E(x9421,x9422)+E(f274(x9421,x9423,x9424,x9425),f274(x9422,x9423,x9424,x9425))
% 52.62/52.43 [943]~E(x9431,x9432)+E(f274(x9433,x9431,x9434,x9435),f274(x9433,x9432,x9434,x9435))
% 52.62/52.43 [944]~E(x9441,x9442)+E(f274(x9443,x9444,x9441,x9445),f274(x9443,x9444,x9442,x9445))
% 52.62/52.43 [945]~E(x9451,x9452)+E(f274(x9453,x9454,x9455,x9451),f274(x9453,x9454,x9455,x9452))
% 52.62/52.43 [946]~E(x9461,x9462)+E(f407(x9461,x9463,x9464,x9465,x9466),f407(x9462,x9463,x9464,x9465,x9466))
% 52.62/52.43 [947]~E(x9471,x9472)+E(f407(x9473,x9471,x9474,x9475,x9476),f407(x9473,x9472,x9474,x9475,x9476))
% 52.62/52.43 [948]~E(x9481,x9482)+E(f407(x9483,x9484,x9481,x9485,x9486),f407(x9483,x9484,x9482,x9485,x9486))
% 52.62/52.43 [949]~E(x9491,x9492)+E(f407(x9493,x9494,x9495,x9491,x9496),f407(x9493,x9494,x9495,x9492,x9496))
% 52.62/52.43 [950]~E(x9501,x9502)+E(f407(x9503,x9504,x9505,x9506,x9501),f407(x9503,x9504,x9505,x9506,x9502))
% 52.62/52.43 [951]~E(x9511,x9512)+E(f301(x9511),f301(x9512))
% 52.62/52.43 [952]~E(x9521,x9522)+E(f777(x9521,x9523,x9524),f777(x9522,x9523,x9524))
% 52.62/52.43 [953]~E(x9531,x9532)+E(f777(x9533,x9531,x9534),f777(x9533,x9532,x9534))
% 52.62/52.43 [954]~E(x9541,x9542)+E(f777(x9543,x9544,x9541),f777(x9543,x9544,x9542))
% 52.62/52.43 [955]~E(x9551,x9552)+E(f358(x9551,x9553,x9554,x9555),f358(x9552,x9553,x9554,x9555))
% 52.62/52.43 [956]~E(x9561,x9562)+E(f358(x9563,x9561,x9564,x9565),f358(x9563,x9562,x9564,x9565))
% 52.62/52.43 [957]~E(x9571,x9572)+E(f358(x9573,x9574,x9571,x9575),f358(x9573,x9574,x9572,x9575))
% 52.62/52.43 [958]~E(x9581,x9582)+E(f358(x9583,x9584,x9585,x9581),f358(x9583,x9584,x9585,x9582))
% 52.62/52.43 [959]~E(x9591,x9592)+E(f717(x9591,x9593,x9594,x9595,x9596),f717(x9592,x9593,x9594,x9595,x9596))
% 52.62/52.43 [960]~E(x9601,x9602)+E(f717(x9603,x9601,x9604,x9605,x9606),f717(x9603,x9602,x9604,x9605,x9606))
% 52.62/52.43 [961]~E(x9611,x9612)+E(f717(x9613,x9614,x9611,x9615,x9616),f717(x9613,x9614,x9612,x9615,x9616))
% 52.62/52.43 [962]~E(x9621,x9622)+E(f717(x9623,x9624,x9625,x9621,x9626),f717(x9623,x9624,x9625,x9622,x9626))
% 52.62/52.43 [963]~E(x9631,x9632)+E(f717(x9633,x9634,x9635,x9636,x9631),f717(x9633,x9634,x9635,x9636,x9632))
% 52.62/52.43 [964]~E(x9641,x9642)+E(f633(x9641,x9643,x9644,x9645,x9646,x9647,x9648,x9649),f633(x9642,x9643,x9644,x9645,x9646,x9647,x9648,x9649))
% 52.62/52.43 [965]~E(x9651,x9652)+E(f633(x9653,x9651,x9654,x9655,x9656,x9657,x9658,x9659),f633(x9653,x9652,x9654,x9655,x9656,x9657,x9658,x9659))
% 52.62/52.43 [966]~E(x9661,x9662)+E(f633(x9663,x9664,x9661,x9665,x9666,x9667,x9668,x9669),f633(x9663,x9664,x9662,x9665,x9666,x9667,x9668,x9669))
% 52.62/52.43 [967]~E(x9671,x9672)+E(f633(x9673,x9674,x9675,x9671,x9676,x9677,x9678,x9679),f633(x9673,x9674,x9675,x9672,x9676,x9677,x9678,x9679))
% 52.62/52.43 [968]~E(x9681,x9682)+E(f633(x9683,x9684,x9685,x9686,x9681,x9687,x9688,x9689),f633(x9683,x9684,x9685,x9686,x9682,x9687,x9688,x9689))
% 52.62/52.43 [969]~E(x9691,x9692)+E(f633(x9693,x9694,x9695,x9696,x9697,x9691,x9698,x9699),f633(x9693,x9694,x9695,x9696,x9697,x9692,x9698,x9699))
% 52.62/52.43 [970]~E(x9701,x9702)+E(f633(x9703,x9704,x9705,x9706,x9707,x9708,x9701,x9709),f633(x9703,x9704,x9705,x9706,x9707,x9708,x9702,x9709))
% 52.62/52.43 [971]~E(x9711,x9712)+E(f633(x9713,x9714,x9715,x9716,x9717,x9718,x9719,x9711),f633(x9713,x9714,x9715,x9716,x9717,x9718,x9719,x9712))
% 52.62/52.43 [972]~E(x9721,x9722)+E(f666(x9721,x9723,x9724,x9725,x9726),f666(x9722,x9723,x9724,x9725,x9726))
% 52.62/52.43 [973]~E(x9731,x9732)+E(f666(x9733,x9731,x9734,x9735,x9736),f666(x9733,x9732,x9734,x9735,x9736))
% 52.62/52.43 [974]~E(x9741,x9742)+E(f666(x9743,x9744,x9741,x9745,x9746),f666(x9743,x9744,x9742,x9745,x9746))
% 52.62/52.43 [975]~E(x9751,x9752)+E(f666(x9753,x9754,x9755,x9751,x9756),f666(x9753,x9754,x9755,x9752,x9756))
% 52.62/52.43 [976]~E(x9761,x9762)+E(f666(x9763,x9764,x9765,x9766,x9761),f666(x9763,x9764,x9765,x9766,x9762))
% 52.62/52.43 [977]~E(x9771,x9772)+E(f504(x9771,x9773,x9774),f504(x9772,x9773,x9774))
% 52.62/52.43 [978]~E(x9781,x9782)+E(f504(x9783,x9781,x9784),f504(x9783,x9782,x9784))
% 52.62/52.43 [979]~E(x9791,x9792)+E(f504(x9793,x9794,x9791),f504(x9793,x9794,x9792))
% 52.62/52.43 [980]~E(x9801,x9802)+E(f234(x9801,x9803),f234(x9802,x9803))
% 52.62/52.43 [981]~E(x9811,x9812)+E(f234(x9813,x9811),f234(x9813,x9812))
% 52.62/52.43 [982]~E(x9821,x9822)+E(f718(x9821,x9823,x9824,x9825,x9826),f718(x9822,x9823,x9824,x9825,x9826))
% 52.62/52.43 [983]~E(x9831,x9832)+E(f718(x9833,x9831,x9834,x9835,x9836),f718(x9833,x9832,x9834,x9835,x9836))
% 52.62/52.43 [984]~E(x9841,x9842)+E(f718(x9843,x9844,x9841,x9845,x9846),f718(x9843,x9844,x9842,x9845,x9846))
% 52.62/52.43 [985]~E(x9851,x9852)+E(f718(x9853,x9854,x9855,x9851,x9856),f718(x9853,x9854,x9855,x9852,x9856))
% 52.62/52.43 [986]~E(x9861,x9862)+E(f718(x9863,x9864,x9865,x9866,x9861),f718(x9863,x9864,x9865,x9866,x9862))
% 52.62/52.43 [987]~E(x9871,x9872)+E(f193(x9871,x9873,x9874,x9875),f193(x9872,x9873,x9874,x9875))
% 52.62/52.43 [988]~E(x9881,x9882)+E(f193(x9883,x9881,x9884,x9885),f193(x9883,x9882,x9884,x9885))
% 52.62/52.43 [989]~E(x9891,x9892)+E(f193(x9893,x9894,x9891,x9895),f193(x9893,x9894,x9892,x9895))
% 52.62/52.43 [990]~E(x9901,x9902)+E(f193(x9903,x9904,x9905,x9901),f193(x9903,x9904,x9905,x9902))
% 52.62/52.43 [991]~E(x9911,x9912)+E(f354(x9911,x9913,x9914,x9915),f354(x9912,x9913,x9914,x9915))
% 52.62/52.43 [992]~E(x9921,x9922)+E(f354(x9923,x9921,x9924,x9925),f354(x9923,x9922,x9924,x9925))
% 52.62/52.43 [993]~E(x9931,x9932)+E(f354(x9933,x9934,x9931,x9935),f354(x9933,x9934,x9932,x9935))
% 52.62/52.43 [994]~E(x9941,x9942)+E(f354(x9943,x9944,x9945,x9941),f354(x9943,x9944,x9945,x9942))
% 52.62/52.43 [995]~E(x9951,x9952)+E(f703(x9951,x9953,x9954,x9955,x9956),f703(x9952,x9953,x9954,x9955,x9956))
% 52.62/52.43 [996]~E(x9961,x9962)+E(f703(x9963,x9961,x9964,x9965,x9966),f703(x9963,x9962,x9964,x9965,x9966))
% 52.62/52.43 [997]~E(x9971,x9972)+E(f703(x9973,x9974,x9971,x9975,x9976),f703(x9973,x9974,x9972,x9975,x9976))
% 52.62/52.43 [998]~E(x9981,x9982)+E(f703(x9983,x9984,x9985,x9981,x9986),f703(x9983,x9984,x9985,x9982,x9986))
% 52.62/52.43 [999]~E(x9991,x9992)+E(f703(x9993,x9994,x9995,x9996,x9991),f703(x9993,x9994,x9995,x9996,x9992))
% 52.62/52.43 [1000]~E(x10001,x10002)+E(f461(x10001,x10003,x10004),f461(x10002,x10003,x10004))
% 52.62/52.43 [1001]~E(x10011,x10012)+E(f461(x10013,x10011,x10014),f461(x10013,x10012,x10014))
% 52.62/52.43 [1002]~E(x10021,x10022)+E(f461(x10023,x10024,x10021),f461(x10023,x10024,x10022))
% 52.62/52.43 [1003]~E(x10031,x10032)+E(f118(x10031,x10033,x10034,x10035),f118(x10032,x10033,x10034,x10035))
% 52.62/52.43 [1004]~E(x10041,x10042)+E(f118(x10043,x10041,x10044,x10045),f118(x10043,x10042,x10044,x10045))
% 52.62/52.43 [1005]~E(x10051,x10052)+E(f118(x10053,x10054,x10051,x10055),f118(x10053,x10054,x10052,x10055))
% 52.62/52.43 [1006]~E(x10061,x10062)+E(f118(x10063,x10064,x10065,x10061),f118(x10063,x10064,x10065,x10062))
% 52.62/52.43 [1007]~E(x10071,x10072)+E(f364(x10071,x10073,x10074,x10075,x10076),f364(x10072,x10073,x10074,x10075,x10076))
% 52.62/52.43 [1008]~E(x10081,x10082)+E(f364(x10083,x10081,x10084,x10085,x10086),f364(x10083,x10082,x10084,x10085,x10086))
% 52.62/52.43 [1009]~E(x10091,x10092)+E(f364(x10093,x10094,x10091,x10095,x10096),f364(x10093,x10094,x10092,x10095,x10096))
% 52.62/52.43 [1010]~E(x10101,x10102)+E(f364(x10103,x10104,x10105,x10101,x10106),f364(x10103,x10104,x10105,x10102,x10106))
% 52.62/52.43 [1011]~E(x10111,x10112)+E(f364(x10113,x10114,x10115,x10116,x10111),f364(x10113,x10114,x10115,x10116,x10112))
% 52.62/52.43 [1012]~E(x10121,x10122)+E(f139(x10121,x10123,x10124,x10125,x10126),f139(x10122,x10123,x10124,x10125,x10126))
% 52.62/52.43 [1013]~E(x10131,x10132)+E(f139(x10133,x10131,x10134,x10135,x10136),f139(x10133,x10132,x10134,x10135,x10136))
% 52.62/52.43 [1014]~E(x10141,x10142)+E(f139(x10143,x10144,x10141,x10145,x10146),f139(x10143,x10144,x10142,x10145,x10146))
% 52.62/52.43 [1015]~E(x10151,x10152)+E(f139(x10153,x10154,x10155,x10151,x10156),f139(x10153,x10154,x10155,x10152,x10156))
% 52.62/52.43 [1016]~E(x10161,x10162)+E(f139(x10163,x10164,x10165,x10166,x10161),f139(x10163,x10164,x10165,x10166,x10162))
% 52.62/52.43 [1017]~E(x10171,x10172)+E(f645(x10171,x10173,x10174,x10175,x10176),f645(x10172,x10173,x10174,x10175,x10176))
% 52.62/52.43 [1018]~E(x10181,x10182)+E(f645(x10183,x10181,x10184,x10185,x10186),f645(x10183,x10182,x10184,x10185,x10186))
% 52.62/52.43 [1019]~E(x10191,x10192)+E(f645(x10193,x10194,x10191,x10195,x10196),f645(x10193,x10194,x10192,x10195,x10196))
% 52.62/52.43 [1020]~E(x10201,x10202)+E(f645(x10203,x10204,x10205,x10201,x10206),f645(x10203,x10204,x10205,x10202,x10206))
% 52.62/52.43 [1021]~E(x10211,x10212)+E(f645(x10213,x10214,x10215,x10216,x10211),f645(x10213,x10214,x10215,x10216,x10212))
% 52.62/52.43 [1022]~E(x10221,x10222)+E(f667(x10221,x10223,x10224,x10225,x10226),f667(x10222,x10223,x10224,x10225,x10226))
% 52.62/52.43 [1023]~E(x10231,x10232)+E(f667(x10233,x10231,x10234,x10235,x10236),f667(x10233,x10232,x10234,x10235,x10236))
% 52.62/52.43 [1024]~E(x10241,x10242)+E(f667(x10243,x10244,x10241,x10245,x10246),f667(x10243,x10244,x10242,x10245,x10246))
% 52.62/52.43 [1025]~E(x10251,x10252)+E(f667(x10253,x10254,x10255,x10251,x10256),f667(x10253,x10254,x10255,x10252,x10256))
% 52.62/52.43 [1026]~E(x10261,x10262)+E(f667(x10263,x10264,x10265,x10266,x10261),f667(x10263,x10264,x10265,x10266,x10262))
% 52.62/52.43 [1027]~E(x10271,x10272)+E(f66(x10271,x10273),f66(x10272,x10273))
% 52.62/52.43 [1028]~E(x10281,x10282)+E(f66(x10283,x10281),f66(x10283,x10282))
% 52.62/52.43 [1029]~E(x10291,x10292)+E(f61(x10291,x10293),f61(x10292,x10293))
% 52.62/52.43 [1030]~E(x10301,x10302)+E(f61(x10303,x10301),f61(x10303,x10302))
% 52.62/52.43 [1031]~E(x10311,x10312)+E(f542(x10311,x10313,x10314,x10315,x10316,x10317),f542(x10312,x10313,x10314,x10315,x10316,x10317))
% 52.62/52.43 [1032]~E(x10321,x10322)+E(f542(x10323,x10321,x10324,x10325,x10326,x10327),f542(x10323,x10322,x10324,x10325,x10326,x10327))
% 52.62/52.43 [1033]~E(x10331,x10332)+E(f542(x10333,x10334,x10331,x10335,x10336,x10337),f542(x10333,x10334,x10332,x10335,x10336,x10337))
% 52.62/52.43 [1034]~E(x10341,x10342)+E(f542(x10343,x10344,x10345,x10341,x10346,x10347),f542(x10343,x10344,x10345,x10342,x10346,x10347))
% 52.62/52.43 [1035]~E(x10351,x10352)+E(f542(x10353,x10354,x10355,x10356,x10351,x10357),f542(x10353,x10354,x10355,x10356,x10352,x10357))
% 52.62/52.43 [1036]~E(x10361,x10362)+E(f542(x10363,x10364,x10365,x10366,x10367,x10361),f542(x10363,x10364,x10365,x10366,x10367,x10362))
% 52.62/52.43 [1037]~E(x10371,x10372)+E(f367(x10371,x10373,x10374,x10375,x10376),f367(x10372,x10373,x10374,x10375,x10376))
% 52.62/52.43 [1038]~E(x10381,x10382)+E(f367(x10383,x10381,x10384,x10385,x10386),f367(x10383,x10382,x10384,x10385,x10386))
% 52.62/52.43 [1039]~E(x10391,x10392)+E(f367(x10393,x10394,x10391,x10395,x10396),f367(x10393,x10394,x10392,x10395,x10396))
% 52.62/52.43 [1040]~E(x10401,x10402)+E(f367(x10403,x10404,x10405,x10401,x10406),f367(x10403,x10404,x10405,x10402,x10406))
% 52.62/52.43 [1041]~E(x10411,x10412)+E(f367(x10413,x10414,x10415,x10416,x10411),f367(x10413,x10414,x10415,x10416,x10412))
% 52.62/52.43 [1042]~E(x10421,x10422)+E(f443(x10421,x10423),f443(x10422,x10423))
% 52.62/52.43 [1043]~E(x10431,x10432)+E(f443(x10433,x10431),f443(x10433,x10432))
% 52.62/52.43 [1044]~E(x10441,x10442)+E(f751(x10441,x10443,x10444,x10445),f751(x10442,x10443,x10444,x10445))
% 52.62/52.43 [1045]~E(x10451,x10452)+E(f751(x10453,x10451,x10454,x10455),f751(x10453,x10452,x10454,x10455))
% 52.62/52.43 [1046]~E(x10461,x10462)+E(f751(x10463,x10464,x10461,x10465),f751(x10463,x10464,x10462,x10465))
% 52.62/52.43 [1047]~E(x10471,x10472)+E(f751(x10473,x10474,x10475,x10471),f751(x10473,x10474,x10475,x10472))
% 52.62/52.43 [1048]~E(x10481,x10482)+E(f706(x10481,x10483,x10484,x10485,x10486,x10487),f706(x10482,x10483,x10484,x10485,x10486,x10487))
% 52.62/52.43 [1049]~E(x10491,x10492)+E(f706(x10493,x10491,x10494,x10495,x10496,x10497),f706(x10493,x10492,x10494,x10495,x10496,x10497))
% 52.62/52.43 [1050]~E(x10501,x10502)+E(f706(x10503,x10504,x10501,x10505,x10506,x10507),f706(x10503,x10504,x10502,x10505,x10506,x10507))
% 52.62/52.43 [1051]~E(x10511,x10512)+E(f706(x10513,x10514,x10515,x10511,x10516,x10517),f706(x10513,x10514,x10515,x10512,x10516,x10517))
% 52.62/52.43 [1052]~E(x10521,x10522)+E(f706(x10523,x10524,x10525,x10526,x10521,x10527),f706(x10523,x10524,x10525,x10526,x10522,x10527))
% 52.62/52.43 [1053]~E(x10531,x10532)+E(f706(x10533,x10534,x10535,x10536,x10537,x10531),f706(x10533,x10534,x10535,x10536,x10537,x10532))
% 52.62/52.43 [1054]~E(x10541,x10542)+E(f679(x10541,x10543,x10544),f679(x10542,x10543,x10544))
% 52.62/52.43 [1055]~E(x10551,x10552)+E(f679(x10553,x10551,x10554),f679(x10553,x10552,x10554))
% 52.62/52.43 [1056]~E(x10561,x10562)+E(f679(x10563,x10564,x10561),f679(x10563,x10564,x10562))
% 52.62/52.43 [1057]~E(x10571,x10572)+E(f196(x10571,x10573),f196(x10572,x10573))
% 52.62/52.43 [1058]~E(x10581,x10582)+E(f196(x10583,x10581),f196(x10583,x10582))
% 52.62/52.43 [1059]~E(x10591,x10592)+E(f289(x10591,x10593,x10594,x10595,x10596),f289(x10592,x10593,x10594,x10595,x10596))
% 52.62/52.43 [1060]~E(x10601,x10602)+E(f289(x10603,x10601,x10604,x10605,x10606),f289(x10603,x10602,x10604,x10605,x10606))
% 52.62/52.43 [1061]~E(x10611,x10612)+E(f289(x10613,x10614,x10611,x10615,x10616),f289(x10613,x10614,x10612,x10615,x10616))
% 52.62/52.43 [1062]~E(x10621,x10622)+E(f289(x10623,x10624,x10625,x10621,x10626),f289(x10623,x10624,x10625,x10622,x10626))
% 52.62/52.43 [1063]~E(x10631,x10632)+E(f289(x10633,x10634,x10635,x10636,x10631),f289(x10633,x10634,x10635,x10636,x10632))
% 52.62/52.43 [1064]~E(x10641,x10642)+E(f599(x10641,x10643,x10644,x10645),f599(x10642,x10643,x10644,x10645))
% 52.62/52.43 [1065]~E(x10651,x10652)+E(f599(x10653,x10651,x10654,x10655),f599(x10653,x10652,x10654,x10655))
% 52.62/52.43 [1066]~E(x10661,x10662)+E(f599(x10663,x10664,x10661,x10665),f599(x10663,x10664,x10662,x10665))
% 52.62/52.43 [1067]~E(x10671,x10672)+E(f599(x10673,x10674,x10675,x10671),f599(x10673,x10674,x10675,x10672))
% 52.62/52.43 [1068]~E(x10681,x10682)+E(f538(x10681,x10683,x10684,x10685,x10686),f538(x10682,x10683,x10684,x10685,x10686))
% 52.62/52.43 [1069]~E(x10691,x10692)+E(f538(x10693,x10691,x10694,x10695,x10696),f538(x10693,x10692,x10694,x10695,x10696))
% 52.62/52.43 [1070]~E(x10701,x10702)+E(f538(x10703,x10704,x10701,x10705,x10706),f538(x10703,x10704,x10702,x10705,x10706))
% 52.62/52.43 [1071]~E(x10711,x10712)+E(f538(x10713,x10714,x10715,x10711,x10716),f538(x10713,x10714,x10715,x10712,x10716))
% 52.62/52.43 [1072]~E(x10721,x10722)+E(f538(x10723,x10724,x10725,x10726,x10721),f538(x10723,x10724,x10725,x10726,x10722))
% 52.62/52.43 [1073]~E(x10731,x10732)+E(f442(x10731,x10733),f442(x10732,x10733))
% 52.62/52.43 [1074]~E(x10741,x10742)+E(f442(x10743,x10741),f442(x10743,x10742))
% 52.62/52.43 [1075]~E(x10751,x10752)+E(f809(x10751,x10753,x10754),f809(x10752,x10753,x10754))
% 52.62/52.43 [1076]~E(x10761,x10762)+E(f809(x10763,x10761,x10764),f809(x10763,x10762,x10764))
% 52.62/52.43 [1077]~E(x10771,x10772)+E(f809(x10773,x10774,x10771),f809(x10773,x10774,x10772))
% 52.62/52.43 [1078]~E(x10781,x10782)+E(f446(x10781,x10783),f446(x10782,x10783))
% 52.62/52.43 [1079]~E(x10791,x10792)+E(f446(x10793,x10791),f446(x10793,x10792))
% 52.62/52.43 [1080]~E(x10801,x10802)+E(f370(x10801,x10803,x10804,x10805,x10806),f370(x10802,x10803,x10804,x10805,x10806))
% 52.62/52.43 [1081]~E(x10811,x10812)+E(f370(x10813,x10811,x10814,x10815,x10816),f370(x10813,x10812,x10814,x10815,x10816))
% 52.62/52.43 [1082]~E(x10821,x10822)+E(f370(x10823,x10824,x10821,x10825,x10826),f370(x10823,x10824,x10822,x10825,x10826))
% 52.62/52.43 [1083]~E(x10831,x10832)+E(f370(x10833,x10834,x10835,x10831,x10836),f370(x10833,x10834,x10835,x10832,x10836))
% 52.62/52.43 [1084]~E(x10841,x10842)+E(f370(x10843,x10844,x10845,x10846,x10841),f370(x10843,x10844,x10845,x10846,x10842))
% 52.62/52.43 [1085]~E(x10851,x10852)+E(f701(x10851,x10853,x10854,x10855),f701(x10852,x10853,x10854,x10855))
% 52.62/52.43 [1086]~E(x10861,x10862)+E(f701(x10863,x10861,x10864,x10865),f701(x10863,x10862,x10864,x10865))
% 52.62/52.43 [1087]~E(x10871,x10872)+E(f701(x10873,x10874,x10871,x10875),f701(x10873,x10874,x10872,x10875))
% 52.62/52.43 [1088]~E(x10881,x10882)+E(f701(x10883,x10884,x10885,x10881),f701(x10883,x10884,x10885,x10882))
% 52.62/52.43 [1089]~E(x10891,x10892)+E(f755(x10891,x10893,x10894),f755(x10892,x10893,x10894))
% 52.62/52.43 [1090]~E(x10901,x10902)+E(f755(x10903,x10901,x10904),f755(x10903,x10902,x10904))
% 52.62/52.43 [1091]~E(x10911,x10912)+E(f755(x10913,x10914,x10911),f755(x10913,x10914,x10912))
% 52.62/52.43 [1092]~E(x10921,x10922)+E(f685(x10921,x10923,x10924),f685(x10922,x10923,x10924))
% 52.62/52.43 [1093]~E(x10931,x10932)+E(f685(x10933,x10931,x10934),f685(x10933,x10932,x10934))
% 52.62/52.43 [1094]~E(x10941,x10942)+E(f685(x10943,x10944,x10941),f685(x10943,x10944,x10942))
% 52.62/52.43 [1095]~E(x10951,x10952)+E(f819(x10951,x10953,x10954),f819(x10952,x10953,x10954))
% 52.62/52.43 [1096]~E(x10961,x10962)+E(f819(x10963,x10961,x10964),f819(x10963,x10962,x10964))
% 52.62/52.43 [1097]~E(x10971,x10972)+E(f819(x10973,x10974,x10971),f819(x10973,x10974,x10972))
% 52.62/52.43 [1098]~E(x10981,x10982)+E(f417(x10981,x10983,x10984,x10985),f417(x10982,x10983,x10984,x10985))
% 52.62/52.43 [1099]~E(x10991,x10992)+E(f417(x10993,x10991,x10994,x10995),f417(x10993,x10992,x10994,x10995))
% 52.62/52.43 [1100]~E(x11001,x11002)+E(f417(x11003,x11004,x11001,x11005),f417(x11003,x11004,x11002,x11005))
% 52.62/52.43 [1101]~E(x11011,x11012)+E(f417(x11013,x11014,x11015,x11011),f417(x11013,x11014,x11015,x11012))
% 52.62/52.43 [1102]~E(x11021,x11022)+E(f366(x11021,x11023,x11024,x11025,x11026),f366(x11022,x11023,x11024,x11025,x11026))
% 52.62/52.43 [1103]~E(x11031,x11032)+E(f366(x11033,x11031,x11034,x11035,x11036),f366(x11033,x11032,x11034,x11035,x11036))
% 52.62/52.43 [1104]~E(x11041,x11042)+E(f366(x11043,x11044,x11041,x11045,x11046),f366(x11043,x11044,x11042,x11045,x11046))
% 52.62/52.43 [1105]~E(x11051,x11052)+E(f366(x11053,x11054,x11055,x11051,x11056),f366(x11053,x11054,x11055,x11052,x11056))
% 52.62/52.43 [1106]~E(x11061,x11062)+E(f366(x11063,x11064,x11065,x11066,x11061),f366(x11063,x11064,x11065,x11066,x11062))
% 52.62/52.43 [1107]~E(x11071,x11072)+E(f456(x11071,x11073),f456(x11072,x11073))
% 52.62/52.43 [1108]~E(x11081,x11082)+E(f456(x11083,x11081),f456(x11083,x11082))
% 52.62/52.43 [1109]~E(x11091,x11092)+E(f590(x11091,x11093,x11094,x11095),f590(x11092,x11093,x11094,x11095))
% 52.62/52.43 [1110]~E(x11101,x11102)+E(f590(x11103,x11101,x11104,x11105),f590(x11103,x11102,x11104,x11105))
% 52.62/52.43 [1111]~E(x11111,x11112)+E(f590(x11113,x11114,x11111,x11115),f590(x11113,x11114,x11112,x11115))
% 52.62/52.43 [1112]~E(x11121,x11122)+E(f590(x11123,x11124,x11125,x11121),f590(x11123,x11124,x11125,x11122))
% 52.62/52.43 [1113]~E(x11131,x11132)+E(f480(x11131,x11133,x11134,x11135,x11136),f480(x11132,x11133,x11134,x11135,x11136))
% 52.62/52.43 [1114]~E(x11141,x11142)+E(f480(x11143,x11141,x11144,x11145,x11146),f480(x11143,x11142,x11144,x11145,x11146))
% 52.62/52.43 [1115]~E(x11151,x11152)+E(f480(x11153,x11154,x11151,x11155,x11156),f480(x11153,x11154,x11152,x11155,x11156))
% 52.62/52.43 [1116]~E(x11161,x11162)+E(f480(x11163,x11164,x11165,x11161,x11166),f480(x11163,x11164,x11165,x11162,x11166))
% 52.62/52.43 [1117]~E(x11171,x11172)+E(f480(x11173,x11174,x11175,x11176,x11171),f480(x11173,x11174,x11175,x11176,x11172))
% 52.62/52.43 [1118]~E(x11181,x11182)+E(f469(x11181,x11183,x11184,x11185,x11186,x11187),f469(x11182,x11183,x11184,x11185,x11186,x11187))
% 52.62/52.43 [1119]~E(x11191,x11192)+E(f469(x11193,x11191,x11194,x11195,x11196,x11197),f469(x11193,x11192,x11194,x11195,x11196,x11197))
% 52.62/52.43 [1120]~E(x11201,x11202)+E(f469(x11203,x11204,x11201,x11205,x11206,x11207),f469(x11203,x11204,x11202,x11205,x11206,x11207))
% 52.62/52.43 [1121]~E(x11211,x11212)+E(f469(x11213,x11214,x11215,x11211,x11216,x11217),f469(x11213,x11214,x11215,x11212,x11216,x11217))
% 52.62/52.43 [1122]~E(x11221,x11222)+E(f469(x11223,x11224,x11225,x11226,x11221,x11227),f469(x11223,x11224,x11225,x11226,x11222,x11227))
% 52.62/52.43 [1123]~E(x11231,x11232)+E(f469(x11233,x11234,x11235,x11236,x11237,x11231),f469(x11233,x11234,x11235,x11236,x11237,x11232))
% 52.62/52.43 [1124]~E(x11241,x11242)+E(f287(x11241,x11243,x11244),f287(x11242,x11243,x11244))
% 52.62/52.43 [1125]~E(x11251,x11252)+E(f287(x11253,x11251,x11254),f287(x11253,x11252,x11254))
% 52.62/52.43 [1126]~E(x11261,x11262)+E(f287(x11263,x11264,x11261),f287(x11263,x11264,x11262))
% 52.62/52.43 [1127]~E(x11271,x11272)+E(f454(x11271,x11273),f454(x11272,x11273))
% 52.62/52.43 [1128]~E(x11281,x11282)+E(f454(x11283,x11281),f454(x11283,x11282))
% 52.62/52.43 [1129]~E(x11291,x11292)+E(f424(x11291,x11293,x11294,x11295),f424(x11292,x11293,x11294,x11295))
% 52.62/52.43 [1130]~E(x11301,x11302)+E(f424(x11303,x11301,x11304,x11305),f424(x11303,x11302,x11304,x11305))
% 52.62/52.43 [1131]~E(x11311,x11312)+E(f424(x11313,x11314,x11311,x11315),f424(x11313,x11314,x11312,x11315))
% 52.62/52.43 [1132]~E(x11321,x11322)+E(f424(x11323,x11324,x11325,x11321),f424(x11323,x11324,x11325,x11322))
% 52.62/52.43 [1133]~E(x11331,x11332)+E(f812(x11331,x11333,x11334),f812(x11332,x11333,x11334))
% 52.62/52.43 [1134]~E(x11341,x11342)+E(f812(x11343,x11341,x11344),f812(x11343,x11342,x11344))
% 52.62/52.43 [1135]~E(x11351,x11352)+E(f812(x11353,x11354,x11351),f812(x11353,x11354,x11352))
% 52.62/52.43 [1136]~E(x11361,x11362)+E(f687(x11361,x11363,x11364,x11365),f687(x11362,x11363,x11364,x11365))
% 52.62/52.43 [1137]~E(x11371,x11372)+E(f687(x11373,x11371,x11374,x11375),f687(x11373,x11372,x11374,x11375))
% 52.62/52.43 [1138]~E(x11381,x11382)+E(f687(x11383,x11384,x11381,x11385),f687(x11383,x11384,x11382,x11385))
% 52.62/52.43 [1139]~E(x11391,x11392)+E(f687(x11393,x11394,x11395,x11391),f687(x11393,x11394,x11395,x11392))
% 52.62/52.43 [1140]~E(x11401,x11402)+E(f724(x11401,x11403,x11404),f724(x11402,x11403,x11404))
% 52.62/52.43 [1141]~E(x11411,x11412)+E(f724(x11413,x11411,x11414),f724(x11413,x11412,x11414))
% 52.62/52.43 [1142]~E(x11421,x11422)+E(f724(x11423,x11424,x11421),f724(x11423,x11424,x11422))
% 52.62/52.43 [1143]~E(x11431,x11432)+E(f607(x11431,x11433),f607(x11432,x11433))
% 52.62/52.43 [1144]~E(x11441,x11442)+E(f607(x11443,x11441),f607(x11443,x11442))
% 52.62/52.43 [1145]~E(x11451,x11452)+E(f637(x11451,x11453,x11454),f637(x11452,x11453,x11454))
% 52.62/52.43 [1146]~E(x11461,x11462)+E(f637(x11463,x11461,x11464),f637(x11463,x11462,x11464))
% 52.62/52.43 [1147]~E(x11471,x11472)+E(f637(x11473,x11474,x11471),f637(x11473,x11474,x11472))
% 52.62/52.43 [1148]~E(x11481,x11482)+E(f564(x11481,x11483,x11484,x11485,x11486,x11487),f564(x11482,x11483,x11484,x11485,x11486,x11487))
% 52.62/52.43 [1149]~E(x11491,x11492)+E(f564(x11493,x11491,x11494,x11495,x11496,x11497),f564(x11493,x11492,x11494,x11495,x11496,x11497))
% 52.62/52.43 [1150]~E(x11501,x11502)+E(f564(x11503,x11504,x11501,x11505,x11506,x11507),f564(x11503,x11504,x11502,x11505,x11506,x11507))
% 52.62/52.43 [1151]~E(x11511,x11512)+E(f564(x11513,x11514,x11515,x11511,x11516,x11517),f564(x11513,x11514,x11515,x11512,x11516,x11517))
% 52.62/52.43 [1152]~E(x11521,x11522)+E(f564(x11523,x11524,x11525,x11526,x11521,x11527),f564(x11523,x11524,x11525,x11526,x11522,x11527))
% 52.62/52.43 [1153]~E(x11531,x11532)+E(f564(x11533,x11534,x11535,x11536,x11537,x11531),f564(x11533,x11534,x11535,x11536,x11537,x11532))
% 52.62/52.43 [1154]~E(x11541,x11542)+E(f320(x11541,x11543,x11544,x11545,x11546,x11547),f320(x11542,x11543,x11544,x11545,x11546,x11547))
% 52.62/52.43 [1155]~E(x11551,x11552)+E(f320(x11553,x11551,x11554,x11555,x11556,x11557),f320(x11553,x11552,x11554,x11555,x11556,x11557))
% 52.62/52.43 [1156]~E(x11561,x11562)+E(f320(x11563,x11564,x11561,x11565,x11566,x11567),f320(x11563,x11564,x11562,x11565,x11566,x11567))
% 52.62/52.43 [1157]~E(x11571,x11572)+E(f320(x11573,x11574,x11575,x11571,x11576,x11577),f320(x11573,x11574,x11575,x11572,x11576,x11577))
% 52.62/52.43 [1158]~E(x11581,x11582)+E(f320(x11583,x11584,x11585,x11586,x11581,x11587),f320(x11583,x11584,x11585,x11586,x11582,x11587))
% 52.62/52.43 [1159]~E(x11591,x11592)+E(f320(x11593,x11594,x11595,x11596,x11597,x11591),f320(x11593,x11594,x11595,x11596,x11597,x11592))
% 52.62/52.43 [1160]~E(x11601,x11602)+E(f628(x11601,x11603,x11604,x11605,x11606,x11607),f628(x11602,x11603,x11604,x11605,x11606,x11607))
% 52.62/52.43 [1161]~E(x11611,x11612)+E(f628(x11613,x11611,x11614,x11615,x11616,x11617),f628(x11613,x11612,x11614,x11615,x11616,x11617))
% 52.62/52.43 [1162]~E(x11621,x11622)+E(f628(x11623,x11624,x11621,x11625,x11626,x11627),f628(x11623,x11624,x11622,x11625,x11626,x11627))
% 52.62/52.43 [1163]~E(x11631,x11632)+E(f628(x11633,x11634,x11635,x11631,x11636,x11637),f628(x11633,x11634,x11635,x11632,x11636,x11637))
% 52.62/52.43 [1164]~E(x11641,x11642)+E(f628(x11643,x11644,x11645,x11646,x11641,x11647),f628(x11643,x11644,x11645,x11646,x11642,x11647))
% 52.62/52.43 [1165]~E(x11651,x11652)+E(f628(x11653,x11654,x11655,x11656,x11657,x11651),f628(x11653,x11654,x11655,x11656,x11657,x11652))
% 52.62/52.43 [1166]~E(x11661,x11662)+E(f726(x11661,x11663),f726(x11662,x11663))
% 52.62/52.43 [1167]~E(x11671,x11672)+E(f726(x11673,x11671),f726(x11673,x11672))
% 52.62/52.43 [1168]~E(x11681,x11682)+E(f561(x11681,x11683,x11684,x11685),f561(x11682,x11683,x11684,x11685))
% 52.62/52.43 [1169]~E(x11691,x11692)+E(f561(x11693,x11691,x11694,x11695),f561(x11693,x11692,x11694,x11695))
% 52.62/52.43 [1170]~E(x11701,x11702)+E(f561(x11703,x11704,x11701,x11705),f561(x11703,x11704,x11702,x11705))
% 52.62/52.43 [1171]~E(x11711,x11712)+E(f561(x11713,x11714,x11715,x11711),f561(x11713,x11714,x11715,x11712))
% 52.62/52.43 [1172]~E(x11721,x11722)+E(f576(x11721,x11723,x11724,x11725,x11726),f576(x11722,x11723,x11724,x11725,x11726))
% 52.62/52.43 [1173]~E(x11731,x11732)+E(f576(x11733,x11731,x11734,x11735,x11736),f576(x11733,x11732,x11734,x11735,x11736))
% 52.62/52.43 [1174]~E(x11741,x11742)+E(f576(x11743,x11744,x11741,x11745,x11746),f576(x11743,x11744,x11742,x11745,x11746))
% 52.62/52.43 [1175]~E(x11751,x11752)+E(f576(x11753,x11754,x11755,x11751,x11756),f576(x11753,x11754,x11755,x11752,x11756))
% 52.62/52.43 [1176]~E(x11761,x11762)+E(f576(x11763,x11764,x11765,x11766,x11761),f576(x11763,x11764,x11765,x11766,x11762))
% 52.62/52.43 [1177]~E(x11771,x11772)+E(f710(x11771,x11773,x11774,x11775),f710(x11772,x11773,x11774,x11775))
% 52.62/52.43 [1178]~E(x11781,x11782)+E(f710(x11783,x11781,x11784,x11785),f710(x11783,x11782,x11784,x11785))
% 52.62/52.43 [1179]~E(x11791,x11792)+E(f710(x11793,x11794,x11791,x11795),f710(x11793,x11794,x11792,x11795))
% 52.62/52.43 [1180]~E(x11801,x11802)+E(f710(x11803,x11804,x11805,x11801),f710(x11803,x11804,x11805,x11802))
% 52.62/52.43 [1181]~E(x11811,x11812)+E(f204(x11811,x11813,x11814,x11815),f204(x11812,x11813,x11814,x11815))
% 52.62/52.43 [1182]~E(x11821,x11822)+E(f204(x11823,x11821,x11824,x11825),f204(x11823,x11822,x11824,x11825))
% 52.62/52.43 [1183]~E(x11831,x11832)+E(f204(x11833,x11834,x11831,x11835),f204(x11833,x11834,x11832,x11835))
% 52.62/52.43 [1184]~E(x11841,x11842)+E(f204(x11843,x11844,x11845,x11841),f204(x11843,x11844,x11845,x11842))
% 52.62/52.43 [1185]~E(x11851,x11852)+E(f432(x11851,x11853,x11854,x11855),f432(x11852,x11853,x11854,x11855))
% 52.62/52.43 [1186]~E(x11861,x11862)+E(f432(x11863,x11861,x11864,x11865),f432(x11863,x11862,x11864,x11865))
% 52.62/52.43 [1187]~E(x11871,x11872)+E(f432(x11873,x11874,x11871,x11875),f432(x11873,x11874,x11872,x11875))
% 52.62/52.43 [1188]~E(x11881,x11882)+E(f432(x11883,x11884,x11885,x11881),f432(x11883,x11884,x11885,x11882))
% 52.62/52.43 [1189]~E(x11891,x11892)+E(f313(x11891,x11893),f313(x11892,x11893))
% 52.62/52.43 [1190]~E(x11901,x11902)+E(f313(x11903,x11901),f313(x11903,x11902))
% 52.62/52.43 [1191]~E(x11911,x11912)+E(f160(x11911,x11913,x11914),f160(x11912,x11913,x11914))
% 52.62/52.43 [1192]~E(x11921,x11922)+E(f160(x11923,x11921,x11924),f160(x11923,x11922,x11924))
% 52.62/52.43 [1193]~E(x11931,x11932)+E(f160(x11933,x11934,x11931),f160(x11933,x11934,x11932))
% 52.62/52.43 [1194]~E(x11941,x11942)+E(f814(x11941,x11943,x11944,x11945),f814(x11942,x11943,x11944,x11945))
% 52.62/52.43 [1195]~E(x11951,x11952)+E(f814(x11953,x11951,x11954,x11955),f814(x11953,x11952,x11954,x11955))
% 52.62/52.43 [1196]~E(x11961,x11962)+E(f814(x11963,x11964,x11961,x11965),f814(x11963,x11964,x11962,x11965))
% 52.62/52.43 [1197]~E(x11971,x11972)+E(f814(x11973,x11974,x11975,x11971),f814(x11973,x11974,x11975,x11972))
% 52.62/52.43 [1198]~E(x11981,x11982)+E(f304(x11981,x11983),f304(x11982,x11983))
% 52.62/52.43 [1199]~E(x11991,x11992)+E(f304(x11993,x11991),f304(x11993,x11992))
% 52.62/52.43 [1200]~E(x12001,x12002)+E(f209(x12001,x12003),f209(x12002,x12003))
% 52.62/52.43 [1201]~E(x12011,x12012)+E(f209(x12013,x12011),f209(x12013,x12012))
% 52.62/52.43 [1202]~E(x12021,x12022)+E(f712(x12021,x12023,x12024,x12025,x12026,x12027,x12028),f712(x12022,x12023,x12024,x12025,x12026,x12027,x12028))
% 52.62/52.43 [1203]~E(x12031,x12032)+E(f712(x12033,x12031,x12034,x12035,x12036,x12037,x12038),f712(x12033,x12032,x12034,x12035,x12036,x12037,x12038))
% 52.62/52.43 [1204]~E(x12041,x12042)+E(f712(x12043,x12044,x12041,x12045,x12046,x12047,x12048),f712(x12043,x12044,x12042,x12045,x12046,x12047,x12048))
% 52.62/52.43 [1205]~E(x12051,x12052)+E(f712(x12053,x12054,x12055,x12051,x12056,x12057,x12058),f712(x12053,x12054,x12055,x12052,x12056,x12057,x12058))
% 52.62/52.43 [1206]~E(x12061,x12062)+E(f712(x12063,x12064,x12065,x12066,x12061,x12067,x12068),f712(x12063,x12064,x12065,x12066,x12062,x12067,x12068))
% 52.62/52.43 [1207]~E(x12071,x12072)+E(f712(x12073,x12074,x12075,x12076,x12077,x12071,x12078),f712(x12073,x12074,x12075,x12076,x12077,x12072,x12078))
% 52.62/52.43 [1208]~E(x12081,x12082)+E(f712(x12083,x12084,x12085,x12086,x12087,x12088,x12081),f712(x12083,x12084,x12085,x12086,x12087,x12088,x12082))
% 52.62/52.43 [1209]~E(x12091,x12092)+E(f824(x12091,x12093,x12094),f824(x12092,x12093,x12094))
% 52.62/52.43 [1210]~E(x12101,x12102)+E(f824(x12103,x12101,x12104),f824(x12103,x12102,x12104))
% 52.62/52.43 [1211]~E(x12111,x12112)+E(f824(x12113,x12114,x12111),f824(x12113,x12114,x12112))
% 52.62/52.43 [1212]~E(x12121,x12122)+E(f319(x12121,x12123,x12124,x12125,x12126),f319(x12122,x12123,x12124,x12125,x12126))
% 52.62/52.43 [1213]~E(x12131,x12132)+E(f319(x12133,x12131,x12134,x12135,x12136),f319(x12133,x12132,x12134,x12135,x12136))
% 52.62/52.43 [1214]~E(x12141,x12142)+E(f319(x12143,x12144,x12141,x12145,x12146),f319(x12143,x12144,x12142,x12145,x12146))
% 52.62/52.43 [1215]~E(x12151,x12152)+E(f319(x12153,x12154,x12155,x12151,x12156),f319(x12153,x12154,x12155,x12152,x12156))
% 52.62/52.43 [1216]~E(x12161,x12162)+E(f319(x12163,x12164,x12165,x12166,x12161),f319(x12163,x12164,x12165,x12166,x12162))
% 52.62/52.43 [1217]~E(x12171,x12172)+E(f661(x12171,x12173,x12174,x12175,x12176),f661(x12172,x12173,x12174,x12175,x12176))
% 52.62/52.43 [1218]~E(x12181,x12182)+E(f661(x12183,x12181,x12184,x12185,x12186),f661(x12183,x12182,x12184,x12185,x12186))
% 52.62/52.43 [1219]~E(x12191,x12192)+E(f661(x12193,x12194,x12191,x12195,x12196),f661(x12193,x12194,x12192,x12195,x12196))
% 52.62/52.43 [1220]~E(x12201,x12202)+E(f661(x12203,x12204,x12205,x12201,x12206),f661(x12203,x12204,x12205,x12202,x12206))
% 52.62/52.43 [1221]~E(x12211,x12212)+E(f661(x12213,x12214,x12215,x12216,x12211),f661(x12213,x12214,x12215,x12216,x12212))
% 52.62/52.43 [1222]~E(x12221,x12222)+E(f482(x12221,x12223,x12224,x12225,x12226),f482(x12222,x12223,x12224,x12225,x12226))
% 52.62/52.43 [1223]~E(x12231,x12232)+E(f482(x12233,x12231,x12234,x12235,x12236),f482(x12233,x12232,x12234,x12235,x12236))
% 52.62/52.43 [1224]~E(x12241,x12242)+E(f482(x12243,x12244,x12241,x12245,x12246),f482(x12243,x12244,x12242,x12245,x12246))
% 52.62/52.43 [1225]~E(x12251,x12252)+E(f482(x12253,x12254,x12255,x12251,x12256),f482(x12253,x12254,x12255,x12252,x12256))
% 52.62/52.43 [1226]~E(x12261,x12262)+E(f482(x12263,x12264,x12265,x12266,x12261),f482(x12263,x12264,x12265,x12266,x12262))
% 52.62/52.43 [1227]~E(x12271,x12272)+E(f669(x12271,x12273),f669(x12272,x12273))
% 52.62/52.43 [1228]~E(x12281,x12282)+E(f669(x12283,x12281),f669(x12283,x12282))
% 52.62/52.43 [1229]~E(x12291,x12292)+E(f559(x12291,x12293,x12294,x12295,x12296,x12297),f559(x12292,x12293,x12294,x12295,x12296,x12297))
% 52.62/52.43 [1230]~E(x12301,x12302)+E(f559(x12303,x12301,x12304,x12305,x12306,x12307),f559(x12303,x12302,x12304,x12305,x12306,x12307))
% 52.62/52.43 [1231]~E(x12311,x12312)+E(f559(x12313,x12314,x12311,x12315,x12316,x12317),f559(x12313,x12314,x12312,x12315,x12316,x12317))
% 52.62/52.43 [1232]~E(x12321,x12322)+E(f559(x12323,x12324,x12325,x12321,x12326,x12327),f559(x12323,x12324,x12325,x12322,x12326,x12327))
% 52.62/52.43 [1233]~E(x12331,x12332)+E(f559(x12333,x12334,x12335,x12336,x12331,x12337),f559(x12333,x12334,x12335,x12336,x12332,x12337))
% 52.62/52.43 [1234]~E(x12341,x12342)+E(f559(x12343,x12344,x12345,x12346,x12347,x12341),f559(x12343,x12344,x12345,x12346,x12347,x12342))
% 52.62/52.43 [1235]~E(x12351,x12352)+E(f327(x12351,x12353,x12354),f327(x12352,x12353,x12354))
% 52.62/52.43 [1236]~E(x12361,x12362)+E(f327(x12363,x12361,x12364),f327(x12363,x12362,x12364))
% 52.62/52.43 [1237]~E(x12371,x12372)+E(f327(x12373,x12374,x12371),f327(x12373,x12374,x12372))
% 52.62/52.43 [1238]~E(x12381,x12382)+E(f747(x12381),f747(x12382))
% 52.62/52.43 [1239]~E(x12391,x12392)+E(f389(x12391,x12393,x12394,x12395,x12396),f389(x12392,x12393,x12394,x12395,x12396))
% 52.62/52.43 [1240]~E(x12401,x12402)+E(f389(x12403,x12401,x12404,x12405,x12406),f389(x12403,x12402,x12404,x12405,x12406))
% 52.62/52.43 [1241]~E(x12411,x12412)+E(f389(x12413,x12414,x12411,x12415,x12416),f389(x12413,x12414,x12412,x12415,x12416))
% 52.62/52.43 [1242]~E(x12421,x12422)+E(f389(x12423,x12424,x12425,x12421,x12426),f389(x12423,x12424,x12425,x12422,x12426))
% 52.62/52.43 [1243]~E(x12431,x12432)+E(f389(x12433,x12434,x12435,x12436,x12431),f389(x12433,x12434,x12435,x12436,x12432))
% 52.62/52.43 [1244]~E(x12441,x12442)+E(f520(x12441),f520(x12442))
% 52.62/52.43 [1245]~E(x12451,x12452)+E(f800(x12451,x12453,x12454),f800(x12452,x12453,x12454))
% 52.62/52.43 [1246]~E(x12461,x12462)+E(f800(x12463,x12461,x12464),f800(x12463,x12462,x12464))
% 52.62/52.43 [1247]~E(x12471,x12472)+E(f800(x12473,x12474,x12471),f800(x12473,x12474,x12472))
% 52.62/52.43 [1248]~E(x12481,x12482)+E(f439(x12481,x12483,x12484,x12485,x12486,x12487,x12488,x12489,x124810),f439(x12482,x12483,x12484,x12485,x12486,x12487,x12488,x12489,x124810))
% 52.62/52.43 [1249]~E(x12491,x12492)+E(f439(x12493,x12491,x12494,x12495,x12496,x12497,x12498,x12499,x124910),f439(x12493,x12492,x12494,x12495,x12496,x12497,x12498,x12499,x124910))
% 52.62/52.43 [1250]~E(x12501,x12502)+E(f439(x12503,x12504,x12501,x12505,x12506,x12507,x12508,x12509,x125010),f439(x12503,x12504,x12502,x12505,x12506,x12507,x12508,x12509,x125010))
% 52.62/52.43 [1251]~E(x12511,x12512)+E(f439(x12513,x12514,x12515,x12511,x12516,x12517,x12518,x12519,x125110),f439(x12513,x12514,x12515,x12512,x12516,x12517,x12518,x12519,x125110))
% 52.62/52.43 [1252]~E(x12521,x12522)+E(f439(x12523,x12524,x12525,x12526,x12521,x12527,x12528,x12529,x125210),f439(x12523,x12524,x12525,x12526,x12522,x12527,x12528,x12529,x125210))
% 52.62/52.43 [1253]~E(x12531,x12532)+E(f439(x12533,x12534,x12535,x12536,x12537,x12531,x12538,x12539,x125310),f439(x12533,x12534,x12535,x12536,x12537,x12532,x12538,x12539,x125310))
% 52.62/52.43 [1254]~E(x12541,x12542)+E(f439(x12543,x12544,x12545,x12546,x12547,x12548,x12541,x12549,x125410),f439(x12543,x12544,x12545,x12546,x12547,x12548,x12542,x12549,x125410))
% 52.62/52.43 [1255]~E(x12551,x12552)+E(f439(x12553,x12554,x12555,x12556,x12557,x12558,x12559,x12551,x125510),f439(x12553,x12554,x12555,x12556,x12557,x12558,x12559,x12552,x125510))
% 52.62/52.43 [1256]~E(x12561,x12562)+E(f439(x12563,x12564,x12565,x12566,x12567,x12568,x12569,x125610,x12561),f439(x12563,x12564,x12565,x12566,x12567,x12568,x12569,x125610,x12562))
% 52.62/52.43 [1257]~E(x12571,x12572)+E(f761(x12571,x12573),f761(x12572,x12573))
% 52.62/52.43 [1258]~E(x12581,x12582)+E(f761(x12583,x12581),f761(x12583,x12582))
% 52.62/52.43 [1259]~E(x12591,x12592)+E(f418(x12591,x12593,x12594),f418(x12592,x12593,x12594))
% 52.62/52.43 [1260]~E(x12601,x12602)+E(f418(x12603,x12601,x12604),f418(x12603,x12602,x12604))
% 52.62/52.43 [1261]~E(x12611,x12612)+E(f418(x12613,x12614,x12611),f418(x12613,x12614,x12612))
% 52.62/52.43 [1262]~E(x12621,x12622)+E(f764(x12621,x12623,x12624),f764(x12622,x12623,x12624))
% 52.62/52.43 [1263]~E(x12631,x12632)+E(f764(x12633,x12631,x12634),f764(x12633,x12632,x12634))
% 52.62/52.43 [1264]~E(x12641,x12642)+E(f764(x12643,x12644,x12641),f764(x12643,x12644,x12642))
% 52.62/52.43 [1265]~E(x12651,x12652)+E(f704(x12651,x12653,x12654,x12655),f704(x12652,x12653,x12654,x12655))
% 52.62/52.43 [1266]~E(x12661,x12662)+E(f704(x12663,x12661,x12664,x12665),f704(x12663,x12662,x12664,x12665))
% 52.62/52.43 [1267]~E(x12671,x12672)+E(f704(x12673,x12674,x12671,x12675),f704(x12673,x12674,x12672,x12675))
% 52.62/52.43 [1268]~E(x12681,x12682)+E(f704(x12683,x12684,x12685,x12681),f704(x12683,x12684,x12685,x12682))
% 52.62/52.43 [1269]~E(x12691,x12692)+E(f692(x12691,x12693,x12694,x12695),f692(x12692,x12693,x12694,x12695))
% 52.62/52.43 [1270]~E(x12701,x12702)+E(f692(x12703,x12701,x12704,x12705),f692(x12703,x12702,x12704,x12705))
% 52.62/52.43 [1271]~E(x12711,x12712)+E(f692(x12713,x12714,x12711,x12715),f692(x12713,x12714,x12712,x12715))
% 52.62/52.43 [1272]~E(x12721,x12722)+E(f692(x12723,x12724,x12725,x12721),f692(x12723,x12724,x12725,x12722))
% 52.62/52.43 [1273]~E(x12731,x12732)+E(f568(x12731,x12733,x12734),f568(x12732,x12733,x12734))
% 52.62/52.43 [1274]~E(x12741,x12742)+E(f568(x12743,x12741,x12744),f568(x12743,x12742,x12744))
% 52.62/52.43 [1275]~E(x12751,x12752)+E(f568(x12753,x12754,x12751),f568(x12753,x12754,x12752))
% 52.62/52.43 [1276]~E(x12761,x12762)+E(f267(x12761,x12763),f267(x12762,x12763))
% 52.62/52.43 [1277]~E(x12771,x12772)+E(f267(x12773,x12771),f267(x12773,x12772))
% 52.62/52.43 [1278]~E(x12781,x12782)+E(f808(x12781,x12783,x12784),f808(x12782,x12783,x12784))
% 52.62/52.43 [1279]~E(x12791,x12792)+E(f808(x12793,x12791,x12794),f808(x12793,x12792,x12794))
% 52.62/52.43 [1280]~E(x12801,x12802)+E(f808(x12803,x12804,x12801),f808(x12803,x12804,x12802))
% 52.62/52.43 [1281]~E(x12811,x12812)+E(f243(x12811,x12813,x12814),f243(x12812,x12813,x12814))
% 52.62/52.43 [1282]~E(x12821,x12822)+E(f243(x12823,x12821,x12824),f243(x12823,x12822,x12824))
% 52.62/52.43 [1283]~E(x12831,x12832)+E(f243(x12833,x12834,x12831),f243(x12833,x12834,x12832))
% 52.62/52.43 [1284]~E(x12841,x12842)+E(f218(x12841,x12843,x12844,x12845,x12846),f218(x12842,x12843,x12844,x12845,x12846))
% 52.62/52.43 [1285]~E(x12851,x12852)+E(f218(x12853,x12851,x12854,x12855,x12856),f218(x12853,x12852,x12854,x12855,x12856))
% 52.62/52.43 [1286]~E(x12861,x12862)+E(f218(x12863,x12864,x12861,x12865,x12866),f218(x12863,x12864,x12862,x12865,x12866))
% 52.62/52.43 [1287]~E(x12871,x12872)+E(f218(x12873,x12874,x12875,x12871,x12876),f218(x12873,x12874,x12875,x12872,x12876))
% 52.62/52.43 [1288]~E(x12881,x12882)+E(f218(x12883,x12884,x12885,x12886,x12881),f218(x12883,x12884,x12885,x12886,x12882))
% 52.62/52.43 [1289]~E(x12891,x12892)+E(f772(x12891,x12893),f772(x12892,x12893))
% 52.62/52.43 [1290]~E(x12901,x12902)+E(f772(x12903,x12901),f772(x12903,x12902))
% 52.62/52.43 [1291]~E(x12911,x12912)+E(f720(x12911,x12913,x12914,x12915,x12916),f720(x12912,x12913,x12914,x12915,x12916))
% 52.62/52.43 [1292]~E(x12921,x12922)+E(f720(x12923,x12921,x12924,x12925,x12926),f720(x12923,x12922,x12924,x12925,x12926))
% 52.62/52.43 [1293]~E(x12931,x12932)+E(f720(x12933,x12934,x12931,x12935,x12936),f720(x12933,x12934,x12932,x12935,x12936))
% 52.62/52.43 [1294]~E(x12941,x12942)+E(f720(x12943,x12944,x12945,x12941,x12946),f720(x12943,x12944,x12945,x12942,x12946))
% 52.62/52.43 [1295]~E(x12951,x12952)+E(f720(x12953,x12954,x12955,x12956,x12951),f720(x12953,x12954,x12955,x12956,x12952))
% 52.62/52.43 [1296]~E(x12961,x12962)+E(f648(x12961,x12963,x12964,x12965,x12966),f648(x12962,x12963,x12964,x12965,x12966))
% 52.62/52.43 [1297]~E(x12971,x12972)+E(f648(x12973,x12971,x12974,x12975,x12976),f648(x12973,x12972,x12974,x12975,x12976))
% 52.62/52.43 [1298]~E(x12981,x12982)+E(f648(x12983,x12984,x12981,x12985,x12986),f648(x12983,x12984,x12982,x12985,x12986))
% 52.62/52.43 [1299]~E(x12991,x12992)+E(f648(x12993,x12994,x12995,x12991,x12996),f648(x12993,x12994,x12995,x12992,x12996))
% 52.62/52.43 [1300]~E(x13001,x13002)+E(f648(x13003,x13004,x13005,x13006,x13001),f648(x13003,x13004,x13005,x13006,x13002))
% 52.62/52.43 [1301]~E(x13011,x13012)+E(f601(x13011,x13013),f601(x13012,x13013))
% 52.62/52.43 [1302]~E(x13021,x13022)+E(f601(x13023,x13021),f601(x13023,x13022))
% 52.62/52.43 [1303]~E(x13031,x13032)+E(f375(x13031,x13033,x13034,x13035),f375(x13032,x13033,x13034,x13035))
% 52.62/52.43 [1304]~E(x13041,x13042)+E(f375(x13043,x13041,x13044,x13045),f375(x13043,x13042,x13044,x13045))
% 52.62/52.43 [1305]~E(x13051,x13052)+E(f375(x13053,x13054,x13051,x13055),f375(x13053,x13054,x13052,x13055))
% 52.62/52.43 [1306]~E(x13061,x13062)+E(f375(x13063,x13064,x13065,x13061),f375(x13063,x13064,x13065,x13062))
% 52.62/52.43 [1307]~E(x13071,x13072)+E(f276(x13071),f276(x13072))
% 52.62/52.43 [1308]~E(x13081,x13082)+E(f485(x13081,x13083,x13084,x13085),f485(x13082,x13083,x13084,x13085))
% 52.62/52.43 [1309]~E(x13091,x13092)+E(f485(x13093,x13091,x13094,x13095),f485(x13093,x13092,x13094,x13095))
% 52.62/52.43 [1310]~E(x13101,x13102)+E(f485(x13103,x13104,x13101,x13105),f485(x13103,x13104,x13102,x13105))
% 52.62/52.43 [1311]~E(x13111,x13112)+E(f485(x13113,x13114,x13115,x13111),f485(x13113,x13114,x13115,x13112))
% 52.62/52.43 [1312]~E(x13121,x13122)+E(f660(x13121,x13123,x13124,x13125,x13126),f660(x13122,x13123,x13124,x13125,x13126))
% 52.62/52.43 [1313]~E(x13131,x13132)+E(f660(x13133,x13131,x13134,x13135,x13136),f660(x13133,x13132,x13134,x13135,x13136))
% 52.62/52.43 [1314]~E(x13141,x13142)+E(f660(x13143,x13144,x13141,x13145,x13146),f660(x13143,x13144,x13142,x13145,x13146))
% 52.62/52.43 [1315]~E(x13151,x13152)+E(f660(x13153,x13154,x13155,x13151,x13156),f660(x13153,x13154,x13155,x13152,x13156))
% 52.62/52.43 [1316]~E(x13161,x13162)+E(f660(x13163,x13164,x13165,x13166,x13161),f660(x13163,x13164,x13165,x13166,x13162))
% 52.62/52.43 [1317]~E(x13171,x13172)+E(f766(x13171,x13173,x13174),f766(x13172,x13173,x13174))
% 52.62/52.43 [1318]~E(x13181,x13182)+E(f766(x13183,x13181,x13184),f766(x13183,x13182,x13184))
% 52.62/52.43 [1319]~E(x13191,x13192)+E(f766(x13193,x13194,x13191),f766(x13193,x13194,x13192))
% 52.62/52.43 [1320]~E(x13201,x13202)+E(f796(x13201,x13203,x13204),f796(x13202,x13203,x13204))
% 52.62/52.43 [1321]~E(x13211,x13212)+E(f796(x13213,x13211,x13214),f796(x13213,x13212,x13214))
% 52.62/52.43 [1322]~E(x13221,x13222)+E(f796(x13223,x13224,x13221),f796(x13223,x13224,x13222))
% 52.62/52.43 [1323]~E(x13231,x13232)+E(f285(x13231,x13233),f285(x13232,x13233))
% 52.62/52.43 [1324]~E(x13241,x13242)+E(f285(x13243,x13241),f285(x13243,x13242))
% 52.62/52.43 [1325]~E(x13251,x13252)+E(f533(x13251,x13253,x13254,x13255,x13256),f533(x13252,x13253,x13254,x13255,x13256))
% 52.62/52.43 [1326]~E(x13261,x13262)+E(f533(x13263,x13261,x13264,x13265,x13266),f533(x13263,x13262,x13264,x13265,x13266))
% 52.62/52.43 [1327]~E(x13271,x13272)+E(f533(x13273,x13274,x13271,x13275,x13276),f533(x13273,x13274,x13272,x13275,x13276))
% 52.62/52.43 [1328]~E(x13281,x13282)+E(f533(x13283,x13284,x13285,x13281,x13286),f533(x13283,x13284,x13285,x13282,x13286))
% 52.62/52.43 [1329]~E(x13291,x13292)+E(f533(x13293,x13294,x13295,x13296,x13291),f533(x13293,x13294,x13295,x13296,x13292))
% 52.62/52.43 [1330]~E(x13301,x13302)+E(f423(x13301,x13303,x13304,x13305),f423(x13302,x13303,x13304,x13305))
% 52.62/52.43 [1331]~E(x13311,x13312)+E(f423(x13313,x13311,x13314,x13315),f423(x13313,x13312,x13314,x13315))
% 52.62/52.43 [1332]~E(x13321,x13322)+E(f423(x13323,x13324,x13321,x13325),f423(x13323,x13324,x13322,x13325))
% 52.62/52.43 [1333]~E(x13331,x13332)+E(f423(x13333,x13334,x13335,x13331),f423(x13333,x13334,x13335,x13332))
% 52.62/52.43 [1334]~E(x13341,x13342)+E(f473(x13341,x13343,x13344),f473(x13342,x13343,x13344))
% 52.62/52.43 [1335]~E(x13351,x13352)+E(f473(x13353,x13351,x13354),f473(x13353,x13352,x13354))
% 52.62/52.43 [1336]~E(x13361,x13362)+E(f473(x13363,x13364,x13361),f473(x13363,x13364,x13362))
% 52.62/52.43 [1337]~E(x13371,x13372)+E(f565(x13371,x13373),f565(x13372,x13373))
% 52.62/52.43 [1338]~E(x13381,x13382)+E(f565(x13383,x13381),f565(x13383,x13382))
% 52.62/52.43 [1339]~E(x13391,x13392)+E(f361(x13391,x13393,x13394,x13395,x13396),f361(x13392,x13393,x13394,x13395,x13396))
% 52.62/52.43 [1340]~E(x13401,x13402)+E(f361(x13403,x13401,x13404,x13405,x13406),f361(x13403,x13402,x13404,x13405,x13406))
% 52.62/52.43 [1341]~E(x13411,x13412)+E(f361(x13413,x13414,x13411,x13415,x13416),f361(x13413,x13414,x13412,x13415,x13416))
% 52.62/52.43 [1342]~E(x13421,x13422)+E(f361(x13423,x13424,x13425,x13421,x13426),f361(x13423,x13424,x13425,x13422,x13426))
% 52.62/52.43 [1343]~E(x13431,x13432)+E(f361(x13433,x13434,x13435,x13436,x13431),f361(x13433,x13434,x13435,x13436,x13432))
% 52.62/52.43 [1344]~E(x13441,x13442)+E(f827(x13441,x13443,x13444),f827(x13442,x13443,x13444))
% 52.62/52.43 [1345]~E(x13451,x13452)+E(f827(x13453,x13451,x13454),f827(x13453,x13452,x13454))
% 52.62/52.43 [1346]~E(x13461,x13462)+E(f827(x13463,x13464,x13461),f827(x13463,x13464,x13462))
% 52.62/52.43 [1347]~E(x13471,x13472)+E(f386(x13471,x13473,x13474,x13475,x13476),f386(x13472,x13473,x13474,x13475,x13476))
% 52.62/52.43 [1348]~E(x13481,x13482)+E(f386(x13483,x13481,x13484,x13485,x13486),f386(x13483,x13482,x13484,x13485,x13486))
% 52.62/52.43 [1349]~E(x13491,x13492)+E(f386(x13493,x13494,x13491,x13495,x13496),f386(x13493,x13494,x13492,x13495,x13496))
% 52.62/52.43 [1350]~E(x13501,x13502)+E(f386(x13503,x13504,x13505,x13501,x13506),f386(x13503,x13504,x13505,x13502,x13506))
% 52.62/52.43 [1351]~E(x13511,x13512)+E(f386(x13513,x13514,x13515,x13516,x13511),f386(x13513,x13514,x13515,x13516,x13512))
% 52.62/52.43 [1352]~E(x13521,x13522)+E(f153(x13521,x13523,x13524,x13525),f153(x13522,x13523,x13524,x13525))
% 52.62/52.43 [1353]~E(x13531,x13532)+E(f153(x13533,x13531,x13534,x13535),f153(x13533,x13532,x13534,x13535))
% 52.62/52.43 [1354]~E(x13541,x13542)+E(f153(x13543,x13544,x13541,x13545),f153(x13543,x13544,x13542,x13545))
% 52.62/52.43 [1355]~E(x13551,x13552)+E(f153(x13553,x13554,x13555,x13551),f153(x13553,x13554,x13555,x13552))
% 52.62/52.43 [1356]~E(x13561,x13562)+E(f483(x13561,x13563,x13564),f483(x13562,x13563,x13564))
% 52.62/52.43 [1357]~E(x13571,x13572)+E(f483(x13573,x13571,x13574),f483(x13573,x13572,x13574))
% 52.62/52.43 [1358]~E(x13581,x13582)+E(f483(x13583,x13584,x13581),f483(x13583,x13584,x13582))
% 52.62/52.43 [1359]~E(x13591,x13592)+E(f121(x13591,x13593,x13594,x13595),f121(x13592,x13593,x13594,x13595))
% 52.62/52.43 [1360]~E(x13601,x13602)+E(f121(x13603,x13601,x13604,x13605),f121(x13603,x13602,x13604,x13605))
% 52.62/52.43 [1361]~E(x13611,x13612)+E(f121(x13613,x13614,x13611,x13615),f121(x13613,x13614,x13612,x13615))
% 52.62/52.43 [1362]~E(x13621,x13622)+E(f121(x13623,x13624,x13625,x13621),f121(x13623,x13624,x13625,x13622))
% 52.62/52.43 [1363]~E(x13631,x13632)+E(f165(x13631),f165(x13632))
% 52.62/52.43 [1364]~E(x13641,x13642)+E(f155(x13641,x13643,x13644),f155(x13642,x13643,x13644))
% 52.62/52.43 [1365]~E(x13651,x13652)+E(f155(x13653,x13651,x13654),f155(x13653,x13652,x13654))
% 52.62/52.43 [1366]~E(x13661,x13662)+E(f155(x13663,x13664,x13661),f155(x13663,x13664,x13662))
% 52.62/52.43 [1367]~E(x13671,x13672)+E(f79(x13671,x13673,x13674,x13675),f79(x13672,x13673,x13674,x13675))
% 52.62/52.43 [1368]~E(x13681,x13682)+E(f79(x13683,x13681,x13684,x13685),f79(x13683,x13682,x13684,x13685))
% 52.62/52.43 [1369]~E(x13691,x13692)+E(f79(x13693,x13694,x13691,x13695),f79(x13693,x13694,x13692,x13695))
% 52.62/52.43 [1370]~E(x13701,x13702)+E(f79(x13703,x13704,x13705,x13701),f79(x13703,x13704,x13705,x13702))
% 52.62/52.43 [1371]~E(x13711,x13712)+E(f197(x13711),f197(x13712))
% 52.62/52.43 [1372]~E(x13721,x13722)+E(f388(x13721,x13723,x13724),f388(x13722,x13723,x13724))
% 52.62/52.43 [1373]~E(x13731,x13732)+E(f388(x13733,x13731,x13734),f388(x13733,x13732,x13734))
% 52.62/52.43 [1374]~E(x13741,x13742)+E(f388(x13743,x13744,x13741),f388(x13743,x13744,x13742))
% 52.62/52.43 [1375]~E(x13751,x13752)+E(f498(x13751,x13753,x13754),f498(x13752,x13753,x13754))
% 52.62/52.43 [1376]~E(x13761,x13762)+E(f498(x13763,x13761,x13764),f498(x13763,x13762,x13764))
% 52.62/52.43 [1377]~E(x13771,x13772)+E(f498(x13773,x13774,x13771),f498(x13773,x13774,x13772))
% 52.62/52.43 [1378]~E(x13781,x13782)+E(f770(x13781,x13783,x13784),f770(x13782,x13783,x13784))
% 52.62/52.43 [1379]~E(x13791,x13792)+E(f770(x13793,x13791,x13794),f770(x13793,x13792,x13794))
% 52.62/52.43 [1380]~E(x13801,x13802)+E(f770(x13803,x13804,x13801),f770(x13803,x13804,x13802))
% 52.62/52.43 [1381]~E(x13811,x13812)+E(f722(x13811,x13813),f722(x13812,x13813))
% 52.62/52.43 [1382]~E(x13821,x13822)+E(f722(x13823,x13821),f722(x13823,x13822))
% 52.62/52.43 [1383]~E(x13831,x13832)+E(f625(x13831,x13833,x13834,x13835,x13836),f625(x13832,x13833,x13834,x13835,x13836))
% 52.62/52.43 [1384]~E(x13841,x13842)+E(f625(x13843,x13841,x13844,x13845,x13846),f625(x13843,x13842,x13844,x13845,x13846))
% 52.62/52.43 [1385]~E(x13851,x13852)+E(f625(x13853,x13854,x13851,x13855,x13856),f625(x13853,x13854,x13852,x13855,x13856))
% 52.62/52.43 [1386]~E(x13861,x13862)+E(f625(x13863,x13864,x13865,x13861,x13866),f625(x13863,x13864,x13865,x13862,x13866))
% 52.62/52.43 [1387]~E(x13871,x13872)+E(f625(x13873,x13874,x13875,x13876,x13871),f625(x13873,x13874,x13875,x13876,x13872))
% 52.62/52.43 [1388]~E(x13881,x13882)+E(f471(x13881,x13883,x13884),f471(x13882,x13883,x13884))
% 52.62/52.43 [1389]~E(x13891,x13892)+E(f471(x13893,x13891,x13894),f471(x13893,x13892,x13894))
% 52.62/52.43 [1390]~E(x13901,x13902)+E(f471(x13903,x13904,x13901),f471(x13903,x13904,x13902))
% 52.62/52.43 [1391]~E(x13911,x13912)+E(f341(x13911,x13913,x13914),f341(x13912,x13913,x13914))
% 52.62/52.43 [1392]~E(x13921,x13922)+E(f341(x13923,x13921,x13924),f341(x13923,x13922,x13924))
% 52.62/52.43 [1393]~E(x13931,x13932)+E(f341(x13933,x13934,x13931),f341(x13933,x13934,x13932))
% 52.62/52.43 [1394]~E(x13941,x13942)+E(f470(x13941,x13943,x13944),f470(x13942,x13943,x13944))
% 52.62/52.43 [1395]~E(x13951,x13952)+E(f470(x13953,x13951,x13954),f470(x13953,x13952,x13954))
% 52.62/52.43 [1396]~E(x13961,x13962)+E(f470(x13963,x13964,x13961),f470(x13963,x13964,x13962))
% 52.62/52.43 [1397]~E(x13971,x13972)+E(f347(x13971,x13973,x13974,x13975),f347(x13972,x13973,x13974,x13975))
% 52.62/52.43 [1398]~E(x13981,x13982)+E(f347(x13983,x13981,x13984,x13985),f347(x13983,x13982,x13984,x13985))
% 52.62/52.43 [1399]~E(x13991,x13992)+E(f347(x13993,x13994,x13991,x13995),f347(x13993,x13994,x13992,x13995))
% 52.62/52.43 [1400]~E(x14001,x14002)+E(f347(x14003,x14004,x14005,x14001),f347(x14003,x14004,x14005,x14002))
% 52.62/52.43 [1401]~E(x14011,x14012)+E(f515(x14011),f515(x14012))
% 52.62/52.43 [1402]~E(x14021,x14022)+E(f733(x14021,x14023,x14024,x14025),f733(x14022,x14023,x14024,x14025))
% 52.62/52.43 [1403]~E(x14031,x14032)+E(f733(x14033,x14031,x14034,x14035),f733(x14033,x14032,x14034,x14035))
% 52.62/52.43 [1404]~E(x14041,x14042)+E(f733(x14043,x14044,x14041,x14045),f733(x14043,x14044,x14042,x14045))
% 52.62/52.43 [1405]~E(x14051,x14052)+E(f733(x14053,x14054,x14055,x14051),f733(x14053,x14054,x14055,x14052))
% 52.62/52.43 [1406]~E(x14061,x14062)+E(f758(x14061,x14063,x14064),f758(x14062,x14063,x14064))
% 52.62/52.43 [1407]~E(x14071,x14072)+E(f758(x14073,x14071,x14074),f758(x14073,x14072,x14074))
% 52.62/52.43 [1408]~E(x14081,x14082)+E(f758(x14083,x14084,x14081),f758(x14083,x14084,x14082))
% 52.62/52.43 [1409]~E(x14091,x14092)+E(f284(x14091,x14093),f284(x14092,x14093))
% 52.62/52.43 [1410]~E(x14101,x14102)+E(f284(x14103,x14101),f284(x14103,x14102))
% 52.62/52.43 [1411]~E(x14111,x14112)+E(f493(x14111,x14113,x14114),f493(x14112,x14113,x14114))
% 52.62/52.43 [1412]~E(x14121,x14122)+E(f493(x14123,x14121,x14124),f493(x14123,x14122,x14124))
% 52.62/52.43 [1413]~E(x14131,x14132)+E(f493(x14133,x14134,x14131),f493(x14133,x14134,x14132))
% 52.62/52.43 [1414]~E(x14141,x14142)+E(f638(x14141,x14143,x14144),f638(x14142,x14143,x14144))
% 52.62/52.43 [1415]~E(x14151,x14152)+E(f638(x14153,x14151,x14154),f638(x14153,x14152,x14154))
% 52.62/52.43 [1416]~E(x14161,x14162)+E(f638(x14163,x14164,x14161),f638(x14163,x14164,x14162))
% 52.62/52.43 [1417]~E(x14171,x14172)+E(f228(x14171,x14173,x14174),f228(x14172,x14173,x14174))
% 52.62/52.43 [1418]~E(x14181,x14182)+E(f228(x14183,x14181,x14184),f228(x14183,x14182,x14184))
% 52.62/52.43 [1419]~E(x14191,x14192)+E(f228(x14193,x14194,x14191),f228(x14193,x14194,x14192))
% 52.62/52.43 [1420]~E(x14201,x14202)+E(f353(x14201,x14203),f353(x14202,x14203))
% 52.62/52.43 [1421]~E(x14211,x14212)+E(f353(x14213,x14211),f353(x14213,x14212))
% 52.62/52.43 [1422]~E(x14221,x14222)+E(f652(x14221,x14223),f652(x14222,x14223))
% 52.62/52.43 [1423]~E(x14231,x14232)+E(f652(x14233,x14231),f652(x14233,x14232))
% 52.62/52.43 [1424]~E(x14241,x14242)+E(f723(x14241),f723(x14242))
% 52.62/52.43 [1425]~E(x14251,x14252)+E(f246(x14251,x14253,x14254),f246(x14252,x14253,x14254))
% 52.62/52.43 [1426]~E(x14261,x14262)+E(f246(x14263,x14261,x14264),f246(x14263,x14262,x14264))
% 52.62/52.43 [1427]~E(x14271,x14272)+E(f246(x14273,x14274,x14271),f246(x14273,x14274,x14272))
% 52.62/52.43 [1428]~E(x14281,x14282)+E(f784(x14281,x14283),f784(x14282,x14283))
% 52.62/52.43 [1429]~E(x14291,x14292)+E(f784(x14293,x14291),f784(x14293,x14292))
% 52.62/52.43 [1430]~E(x14301,x14302)+E(f352(x14301,x14303),f352(x14302,x14303))
% 52.62/52.43 [1431]~E(x14311,x14312)+E(f352(x14313,x14311),f352(x14313,x14312))
% 52.62/52.43 [1432]~E(x14321,x14322)+E(f230(x14321,x14323,x14324,x14325,x14326),f230(x14322,x14323,x14324,x14325,x14326))
% 52.62/52.43 [1433]~E(x14331,x14332)+E(f230(x14333,x14331,x14334,x14335,x14336),f230(x14333,x14332,x14334,x14335,x14336))
% 52.62/52.43 [1434]~E(x14341,x14342)+E(f230(x14343,x14344,x14341,x14345,x14346),f230(x14343,x14344,x14342,x14345,x14346))
% 52.62/52.43 [1435]~E(x14351,x14352)+E(f230(x14353,x14354,x14355,x14351,x14356),f230(x14353,x14354,x14355,x14352,x14356))
% 52.62/52.43 [1436]~E(x14361,x14362)+E(f230(x14363,x14364,x14365,x14366,x14361),f230(x14363,x14364,x14365,x14366,x14362))
% 52.62/52.43 [1437]~E(x14371,x14372)+E(f602(x14371,x14373),f602(x14372,x14373))
% 52.62/52.43 [1438]~E(x14381,x14382)+E(f602(x14383,x14381),f602(x14383,x14382))
% 52.62/52.43 [1439]~E(x14391,x14392)+E(f363(x14391,x14393,x14394,x14395,x14396),f363(x14392,x14393,x14394,x14395,x14396))
% 52.62/52.43 [1440]~E(x14401,x14402)+E(f363(x14403,x14401,x14404,x14405,x14406),f363(x14403,x14402,x14404,x14405,x14406))
% 52.62/52.43 [1441]~E(x14411,x14412)+E(f363(x14413,x14414,x14411,x14415,x14416),f363(x14413,x14414,x14412,x14415,x14416))
% 52.62/52.43 [1442]~E(x14421,x14422)+E(f363(x14423,x14424,x14425,x14421,x14426),f363(x14423,x14424,x14425,x14422,x14426))
% 52.62/52.43 [1443]~E(x14431,x14432)+E(f363(x14433,x14434,x14435,x14436,x14431),f363(x14433,x14434,x14435,x14436,x14432))
% 52.62/52.43 [1444]~E(x14441,x14442)+E(f399(x14441,x14443,x14444,x14445),f399(x14442,x14443,x14444,x14445))
% 52.62/52.43 [1445]~E(x14451,x14452)+E(f399(x14453,x14451,x14454,x14455),f399(x14453,x14452,x14454,x14455))
% 52.62/52.43 [1446]~E(x14461,x14462)+E(f399(x14463,x14464,x14461,x14465),f399(x14463,x14464,x14462,x14465))
% 52.62/52.43 [1447]~E(x14471,x14472)+E(f399(x14473,x14474,x14475,x14471),f399(x14473,x14474,x14475,x14472))
% 52.62/52.43 [1448]~E(x14481,x14482)+E(f689(x14481,x14483,x14484,x14485),f689(x14482,x14483,x14484,x14485))
% 52.62/52.43 [1449]~E(x14491,x14492)+E(f689(x14493,x14491,x14494,x14495),f689(x14493,x14492,x14494,x14495))
% 52.62/52.43 [1450]~E(x14501,x14502)+E(f689(x14503,x14504,x14501,x14505),f689(x14503,x14504,x14502,x14505))
% 52.62/52.43 [1451]~E(x14511,x14512)+E(f689(x14513,x14514,x14515,x14511),f689(x14513,x14514,x14515,x14512))
% 52.62/52.43 [1452]~E(x14521,x14522)+E(f396(x14521,x14523,x14524),f396(x14522,x14523,x14524))
% 52.62/52.43 [1453]~E(x14531,x14532)+E(f396(x14533,x14531,x14534),f396(x14533,x14532,x14534))
% 52.62/52.43 [1454]~E(x14541,x14542)+E(f396(x14543,x14544,x14541),f396(x14543,x14544,x14542))
% 52.62/52.43 [1455]~E(x14551,x14552)+E(f537(x14551,x14553,x14554,x14555),f537(x14552,x14553,x14554,x14555))
% 52.62/52.43 [1456]~E(x14561,x14562)+E(f537(x14563,x14561,x14564,x14565),f537(x14563,x14562,x14564,x14565))
% 52.62/52.43 [1457]~E(x14571,x14572)+E(f537(x14573,x14574,x14571,x14575),f537(x14573,x14574,x14572,x14575))
% 52.62/52.43 [1458]~E(x14581,x14582)+E(f537(x14583,x14584,x14585,x14581),f537(x14583,x14584,x14585,x14582))
% 52.62/52.43 [1459]~E(x14591,x14592)+E(f534(x14591,x14593,x14594,x14595,x14596),f534(x14592,x14593,x14594,x14595,x14596))
% 52.62/52.43 [1460]~E(x14601,x14602)+E(f534(x14603,x14601,x14604,x14605,x14606),f534(x14603,x14602,x14604,x14605,x14606))
% 52.62/52.43 [1461]~E(x14611,x14612)+E(f534(x14613,x14614,x14611,x14615,x14616),f534(x14613,x14614,x14612,x14615,x14616))
% 52.62/52.43 [1462]~E(x14621,x14622)+E(f534(x14623,x14624,x14625,x14621,x14626),f534(x14623,x14624,x14625,x14622,x14626))
% 52.62/52.43 [1463]~E(x14631,x14632)+E(f534(x14633,x14634,x14635,x14636,x14631),f534(x14633,x14634,x14635,x14636,x14632))
% 52.62/52.43 [1464]~E(x14641,x14642)+E(f263(x14641,x14643),f263(x14642,x14643))
% 52.62/52.43 [1465]~E(x14651,x14652)+E(f263(x14653,x14651),f263(x14653,x14652))
% 52.62/52.43 [1466]~E(x14661,x14662)+E(f753(x14661,x14663,x14664,x14665),f753(x14662,x14663,x14664,x14665))
% 52.62/52.43 [1467]~E(x14671,x14672)+E(f753(x14673,x14671,x14674,x14675),f753(x14673,x14672,x14674,x14675))
% 52.62/52.43 [1468]~E(x14681,x14682)+E(f753(x14683,x14684,x14681,x14685),f753(x14683,x14684,x14682,x14685))
% 52.62/52.43 [1469]~E(x14691,x14692)+E(f753(x14693,x14694,x14695,x14691),f753(x14693,x14694,x14695,x14692))
% 52.62/52.43 [1470]~E(x14701,x14702)+E(f828(x14701,x14703,x14704),f828(x14702,x14703,x14704))
% 52.62/52.43 [1471]~E(x14711,x14712)+E(f828(x14713,x14711,x14714),f828(x14713,x14712,x14714))
% 52.62/52.43 [1472]~E(x14721,x14722)+E(f828(x14723,x14724,x14721),f828(x14723,x14724,x14722))
% 52.62/52.43 [1473]~E(x14731,x14732)+E(f426(x14731,x14733,x14734,x14735),f426(x14732,x14733,x14734,x14735))
% 52.62/52.43 [1474]~E(x14741,x14742)+E(f426(x14743,x14741,x14744,x14745),f426(x14743,x14742,x14744,x14745))
% 52.62/52.43 [1475]~E(x14751,x14752)+E(f426(x14753,x14754,x14751,x14755),f426(x14753,x14754,x14752,x14755))
% 52.62/52.43 [1476]~E(x14761,x14762)+E(f426(x14763,x14764,x14765,x14761),f426(x14763,x14764,x14765,x14762))
% 52.62/52.43 [1477]~E(x14771,x14772)+E(f798(x14771,x14773,x14774),f798(x14772,x14773,x14774))
% 52.62/52.43 [1478]~E(x14781,x14782)+E(f798(x14783,x14781,x14784),f798(x14783,x14782,x14784))
% 52.62/52.43 [1479]~E(x14791,x14792)+E(f798(x14793,x14794,x14791),f798(x14793,x14794,x14792))
% 52.62/52.43 [1480]~E(x14801,x14802)+E(f394(x14801,x14803,x14804,x14805,x14806),f394(x14802,x14803,x14804,x14805,x14806))
% 52.62/52.43 [1481]~E(x14811,x14812)+E(f394(x14813,x14811,x14814,x14815,x14816),f394(x14813,x14812,x14814,x14815,x14816))
% 52.62/52.43 [1482]~E(x14821,x14822)+E(f394(x14823,x14824,x14821,x14825,x14826),f394(x14823,x14824,x14822,x14825,x14826))
% 52.62/52.43 [1483]~E(x14831,x14832)+E(f394(x14833,x14834,x14835,x14831,x14836),f394(x14833,x14834,x14835,x14832,x14836))
% 52.62/52.43 [1484]~E(x14841,x14842)+E(f394(x14843,x14844,x14845,x14846,x14841),f394(x14843,x14844,x14845,x14846,x14842))
% 52.62/52.43 [1485]~E(x14851,x14852)+E(f247(x14851,x14853,x14854),f247(x14852,x14853,x14854))
% 52.62/52.43 [1486]~E(x14861,x14862)+E(f247(x14863,x14861,x14864),f247(x14863,x14862,x14864))
% 52.62/52.43 [1487]~E(x14871,x14872)+E(f247(x14873,x14874,x14871),f247(x14873,x14874,x14872))
% 52.62/52.43 [1488]~E(x14881,x14882)+E(f392(x14881,x14883,x14884,x14885,x14886),f392(x14882,x14883,x14884,x14885,x14886))
% 52.62/52.43 [1489]~E(x14891,x14892)+E(f392(x14893,x14891,x14894,x14895,x14896),f392(x14893,x14892,x14894,x14895,x14896))
% 52.62/52.43 [1490]~E(x14901,x14902)+E(f392(x14903,x14904,x14901,x14905,x14906),f392(x14903,x14904,x14902,x14905,x14906))
% 52.62/52.43 [1491]~E(x14911,x14912)+E(f392(x14913,x14914,x14915,x14911,x14916),f392(x14913,x14914,x14915,x14912,x14916))
% 52.62/52.43 [1492]~E(x14921,x14922)+E(f392(x14923,x14924,x14925,x14926,x14921),f392(x14923,x14924,x14925,x14926,x14922))
% 52.62/52.43 [1493]~E(x14931,x14932)+E(f831(x14931,x14933,x14934,x14935,x14936,x14937,x14938),f831(x14932,x14933,x14934,x14935,x14936,x14937,x14938))
% 52.62/52.43 [1494]~E(x14941,x14942)+E(f831(x14943,x14941,x14944,x14945,x14946,x14947,x14948),f831(x14943,x14942,x14944,x14945,x14946,x14947,x14948))
% 52.62/52.43 [1495]~E(x14951,x14952)+E(f831(x14953,x14954,x14951,x14955,x14956,x14957,x14958),f831(x14953,x14954,x14952,x14955,x14956,x14957,x14958))
% 52.62/52.43 [1496]~E(x14961,x14962)+E(f831(x14963,x14964,x14965,x14961,x14966,x14967,x14968),f831(x14963,x14964,x14965,x14962,x14966,x14967,x14968))
% 52.62/52.43 [1497]~E(x14971,x14972)+E(f831(x14973,x14974,x14975,x14976,x14971,x14977,x14978),f831(x14973,x14974,x14975,x14976,x14972,x14977,x14978))
% 52.62/52.43 [1498]~E(x14981,x14982)+E(f831(x14983,x14984,x14985,x14986,x14987,x14981,x14988),f831(x14983,x14984,x14985,x14986,x14987,x14982,x14988))
% 52.62/52.43 [1499]~E(x14991,x14992)+E(f831(x14993,x14994,x14995,x14996,x14997,x14998,x14991),f831(x14993,x14994,x14995,x14996,x14997,x14998,x14992))
% 52.62/52.43 [1500]~E(x15001,x15002)+E(f484(x15001,x15003,x15004,x15005),f484(x15002,x15003,x15004,x15005))
% 52.62/52.43 [1501]~E(x15011,x15012)+E(f484(x15013,x15011,x15014,x15015),f484(x15013,x15012,x15014,x15015))
% 52.62/52.43 [1502]~E(x15021,x15022)+E(f484(x15023,x15024,x15021,x15025),f484(x15023,x15024,x15022,x15025))
% 52.62/52.43 [1503]~E(x15031,x15032)+E(f484(x15033,x15034,x15035,x15031),f484(x15033,x15034,x15035,x15032))
% 52.62/52.43 [1504]~E(x15041,x15042)+E(f560(x15041,x15043,x15044,x15045),f560(x15042,x15043,x15044,x15045))
% 52.62/52.43 [1505]~E(x15051,x15052)+E(f560(x15053,x15051,x15054,x15055),f560(x15053,x15052,x15054,x15055))
% 52.62/52.43 [1506]~E(x15061,x15062)+E(f560(x15063,x15064,x15061,x15065),f560(x15063,x15064,x15062,x15065))
% 52.62/52.43 [1507]~E(x15071,x15072)+E(f560(x15073,x15074,x15075,x15071),f560(x15073,x15074,x15075,x15072))
% 52.62/52.43 [1508]~E(x15081,x15082)+E(f245(x15081,x15083),f245(x15082,x15083))
% 52.62/52.43 [1509]~E(x15091,x15092)+E(f245(x15093,x15091),f245(x15093,x15092))
% 52.62/52.43 [1510]~E(x15101,x15102)+E(f156(x15101,x15103),f156(x15102,x15103))
% 52.62/52.43 [1511]~E(x15111,x15112)+E(f156(x15113,x15111),f156(x15113,x15112))
% 52.62/52.43 [1512]~E(x15121,x15122)+E(f368(x15121,x15123,x15124,x15125,x15126),f368(x15122,x15123,x15124,x15125,x15126))
% 52.62/52.43 [1513]~E(x15131,x15132)+E(f368(x15133,x15131,x15134,x15135,x15136),f368(x15133,x15132,x15134,x15135,x15136))
% 52.62/52.43 [1514]~E(x15141,x15142)+E(f368(x15143,x15144,x15141,x15145,x15146),f368(x15143,x15144,x15142,x15145,x15146))
% 52.62/52.43 [1515]~E(x15151,x15152)+E(f368(x15153,x15154,x15155,x15151,x15156),f368(x15153,x15154,x15155,x15152,x15156))
% 52.62/52.43 [1516]~E(x15161,x15162)+E(f368(x15163,x15164,x15165,x15166,x15161),f368(x15163,x15164,x15165,x15166,x15162))
% 52.62/52.43 [1517]~E(x15171,x15172)+E(f318(x15171,x15173,x15174,x15175,x15176),f318(x15172,x15173,x15174,x15175,x15176))
% 52.62/52.43 [1518]~E(x15181,x15182)+E(f318(x15183,x15181,x15184,x15185,x15186),f318(x15183,x15182,x15184,x15185,x15186))
% 52.62/52.43 [1519]~E(x15191,x15192)+E(f318(x15193,x15194,x15191,x15195,x15196),f318(x15193,x15194,x15192,x15195,x15196))
% 52.62/52.43 [1520]~E(x15201,x15202)+E(f318(x15203,x15204,x15205,x15201,x15206),f318(x15203,x15204,x15205,x15202,x15206))
% 52.62/52.43 [1521]~E(x15211,x15212)+E(f318(x15213,x15214,x15215,x15216,x15211),f318(x15213,x15214,x15215,x15216,x15212))
% 52.62/52.43 [1522]~E(x15221,x15222)+E(f339(x15221,x15223),f339(x15222,x15223))
% 52.62/52.43 [1523]~E(x15231,x15232)+E(f339(x15233,x15231),f339(x15233,x15232))
% 52.62/52.43 [1524]~E(x15241,x15242)+E(f365(x15241,x15243,x15244,x15245,x15246),f365(x15242,x15243,x15244,x15245,x15246))
% 52.62/52.43 [1525]~E(x15251,x15252)+E(f365(x15253,x15251,x15254,x15255,x15256),f365(x15253,x15252,x15254,x15255,x15256))
% 52.62/52.43 [1526]~E(x15261,x15262)+E(f365(x15263,x15264,x15261,x15265,x15266),f365(x15263,x15264,x15262,x15265,x15266))
% 52.62/52.43 [1527]~E(x15271,x15272)+E(f365(x15273,x15274,x15275,x15271,x15276),f365(x15273,x15274,x15275,x15272,x15276))
% 52.62/52.43 [1528]~E(x15281,x15282)+E(f365(x15283,x15284,x15285,x15286,x15281),f365(x15283,x15284,x15285,x15286,x15282))
% 52.62/52.43 [1529]~E(x15291,x15292)+E(f420(x15291,x15293,x15294),f420(x15292,x15293,x15294))
% 52.62/52.43 [1530]~E(x15301,x15302)+E(f420(x15303,x15301,x15304),f420(x15303,x15302,x15304))
% 52.62/52.43 [1531]~E(x15311,x15312)+E(f420(x15313,x15314,x15311),f420(x15313,x15314,x15312))
% 52.62/52.43 [1532]~E(x15321,x15322)+E(f580(x15321,x15323),f580(x15322,x15323))
% 52.62/52.43 [1533]~E(x15331,x15332)+E(f580(x15333,x15331),f580(x15333,x15332))
% 52.62/52.43 [1534]~E(x15341,x15342)+E(f579(x15341),f579(x15342))
% 52.62/52.43 [1535]~E(x15351,x15352)+E(f788(x15351,x15353,x15354),f788(x15352,x15353,x15354))
% 52.62/52.43 [1536]~E(x15361,x15362)+E(f788(x15363,x15361,x15364),f788(x15363,x15362,x15364))
% 52.62/52.43 [1537]~E(x15371,x15372)+E(f788(x15373,x15374,x15371),f788(x15373,x15374,x15372))
% 52.62/52.43 [1538]~E(x15381,x15382)+E(f406(x15381,x15383,x15384),f406(x15382,x15383,x15384))
% 52.62/52.43 [1539]~E(x15391,x15392)+E(f406(x15393,x15391,x15394),f406(x15393,x15392,x15394))
% 52.62/52.43 [1540]~E(x15401,x15402)+E(f406(x15403,x15404,x15401),f406(x15403,x15404,x15402))
% 52.62/52.43 [1541]~E(x15411,x15412)+E(f711(x15411,x15413,x15414,x15415),f711(x15412,x15413,x15414,x15415))
% 52.62/52.43 [1542]~E(x15421,x15422)+E(f711(x15423,x15421,x15424,x15425),f711(x15423,x15422,x15424,x15425))
% 52.62/52.43 [1543]~E(x15431,x15432)+E(f711(x15433,x15434,x15431,x15435),f711(x15433,x15434,x15432,x15435))
% 52.62/52.43 [1544]~E(x15441,x15442)+E(f711(x15443,x15444,x15445,x15441),f711(x15443,x15444,x15445,x15442))
% 52.62/52.43 [1545]~E(x15451,x15452)+E(f444(x15451,x15453,x15454,x15455,x15456),f444(x15452,x15453,x15454,x15455,x15456))
% 52.62/52.43 [1546]~E(x15461,x15462)+E(f444(x15463,x15461,x15464,x15465,x15466),f444(x15463,x15462,x15464,x15465,x15466))
% 52.62/52.43 [1547]~E(x15471,x15472)+E(f444(x15473,x15474,x15471,x15475,x15476),f444(x15473,x15474,x15472,x15475,x15476))
% 52.62/52.43 [1548]~E(x15481,x15482)+E(f444(x15483,x15484,x15485,x15481,x15486),f444(x15483,x15484,x15485,x15482,x15486))
% 52.62/52.43 [1549]~E(x15491,x15492)+E(f444(x15493,x15494,x15495,x15496,x15491),f444(x15493,x15494,x15495,x15496,x15492))
% 52.62/52.43 [1550]~E(x15501,x15502)+E(f514(x15501,x15503),f514(x15502,x15503))
% 52.62/52.43 [1551]~E(x15511,x15512)+E(f514(x15513,x15511),f514(x15513,x15512))
% 52.62/52.43 [1552]~E(x15521,x15522)+E(f795(x15521,x15523),f795(x15522,x15523))
% 52.62/52.43 [1553]~E(x15531,x15532)+E(f795(x15533,x15531),f795(x15533,x15532))
% 52.62/52.43 [1554]~E(x15541,x15542)+E(f644(x15541,x15543,x15544,x15545,x15546),f644(x15542,x15543,x15544,x15545,x15546))
% 52.62/52.43 [1555]~E(x15551,x15552)+E(f644(x15553,x15551,x15554,x15555,x15556),f644(x15553,x15552,x15554,x15555,x15556))
% 52.62/52.43 [1556]~E(x15561,x15562)+E(f644(x15563,x15564,x15561,x15565,x15566),f644(x15563,x15564,x15562,x15565,x15566))
% 52.62/52.43 [1557]~E(x15571,x15572)+E(f644(x15573,x15574,x15575,x15571,x15576),f644(x15573,x15574,x15575,x15572,x15576))
% 52.62/52.43 [1558]~E(x15581,x15582)+E(f644(x15583,x15584,x15585,x15586,x15581),f644(x15583,x15584,x15585,x15586,x15582))
% 52.62/52.43 [1559]~E(x15591,x15592)+E(f95(x15591,x15593,x15594),f95(x15592,x15593,x15594))
% 52.62/52.43 [1560]~E(x15601,x15602)+E(f95(x15603,x15601,x15604),f95(x15603,x15602,x15604))
% 52.62/52.43 [1561]~E(x15611,x15612)+E(f95(x15613,x15614,x15611),f95(x15613,x15614,x15612))
% 52.62/52.43 [1562]~E(x15621,x15622)+E(f182(x15621,x15623,x15624,x15625),f182(x15622,x15623,x15624,x15625))
% 52.62/52.43 [1563]~E(x15631,x15632)+E(f182(x15633,x15631,x15634,x15635),f182(x15633,x15632,x15634,x15635))
% 52.62/52.43 [1564]~E(x15641,x15642)+E(f182(x15643,x15644,x15641,x15645),f182(x15643,x15644,x15642,x15645))
% 52.62/52.43 [1565]~E(x15651,x15652)+E(f182(x15653,x15654,x15655,x15651),f182(x15653,x15654,x15655,x15652))
% 52.62/52.43 [1566]~E(x15661,x15662)+E(f803(x15661,x15663,x15664),f803(x15662,x15663,x15664))
% 52.62/52.43 [1567]~E(x15671,x15672)+E(f803(x15673,x15671,x15674),f803(x15673,x15672,x15674))
% 52.62/52.43 [1568]~E(x15681,x15682)+E(f803(x15683,x15684,x15681),f803(x15683,x15684,x15682))
% 52.62/52.43 [1569]~E(x15691,x15692)+E(f566(x15691,x15693),f566(x15692,x15693))
% 52.62/52.43 [1570]~E(x15701,x15702)+E(f566(x15703,x15701),f566(x15703,x15702))
% 52.62/52.43 [1571]~E(x15711,x15712)+E(f756(x15711,x15713,x15714,x15715),f756(x15712,x15713,x15714,x15715))
% 52.62/52.43 [1572]~E(x15721,x15722)+E(f756(x15723,x15721,x15724,x15725),f756(x15723,x15722,x15724,x15725))
% 52.62/52.43 [1573]~E(x15731,x15732)+E(f756(x15733,x15734,x15731,x15735),f756(x15733,x15734,x15732,x15735))
% 52.62/52.43 [1574]~E(x15741,x15742)+E(f756(x15743,x15744,x15745,x15741),f756(x15743,x15744,x15745,x15742))
% 52.62/52.43 [1575]~E(x15751,x15752)+E(f403(x15751),f403(x15752))
% 52.62/52.43 [1576]~E(x15761,x15762)+E(f676(x15761,x15763,x15764),f676(x15762,x15763,x15764))
% 52.62/52.43 [1577]~E(x15771,x15772)+E(f676(x15773,x15771,x15774),f676(x15773,x15772,x15774))
% 52.62/52.43 [1578]~E(x15781,x15782)+E(f676(x15783,x15784,x15781),f676(x15783,x15784,x15782))
% 52.62/52.43 [1579]~E(x15791,x15792)+E(f640(x15791,x15793,x15794),f640(x15792,x15793,x15794))
% 52.62/52.43 [1580]~E(x15801,x15802)+E(f640(x15803,x15801,x15804),f640(x15803,x15802,x15804))
% 52.62/52.43 [1581]~E(x15811,x15812)+E(f640(x15813,x15814,x15811),f640(x15813,x15814,x15812))
% 52.62/52.43 [1582]~E(x15821,x15822)+E(f273(x15821),f273(x15822))
% 52.62/52.43 [1583]~E(x15831,x15832)+E(f223(x15831,x15833,x15834,x15835),f223(x15832,x15833,x15834,x15835))
% 52.62/52.43 [1584]~E(x15841,x15842)+E(f223(x15843,x15841,x15844,x15845),f223(x15843,x15842,x15844,x15845))
% 52.62/52.43 [1585]~E(x15851,x15852)+E(f223(x15853,x15854,x15851,x15855),f223(x15853,x15854,x15852,x15855))
% 52.62/52.43 [1586]~E(x15861,x15862)+E(f223(x15863,x15864,x15865,x15861),f223(x15863,x15864,x15865,x15862))
% 52.62/52.43 [1587]~E(x15871,x15872)+E(f508(x15871,x15873,x15874,x15875,x15876),f508(x15872,x15873,x15874,x15875,x15876))
% 52.62/52.43 [1588]~E(x15881,x15882)+E(f508(x15883,x15881,x15884,x15885,x15886),f508(x15883,x15882,x15884,x15885,x15886))
% 52.62/52.43 [1589]~E(x15891,x15892)+E(f508(x15893,x15894,x15891,x15895,x15896),f508(x15893,x15894,x15892,x15895,x15896))
% 52.62/52.43 [1590]~E(x15901,x15902)+E(f508(x15903,x15904,x15905,x15901,x15906),f508(x15903,x15904,x15905,x15902,x15906))
% 52.62/52.43 [1591]~E(x15911,x15912)+E(f508(x15913,x15914,x15915,x15916,x15911),f508(x15913,x15914,x15915,x15916,x15912))
% 52.62/52.43 [1592]~E(x15921,x15922)+E(f255(x15921,x15923,x15924,x15925,x15926),f255(x15922,x15923,x15924,x15925,x15926))
% 52.62/52.43 [1593]~E(x15931,x15932)+E(f255(x15933,x15931,x15934,x15935,x15936),f255(x15933,x15932,x15934,x15935,x15936))
% 52.62/52.43 [1594]~E(x15941,x15942)+E(f255(x15943,x15944,x15941,x15945,x15946),f255(x15943,x15944,x15942,x15945,x15946))
% 52.62/52.43 [1595]~E(x15951,x15952)+E(f255(x15953,x15954,x15955,x15951,x15956),f255(x15953,x15954,x15955,x15952,x15956))
% 52.62/52.43 [1596]~E(x15961,x15962)+E(f255(x15963,x15964,x15965,x15966,x15961),f255(x15963,x15964,x15965,x15966,x15962))
% 52.62/52.43 [1597]~E(x15971,x15972)+E(f569(x15971,x15973,x15974,x15975,x15976),f569(x15972,x15973,x15974,x15975,x15976))
% 52.62/52.43 [1598]~E(x15981,x15982)+E(f569(x15983,x15981,x15984,x15985,x15986),f569(x15983,x15982,x15984,x15985,x15986))
% 52.62/52.43 [1599]~E(x15991,x15992)+E(f569(x15993,x15994,x15991,x15995,x15996),f569(x15993,x15994,x15992,x15995,x15996))
% 52.62/52.43 [1600]~E(x16001,x16002)+E(f569(x16003,x16004,x16005,x16001,x16006),f569(x16003,x16004,x16005,x16002,x16006))
% 52.62/52.43 [1601]~E(x16011,x16012)+E(f569(x16013,x16014,x16015,x16016,x16011),f569(x16013,x16014,x16015,x16016,x16012))
% 52.62/52.43 [1602]~E(x16021,x16022)+E(f719(x16021,x16023,x16024,x16025,x16026),f719(x16022,x16023,x16024,x16025,x16026))
% 52.62/52.43 [1603]~E(x16031,x16032)+E(f719(x16033,x16031,x16034,x16035,x16036),f719(x16033,x16032,x16034,x16035,x16036))
% 52.62/52.43 [1604]~E(x16041,x16042)+E(f719(x16043,x16044,x16041,x16045,x16046),f719(x16043,x16044,x16042,x16045,x16046))
% 52.62/52.43 [1605]~E(x16051,x16052)+E(f719(x16053,x16054,x16055,x16051,x16056),f719(x16053,x16054,x16055,x16052,x16056))
% 52.62/52.43 [1606]~E(x16061,x16062)+E(f719(x16063,x16064,x16065,x16066,x16061),f719(x16063,x16064,x16065,x16066,x16062))
% 52.62/52.43 [1607]~E(x16071,x16072)+E(f415(x16071,x16073,x16074,x16075),f415(x16072,x16073,x16074,x16075))
% 52.62/52.43 [1608]~E(x16081,x16082)+E(f415(x16083,x16081,x16084,x16085),f415(x16083,x16082,x16084,x16085))
% 52.62/52.43 [1609]~E(x16091,x16092)+E(f415(x16093,x16094,x16091,x16095),f415(x16093,x16094,x16092,x16095))
% 52.62/52.43 [1610]~E(x16101,x16102)+E(f415(x16103,x16104,x16105,x16101),f415(x16103,x16104,x16105,x16102))
% 52.62/52.43 [1611]~E(x16111,x16112)+E(f754(x16111,x16113,x16114),f754(x16112,x16113,x16114))
% 52.62/52.43 [1612]~E(x16121,x16122)+E(f754(x16123,x16121,x16124),f754(x16123,x16122,x16124))
% 52.62/52.43 [1613]~E(x16131,x16132)+E(f754(x16133,x16134,x16131),f754(x16133,x16134,x16132))
% 52.62/52.43 [1614]~E(x16141,x16142)+E(f489(x16141,x16143,x16144,x16145,x16146),f489(x16142,x16143,x16144,x16145,x16146))
% 52.62/52.43 [1615]~E(x16151,x16152)+E(f489(x16153,x16151,x16154,x16155,x16156),f489(x16153,x16152,x16154,x16155,x16156))
% 52.62/52.43 [1616]~E(x16161,x16162)+E(f489(x16163,x16164,x16161,x16165,x16166),f489(x16163,x16164,x16162,x16165,x16166))
% 52.62/52.43 [1617]~E(x16171,x16172)+E(f489(x16173,x16174,x16175,x16171,x16176),f489(x16173,x16174,x16175,x16172,x16176))
% 52.62/52.43 [1618]~E(x16181,x16182)+E(f489(x16183,x16184,x16185,x16186,x16181),f489(x16183,x16184,x16185,x16186,x16182))
% 52.62/52.43 [1619]~E(x16191,x16192)+E(f472(x16191,x16193,x16194),f472(x16192,x16193,x16194))
% 52.62/52.43 [1620]~E(x16201,x16202)+E(f472(x16203,x16201,x16204),f472(x16203,x16202,x16204))
% 52.62/52.43 [1621]~E(x16211,x16212)+E(f472(x16213,x16214,x16211),f472(x16213,x16214,x16212))
% 52.62/52.43 [1622]~E(x16221,x16222)+E(f647(x16221,x16223,x16224,x16225,x16226),f647(x16222,x16223,x16224,x16225,x16226))
% 52.62/52.43 [1623]~E(x16231,x16232)+E(f647(x16233,x16231,x16234,x16235,x16236),f647(x16233,x16232,x16234,x16235,x16236))
% 52.62/52.43 [1624]~E(x16241,x16242)+E(f647(x16243,x16244,x16241,x16245,x16246),f647(x16243,x16244,x16242,x16245,x16246))
% 52.62/52.43 [1625]~E(x16251,x16252)+E(f647(x16253,x16254,x16255,x16251,x16256),f647(x16253,x16254,x16255,x16252,x16256))
% 52.62/52.43 [1626]~E(x16261,x16262)+E(f647(x16263,x16264,x16265,x16266,x16261),f647(x16263,x16264,x16265,x16266,x16262))
% 52.62/52.43 [1627]~E(x16271,x16272)+E(f743(x16271,x16273,x16274,x16275),f743(x16272,x16273,x16274,x16275))
% 52.62/52.43 [1628]~E(x16281,x16282)+E(f743(x16283,x16281,x16284,x16285),f743(x16283,x16282,x16284,x16285))
% 52.62/52.43 [1629]~E(x16291,x16292)+E(f743(x16293,x16294,x16291,x16295),f743(x16293,x16294,x16292,x16295))
% 52.62/52.43 [1630]~E(x16301,x16302)+E(f743(x16303,x16304,x16305,x16301),f743(x16303,x16304,x16305,x16302))
% 52.62/52.43 [1631]~E(x16311,x16312)+E(f801(x16311,x16313,x16314),f801(x16312,x16313,x16314))
% 52.62/52.43 [1632]~E(x16321,x16322)+E(f801(x16323,x16321,x16324),f801(x16323,x16322,x16324))
% 52.62/52.43 [1633]~E(x16331,x16332)+E(f801(x16333,x16334,x16331),f801(x16333,x16334,x16332))
% 52.62/52.43 [1634]~E(x16341,x16342)+E(f288(x16341,x16343,x16344),f288(x16342,x16343,x16344))
% 52.62/52.43 [1635]~E(x16351,x16352)+E(f288(x16353,x16351,x16354),f288(x16353,x16352,x16354))
% 52.62/52.43 [1636]~E(x16361,x16362)+E(f288(x16363,x16364,x16361),f288(x16363,x16364,x16362))
% 52.62/52.43 [1637]~E(x16371,x16372)+E(f531(x16371,x16373,x16374,x16375,x16376),f531(x16372,x16373,x16374,x16375,x16376))
% 52.62/52.43 [1638]~E(x16381,x16382)+E(f531(x16383,x16381,x16384,x16385,x16386),f531(x16383,x16382,x16384,x16385,x16386))
% 52.62/52.43 [1639]~E(x16391,x16392)+E(f531(x16393,x16394,x16391,x16395,x16396),f531(x16393,x16394,x16392,x16395,x16396))
% 52.62/52.43 [1640]~E(x16401,x16402)+E(f531(x16403,x16404,x16405,x16401,x16406),f531(x16403,x16404,x16405,x16402,x16406))
% 52.62/52.43 [1641]~E(x16411,x16412)+E(f531(x16413,x16414,x16415,x16416,x16411),f531(x16413,x16414,x16415,x16416,x16412))
% 52.62/52.43 [1642]~E(x16421,x16422)+E(f188(x16421,x16423),f188(x16422,x16423))
% 52.62/52.43 [1643]~E(x16431,x16432)+E(f188(x16433,x16431),f188(x16433,x16432))
% 52.62/52.43 [1644]~E(x16441,x16442)+E(f551(x16441,x16443,x16444,x16445,x16446),f551(x16442,x16443,x16444,x16445,x16446))
% 52.62/52.43 [1645]~E(x16451,x16452)+E(f551(x16453,x16451,x16454,x16455,x16456),f551(x16453,x16452,x16454,x16455,x16456))
% 52.62/52.43 [1646]~E(x16461,x16462)+E(f551(x16463,x16464,x16461,x16465,x16466),f551(x16463,x16464,x16462,x16465,x16466))
% 52.62/52.43 [1647]~E(x16471,x16472)+E(f551(x16473,x16474,x16475,x16471,x16476),f551(x16473,x16474,x16475,x16472,x16476))
% 52.62/52.43 [1648]~E(x16481,x16482)+E(f551(x16483,x16484,x16485,x16486,x16481),f551(x16483,x16484,x16485,x16486,x16482))
% 52.62/52.43 [1649]~E(x16491,x16492)+E(f451(x16491,x16493),f451(x16492,x16493))
% 52.62/52.43 [1650]~E(x16501,x16502)+E(f451(x16503,x16501),f451(x16503,x16502))
% 52.62/52.43 [1651]~E(x16511,x16512)+E(f762(x16511,x16513,x16514),f762(x16512,x16513,x16514))
% 52.62/52.43 [1652]~E(x16521,x16522)+E(f762(x16523,x16521,x16524),f762(x16523,x16522,x16524))
% 52.62/52.43 [1653]~E(x16531,x16532)+E(f762(x16533,x16534,x16531),f762(x16533,x16534,x16532))
% 52.62/52.43 [1654]~E(x16541,x16542)+E(f475(x16541,x16543,x16544),f475(x16542,x16543,x16544))
% 52.62/52.43 [1655]~E(x16551,x16552)+E(f475(x16553,x16551,x16554),f475(x16553,x16552,x16554))
% 52.62/52.43 [1656]~E(x16561,x16562)+E(f475(x16563,x16564,x16561),f475(x16563,x16564,x16562))
% 52.62/52.43 [1657]~E(x16571,x16572)+E(f573(x16571,x16573,x16574,x16575,x16576,x16577,x16578,x16579),f573(x16572,x16573,x16574,x16575,x16576,x16577,x16578,x16579))
% 52.62/52.43 [1658]~E(x16581,x16582)+E(f573(x16583,x16581,x16584,x16585,x16586,x16587,x16588,x16589),f573(x16583,x16582,x16584,x16585,x16586,x16587,x16588,x16589))
% 52.62/52.43 [1659]~E(x16591,x16592)+E(f573(x16593,x16594,x16591,x16595,x16596,x16597,x16598,x16599),f573(x16593,x16594,x16592,x16595,x16596,x16597,x16598,x16599))
% 52.62/52.43 [1660]~E(x16601,x16602)+E(f573(x16603,x16604,x16605,x16601,x16606,x16607,x16608,x16609),f573(x16603,x16604,x16605,x16602,x16606,x16607,x16608,x16609))
% 52.62/52.43 [1661]~E(x16611,x16612)+E(f573(x16613,x16614,x16615,x16616,x16611,x16617,x16618,x16619),f573(x16613,x16614,x16615,x16616,x16612,x16617,x16618,x16619))
% 52.62/52.43 [1662]~E(x16621,x16622)+E(f573(x16623,x16624,x16625,x16626,x16627,x16621,x16628,x16629),f573(x16623,x16624,x16625,x16626,x16627,x16622,x16628,x16629))
% 52.62/52.43 [1663]~E(x16631,x16632)+E(f573(x16633,x16634,x16635,x16636,x16637,x16638,x16631,x16639),f573(x16633,x16634,x16635,x16636,x16637,x16638,x16632,x16639))
% 52.62/52.43 [1664]~E(x16641,x16642)+E(f573(x16643,x16644,x16645,x16646,x16647,x16648,x16649,x16641),f573(x16643,x16644,x16645,x16646,x16647,x16648,x16649,x16642))
% 52.62/52.43 [1665]~E(x16651,x16652)+E(f356(x16651,x16653,x16654,x16655),f356(x16652,x16653,x16654,x16655))
% 52.62/52.43 [1666]~E(x16661,x16662)+E(f356(x16663,x16661,x16664,x16665),f356(x16663,x16662,x16664,x16665))
% 52.62/52.43 [1667]~E(x16671,x16672)+E(f356(x16673,x16674,x16671,x16675),f356(x16673,x16674,x16672,x16675))
% 52.62/52.43 [1668]~E(x16681,x16682)+E(f356(x16683,x16684,x16685,x16681),f356(x16683,x16684,x16685,x16682))
% 52.62/52.43 [1669]~E(x16691,x16692)+E(f773(x16691,x16693,x16694),f773(x16692,x16693,x16694))
% 52.62/52.43 [1670]~E(x16701,x16702)+E(f773(x16703,x16701,x16704),f773(x16703,x16702,x16704))
% 52.62/52.43 [1671]~E(x16711,x16712)+E(f773(x16713,x16714,x16711),f773(x16713,x16714,x16712))
% 52.62/52.43 [1672]~E(x16721,x16722)+E(f464(x16721,x16723,x16724),f464(x16722,x16723,x16724))
% 52.62/52.43 [1673]~E(x16731,x16732)+E(f464(x16733,x16731,x16734),f464(x16733,x16732,x16734))
% 52.62/52.43 [1674]~E(x16741,x16742)+E(f464(x16743,x16744,x16741),f464(x16743,x16744,x16742))
% 52.62/52.43 [1675]~E(x16751,x16752)+E(f49(x16751),f49(x16752))
% 52.62/52.43 [1676]~E(x16761,x16762)+E(f624(x16761,x16763,x16764,x16765),f624(x16762,x16763,x16764,x16765))
% 52.62/52.43 [1677]~E(x16771,x16772)+E(f624(x16773,x16771,x16774,x16775),f624(x16773,x16772,x16774,x16775))
% 52.62/52.43 [1678]~E(x16781,x16782)+E(f624(x16783,x16784,x16781,x16785),f624(x16783,x16784,x16782,x16785))
% 52.62/52.43 [1679]~E(x16791,x16792)+E(f624(x16793,x16794,x16795,x16791),f624(x16793,x16794,x16795,x16792))
% 52.62/52.43 [1680]~E(x16801,x16802)+E(f519(x16801,x16803,x16804,x16805),f519(x16802,x16803,x16804,x16805))
% 52.62/52.43 [1681]~E(x16811,x16812)+E(f519(x16813,x16811,x16814,x16815),f519(x16813,x16812,x16814,x16815))
% 52.62/52.43 [1682]~E(x16821,x16822)+E(f519(x16823,x16824,x16821,x16825),f519(x16823,x16824,x16822,x16825))
% 52.62/52.43 [1683]~E(x16831,x16832)+E(f519(x16833,x16834,x16835,x16831),f519(x16833,x16834,x16835,x16832))
% 52.62/52.43 [1684]~E(x16841,x16842)+E(f249(x16841,x16843,x16844,x16845),f249(x16842,x16843,x16844,x16845))
% 52.62/52.43 [1685]~E(x16851,x16852)+E(f249(x16853,x16851,x16854,x16855),f249(x16853,x16852,x16854,x16855))
% 52.62/52.43 [1686]~E(x16861,x16862)+E(f249(x16863,x16864,x16861,x16865),f249(x16863,x16864,x16862,x16865))
% 52.62/52.43 [1687]~E(x16871,x16872)+E(f249(x16873,x16874,x16875,x16871),f249(x16873,x16874,x16875,x16872))
% 52.62/52.43 [1688]~E(x16881,x16882)+E(f438(x16881,x16883,x16884,x16885,x16886),f438(x16882,x16883,x16884,x16885,x16886))
% 52.62/52.43 [1689]~E(x16891,x16892)+E(f438(x16893,x16891,x16894,x16895,x16896),f438(x16893,x16892,x16894,x16895,x16896))
% 52.62/52.43 [1690]~E(x16901,x16902)+E(f438(x16903,x16904,x16901,x16905,x16906),f438(x16903,x16904,x16902,x16905,x16906))
% 52.62/52.43 [1691]~E(x16911,x16912)+E(f438(x16913,x16914,x16915,x16911,x16916),f438(x16913,x16914,x16915,x16912,x16916))
% 52.62/52.43 [1692]~E(x16921,x16922)+E(f438(x16923,x16924,x16925,x16926,x16921),f438(x16923,x16924,x16925,x16926,x16922))
% 52.62/52.43 [1693]~E(x16931,x16932)+E(f605(x16931,x16933),f605(x16932,x16933))
% 52.62/52.43 [1694]~E(x16941,x16942)+E(f605(x16943,x16941),f605(x16943,x16942))
% 52.62/52.43 [1695]~E(x16951,x16952)+E(f460(x16951,x16953,x16954,x16955),f460(x16952,x16953,x16954,x16955))
% 52.62/52.43 [1696]~E(x16961,x16962)+E(f460(x16963,x16961,x16964,x16965),f460(x16963,x16962,x16964,x16965))
% 52.62/52.43 [1697]~E(x16971,x16972)+E(f460(x16973,x16974,x16971,x16975),f460(x16973,x16974,x16972,x16975))
% 52.62/52.43 [1698]~E(x16981,x16982)+E(f460(x16983,x16984,x16985,x16981),f460(x16983,x16984,x16985,x16982))
% 52.62/52.43 [1699]~E(x16991,x16992)+E(f611(x16991,x16993,x16994),f611(x16992,x16993,x16994))
% 52.62/52.43 [1700]~E(x17001,x17002)+E(f611(x17003,x17001,x17004),f611(x17003,x17002,x17004))
% 52.62/52.43 [1701]~E(x17011,x17012)+E(f611(x17013,x17014,x17011),f611(x17013,x17014,x17012))
% 52.62/52.43 [1702]~E(x17021,x17022)+E(f619(x17021,x17023),f619(x17022,x17023))
% 52.62/52.43 [1703]~E(x17031,x17032)+E(f619(x17033,x17031),f619(x17033,x17032))
% 52.62/52.43 [1704]~E(x17041,x17042)+E(f730(x17041,x17043,x17044),f730(x17042,x17043,x17044))
% 52.62/52.43 [1705]~E(x17051,x17052)+E(f730(x17053,x17051,x17054),f730(x17053,x17052,x17054))
% 52.62/52.43 [1706]~E(x17061,x17062)+E(f730(x17063,x17064,x17061),f730(x17063,x17064,x17062))
% 52.62/52.43 [1707]~E(x17071,x17072)+E(f682(x17071,x17073),f682(x17072,x17073))
% 52.62/52.43 [1708]~E(x17081,x17082)+E(f682(x17083,x17081),f682(x17083,x17082))
% 52.62/52.43 [1709]~E(x17091,x17092)+E(f635(x17091,x17093,x17094),f635(x17092,x17093,x17094))
% 52.62/52.43 [1710]~E(x17101,x17102)+E(f635(x17103,x17101,x17104),f635(x17103,x17102,x17104))
% 52.62/52.43 [1711]~E(x17111,x17112)+E(f635(x17113,x17114,x17111),f635(x17113,x17114,x17112))
% 52.62/52.43 [1712]~E(x17121,x17122)+E(f479(x17121,x17123,x17124,x17125,x17126),f479(x17122,x17123,x17124,x17125,x17126))
% 52.62/52.43 [1713]~E(x17131,x17132)+E(f479(x17133,x17131,x17134,x17135,x17136),f479(x17133,x17132,x17134,x17135,x17136))
% 52.62/52.43 [1714]~E(x17141,x17142)+E(f479(x17143,x17144,x17141,x17145,x17146),f479(x17143,x17144,x17142,x17145,x17146))
% 52.62/52.43 [1715]~E(x17151,x17152)+E(f479(x17153,x17154,x17155,x17151,x17156),f479(x17153,x17154,x17155,x17152,x17156))
% 52.62/52.43 [1716]~E(x17161,x17162)+E(f479(x17163,x17164,x17165,x17166,x17161),f479(x17163,x17164,x17165,x17166,x17162))
% 52.62/52.43 [1717]~E(x17171,x17172)+E(f618(x17171,x17173),f618(x17172,x17173))
% 52.62/52.43 [1718]~E(x17181,x17182)+E(f618(x17183,x17181),f618(x17183,x17182))
% 52.62/52.43 [1719]~E(x17191,x17192)+E(f725(x17191,x17193,x17194),f725(x17192,x17193,x17194))
% 52.62/52.43 [1720]~E(x17201,x17202)+E(f725(x17203,x17201,x17204),f725(x17203,x17202,x17204))
% 52.62/52.43 [1721]~E(x17211,x17212)+E(f725(x17213,x17214,x17211),f725(x17213,x17214,x17212))
% 52.62/52.43 [1722]~E(x17221,x17222)+E(f774(x17221,x17223,x17224),f774(x17222,x17223,x17224))
% 52.62/52.43 [1723]~E(x17231,x17232)+E(f774(x17233,x17231,x17234),f774(x17233,x17232,x17234))
% 52.62/52.43 [1724]~E(x17241,x17242)+E(f774(x17243,x17244,x17241),f774(x17243,x17244,x17242))
% 52.62/52.43 [1725]~E(x17251,x17252)+E(f433(x17251,x17253,x17254,x17255),f433(x17252,x17253,x17254,x17255))
% 52.62/52.43 [1726]~E(x17261,x17262)+E(f433(x17263,x17261,x17264,x17265),f433(x17263,x17262,x17264,x17265))
% 52.62/52.43 [1727]~E(x17271,x17272)+E(f433(x17273,x17274,x17271,x17275),f433(x17273,x17274,x17272,x17275))
% 52.62/52.43 [1728]~E(x17281,x17282)+E(f433(x17283,x17284,x17285,x17281),f433(x17283,x17284,x17285,x17282))
% 52.62/52.43 [1729]~E(x17291,x17292)+E(f384(x17291,x17293,x17294,x17295,x17296),f384(x17292,x17293,x17294,x17295,x17296))
% 52.62/52.43 [1730]~E(x17301,x17302)+E(f384(x17303,x17301,x17304,x17305,x17306),f384(x17303,x17302,x17304,x17305,x17306))
% 52.62/52.43 [1731]~E(x17311,x17312)+E(f384(x17313,x17314,x17311,x17315,x17316),f384(x17313,x17314,x17312,x17315,x17316))
% 52.62/52.43 [1732]~E(x17321,x17322)+E(f384(x17323,x17324,x17325,x17321,x17326),f384(x17323,x17324,x17325,x17322,x17326))
% 52.62/52.43 [1733]~E(x17331,x17332)+E(f384(x17333,x17334,x17335,x17336,x17331),f384(x17333,x17334,x17335,x17336,x17332))
% 52.62/52.43 [1734]~E(x17341,x17342)+E(f541(x17341,x17343,x17344,x17345,x17346,x17347),f541(x17342,x17343,x17344,x17345,x17346,x17347))
% 52.62/52.43 [1735]~E(x17351,x17352)+E(f541(x17353,x17351,x17354,x17355,x17356,x17357),f541(x17353,x17352,x17354,x17355,x17356,x17357))
% 52.62/52.43 [1736]~E(x17361,x17362)+E(f541(x17363,x17364,x17361,x17365,x17366,x17367),f541(x17363,x17364,x17362,x17365,x17366,x17367))
% 52.62/52.43 [1737]~E(x17371,x17372)+E(f541(x17373,x17374,x17375,x17371,x17376,x17377),f541(x17373,x17374,x17375,x17372,x17376,x17377))
% 52.62/52.43 [1738]~E(x17381,x17382)+E(f541(x17383,x17384,x17385,x17386,x17381,x17387),f541(x17383,x17384,x17385,x17386,x17382,x17387))
% 52.62/52.43 [1739]~E(x17391,x17392)+E(f541(x17393,x17394,x17395,x17396,x17397,x17391),f541(x17393,x17394,x17395,x17396,x17397,x17392))
% 52.62/52.43 [1740]~E(x17401,x17402)+E(f805(x17401,x17403,x17404),f805(x17402,x17403,x17404))
% 52.62/52.43 [1741]~E(x17411,x17412)+E(f805(x17413,x17411,x17414),f805(x17413,x17412,x17414))
% 52.62/52.43 [1742]~E(x17421,x17422)+E(f805(x17423,x17424,x17421),f805(x17423,x17424,x17422))
% 52.62/52.43 [1743]~E(x17431,x17432)+E(f622(x17431,x17433,x17434),f622(x17432,x17433,x17434))
% 52.62/52.43 [1744]~E(x17441,x17442)+E(f622(x17443,x17441,x17444),f622(x17443,x17442,x17444))
% 52.62/52.43 [1745]~E(x17451,x17452)+E(f622(x17453,x17454,x17451),f622(x17453,x17454,x17452))
% 52.62/52.43 [1746]~E(x17461,x17462)+E(f213(x17461,x17463),f213(x17462,x17463))
% 52.62/52.43 [1747]~E(x17471,x17472)+E(f213(x17473,x17471),f213(x17473,x17472))
% 52.62/52.43 [1748]~E(x17481,x17482)+E(f543(x17481,x17483,x17484,x17485,x17486,x17487),f543(x17482,x17483,x17484,x17485,x17486,x17487))
% 52.62/52.43 [1749]~E(x17491,x17492)+E(f543(x17493,x17491,x17494,x17495,x17496,x17497),f543(x17493,x17492,x17494,x17495,x17496,x17497))
% 52.62/52.43 [1750]~E(x17501,x17502)+E(f543(x17503,x17504,x17501,x17505,x17506,x17507),f543(x17503,x17504,x17502,x17505,x17506,x17507))
% 52.62/52.43 [1751]~E(x17511,x17512)+E(f543(x17513,x17514,x17515,x17511,x17516,x17517),f543(x17513,x17514,x17515,x17512,x17516,x17517))
% 52.62/52.43 [1752]~E(x17521,x17522)+E(f543(x17523,x17524,x17525,x17526,x17521,x17527),f543(x17523,x17524,x17525,x17526,x17522,x17527))
% 52.62/52.43 [1753]~E(x17531,x17532)+E(f543(x17533,x17534,x17535,x17536,x17537,x17531),f543(x17533,x17534,x17535,x17536,x17537,x17532))
% 52.62/52.43 [1754]~E(x17541,x17542)+E(f150(x17541,x17543),f150(x17542,x17543))
% 52.62/52.43 [1755]~E(x17551,x17552)+E(f150(x17553,x17551),f150(x17553,x17552))
% 52.62/52.43 [1756]~E(x17561,x17562)+E(f379(x17561,x17563),f379(x17562,x17563))
% 52.62/52.43 [1757]~E(x17571,x17572)+E(f379(x17573,x17571),f379(x17573,x17572))
% 52.62/52.43 [1758]~E(x17581,x17582)+E(f272(x17581,x17583,x17584,x17585),f272(x17582,x17583,x17584,x17585))
% 52.62/52.43 [1759]~E(x17591,x17592)+E(f272(x17593,x17591,x17594,x17595),f272(x17593,x17592,x17594,x17595))
% 52.62/52.43 [1760]~E(x17601,x17602)+E(f272(x17603,x17604,x17601,x17605),f272(x17603,x17604,x17602,x17605))
% 52.62/52.43 [1761]~E(x17611,x17612)+E(f272(x17613,x17614,x17615,x17611),f272(x17613,x17614,x17615,x17612))
% 52.62/52.43 [1762]~E(x17621,x17622)+E(f349(x17621,x17623,x17624,x17625),f349(x17622,x17623,x17624,x17625))
% 52.62/52.43 [1763]~E(x17631,x17632)+E(f349(x17633,x17631,x17634,x17635),f349(x17633,x17632,x17634,x17635))
% 52.62/52.43 [1764]~E(x17641,x17642)+E(f349(x17643,x17644,x17641,x17645),f349(x17643,x17644,x17642,x17645))
% 52.62/52.43 [1765]~E(x17651,x17652)+E(f349(x17653,x17654,x17655,x17651),f349(x17653,x17654,x17655,x17652))
% 52.62/52.43 [1766]~E(x17661,x17662)+E(f355(x17661,x17663),f355(x17662,x17663))
% 52.62/52.43 [1767]~E(x17671,x17672)+E(f355(x17673,x17671),f355(x17673,x17672))
% 52.62/52.43 [1768]~E(x17681,x17682)+E(f409(x17681,x17683,x17684,x17685,x17686,x17687,x17688),f409(x17682,x17683,x17684,x17685,x17686,x17687,x17688))
% 52.62/52.43 [1769]~E(x17691,x17692)+E(f409(x17693,x17691,x17694,x17695,x17696,x17697,x17698),f409(x17693,x17692,x17694,x17695,x17696,x17697,x17698))
% 52.62/52.43 [1770]~E(x17701,x17702)+E(f409(x17703,x17704,x17701,x17705,x17706,x17707,x17708),f409(x17703,x17704,x17702,x17705,x17706,x17707,x17708))
% 52.62/52.43 [1771]~E(x17711,x17712)+E(f409(x17713,x17714,x17715,x17711,x17716,x17717,x17718),f409(x17713,x17714,x17715,x17712,x17716,x17717,x17718))
% 52.62/52.43 [1772]~E(x17721,x17722)+E(f409(x17723,x17724,x17725,x17726,x17721,x17727,x17728),f409(x17723,x17724,x17725,x17726,x17722,x17727,x17728))
% 52.62/52.43 [1773]~E(x17731,x17732)+E(f409(x17733,x17734,x17735,x17736,x17737,x17731,x17738),f409(x17733,x17734,x17735,x17736,x17737,x17732,x17738))
% 52.62/52.43 [1774]~E(x17741,x17742)+E(f409(x17743,x17744,x17745,x17746,x17747,x17748,x17741),f409(x17743,x17744,x17745,x17746,x17747,x17748,x17742))
% 52.62/52.43 [1775]~E(x17751,x17752)+E(f24(x17751,x17753),f24(x17752,x17753))
% 52.62/52.43 [1776]~E(x17761,x17762)+E(f24(x17763,x17761),f24(x17763,x17762))
% 52.62/52.43 [1777]~E(x17771,x17772)+E(f434(x17771,x17773,x17774,x17775),f434(x17772,x17773,x17774,x17775))
% 52.62/52.43 [1778]~E(x17781,x17782)+E(f434(x17783,x17781,x17784,x17785),f434(x17783,x17782,x17784,x17785))
% 52.62/52.43 [1779]~E(x17791,x17792)+E(f434(x17793,x17794,x17791,x17795),f434(x17793,x17794,x17792,x17795))
% 52.62/52.43 [1780]~E(x17801,x17802)+E(f434(x17803,x17804,x17805,x17801),f434(x17803,x17804,x17805,x17802))
% 52.62/52.43 [1781]~E(x17811,x17812)+E(f782(x17811,x17813,x17814,x17815),f782(x17812,x17813,x17814,x17815))
% 52.62/52.43 [1782]~E(x17821,x17822)+E(f782(x17823,x17821,x17824,x17825),f782(x17823,x17822,x17824,x17825))
% 52.62/52.43 [1783]~E(x17831,x17832)+E(f782(x17833,x17834,x17831,x17835),f782(x17833,x17834,x17832,x17835))
% 52.62/52.43 [1784]~E(x17841,x17842)+E(f782(x17843,x17844,x17845,x17841),f782(x17843,x17844,x17845,x17842))
% 52.62/52.43 [1785]~E(x17851,x17852)+E(f567(x17851,x17853,x17854),f567(x17852,x17853,x17854))
% 52.62/52.43 [1786]~E(x17861,x17862)+E(f567(x17863,x17861,x17864),f567(x17863,x17862,x17864))
% 52.62/52.43 [1787]~E(x17871,x17872)+E(f567(x17873,x17874,x17871),f567(x17873,x17874,x17872))
% 52.62/52.43 [1788]~E(x17881,x17882)+E(f670(x17881,x17883,x17884),f670(x17882,x17883,x17884))
% 52.62/52.43 [1789]~E(x17891,x17892)+E(f670(x17893,x17891,x17894),f670(x17893,x17892,x17894))
% 52.62/52.43 [1790]~E(x17901,x17902)+E(f670(x17903,x17904,x17901),f670(x17903,x17904,x17902))
% 52.62/52.43 [1791]~E(x17911,x17912)+E(f672(x17911,x17913,x17914,x17915),f672(x17912,x17913,x17914,x17915))
% 52.62/52.43 [1792]~E(x17921,x17922)+E(f672(x17923,x17921,x17924,x17925),f672(x17923,x17922,x17924,x17925))
% 52.62/52.43 [1793]~E(x17931,x17932)+E(f672(x17933,x17934,x17931,x17935),f672(x17933,x17934,x17932,x17935))
% 52.62/52.43 [1794]~E(x17941,x17942)+E(f672(x17943,x17944,x17945,x17941),f672(x17943,x17944,x17945,x17942))
% 52.62/52.43 [1795]~E(x17951,x17952)+E(f572(x17951,x17953,x17954),f572(x17952,x17953,x17954))
% 52.62/52.43 [1796]~E(x17961,x17962)+E(f572(x17963,x17961,x17964),f572(x17963,x17962,x17964))
% 52.62/52.43 [1797]~E(x17971,x17972)+E(f572(x17973,x17974,x17971),f572(x17973,x17974,x17972))
% 52.62/52.43 [1798]~E(x17981,x17982)+E(f696(x17981,x17983,x17984),f696(x17982,x17983,x17984))
% 52.62/52.43 [1799]~E(x17991,x17992)+E(f696(x17993,x17991,x17994),f696(x17993,x17992,x17994))
% 52.62/52.43 [1800]~E(x18001,x18002)+E(f696(x18003,x18004,x18001),f696(x18003,x18004,x18002))
% 52.62/52.43 [1801]~E(x18011,x18012)+E(f467(x18011,x18013,x18014),f467(x18012,x18013,x18014))
% 52.62/52.43 [1802]~E(x18021,x18022)+E(f467(x18023,x18021,x18024),f467(x18023,x18022,x18024))
% 52.62/52.43 [1803]~E(x18031,x18032)+E(f467(x18033,x18034,x18031),f467(x18033,x18034,x18032))
% 52.62/52.43 [1804]~E(x18041,x18042)+E(f90(x18041),f90(x18042))
% 52.62/52.43 [1805]~E(x18051,x18052)+E(f600(x18051),f600(x18052))
% 52.62/52.43 [1806]~E(x18061,x18062)+E(f362(x18061,x18063,x18064,x18065,x18066),f362(x18062,x18063,x18064,x18065,x18066))
% 52.62/52.43 [1807]~E(x18071,x18072)+E(f362(x18073,x18071,x18074,x18075,x18076),f362(x18073,x18072,x18074,x18075,x18076))
% 52.62/52.43 [1808]~E(x18081,x18082)+E(f362(x18083,x18084,x18081,x18085,x18086),f362(x18083,x18084,x18082,x18085,x18086))
% 52.62/52.43 [1809]~E(x18091,x18092)+E(f362(x18093,x18094,x18095,x18091,x18096),f362(x18093,x18094,x18095,x18092,x18096))
% 52.62/52.43 [1810]~E(x18101,x18102)+E(f362(x18103,x18104,x18105,x18106,x18101),f362(x18103,x18104,x18105,x18106,x18102))
% 52.62/52.43 [1811]~E(x18111,x18112)+E(f337(x18111),f337(x18112))
% 52.62/52.43 [1812]~E(x18121,x18122)+E(f804(x18121,x18123,x18124),f804(x18122,x18123,x18124))
% 52.62/52.43 [1813]~E(x18131,x18132)+E(f804(x18133,x18131,x18134),f804(x18133,x18132,x18134))
% 52.62/52.43 [1814]~E(x18141,x18142)+E(f804(x18143,x18144,x18141),f804(x18143,x18144,x18142))
% 52.62/52.43 [1815]~E(x18151,x18152)+E(f419(x18151,x18153,x18154),f419(x18152,x18153,x18154))
% 52.62/52.43 [1816]~E(x18161,x18162)+E(f419(x18163,x18161,x18164),f419(x18163,x18162,x18164))
% 52.62/52.43 [1817]~E(x18171,x18172)+E(f419(x18173,x18174,x18171),f419(x18173,x18174,x18172))
% 52.62/52.43 [1818]~E(x18181,x18182)+E(f581(x18181,x18183),f581(x18182,x18183))
% 52.62/52.43 [1819]~E(x18191,x18192)+E(f581(x18193,x18191),f581(x18193,x18192))
% 52.62/52.43 [1820]~E(x18201,x18202)+E(f588(x18201,x18203),f588(x18202,x18203))
% 52.62/52.43 [1821]~E(x18211,x18212)+E(f588(x18213,x18211),f588(x18213,x18212))
% 52.62/52.43 [1822]~E(x18221,x18222)+E(f663(x18221,x18223,x18224,x18225,x18226,x18227,x18228),f663(x18222,x18223,x18224,x18225,x18226,x18227,x18228))
% 52.62/52.43 [1823]~E(x18231,x18232)+E(f663(x18233,x18231,x18234,x18235,x18236,x18237,x18238),f663(x18233,x18232,x18234,x18235,x18236,x18237,x18238))
% 52.62/52.43 [1824]~E(x18241,x18242)+E(f663(x18243,x18244,x18241,x18245,x18246,x18247,x18248),f663(x18243,x18244,x18242,x18245,x18246,x18247,x18248))
% 52.62/52.43 [1825]~E(x18251,x18252)+E(f663(x18253,x18254,x18255,x18251,x18256,x18257,x18258),f663(x18253,x18254,x18255,x18252,x18256,x18257,x18258))
% 52.62/52.43 [1826]~E(x18261,x18262)+E(f663(x18263,x18264,x18265,x18266,x18261,x18267,x18268),f663(x18263,x18264,x18265,x18266,x18262,x18267,x18268))
% 52.62/52.43 [1827]~E(x18271,x18272)+E(f663(x18273,x18274,x18275,x18276,x18277,x18271,x18278),f663(x18273,x18274,x18275,x18276,x18277,x18272,x18278))
% 52.62/52.43 [1828]~E(x18281,x18282)+E(f663(x18283,x18284,x18285,x18286,x18287,x18288,x18281),f663(x18283,x18284,x18285,x18286,x18287,x18288,x18282))
% 52.62/52.43 [1829]~E(x18291,x18292)+E(f266(x18291,x18293),f266(x18292,x18293))
% 52.62/52.43 [1830]~E(x18301,x18302)+E(f266(x18303,x18301),f266(x18303,x18302))
% 52.62/52.43 [1831]~E(x18311,x18312)+E(f697(x18311,x18313,x18314),f697(x18312,x18313,x18314))
% 52.62/52.43 [1832]~E(x18321,x18322)+E(f697(x18323,x18321,x18324),f697(x18323,x18322,x18324))
% 52.62/52.43 [1833]~E(x18331,x18332)+E(f697(x18333,x18334,x18331),f697(x18333,x18334,x18332))
% 52.62/52.43 [1834]~E(x18341,x18342)+E(f481(x18341,x18343,x18344,x18345,x18346),f481(x18342,x18343,x18344,x18345,x18346))
% 52.62/52.43 [1835]~E(x18351,x18352)+E(f481(x18353,x18351,x18354,x18355,x18356),f481(x18353,x18352,x18354,x18355,x18356))
% 52.62/52.43 [1836]~E(x18361,x18362)+E(f481(x18363,x18364,x18361,x18365,x18366),f481(x18363,x18364,x18362,x18365,x18366))
% 52.62/52.43 [1837]~E(x18371,x18372)+E(f481(x18373,x18374,x18375,x18371,x18376),f481(x18373,x18374,x18375,x18372,x18376))
% 52.62/52.43 [1838]~E(x18381,x18382)+E(f481(x18383,x18384,x18385,x18386,x18381),f481(x18383,x18384,x18385,x18386,x18382))
% 52.62/52.43 [1839]~E(x18391,x18392)+E(f447(x18391,x18393),f447(x18392,x18393))
% 52.62/52.43 [1840]~E(x18401,x18402)+E(f447(x18403,x18401),f447(x18403,x18402))
% 52.62/52.43 [1841]~E(x18411,x18412)+E(f336(x18411,x18413,x18414,x18415),f336(x18412,x18413,x18414,x18415))
% 52.62/52.43 [1842]~E(x18421,x18422)+E(f336(x18423,x18421,x18424,x18425),f336(x18423,x18422,x18424,x18425))
% 52.62/52.43 [1843]~E(x18431,x18432)+E(f336(x18433,x18434,x18431,x18435),f336(x18433,x18434,x18432,x18435))
% 52.62/52.43 [1844]~E(x18441,x18442)+E(f336(x18443,x18444,x18445,x18441),f336(x18443,x18444,x18445,x18442))
% 52.62/52.43 [1845]~E(x18451,x18452)+E(f206(x18451,x18453,x18454,x18455,x18456,x18457,x18458),f206(x18452,x18453,x18454,x18455,x18456,x18457,x18458))
% 52.62/52.43 [1846]~E(x18461,x18462)+E(f206(x18463,x18461,x18464,x18465,x18466,x18467,x18468),f206(x18463,x18462,x18464,x18465,x18466,x18467,x18468))
% 52.62/52.43 [1847]~E(x18471,x18472)+E(f206(x18473,x18474,x18471,x18475,x18476,x18477,x18478),f206(x18473,x18474,x18472,x18475,x18476,x18477,x18478))
% 52.62/52.43 [1848]~E(x18481,x18482)+E(f206(x18483,x18484,x18485,x18481,x18486,x18487,x18488),f206(x18483,x18484,x18485,x18482,x18486,x18487,x18488))
% 52.62/52.43 [1849]~E(x18491,x18492)+E(f206(x18493,x18494,x18495,x18496,x18491,x18497,x18498),f206(x18493,x18494,x18495,x18496,x18492,x18497,x18498))
% 52.62/52.43 [1850]~E(x18501,x18502)+E(f206(x18503,x18504,x18505,x18506,x18507,x18501,x18508),f206(x18503,x18504,x18505,x18506,x18507,x18502,x18508))
% 52.62/52.43 [1851]~E(x18511,x18512)+E(f206(x18513,x18514,x18515,x18516,x18517,x18518,x18511),f206(x18513,x18514,x18515,x18516,x18517,x18518,x18512))
% 52.62/52.43 [1852]~E(x18521,x18522)+E(f465(x18521,x18523,x18524,x18525),f465(x18522,x18523,x18524,x18525))
% 52.62/52.43 [1853]~E(x18531,x18532)+E(f465(x18533,x18531,x18534,x18535),f465(x18533,x18532,x18534,x18535))
% 52.62/52.43 [1854]~E(x18541,x18542)+E(f465(x18543,x18544,x18541,x18545),f465(x18543,x18544,x18542,x18545))
% 52.62/52.43 [1855]~E(x18551,x18552)+E(f465(x18553,x18554,x18555,x18551),f465(x18553,x18554,x18555,x18552))
% 52.62/52.43 [1856]~E(x18561,x18562)+E(f391(x18561,x18563,x18564,x18565,x18566),f391(x18562,x18563,x18564,x18565,x18566))
% 52.62/52.43 [1857]~E(x18571,x18572)+E(f391(x18573,x18571,x18574,x18575,x18576),f391(x18573,x18572,x18574,x18575,x18576))
% 52.62/52.43 [1858]~E(x18581,x18582)+E(f391(x18583,x18584,x18581,x18585,x18586),f391(x18583,x18584,x18582,x18585,x18586))
% 52.62/52.43 [1859]~E(x18591,x18592)+E(f391(x18593,x18594,x18595,x18591,x18596),f391(x18593,x18594,x18595,x18592,x18596))
% 52.62/52.43 [1860]~E(x18601,x18602)+E(f391(x18603,x18604,x18605,x18606,x18601),f391(x18603,x18604,x18605,x18606,x18602))
% 52.62/52.43 [1861]~E(x18611,x18612)+E(f459(x18611,x18613,x18614,x18615),f459(x18612,x18613,x18614,x18615))
% 52.62/52.43 [1862]~E(x18621,x18622)+E(f459(x18623,x18621,x18624,x18625),f459(x18623,x18622,x18624,x18625))
% 52.62/52.43 [1863]~E(x18631,x18632)+E(f459(x18633,x18634,x18631,x18635),f459(x18633,x18634,x18632,x18635))
% 52.62/52.43 [1864]~E(x18641,x18642)+E(f459(x18643,x18644,x18645,x18641),f459(x18643,x18644,x18645,x18642))
% 52.62/52.43 [1865]~E(x18651,x18652)+E(f374(x18651,x18653,x18654,x18655,x18656,x18657,x18658,x18659),f374(x18652,x18653,x18654,x18655,x18656,x18657,x18658,x18659))
% 52.62/52.43 [1866]~E(x18661,x18662)+E(f374(x18663,x18661,x18664,x18665,x18666,x18667,x18668,x18669),f374(x18663,x18662,x18664,x18665,x18666,x18667,x18668,x18669))
% 52.62/52.43 [1867]~E(x18671,x18672)+E(f374(x18673,x18674,x18671,x18675,x18676,x18677,x18678,x18679),f374(x18673,x18674,x18672,x18675,x18676,x18677,x18678,x18679))
% 52.62/52.43 [1868]~E(x18681,x18682)+E(f374(x18683,x18684,x18685,x18681,x18686,x18687,x18688,x18689),f374(x18683,x18684,x18685,x18682,x18686,x18687,x18688,x18689))
% 52.62/52.43 [1869]~E(x18691,x18692)+E(f374(x18693,x18694,x18695,x18696,x18691,x18697,x18698,x18699),f374(x18693,x18694,x18695,x18696,x18692,x18697,x18698,x18699))
% 52.62/52.43 [1870]~E(x18701,x18702)+E(f374(x18703,x18704,x18705,x18706,x18707,x18701,x18708,x18709),f374(x18703,x18704,x18705,x18706,x18707,x18702,x18708,x18709))
% 52.62/52.43 [1871]~E(x18711,x18712)+E(f374(x18713,x18714,x18715,x18716,x18717,x18718,x18711,x18719),f374(x18713,x18714,x18715,x18716,x18717,x18718,x18712,x18719))
% 52.62/52.43 [1872]~E(x18721,x18722)+E(f374(x18723,x18724,x18725,x18726,x18727,x18728,x18729,x18721),f374(x18723,x18724,x18725,x18726,x18727,x18728,x18729,x18722))
% 52.62/52.43 [1873]~E(x18731,x18732)+E(f615(x18731,x18733,x18734,x18735,x18736,x18737),f615(x18732,x18733,x18734,x18735,x18736,x18737))
% 52.62/52.43 [1874]~E(x18741,x18742)+E(f615(x18743,x18741,x18744,x18745,x18746,x18747),f615(x18743,x18742,x18744,x18745,x18746,x18747))
% 52.62/52.43 [1875]~E(x18751,x18752)+E(f615(x18753,x18754,x18751,x18755,x18756,x18757),f615(x18753,x18754,x18752,x18755,x18756,x18757))
% 52.62/52.43 [1876]~E(x18761,x18762)+E(f615(x18763,x18764,x18765,x18761,x18766,x18767),f615(x18763,x18764,x18765,x18762,x18766,x18767))
% 52.62/52.43 [1877]~E(x18771,x18772)+E(f615(x18773,x18774,x18775,x18776,x18771,x18777),f615(x18773,x18774,x18775,x18776,x18772,x18777))
% 52.62/52.43 [1878]~E(x18781,x18782)+E(f615(x18783,x18784,x18785,x18786,x18787,x18781),f615(x18783,x18784,x18785,x18786,x18787,x18782))
% 52.62/52.43 [1879]~E(x18791,x18792)+E(f290(x18791,x18793,x18794),f290(x18792,x18793,x18794))
% 52.62/52.43 [1880]~E(x18801,x18802)+E(f290(x18803,x18801,x18804),f290(x18803,x18802,x18804))
% 52.62/52.43 [1881]~E(x18811,x18812)+E(f290(x18813,x18814,x18811),f290(x18813,x18814,x18812))
% 52.62/52.43 [1882]~E(x18821,x18822)+E(f441(x18821,x18823,x18824,x18825),f441(x18822,x18823,x18824,x18825))
% 52.62/52.43 [1883]~E(x18831,x18832)+E(f441(x18833,x18831,x18834,x18835),f441(x18833,x18832,x18834,x18835))
% 52.62/52.43 [1884]~E(x18841,x18842)+E(f441(x18843,x18844,x18841,x18845),f441(x18843,x18844,x18842,x18845))
% 52.62/52.43 [1885]~E(x18851,x18852)+E(f441(x18853,x18854,x18855,x18851),f441(x18853,x18854,x18855,x18852))
% 52.62/52.43 [1886]~E(x18861,x18862)+E(f458(x18861,x18863,x18864,x18865),f458(x18862,x18863,x18864,x18865))
% 52.62/52.43 [1887]~E(x18871,x18872)+E(f458(x18873,x18871,x18874,x18875),f458(x18873,x18872,x18874,x18875))
% 52.62/52.43 [1888]~E(x18881,x18882)+E(f458(x18883,x18884,x18881,x18885),f458(x18883,x18884,x18882,x18885))
% 52.62/52.43 [1889]~E(x18891,x18892)+E(f458(x18893,x18894,x18895,x18891),f458(x18893,x18894,x18895,x18892))
% 52.62/52.43 [1890]~E(x18901,x18902)+E(f546(x18901,x18903,x18904,x18905,x18906),f546(x18902,x18903,x18904,x18905,x18906))
% 52.62/52.43 [1891]~E(x18911,x18912)+E(f546(x18913,x18911,x18914,x18915,x18916),f546(x18913,x18912,x18914,x18915,x18916))
% 52.62/52.43 [1892]~E(x18921,x18922)+E(f546(x18923,x18924,x18921,x18925,x18926),f546(x18923,x18924,x18922,x18925,x18926))
% 52.62/52.43 [1893]~E(x18931,x18932)+E(f546(x18933,x18934,x18935,x18931,x18936),f546(x18933,x18934,x18935,x18932,x18936))
% 52.62/52.43 [1894]~E(x18941,x18942)+E(f546(x18943,x18944,x18945,x18946,x18941),f546(x18943,x18944,x18945,x18946,x18942))
% 52.62/52.43 [1895]~E(x18951,x18952)+E(f674(x18951,x18953,x18954),f674(x18952,x18953,x18954))
% 52.62/52.43 [1896]~E(x18961,x18962)+E(f674(x18963,x18961,x18964),f674(x18963,x18962,x18964))
% 52.62/52.43 [1897]~E(x18971,x18972)+E(f674(x18973,x18974,x18971),f674(x18973,x18974,x18972))
% 52.62/52.43 [1898]~E(x18981,x18982)+E(f608(x18981,x18983,x18984,x18985),f608(x18982,x18983,x18984,x18985))
% 52.62/52.43 [1899]~E(x18991,x18992)+E(f608(x18993,x18991,x18994,x18995),f608(x18993,x18992,x18994,x18995))
% 52.62/52.43 [1900]~E(x19001,x19002)+E(f608(x19003,x19004,x19001,x19005),f608(x19003,x19004,x19002,x19005))
% 52.62/52.43 [1901]~E(x19011,x19012)+E(f608(x19013,x19014,x19015,x19011),f608(x19013,x19014,x19015,x19012))
% 52.62/52.43 [1902]~E(x19021,x19022)+E(f517(x19021,x19023,x19024,x19025),f517(x19022,x19023,x19024,x19025))
% 52.62/52.43 [1903]~E(x19031,x19032)+E(f517(x19033,x19031,x19034,x19035),f517(x19033,x19032,x19034,x19035))
% 52.62/52.43 [1904]~E(x19041,x19042)+E(f517(x19043,x19044,x19041,x19045),f517(x19043,x19044,x19042,x19045))
% 52.62/52.43 [1905]~E(x19051,x19052)+E(f517(x19053,x19054,x19055,x19051),f517(x19053,x19054,x19055,x19052))
% 52.62/52.43 [1906]~E(x19061,x19062)+E(f346(x19061,x19063,x19064,x19065),f346(x19062,x19063,x19064,x19065))
% 52.62/52.43 [1907]~E(x19071,x19072)+E(f346(x19073,x19071,x19074,x19075),f346(x19073,x19072,x19074,x19075))
% 52.62/52.43 [1908]~E(x19081,x19082)+E(f346(x19083,x19084,x19081,x19085),f346(x19083,x19084,x19082,x19085))
% 52.62/52.43 [1909]~E(x19091,x19092)+E(f346(x19093,x19094,x19095,x19091),f346(x19093,x19094,x19095,x19092))
% 52.62/52.43 [1910]~E(x19101,x19102)+E(f496(x19101,x19103,x19104,x19105,x19106,x19107),f496(x19102,x19103,x19104,x19105,x19106,x19107))
% 52.62/52.43 [1911]~E(x19111,x19112)+E(f496(x19113,x19111,x19114,x19115,x19116,x19117),f496(x19113,x19112,x19114,x19115,x19116,x19117))
% 52.62/52.43 [1912]~E(x19121,x19122)+E(f496(x19123,x19124,x19121,x19125,x19126,x19127),f496(x19123,x19124,x19122,x19125,x19126,x19127))
% 52.62/52.43 [1913]~E(x19131,x19132)+E(f496(x19133,x19134,x19135,x19131,x19136,x19137),f496(x19133,x19134,x19135,x19132,x19136,x19137))
% 52.62/52.43 [1914]~E(x19141,x19142)+E(f496(x19143,x19144,x19145,x19146,x19141,x19147),f496(x19143,x19144,x19145,x19146,x19142,x19147))
% 52.62/52.43 [1915]~E(x19151,x19152)+E(f496(x19153,x19154,x19155,x19156,x19157,x19151),f496(x19153,x19154,x19155,x19156,x19157,x19152))
% 52.62/52.43 [1916]~E(x19161,x19162)+E(f757(x19161,x19163,x19164,x19165),f757(x19162,x19163,x19164,x19165))
% 52.62/52.43 [1917]~E(x19171,x19172)+E(f757(x19173,x19171,x19174,x19175),f757(x19173,x19172,x19174,x19175))
% 52.62/52.43 [1918]~E(x19181,x19182)+E(f757(x19183,x19184,x19181,x19185),f757(x19183,x19184,x19182,x19185))
% 52.62/52.43 [1919]~E(x19191,x19192)+E(f757(x19193,x19194,x19195,x19191),f757(x19193,x19194,x19195,x19192))
% 52.62/52.43 [1920]~E(x19201,x19202)+E(f815(x19201,x19203,x19204),f815(x19202,x19203,x19204))
% 52.62/52.43 [1921]~E(x19211,x19212)+E(f815(x19213,x19211,x19214),f815(x19213,x19212,x19214))
% 52.62/52.43 [1922]~E(x19221,x19222)+E(f815(x19223,x19224,x19221),f815(x19223,x19224,x19222))
% 52.62/52.43 [1923]~E(x19231,x19232)+E(f571(x19231),f571(x19232))
% 52.62/52.43 [1924]~E(x19241,x19242)+E(f643(x19241,x19243,x19244,x19245,x19246),f643(x19242,x19243,x19244,x19245,x19246))
% 52.62/52.43 [1925]~E(x19251,x19252)+E(f643(x19253,x19251,x19254,x19255,x19256),f643(x19253,x19252,x19254,x19255,x19256))
% 52.62/52.43 [1926]~E(x19261,x19262)+E(f643(x19263,x19264,x19261,x19265,x19266),f643(x19263,x19264,x19262,x19265,x19266))
% 52.62/52.43 [1927]~E(x19271,x19272)+E(f643(x19273,x19274,x19275,x19271,x19276),f643(x19273,x19274,x19275,x19272,x19276))
% 52.62/52.43 [1928]~E(x19281,x19282)+E(f643(x19283,x19284,x19285,x19286,x19281),f643(x19283,x19284,x19285,x19286,x19282))
% 52.62/52.43 [1929]~E(x19291,x19292)+E(f763(x19291,x19293,x19294),f763(x19292,x19293,x19294))
% 52.62/52.43 [1930]~E(x19301,x19302)+E(f763(x19303,x19301,x19304),f763(x19303,x19302,x19304))
% 52.62/52.43 [1931]~E(x19311,x19312)+E(f763(x19313,x19314,x19311),f763(x19313,x19314,x19312))
% 52.62/52.43 [1932]~E(x19321,x19322)+E(f596(x19321,x19323),f596(x19322,x19323))
% 52.62/52.43 [1933]~E(x19331,x19332)+E(f596(x19333,x19331),f596(x19333,x19332))
% 52.62/52.43 [1934]~E(x19341,x19342)+E(f834(x19341,x19343),f834(x19342,x19343))
% 52.62/52.43 [1935]~E(x19351,x19352)+E(f834(x19353,x19351),f834(x19353,x19352))
% 52.62/52.43 [1936]~E(x19361,x19362)+E(f19(x19361,x19363,x19364,x19365),f19(x19362,x19363,x19364,x19365))
% 52.62/52.43 [1937]~E(x19371,x19372)+E(f19(x19373,x19371,x19374,x19375),f19(x19373,x19372,x19374,x19375))
% 52.62/52.43 [1938]~E(x19381,x19382)+E(f19(x19383,x19384,x19381,x19385),f19(x19383,x19384,x19382,x19385))
% 52.62/52.43 [1939]~E(x19391,x19392)+E(f19(x19393,x19394,x19395,x19391),f19(x19393,x19394,x19395,x19392))
% 52.62/52.43 [1940]~E(x19401,x19402)+E(f593(x19401,x19403,x19404,x19405),f593(x19402,x19403,x19404,x19405))
% 52.62/52.43 [1941]~E(x19411,x19412)+E(f593(x19413,x19411,x19414,x19415),f593(x19413,x19412,x19414,x19415))
% 52.62/52.43 [1942]~E(x19421,x19422)+E(f593(x19423,x19424,x19421,x19425),f593(x19423,x19424,x19422,x19425))
% 52.62/52.43 [1943]~E(x19431,x19432)+E(f593(x19433,x19434,x19435,x19431),f593(x19433,x19434,x19435,x19432))
% 52.62/52.43 [1944]~E(x19441,x19442)+E(f198(x19441,x19443),f198(x19442,x19443))
% 52.62/52.43 [1945]~E(x19451,x19452)+E(f198(x19453,x19451),f198(x19453,x19452))
% 52.62/52.43 [1946]~E(x19461,x19462)+E(f70(x19461,x19463,x19464),f70(x19462,x19463,x19464))
% 52.62/52.43 [1947]~E(x19471,x19472)+E(f70(x19473,x19471,x19474),f70(x19473,x19472,x19474))
% 52.62/52.43 [1948]~E(x19481,x19482)+E(f70(x19483,x19484,x19481),f70(x19483,x19484,x19482))
% 52.62/52.43 [1949]~E(x19491,x19492)+E(f510(x19491,x19493,x19494,x19495,x19496),f510(x19492,x19493,x19494,x19495,x19496))
% 52.62/52.43 [1950]~E(x19501,x19502)+E(f510(x19503,x19501,x19504,x19505,x19506),f510(x19503,x19502,x19504,x19505,x19506))
% 52.62/52.43 [1951]~E(x19511,x19512)+E(f510(x19513,x19514,x19511,x19515,x19516),f510(x19513,x19514,x19512,x19515,x19516))
% 52.62/52.43 [1952]~E(x19521,x19522)+E(f510(x19523,x19524,x19525,x19521,x19526),f510(x19523,x19524,x19525,x19522,x19526))
% 52.62/52.43 [1953]~E(x19531,x19532)+E(f510(x19533,x19534,x19535,x19536,x19531),f510(x19533,x19534,x19535,x19536,x19532))
% 52.62/52.43 [1954]~E(x19541,x19542)+E(f832(x19541,x19543,x19544,x19545,x19546,x19547,x19548),f832(x19542,x19543,x19544,x19545,x19546,x19547,x19548))
% 52.62/52.43 [1955]~E(x19551,x19552)+E(f832(x19553,x19551,x19554,x19555,x19556,x19557,x19558),f832(x19553,x19552,x19554,x19555,x19556,x19557,x19558))
% 52.62/52.43 [1956]~E(x19561,x19562)+E(f832(x19563,x19564,x19561,x19565,x19566,x19567,x19568),f832(x19563,x19564,x19562,x19565,x19566,x19567,x19568))
% 52.62/52.43 [1957]~E(x19571,x19572)+E(f832(x19573,x19574,x19575,x19571,x19576,x19577,x19578),f832(x19573,x19574,x19575,x19572,x19576,x19577,x19578))
% 52.62/52.43 [1958]~E(x19581,x19582)+E(f832(x19583,x19584,x19585,x19586,x19581,x19587,x19588),f832(x19583,x19584,x19585,x19586,x19582,x19587,x19588))
% 52.62/52.43 [1959]~E(x19591,x19592)+E(f832(x19593,x19594,x19595,x19596,x19597,x19591,x19598),f832(x19593,x19594,x19595,x19596,x19597,x19592,x19598))
% 52.62/52.43 [1960]~E(x19601,x19602)+E(f832(x19603,x19604,x19605,x19606,x19607,x19608,x19601),f832(x19603,x19604,x19605,x19606,x19607,x19608,x19602))
% 52.62/52.43 [1961]~E(x19611,x19612)+E(f410(x19611,x19613),f410(x19612,x19613))
% 52.62/52.43 [1962]~E(x19621,x19622)+E(f410(x19623,x19621),f410(x19623,x19622))
% 52.62/52.43 [1963]~E(x19631,x19632)+E(f445(x19631,x19633),f445(x19632,x19633))
% 52.62/52.43 [1964]~E(x19641,x19642)+E(f445(x19643,x19641),f445(x19643,x19642))
% 52.62/52.43 [1965]~E(x19651,x19652)+E(f513(x19651,x19653),f513(x19652,x19653))
% 52.62/52.43 [1966]~E(x19661,x19662)+E(f513(x19663,x19661),f513(x19663,x19662))
% 52.62/52.43 [1967]~E(x19671,x19672)+E(f306(x19671,x19673),f306(x19672,x19673))
% 52.62/52.43 [1968]~E(x19681,x19682)+E(f306(x19683,x19681),f306(x19683,x19682))
% 52.62/52.43 [1969]~E(x19691,x19692)+E(f818(x19691,x19693,x19694),f818(x19692,x19693,x19694))
% 52.62/52.43 [1970]~E(x19701,x19702)+E(f818(x19703,x19701,x19704),f818(x19703,x19702,x19704))
% 52.62/52.43 [1971]~E(x19711,x19712)+E(f818(x19713,x19714,x19711),f818(x19713,x19714,x19712))
% 52.62/52.43 [1972]~E(x19721,x19722)+E(f826(x19721,x19723,x19724),f826(x19722,x19723,x19724))
% 52.62/52.43 [1973]~E(x19731,x19732)+E(f826(x19733,x19731,x19734),f826(x19733,x19732,x19734))
% 52.62/52.43 [1974]~E(x19741,x19742)+E(f826(x19743,x19744,x19741),f826(x19743,x19744,x19742))
% 52.62/52.43 [1975]~E(x19751,x19752)+E(f518(x19751,x19753),f518(x19752,x19753))
% 52.62/52.43 [1976]~E(x19761,x19762)+E(f518(x19763,x19761),f518(x19763,x19762))
% 52.62/52.43 [1977]~E(x19771,x19772)+E(f416(x19771,x19773,x19774),f416(x19772,x19773,x19774))
% 52.62/52.43 [1978]~E(x19781,x19782)+E(f416(x19783,x19781,x19784),f416(x19783,x19782,x19784))
% 52.62/52.43 [1979]~E(x19791,x19792)+E(f416(x19793,x19794,x19791),f416(x19793,x19794,x19792))
% 52.62/52.43 [1980]~E(x19801,x19802)+E(f427(x19801,x19803,x19804,x19805),f427(x19802,x19803,x19804,x19805))
% 52.62/52.43 [1981]~E(x19811,x19812)+E(f427(x19813,x19811,x19814,x19815),f427(x19813,x19812,x19814,x19815))
% 52.62/52.43 [1982]~E(x19821,x19822)+E(f427(x19823,x19824,x19821,x19825),f427(x19823,x19824,x19822,x19825))
% 52.62/52.43 [1983]~E(x19831,x19832)+E(f427(x19833,x19834,x19835,x19831),f427(x19833,x19834,x19835,x19832))
% 52.62/52.43 [1984]~E(x19841,x19842)+E(f636(x19841),f636(x19842))
% 52.62/52.43 [1985]~E(x19851,x19852)+E(f746(x19851,x19853,x19854),f746(x19852,x19853,x19854))
% 52.62/52.43 [1986]~E(x19861,x19862)+E(f746(x19863,x19861,x19864),f746(x19863,x19862,x19864))
% 52.62/52.43 [1987]~E(x19871,x19872)+E(f746(x19873,x19874,x19871),f746(x19873,x19874,x19872))
% 52.62/52.43 [1988]~E(x19881,x19882)+E(f799(x19881,x19883,x19884),f799(x19882,x19883,x19884))
% 52.62/52.43 [1989]~E(x19891,x19892)+E(f799(x19893,x19891,x19894),f799(x19893,x19892,x19894))
% 52.62/52.43 [1990]~E(x19901,x19902)+E(f799(x19903,x19904,x19901),f799(x19903,x19904,x19902))
% 52.62/52.43 [1991]~E(x19911,x19912)+E(f340(x19911,x19913),f340(x19912,x19913))
% 52.62/52.43 [1992]~E(x19921,x19922)+E(f340(x19923,x19921),f340(x19923,x19922))
% 52.62/52.43 [1993]~E(x19931,x19932)+E(f651(x19931,x19933,x19934,x19935),f651(x19932,x19933,x19934,x19935))
% 52.62/52.43 [1994]~E(x19941,x19942)+E(f651(x19943,x19941,x19944,x19945),f651(x19943,x19942,x19944,x19945))
% 52.62/52.43 [1995]~E(x19951,x19952)+E(f651(x19953,x19954,x19951,x19955),f651(x19953,x19954,x19952,x19955))
% 52.62/52.43 [1996]~E(x19961,x19962)+E(f651(x19963,x19964,x19965,x19961),f651(x19963,x19964,x19965,x19962))
% 52.62/52.43 [1997]~E(x19971,x19972)+E(f578(x19971,x19973,x19974,x19975,x19976,x19977,x19978),f578(x19972,x19973,x19974,x19975,x19976,x19977,x19978))
% 52.62/52.43 [1998]~E(x19981,x19982)+E(f578(x19983,x19981,x19984,x19985,x19986,x19987,x19988),f578(x19983,x19982,x19984,x19985,x19986,x19987,x19988))
% 52.62/52.43 [1999]~E(x19991,x19992)+E(f578(x19993,x19994,x19991,x19995,x19996,x19997,x19998),f578(x19993,x19994,x19992,x19995,x19996,x19997,x19998))
% 52.62/52.43 [2000]~E(x20001,x20002)+E(f578(x20003,x20004,x20005,x20001,x20006,x20007,x20008),f578(x20003,x20004,x20005,x20002,x20006,x20007,x20008))
% 52.62/52.43 [2001]~E(x20011,x20012)+E(f578(x20013,x20014,x20015,x20016,x20011,x20017,x20018),f578(x20013,x20014,x20015,x20016,x20012,x20017,x20018))
% 52.62/52.43 [2002]~E(x20021,x20022)+E(f578(x20023,x20024,x20025,x20026,x20027,x20021,x20028),f578(x20023,x20024,x20025,x20026,x20027,x20022,x20028))
% 52.62/52.43 [2003]~E(x20031,x20032)+E(f578(x20033,x20034,x20035,x20036,x20037,x20038,x20031),f578(x20033,x20034,x20035,x20036,x20037,x20038,x20032))
% 52.62/52.43 [2004]~E(x20041,x20042)+E(f785(x20041,x20043),f785(x20042,x20043))
% 52.62/52.43 [2005]~E(x20051,x20052)+E(f785(x20053,x20051),f785(x20053,x20052))
% 52.62/52.43 [2006]~E(x20061,x20062)+E(f343(x20061,x20063),f343(x20062,x20063))
% 52.62/52.43 [2007]~E(x20071,x20072)+E(f343(x20073,x20071),f343(x20073,x20072))
% 52.62/52.43 [2008]~E(x20081,x20082)+E(f786(x20081,x20083),f786(x20082,x20083))
% 52.62/52.43 [2009]~E(x20091,x20092)+E(f786(x20093,x20091),f786(x20093,x20092))
% 52.62/52.43 [2010]~E(x20101,x20102)+E(f552(x20101,x20103,x20104),f552(x20102,x20103,x20104))
% 52.62/52.43 [2011]~E(x20111,x20112)+E(f552(x20113,x20111,x20114),f552(x20113,x20112,x20114))
% 52.62/52.43 [2012]~E(x20121,x20122)+E(f552(x20123,x20124,x20121),f552(x20123,x20124,x20122))
% 52.62/52.43 [2013]~E(x20131,x20132)+E(f21(x20131,x20133,x20134,x20135),f21(x20132,x20133,x20134,x20135))
% 52.62/52.43 [2014]~E(x20141,x20142)+E(f21(x20143,x20141,x20144,x20145),f21(x20143,x20142,x20144,x20145))
% 52.62/52.43 [2015]~E(x20151,x20152)+E(f21(x20153,x20154,x20151,x20155),f21(x20153,x20154,x20152,x20155))
% 52.62/52.43 [2016]~E(x20161,x20162)+E(f21(x20163,x20164,x20165,x20161),f21(x20163,x20164,x20165,x20162))
% 52.62/52.43 [2017]~E(x20171,x20172)+E(f657(x20171,x20173,x20174,x20175,x20176),f657(x20172,x20173,x20174,x20175,x20176))
% 52.62/52.43 [2018]~E(x20181,x20182)+E(f657(x20183,x20181,x20184,x20185,x20186),f657(x20183,x20182,x20184,x20185,x20186))
% 52.62/52.43 [2019]~E(x20191,x20192)+E(f657(x20193,x20194,x20191,x20195,x20196),f657(x20193,x20194,x20192,x20195,x20196))
% 52.62/52.43 [2020]~E(x20201,x20202)+E(f657(x20203,x20204,x20205,x20201,x20206),f657(x20203,x20204,x20205,x20202,x20206))
% 52.62/52.43 [2021]~E(x20211,x20212)+E(f657(x20213,x20214,x20215,x20216,x20211),f657(x20213,x20214,x20215,x20216,x20212))
% 52.62/52.43 [2022]~E(x20221,x20222)+E(f428(x20221,x20223),f428(x20222,x20223))
% 52.62/52.43 [2023]~E(x20231,x20232)+E(f428(x20233,x20231),f428(x20233,x20232))
% 52.62/52.43 [2024]~E(x20241,x20242)+E(f745(x20241,x20243,x20244),f745(x20242,x20243,x20244))
% 52.62/52.43 [2025]~E(x20251,x20252)+E(f745(x20253,x20251,x20254),f745(x20253,x20252,x20254))
% 52.62/52.43 [2026]~E(x20261,x20262)+E(f745(x20263,x20264,x20261),f745(x20263,x20264,x20262))
% 52.62/52.43 [2027]~E(x20271,x20272)+E(f806(x20271,x20273,x20274),f806(x20272,x20273,x20274))
% 52.62/52.43 [2028]~E(x20281,x20282)+E(f806(x20283,x20281,x20284),f806(x20283,x20282,x20284))
% 52.62/52.43 [2029]~E(x20291,x20292)+E(f806(x20293,x20294,x20291),f806(x20293,x20294,x20292))
% 52.62/52.43 [2030]~E(x20301,x20302)+E(f495(x20301,x20303,x20304,x20305),f495(x20302,x20303,x20304,x20305))
% 52.62/52.43 [2031]~E(x20311,x20312)+E(f495(x20313,x20311,x20314,x20315),f495(x20313,x20312,x20314,x20315))
% 52.62/52.43 [2032]~E(x20321,x20322)+E(f495(x20323,x20324,x20321,x20325),f495(x20323,x20324,x20322,x20325))
% 52.62/52.43 [2033]~E(x20331,x20332)+E(f495(x20333,x20334,x20335,x20331),f495(x20333,x20334,x20335,x20332))
% 52.62/52.43 [2034]~E(x20341,x20342)+E(f478(x20341,x20343,x20344),f478(x20342,x20343,x20344))
% 52.62/52.43 [2035]~E(x20351,x20352)+E(f478(x20353,x20351,x20354),f478(x20353,x20352,x20354))
% 52.62/52.43 [2036]~E(x20361,x20362)+E(f478(x20363,x20364,x20361),f478(x20363,x20364,x20362))
% 52.62/52.43 [2037]~E(x20371,x20372)+E(f630(x20371,x20373,x20374),f630(x20372,x20373,x20374))
% 52.62/52.43 [2038]~E(x20381,x20382)+E(f630(x20383,x20381,x20384),f630(x20383,x20382,x20384))
% 52.62/52.43 [2039]~E(x20391,x20392)+E(f630(x20393,x20394,x20391),f630(x20393,x20394,x20392))
% 52.62/52.43 [2040]~E(x20401,x20402)+E(f680(x20401,x20403),f680(x20402,x20403))
% 52.62/52.43 [2041]~E(x20411,x20412)+E(f680(x20413,x20411),f680(x20413,x20412))
% 52.62/52.43 [2042]~E(x20421,x20422)+E(f583(x20421,x20423),f583(x20422,x20423))
% 52.62/52.43 [2043]~E(x20431,x20432)+E(f583(x20433,x20431),f583(x20433,x20432))
% 52.62/52.43 [2044]~E(x20441,x20442)+E(f539(x20441,x20443,x20444,x20445),f539(x20442,x20443,x20444,x20445))
% 52.62/52.43 [2045]~E(x20451,x20452)+E(f539(x20453,x20451,x20454,x20455),f539(x20453,x20452,x20454,x20455))
% 52.62/52.43 [2046]~E(x20461,x20462)+E(f539(x20463,x20464,x20461,x20465),f539(x20463,x20464,x20462,x20465))
% 52.62/52.43 [2047]~E(x20471,x20472)+E(f539(x20473,x20474,x20475,x20471),f539(x20473,x20474,x20475,x20472))
% 52.62/52.43 [2048]~E(x20481,x20482)+E(f587(x20481,x20483,x20484,x20485),f587(x20482,x20483,x20484,x20485))
% 52.62/52.43 [2049]~E(x20491,x20492)+E(f587(x20493,x20491,x20494,x20495),f587(x20493,x20492,x20494,x20495))
% 52.62/52.43 [2050]~E(x20501,x20502)+E(f587(x20503,x20504,x20501,x20505),f587(x20503,x20504,x20502,x20505))
% 52.62/52.43 [2051]~E(x20511,x20512)+E(f587(x20513,x20514,x20515,x20511),f587(x20513,x20514,x20515,x20512))
% 52.66/52.43 [2052]~E(x20521,x20522)+E(f317(x20521,x20523,x20524,x20525),f317(x20522,x20523,x20524,x20525))
% 52.66/52.43 [2053]~E(x20531,x20532)+E(f317(x20533,x20531,x20534,x20535),f317(x20533,x20532,x20534,x20535))
% 52.66/52.43 [2054]~E(x20541,x20542)+E(f317(x20543,x20544,x20541,x20545),f317(x20543,x20544,x20542,x20545))
% 52.66/52.43 [2055]~E(x20551,x20552)+E(f317(x20553,x20554,x20555,x20551),f317(x20553,x20554,x20555,x20552))
% 52.66/52.43 [2056]~E(x20561,x20562)+E(f199(x20561),f199(x20562))
% 52.66/52.43 [2057]~E(x20571,x20572)+E(f658(x20571,x20573,x20574,x20575,x20576),f658(x20572,x20573,x20574,x20575,x20576))
% 52.66/52.43 [2058]~E(x20581,x20582)+E(f658(x20583,x20581,x20584,x20585,x20586),f658(x20583,x20582,x20584,x20585,x20586))
% 52.66/52.43 [2059]~E(x20591,x20592)+E(f658(x20593,x20594,x20591,x20595,x20596),f658(x20593,x20594,x20592,x20595,x20596))
% 52.66/52.43 [2060]~E(x20601,x20602)+E(f658(x20603,x20604,x20605,x20601,x20606),f658(x20603,x20604,x20605,x20602,x20606))
% 52.66/52.43 [2061]~E(x20611,x20612)+E(f658(x20613,x20614,x20615,x20616,x20611),f658(x20613,x20614,x20615,x20616,x20612))
% 52.66/52.43 [2062]~E(x20621,x20622)+E(f119(x20621,x20623,x20624,x20625),f119(x20622,x20623,x20624,x20625))
% 52.66/52.43 [2063]~E(x20631,x20632)+E(f119(x20633,x20631,x20634,x20635),f119(x20633,x20632,x20634,x20635))
% 52.66/52.43 [2064]~E(x20641,x20642)+E(f119(x20643,x20644,x20641,x20645),f119(x20643,x20644,x20642,x20645))
% 52.66/52.43 [2065]~E(x20651,x20652)+E(f119(x20653,x20654,x20655,x20651),f119(x20653,x20654,x20655,x20652))
% 52.66/52.43 [2066]~E(x20661,x20662)+E(f421(x20661,x20663,x20664),f421(x20662,x20663,x20664))
% 52.66/52.43 [2067]~E(x20671,x20672)+E(f421(x20673,x20671,x20674),f421(x20673,x20672,x20674))
% 52.66/52.43 [2068]~E(x20681,x20682)+E(f421(x20683,x20684,x20681),f421(x20683,x20684,x20682))
% 52.66/52.43 [2069]~E(x20691,x20692)+E(f604(x20691,x20693),f604(x20692,x20693))
% 52.66/52.43 [2070]~E(x20701,x20702)+E(f604(x20703,x20701),f604(x20703,x20702))
% 52.66/52.43 [2071]~E(x20711,x20712)+E(f357(x20711,x20713,x20714,x20715),f357(x20712,x20713,x20714,x20715))
% 52.66/52.43 [2072]~E(x20721,x20722)+E(f357(x20723,x20721,x20724,x20725),f357(x20723,x20722,x20724,x20725))
% 52.66/52.43 [2073]~E(x20731,x20732)+E(f357(x20733,x20734,x20731,x20735),f357(x20733,x20734,x20732,x20735))
% 52.66/52.43 [2074]~E(x20741,x20742)+E(f357(x20743,x20744,x20745,x20741),f357(x20743,x20744,x20745,x20742))
% 52.66/52.43 [2075]~E(x20751,x20752)+E(f714(x20751,x20753,x20754,x20755,x20756),f714(x20752,x20753,x20754,x20755,x20756))
% 52.66/52.43 [2076]~E(x20761,x20762)+E(f714(x20763,x20761,x20764,x20765,x20766),f714(x20763,x20762,x20764,x20765,x20766))
% 52.66/52.43 [2077]~E(x20771,x20772)+E(f714(x20773,x20774,x20771,x20775,x20776),f714(x20773,x20774,x20772,x20775,x20776))
% 52.66/52.43 [2078]~E(x20781,x20782)+E(f714(x20783,x20784,x20785,x20781,x20786),f714(x20783,x20784,x20785,x20782,x20786))
% 52.66/52.43 [2079]~E(x20791,x20792)+E(f714(x20793,x20794,x20795,x20796,x20791),f714(x20793,x20794,x20795,x20796,x20792))
% 52.66/52.43 [2080]~E(x20801,x20802)+E(f797(x20801,x20803,x20804),f797(x20802,x20803,x20804))
% 52.66/52.43 [2081]~E(x20811,x20812)+E(f797(x20813,x20811,x20814),f797(x20813,x20812,x20814))
% 52.66/52.43 [2082]~E(x20821,x20822)+E(f797(x20823,x20824,x20821),f797(x20823,x20824,x20822))
% 52.66/52.43 [2083]~E(x20831,x20832)+E(f270(x20831,x20833),f270(x20832,x20833))
% 52.66/52.43 [2084]~E(x20841,x20842)+E(f270(x20843,x20841),f270(x20843,x20842))
% 52.66/52.43 [2085]~E(x20851,x20852)+E(f623(x20851,x20853,x20854,x20855),f623(x20852,x20853,x20854,x20855))
% 52.66/52.43 [2086]~E(x20861,x20862)+E(f623(x20863,x20861,x20864,x20865),f623(x20863,x20862,x20864,x20865))
% 52.66/52.43 [2087]~E(x20871,x20872)+E(f623(x20873,x20874,x20871,x20875),f623(x20873,x20874,x20872,x20875))
% 52.66/52.43 [2088]~E(x20881,x20882)+E(f623(x20883,x20884,x20885,x20881),f623(x20883,x20884,x20885,x20882))
% 52.66/52.43 [2089]~E(x20891,x20892)+E(f548(x20891,x20893,x20894),f548(x20892,x20893,x20894))
% 52.66/52.43 [2090]~E(x20901,x20902)+E(f548(x20903,x20901,x20904),f548(x20903,x20902,x20904))
% 52.66/52.43 [2091]~E(x20911,x20912)+E(f548(x20913,x20914,x20911),f548(x20913,x20914,x20912))
% 52.66/52.43 [2092]~E(x20921,x20922)+E(f807(x20921,x20923,x20924),f807(x20922,x20923,x20924))
% 52.66/52.43 [2093]~E(x20931,x20932)+E(f807(x20933,x20931,x20934),f807(x20933,x20932,x20934))
% 52.66/52.43 [2094]~E(x20941,x20942)+E(f807(x20943,x20944,x20941),f807(x20943,x20944,x20942))
% 52.66/52.43 [2095]~E(x20951,x20952)+E(f387(x20951,x20953,x20954,x20955),f387(x20952,x20953,x20954,x20955))
% 52.66/52.43 [2096]~E(x20961,x20962)+E(f387(x20963,x20961,x20964,x20965),f387(x20963,x20962,x20964,x20965))
% 52.66/52.43 [2097]~E(x20971,x20972)+E(f387(x20973,x20974,x20971,x20975),f387(x20973,x20974,x20972,x20975))
% 52.66/52.43 [2098]~E(x20981,x20982)+E(f387(x20983,x20984,x20985,x20981),f387(x20983,x20984,x20985,x20982))
% 52.66/52.43 [2099]~E(x20991,x20992)+E(f499(x20991,x20993,x20994,x20995),f499(x20992,x20993,x20994,x20995))
% 52.66/52.43 [2100]~E(x21001,x21002)+E(f499(x21003,x21001,x21004,x21005),f499(x21003,x21002,x21004,x21005))
% 52.66/52.43 [2101]~E(x21011,x21012)+E(f499(x21013,x21014,x21011,x21015),f499(x21013,x21014,x21012,x21015))
% 52.66/52.43 [2102]~E(x21021,x21022)+E(f499(x21023,x21024,x21025,x21021),f499(x21023,x21024,x21025,x21022))
% 52.66/52.43 [2103]~E(x21031,x21032)+E(f435(x21031,x21033,x21034,x21035),f435(x21032,x21033,x21034,x21035))
% 52.66/52.43 [2104]~E(x21041,x21042)+E(f435(x21043,x21041,x21044,x21045),f435(x21043,x21042,x21044,x21045))
% 52.66/52.43 [2105]~E(x21051,x21052)+E(f435(x21053,x21054,x21051,x21055),f435(x21053,x21054,x21052,x21055))
% 52.66/52.43 [2106]~E(x21061,x21062)+E(f435(x21063,x21064,x21065,x21061),f435(x21063,x21064,x21065,x21062))
% 52.66/52.43 [2107]~E(x21071,x21072)+E(f668(x21071,x21073,x21074,x21075,x21076,x21077,x21078),f668(x21072,x21073,x21074,x21075,x21076,x21077,x21078))
% 52.66/52.43 [2108]~E(x21081,x21082)+E(f668(x21083,x21081,x21084,x21085,x21086,x21087,x21088),f668(x21083,x21082,x21084,x21085,x21086,x21087,x21088))
% 52.66/52.43 [2109]~E(x21091,x21092)+E(f668(x21093,x21094,x21091,x21095,x21096,x21097,x21098),f668(x21093,x21094,x21092,x21095,x21096,x21097,x21098))
% 52.66/52.43 [2110]~E(x21101,x21102)+E(f668(x21103,x21104,x21105,x21101,x21106,x21107,x21108),f668(x21103,x21104,x21105,x21102,x21106,x21107,x21108))
% 52.66/52.43 [2111]~E(x21111,x21112)+E(f668(x21113,x21114,x21115,x21116,x21111,x21117,x21118),f668(x21113,x21114,x21115,x21116,x21112,x21117,x21118))
% 52.66/52.43 [2112]~E(x21121,x21122)+E(f668(x21123,x21124,x21125,x21126,x21127,x21121,x21128),f668(x21123,x21124,x21125,x21126,x21127,x21122,x21128))
% 52.66/52.43 [2113]~E(x21131,x21132)+E(f668(x21133,x21134,x21135,x21136,x21137,x21138,x21131),f668(x21133,x21134,x21135,x21136,x21137,x21138,x21132))
% 52.66/52.43 [2114]~E(x21141,x21142)+E(f752(x21141,x21143,x21144,x21145,x21146),f752(x21142,x21143,x21144,x21145,x21146))
% 52.66/52.43 [2115]~E(x21151,x21152)+E(f752(x21153,x21151,x21154,x21155,x21156),f752(x21153,x21152,x21154,x21155,x21156))
% 52.66/52.43 [2116]~E(x21161,x21162)+E(f752(x21163,x21164,x21161,x21165,x21166),f752(x21163,x21164,x21162,x21165,x21166))
% 52.66/52.43 [2117]~E(x21171,x21172)+E(f752(x21173,x21174,x21175,x21171,x21176),f752(x21173,x21174,x21175,x21172,x21176))
% 52.66/52.43 [2118]~E(x21181,x21182)+E(f752(x21183,x21184,x21185,x21186,x21181),f752(x21183,x21184,x21185,x21186,x21182))
% 52.66/52.43 [2119]~E(x21191,x21192)+E(f727(x21191),f727(x21192))
% 52.66/52.43 [2120]~E(x21201,x21202)+E(f641(x21201,x21203),f641(x21202,x21203))
% 52.66/52.43 [2121]~E(x21211,x21212)+E(f641(x21213,x21211),f641(x21213,x21212))
% 52.66/52.43 [2122]~E(x21221,x21222)+E(f621(x21221,x21223,x21224,x21225,x21226,x21227),f621(x21222,x21223,x21224,x21225,x21226,x21227))
% 52.66/52.43 [2123]~E(x21231,x21232)+E(f621(x21233,x21231,x21234,x21235,x21236,x21237),f621(x21233,x21232,x21234,x21235,x21236,x21237))
% 52.66/52.43 [2124]~E(x21241,x21242)+E(f621(x21243,x21244,x21241,x21245,x21246,x21247),f621(x21243,x21244,x21242,x21245,x21246,x21247))
% 52.66/52.43 [2125]~E(x21251,x21252)+E(f621(x21253,x21254,x21255,x21251,x21256,x21257),f621(x21253,x21254,x21255,x21252,x21256,x21257))
% 52.66/52.43 [2126]~E(x21261,x21262)+E(f621(x21263,x21264,x21265,x21266,x21261,x21267),f621(x21263,x21264,x21265,x21266,x21262,x21267))
% 52.66/52.43 [2127]~E(x21271,x21272)+E(f621(x21273,x21274,x21275,x21276,x21277,x21271),f621(x21273,x21274,x21275,x21276,x21277,x21272))
% 52.66/52.43 [2128]~E(x21281,x21282)+E(f436(x21281,x21283,x21284,x21285),f436(x21282,x21283,x21284,x21285))
% 52.66/52.43 [2129]~E(x21291,x21292)+E(f436(x21293,x21291,x21294,x21295),f436(x21293,x21292,x21294,x21295))
% 52.66/52.43 [2130]~E(x21301,x21302)+E(f436(x21303,x21304,x21301,x21305),f436(x21303,x21304,x21302,x21305))
% 52.66/52.43 [2131]~E(x21311,x21312)+E(f436(x21313,x21314,x21315,x21311),f436(x21313,x21314,x21315,x21312))
% 52.66/52.43 [2132]~E(x21321,x21322)+E(f612(x21321,x21323,x21324,x21325,x21326,x21327),f612(x21322,x21323,x21324,x21325,x21326,x21327))
% 52.66/52.43 [2133]~E(x21331,x21332)+E(f612(x21333,x21331,x21334,x21335,x21336,x21337),f612(x21333,x21332,x21334,x21335,x21336,x21337))
% 52.66/52.43 [2134]~E(x21341,x21342)+E(f612(x21343,x21344,x21341,x21345,x21346,x21347),f612(x21343,x21344,x21342,x21345,x21346,x21347))
% 52.66/52.43 [2135]~E(x21351,x21352)+E(f612(x21353,x21354,x21355,x21351,x21356,x21357),f612(x21353,x21354,x21355,x21352,x21356,x21357))
% 52.66/52.43 [2136]~E(x21361,x21362)+E(f612(x21363,x21364,x21365,x21366,x21361,x21367),f612(x21363,x21364,x21365,x21366,x21362,x21367))
% 52.66/52.43 [2137]~E(x21371,x21372)+E(f612(x21373,x21374,x21375,x21376,x21377,x21371),f612(x21373,x21374,x21375,x21376,x21377,x21372))
% 52.66/52.43 [2138]~E(x21381,x21382)+E(f382(x21381,x21383),f382(x21382,x21383))
% 52.66/52.43 [2139]~E(x21391,x21392)+E(f382(x21393,x21391),f382(x21393,x21392))
% 52.66/52.43 [2140]~E(x21401,x21402)+E(f466(x21401,x21403,x21404),f466(x21402,x21403,x21404))
% 52.66/52.43 [2141]~E(x21411,x21412)+E(f466(x21413,x21411,x21414),f466(x21413,x21412,x21414))
% 52.66/52.43 [2142]~E(x21421,x21422)+E(f466(x21423,x21424,x21421),f466(x21423,x21424,x21422))
% 52.66/52.43 [2143]~E(x21431,x21432)+E(f557(x21431,x21433),f557(x21432,x21433))
% 52.66/52.43 [2144]~E(x21441,x21442)+E(f557(x21443,x21441),f557(x21443,x21442))
% 52.66/52.43 [2145]~E(x21451,x21452)+E(f491(x21451),f491(x21452))
% 52.66/52.43 [2146]~E(x21461,x21462)+E(f595(x21461,x21463,x21464,x21465),f595(x21462,x21463,x21464,x21465))
% 52.66/52.43 [2147]~E(x21471,x21472)+E(f595(x21473,x21471,x21474,x21475),f595(x21473,x21472,x21474,x21475))
% 52.66/52.43 [2148]~E(x21481,x21482)+E(f595(x21483,x21484,x21481,x21485),f595(x21483,x21484,x21482,x21485))
% 52.66/52.43 [2149]~E(x21491,x21492)+E(f595(x21493,x21494,x21495,x21491),f595(x21493,x21494,x21495,x21492))
% 52.66/52.43 [2150]~E(x21501,x21502)+E(f694(x21501,x21503,x21504),f694(x21502,x21503,x21504))
% 52.66/52.43 [2151]~E(x21511,x21512)+E(f694(x21513,x21511,x21514),f694(x21513,x21512,x21514))
% 52.66/52.43 [2152]~E(x21521,x21522)+E(f694(x21523,x21524,x21521),f694(x21523,x21524,x21522))
% 52.66/52.43 [2153]~E(x21531,x21532)+E(f699(x21531,x21533,x21534,x21535,x21536),f699(x21532,x21533,x21534,x21535,x21536))
% 52.66/52.43 [2154]~E(x21541,x21542)+E(f699(x21543,x21541,x21544,x21545,x21546),f699(x21543,x21542,x21544,x21545,x21546))
% 52.66/52.43 [2155]~E(x21551,x21552)+E(f699(x21553,x21554,x21551,x21555,x21556),f699(x21553,x21554,x21552,x21555,x21556))
% 52.66/52.43 [2156]~E(x21561,x21562)+E(f699(x21563,x21564,x21565,x21561,x21566),f699(x21563,x21564,x21565,x21562,x21566))
% 52.66/52.43 [2157]~E(x21571,x21572)+E(f699(x21573,x21574,x21575,x21576,x21571),f699(x21573,x21574,x21575,x21576,x21572))
% 52.66/52.43 [2158]~E(x21581,x21582)+E(f620(x21581,x21583,x21584),f620(x21582,x21583,x21584))
% 52.66/52.43 [2159]~E(x21591,x21592)+E(f620(x21593,x21591,x21594),f620(x21593,x21592,x21594))
% 52.66/52.43 [2160]~E(x21601,x21602)+E(f620(x21603,x21604,x21601),f620(x21603,x21604,x21602))
% 52.66/52.43 [2161]~E(x21611,x21612)+E(f646(x21611,x21613,x21614),f646(x21612,x21613,x21614))
% 52.66/52.43 [2162]~E(x21621,x21622)+E(f646(x21623,x21621,x21624),f646(x21623,x21622,x21624))
% 52.66/52.43 [2163]~E(x21631,x21632)+E(f646(x21633,x21634,x21631),f646(x21633,x21634,x21632))
% 52.66/52.43 [2164]~E(x21641,x21642)+E(f671(x21641,x21643,x21644),f671(x21642,x21643,x21644))
% 52.66/52.43 [2165]~E(x21651,x21652)+E(f671(x21653,x21651,x21654),f671(x21653,x21652,x21654))
% 52.66/52.43 [2166]~E(x21661,x21662)+E(f671(x21663,x21664,x21661),f671(x21663,x21664,x21662))
% 52.66/52.43 [2167]~E(x21671,x21672)+E(f222(x21671,x21673,x21674),f222(x21672,x21673,x21674))
% 52.66/52.43 [2168]~E(x21681,x21682)+E(f222(x21683,x21681,x21684),f222(x21683,x21682,x21684))
% 52.66/52.43 [2169]~E(x21691,x21692)+E(f222(x21693,x21694,x21691),f222(x21693,x21694,x21692))
% 52.66/52.43 [2170]~E(x21701,x21702)+E(f529(x21701,x21703,x21704,x21705),f529(x21702,x21703,x21704,x21705))
% 52.66/52.43 [2171]~E(x21711,x21712)+E(f529(x21713,x21711,x21714,x21715),f529(x21713,x21712,x21714,x21715))
% 52.66/52.43 [2172]~E(x21721,x21722)+E(f529(x21723,x21724,x21721,x21725),f529(x21723,x21724,x21722,x21725))
% 52.66/52.43 [2173]~E(x21731,x21732)+E(f529(x21733,x21734,x21735,x21731),f529(x21733,x21734,x21735,x21732))
% 52.66/52.43 [2174]~E(x21741,x21742)+E(f662(x21741,x21743,x21744,x21745),f662(x21742,x21743,x21744,x21745))
% 52.66/52.43 [2175]~E(x21751,x21752)+E(f662(x21753,x21751,x21754,x21755),f662(x21753,x21752,x21754,x21755))
% 52.66/52.43 [2176]~E(x21761,x21762)+E(f662(x21763,x21764,x21761,x21765),f662(x21763,x21764,x21762,x21765))
% 52.66/52.43 [2177]~E(x21771,x21772)+E(f662(x21773,x21774,x21775,x21771),f662(x21773,x21774,x21775,x21772))
% 52.66/52.43 [2178]~E(x21781,x21782)+E(f507(x21781,x21783,x21784,x21785,x21786,x21787,x21788),f507(x21782,x21783,x21784,x21785,x21786,x21787,x21788))
% 52.66/52.43 [2179]~E(x21791,x21792)+E(f507(x21793,x21791,x21794,x21795,x21796,x21797,x21798),f507(x21793,x21792,x21794,x21795,x21796,x21797,x21798))
% 52.66/52.43 [2180]~E(x21801,x21802)+E(f507(x21803,x21804,x21801,x21805,x21806,x21807,x21808),f507(x21803,x21804,x21802,x21805,x21806,x21807,x21808))
% 52.66/52.43 [2181]~E(x21811,x21812)+E(f507(x21813,x21814,x21815,x21811,x21816,x21817,x21818),f507(x21813,x21814,x21815,x21812,x21816,x21817,x21818))
% 52.66/52.43 [2182]~E(x21821,x21822)+E(f507(x21823,x21824,x21825,x21826,x21821,x21827,x21828),f507(x21823,x21824,x21825,x21826,x21822,x21827,x21828))
% 52.66/52.43 [2183]~E(x21831,x21832)+E(f507(x21833,x21834,x21835,x21836,x21837,x21831,x21838),f507(x21833,x21834,x21835,x21836,x21837,x21832,x21838))
% 52.66/52.43 [2184]~E(x21841,x21842)+E(f507(x21843,x21844,x21845,x21846,x21847,x21848,x21841),f507(x21843,x21844,x21845,x21846,x21847,x21848,x21842))
% 52.66/52.43 [2185]~E(x21851,x21852)+E(f610(x21851,x21853,x21854),f610(x21852,x21853,x21854))
% 52.66/52.43 [2186]~E(x21861,x21862)+E(f610(x21863,x21861,x21864),f610(x21863,x21862,x21864))
% 52.66/52.43 [2187]~E(x21871,x21872)+E(f610(x21873,x21874,x21871),f610(x21873,x21874,x21872))
% 52.66/52.43 [2188]~E(x21881,x21882)+E(f649(x21881,x21883,x21884,x21885),f649(x21882,x21883,x21884,x21885))
% 52.66/52.43 [2189]~E(x21891,x21892)+E(f649(x21893,x21891,x21894,x21895),f649(x21893,x21892,x21894,x21895))
% 52.66/52.43 [2190]~E(x21901,x21902)+E(f649(x21903,x21904,x21901,x21905),f649(x21903,x21904,x21902,x21905))
% 52.66/52.43 [2191]~E(x21911,x21912)+E(f649(x21913,x21914,x21915,x21911),f649(x21913,x21914,x21915,x21912))
% 52.66/52.43 [2192]~E(x21921,x21922)+E(f631(x21921,x21923),f631(x21922,x21923))
% 52.66/52.43 [2193]~E(x21931,x21932)+E(f631(x21933,x21931),f631(x21933,x21932))
% 52.66/52.43 [2194]~E(x21941,x21942)+E(f449(x21941,x21943,x21944),f449(x21942,x21943,x21944))
% 52.66/52.43 [2195]~E(x21951,x21952)+E(f449(x21953,x21951,x21954),f449(x21953,x21952,x21954))
% 52.66/52.43 [2196]~E(x21961,x21962)+E(f449(x21963,x21964,x21961),f449(x21963,x21964,x21962))
% 52.66/52.43 [2197]~E(x21971,x21972)+E(f523(x21971,x21973,x21974,x21975,x21976),f523(x21972,x21973,x21974,x21975,x21976))
% 52.66/52.43 [2198]~E(x21981,x21982)+E(f523(x21983,x21981,x21984,x21985,x21986),f523(x21983,x21982,x21984,x21985,x21986))
% 52.66/52.43 [2199]~E(x21991,x21992)+E(f523(x21993,x21994,x21991,x21995,x21996),f523(x21993,x21994,x21992,x21995,x21996))
% 52.66/52.43 [2200]~E(x22001,x22002)+E(f523(x22003,x22004,x22005,x22001,x22006),f523(x22003,x22004,x22005,x22002,x22006))
% 52.66/52.43 [2201]~E(x22011,x22012)+E(f523(x22013,x22014,x22015,x22016,x22011),f523(x22013,x22014,x22015,x22016,x22012))
% 52.66/52.43 [2202]~E(x22021,x22022)+E(f629(x22021,x22023,x22024),f629(x22022,x22023,x22024))
% 52.66/52.43 [2203]~E(x22031,x22032)+E(f629(x22033,x22031,x22034),f629(x22033,x22032,x22034))
% 52.66/52.43 [2204]~E(x22041,x22042)+E(f629(x22043,x22044,x22041),f629(x22043,x22044,x22042))
% 52.66/52.43 [2205]~E(x22051,x22052)+E(f740(x22051,x22053,x22054,x22055,x22056),f740(x22052,x22053,x22054,x22055,x22056))
% 52.66/52.43 [2206]~E(x22061,x22062)+E(f740(x22063,x22061,x22064,x22065,x22066),f740(x22063,x22062,x22064,x22065,x22066))
% 52.66/52.43 [2207]~E(x22071,x22072)+E(f740(x22073,x22074,x22071,x22075,x22076),f740(x22073,x22074,x22072,x22075,x22076))
% 52.66/52.43 [2208]~E(x22081,x22082)+E(f740(x22083,x22084,x22085,x22081,x22086),f740(x22083,x22084,x22085,x22082,x22086))
% 52.66/52.43 [2209]~E(x22091,x22092)+E(f740(x22093,x22094,x22095,x22096,x22091),f740(x22093,x22094,x22095,x22096,x22092))
% 52.66/52.43 [2210]~E(x22101,x22102)+E(f401(x22101,x22103,x22104,x22105),f401(x22102,x22103,x22104,x22105))
% 52.66/52.43 [2211]~E(x22111,x22112)+E(f401(x22113,x22111,x22114,x22115),f401(x22113,x22112,x22114,x22115))
% 52.66/52.43 [2212]~E(x22121,x22122)+E(f401(x22123,x22124,x22121,x22125),f401(x22123,x22124,x22122,x22125))
% 52.66/52.43 [2213]~E(x22131,x22132)+E(f401(x22133,x22134,x22135,x22131),f401(x22133,x22134,x22135,x22132))
% 52.66/52.43 [2214]~E(x22141,x22142)+E(f748(x22141,x22143,x22144),f748(x22142,x22143,x22144))
% 52.66/52.43 [2215]~E(x22151,x22152)+E(f748(x22153,x22151,x22154),f748(x22153,x22152,x22154))
% 52.66/52.43 [2216]~E(x22161,x22162)+E(f748(x22163,x22164,x22161),f748(x22163,x22164,x22162))
% 52.66/52.43 [2217]~E(x22171,x22172)+E(f613(x22171,x22173,x22174,x22175,x22176,x22177),f613(x22172,x22173,x22174,x22175,x22176,x22177))
% 52.66/52.43 [2218]~E(x22181,x22182)+E(f613(x22183,x22181,x22184,x22185,x22186,x22187),f613(x22183,x22182,x22184,x22185,x22186,x22187))
% 52.66/52.43 [2219]~E(x22191,x22192)+E(f613(x22193,x22194,x22191,x22195,x22196,x22197),f613(x22193,x22194,x22192,x22195,x22196,x22197))
% 52.66/52.43 [2220]~E(x22201,x22202)+E(f613(x22203,x22204,x22205,x22201,x22206,x22207),f613(x22203,x22204,x22205,x22202,x22206,x22207))
% 52.66/52.43 [2221]~E(x22211,x22212)+E(f613(x22213,x22214,x22215,x22216,x22211,x22217),f613(x22213,x22214,x22215,x22216,x22212,x22217))
% 52.66/52.43 [2222]~E(x22221,x22222)+E(f613(x22223,x22224,x22225,x22226,x22227,x22221),f613(x22223,x22224,x22225,x22226,x22227,x22222))
% 52.66/52.43 [2223]~E(x22231,x22232)+E(f744(x22231,x22233,x22234,x22235),f744(x22232,x22233,x22234,x22235))
% 52.66/52.43 [2224]~E(x22241,x22242)+E(f744(x22243,x22241,x22244,x22245),f744(x22243,x22242,x22244,x22245))
% 52.66/52.43 [2225]~E(x22251,x22252)+E(f744(x22253,x22254,x22251,x22255),f744(x22253,x22254,x22252,x22255))
% 52.66/52.43 [2226]~E(x22261,x22262)+E(f744(x22263,x22264,x22265,x22261),f744(x22263,x22264,x22265,x22262))
% 52.66/52.43 [2227]~E(x22271,x22272)+E(f665(x22271,x22273,x22274,x22275,x22276),f665(x22272,x22273,x22274,x22275,x22276))
% 52.66/52.43 [2228]~E(x22281,x22282)+E(f665(x22283,x22281,x22284,x22285,x22286),f665(x22283,x22282,x22284,x22285,x22286))
% 52.66/52.43 [2229]~E(x22291,x22292)+E(f665(x22293,x22294,x22291,x22295,x22296),f665(x22293,x22294,x22292,x22295,x22296))
% 52.66/52.43 [2230]~E(x22301,x22302)+E(f665(x22303,x22304,x22305,x22301,x22306),f665(x22303,x22304,x22305,x22302,x22306))
% 52.66/52.43 [2231]~E(x22311,x22312)+E(f665(x22313,x22314,x22315,x22316,x22311),f665(x22313,x22314,x22315,x22316,x22312))
% 52.66/52.43 [2232]~E(x22321,x22322)+E(f614(x22321,x22323,x22324,x22325,x22326,x22327),f614(x22322,x22323,x22324,x22325,x22326,x22327))
% 52.66/52.43 [2233]~E(x22331,x22332)+E(f614(x22333,x22331,x22334,x22335,x22336,x22337),f614(x22333,x22332,x22334,x22335,x22336,x22337))
% 52.66/52.43 [2234]~E(x22341,x22342)+E(f614(x22343,x22344,x22341,x22345,x22346,x22347),f614(x22343,x22344,x22342,x22345,x22346,x22347))
% 52.66/52.43 [2235]~E(x22351,x22352)+E(f614(x22353,x22354,x22355,x22351,x22356,x22357),f614(x22353,x22354,x22355,x22352,x22356,x22357))
% 52.66/52.43 [2236]~E(x22361,x22362)+E(f614(x22363,x22364,x22365,x22366,x22361,x22367),f614(x22363,x22364,x22365,x22366,x22362,x22367))
% 52.66/52.43 [2237]~E(x22371,x22372)+E(f614(x22373,x22374,x22375,x22376,x22377,x22371),f614(x22373,x22374,x22375,x22376,x22377,x22372))
% 52.66/52.43 [2238]~E(x22381,x22382)+E(f393(x22381,x22383,x22384,x22385,x22386),f393(x22382,x22383,x22384,x22385,x22386))
% 52.66/52.43 [2239]~E(x22391,x22392)+E(f393(x22393,x22391,x22394,x22395,x22396),f393(x22393,x22392,x22394,x22395,x22396))
% 52.66/52.43 [2240]~E(x22401,x22402)+E(f393(x22403,x22404,x22401,x22405,x22406),f393(x22403,x22404,x22402,x22405,x22406))
% 52.66/52.43 [2241]~E(x22411,x22412)+E(f393(x22413,x22414,x22415,x22411,x22416),f393(x22413,x22414,x22415,x22412,x22416))
% 52.66/52.43 [2242]~E(x22421,x22422)+E(f393(x22423,x22424,x22425,x22426,x22421),f393(x22423,x22424,x22425,x22426,x22422))
% 52.66/52.43 [2243]~E(x22431,x22432)+E(f453(x22431,x22433,x22434,x22435,x22436,x22437,x22438),f453(x22432,x22433,x22434,x22435,x22436,x22437,x22438))
% 52.66/52.43 [2244]~E(x22441,x22442)+E(f453(x22443,x22441,x22444,x22445,x22446,x22447,x22448),f453(x22443,x22442,x22444,x22445,x22446,x22447,x22448))
% 52.66/52.43 [2245]~E(x22451,x22452)+E(f453(x22453,x22454,x22451,x22455,x22456,x22457,x22458),f453(x22453,x22454,x22452,x22455,x22456,x22457,x22458))
% 52.66/52.43 [2246]~E(x22461,x22462)+E(f453(x22463,x22464,x22465,x22461,x22466,x22467,x22468),f453(x22463,x22464,x22465,x22462,x22466,x22467,x22468))
% 52.66/52.43 [2247]~E(x22471,x22472)+E(f453(x22473,x22474,x22475,x22476,x22471,x22477,x22478),f453(x22473,x22474,x22475,x22476,x22472,x22477,x22478))
% 52.66/52.43 [2248]~E(x22481,x22482)+E(f453(x22483,x22484,x22485,x22486,x22487,x22481,x22488),f453(x22483,x22484,x22485,x22486,x22487,x22482,x22488))
% 52.66/52.43 [2249]~E(x22491,x22492)+E(f453(x22493,x22494,x22495,x22496,x22497,x22498,x22491),f453(x22493,x22494,x22495,x22496,x22497,x22498,x22492))
% 52.66/52.43 [2250]~E(x22501,x22502)+E(f715(x22501,x22503,x22504,x22505,x22506),f715(x22502,x22503,x22504,x22505,x22506))
% 52.66/52.43 [2251]~E(x22511,x22512)+E(f715(x22513,x22511,x22514,x22515,x22516),f715(x22513,x22512,x22514,x22515,x22516))
% 52.66/52.43 [2252]~E(x22521,x22522)+E(f715(x22523,x22524,x22521,x22525,x22526),f715(x22523,x22524,x22522,x22525,x22526))
% 52.66/52.43 [2253]~E(x22531,x22532)+E(f715(x22533,x22534,x22535,x22531,x22536),f715(x22533,x22534,x22535,x22532,x22536))
% 52.66/52.43 [2254]~E(x22541,x22542)+E(f715(x22543,x22544,x22545,x22546,x22541),f715(x22543,x22544,x22545,x22546,x22542))
% 52.66/52.43 [2255]~E(x22551,x22552)+E(f654(x22551,x22553,x22554,x22555),f654(x22552,x22553,x22554,x22555))
% 52.66/52.43 [2256]~E(x22561,x22562)+E(f654(x22563,x22561,x22564,x22565),f654(x22563,x22562,x22564,x22565))
% 52.66/52.43 [2257]~E(x22571,x22572)+E(f654(x22573,x22574,x22571,x22575),f654(x22573,x22574,x22572,x22575))
% 52.66/52.43 [2258]~E(x22581,x22582)+E(f654(x22583,x22584,x22585,x22581),f654(x22583,x22584,x22585,x22582))
% 52.66/52.43 [2259]~E(x22591,x22592)+E(f597(x22591,x22593,x22594,x22595),f597(x22592,x22593,x22594,x22595))
% 52.66/52.43 [2260]~E(x22601,x22602)+E(f597(x22603,x22601,x22604,x22605),f597(x22603,x22602,x22604,x22605))
% 52.66/52.43 [2261]~E(x22611,x22612)+E(f597(x22613,x22614,x22611,x22615),f597(x22613,x22614,x22612,x22615))
% 52.66/52.43 [2262]~E(x22621,x22622)+E(f597(x22623,x22624,x22625,x22621),f597(x22623,x22624,x22625,x22622))
% 52.66/52.43 [2263]~E(x22631,x22632)+E(f217(x22631,x22633,x22634),f217(x22632,x22633,x22634))
% 52.66/52.43 [2264]~E(x22641,x22642)+E(f217(x22643,x22641,x22644),f217(x22643,x22642,x22644))
% 52.66/52.43 [2265]~E(x22651,x22652)+E(f217(x22653,x22654,x22651),f217(x22653,x22654,x22652))
% 52.66/52.43 [2266]~E(x22661,x22662)+E(f771(x22661,x22663),f771(x22662,x22663))
% 52.66/52.43 [2267]~E(x22671,x22672)+E(f771(x22673,x22671),f771(x22673,x22672))
% 52.66/52.43 [2268]~E(x22681,x22682)+E(f835(x22681,x22683,x22684),f835(x22682,x22683,x22684))
% 52.66/52.43 [2269]~E(x22691,x22692)+E(f835(x22693,x22691,x22694),f835(x22693,x22692,x22694))
% 52.66/52.43 [2270]~E(x22701,x22702)+E(f835(x22703,x22704,x22701),f835(x22703,x22704,x22702))
% 52.66/52.43 [2271]~E(x22711,x22712)+E(f632(x22711,x22713,x22714),f632(x22712,x22713,x22714))
% 52.66/52.43 [2272]~E(x22721,x22722)+E(f632(x22723,x22721,x22724),f632(x22723,x22722,x22724))
% 52.66/52.43 [2273]~E(x22731,x22732)+E(f632(x22733,x22734,x22731),f632(x22733,x22734,x22732))
% 52.66/52.43 [2274]~E(x22741,x22742)+E(f820(x22741,x22743,x22744),f820(x22742,x22743,x22744))
% 52.66/52.43 [2275]~E(x22751,x22752)+E(f820(x22753,x22751,x22754),f820(x22753,x22752,x22754))
% 52.66/52.43 [2276]~E(x22761,x22762)+E(f820(x22763,x22764,x22761),f820(x22763,x22764,x22762))
% 52.66/52.43 [2277]~E(x22771,x22772)+E(f500(x22771,x22773,x22774,x22775,x22776,x22777,x22778),f500(x22772,x22773,x22774,x22775,x22776,x22777,x22778))
% 52.66/52.43 [2278]~E(x22781,x22782)+E(f500(x22783,x22781,x22784,x22785,x22786,x22787,x22788),f500(x22783,x22782,x22784,x22785,x22786,x22787,x22788))
% 52.66/52.43 [2279]~E(x22791,x22792)+E(f500(x22793,x22794,x22791,x22795,x22796,x22797,x22798),f500(x22793,x22794,x22792,x22795,x22796,x22797,x22798))
% 52.66/52.43 [2280]~E(x22801,x22802)+E(f500(x22803,x22804,x22805,x22801,x22806,x22807,x22808),f500(x22803,x22804,x22805,x22802,x22806,x22807,x22808))
% 52.66/52.43 [2281]~E(x22811,x22812)+E(f500(x22813,x22814,x22815,x22816,x22811,x22817,x22818),f500(x22813,x22814,x22815,x22816,x22812,x22817,x22818))
% 52.66/52.43 [2282]~E(x22821,x22822)+E(f500(x22823,x22824,x22825,x22826,x22827,x22821,x22828),f500(x22823,x22824,x22825,x22826,x22827,x22822,x22828))
% 52.66/52.43 [2283]~E(x22831,x22832)+E(f500(x22833,x22834,x22835,x22836,x22837,x22838,x22831),f500(x22833,x22834,x22835,x22836,x22837,x22838,x22832))
% 52.66/52.43 [2284]~E(x22841,x22842)+E(f488(x22841,x22843,x22844,x22845,x22846),f488(x22842,x22843,x22844,x22845,x22846))
% 52.66/52.43 [2285]~E(x22851,x22852)+E(f488(x22853,x22851,x22854,x22855,x22856),f488(x22853,x22852,x22854,x22855,x22856))
% 52.66/52.43 [2286]~E(x22861,x22862)+E(f488(x22863,x22864,x22861,x22865,x22866),f488(x22863,x22864,x22862,x22865,x22866))
% 52.66/52.43 [2287]~E(x22871,x22872)+E(f488(x22873,x22874,x22875,x22871,x22876),f488(x22873,x22874,x22875,x22872,x22876))
% 52.66/52.43 [2288]~E(x22881,x22882)+E(f488(x22883,x22884,x22885,x22886,x22881),f488(x22883,x22884,x22885,x22886,x22882))
% 52.66/52.43 [2289]~E(x22891,x22892)+E(f201(x22891,x22893,x22894,x22895),f201(x22892,x22893,x22894,x22895))
% 52.66/52.43 [2290]~E(x22901,x22902)+E(f201(x22903,x22901,x22904,x22905),f201(x22903,x22902,x22904,x22905))
% 52.66/52.43 [2291]~E(x22911,x22912)+E(f201(x22913,x22914,x22911,x22915),f201(x22913,x22914,x22912,x22915))
% 52.66/52.43 [2292]~E(x22921,x22922)+E(f201(x22923,x22924,x22925,x22921),f201(x22923,x22924,x22925,x22922))
% 52.66/52.43 [2293]~E(x22931,x22932)+E(f664(x22931,x22933,x22934,x22935),f664(x22932,x22933,x22934,x22935))
% 52.66/52.43 [2294]~E(x22941,x22942)+E(f664(x22943,x22941,x22944,x22945),f664(x22943,x22942,x22944,x22945))
% 52.66/52.43 [2295]~E(x22951,x22952)+E(f664(x22953,x22954,x22951,x22955),f664(x22953,x22954,x22952,x22955))
% 52.66/52.43 [2296]~E(x22961,x22962)+E(f664(x22963,x22964,x22965,x22961),f664(x22963,x22964,x22965,x22962))
% 52.66/52.43 [2297]~E(x22971,x22972)+E(f397(x22971,x22973,x22974,x22975,x22976),f397(x22972,x22973,x22974,x22975,x22976))
% 52.66/52.43 [2298]~E(x22981,x22982)+E(f397(x22983,x22981,x22984,x22985,x22986),f397(x22983,x22982,x22984,x22985,x22986))
% 52.66/52.43 [2299]~E(x22991,x22992)+E(f397(x22993,x22994,x22991,x22995,x22996),f397(x22993,x22994,x22992,x22995,x22996))
% 52.66/52.43 [2300]~E(x23001,x23002)+E(f397(x23003,x23004,x23005,x23001,x23006),f397(x23003,x23004,x23005,x23002,x23006))
% 52.66/52.43 [2301]~E(x23011,x23012)+E(f397(x23013,x23014,x23015,x23016,x23011),f397(x23013,x23014,x23015,x23016,x23012))
% 52.66/52.43 [2302]~E(x23021,x23022)+E(f315(x23021,x23023,x23024),f315(x23022,x23023,x23024))
% 52.66/52.43 [2303]~E(x23031,x23032)+E(f315(x23033,x23031,x23034),f315(x23033,x23032,x23034))
% 52.66/52.43 [2304]~E(x23041,x23042)+E(f315(x23043,x23044,x23041),f315(x23043,x23044,x23042))
% 52.66/52.43 [2305]~E(x23051,x23052)+E(f425(x23051,x23053,x23054,x23055),f425(x23052,x23053,x23054,x23055))
% 52.66/52.43 [2306]~E(x23061,x23062)+E(f425(x23063,x23061,x23064,x23065),f425(x23063,x23062,x23064,x23065))
% 52.66/52.43 [2307]~E(x23071,x23072)+E(f425(x23073,x23074,x23071,x23075),f425(x23073,x23074,x23072,x23075))
% 52.66/52.43 [2308]~E(x23081,x23082)+E(f425(x23083,x23084,x23085,x23081),f425(x23083,x23084,x23085,x23082))
% 52.66/52.43 [2309]~E(x23091,x23092)+E(f271(x23091,x23093,x23094,x23095),f271(x23092,x23093,x23094,x23095))
% 52.66/52.43 [2310]~E(x23101,x23102)+E(f271(x23103,x23101,x23104,x23105),f271(x23103,x23102,x23104,x23105))
% 52.66/52.43 [2311]~E(x23111,x23112)+E(f271(x23113,x23114,x23111,x23115),f271(x23113,x23114,x23112,x23115))
% 52.66/52.43 [2312]~E(x23121,x23122)+E(f271(x23123,x23124,x23125,x23121),f271(x23123,x23124,x23125,x23122))
% 52.66/52.43 [2313]~E(x23131,x23132)+E(f129(x23131),f129(x23132))
% 52.66/52.43 [2314]~E(x23141,x23142)+E(f683(x23141),f683(x23142))
% 52.66/52.43 [2315]~E(x23151,x23152)+E(f437(x23151,x23153,x23154,x23155),f437(x23152,x23153,x23154,x23155))
% 52.66/52.43 [2316]~E(x23161,x23162)+E(f437(x23163,x23161,x23164,x23165),f437(x23163,x23162,x23164,x23165))
% 52.66/52.43 [2317]~E(x23171,x23172)+E(f437(x23173,x23174,x23171,x23175),f437(x23173,x23174,x23172,x23175))
% 52.66/52.43 [2318]~E(x23181,x23182)+E(f437(x23183,x23184,x23185,x23181),f437(x23183,x23184,x23185,x23182))
% 52.66/52.43 [2319]~E(x23191,x23192)+E(f794(x23191,x23193),f794(x23192,x23193))
% 52.66/52.43 [2320]~E(x23201,x23202)+E(f794(x23203,x23201),f794(x23203,x23202))
% 52.66/52.43 [2321]~E(x23211,x23212)+E(f850(x23211,x23213),f850(x23212,x23213))
% 52.66/52.43 [2322]~E(x23221,x23222)+E(f850(x23223,x23221),f850(x23223,x23222))
% 52.66/52.43 [2323]~E(x23231,x23232)+E(f124(x23231),f124(x23232))
% 52.66/52.43 [2324]~E(x23241,x23242)+E(f97(x23241,x23243,x23244,x23245),f97(x23242,x23243,x23244,x23245))
% 52.66/52.43 [2325]~E(x23251,x23252)+E(f97(x23253,x23251,x23254,x23255),f97(x23253,x23252,x23254,x23255))
% 52.66/52.43 [2326]~E(x23261,x23262)+E(f97(x23263,x23264,x23261,x23265),f97(x23263,x23264,x23262,x23265))
% 52.66/52.43 [2327]~E(x23271,x23272)+E(f97(x23273,x23274,x23275,x23271),f97(x23273,x23274,x23275,x23272))
% 52.66/52.43 [2328]~E(x23281,x23282)+E(f791(x23281,x23283,x23284),f791(x23282,x23283,x23284))
% 52.66/52.43 [2329]~E(x23291,x23292)+E(f791(x23293,x23291,x23294),f791(x23293,x23292,x23294))
% 52.66/52.43 [2330]~E(x23301,x23302)+E(f791(x23303,x23304,x23301),f791(x23303,x23304,x23302))
% 52.66/52.43 [2331]~E(x23311,x23312)+E(f501(x23311,x23313,x23314,x23315,x23316,x23317,x23318),f501(x23312,x23313,x23314,x23315,x23316,x23317,x23318))
% 52.66/52.43 [2332]~E(x23321,x23322)+E(f501(x23323,x23321,x23324,x23325,x23326,x23327,x23328),f501(x23323,x23322,x23324,x23325,x23326,x23327,x23328))
% 52.66/52.43 [2333]~E(x23331,x23332)+E(f501(x23333,x23334,x23331,x23335,x23336,x23337,x23338),f501(x23333,x23334,x23332,x23335,x23336,x23337,x23338))
% 52.66/52.43 [2334]~E(x23341,x23342)+E(f501(x23343,x23344,x23345,x23341,x23346,x23347,x23348),f501(x23343,x23344,x23345,x23342,x23346,x23347,x23348))
% 52.66/52.43 [2335]~E(x23351,x23352)+E(f501(x23353,x23354,x23355,x23356,x23351,x23357,x23358),f501(x23353,x23354,x23355,x23356,x23352,x23357,x23358))
% 52.66/52.43 [2336]~E(x23361,x23362)+E(f501(x23363,x23364,x23365,x23366,x23367,x23361,x23368),f501(x23363,x23364,x23365,x23366,x23367,x23362,x23368))
% 52.66/52.43 [2337]~E(x23371,x23372)+E(f501(x23373,x23374,x23375,x23376,x23377,x23378,x23371),f501(x23373,x23374,x23375,x23376,x23377,x23378,x23372))
% 52.66/52.43 [2338]~E(x23381,x23382)+E(f455(x23381,x23383),f455(x23382,x23383))
% 52.66/52.43 [2339]~E(x23391,x23392)+E(f455(x23393,x23391),f455(x23393,x23392))
% 52.66/52.43 [2340]~E(x23401,x23402)+E(f558(x23401,x23403,x23404),f558(x23402,x23403,x23404))
% 52.66/52.43 [2341]~E(x23411,x23412)+E(f558(x23413,x23411,x23414),f558(x23413,x23412,x23414))
% 52.66/52.43 [2342]~E(x23421,x23422)+E(f558(x23423,x23424,x23421),f558(x23423,x23424,x23422))
% 52.66/52.43 [2343]~E(x23431,x23432)+E(f244(x23431,x23433,x23434),f244(x23432,x23433,x23434))
% 52.66/52.43 [2344]~E(x23441,x23442)+E(f244(x23443,x23441,x23444),f244(x23443,x23442,x23444))
% 52.66/52.43 [2345]~E(x23451,x23452)+E(f244(x23453,x23454,x23451),f244(x23453,x23454,x23452))
% 52.66/52.43 [2346]~E(x23461,x23462)+E(f525(x23461),f525(x23462))
% 52.66/52.43 [2347]~E(x23471,x23472)+E(f264(x23471),f264(x23472))
% 52.66/52.43 [2348]~E(x23481,x23482)+E(f202(x23481,x23483,x23484,x23485,x23486,x23487,x23488),f202(x23482,x23483,x23484,x23485,x23486,x23487,x23488))
% 52.66/52.43 [2349]~E(x23491,x23492)+E(f202(x23493,x23491,x23494,x23495,x23496,x23497,x23498),f202(x23493,x23492,x23494,x23495,x23496,x23497,x23498))
% 52.66/52.43 [2350]~E(x23501,x23502)+E(f202(x23503,x23504,x23501,x23505,x23506,x23507,x23508),f202(x23503,x23504,x23502,x23505,x23506,x23507,x23508))
% 52.66/52.43 [2351]~E(x23511,x23512)+E(f202(x23513,x23514,x23515,x23511,x23516,x23517,x23518),f202(x23513,x23514,x23515,x23512,x23516,x23517,x23518))
% 52.66/52.43 [2352]~E(x23521,x23522)+E(f202(x23523,x23524,x23525,x23526,x23521,x23527,x23528),f202(x23523,x23524,x23525,x23526,x23522,x23527,x23528))
% 52.66/52.43 [2353]~E(x23531,x23532)+E(f202(x23533,x23534,x23535,x23536,x23537,x23531,x23538),f202(x23533,x23534,x23535,x23536,x23537,x23532,x23538))
% 52.66/52.43 [2354]~E(x23541,x23542)+E(f202(x23543,x23544,x23545,x23546,x23547,x23548,x23541),f202(x23543,x23544,x23545,x23546,x23547,x23548,x23542))
% 52.66/52.43 [2355]~E(x23551,x23552)+E(f768(x23551),f768(x23552))
% 52.66/52.43 [2356]~E(x23561,x23562)+E(f430(x23561,x23563,x23564,x23565),f430(x23562,x23563,x23564,x23565))
% 52.66/52.43 [2357]~E(x23571,x23572)+E(f430(x23573,x23571,x23574,x23575),f430(x23573,x23572,x23574,x23575))
% 52.66/52.43 [2358]~E(x23581,x23582)+E(f430(x23583,x23584,x23581,x23585),f430(x23583,x23584,x23582,x23585))
% 52.66/52.43 [2359]~E(x23591,x23592)+E(f430(x23593,x23594,x23595,x23591),f430(x23593,x23594,x23595,x23592))
% 52.66/52.43 [2360]~E(x23601,x23602)+E(f562(x23601,x23603,x23604,x23605),f562(x23602,x23603,x23604,x23605))
% 52.66/52.43 [2361]~E(x23611,x23612)+E(f562(x23613,x23611,x23614,x23615),f562(x23613,x23612,x23614,x23615))
% 52.66/52.43 [2362]~E(x23621,x23622)+E(f562(x23623,x23624,x23621,x23625),f562(x23623,x23624,x23622,x23625))
% 52.66/52.43 [2363]~E(x23631,x23632)+E(f562(x23633,x23634,x23635,x23631),f562(x23633,x23634,x23635,x23632))
% 52.66/52.43 [2364]~E(x23641,x23642)+E(f765(x23641,x23643,x23644),f765(x23642,x23643,x23644))
% 52.66/52.43 [2365]~E(x23651,x23652)+E(f765(x23653,x23651,x23654),f765(x23653,x23652,x23654))
% 52.66/52.43 [2366]~E(x23661,x23662)+E(f765(x23663,x23664,x23661),f765(x23663,x23664,x23662))
% 52.66/52.43 [2367]~E(x23671,x23672)+E(f693(x23671,x23673,x23674,x23675),f693(x23672,x23673,x23674,x23675))
% 52.66/52.43 [2368]~E(x23681,x23682)+E(f693(x23683,x23681,x23684,x23685),f693(x23683,x23682,x23684,x23685))
% 52.66/52.43 [2369]~E(x23691,x23692)+E(f693(x23693,x23694,x23691,x23695),f693(x23693,x23694,x23692,x23695))
% 52.66/52.43 [2370]~E(x23701,x23702)+E(f693(x23703,x23704,x23705,x23701),f693(x23703,x23704,x23705,x23702))
% 52.66/52.43 [2371]~E(x23711,x23712)+E(f400(x23711,x23713,x23714,x23715),f400(x23712,x23713,x23714,x23715))
% 52.66/52.43 [2372]~E(x23721,x23722)+E(f400(x23723,x23721,x23724,x23725),f400(x23723,x23722,x23724,x23725))
% 52.66/52.43 [2373]~E(x23731,x23732)+E(f400(x23733,x23734,x23731,x23735),f400(x23733,x23734,x23732,x23735))
% 52.66/52.43 [2374]~E(x23741,x23742)+E(f400(x23743,x23744,x23745,x23741),f400(x23743,x23744,x23745,x23742))
% 52.66/52.43 [2375]~E(x23751,x23752)+E(f527(x23751,x23753,x23754),f527(x23752,x23753,x23754))
% 52.66/52.43 [2376]~E(x23761,x23762)+E(f527(x23763,x23761,x23764),f527(x23763,x23762,x23764))
% 52.66/52.43 [2377]~E(x23771,x23772)+E(f527(x23773,x23774,x23771),f527(x23773,x23774,x23772))
% 52.66/52.43 [2378]~E(x23781,x23782)+E(f511(x23781,x23783,x23784,x23785,x23786),f511(x23782,x23783,x23784,x23785,x23786))
% 52.66/52.43 [2379]~E(x23791,x23792)+E(f511(x23793,x23791,x23794,x23795,x23796),f511(x23793,x23792,x23794,x23795,x23796))
% 52.66/52.43 [2380]~E(x23801,x23802)+E(f511(x23803,x23804,x23801,x23805,x23806),f511(x23803,x23804,x23802,x23805,x23806))
% 52.66/52.43 [2381]~E(x23811,x23812)+E(f511(x23813,x23814,x23815,x23811,x23816),f511(x23813,x23814,x23815,x23812,x23816))
% 52.66/52.43 [2382]~E(x23821,x23822)+E(f511(x23823,x23824,x23825,x23826,x23821),f511(x23823,x23824,x23825,x23826,x23822))
% 52.66/52.43 [2383]~E(x23831,x23832)+E(f373(x23831,x23833,x23834,x23835,x23836),f373(x23832,x23833,x23834,x23835,x23836))
% 52.66/52.43 [2384]~E(x23841,x23842)+E(f373(x23843,x23841,x23844,x23845,x23846),f373(x23843,x23842,x23844,x23845,x23846))
% 52.66/52.43 [2385]~E(x23851,x23852)+E(f373(x23853,x23854,x23851,x23855,x23856),f373(x23853,x23854,x23852,x23855,x23856))
% 52.66/52.43 [2386]~E(x23861,x23862)+E(f373(x23863,x23864,x23865,x23861,x23866),f373(x23863,x23864,x23865,x23862,x23866))
% 52.66/52.43 [2387]~E(x23871,x23872)+E(f373(x23873,x23874,x23875,x23876,x23871),f373(x23873,x23874,x23875,x23876,x23872))
% 52.66/52.43 [2388]~E(x23881,x23882)+E(f381(x23881,x23883),f381(x23882,x23883))
% 52.66/52.43 [2389]~E(x23891,x23892)+E(f381(x23893,x23891),f381(x23893,x23892))
% 52.66/52.43 [2390]~E(x23901,x23902)+E(f547(x23901,x23903,x23904),f547(x23902,x23903,x23904))
% 52.66/52.43 [2391]~E(x23911,x23912)+E(f547(x23913,x23911,x23914),f547(x23913,x23912,x23914))
% 52.66/52.43 [2392]~E(x23921,x23922)+E(f547(x23923,x23924,x23921),f547(x23923,x23924,x23922))
% 52.66/52.43 [2393]~E(x23931,x23932)+E(f413(x23931,x23933,x23934),f413(x23932,x23933,x23934))
% 52.66/52.43 [2394]~E(x23941,x23942)+E(f413(x23943,x23941,x23944),f413(x23943,x23942,x23944))
% 52.66/52.43 [2395]~E(x23951,x23952)+E(f413(x23953,x23954,x23951),f413(x23953,x23954,x23952))
% 52.66/52.43 [2396]~E(x23961,x23962)+E(f309(x23961,x23963,x23964),f309(x23962,x23963,x23964))
% 52.66/52.43 [2397]~E(x23971,x23972)+E(f309(x23973,x23971,x23974),f309(x23973,x23972,x23974))
% 52.66/52.43 [2398]~E(x23981,x23982)+E(f309(x23983,x23984,x23981),f309(x23983,x23984,x23982))
% 52.66/52.43 [2399]~E(x23991,x23992)+E(f404(x23991,x23993,x23994),f404(x23992,x23993,x23994))
% 52.66/52.43 [2400]~E(x24001,x24002)+E(f404(x24003,x24001,x24004),f404(x24003,x24002,x24004))
% 52.66/52.43 [2401]~E(x24011,x24012)+E(f404(x24013,x24014,x24011),f404(x24013,x24014,x24012))
% 52.66/52.43 [2402]~E(x24021,x24022)+E(f476(x24021,x24023,x24024),f476(x24022,x24023,x24024))
% 52.66/52.43 [2403]~E(x24031,x24032)+E(f476(x24033,x24031,x24034),f476(x24033,x24032,x24034))
% 52.66/52.43 [2404]~E(x24041,x24042)+E(f476(x24043,x24044,x24041),f476(x24043,x24044,x24042))
% 52.66/52.43 [2405]~E(x24051,x24052)+E(f50(x24051),f50(x24052))
% 52.66/52.43 [2406]~E(x24061,x24062)+E(f702(x24061,x24063,x24064,x24065,x24066),f702(x24062,x24063,x24064,x24065,x24066))
% 52.66/52.43 [2407]~E(x24071,x24072)+E(f702(x24073,x24071,x24074,x24075,x24076),f702(x24073,x24072,x24074,x24075,x24076))
% 52.66/52.43 [2408]~E(x24081,x24082)+E(f702(x24083,x24084,x24081,x24085,x24086),f702(x24083,x24084,x24082,x24085,x24086))
% 52.66/52.43 [2409]~E(x24091,x24092)+E(f702(x24093,x24094,x24095,x24091,x24096),f702(x24093,x24094,x24095,x24092,x24096))
% 52.66/52.43 [2410]~E(x24101,x24102)+E(f702(x24103,x24104,x24105,x24106,x24101),f702(x24103,x24104,x24105,x24106,x24102))
% 52.66/52.43 [2411]~E(x24111,x24112)+E(f700(x24111,x24113,x24114,x24115),f700(x24112,x24113,x24114,x24115))
% 52.66/52.43 [2412]~E(x24121,x24122)+E(f700(x24123,x24121,x24124,x24125),f700(x24123,x24122,x24124,x24125))
% 52.66/52.43 [2413]~E(x24131,x24132)+E(f700(x24133,x24134,x24131,x24135),f700(x24133,x24134,x24132,x24135))
% 52.66/52.43 [2414]~E(x24141,x24142)+E(f700(x24143,x24144,x24145,x24141),f700(x24143,x24144,x24145,x24142))
% 52.66/52.43 [2415]~E(x24151,x24152)+E(f570(x24151,x24153,x24154,x24155,x24156),f570(x24152,x24153,x24154,x24155,x24156))
% 52.66/52.43 [2416]~E(x24161,x24162)+E(f570(x24163,x24161,x24164,x24165,x24166),f570(x24163,x24162,x24164,x24165,x24166))
% 52.66/52.43 [2417]~E(x24171,x24172)+E(f570(x24173,x24174,x24171,x24175,x24176),f570(x24173,x24174,x24172,x24175,x24176))
% 52.66/52.43 [2418]~E(x24181,x24182)+E(f570(x24183,x24184,x24185,x24181,x24186),f570(x24183,x24184,x24185,x24182,x24186))
% 52.66/52.43 [2419]~E(x24191,x24192)+E(f570(x24193,x24194,x24195,x24196,x24191),f570(x24193,x24194,x24195,x24196,x24192))
% 52.66/52.43 [2420]~E(x24201,x24202)+E(f405(x24201,x24203,x24204,x24205),f405(x24202,x24203,x24204,x24205))
% 52.66/52.43 [2421]~E(x24211,x24212)+E(f405(x24213,x24211,x24214,x24215),f405(x24213,x24212,x24214,x24215))
% 52.66/52.43 [2422]~E(x24221,x24222)+E(f405(x24223,x24224,x24221,x24225),f405(x24223,x24224,x24222,x24225))
% 52.66/52.43 [2423]~E(x24231,x24232)+E(f405(x24233,x24234,x24235,x24231),f405(x24233,x24234,x24235,x24232))
% 52.66/52.43 [2424]~E(x24241,x24242)+E(f205(x24241,x24243,x24244,x24245),f205(x24242,x24243,x24244,x24245))
% 52.66/52.43 [2425]~E(x24251,x24252)+E(f205(x24253,x24251,x24254,x24255),f205(x24253,x24252,x24254,x24255))
% 52.66/52.43 [2426]~E(x24261,x24262)+E(f205(x24263,x24264,x24261,x24265),f205(x24263,x24264,x24262,x24265))
% 52.66/52.43 [2427]~E(x24271,x24272)+E(f205(x24273,x24274,x24275,x24271),f205(x24273,x24274,x24275,x24272))
% 52.66/52.43 [2428]~E(x24281,x24282)+E(f385(x24281,x24283),f385(x24282,x24283))
% 52.66/52.43 [2429]~E(x24291,x24292)+E(f385(x24293,x24291),f385(x24293,x24292))
% 52.66/52.43 [2430]~E(x24301,x24302)+E(f220(x24301,x24303,x24304,x24305,x24306),f220(x24302,x24303,x24304,x24305,x24306))
% 52.66/52.43 [2431]~E(x24311,x24312)+E(f220(x24313,x24311,x24314,x24315,x24316),f220(x24313,x24312,x24314,x24315,x24316))
% 52.66/52.43 [2432]~E(x24321,x24322)+E(f220(x24323,x24324,x24321,x24325,x24326),f220(x24323,x24324,x24322,x24325,x24326))
% 52.66/52.43 [2433]~E(x24331,x24332)+E(f220(x24333,x24334,x24335,x24331,x24336),f220(x24333,x24334,x24335,x24332,x24336))
% 52.66/52.43 [2434]~E(x24341,x24342)+E(f220(x24343,x24344,x24345,x24346,x24341),f220(x24343,x24344,x24345,x24346,x24342))
% 52.66/52.43 [2435]~E(x24351,x24352)+E(f52(x24351),f52(x24352))
% 52.66/52.43 [2436]~E(x24361,x24362)+E(f802(x24361,x24363,x24364),f802(x24362,x24363,x24364))
% 52.66/52.43 [2437]~E(x24371,x24372)+E(f802(x24373,x24371,x24374),f802(x24373,x24372,x24374))
% 52.66/52.43 [2438]~E(x24381,x24382)+E(f802(x24383,x24384,x24381),f802(x24383,x24384,x24382))
% 52.66/52.43 [2439]~E(x24391,x24392)+E(f440(x24391,x24393,x24394,x24395,x24396),f440(x24392,x24393,x24394,x24395,x24396))
% 52.66/52.43 [2440]~E(x24401,x24402)+E(f440(x24403,x24401,x24404,x24405,x24406),f440(x24403,x24402,x24404,x24405,x24406))
% 52.66/52.43 [2441]~E(x24411,x24412)+E(f440(x24413,x24414,x24411,x24415,x24416),f440(x24413,x24414,x24412,x24415,x24416))
% 52.66/52.43 [2442]~E(x24421,x24422)+E(f440(x24423,x24424,x24425,x24421,x24426),f440(x24423,x24424,x24425,x24422,x24426))
% 52.66/52.43 [2443]~E(x24431,x24432)+E(f440(x24433,x24434,x24435,x24436,x24431),f440(x24433,x24434,x24435,x24436,x24432))
% 52.66/52.43 [2444]~E(x24441,x24442)+E(f769(x24441),f769(x24442))
% 52.66/52.43 [2445]~E(x24451,x24452)+E(f344(x24451,x24453),f344(x24452,x24453))
% 52.66/52.43 [2446]~E(x24461,x24462)+E(f344(x24463,x24461),f344(x24463,x24462))
% 52.66/52.43 [2447]~E(x24471,x24472)+E(f563(x24471,x24473,x24474,x24475,x24476,x24477),f563(x24472,x24473,x24474,x24475,x24476,x24477))
% 52.66/52.43 [2448]~E(x24481,x24482)+E(f563(x24483,x24481,x24484,x24485,x24486,x24487),f563(x24483,x24482,x24484,x24485,x24486,x24487))
% 52.66/52.43 [2449]~E(x24491,x24492)+E(f563(x24493,x24494,x24491,x24495,x24496,x24497),f563(x24493,x24494,x24492,x24495,x24496,x24497))
% 52.66/52.43 [2450]~E(x24501,x24502)+E(f563(x24503,x24504,x24505,x24501,x24506,x24507),f563(x24503,x24504,x24505,x24502,x24506,x24507))
% 52.66/52.43 [2451]~E(x24511,x24512)+E(f563(x24513,x24514,x24515,x24516,x24511,x24517),f563(x24513,x24514,x24515,x24516,x24512,x24517))
% 52.66/52.43 [2452]~E(x24521,x24522)+E(f563(x24523,x24524,x24525,x24526,x24527,x24521),f563(x24523,x24524,x24525,x24526,x24527,x24522))
% 52.66/52.43 [2453]~E(x24531,x24532)+E(f555(x24531),f555(x24532))
% 52.66/52.43 [2454]~E(x24541,x24542)+E(f713(x24541,x24543,x24544),f713(x24542,x24543,x24544))
% 52.66/52.43 [2455]~E(x24551,x24552)+E(f713(x24553,x24551,x24554),f713(x24553,x24552,x24554))
% 52.66/52.43 [2456]~E(x24561,x24562)+E(f713(x24563,x24564,x24561),f713(x24563,x24564,x24562))
% 52.66/52.43 [2457]~E(x24571,x24572)+E(f617(x24571),f617(x24572))
% 52.66/52.43 [2458]~E(x24581,x24582)+E(f506(x24581,x24583,x24584),f506(x24582,x24583,x24584))
% 52.66/52.43 [2459]~E(x24591,x24592)+E(f506(x24593,x24591,x24594),f506(x24593,x24592,x24594))
% 52.66/52.43 [2460]~E(x24601,x24602)+E(f506(x24603,x24604,x24601),f506(x24603,x24604,x24602))
% 52.66/52.43 [2461]~E(x24611,x24612)+E(f589(x24611,x24613,x24614),f589(x24612,x24613,x24614))
% 52.66/52.43 [2462]~E(x24621,x24622)+E(f589(x24623,x24621,x24624),f589(x24623,x24622,x24624))
% 52.66/52.43 [2463]~E(x24631,x24632)+E(f589(x24633,x24634,x24631),f589(x24633,x24634,x24632))
% 52.66/52.43 [2464]~E(x24641,x24642)+E(f553(x24641,x24643,x24644),f553(x24642,x24643,x24644))
% 52.66/52.43 [2465]~E(x24651,x24652)+E(f553(x24653,x24651,x24654),f553(x24653,x24652,x24654))
% 52.66/52.43 [2466]~E(x24661,x24662)+E(f553(x24663,x24664,x24661),f553(x24663,x24664,x24662))
% 52.66/52.43 [2467]~E(x24671,x24672)+E(f575(x24671,x24673),f575(x24672,x24673))
% 52.66/52.43 [2468]~E(x24681,x24682)+E(f575(x24683,x24681),f575(x24683,x24682))
% 52.66/52.43 [2469]~E(x24691,x24692)+E(f429(x24691,x24693,x24694,x24695),f429(x24692,x24693,x24694,x24695))
% 52.66/52.43 [2470]~E(x24701,x24702)+E(f429(x24703,x24701,x24704,x24705),f429(x24703,x24702,x24704,x24705))
% 52.66/52.43 [2471]~E(x24711,x24712)+E(f429(x24713,x24714,x24711,x24715),f429(x24713,x24714,x24712,x24715))
% 52.66/52.43 [2472]~E(x24721,x24722)+E(f429(x24723,x24724,x24725,x24721),f429(x24723,x24724,x24725,x24722))
% 52.66/52.43 [2473]~E(x24731,x24732)+E(f348(x24731,x24733,x24734,x24735),f348(x24732,x24733,x24734,x24735))
% 52.66/52.43 [2474]~E(x24741,x24742)+E(f348(x24743,x24741,x24744,x24745),f348(x24743,x24742,x24744,x24745))
% 52.66/52.43 [2475]~E(x24751,x24752)+E(f348(x24753,x24754,x24751,x24755),f348(x24753,x24754,x24752,x24755))
% 52.66/52.43 [2476]~E(x24761,x24762)+E(f348(x24763,x24764,x24765,x24761),f348(x24763,x24764,x24765,x24762))
% 52.66/52.43 [2477]~E(x24771,x24772)+E(f681(x24771,x24773),f681(x24772,x24773))
% 52.66/52.43 [2478]~E(x24781,x24782)+E(f681(x24783,x24781),f681(x24783,x24782))
% 52.66/52.43 [2479]~E(x24791,x24792)+E(f312(x24791,x24793,x24794),f312(x24792,x24793,x24794))
% 52.66/52.43 [2480]~E(x24801,x24802)+E(f312(x24803,x24801,x24804),f312(x24803,x24802,x24804))
% 52.66/52.43 [2481]~E(x24811,x24812)+E(f312(x24813,x24814,x24811),f312(x24813,x24814,x24812))
% 52.66/52.43 [2482]~E(x24821,x24822)+E(f639(x24821,x24823,x24824),f639(x24822,x24823,x24824))
% 52.66/52.43 [2483]~E(x24831,x24832)+E(f639(x24833,x24831,x24834),f639(x24833,x24832,x24834))
% 52.66/52.43 [2484]~E(x24841,x24842)+E(f639(x24843,x24844,x24841),f639(x24843,x24844,x24842))
% 52.66/52.43 [2485]~E(x24851,x24852)+E(f750(x24851,x24853,x24854),f750(x24852,x24853,x24854))
% 52.66/52.43 [2486]~E(x24861,x24862)+E(f750(x24863,x24861,x24864),f750(x24863,x24862,x24864))
% 52.66/52.43 [2487]~E(x24871,x24872)+E(f750(x24873,x24874,x24871),f750(x24873,x24874,x24872))
% 52.66/52.43 [2488]~E(x24881,x24882)+E(f721(x24881,x24883),f721(x24882,x24883))
% 52.66/52.43 [2489]~E(x24891,x24892)+E(f721(x24893,x24891),f721(x24893,x24892))
% 52.66/52.43 [2490]~E(x24901,x24902)+E(f833(x24901,x24903,x24904),f833(x24902,x24903,x24904))
% 52.66/52.43 [2491]~E(x24911,x24912)+E(f833(x24913,x24911,x24914),f833(x24913,x24912,x24914))
% 52.66/52.43 [2492]~E(x24921,x24922)+E(f833(x24923,x24924,x24921),f833(x24923,x24924,x24922))
% 52.66/52.43 [2493]~E(x24931,x24932)+E(f96(x24931,x24933,x24934,x24935),f96(x24932,x24933,x24934,x24935))
% 52.66/52.43 [2494]~E(x24941,x24942)+E(f96(x24943,x24941,x24944,x24945),f96(x24943,x24942,x24944,x24945))
% 52.66/52.43 [2495]~E(x24951,x24952)+E(f96(x24953,x24954,x24951,x24955),f96(x24953,x24954,x24952,x24955))
% 52.66/52.43 [2496]~E(x24961,x24962)+E(f96(x24963,x24964,x24965,x24961),f96(x24963,x24964,x24965,x24962))
% 52.66/52.43 [2497]~E(x24971,x24972)+E(f369(x24971,x24973,x24974,x24975,x24976),f369(x24972,x24973,x24974,x24975,x24976))
% 52.66/52.43 [2498]~E(x24981,x24982)+E(f369(x24983,x24981,x24984,x24985,x24986),f369(x24983,x24982,x24984,x24985,x24986))
% 52.66/52.43 [2499]~E(x24991,x24992)+E(f369(x24993,x24994,x24991,x24995,x24996),f369(x24993,x24994,x24992,x24995,x24996))
% 52.66/52.43 [2500]~E(x25001,x25002)+E(f369(x25003,x25004,x25005,x25001,x25006),f369(x25003,x25004,x25005,x25002,x25006))
% 52.66/52.43 [2501]~E(x25011,x25012)+E(f369(x25013,x25014,x25015,x25016,x25011),f369(x25013,x25014,x25015,x25016,x25012))
% 52.66/52.43 [2502]~E(x25021,x25022)+E(f308(x25021,x25023,x25024),f308(x25022,x25023,x25024))
% 52.66/52.43 [2503]~E(x25031,x25032)+E(f308(x25033,x25031,x25034),f308(x25033,x25032,x25034))
% 52.66/52.43 [2504]~E(x25041,x25042)+E(f308(x25043,x25044,x25041),f308(x25043,x25044,x25042))
% 52.66/52.43 [2505]~E(x25051,x25052)+E(f592(x25051,x25053),f592(x25052,x25053))
% 52.66/52.43 [2506]~E(x25061,x25062)+E(f592(x25063,x25061),f592(x25063,x25062))
% 52.66/52.43 [2507]~E(x25071,x25072)+E(f509(x25071,x25073,x25074,x25075,x25076),f509(x25072,x25073,x25074,x25075,x25076))
% 52.66/52.43 [2508]~E(x25081,x25082)+E(f509(x25083,x25081,x25084,x25085,x25086),f509(x25083,x25082,x25084,x25085,x25086))
% 52.66/52.43 [2509]~E(x25091,x25092)+E(f509(x25093,x25094,x25091,x25095,x25096),f509(x25093,x25094,x25092,x25095,x25096))
% 52.66/52.43 [2510]~E(x25101,x25102)+E(f509(x25103,x25104,x25105,x25101,x25106),f509(x25103,x25104,x25105,x25102,x25106))
% 52.66/52.43 [2511]~E(x25111,x25112)+E(f509(x25113,x25114,x25115,x25116,x25111),f509(x25113,x25114,x25115,x25116,x25112))
% 52.66/52.43 [2512]~E(x25121,x25122)+E(f254(x25121,x25123,x25124,x25125,x25126),f254(x25122,x25123,x25124,x25125,x25126))
% 52.66/52.43 [2513]~E(x25131,x25132)+E(f254(x25133,x25131,x25134,x25135,x25136),f254(x25133,x25132,x25134,x25135,x25136))
% 52.66/52.43 [2514]~E(x25141,x25142)+E(f254(x25143,x25144,x25141,x25145,x25146),f254(x25143,x25144,x25142,x25145,x25146))
% 52.66/52.43 [2515]~E(x25151,x25152)+E(f254(x25153,x25154,x25155,x25151,x25156),f254(x25153,x25154,x25155,x25152,x25156))
% 52.66/52.43 [2516]~E(x25161,x25162)+E(f254(x25163,x25164,x25165,x25166,x25161),f254(x25163,x25164,x25165,x25166,x25162))
% 52.66/52.43 [2517]~E(x25171,x25172)+E(f192(x25171,x25173,x25174,x25175),f192(x25172,x25173,x25174,x25175))
% 52.66/52.43 [2518]~E(x25181,x25182)+E(f192(x25183,x25181,x25184,x25185),f192(x25183,x25182,x25184,x25185))
% 52.66/52.43 [2519]~E(x25191,x25192)+E(f192(x25193,x25194,x25191,x25195),f192(x25193,x25194,x25192,x25195))
% 52.66/52.43 [2520]~E(x25201,x25202)+E(f192(x25203,x25204,x25205,x25201),f192(x25203,x25204,x25205,x25202))
% 52.66/52.43 [2521]~E(x25211,x25212)+E(f673(x25211,x25213,x25214),f673(x25212,x25213,x25214))
% 52.66/52.43 [2522]~E(x25221,x25222)+E(f673(x25223,x25221,x25224),f673(x25223,x25222,x25224))
% 52.66/52.43 [2523]~E(x25231,x25232)+E(f673(x25233,x25234,x25231),f673(x25233,x25234,x25232))
% 52.66/52.43 [2524]~E(x25241,x25242)+E(f490(x25241),f490(x25242))
% 52.66/52.43 [2525]~E(x25251,x25252)+E(f522(x25251,x25253,x25254,x25255),f522(x25252,x25253,x25254,x25255))
% 52.66/52.43 [2526]~E(x25261,x25262)+E(f522(x25263,x25261,x25264,x25265),f522(x25263,x25262,x25264,x25265))
% 52.66/52.43 [2527]~E(x25271,x25272)+E(f522(x25273,x25274,x25271,x25275),f522(x25273,x25274,x25272,x25275))
% 52.66/52.43 [2528]~E(x25281,x25282)+E(f522(x25283,x25284,x25285,x25281),f522(x25283,x25284,x25285,x25282))
% 52.66/52.43 [2529]~E(x25291,x25292)+E(f462(x25291,x25293,x25294),f462(x25292,x25293,x25294))
% 52.66/52.43 [2530]~E(x25301,x25302)+E(f462(x25303,x25301,x25304),f462(x25303,x25302,x25304))
% 52.66/52.43 [2531]~E(x25311,x25312)+E(f462(x25313,x25314,x25311),f462(x25313,x25314,x25312))
% 52.66/52.43 [2532]~E(x25321,x25322)+E(f411(x25321),f411(x25322))
% 52.66/52.43 [2533]~E(x25331,x25332)+E(f398(x25331,x25333,x25334),f398(x25332,x25333,x25334))
% 52.66/52.43 [2534]~E(x25341,x25342)+E(f398(x25343,x25341,x25344),f398(x25343,x25342,x25344))
% 52.66/52.43 [2535]~E(x25351,x25352)+E(f398(x25353,x25354,x25351),f398(x25353,x25354,x25352))
% 52.66/52.43 [2536]~E(x25361,x25362)+E(f749(x25361,x25363,x25364),f749(x25362,x25363,x25364))
% 52.66/52.43 [2537]~E(x25371,x25372)+E(f749(x25373,x25371,x25374),f749(x25373,x25372,x25374))
% 52.66/52.43 [2538]~E(x25381,x25382)+E(f749(x25383,x25384,x25381),f749(x25383,x25384,x25382))
% 52.66/52.43 [2539]~E(x25391,x25392)+E(f556(x25391),f556(x25392))
% 52.66/52.43 [2540]~E(x25401,x25402)+E(f594(x25401,x25403,x25404,x25405),f594(x25402,x25403,x25404,x25405))
% 52.66/52.43 [2541]~E(x25411,x25412)+E(f594(x25413,x25411,x25414,x25415),f594(x25413,x25412,x25414,x25415))
% 52.66/52.43 [2542]~E(x25421,x25422)+E(f594(x25423,x25424,x25421,x25425),f594(x25423,x25424,x25422,x25425))
% 52.66/52.43 [2543]~E(x25431,x25432)+E(f594(x25433,x25434,x25435,x25431),f594(x25433,x25434,x25435,x25432))
% 52.66/52.43 [2544]~E(x25441,x25442)+E(f524(x25441,x25443,x25444,x25445),f524(x25442,x25443,x25444,x25445))
% 52.66/52.43 [2545]~E(x25451,x25452)+E(f524(x25453,x25451,x25454,x25455),f524(x25453,x25452,x25454,x25455))
% 52.66/52.43 [2546]~E(x25461,x25462)+E(f524(x25463,x25464,x25461,x25465),f524(x25463,x25464,x25462,x25465))
% 52.66/52.43 [2547]~E(x25471,x25472)+E(f524(x25473,x25474,x25475,x25471),f524(x25473,x25474,x25475,x25472))
% 52.66/52.43 [2548]~P1(x25481)+P1(x25482)+~E(x25481,x25482)
% 52.66/52.43 [2549]~P2(x25491)+P2(x25492)+~E(x25491,x25492)
% 52.66/52.43 [2550]~P100(x25501)+P100(x25502)+~E(x25501,x25502)
% 52.66/52.43 [2551]~P93(x25511)+P93(x25512)+~E(x25511,x25512)
% 52.66/52.43 [2552]~P3(x25521)+P3(x25522)+~E(x25521,x25522)
% 52.66/52.43 [2553]P41(x25532,x25533,x25534,x25535)+~E(x25531,x25532)+~P41(x25531,x25533,x25534,x25535)
% 52.66/52.43 [2554]P41(x25543,x25542,x25544,x25545)+~E(x25541,x25542)+~P41(x25543,x25541,x25544,x25545)
% 52.66/52.43 [2555]P41(x25553,x25554,x25552,x25555)+~E(x25551,x25552)+~P41(x25553,x25554,x25551,x25555)
% 52.66/52.43 [2556]P41(x25563,x25564,x25565,x25562)+~E(x25561,x25562)+~P41(x25563,x25564,x25565,x25561)
% 52.66/52.43 [2557]~P15(x25571)+P15(x25572)+~E(x25571,x25572)
% 52.66/52.43 [2558]~P73(x25581)+P73(x25582)+~E(x25581,x25582)
% 52.66/52.43 [2559]P38(x25592,x25593)+~E(x25591,x25592)+~P38(x25591,x25593)
% 52.66/52.43 [2560]P38(x25603,x25602)+~E(x25601,x25602)+~P38(x25603,x25601)
% 52.66/52.43 [2561]P31(x25612,x25613,x25614,x25615)+~E(x25611,x25612)+~P31(x25611,x25613,x25614,x25615)
% 52.66/52.43 [2562]P31(x25623,x25622,x25624,x25625)+~E(x25621,x25622)+~P31(x25623,x25621,x25624,x25625)
% 52.66/52.43 [2563]P31(x25633,x25634,x25632,x25635)+~E(x25631,x25632)+~P31(x25633,x25634,x25631,x25635)
% 52.66/52.43 [2564]P31(x25643,x25644,x25645,x25642)+~E(x25641,x25642)+~P31(x25643,x25644,x25645,x25641)
% 52.66/52.43 [2565]~P4(x25651)+P4(x25652)+~E(x25651,x25652)
% 52.66/52.43 [2566]~P110(x25661)+P110(x25662)+~E(x25661,x25662)
% 52.66/52.43 [2567]P33(x25672,x25673,x25674)+~E(x25671,x25672)+~P33(x25671,x25673,x25674)
% 52.66/52.43 [2568]P33(x25683,x25682,x25684)+~E(x25681,x25682)+~P33(x25683,x25681,x25684)
% 52.66/52.43 [2569]P33(x25693,x25694,x25692)+~E(x25691,x25692)+~P33(x25693,x25694,x25691)
% 52.66/52.43 [2570]~P68(x25701)+P68(x25702)+~E(x25701,x25702)
% 52.66/52.43 [2571]~P137(x25711)+P137(x25712)+~E(x25711,x25712)
% 52.66/52.43 [2572]~P64(x25721)+P64(x25722)+~E(x25721,x25722)
% 52.66/52.43 [2573]~P74(x25731)+P74(x25732)+~E(x25731,x25732)
% 52.66/52.43 [2574]P140(x25742,x25743,x25744)+~E(x25741,x25742)+~P140(x25741,x25743,x25744)
% 52.66/52.43 [2575]P140(x25753,x25752,x25754)+~E(x25751,x25752)+~P140(x25753,x25751,x25754)
% 52.66/52.43 [2576]P140(x25763,x25764,x25762)+~E(x25761,x25762)+~P140(x25763,x25764,x25761)
% 52.66/52.43 [2577]P141(x25772,x25773,x25774)+~E(x25771,x25772)+~P141(x25771,x25773,x25774)
% 52.66/52.43 [2578]P141(x25783,x25782,x25784)+~E(x25781,x25782)+~P141(x25783,x25781,x25784)
% 52.66/52.43 [2579]P141(x25793,x25794,x25792)+~E(x25791,x25792)+~P141(x25793,x25794,x25791)
% 52.66/52.43 [2580]~P5(x25801)+P5(x25802)+~E(x25801,x25802)
% 52.66/52.43 [2581]~P117(x25811)+P117(x25812)+~E(x25811,x25812)
% 52.66/52.43 [2582]~P123(x25821)+P123(x25822)+~E(x25821,x25822)
% 52.66/52.43 [2583]~P6(x25831)+P6(x25832)+~E(x25831,x25832)
% 52.66/52.43 [2584]P25(x25842,x25843,x25844,x25845)+~E(x25841,x25842)+~P25(x25841,x25843,x25844,x25845)
% 52.66/52.43 [2585]P25(x25853,x25852,x25854,x25855)+~E(x25851,x25852)+~P25(x25853,x25851,x25854,x25855)
% 52.66/52.43 [2586]P25(x25863,x25864,x25862,x25865)+~E(x25861,x25862)+~P25(x25863,x25864,x25861,x25865)
% 52.66/52.43 [2587]P25(x25873,x25874,x25875,x25872)+~E(x25871,x25872)+~P25(x25873,x25874,x25875,x25871)
% 52.66/52.43 [2588]~P118(x25881)+P118(x25882)+~E(x25881,x25882)
% 52.66/52.43 [2589]~P7(x25891)+P7(x25892)+~E(x25891,x25892)
% 52.66/52.43 [2590]~P89(x25901)+P89(x25902)+~E(x25901,x25902)
% 52.66/52.43 [2591]~P99(x25911)+P99(x25912)+~E(x25911,x25912)
% 52.66/52.43 [2592]~P75(x25921)+P75(x25922)+~E(x25921,x25922)
% 52.66/52.43 [2593]~P40(x25931)+P40(x25932)+~E(x25931,x25932)
% 52.66/52.43 [2594]~P9(x25941)+P9(x25942)+~E(x25941,x25942)
% 52.66/52.43 [2595]~P81(x25951)+P81(x25952)+~E(x25951,x25952)
% 52.66/52.43 [2596]~P88(x25961)+P88(x25962)+~E(x25961,x25962)
% 52.66/52.43 [2597]~P70(x25971)+P70(x25972)+~E(x25971,x25972)
% 52.66/52.43 [2598]~P82(x25981)+P82(x25982)+~E(x25981,x25982)
% 52.66/52.43 [2599]~P78(x25991)+P78(x25992)+~E(x25991,x25992)
% 52.66/52.43 [2600]~P133(x26001)+P133(x26002)+~E(x26001,x26002)
% 52.66/52.43 [2601]~P98(x26011)+P98(x26012)+~E(x26011,x26012)
% 52.66/52.43 [2602]~P65(x26021)+P65(x26022)+~E(x26021,x26022)
% 52.66/52.43 [2603]~P80(x26031)+P80(x26032)+~E(x26031,x26032)
% 52.66/52.43 [2604]P30(x26042,x26043,x26044)+~E(x26041,x26042)+~P30(x26041,x26043,x26044)
% 52.66/52.43 [2605]P30(x26053,x26052,x26054)+~E(x26051,x26052)+~P30(x26053,x26051,x26054)
% 52.66/52.43 [2606]P30(x26063,x26064,x26062)+~E(x26061,x26062)+~P30(x26063,x26064,x26061)
% 52.66/52.43 [2607]~P86(x26071)+P86(x26072)+~E(x26071,x26072)
% 52.66/52.43 [2608]~P119(x26081)+P119(x26082)+~E(x26081,x26082)
% 52.66/52.43 [2609]P60(x26092,x26093)+~E(x26091,x26092)+~P60(x26091,x26093)
% 52.66/52.43 [2610]P60(x26103,x26102)+~E(x26101,x26102)+~P60(x26103,x26101)
% 52.66/52.43 [2611]~P127(x26111)+P127(x26112)+~E(x26111,x26112)
% 52.66/52.43 [2612]~P69(x26121)+P69(x26122)+~E(x26121,x26122)
% 52.66/52.43 [2613]P49(x26132,x26133,x26134)+~E(x26131,x26132)+~P49(x26131,x26133,x26134)
% 52.66/52.43 [2614]P49(x26143,x26142,x26144)+~E(x26141,x26142)+~P49(x26143,x26141,x26144)
% 52.66/52.43 [2615]P49(x26153,x26154,x26152)+~E(x26151,x26152)+~P49(x26153,x26154,x26151)
% 52.66/52.43 [2616]P36(x26162,x26163,x26164,x26165)+~E(x26161,x26162)+~P36(x26161,x26163,x26164,x26165)
% 52.66/52.43 [2617]P36(x26173,x26172,x26174,x26175)+~E(x26171,x26172)+~P36(x26173,x26171,x26174,x26175)
% 52.66/52.43 [2618]P36(x26183,x26184,x26182,x26185)+~E(x26181,x26182)+~P36(x26183,x26184,x26181,x26185)
% 52.66/52.43 [2619]P36(x26193,x26194,x26195,x26192)+~E(x26191,x26192)+~P36(x26193,x26194,x26195,x26191)
% 52.66/52.43 [2620]~P103(x26201)+P103(x26202)+~E(x26201,x26202)
% 52.66/52.43 [2621]P22(x26212,x26213,x26214)+~E(x26211,x26212)+~P22(x26211,x26213,x26214)
% 52.66/52.43 [2622]P22(x26223,x26222,x26224)+~E(x26221,x26222)+~P22(x26223,x26221,x26224)
% 52.66/52.43 [2623]P22(x26233,x26234,x26232)+~E(x26231,x26232)+~P22(x26233,x26234,x26231)
% 52.66/52.43 [2624]~P136(x26241)+P136(x26242)+~E(x26241,x26242)
% 52.66/52.43 [2625]~P102(x26251)+P102(x26252)+~E(x26251,x26252)
% 52.66/52.43 [2626]~P11(x26261)+P11(x26262)+~E(x26261,x26262)
% 52.66/52.43 [2627]P20(x26272,x26273)+~E(x26271,x26272)+~P20(x26271,x26273)
% 52.66/52.43 [2628]P20(x26283,x26282)+~E(x26281,x26282)+~P20(x26283,x26281)
% 52.66/52.43 [2629]P14(x26292,x26293,x26294)+~E(x26291,x26292)+~P14(x26291,x26293,x26294)
% 52.66/52.43 [2630]P14(x26303,x26302,x26304)+~E(x26301,x26302)+~P14(x26303,x26301,x26304)
% 52.66/52.43 [2631]P14(x26313,x26314,x26312)+~E(x26311,x26312)+~P14(x26313,x26314,x26311)
% 52.66/52.43 [2632]~P111(x26321)+P111(x26322)+~E(x26321,x26322)
% 52.66/52.43 [2633]P35(x26332,x26333)+~E(x26331,x26332)+~P35(x26331,x26333)
% 52.66/52.43 [2634]P35(x26343,x26342)+~E(x26341,x26342)+~P35(x26343,x26341)
% 52.66/52.43 [2635]~P91(x26351)+P91(x26352)+~E(x26351,x26352)
% 52.66/52.43 [2636]~P121(x26361)+P121(x26362)+~E(x26361,x26362)
% 52.66/52.43 [2637]~P105(x26371)+P105(x26372)+~E(x26371,x26372)
% 52.66/52.43 [2638]~P120(x26381)+P120(x26382)+~E(x26381,x26382)
% 52.66/52.43 [2639]P55(x26392,x26393,x26394)+~E(x26391,x26392)+~P55(x26391,x26393,x26394)
% 52.66/52.43 [2640]P55(x26403,x26402,x26404)+~E(x26401,x26402)+~P55(x26403,x26401,x26404)
% 52.66/52.43 [2641]P55(x26413,x26414,x26412)+~E(x26411,x26412)+~P55(x26413,x26414,x26411)
% 52.66/52.43 [2642]~P66(x26421)+P66(x26422)+~E(x26421,x26422)
% 52.66/52.43 [2643]~P134(x26431)+P134(x26432)+~E(x26431,x26432)
% 52.66/52.43 [2644]P58(x26442,x26443)+~E(x26441,x26442)+~P58(x26441,x26443)
% 52.66/52.43 [2645]P58(x26453,x26452)+~E(x26451,x26452)+~P58(x26453,x26451)
% 52.66/52.43 [2646]~P129(x26461)+P129(x26462)+~E(x26461,x26462)
% 52.66/52.43 [2647]~P87(x26471)+P87(x26472)+~E(x26471,x26472)
% 52.66/52.43 [2648]P17(x26482,x26483,x26484,x26485,x26486)+~E(x26481,x26482)+~P17(x26481,x26483,x26484,x26485,x26486)
% 52.66/52.43 [2649]P17(x26493,x26492,x26494,x26495,x26496)+~E(x26491,x26492)+~P17(x26493,x26491,x26494,x26495,x26496)
% 52.66/52.43 [2650]P17(x26503,x26504,x26502,x26505,x26506)+~E(x26501,x26502)+~P17(x26503,x26504,x26501,x26505,x26506)
% 52.66/52.43 [2651]P17(x26513,x26514,x26515,x26512,x26516)+~E(x26511,x26512)+~P17(x26513,x26514,x26515,x26511,x26516)
% 52.66/52.43 [2652]P17(x26523,x26524,x26525,x26526,x26522)+~E(x26521,x26522)+~P17(x26523,x26524,x26525,x26526,x26521)
% 52.66/52.43 [2653]P44(x26532,x26533)+~E(x26531,x26532)+~P44(x26531,x26533)
% 52.66/52.43 [2654]P44(x26543,x26542)+~E(x26541,x26542)+~P44(x26543,x26541)
% 52.66/52.43 [2655]P19(x26552,x26553,x26554,x26555,x26556,x26557)+~E(x26551,x26552)+~P19(x26551,x26553,x26554,x26555,x26556,x26557)
% 52.66/52.43 [2656]P19(x26563,x26562,x26564,x26565,x26566,x26567)+~E(x26561,x26562)+~P19(x26563,x26561,x26564,x26565,x26566,x26567)
% 52.66/52.43 [2657]P19(x26573,x26574,x26572,x26575,x26576,x26577)+~E(x26571,x26572)+~P19(x26573,x26574,x26571,x26575,x26576,x26577)
% 52.66/52.43 [2658]P19(x26583,x26584,x26585,x26582,x26586,x26587)+~E(x26581,x26582)+~P19(x26583,x26584,x26585,x26581,x26586,x26587)
% 52.66/52.43 [2659]P19(x26593,x26594,x26595,x26596,x26592,x26597)+~E(x26591,x26592)+~P19(x26593,x26594,x26595,x26596,x26591,x26597)
% 52.66/52.43 [2660]P19(x26603,x26604,x26605,x26606,x26607,x26602)+~E(x26601,x26602)+~P19(x26603,x26604,x26605,x26606,x26607,x26601)
% 52.66/52.43 [2661]~P76(x26611)+P76(x26612)+~E(x26611,x26612)
% 52.66/52.43 [2662]~P109(x26621)+P109(x26622)+~E(x26621,x26622)
% 52.66/52.43 [2663]~P101(x26631)+P101(x26632)+~E(x26631,x26632)
% 52.66/52.43 [2664]~P77(x26641)+P77(x26642)+~E(x26641,x26642)
% 52.66/52.43 [2665]P47(x26652,x26653,x26654)+~E(x26651,x26652)+~P47(x26651,x26653,x26654)
% 52.66/52.43 [2666]P47(x26663,x26662,x26664)+~E(x26661,x26662)+~P47(x26663,x26661,x26664)
% 52.66/52.43 [2667]P47(x26673,x26674,x26672)+~E(x26671,x26672)+~P47(x26673,x26674,x26671)
% 52.66/52.43 [2668]~P95(x26681)+P95(x26682)+~E(x26681,x26682)
% 52.66/52.43 [2669]~P92(x26691)+P92(x26692)+~E(x26691,x26692)
% 52.66/52.43 [2670]~P104(x26701)+P104(x26702)+~E(x26701,x26702)
% 52.66/52.43 [2671]~P10(x26711)+P10(x26712)+~E(x26711,x26712)
% 52.66/52.43 [2672]~P8(x26721)+P8(x26722)+~E(x26721,x26722)
% 52.66/52.43 [2673]~P122(x26731)+P122(x26732)+~E(x26731,x26732)
% 52.66/52.43 [2674]P144(x26742,x26743)+~E(x26741,x26742)+~P144(x26741,x26743)
% 52.66/52.43 [2675]P144(x26753,x26752)+~E(x26751,x26752)+~P144(x26753,x26751)
% 52.66/52.43 [2676]~P12(x26761)+P12(x26762)+~E(x26761,x26762)
% 52.66/52.43 [2677]~P62(x26771)+P62(x26772)+~E(x26771,x26772)
% 52.66/52.43 [2678]~P112(x26781)+P112(x26782)+~E(x26781,x26782)
% 52.66/52.43 [2679]~P128(x26791)+P128(x26792)+~E(x26791,x26792)
% 52.66/52.43 [2680]~P113(x26801)+P113(x26802)+~E(x26801,x26802)
% 52.66/52.43 [2681]~P138(x26811)+P138(x26812)+~E(x26811,x26812)
% 52.66/52.43 [2682]P24(x26822,x26823,x26824)+~E(x26821,x26822)+~P24(x26821,x26823,x26824)
% 52.66/52.43 [2683]P24(x26833,x26832,x26834)+~E(x26831,x26832)+~P24(x26833,x26831,x26834)
% 52.66/52.43 [2684]P24(x26843,x26844,x26842)+~E(x26841,x26842)+~P24(x26843,x26844,x26841)
% 52.66/52.43 [2685]P54(x26852,x26853,x26854,x26855)+~E(x26851,x26852)+~P54(x26851,x26853,x26854,x26855)
% 52.66/52.43 [2686]P54(x26863,x26862,x26864,x26865)+~E(x26861,x26862)+~P54(x26863,x26861,x26864,x26865)
% 52.66/52.43 [2687]P54(x26873,x26874,x26872,x26875)+~E(x26871,x26872)+~P54(x26873,x26874,x26871,x26875)
% 52.66/52.43 [2688]P54(x26883,x26884,x26885,x26882)+~E(x26881,x26882)+~P54(x26883,x26884,x26885,x26881)
% 52.66/52.43 [2689]P56(x26892,x26893,x26894)+~E(x26891,x26892)+~P56(x26891,x26893,x26894)
% 52.66/52.43 [2690]P56(x26903,x26902,x26904)+~E(x26901,x26902)+~P56(x26903,x26901,x26904)
% 52.66/52.43 [2691]P56(x26913,x26914,x26912)+~E(x26911,x26912)+~P56(x26913,x26914,x26911)
% 52.66/52.43 [2692]P142(x26922,x26923)+~E(x26921,x26922)+~P142(x26921,x26923)
% 52.66/52.43 [2693]P142(x26933,x26932)+~E(x26931,x26932)+~P142(x26933,x26931)
% 52.66/52.43 [2694]~P90(x26941)+P90(x26942)+~E(x26941,x26942)
% 52.66/52.43 [2695]~P135(x26951)+P135(x26952)+~E(x26951,x26952)
% 52.66/52.43 [2696]P18(x26962,x26963,x26964,x26965)+~E(x26961,x26962)+~P18(x26961,x26963,x26964,x26965)
% 52.66/52.43 [2697]P18(x26973,x26972,x26974,x26975)+~E(x26971,x26972)+~P18(x26973,x26971,x26974,x26975)
% 52.66/52.43 [2698]P18(x26983,x26984,x26982,x26985)+~E(x26981,x26982)+~P18(x26983,x26984,x26981,x26985)
% 52.66/52.43 [2699]P18(x26993,x26994,x26995,x26992)+~E(x26991,x26992)+~P18(x26993,x26994,x26995,x26991)
% 52.66/52.43 [2700]~P63(x27001)+P63(x27002)+~E(x27001,x27002)
% 52.66/52.43 [2701]P21(x27012,x27013,x27014)+~E(x27011,x27012)+~P21(x27011,x27013,x27014)
% 52.66/52.43 [2702]P21(x27023,x27022,x27024)+~E(x27021,x27022)+~P21(x27023,x27021,x27024)
% 52.66/52.43 [2703]P21(x27033,x27034,x27032)+~E(x27031,x27032)+~P21(x27033,x27034,x27031)
% 52.66/52.43 [2704]~P85(x27041)+P85(x27042)+~E(x27041,x27042)
% 52.66/52.43 [2705]~P83(x27051)+P83(x27052)+~E(x27051,x27052)
% 52.66/52.43 [2706]P43(x27062,x27063,x27064,x27065,x27066,x27067)+~E(x27061,x27062)+~P43(x27061,x27063,x27064,x27065,x27066,x27067)
% 52.66/52.43 [2707]P43(x27073,x27072,x27074,x27075,x27076,x27077)+~E(x27071,x27072)+~P43(x27073,x27071,x27074,x27075,x27076,x27077)
% 52.66/52.43 [2708]P43(x27083,x27084,x27082,x27085,x27086,x27087)+~E(x27081,x27082)+~P43(x27083,x27084,x27081,x27085,x27086,x27087)
% 52.66/52.43 [2709]P43(x27093,x27094,x27095,x27092,x27096,x27097)+~E(x27091,x27092)+~P43(x27093,x27094,x27095,x27091,x27096,x27097)
% 52.66/52.43 [2710]P43(x27103,x27104,x27105,x27106,x27102,x27107)+~E(x27101,x27102)+~P43(x27103,x27104,x27105,x27106,x27101,x27107)
% 52.66/52.43 [2711]P43(x27113,x27114,x27115,x27116,x27117,x27112)+~E(x27111,x27112)+~P43(x27113,x27114,x27115,x27116,x27117,x27111)
% 52.66/52.43 [2712]P59(x27122,x27123,x27124,x27125)+~E(x27121,x27122)+~P59(x27121,x27123,x27124,x27125)
% 52.66/52.43 [2713]P59(x27133,x27132,x27134,x27135)+~E(x27131,x27132)+~P59(x27133,x27131,x27134,x27135)
% 52.66/52.43 [2714]P59(x27143,x27144,x27142,x27145)+~E(x27141,x27142)+~P59(x27143,x27144,x27141,x27145)
% 52.66/52.43 [2715]P59(x27153,x27154,x27155,x27152)+~E(x27151,x27152)+~P59(x27153,x27154,x27155,x27151)
% 52.66/52.43 [2716]~P115(x27161)+P115(x27162)+~E(x27161,x27162)
% 52.66/52.43 [2717]~P124(x27171)+P124(x27172)+~E(x27171,x27172)
% 52.66/52.43 [2718]~P132(x27181)+P132(x27182)+~E(x27181,x27182)
% 52.66/52.43 [2719]~P114(x27191)+P114(x27192)+~E(x27191,x27192)
% 52.66/52.43 [2720]P57(x27202,x27203,x27204,x27205,x27206)+~E(x27201,x27202)+~P57(x27201,x27203,x27204,x27205,x27206)
% 52.66/52.43 [2721]P57(x27213,x27212,x27214,x27215,x27216)+~E(x27211,x27212)+~P57(x27213,x27211,x27214,x27215,x27216)
% 52.66/52.43 [2722]P57(x27223,x27224,x27222,x27225,x27226)+~E(x27221,x27222)+~P57(x27223,x27224,x27221,x27225,x27226)
% 52.66/52.43 [2723]P57(x27233,x27234,x27235,x27232,x27236)+~E(x27231,x27232)+~P57(x27233,x27234,x27235,x27231,x27236)
% 52.66/52.43 [2724]P57(x27243,x27244,x27245,x27246,x27242)+~E(x27241,x27242)+~P57(x27243,x27244,x27245,x27246,x27241)
% 52.66/52.43 [2725]~P79(x27251)+P79(x27252)+~E(x27251,x27252)
% 52.66/52.43 [2726]P53(x27262,x27263,x27264,x27265,x27266,x27267,x27268)+~E(x27261,x27262)+~P53(x27261,x27263,x27264,x27265,x27266,x27267,x27268)
% 52.66/52.43 [2727]P53(x27273,x27272,x27274,x27275,x27276,x27277,x27278)+~E(x27271,x27272)+~P53(x27273,x27271,x27274,x27275,x27276,x27277,x27278)
% 52.66/52.43 [2728]P53(x27283,x27284,x27282,x27285,x27286,x27287,x27288)+~E(x27281,x27282)+~P53(x27283,x27284,x27281,x27285,x27286,x27287,x27288)
% 52.66/52.43 [2729]P53(x27293,x27294,x27295,x27292,x27296,x27297,x27298)+~E(x27291,x27292)+~P53(x27293,x27294,x27295,x27291,x27296,x27297,x27298)
% 52.66/52.43 [2730]P53(x27303,x27304,x27305,x27306,x27302,x27307,x27308)+~E(x27301,x27302)+~P53(x27303,x27304,x27305,x27306,x27301,x27307,x27308)
% 52.66/52.43 [2731]P53(x27313,x27314,x27315,x27316,x27317,x27312,x27318)+~E(x27311,x27312)+~P53(x27313,x27314,x27315,x27316,x27317,x27311,x27318)
% 52.66/52.43 [2732]P53(x27323,x27324,x27325,x27326,x27327,x27328,x27322)+~E(x27321,x27322)+~P53(x27323,x27324,x27325,x27326,x27327,x27328,x27321)
% 52.66/52.43 [2733]~P67(x27331)+P67(x27332)+~E(x27331,x27332)
% 52.66/52.43 [2734]~P96(x27341)+P96(x27342)+~E(x27341,x27342)
% 52.66/52.43 [2735]~P94(x27351)+P94(x27352)+~E(x27351,x27352)
% 52.66/52.43 [2736]~P106(x27361)+P106(x27362)+~E(x27361,x27362)
% 52.66/52.43 [2737]P23(x27372,x27373,x27374)+~E(x27371,x27372)+~P23(x27371,x27373,x27374)
% 52.66/52.43 [2738]P23(x27383,x27382,x27384)+~E(x27381,x27382)+~P23(x27383,x27381,x27384)
% 52.66/52.43 [2739]P23(x27393,x27394,x27392)+~E(x27391,x27392)+~P23(x27393,x27394,x27391)
% 52.66/52.43 [2740]~P131(x27401)+P131(x27402)+~E(x27401,x27402)
% 52.66/52.43 [2741]P42(x27412,x27413,x27414,x27415)+~E(x27411,x27412)+~P42(x27411,x27413,x27414,x27415)
% 52.66/52.43 [2742]P42(x27423,x27422,x27424,x27425)+~E(x27421,x27422)+~P42(x27423,x27421,x27424,x27425)
% 52.66/52.43 [2743]P42(x27433,x27434,x27432,x27435)+~E(x27431,x27432)+~P42(x27433,x27434,x27431,x27435)
% 52.66/52.43 [2744]P42(x27443,x27444,x27445,x27442)+~E(x27441,x27442)+~P42(x27443,x27444,x27445,x27441)
% 52.66/52.43 [2745]~P72(x27451)+P72(x27452)+~E(x27451,x27452)
% 52.66/52.43 [2746]~P130(x27461)+P130(x27462)+~E(x27461,x27462)
% 52.66/52.43 [2747]P28(x27472,x27473,x27474,x27475,x27476,x27477)+~E(x27471,x27472)+~P28(x27471,x27473,x27474,x27475,x27476,x27477)
% 52.66/52.43 [2748]P28(x27483,x27482,x27484,x27485,x27486,x27487)+~E(x27481,x27482)+~P28(x27483,x27481,x27484,x27485,x27486,x27487)
% 52.66/52.43 [2749]P28(x27493,x27494,x27492,x27495,x27496,x27497)+~E(x27491,x27492)+~P28(x27493,x27494,x27491,x27495,x27496,x27497)
% 52.66/52.43 [2750]P28(x27503,x27504,x27505,x27502,x27506,x27507)+~E(x27501,x27502)+~P28(x27503,x27504,x27505,x27501,x27506,x27507)
% 52.66/52.43 [2751]P28(x27513,x27514,x27515,x27516,x27512,x27517)+~E(x27511,x27512)+~P28(x27513,x27514,x27515,x27516,x27511,x27517)
% 52.66/52.43 [2752]P28(x27523,x27524,x27525,x27526,x27527,x27522)+~E(x27521,x27522)+~P28(x27523,x27524,x27525,x27526,x27527,x27521)
% 52.66/52.43 [2753]P29(x27532,x27533,x27534,x27535,x27536,x27537)+~E(x27531,x27532)+~P29(x27531,x27533,x27534,x27535,x27536,x27537)
% 52.66/52.43 [2754]P29(x27543,x27542,x27544,x27545,x27546,x27547)+~E(x27541,x27542)+~P29(x27543,x27541,x27544,x27545,x27546,x27547)
% 52.66/52.43 [2755]P29(x27553,x27554,x27552,x27555,x27556,x27557)+~E(x27551,x27552)+~P29(x27553,x27554,x27551,x27555,x27556,x27557)
% 52.66/52.43 [2756]P29(x27563,x27564,x27565,x27562,x27566,x27567)+~E(x27561,x27562)+~P29(x27563,x27564,x27565,x27561,x27566,x27567)
% 52.66/52.43 [2757]P29(x27573,x27574,x27575,x27576,x27572,x27577)+~E(x27571,x27572)+~P29(x27573,x27574,x27575,x27576,x27571,x27577)
% 52.66/52.43 [2758]P29(x27583,x27584,x27585,x27586,x27587,x27582)+~E(x27581,x27582)+~P29(x27583,x27584,x27585,x27586,x27587,x27581)
% 52.66/52.43 [2759]~P125(x27591)+P125(x27592)+~E(x27591,x27592)
% 52.66/52.43 [2760]P13(x27602,x27603)+~E(x27601,x27602)+~P13(x27601,x27603)
% 52.66/52.43 [2761]P13(x27613,x27612)+~E(x27611,x27612)+~P13(x27613,x27611)
% 52.66/52.43 [2762]~P61(x27621)+P61(x27622)+~E(x27621,x27622)
% 52.66/52.43 [2763]~P126(x27631)+P126(x27632)+~E(x27631,x27632)
% 52.66/52.43 [2764]P26(x27642,x27643,x27644,x27645)+~E(x27641,x27642)+~P26(x27641,x27643,x27644,x27645)
% 52.66/52.43 [2765]P26(x27653,x27652,x27654,x27655)+~E(x27651,x27652)+~P26(x27653,x27651,x27654,x27655)
% 52.66/52.43 [2766]P26(x27663,x27664,x27662,x27665)+~E(x27661,x27662)+~P26(x27663,x27664,x27661,x27665)
% 52.66/52.43 [2767]P26(x27673,x27674,x27675,x27672)+~E(x27671,x27672)+~P26(x27673,x27674,x27675,x27671)
% 52.66/52.43 [2768]P52(x27682,x27683,x27684,x27685)+~E(x27681,x27682)+~P52(x27681,x27683,x27684,x27685)
% 52.66/52.43 [2769]P52(x27693,x27692,x27694,x27695)+~E(x27691,x27692)+~P52(x27693,x27691,x27694,x27695)
% 52.66/52.43 [2770]P52(x27703,x27704,x27702,x27705)+~E(x27701,x27702)+~P52(x27703,x27704,x27701,x27705)
% 52.66/52.43 [2771]P52(x27713,x27714,x27715,x27712)+~E(x27711,x27712)+~P52(x27713,x27714,x27715,x27711)
% 52.66/52.43 [2772]P32(x27722,x27723)+~E(x27721,x27722)+~P32(x27721,x27723)
% 52.66/52.43 [2773]P32(x27733,x27732)+~E(x27731,x27732)+~P32(x27733,x27731)
% 52.66/52.43 [2774]P34(x27742,x27743,x27744)+~E(x27741,x27742)+~P34(x27741,x27743,x27744)
% 52.66/52.43 [2775]P34(x27753,x27752,x27754)+~E(x27751,x27752)+~P34(x27753,x27751,x27754)
% 52.66/52.43 [2776]P34(x27763,x27764,x27762)+~E(x27761,x27762)+~P34(x27763,x27764,x27761)
% 52.66/52.43 [2777]P50(x27772,x27773)+~E(x27771,x27772)+~P50(x27771,x27773)
% 52.66/52.43 [2778]P50(x27783,x27782)+~E(x27781,x27782)+~P50(x27783,x27781)
% 52.66/52.43 [2779]~P97(x27791)+P97(x27792)+~E(x27791,x27792)
% 52.66/52.43 [2780]~P84(x27801)+P84(x27802)+~E(x27801,x27802)
% 52.66/52.43 [2781]~P71(x27811)+P71(x27812)+~E(x27811,x27812)
% 52.66/52.43 [2782]~P107(x27821)+P107(x27822)+~E(x27821,x27822)
% 52.66/52.43 [2783]P48(x27832,x27833,x27834)+~E(x27831,x27832)+~P48(x27831,x27833,x27834)
% 52.66/52.43 [2784]P48(x27843,x27842,x27844)+~E(x27841,x27842)+~P48(x27843,x27841,x27844)
% 52.66/52.43 [2785]P48(x27853,x27854,x27852)+~E(x27851,x27852)+~P48(x27853,x27854,x27851)
% 52.66/52.43 [2786]~P108(x27861)+P108(x27862)+~E(x27861,x27862)
% 52.66/52.43 [2787]P51(x27872,x27873)+~E(x27871,x27872)+~P51(x27871,x27873)
% 52.66/52.43 [2788]P51(x27883,x27882)+~E(x27881,x27882)+~P51(x27883,x27881)
% 52.66/52.43 [2789]P39(x27892,x27893)+~E(x27891,x27892)+~P39(x27891,x27893)
% 52.66/52.43 [2790]P39(x27903,x27902)+~E(x27901,x27902)+~P39(x27903,x27901)
% 52.66/52.43 [2791]~P37(x27911)+P37(x27912)+~E(x27911,x27912)
% 52.66/52.43 [2792]P27(x27922,x27923,x27924,x27925,x27926)+~E(x27921,x27922)+~P27(x27921,x27923,x27924,x27925,x27926)
% 52.66/52.43 [2793]P27(x27933,x27932,x27934,x27935,x27936)+~E(x27931,x27932)+~P27(x27933,x27931,x27934,x27935,x27936)
% 52.66/52.43 [2794]P27(x27943,x27944,x27942,x27945,x27946)+~E(x27941,x27942)+~P27(x27943,x27944,x27941,x27945,x27946)
% 52.66/52.43 [2795]P27(x27953,x27954,x27955,x27952,x27956)+~E(x27951,x27952)+~P27(x27953,x27954,x27955,x27951,x27956)
% 52.66/52.43 [2796]P27(x27963,x27964,x27965,x27966,x27962)+~E(x27961,x27962)+~P27(x27963,x27964,x27965,x27966,x27961)
% 52.66/52.43 [2797]P46(x27972,x27973)+~E(x27971,x27972)+~P46(x27971,x27973)
% 52.66/52.43 [2798]P46(x27983,x27982)+~E(x27981,x27982)+~P46(x27983,x27981)
% 52.66/52.43 [2799]~P45(x27991)+P45(x27992)+~E(x27991,x27992)
% 52.66/52.43 [2800]~P139(x28001)+P139(x28002)+~E(x28001,x28002)
% 52.66/52.43 [2801]P16(x28012,x28013,x28014)+~E(x28011,x28012)+~P16(x28011,x28013,x28014)
% 52.66/52.43 [2802]P16(x28023,x28022,x28024)+~E(x28021,x28022)+~P16(x28023,x28021,x28024)
% 52.66/52.43 [2803]P16(x28033,x28034,x28032)+~E(x28031,x28032)+~P16(x28033,x28034,x28031)
% 52.66/52.43 [2804]~P116(x28041)+P116(x28042)+~E(x28041,x28042)
% 52.66/52.43 [2805]P143(x28052,x28053)+~E(x28051,x28052)+~P143(x28051,x28053)
% 52.66/52.43 [2806]P143(x28063,x28062)+~E(x28061,x28062)+~P143(x28063,x28061)
% 52.66/52.43
% 52.66/52.43 %-------------------------------------------
% 52.67/52.44 cnf(10043,plain,
% 52.67/52.44 (~E(f332(f332(f140(x100431),x100432),x100433),x100433)),
% 52.67/52.44 inference(rename_variables,[],[4399])).
% 52.67/52.44 cnf(10050,plain,
% 52.67/52.44 (~E(f332(f332(f140(x100501),x100502),x100503),x100503)),
% 52.67/52.44 inference(rename_variables,[],[4399])).
% 52.67/52.44 cnf(10059,plain,
% 52.67/52.44 (~E(f332(a114,x100591),x100591)),
% 52.67/52.44 inference(rename_variables,[],[4365])).
% 52.67/52.44 cnf(10066,plain,
% 52.67/52.44 (~E(f332(a114,x100661),x100661)),
% 52.67/52.44 inference(rename_variables,[],[4365])).
% 52.67/52.44 cnf(10069,plain,
% 52.67/52.44 (E(f37(x100691,x100692,x100693,x100694,x100695,x100696,x100697,x100698,x100699,a25),x100692)),
% 52.67/52.44 inference(rename_variables,[],[4339])).
% 52.67/52.44 cnf(10072,plain,
% 52.67/52.44 (P1(f332(f332(f232(a845),f53(a845,x100721,x100722)),x100721))),
% 52.67/52.44 inference(rename_variables,[],[3638])).
% 52.67/52.44 cnf(10075,plain,
% 52.67/52.44 (~P1(f332(f332(f233(a845),f332(f332(f82(a845),x100751),x100752)),x100752))),
% 52.67/52.44 inference(rename_variables,[],[4478])).
% 52.67/52.44 cnf(10078,plain,
% 52.67/52.44 (~P1(f332(f332(f233(a845),f332(f332(f82(a845),x100781),x100782)),x100782))),
% 52.67/52.44 inference(rename_variables,[],[4478])).
% 52.67/52.44 cnf(10081,plain,
% 52.67/52.44 (~P1(f332(f332(f233(a845),x100811),x100811))),
% 52.67/52.44 inference(rename_variables,[],[4449])).
% 52.67/52.44 cnf(10092,plain,
% 52.67/52.44 (~E(f332(f313(x100921,x100922),x100923),f332(f304(x100922,x100921),x100924))),
% 52.67/52.44 inference(rename_variables,[],[4436])).
% 52.67/52.44 cnf(10094,plain,
% 52.67/52.44 (P1(f332(f332(f334(x100941),x100942),f239(f853(x100941,a839))))),
% 52.67/52.44 inference(rename_variables,[],[3340])).
% 52.67/52.44 cnf(10097,plain,
% 52.67/52.44 (~E(f332(a114,x100971),x100971)),
% 52.67/52.44 inference(rename_variables,[],[4365])).
% 52.67/52.44 cnf(10100,plain,
% 52.67/52.44 (E(f319(x101001,x101002,x101003,f332(f332(f10(f854(x101001,x101003),x101002,x101001),x101004),f304(x101001,x101003)),f332(f332(f10(f854(x101001,x101003),x101002,x101003),x101004),f313(x101003,x101001))),x101004)),
% 52.67/52.44 inference(rename_variables,[],[4047])).
% 52.67/52.44 cnf(10106,plain,
% 52.67/52.44 (~E(f332(a27,x101061),a25)),
% 52.67/52.44 inference(rename_variables,[],[4363])).
% 52.67/52.44 cnf(10111,plain,
% 52.67/52.44 (P1(f332(f332(f232(a845),x101111),x101111))),
% 52.67/52.44 inference(rename_variables,[],[3185])).
% 52.67/52.44 cnf(10128,plain,
% 52.67/52.44 (P1(f332(f332(f334(x101281),x101282),f239(f853(x101281,a839))))),
% 52.67/52.44 inference(rename_variables,[],[3340])).
% 52.67/52.44 cnf(10133,plain,
% 52.67/52.44 (P1(f332(f332(f233(a845),x101331),f332(a114,x101331)))),
% 52.67/52.44 inference(rename_variables,[],[3254])).
% 52.67/52.44 cnf(10157,plain,
% 52.67/52.44 (P1(f332(f332(f233(a845),x101571),f332(a114,x101571)))),
% 52.67/52.44 inference(rename_variables,[],[3254])).
% 52.67/52.44 cnf(10166,plain,
% 52.67/52.44 (P1(f332(f332(f187(a25),x101661),x101661))),
% 52.67/52.44 inference(rename_variables,[],[3183])).
% 52.67/52.44 cnf(10181,plain,
% 52.67/52.44 (~P1(f332(f332(f233(a845),x101811),x101811))),
% 52.67/52.44 inference(rename_variables,[],[4449])).
% 52.67/52.44 cnf(10196,plain,
% 52.67/52.44 (P1(f332(f332(f233(a845),x101961),f332(a114,x101961)))),
% 52.67/52.44 inference(rename_variables,[],[3254])).
% 52.67/52.44 cnf(10199,plain,
% 52.67/52.44 (P1(f332(f332(f233(a845),x101991),f332(a114,x101991)))),
% 52.67/52.44 inference(rename_variables,[],[3254])).
% 52.67/52.44 cnf(10226,plain,
% 52.67/52.44 (~P1(f332(f332(f233(a845),f332(f332(f82(a845),x102261),x102262)),x102262))),
% 52.67/52.44 inference(rename_variables,[],[4478])).
% 52.67/52.44 cnf(10231,plain,
% 52.67/52.44 (~P1(f332(f332(f232(a845),f332(a114,x102311)),x102311))),
% 52.67/52.44 inference(rename_variables,[],[4463])).
% 52.67/52.44 cnf(10234,plain,
% 52.67/52.44 (E(f332(f256(x102341),x102342),x102342)),
% 52.67/52.44 inference(rename_variables,[],[3029])).
% 52.67/52.44 cnf(10245,plain,
% 52.67/52.44 (E(f37(x102451,x102452,x102453,x102454,x102455,x102456,x102457,x102458,x102459,a25),x102452)),
% 52.67/52.44 inference(rename_variables,[],[4339])).
% 52.67/52.44 cnf(10248,plain,
% 52.67/52.44 (E(f38(x102481,x102482,x102483,x102484,x102485,x102486,x102487,x102488,x102489,a25),x102482)),
% 52.67/52.44 inference(rename_variables,[],[4340])).
% 52.67/52.44 cnf(10257,plain,
% 52.67/52.44 (~P1(f332(f332(f334(x102571),x102572),f180(f853(x102571,a839))))),
% 52.67/52.44 inference(rename_variables,[],[4465])).
% 52.67/52.44 cnf(10260,plain,
% 52.67/52.44 (E(f37(x102601,x102602,x102603,x102604,x102605,x102606,x102607,x102608,x102609,a25),x102602)),
% 52.67/52.44 inference(rename_variables,[],[4339])).
% 52.67/52.44 cnf(10272,plain,
% 52.67/52.44 (P1(f332(f332(f232(f853(x102721,a839)),x102722),x102722))),
% 52.67/52.44 inference(rename_variables,[],[3484])).
% 52.67/52.44 cnf(10277,plain,
% 52.67/52.44 (P1(f332(f332(f233(a845),x102771),f332(a114,x102771)))),
% 52.67/52.44 inference(rename_variables,[],[3254])).
% 52.67/52.44 cnf(10296,plain,
% 52.67/52.44 (P1(f332(f332(f187(a25),x102961),x102961))),
% 52.67/52.44 inference(rename_variables,[],[3183])).
% 52.67/52.44 cnf(10299,plain,
% 52.67/52.44 (P1(f332(f332(f233(a845),x102991),f332(a114,x102991)))),
% 52.67/52.44 inference(rename_variables,[],[3254])).
% 52.67/52.44 cnf(10306,plain,
% 52.67/52.44 (P1(f332(f332(f233(a845),x103061),f332(a114,x103061)))),
% 52.67/52.44 inference(rename_variables,[],[3254])).
% 52.67/52.44 cnf(10309,plain,
% 52.67/52.44 (P1(f332(f332(f233(a845),x103091),f332(a114,x103091)))),
% 52.67/52.44 inference(rename_variables,[],[3254])).
% 52.67/52.44 cnf(10314,plain,
% 52.67/52.44 (P1(f332(f332(f187(a25),x103141),x103141))),
% 52.67/52.44 inference(rename_variables,[],[3183])).
% 52.67/52.44 cnf(10327,plain,
% 52.67/52.44 (~P1(f332(f332(f233(a845),x103271),x103271))),
% 52.67/52.44 inference(rename_variables,[],[4449])).
% 52.67/52.44 cnf(10334,plain,
% 52.67/52.44 (~E(f332(a27,x103341),a25)),
% 52.67/52.44 inference(rename_variables,[],[4363])).
% 52.67/52.44 cnf(10343,plain,
% 52.67/52.44 (~P1(f332(f332(f233(a845),x103431),x103431))),
% 52.67/52.44 inference(rename_variables,[],[4449])).
% 52.67/52.44 cnf(10352,plain,
% 52.67/52.44 (~E(f332(a114,x103521),x103521)),
% 52.67/52.44 inference(rename_variables,[],[4365])).
% 52.67/52.44 cnf(10355,plain,
% 52.67/52.44 (~E(f332(f332(f140(x103551),x103552),x103553),x103553)),
% 52.67/52.44 inference(rename_variables,[],[4399])).
% 52.67/52.44 cnf(10383,plain,
% 52.67/52.44 (P1(f332(f332(f187(a25),x103831),x103831))),
% 52.67/52.44 inference(rename_variables,[],[3183])).
% 52.67/52.44 cnf(10388,plain,
% 52.67/52.44 (~P1(f332(f332(f233(a845),x103881),x103881))),
% 52.67/52.44 inference(rename_variables,[],[4449])).
% 52.67/52.44 cnf(10398,plain,
% 52.67/52.44 (E(f37(x103981,x103982,x103983,x103984,x103985,x103986,x103987,x103988,x103989,a25),x103982)),
% 52.67/52.44 inference(rename_variables,[],[4339])).
% 52.67/52.44 cnf(10401,plain,
% 52.67/52.44 (E(f37(x104011,x104012,x104013,x104014,x104015,x104016,x104017,x104018,x104019,a25),x104012)),
% 52.67/52.44 inference(rename_variables,[],[4339])).
% 52.67/52.44 cnf(10404,plain,
% 52.67/52.44 (~E(f332(a114,x104041),x104041)),
% 52.67/52.44 inference(rename_variables,[],[4365])).
% 52.67/52.44 cnf(10407,plain,
% 52.67/52.44 (~P1(f332(f65(x104071,x104072,f180(f853(x104071,a839))),x104073))),
% 52.67/52.44 inference(rename_variables,[],[4477])).
% 52.67/52.44 cnf(10412,plain,
% 52.67/52.44 (~P1(f332(f65(x104121,x104122,f180(f853(x104121,a839))),x104123))),
% 52.67/52.44 inference(rename_variables,[],[4477])).
% 52.67/52.44 cnf(10431,plain,
% 52.67/52.44 (~P1(f332(f332(f233(f853(x104311,a839)),x104312),f180(f853(x104311,a839))))),
% 52.67/52.44 inference(rename_variables,[],[4475])).
% 52.67/52.44 cnf(10436,plain,
% 52.67/52.44 (~P1(f332(f332(f232(a845),f332(a114,x104361)),x104361))),
% 52.67/52.44 inference(rename_variables,[],[4463])).
% 52.67/52.44 cnf(10439,plain,
% 52.67/52.44 (~P1(f332(f332(f232(a845),f332(a114,x104391)),x104391))),
% 52.67/52.44 inference(rename_variables,[],[4463])).
% 52.67/52.44 cnf(10444,plain,
% 52.67/52.44 (~E(f332(f303(x104441,f853(x104441,a839),x104442),x104443),f332(f301(x104441),x104443))),
% 52.67/52.44 inference(rename_variables,[],[4464])).
% 52.67/52.44 cnf(10453,plain,
% 52.67/52.44 (P1(f332(f332(f232(a845),f2(a845)),x104531))),
% 52.67/52.44 inference(rename_variables,[],[3207])).
% 52.67/52.44 cnf(10456,plain,
% 52.67/52.44 (P1(f332(f332(f279(a845),x104561),x104561))),
% 52.67/52.44 inference(rename_variables,[],[3187])).
% 52.67/52.44 cnf(10459,plain,
% 52.67/52.44 (P1(f332(f332(f232(a1),x104591),x104591))),
% 52.67/52.44 inference(rename_variables,[],[3186])).
% 52.67/52.44 cnf(10464,plain,
% 52.67/52.44 (P1(f332(f332(f232(a845),x104641),f332(f332(f83(a845),x104641),x104641)))),
% 52.67/52.44 inference(rename_variables,[],[3455])).
% 52.67/52.44 cnf(10467,plain,
% 52.67/52.44 (P1(f332(f332(f232(a845),x104671),f332(f332(f83(a845),x104671),x104671)))),
% 52.67/52.44 inference(rename_variables,[],[3455])).
% 52.67/52.44 cnf(10470,plain,
% 52.67/52.44 (P1(f332(f332(f232(a845),x104701),f332(f332(f82(a845),x104702),x104701)))),
% 52.67/52.44 inference(rename_variables,[],[3453])).
% 52.67/52.44 cnf(10473,plain,
% 52.67/52.44 (P1(f332(f332(f232(a845),x104731),f332(f332(f82(a845),x104732),x104731)))),
% 52.67/52.44 inference(rename_variables,[],[3453])).
% 52.67/52.44 cnf(10476,plain,
% 52.67/52.44 (P1(f332(f332(f233(a845),x104761),f332(a114,f332(f332(f82(a845),x104762),x104761))))),
% 52.67/52.44 inference(rename_variables,[],[3631])).
% 52.67/52.44 cnf(10481,plain,
% 52.67/52.44 (P1(f332(f332(f232(f853(x104811,a839)),f332(f303(x104812,x104811,x104813),f332(f305(x104812,x104811,x104813),x104814))),x104814))),
% 52.67/52.44 inference(rename_variables,[],[4067])).
% 52.67/52.44 cnf(10484,plain,
% 52.67/52.44 (P1(f332(f332(f279(a845),x104841),x104841))),
% 52.67/52.44 inference(rename_variables,[],[3187])).
% 52.67/52.44 cnf(10489,plain,
% 52.67/52.44 (~P1(f332(f332(f233(a845),x104891),x104891))),
% 52.67/52.44 inference(rename_variables,[],[4449])).
% 52.67/52.44 cnf(10496,plain,
% 52.67/52.44 (~P1(f332(f332(f233(a845),x104961),x104961))),
% 52.67/52.44 inference(rename_variables,[],[4449])).
% 52.67/52.44 cnf(10503,plain,
% 52.67/52.44 (P1(f332(f332(f232(a1),x105031),x105031))),
% 52.67/52.44 inference(rename_variables,[],[3186])).
% 52.67/52.44 cnf(10520,plain,
% 52.67/52.44 (P1(f332(f332(f232(a845),x105201),f332(f332(f83(a845),x105201),x105201)))),
% 52.67/52.44 inference(rename_variables,[],[3455])).
% 52.67/52.44 cnf(10523,plain,
% 52.67/52.44 (~P1(f332(f332(f232(a845),f332(a114,x105231)),x105231))),
% 52.67/52.44 inference(rename_variables,[],[4463])).
% 52.67/52.44 cnf(10528,plain,
% 52.67/52.44 (~P1(f332(f332(f232(a845),f332(a114,x105281)),x105281))),
% 52.67/52.44 inference(rename_variables,[],[4463])).
% 52.67/52.44 cnf(10533,plain,
% 52.67/52.44 (~P1(f332(f332(f233(a845),f332(f332(f82(a845),x105331),x105332)),x105332))),
% 52.67/52.44 inference(rename_variables,[],[4478])).
% 52.67/52.44 cnf(10536,plain,
% 52.67/52.44 (~P1(f332(f332(f233(a845),f332(f332(f82(a845),x105361),x105362)),x105361))),
% 52.67/52.44 inference(rename_variables,[],[4479])).
% 52.67/52.44 cnf(10539,plain,
% 52.67/52.44 (~P1(f332(f332(f233(a845),f332(f332(f82(a845),x105391),x105392)),x105392))),
% 52.67/52.44 inference(rename_variables,[],[4478])).
% 52.67/52.44 cnf(10545,plain,
% 52.67/52.44 (P1(f332(f332(f232(a845),x105451),x105451))),
% 52.67/52.44 inference(rename_variables,[],[3185])).
% 52.67/52.44 cnf(10548,plain,
% 52.67/52.44 (P1(f332(f332(f232(a845),x105481),f332(f332(f83(a845),x105481),x105481)))),
% 52.67/52.44 inference(rename_variables,[],[3455])).
% 52.67/52.44 cnf(10557,plain,
% 52.67/52.44 (P1(f332(f332(f233(a845),x105571),f332(a114,x105571)))),
% 52.67/52.44 inference(rename_variables,[],[3254])).
% 52.67/52.44 cnf(10678,plain,
% 52.67/52.44 (~E(f332(a114,x106781),x106781)),
% 52.67/52.44 inference(rename_variables,[],[4365])).
% 52.67/52.44 cnf(10691,plain,
% 52.67/52.44 (P1(f332(f332(f334(x106911),x106912),f239(f853(x106911,a839))))),
% 52.67/52.44 inference(rename_variables,[],[3340])).
% 52.67/52.44 cnf(10694,plain,
% 52.67/52.44 (P1(f332(f332(f334(x106941),x106942),f332(f332(f302(x106941),x106942),x106943)))),
% 52.67/52.44 inference(rename_variables,[],[3499])).
% 52.67/52.44 cnf(10697,plain,
% 52.67/52.44 (P1(f332(f332(f334(x106971),x106972),f239(f853(x106971,a839))))),
% 52.67/52.44 inference(rename_variables,[],[3340])).
% 52.67/52.44 cnf(10700,plain,
% 52.67/52.44 (~P1(f332(f332(f334(x107001),x107002),f180(f853(x107001,a839))))),
% 52.67/52.44 inference(rename_variables,[],[4465])).
% 52.67/52.44 cnf(10708,plain,
% 52.67/52.44 (~E(f332(a114,x107081),x107081)),
% 52.67/52.44 inference(rename_variables,[],[4365])).
% 52.67/52.44 cnf(10715,plain,
% 52.67/52.44 (~P1(f332(f332(f334(x107151),x107152),f180(f853(x107151,a839))))),
% 52.67/52.44 inference(rename_variables,[],[4465])).
% 52.67/52.44 cnf(10761,plain,
% 52.67/52.44 (~P1(f332(f332(f233(a845),x107611),f2(a845)))),
% 52.67/52.44 inference(rename_variables,[],[4452])).
% 52.67/52.44 cnf(10764,plain,
% 52.67/52.44 (~P1(f332(f332(f180(f853(x107641,f853(x107642,a839))),x107643),x107644))),
% 52.67/52.44 inference(rename_variables,[],[4481])).
% 52.67/52.44 cnf(10788,plain,
% 52.67/52.44 (P1(f332(f332(f232(a845),x107881),x107881))),
% 52.67/52.44 inference(rename_variables,[],[3185])).
% 52.67/52.44 cnf(10791,plain,
% 52.67/52.44 (P1(f332(f332(f233(a845),x107911),f332(a114,x107911)))),
% 52.67/52.44 inference(rename_variables,[],[3254])).
% 52.67/52.44 cnf(10796,plain,
% 52.67/52.44 (~P1(f332(f332(f233(a845),x107961),x107961))),
% 52.67/52.44 inference(rename_variables,[],[4449])).
% 52.67/52.44 cnf(10799,plain,
% 52.67/52.44 (P1(f332(f332(f232(a845),x107991),x107991))),
% 52.67/52.44 inference(rename_variables,[],[3185])).
% 52.67/52.44 cnf(10806,plain,
% 52.67/52.44 (P1(f332(f332(f232(a845),x108061),x108061))),
% 52.67/52.44 inference(rename_variables,[],[3185])).
% 52.67/52.44 cnf(10827,plain,
% 52.67/52.44 (P1(f332(f332(f232(a845),x108271),x108271))),
% 52.67/52.44 inference(rename_variables,[],[3185])).
% 52.67/52.44 cnf(10838,plain,
% 52.67/52.44 (~P1(f332(f332(f233(a845),x108381),f2(a845)))),
% 52.67/52.44 inference(rename_variables,[],[4452])).
% 52.67/52.44 cnf(10841,plain,
% 52.67/52.44 (~E(f332(a114,x108411),x108411)),
% 52.67/52.44 inference(rename_variables,[],[4365])).
% 52.67/52.44 cnf(10848,plain,
% 52.67/52.44 (~P1(f332(f332(f180(f853(x108481,f853(x108482,a839))),x108483),x108484))),
% 52.67/52.44 inference(rename_variables,[],[4481])).
% 52.67/52.44 cnf(10865,plain,
% 52.67/52.44 (E(f332(f332(f125(x108651),f115(x108651)),x108652),x108652)),
% 52.67/52.44 inference(rename_variables,[],[3140])).
% 52.67/52.44 cnf(10879,plain,
% 52.67/52.44 (E(f37(x108791,x108792,x108793,x108794,x108795,x108796,x108797,x108798,x108799,a25),x108792)),
% 52.67/52.44 inference(rename_variables,[],[4339])).
% 52.67/52.44 cnf(10882,plain,
% 52.67/52.44 (E(f37(x108821,x108822,x108823,x108824,x108825,x108826,x108827,x108828,x108829,a25),x108822)),
% 52.67/52.44 inference(rename_variables,[],[4339])).
% 52.67/52.44 cnf(10885,plain,
% 52.67/52.44 (~E(f332(a114,x108851),x108851)),
% 52.67/52.44 inference(rename_variables,[],[4365])).
% 52.67/52.44 cnf(10888,plain,
% 52.67/52.44 (~E(f332(a114,x108881),x108881)),
% 52.67/52.44 inference(rename_variables,[],[4365])).
% 52.67/52.44 cnf(10910,plain,
% 52.67/52.44 (~P1(f332(f332(f334(x109101),x109102),f180(f853(x109101,a839))))),
% 52.67/52.44 inference(rename_variables,[],[4465])).
% 52.67/52.44 cnf(10917,plain,
% 52.67/52.44 (P1(f332(f332(f232(f853(x109171,a839)),f180(f853(x109171,a839))),x109172))),
% 52.67/52.44 inference(rename_variables,[],[3630])).
% 52.67/52.44 cnf(10922,plain,
% 52.67/52.44 (~E(f332(a114,x109221),x109221)),
% 52.67/52.44 inference(rename_variables,[],[4365])).
% 52.67/52.44 cnf(10925,plain,
% 52.67/52.44 (P1(f332(f332(f233(a845),x109251),f332(a114,x109251)))),
% 52.67/52.44 inference(rename_variables,[],[3254])).
% 52.67/52.44 cnf(10930,plain,
% 52.67/52.44 (P1(f332(f332(f232(f853(x109301,a839)),x109302),f332(f332(f302(x109301),x109303),x109302)))),
% 52.67/52.44 inference(rename_variables,[],[3626])).
% 52.67/52.44 cnf(10935,plain,
% 52.67/52.44 (P1(f332(f332(f232(f853(x109351,a839)),x109352),f332(f332(f302(x109351),x109353),x109352)))),
% 52.67/52.44 inference(rename_variables,[],[3626])).
% 52.67/52.44 cnf(10941,plain,
% 52.67/52.44 (P1(f332(f332(f334(x109411),x109412),f239(f853(x109411,a839))))),
% 52.67/52.44 inference(rename_variables,[],[3340])).
% 52.67/52.44 cnf(10950,plain,
% 52.67/52.44 (P1(f332(f332(f334(x109501),x109502),f239(f853(x109501,a839))))),
% 52.67/52.44 inference(rename_variables,[],[3340])).
% 52.67/52.44 cnf(10957,plain,
% 52.67/52.44 (~P1(f332(f332(f233(a845),x109571),x109571))),
% 52.67/52.44 inference(rename_variables,[],[4449])).
% 52.67/52.44 cnf(10972,plain,
% 52.67/52.44 (P1(f332(f332(f232(a845),x109721),x109721))),
% 52.67/52.44 inference(rename_variables,[],[3185])).
% 52.67/52.44 cnf(10978,plain,
% 52.67/52.44 (P1(f332(f332(f232(a845),x109781),x109781))),
% 52.67/52.44 inference(rename_variables,[],[3185])).
% 52.67/52.44 cnf(10985,plain,
% 52.67/52.44 (P1(f332(f239(f853(x109851,a839)),x109852))),
% 52.67/52.44 inference(rename_variables,[],[3248])).
% 52.67/52.44 cnf(11007,plain,
% 52.67/52.44 (~E(f332(a114,x110071),x110071)),
% 52.67/52.44 inference(rename_variables,[],[4365])).
% 52.67/52.44 cnf(11012,plain,
% 52.67/52.44 (E(f332(f43(a845),f332(f257(a845),x110121)),x110121)),
% 52.67/52.44 inference(rename_variables,[],[3084])).
% 52.67/52.44 cnf(11017,plain,
% 52.67/52.44 (~P1(f332(f332(f334(f852(f846(x110171),f846(x110171))),f332(f332(f241(f846(x110171),f846(x110171)),x110172),f115(x110171))),f137(x110171,x110173)))),
% 52.67/52.44 inference(rename_variables,[],[4483])).
% 52.67/52.44 cnf(11024,plain,
% 52.67/52.44 (P1(f332(f332(f232(f853(x110241,a839)),f180(f853(x110241,a839))),x110242))),
% 52.67/52.44 inference(rename_variables,[],[3630])).
% 52.67/52.44 cnf(11030,plain,
% 52.67/52.44 (~E(f332(f313(x110301,x110302),x110303),f332(f304(x110302,x110301),x110304))),
% 52.67/52.44 inference(rename_variables,[],[4436])).
% 52.67/52.44 cnf(11042,plain,
% 52.67/52.44 (P1(f332(f332(f232(f853(x110421,a839)),x110422),x110422))),
% 52.67/52.44 inference(rename_variables,[],[3484])).
% 52.67/52.44 cnf(11048,plain,
% 52.67/52.44 (~P1(f332(f332(f334(x110481),x110482),f180(f853(x110481,a839))))),
% 52.67/52.44 inference(rename_variables,[],[4465])).
% 52.67/52.44 cnf(11072,plain,
% 52.67/52.44 (~P1(f332(f332(f334(x110721),x110722),f180(f853(x110721,a839))))),
% 52.67/52.44 inference(rename_variables,[],[4465])).
% 52.67/52.44 cnf(11078,plain,
% 52.67/52.44 (~P1(f332(f332(f334(x110781),x110782),f180(f853(x110781,a839))))),
% 52.67/52.44 inference(rename_variables,[],[4465])).
% 52.67/52.44 cnf(11083,plain,
% 52.67/52.44 (~P1(f332(f65(x110831,x110832,f180(f853(x110831,a839))),x110833))),
% 52.67/52.44 inference(rename_variables,[],[4477])).
% 52.67/52.44 cnf(11088,plain,
% 52.67/52.44 (~E(f332(a114,x110881),x110881)),
% 52.67/52.44 inference(rename_variables,[],[4365])).
% 52.67/52.44 cnf(11096,plain,
% 52.67/52.44 (P1(f332(f332(f334(x110961),x110962),f239(f853(x110961,a839))))),
% 52.67/52.44 inference(rename_variables,[],[3340])).
% 52.67/52.44 cnf(11103,plain,
% 52.67/52.44 (~P1(f332(f332(f334(x111031),x111032),f180(f853(x111031,a839))))),
% 52.67/52.44 inference(rename_variables,[],[4465])).
% 52.67/52.44 cnf(11106,plain,
% 52.67/52.44 (P1(f332(f332(f232(f853(x111061,a839)),x111062),f239(f853(x111061,a839))))),
% 52.67/52.44 inference(rename_variables,[],[3562])).
% 52.67/52.44 cnf(11109,plain,
% 52.67/52.44 (P1(f332(f332(f232(f853(x111091,a839)),x111092),f239(f853(x111091,a839))))),
% 52.67/52.44 inference(rename_variables,[],[3562])).
% 52.67/52.44 cnf(11116,plain,
% 52.67/52.44 (P1(f332(f332(f232(a845),x111161),x111161))),
% 52.67/52.44 inference(rename_variables,[],[3185])).
% 52.67/52.44 cnf(11127,plain,
% 52.67/52.44 (P1(f332(f332(f334(x111271),x111272),f239(f853(x111271,a839))))),
% 52.67/52.44 inference(rename_variables,[],[3340])).
% 52.67/52.44 cnf(11130,plain,
% 52.67/52.44 (P1(f332(f332(f334(x111301),x111302),f239(f853(x111301,a839))))),
% 52.67/52.44 inference(rename_variables,[],[3340])).
% 52.67/52.44 cnf(11153,plain,
% 52.67/52.44 (~P1(f332(f332(f233(a845),x111531),x111531))),
% 52.67/52.44 inference(rename_variables,[],[4449])).
% 52.67/52.44 cnf(11159,plain,
% 52.67/52.44 (P1(f332(f332(f232(f853(x111591,a839)),x111592),x111592))),
% 52.67/52.44 inference(rename_variables,[],[3484])).
% 52.67/52.44 cnf(11162,plain,
% 52.67/52.44 (~P1(f332(f332(f334(x111621),x111622),f180(f853(x111621,a839))))),
% 52.67/52.44 inference(rename_variables,[],[4465])).
% 52.67/52.44 cnf(11168,plain,
% 52.67/52.44 (P1(f332(f332(f232(f853(x111681,a839)),x111682),f239(f853(x111681,a839))))),
% 52.67/52.44 inference(rename_variables,[],[3562])).
% 52.67/52.44 cnf(11171,plain,
% 52.67/52.44 (P1(f332(f332(f232(f853(x111711,a839)),x111712),f239(f853(x111711,a839))))),
% 52.67/52.44 inference(rename_variables,[],[3562])).
% 52.67/52.44 cnf(11174,plain,
% 52.67/52.44 (~P1(f332(f332(f334(x111741),x111742),f180(f853(x111741,a839))))),
% 52.67/52.44 inference(rename_variables,[],[4465])).
% 52.67/52.44 cnf(11179,plain,
% 52.67/52.44 (P1(f332(f332(f232(f853(x111791,a839)),x111792),f239(f853(x111791,a839))))),
% 52.67/52.44 inference(rename_variables,[],[3562])).
% 52.67/52.44 cnf(11184,plain,
% 52.67/52.44 (~P1(f332(f332(f334(x111841),x111842),f180(f853(x111841,a839))))),
% 52.67/52.44 inference(rename_variables,[],[4465])).
% 52.67/52.44 cnf(11187,plain,
% 52.67/52.44 (~P1(f332(f332(f334(x111871),x111872),f180(f853(x111871,a839))))),
% 52.67/52.44 inference(rename_variables,[],[4465])).
% 52.67/52.44 cnf(11192,plain,
% 52.67/52.44 (P1(f332(f332(f232(a845),x111921),x111921))),
% 52.67/52.44 inference(rename_variables,[],[3185])).
% 52.67/52.44 cnf(11202,plain,
% 52.67/52.44 (P1(f332(f332(f334(x112021),x112022),f239(f853(x112021,a839))))),
% 52.67/52.44 inference(rename_variables,[],[3340])).
% 52.67/52.44 cnf(11207,plain,
% 52.67/52.44 (~P1(f332(f332(f334(x112071),x112072),f180(f853(x112071,a839))))),
% 52.67/52.44 inference(rename_variables,[],[4465])).
% 52.67/52.44 cnf(11214,plain,
% 52.67/52.44 (~P1(f332(f332(f334(x112141),x112142),f180(f853(x112141,a839))))),
% 52.67/52.44 inference(rename_variables,[],[4465])).
% 52.67/52.44 cnf(11219,plain,
% 52.67/52.44 (P1(f332(f332(f232(f853(x112191,a839)),x112192),f239(f853(x112191,a839))))),
% 52.67/52.44 inference(rename_variables,[],[3562])).
% 52.67/52.44 cnf(11222,plain,
% 52.67/52.44 (P1(f332(f332(f334(x112221),x112222),f239(f853(x112221,a839))))),
% 52.67/52.44 inference(rename_variables,[],[3340])).
% 52.67/52.44 cnf(11225,plain,
% 52.67/52.44 (P1(f332(f332(f334(x112251),x112252),f332(f332(f302(x112251),x112252),x112253)))),
% 52.67/52.44 inference(rename_variables,[],[3499])).
% 52.67/52.44 cnf(11228,plain,
% 52.67/52.44 (P1(f332(f332(f334(x112281),x112282),f239(f853(x112281,a839))))),
% 52.67/52.44 inference(rename_variables,[],[3340])).
% 52.67/52.44 cnf(11231,plain,
% 52.67/52.44 (P1(f332(f332(f334(x112311),x112312),f332(f332(f302(x112311),x112312),x112313)))),
% 52.67/52.44 inference(rename_variables,[],[3499])).
% 52.67/52.44 cnf(11234,plain,
% 52.67/52.44 (P1(f332(f332(f232(f853(x112341,a839)),x112342),f239(f853(x112341,a839))))),
% 52.67/52.44 inference(rename_variables,[],[3562])).
% 52.67/52.44 cnf(11258,plain,
% 52.67/52.44 (~P1(f332(f332(f233(a845),x112581),x112581))),
% 52.67/52.44 inference(rename_variables,[],[4449])).
% 52.67/52.44 cnf(11264,plain,
% 52.67/52.44 (E(f37(x112641,x112642,x112643,x112644,x112645,x112646,x112647,x112648,x112649,a25),x112642)),
% 52.67/52.44 inference(rename_variables,[],[4339])).
% 52.67/52.44 cnf(11267,plain,
% 52.67/52.44 (~E(f332(a114,x112671),x112671)),
% 52.67/52.44 inference(rename_variables,[],[4365])).
% 52.67/52.44 cnf(11270,plain,
% 52.67/52.44 (~P1(f332(f332(f180(f853(x112701,f853(x112702,a839))),x112703),x112704))),
% 52.67/52.44 inference(rename_variables,[],[4481])).
% 52.67/52.44 cnf(11281,plain,
% 52.67/52.44 (P1(f332(f332(f334(x112811),x112812),f239(f853(x112811,a839))))),
% 52.67/52.44 inference(rename_variables,[],[3340])).
% 52.67/52.44 cnf(11284,plain,
% 52.67/52.44 (~P1(f332(f332(f334(x112841),x112842),f180(f853(x112841,a839))))),
% 52.67/52.44 inference(rename_variables,[],[4465])).
% 52.67/52.44 cnf(11294,plain,
% 52.67/52.44 (~P1(f332(f332(f334(x112941),x112942),f180(f853(x112941,a839))))),
% 52.67/52.44 inference(rename_variables,[],[4465])).
% 52.67/52.44 cnf(11299,plain,
% 52.67/52.44 (P1(f332(f332(f232(f853(x112991,a839)),x112992),x112992))),
% 52.67/52.44 inference(rename_variables,[],[3484])).
% 52.67/52.44 cnf(11304,plain,
% 52.67/52.44 (~P1(f332(f332(f334(x113041),x113042),f180(f853(x113041,a839))))),
% 52.67/52.44 inference(rename_variables,[],[4465])).
% 52.67/52.44 cnf(11307,plain,
% 52.67/52.44 (~P1(f332(f332(f334(f852(f846(x113071),f846(x113071))),f332(f332(f241(f846(x113071),f846(x113071)),x113072),f115(x113071))),f135(x113071,x113073)))),
% 52.67/52.44 inference(rename_variables,[],[4482])).
% 52.67/52.44 cnf(11313,plain,
% 52.67/52.44 (P1(f332(f332(f334(x113131),x113132),f239(f853(x113131,a839))))),
% 52.67/52.44 inference(rename_variables,[],[3340])).
% 52.67/52.44 cnf(11319,plain,
% 52.67/52.44 (P1(f332(f332(f334(x113191),x113192),f239(f853(x113191,a839))))),
% 52.67/52.44 inference(rename_variables,[],[3340])).
% 52.67/52.44 cnf(11324,plain,
% 52.67/52.44 (P1(f332(f332(f334(x113241),x113242),f239(f853(x113241,a839))))),
% 52.67/52.44 inference(rename_variables,[],[3340])).
% 52.67/52.44 cnf(11327,plain,
% 52.67/52.44 (~P1(f332(f332(f334(x113271),x113272),f180(f853(x113271,a839))))),
% 52.67/52.44 inference(rename_variables,[],[4465])).
% 52.67/52.44 cnf(11330,plain,
% 52.67/52.44 (P1(f332(f332(f232(f853(x113301,a839)),x113302),x113302))),
% 52.67/52.44 inference(rename_variables,[],[3484])).
% 52.67/52.44 cnf(11333,plain,
% 52.67/52.44 (~P1(f332(f332(f334(x113331),x113332),f180(f853(x113331,a839))))),
% 52.67/52.44 inference(rename_variables,[],[4465])).
% 52.67/52.44 cnf(11339,plain,
% 52.67/52.44 (~P1(f332(f332(f334(x113391),x113392),f180(f853(x113391,a839))))),
% 52.67/52.44 inference(rename_variables,[],[4465])).
% 52.67/52.44 cnf(11342,plain,
% 52.67/52.44 (~P1(f332(f332(f334(f852(f846(x113421),f846(x113421))),f332(f332(f241(f846(x113421),f846(x113421)),x113422),f115(x113421))),f135(x113421,x113423)))),
% 52.67/52.44 inference(rename_variables,[],[4482])).
% 52.67/52.44 cnf(11345,plain,
% 52.67/52.44 (~P1(f332(f332(f334(x113451),x113452),f180(f853(x113451,a839))))),
% 52.67/52.44 inference(rename_variables,[],[4465])).
% 52.67/52.44 cnf(11348,plain,
% 52.67/52.44 (~P1(f332(f332(f334(f852(f846(x113481),f846(x113481))),f332(f332(f241(f846(x113481),f846(x113481)),f115(x113481)),x113482)),f135(x113481,x113483)))),
% 52.67/52.44 inference(rename_variables,[],[4485])).
% 52.67/52.44 cnf(11351,plain,
% 52.67/52.44 (P1(f332(f332(f232(f853(x113511,a839)),x113512),x113512))),
% 52.67/52.44 inference(rename_variables,[],[3484])).
% 52.67/52.44 cnf(11354,plain,
% 52.67/52.44 (P1(f332(f332(f232(f853(x113541,a839)),x113542),x113542))),
% 52.67/52.44 inference(rename_variables,[],[3484])).
% 52.67/52.44 cnf(11357,plain,
% 52.67/52.44 (~P1(f332(f332(f334(x113571),x113572),f180(f853(x113571,a839))))),
% 52.67/52.44 inference(rename_variables,[],[4465])).
% 52.67/52.44 cnf(11362,plain,
% 52.67/52.44 (P1(f332(f332(f334(x113621),x113622),f239(f853(x113621,a839))))),
% 52.67/52.44 inference(rename_variables,[],[3340])).
% 52.67/52.44 cnf(11365,plain,
% 52.67/52.44 (P1(f332(f332(f334(x113651),x113652),f332(f332(f302(x113651),x113652),x113653)))),
% 52.67/52.44 inference(rename_variables,[],[3499])).
% 52.67/52.44 cnf(11370,plain,
% 52.67/52.44 (~P1(f332(f332(f334(x113701),x113702),f180(f853(x113701,a839))))),
% 52.67/52.44 inference(rename_variables,[],[4465])).
% 52.67/52.44 cnf(11379,plain,
% 52.67/52.44 (P1(f332(f332(f334(x113791),x113792),f239(f853(x113791,a839))))),
% 52.67/52.44 inference(rename_variables,[],[3340])).
% 52.67/52.44 cnf(11382,plain,
% 52.67/52.44 (P1(f332(f332(f334(x113821),x113822),f239(f853(x113821,a839))))),
% 52.67/52.44 inference(rename_variables,[],[3340])).
% 52.67/52.44 cnf(11385,plain,
% 52.67/52.44 (P1(f332(f332(f334(x113851),x113852),f239(f853(x113851,a839))))),
% 52.67/52.44 inference(rename_variables,[],[3340])).
% 52.67/52.44 cnf(11390,plain,
% 52.67/52.44 (~P1(f332(f332(f334(x113901),x113902),f180(f853(x113901,a839))))),
% 52.67/52.44 inference(rename_variables,[],[4465])).
% 52.67/52.44 cnf(11396,plain,
% 52.67/52.44 (~P1(f332(f332(f334(x113961),x113962),f180(f853(x113961,a839))))),
% 52.67/52.44 inference(rename_variables,[],[4465])).
% 52.67/52.44 cnf(11404,plain,
% 52.67/52.44 (~E(f332(f313(x114041,x114042),x114043),f332(f304(x114042,x114041),x114044))),
% 52.67/52.44 inference(rename_variables,[],[4436])).
% 52.67/52.44 cnf(11415,plain,
% 52.67/52.44 (~P1(f332(f332(f334(x114151),x114152),f180(f853(x114151,a839))))),
% 52.67/52.44 inference(rename_variables,[],[4465])).
% 52.67/52.44 cnf(11418,plain,
% 52.67/52.44 (~P1(f332(f332(f334(x114181),x114182),f180(f853(x114181,a839))))),
% 52.67/52.44 inference(rename_variables,[],[4465])).
% 52.67/52.44 cnf(11421,plain,
% 52.67/52.44 (~P1(f332(f332(f334(x114211),x114212),f180(f853(x114211,a839))))),
% 52.67/52.44 inference(rename_variables,[],[4465])).
% 52.67/52.44 cnf(11424,plain,
% 52.67/52.44 (~P1(f332(f332(f334(x114241),x114242),f180(f853(x114241,a839))))),
% 52.67/52.44 inference(rename_variables,[],[4465])).
% 52.67/52.44 cnf(11427,plain,
% 52.67/52.44 (P1(f332(f332(f334(f852(f846(x114271),f846(x114271))),f332(f332(f241(f846(x114271),f846(x114271)),x114272),x114272)),f147(x114271,f300(x114271,x114273))))),
% 52.67/52.44 inference(rename_variables,[],[3956])).
% 52.67/52.44 cnf(11430,plain,
% 52.67/52.44 (P1(f332(f332(f334(f852(f846(x114301),f846(x114301))),f332(f332(f241(f846(x114301),f846(x114301)),x114302),x114302)),f147(x114301,f300(x114301,x114303))))),
% 52.67/52.44 inference(rename_variables,[],[3956])).
% 52.67/52.44 cnf(11433,plain,
% 52.67/52.44 (P1(f332(f332(f232(f853(x114331,a839)),x114332),x114332))),
% 52.67/52.44 inference(rename_variables,[],[3484])).
% 52.67/52.44 cnf(11438,plain,
% 52.67/52.44 (~P1(f332(f332(f334(x114381),x114382),f180(f853(x114381,a839))))),
% 52.67/52.44 inference(rename_variables,[],[4465])).
% 52.67/52.44 cnf(11457,plain,
% 52.67/52.44 (~P1(f332(f332(f334(x114571),x114572),f180(f853(x114571,a839))))),
% 52.67/52.44 inference(rename_variables,[],[4465])).
% 52.67/52.44 cnf(11463,plain,
% 52.67/52.44 (P1(f332(f332(f232(f853(x114631,a839)),x114632),f239(f853(x114631,a839))))),
% 52.67/52.44 inference(rename_variables,[],[3562])).
% 52.67/52.44 cnf(11495,plain,
% 52.67/52.44 (E(f37(x114951,x114952,x114953,x114954,x114955,x114956,x114957,x114958,x114959,a25),x114952)),
% 52.67/52.44 inference(rename_variables,[],[4339])).
% 52.67/52.44 cnf(11504,plain,
% 52.67/52.44 (E(f37(x115041,x115042,x115043,x115044,x115045,x115046,x115047,x115048,x115049,a25),x115042)),
% 52.67/52.44 inference(rename_variables,[],[4339])).
% 52.67/52.44 cnf(11533,plain,
% 52.67/52.44 (E(f37(x115331,x115332,x115333,x115334,x115335,x115336,x115337,x115338,x115339,a25),x115332)),
% 52.67/52.44 inference(rename_variables,[],[4339])).
% 52.67/52.44 cnf(11562,plain,
% 52.67/52.44 (E(f37(x115621,x115622,x115623,x115624,x115625,x115626,x115627,x115628,x115629,a25),x115622)),
% 52.67/52.44 inference(rename_variables,[],[4339])).
% 52.67/52.44 cnf(11624,plain,
% 52.67/52.44 ($false),
% 52.67/52.44 inference(scs_inference,[],[4362,3403,3005,3394,2812,2815,2818,2821,2823,2825,2827,2830,2833,2836,2839,2842,2845,2847,2849,2852,2856,2860,2863,2867,2869,2870,2871,2873,2876,2878,2881,2884,2886,2887,2888,2891,2893,2895,2898,2901,2904,2906,2907,2909,2912,2914,2915,2917,2920,2922,2924,2927,2930,2932,2935,2937,2939,2942,2944,2946,2948,2949,2950,2952,2955,2958,2960,2963,2966,2977,2980,2982,2985,2988,3002,3004,3392,3393,4360,2807,2808,2998,2991,3846,3854,4394,4395,3485,3498,3463,3011,3382,4442,4443,4445,3163,3164,3166,4444,4446,3165,3032,3188,4451,4462,4461,3071,3215,3213,3214,3696,3280,3984,4192,3428,3156,3157,3026,4339,10069,10245,10260,10398,10401,10879,10882,11264,11495,11504,11533,11562,4340,10248,4365,10059,10066,10097,10352,10404,10678,10708,10841,10885,10888,10922,11007,11088,11267,3022,3060,4363,10106,10334,3435,4128,4129,3160,3486,3205,4373,3029,10234,4398,3641,3239,3244,4399,10043,10050,10355,3290,3103,3395,3183,10166,10296,10314,10383,3185,10111,10545,10788,10799,10806,10827,10972,10978,11116,11192,3186,10459,10503,3187,10456,10484,4449,10081,10181,10327,10343,10388,10489,10496,10796,10957,11153,11258,3248,10985,4436,10092,11030,11404,3052,3741,3120,3140,10865,3096,3084,11012,3254,10133,10157,10196,10199,10277,10299,10306,10309,10557,10791,10925,4452,10761,10838,3207,10453,3638,10072,4463,10231,10436,10439,10523,10528,4477,10407,10412,11083,3484,10272,11042,11159,11299,11330,11351,11354,11433,4464,10444,3510,3268,3509,3340,10094,10128,10691,10697,10941,10950,11096,11127,11130,11202,11222,11228,11281,11313,11319,11324,11362,11379,11382,11385,4465,10257,10700,10715,10910,11048,11072,11078,11103,11162,11174,11184,11187,11207,11214,11284,11294,11304,11327,11333,11339,11345,11357,11370,11390,11396,11415,11418,11421,11424,11438,11457,3342,4481,10764,10848,11270,4352,3555,3257,3383,4470,3562,11106,11109,11168,11171,11179,11219,11234,11463,4475,10431,3710,3499,10694,11225,11231,11365,3630,10917,11024,4467,3455,10464,10467,10520,10548,3453,10470,10473,3454,4478,10075,10078,10226,10533,10539,4479,10536,3580,3633,3626,10930,10935,3631,10476,3632,3289,3816,3787,4067,10481,3490,3743,3770,3881,3912,4480,4047,10100,4474,3906,3481,3702,4142,4482,11307,11342,4483,11017,4484,4485,11348,3956,11427,11430,4007,4171,2,9486,6173,5143,4945,4898,4856,4855,4690,4594,4593,4502,4496,5102,5092,5014,4951,4491,4979,4895,9,8,9722,9487,9122,9121,8549,7639,7019,6621,6334,6314,6166,6165,6158,6141,6011,5925,5795,5771,5704,5693,5692,5637,5622,5621,5617,5615,5563,5557,5556,5551,5538,5520,5509,5506,5489,5488,5479,5392,5300,5293,5284,5283,5240,5226,5218,5210,5209,5201,5135,5111,5077,5071,5070,5069,5068,5067,5066,5025,5017,5004,5003,4941,4924,4918,4684,4618,4566,4564,4563,4557,4556,9664,8635,8470,8469,8459,7439,7177,6877,6663,6477,6476,6474,6473,6360,6335,6267,6266,6167,6147,6135,6058,6016,6010,6009,6003,5983,5980,5979,5895,5894,5822,5779,5757,5713,5708,5701,5700,5672,5666,5641,5638,5573,5491,5490,5475,5461,5450,5439,5417,5370,5325,5297,5296,5295,5269,5230,5219,5128,5100,5090,5088,4995,4957,4956,4832,4794,4674,4795,9793,9750,9749,9748,9747,9735,9410,8985,8952,8780,8747,8702,8657,8617,8613,8317,7806,7617,7373,7354,7293,7275,7274,7273,7272,7271,7231,6824,6821,6713,6700,6612,6611,6591,6542,6541,6531,6259,6258,6256,6255,6254,6253,6213,6206,6120,6119,6118,6117,6116,6115,6114,6113,5989,5988,5987,5986,5985,5966,5964,5963,5962,5961,5960,5922,5813,5812,5811,5805,5734,5707,5673,5628,5627,5626,5625,5624,5623,5576,5531,5451,5448,5447,5446,5445,5444,5443,5420,5419,5416,5366,5358,5292,5262,5261,5251,5245,5244,5243,5213,5193,5176,5138,5115,5114,5112,5079,5019,4881,4880,4879,4655,4654,4653,4619,4612,4611,4513,8499,8498,8497,8496,8389,8388,8387,7771,7678,7567,7364,7246,6903,6807,6716,6715,6556,6250,5947,5944,5943,5699,5698,5652,5651,5612,5611,5610,5568,5460,5398,5343,5342,5331,5217,9818,9813,9423,9422,9421,9420,8571,8479,8478,8477,8476,8401,7669,7668,7587,7434,7301,6961,6825,6801,6730,6729,6686,6685,6684,6683,6682,6681,6680,6662,6633,6632,6631,6630,6596,6523,6454,6453,6431,6416,6415,6414,6150,6014,6013,5840,5565,5564,5341,5282,5281,5235,5232,5231,5200,5199,4946,8989,8988,8987,8986,8811,8810,8789,8788,8783,8671,8670,8480,8471,8464,8376,8341,8188,8126,7990,7962,7717,7593,7574,7573,7438,7299,7298,7165,7107,7106,6938,6937,6786,6785,6674,6673,6375,6364,6305,6199,6143,6130,6077,6068,6059,5843,5783,5631,5630,5496,5434,5186,5091,8520,8463,8462,8451,8450,8407,8406,8336,8145,8078,7930,7901,7896,7895,7781,7719,7686,7486,7485,7431,7261,6799,6770,6727,6656,6655,6376,5620,5317,5196,5195,9100,8819,8806,8709,8411,8355,8311,8280,8210,7975,7911,7910,7909,7908,7727,7386,6862,6861,6800,6677,6676,6619,6618,6384,6383,9290,9090,9089,8992,8958,8828,8736,8735,8693,8600,8570,8500,7864,7715,7504,6988,6870,6132,5872,9317,9316,9102,9101,8713,8712,8660,8656,8538,8537,8536,8535,8522,8337,8314,8313,8309,7653,7370,7369,7244,7104,7103,7076,6905,6249,5880,9029,8885,8812,8809,8793,8659,8508,8435,8169,6396,9524,9523,9146,9032,8924,8923,8922,8544,8489,9889,9424,9148,9136,9111,9591,9482,9480,9479,9289,9288,9392,9358,8938,8937,8893,8892,8720,9767,9766,9624,9515,9324,9323,9161,9597,9525,9351,9167,9123,9755,9754,9250,9189,9792,9787,9704,9621,9576,9549,9334,9757,9573,9439,9371,9370,9697,9575,9444,9369,9966,9965,9908,9907,10018,10030,9924,9888,9972,9943,2800,2797,2790,2789,2786,2781,2780,2779,2778,2777,2776,2774,2763,2762,2761,2759,2746,2745,2742,2741,2740,2736,2733,2731,2729,2725,2723,2720,2718,2717,2716,2711,2710,2709,2706,2705,2704,2703,2701,2698,2696,2695,2690,2689,2681,2679,2678,2676,2673,2672,2671,2670,2669,2664,2662,2661,2647,2646,2643,2642,2640,2639,2638,2637,2636,2632,2628,2627,2625,2624,2620,2619,2618,2616,2615,2614,2613,2612,2611,2609,2608,2607,2606,2605,2604,2603,2601,2600,2599,2598,2597,2596,2595,2594,2593,2592,2591,2590,2589,2588,2583,2582,2581,2580,2579,2578,2577,2576,2575,2574,2573,2571,2570,2569,2568,2567,2566,2565,2564,2563,2562,2561,2560,2559,2558,2556,2554,2553,2552,2551,2550,2549,2548,3,6107,6106]),
% 52.67/52.44 ['proof']).
% 52.67/52.44 % SZS output end Proof
% 52.67/52.44 % Total time :48.680000s
%------------------------------------------------------------------------------