TSTP Solution File: SWW327+1 by CSE---1.7
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%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : SWW327+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 18:07:32 EDT 2024
% Result : Theorem 191.21s 191.72s
% Output : CNFRefutation 191.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : SWW327+1 : TPTP v8.2.0. Released v5.2.0.
% 0.02/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.11/0.34 % Computer : n011.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8042.1875MB
% 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Wed Jun 19 06:08:09 EDT 2024
% 0.11/0.34 % CPUTime :
% 0.48/0.56 start to proof:theBenchmark
% 190.74/191.55 %-------------------------------------------
% 190.74/191.55 % File :CSE---1.7
% 190.74/191.55 % Problem :theBenchmark
% 190.74/191.55 % Transform :cnf
% 190.74/191.55 % Format :tptp:raw
% 190.74/191.55 % Command :java -jar mcs_scs.jar %d %s
% 190.74/191.55
% 190.74/191.55 % Result :Theorem 162.710000s
% 190.74/191.55 % Output :CNFRefutation 162.710000s
% 190.74/191.55 %-------------------------------------------
% 190.77/191.56 %------------------------------------------------------------------------------
% 190.77/191.56 % File : SWW327+1 : TPTP v8.2.0. Released v5.2.0.
% 190.77/191.56 % Domain : Software Verification
% 190.77/191.56 % Problem : Hoare's Logic with Procedures 435097, 5000 axioms selected
% 190.77/191.56 % Version : Especial.
% 190.77/191.56 % English :
% 190.77/191.56
% 190.77/191.56 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 190.77/191.56 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 190.77/191.56 % Source : [Bla11]
% 190.77/191.56 % Names : hoare_435097.5000.p [Bla11]
% 190.77/191.56
% 190.77/191.56 % Status : ContradictoryAxioms
% 190.77/191.56 % Rating : 0.81 v8.2.0, 0.78 v8.1.0, 0.81 v7.4.0, 0.90 v7.3.0, 0.86 v7.1.0, 0.87 v7.0.0, 0.90 v6.4.0, 0.88 v6.2.0, 0.92 v6.1.0, 0.93 v6.0.0, 0.91 v5.5.0, 0.96 v5.4.0, 1.00 v5.2.0
% 190.77/191.56 % Syntax : Number of formulae : 5207 (1706 unt; 0 def)
% 190.77/191.56 % Number of atoms : 12607 (4535 equ)
% 190.77/191.56 % Maximal formula atoms : 13 ( 2 avg)
% 190.77/191.56 % Number of connectives : 8491 (1091 ~; 158 |; 712 &)
% 190.77/191.56 % ( 875 <=>;5655 =>; 0 <=; 0 <~>)
% 190.77/191.56 % Maximal formula depth : 22 ( 6 avg)
% 190.77/191.56 % Maximal term depth : 19 ( 2 avg)
% 190.77/191.56 % Number of predicates : 141 ( 140 usr; 1 prp; 0-7 aty)
% 190.77/191.56 % Number of functors : 392 ( 392 usr; 61 con; 0-10 aty)
% 190.77/191.56 % Number of variables : 16771 (16642 !; 129 ?)
% 190.77/191.56 % SPC : FOF_CAX_RFO_SEQ
% 190.77/191.56
% 190.77/191.56 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 190.77/191.56 % 2011-03-01 11:56:31
% 190.77/191.56 %------------------------------------------------------------------------------
% 190.77/191.56 %----Relevant facts (4983)
% 190.77/191.56 fof(fact_ext,axiom,
% 190.77/191.56 ! [V_g_2,V_f_2] :
% 190.77/191.56 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 190.77/191.56 => V_f_2 = V_g_2 ) ).
% 190.77/191.56
% 190.77/191.56 fof(fact_hoare__valids__def,axiom,
% 190.77/191.56 ! [V_ts_2,V_Ga_2,T_b] :
% 190.77/191.56 ( c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,V_ts_2)
% 190.77/191.56 <=> ! [B_n] :
% 190.77/191.56 ( ! [B_x] :
% 190.77/191.56 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_Ga_2))
% 190.77/191.56 => c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x) )
% 190.77/191.56 => ! [B_x] :
% 190.77/191.56 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_ts_2))
% 190.77/191.56 => c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x) ) ) ) ).
% 190.77/191.56
% 190.77/191.56 fof(fact_evaln_OWhileFalse,axiom,
% 190.77/191.56 ! [V_n_2,V_ca_2,V_s_2,V_ba_2] :
% 190.77/191.56 ( ~ hBOOL(hAPP(V_ba_2,V_s_2))
% 190.77/191.56 => c_Natural_Oevaln(c_Com_Ocom_OWhile(V_ba_2,V_ca_2),V_s_2,V_n_2,V_s_2) ) ).
% 190.77/191.56
% 190.77/191.56 fof(fact_evaln_OWhileTrue,axiom,
% 190.77/191.56 ! [V_s2_2,V_s1_2,V_n_2,V_ca_2,V_s0_2,V_ba_2] :
% 190.77/191.56 ( hBOOL(hAPP(V_ba_2,V_s0_2))
% 190.77/191.56 => ( c_Natural_Oevaln(V_ca_2,V_s0_2,V_n_2,V_s1_2)
% 190.77/191.56 => ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_ba_2,V_ca_2),V_s1_2,V_n_2,V_s2_2)
% 190.77/191.56 => c_Natural_Oevaln(c_Com_Ocom_OWhile(V_ba_2,V_ca_2),V_s0_2,V_n_2,V_s2_2) ) ) ) ).
% 190.77/191.56
% 190.77/191.56 fof(fact_evaln_Oequations_I7_J,axiom,
% 190.77/191.56 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2] :
% 190.77/191.56 ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),V_a2_2,V_a4_2,V_a2_2)
% 190.77/191.56 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 190.77/191.56 => ? [B_s1] :
% 190.77/191.56 ( c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,B_s1)
% 190.77/191.56 & c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),B_s1,V_a4_2,V_a2_2) ) ) ) ).
% 190.77/191.56
% 190.77/191.56 fof(fact_evaln_Oequations_I8_J,axiom,
% 190.77/191.56 ! [V_a6_2,V_a4_2,V_a2_2,V_a3_2,V_a1_2] :
% 190.77/191.56 ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),V_a2_2,V_a4_2,V_a6_2)
% 190.77/191.56 <=> ( ( V_a6_2 = V_a2_2
% 190.77/191.56 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
% 190.77/191.56 | ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 190.77/191.57 & ? [B_s1] :
% 190.77/191.57 ( c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,B_s1)
% 190.77/191.57 & c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),B_s1,V_a4_2,V_a6_2) ) ) ) ) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_com_Osimps_I5_J,axiom,
% 190.77/191.57 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] :
% 190.77/191.57 ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2)
% 190.77/191.57 <=> ( V_fun_2 = V_fun_H_2
% 190.77/191.57 & V_com_2 = V_com_H_2 ) ) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_triples__valid__Suc,axiom,
% 190.77/191.57 ! [V_n_2,V_ts_2,T_b] :
% 190.77/191.57 ( ! [B_x] :
% 190.77/191.57 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_ts_2))
% 190.77/191.57 => c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),B_x) )
% 190.77/191.57 => ! [B_x] :
% 190.77/191.57 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_ts_2))
% 190.77/191.57 => c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,B_x) ) ) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_triple__valid__def2,axiom,
% 190.77/191.57 ! [V_Q_2,V_ca_2,V_Pa_2,V_n_2,T_b] :
% 190.77/191.57 ( c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_ca_2),V_Q_2))
% 190.77/191.57 <=> ! [B_Z,B_s] :
% 190.77/191.57 ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s))
% 190.77/191.57 => ! [B_s_H] :
% 190.77/191.57 ( c_Natural_Oevaln(V_ca_2,B_s,V_n_2,B_s_H)
% 190.77/191.57 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s_H)) ) ) ) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_evaln__WHILE__case,axiom,
% 190.77/191.57 ! [V_t_2,V_n_2,V_s_2,V_ca_2,V_ba_2] :
% 190.77/191.57 ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_ba_2,V_ca_2),V_s_2,V_n_2,V_t_2)
% 190.77/191.57 => ( ( V_t_2 = V_s_2
% 190.77/191.57 => hBOOL(hAPP(V_ba_2,V_s_2)) )
% 190.77/191.57 => ~ ( hBOOL(hAPP(V_ba_2,V_s_2))
% 190.77/191.57 => ! [B_s1] :
% 190.77/191.57 ( c_Natural_Oevaln(V_ca_2,V_s_2,V_n_2,B_s1)
% 190.77/191.57 => ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(V_ba_2,V_ca_2),B_s1,V_n_2,V_t_2) ) ) ) ) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_triple__valid__Suc,axiom,
% 190.77/191.57 ! [V_t,V_n,T_a] :
% 190.77/191.57 ( c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n),V_t)
% 190.77/191.57 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n,V_t) ) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_com_Osimps_I69_J,axiom,
% 190.77/191.57 ! [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) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_evaln_OSkip,axiom,
% 190.77/191.57 ! [V_n,V_s] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_s) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_evaln__elim__cases_I1_J,axiom,
% 190.77/191.57 ! [V_t,V_n,V_s] :
% 190.77/191.57 ( c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_t)
% 190.77/191.57 => V_t = V_s ) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_triple_Oinject,axiom,
% 190.77/191.57 ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_b] :
% 190.77/191.57 ( 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)
% 190.77/191.57 <=> ( V_fun1_2 = V_fun1_H_2
% 190.77/191.57 & V_com_2 = V_com_H_2
% 190.77/191.57 & V_fun2_2 = V_fun2_H_2 ) ) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_com_Osimps_I64_J,axiom,
% 190.77/191.57 ! [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 ).
% 190.77/191.57
% 190.77/191.57 fof(fact_evaln__Suc,axiom,
% 190.77/191.57 ! [V_s_H,V_n,V_s,V_c] :
% 190.77/191.57 ( c_Natural_Oevaln(V_c,V_s,V_n,V_s_H)
% 190.77/191.57 => c_Natural_Oevaln(V_c,V_s,hAPP(c_Nat_OSuc,V_n),V_s_H) ) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_evaln_Oequations_I1_J,axiom,
% 190.77/191.57 ! [V_a2,V_a1] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_a1,V_a2,V_a1) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_com_Osimps_I17_J,axiom,
% 190.77/191.57 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ).
% 190.77/191.57
% 190.77/191.57 fof(fact_com_Osimps_I16_J,axiom,
% 190.77/191.57 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_triple_Orecs,axiom,
% 190.77/191.57 ! [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) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_triple_Osimps_I2_J,axiom,
% 190.77/191.57 ! [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) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_n__not__Suc__n,axiom,
% 190.77/191.57 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_Suc__n__not__n,axiom,
% 190.77/191.57 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ).
% 190.77/191.57
% 190.77/191.57 fof(fact_nat_Oinject,axiom,
% 190.77/191.57 ! [V_nat_H_2,V_nat_2] :
% 190.77/191.57 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2)
% 190.77/191.57 <=> V_nat_2 = V_nat_H_2 ) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_Suc__inject,axiom,
% 190.77/191.57 ! [V_y,V_x] :
% 190.77/191.57 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y)
% 190.77/191.57 => V_x = V_y ) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_evaln_OSemi,axiom,
% 190.77/191.57 ! [V_s2,V_c1,V_s1,V_n,V_s0,V_c0] :
% 190.77/191.57 ( c_Natural_Oevaln(V_c0,V_s0,V_n,V_s1)
% 190.77/191.57 => ( c_Natural_Oevaln(V_c1,V_s1,V_n,V_s2)
% 190.77/191.57 => c_Natural_Oevaln(c_Com_Ocom_OSemi(V_c0,V_c1),V_s0,V_n,V_s2) ) ) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_com_Orecs_I1_J,axiom,
% 190.77/191.57 ! [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 ).
% 190.77/191.57
% 190.77/191.57 fof(fact_com_Osimps_I67_J,axiom,
% 190.77/191.57 ! [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) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_com_Orecs_I6_J,axiom,
% 190.77/191.57 ! [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)) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_evaln__elim__cases_I5_J,axiom,
% 190.77/191.57 ! [V_t_2,V_n_2,V_s_2,V_c2_2,V_c1_2,V_ba_2] :
% 190.77/191.57 ( c_Natural_Oevaln(c_Com_Ocom_OCond(V_ba_2,V_c1_2,V_c2_2),V_s_2,V_n_2,V_t_2)
% 190.77/191.57 => ( ( hBOOL(hAPP(V_ba_2,V_s_2))
% 190.77/191.57 => ~ c_Natural_Oevaln(V_c1_2,V_s_2,V_n_2,V_t_2) )
% 190.77/191.57 => ~ ( ~ hBOOL(hAPP(V_ba_2,V_s_2))
% 190.77/191.57 => ~ c_Natural_Oevaln(V_c2_2,V_s_2,V_n_2,V_t_2) ) ) ) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_evaln_OIfFalse,axiom,
% 190.77/191.57 ! [V_c0_2,V_s1_2,V_n_2,V_c1_2,V_s_2,V_ba_2] :
% 190.77/191.57 ( ~ hBOOL(hAPP(V_ba_2,V_s_2))
% 190.77/191.57 => ( c_Natural_Oevaln(V_c1_2,V_s_2,V_n_2,V_s1_2)
% 190.77/191.57 => c_Natural_Oevaln(c_Com_Ocom_OCond(V_ba_2,V_c0_2,V_c1_2),V_s_2,V_n_2,V_s1_2) ) ) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_evaln_OIfTrue,axiom,
% 190.77/191.57 ! [V_c1_2,V_s1_2,V_n_2,V_c0_2,V_s_2,V_ba_2] :
% 190.77/191.57 ( hBOOL(hAPP(V_ba_2,V_s_2))
% 190.77/191.57 => ( c_Natural_Oevaln(V_c0_2,V_s_2,V_n_2,V_s1_2)
% 190.77/191.57 => c_Natural_Oevaln(c_Com_Ocom_OCond(V_ba_2,V_c0_2,V_c1_2),V_s_2,V_n_2,V_s1_2) ) ) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_com_Osimps_I44_J,axiom,
% 190.77/191.57 ! [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) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_com_Osimps_I45_J,axiom,
% 190.77/191.57 ! [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) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_com_Osimps_I3_J,axiom,
% 190.77/191.57 ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] :
% 190.77/191.57 ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2)
% 190.77/191.57 <=> ( V_com1_2 = V_com1_H_2
% 190.77/191.57 & V_com2_2 = V_com2_H_2 ) ) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_com_Osimps_I4_J,axiom,
% 190.77/191.57 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] :
% 190.77/191.57 ( 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)
% 190.77/191.57 <=> ( V_fun_2 = V_fun_H_2
% 190.77/191.57 & V_com1_2 = V_com1_H_2
% 190.77/191.57 & V_com2_2 = V_com2_H_2 ) ) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_com_Orecs_I4_J,axiom,
% 190.77/191.57 ! [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)) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_com_Orecs_I5_J,axiom,
% 190.77/191.57 ! [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)) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_evaln_Oequations_I5_J,axiom,
% 190.77/191.57 ! [V_a5_2,V_a4_2,V_a2_2,V_a6_2,V_a3_2,V_a1_2] :
% 190.77/191.57 ( 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)
% 190.77/191.57 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 190.77/191.57 & c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,V_a5_2) )
% 190.77/191.57 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 190.77/191.57 & c_Natural_Oevaln(V_a6_2,V_a2_2,V_a4_2,V_a5_2) ) ) ) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_evaln_Oequations_I6_J,axiom,
% 190.77/191.57 ! [V_a5_2,V_a4_2,V_a2_2,V_a3_2,V_a6_2,V_a1_2] :
% 190.77/191.57 ( 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)
% 190.77/191.57 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 190.77/191.57 & c_Natural_Oevaln(V_a6_2,V_a2_2,V_a4_2,V_a5_2) )
% 190.77/191.57 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 190.77/191.57 & c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,V_a5_2) ) ) ) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_com_Osimps_I53_J,axiom,
% 190.77/191.57 ! [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) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_com_Osimps_I52_J,axiom,
% 190.77/191.57 ! [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) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_evaln_Oequations_I4_J,axiom,
% 190.77/191.57 ! [V_a6_2,V_a3_2,V_a2_2,V_a5_2,V_a1_2] :
% 190.77/191.57 ( c_Natural_Oevaln(c_Com_Ocom_OSemi(V_a1_2,V_a5_2),V_a2_2,V_a3_2,V_a6_2)
% 190.77/191.57 <=> ? [B_s1] :
% 190.77/191.57 ( c_Natural_Oevaln(V_a1_2,V_a2_2,V_a3_2,B_s1)
% 190.77/191.57 & c_Natural_Oevaln(V_a5_2,B_s1,V_a3_2,V_a6_2) ) ) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_com_Osimps_I15_J,axiom,
% 190.77/191.57 ! [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 ).
% 190.77/191.57
% 190.77/191.57 fof(fact_com_Osimps_I14_J,axiom,
% 190.77/191.57 ! [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) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_com_Osimps_I46_J,axiom,
% 190.77/191.57 ! [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) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_com_Osimps_I47_J,axiom,
% 190.77/191.57 ! [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) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_com_Osimps_I13_J,axiom,
% 190.77/191.57 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ).
% 190.77/191.57
% 190.77/191.57 fof(fact_com_Osimps_I12_J,axiom,
% 190.77/191.57 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_com_Osimps_I68_J,axiom,
% 190.77/191.57 ! [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) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_evaln__elim__cases_I4_J,axiom,
% 190.77/191.57 ! [V_t,V_n,V_s,V_c2,V_c1] :
% 190.77/191.57 ( c_Natural_Oevaln(c_Com_Ocom_OSemi(V_c1,V_c2),V_s,V_n,V_t)
% 190.77/191.57 => ~ ! [B_s1] :
% 190.77/191.57 ( c_Natural_Oevaln(V_c1,V_s,V_n,B_s1)
% 190.77/191.57 => ~ c_Natural_Oevaln(V_c2,B_s1,V_n,V_t) ) ) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_of__nat__aux_Osimps_I2_J,axiom,
% 190.77/191.57 ! [V_i_2,V_n_2,V_inc_2,T_b] :
% 190.77/191.57 ( class_Rings_Osemiring__1(T_b)
% 190.77/191.57 => 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)) ) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_nat__case__Suc,axiom,
% 190.77/191.57 ! [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) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_nat__rec__Suc,axiom,
% 190.77/191.57 ! [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)) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_WTs__elim__cases_I4_J,axiom,
% 190.77/191.57 ! [V_c2,V_c1] :
% 190.77/191.57 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c1,V_c2)))
% 190.77/191.57 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1))
% 190.77/191.57 => ~ hBOOL(hAPP(c_Com_OWT,V_c2)) ) ) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_com_Osimps_I66_J,axiom,
% 190.77/191.57 ! [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) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_com_Osimps_I71_J,axiom,
% 190.77/191.57 ! [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) ).
% 190.77/191.57
% 190.77/191.57 fof(fact_WTs__elim__cases_I5_J,axiom,
% 190.77/191.57 ! [V_c2_2,V_c1_2,V_ba_2] :
% 190.77/191.58 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_ba_2,V_c1_2,V_c2_2)))
% 190.77/191.58 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1_2))
% 190.77/191.58 => ~ hBOOL(hAPP(c_Com_OWT,V_c2_2)) ) ) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I65_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_WTs__elim__cases_I6_J,axiom,
% 190.77/191.58 ! [V_ca_2,V_ba_2] :
% 190.77/191.58 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_ba_2,V_ca_2)))
% 190.77/191.58 => hBOOL(hAPP(c_Com_OWT,V_ca_2)) ) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I70_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_WTs__elim__cases_I3_J,axiom,
% 190.77/191.58 ! [V_ca_2,V_a_2,V_Y_2] :
% 190.77/191.58 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_ca_2)))
% 190.77/191.58 => hBOOL(hAPP(c_Com_OWT,V_ca_2)) ) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_WTs__elim__cases_I8_J,axiom,
% 190.77/191.58 ! [V_a_2,V_Pa_2,V_X_2] :
% 190.77/191.58 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_Pa_2,V_a_2)))
% 190.77/191.58 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_Pa_2))) ) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_WT_OCall,axiom,
% 190.77/191.58 ! [V_a_2,V_X_2,V_pn_2] :
% 190.77/191.58 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn_2)))
% 190.77/191.58 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_pn_2,V_a_2))) ) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_WT_OLocal,axiom,
% 190.77/191.58 ! [V_a_2,V_Y_2,V_ca_2] :
% 190.77/191.58 ( hBOOL(hAPP(c_Com_OWT,V_ca_2))
% 190.77/191.58 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_ca_2))) ) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I2_J,axiom,
% 190.77/191.58 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] :
% 190.77/191.58 ( 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)
% 190.77/191.58 <=> ( V_loc_2 = V_loc_H_2
% 190.77/191.58 & V_fun_2 = V_fun_H_2
% 190.77/191.58 & V_com_2 = V_com_H_2 ) ) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I7_J,axiom,
% 190.77/191.58 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_fun_2,V_pname_2,V_vname_2] :
% 190.77/191.58 ( 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)
% 190.77/191.58 <=> ( V_vname_2 = V_vname_H_2
% 190.77/191.58 & V_pname_2 = V_pname_H_2
% 190.77/191.58 & V_fun_2 = V_fun_H_2 ) ) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I1_J,axiom,
% 190.77/191.58 ! [V_fun_H_2,V_vname_H_2,V_fun_2,V_vname_2] :
% 190.77/191.58 ( c_Com_Ocom_OAss(V_vname_2,V_fun_2) = c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2)
% 190.77/191.58 <=> ( V_vname_2 = V_vname_H_2
% 190.77/191.58 & V_fun_2 = V_fun_H_2 ) ) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I6_J,axiom,
% 190.77/191.58 ! [V_pname_H_2,V_pname_2] :
% 190.77/191.58 ( hAPP(c_Com_Ocom_OBODY,V_pname_2) = hAPP(c_Com_Ocom_OBODY,V_pname_H_2)
% 190.77/191.58 <=> V_pname_2 = V_pname_H_2 ) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_WT_Oequations_I8_J,axiom,
% 190.77/191.58 ! [V_a3_2,V_a1_2,V_a2_2] :
% 190.77/191.58 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_a2_2,V_a1_2,V_a3_2)))
% 190.77/191.58 <=> hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a1_2))) ) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_WT_Oequations_I3_J,axiom,
% 190.77/191.58 ! [V_a1_2,V_a3_2,V_a2_2] :
% 190.77/191.58 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_a2_2,V_a3_2,V_a1_2)))
% 190.77/191.58 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_WT_Oequations_I2_J,axiom,
% 190.77/191.58 ! [V_a2_2,V_a1_2] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(V_a1_2,V_a2_2))) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I42_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I43_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I23_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I33_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I40_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I63_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I22_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I32_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I30_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I41_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I62_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I31_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_WT_OAssign,axiom,
% 190.77/191.58 ! [V_a_2,V_X_2] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(V_X_2,V_a_2))) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I58_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I59_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I54_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I55_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I48_J,axiom,
% 190.77/191.58 ! [V_pname_H,V_com2,V_com1] : c_Com_Ocom_OSemi(V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I49_J,axiom,
% 190.77/191.58 ! [V_com2,V_com1,V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I18_J,axiom,
% 190.77/191.58 ! [V_pname_H] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,V_pname_H) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I19_J,axiom,
% 190.77/191.58 ! [V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSKIP ).
% 190.77/191.58
% 190.77/191.58 fof(fact_While,axiom,
% 190.77/191.58 ! [V_ba_2,V_ca_2] :
% 190.77/191.58 ( hBOOL(hAPP(c_Com_OWT,V_ca_2))
% 190.77/191.58 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_ba_2,V_ca_2))) ) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_WT_Oequations_I6_J,axiom,
% 190.77/191.58 ! [V_a1_2,V_a2_2] :
% 190.77/191.58 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_a2_2,V_a1_2)))
% 190.77/191.58 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_WT_OIf,axiom,
% 190.77/191.58 ! [V_ba_2,V_c1_2,V_c0_2] :
% 190.77/191.58 ( hBOOL(hAPP(c_Com_OWT,V_c0_2))
% 190.77/191.58 => ( hBOOL(hAPP(c_Com_OWT,V_c1_2))
% 190.77/191.58 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_ba_2,V_c0_2,V_c1_2))) ) ) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_WT_Oequations_I5_J,axiom,
% 190.77/191.58 ! [V_a2_2,V_a1_2,V_a3_2] :
% 190.77/191.58 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_a3_2,V_a1_2,V_a2_2)))
% 190.77/191.58 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2))
% 190.77/191.58 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_WT_OSemi,axiom,
% 190.77/191.58 ! [V_c1,V_c0] :
% 190.77/191.58 ( hBOOL(hAPP(c_Com_OWT,V_c0))
% 190.77/191.58 => ( hBOOL(hAPP(c_Com_OWT,V_c1))
% 190.77/191.58 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c0,V_c1))) ) ) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_WT_Oequations_I4_J,axiom,
% 190.77/191.58 ! [V_a2_2,V_a1_2] :
% 190.77/191.58 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_a1_2,V_a2_2)))
% 190.77/191.58 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2))
% 190.77/191.58 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_WT_OSkip,axiom,
% 190.77/191.58 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_WT_Oequations_I1_J,axiom,
% 190.77/191.58 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I29_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I28_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I38_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I61_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I39_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I60_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I27_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I26_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I36_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I37_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I56_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I57_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I25_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I24_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I8_J,axiom,
% 190.77/191.58 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I9_J,axiom,
% 190.77/191.58 ! [V_fun_H_2,V_vname_H_2] : c_Com_Ocom_OAss(V_vname_H_2,V_fun_H_2) != c_Com_Ocom_OSKIP ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I34_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I51_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I35_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I50_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I20_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I10_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I21_J,axiom,
% 190.77/191.58 ! [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 ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Osimps_I11_J,axiom,
% 190.77/191.58 ! [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 ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Orecs_I7_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Orecs_I2_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Orecs_I3_J,axiom,
% 190.77/191.58 ! [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)) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com_Orecs_I8_J,axiom,
% 190.77/191.58 ! [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) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_Body__triple__valid__0,axiom,
% 190.77/191.58 ! [V_Q_2,V_pn_2,V_Pa_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_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_evaln__elim__cases_I2_J,axiom,
% 190.77/191.58 ! [V_t_2,V_n_2,V_s_2,V_a_2,V_X_2] :
% 190.77/191.58 ( c_Natural_Oevaln(c_Com_Ocom_OAss(V_X_2,V_a_2),V_s_2,V_n_2,V_t_2)
% 190.77/191.58 => V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)) ) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_evaln_OAssign,axiom,
% 190.77/191.58 ! [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))) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_Body__triple__valid__Suc,axiom,
% 190.77/191.58 ! [V_Q_2,V_pn_2,V_Pa_2,V_n_2,T_b] :
% 190.77/191.58 ( c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2))
% 190.77/191.58 <=> 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_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)) ) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_def__nat__rec__Suc,axiom,
% 190.77/191.58 ! [V_n_2,V_h_2,V_ca_2,T_b,V_f_2] :
% 190.77/191.58 ( ! [B_n] : hAPP(V_f_2,B_n) = hAPP(c_Nat_Onat_Onat__rec(T_b,V_ca_2,V_h_2),B_n)
% 190.77/191.58 => 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)) ) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_evaln_Oequations_I2_J,axiom,
% 190.77/191.58 ! [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))) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_evaln_OBody,axiom,
% 190.77/191.58 ! [V_s1,V_n,V_s0,V_pn] :
% 190.77/191.58 ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn)),V_s0,V_n,V_s1)
% 190.77/191.58 => c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_pn),V_s0,hAPP(c_Nat_OSuc,V_n),V_s1) ) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_evaln_Oequations_I9_J,axiom,
% 190.77/191.58 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] :
% 190.77/191.58 ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_a1_2),V_a2_2,hAPP(c_Nat_OSuc,V_a3_2),V_a4_2)
% 190.77/191.58 <=> 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) ) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_of__nat__aux_Osimps_I1_J,axiom,
% 190.77/191.58 ! [V_i_2,V_inc_2,T_b] :
% 190.77/191.58 ( class_Rings_Osemiring__1(T_b)
% 190.77/191.58 => 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 ) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_nat__rec__0,axiom,
% 190.77/191.58 ! [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 ).
% 190.77/191.58
% 190.77/191.58 fof(fact_evalc_OSkip,axiom,
% 190.77/191.58 ! [V_s] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s)) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_evalc__elim__cases_I1_J,axiom,
% 190.77/191.58 ! [V_t,V_s] :
% 190.77/191.58 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_t))
% 190.77/191.58 => V_t = V_s ) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_evalc_OWhileFalse,axiom,
% 190.77/191.58 ! [V_ca_2,V_s_2,V_ba_2] :
% 190.77/191.58 ( ~ hBOOL(hAPP(V_ba_2,V_s_2))
% 190.77/191.58 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_ba_2,V_ca_2)),V_s_2),V_s_2)) ) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_evalc_OWhileTrue,axiom,
% 190.77/191.58 ! [V_s2_2,V_s1_2,V_ca_2,V_s0_2,V_ba_2] :
% 190.77/191.58 ( hBOOL(hAPP(V_ba_2,V_s0_2))
% 190.77/191.58 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),V_s0_2),V_s1_2))
% 190.77/191.58 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_ba_2,V_ca_2)),V_s1_2),V_s2_2))
% 190.77/191.58 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_ba_2,V_ca_2)),V_s0_2),V_s2_2)) ) ) ) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_evalc_OIfFalse,axiom,
% 190.77/191.58 ! [V_c0_2,V_s1_2,V_c1_2,V_s_2,V_ba_2] :
% 190.77/191.58 ( ~ hBOOL(hAPP(V_ba_2,V_s_2))
% 190.77/191.58 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_s1_2))
% 190.77/191.58 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_ba_2,V_c0_2,V_c1_2)),V_s_2),V_s1_2)) ) ) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_evalc_OIfTrue,axiom,
% 190.77/191.58 ! [V_c1_2,V_s1_2,V_c0_2,V_s_2,V_ba_2] :
% 190.77/191.58 ( hBOOL(hAPP(V_ba_2,V_s_2))
% 190.77/191.58 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0_2),V_s_2),V_s1_2))
% 190.77/191.58 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_ba_2,V_c0_2,V_c1_2)),V_s_2),V_s1_2)) ) ) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_evalc__elim__cases_I5_J,axiom,
% 190.77/191.58 ! [V_t_2,V_s_2,V_c2_2,V_c1_2,V_ba_2] :
% 190.77/191.58 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_ba_2,V_c1_2,V_c2_2)),V_s_2),V_t_2))
% 190.77/191.58 => ( ( hBOOL(hAPP(V_ba_2,V_s_2))
% 190.77/191.58 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_t_2)) )
% 190.77/191.58 => ~ ( ~ hBOOL(hAPP(V_ba_2,V_s_2))
% 190.77/191.58 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2_2),V_s_2),V_t_2)) ) ) ) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_evalc_OSemi,axiom,
% 190.77/191.58 ! [V_s2,V_c1,V_s1,V_s0,V_c0] :
% 190.77/191.58 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0),V_s0),V_s1))
% 190.77/191.58 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s1),V_s2))
% 190.77/191.58 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_s2)) ) ) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_evalc_OAssign,axiom,
% 190.77/191.58 ! [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)))) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_evalc__elim__cases_I2_J,axiom,
% 190.77/191.58 ! [V_t_2,V_s_2,V_a_2,V_X_2] :
% 190.77/191.58 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(V_X_2,V_a_2)),V_s_2),V_t_2))
% 190.77/191.58 => V_t_2 = hAPP(hAPP(hAPP(c_Natural_Oupdate,V_s_2),V_X_2),hAPP(V_a_2,V_s_2)) ) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_evalc__elim__cases_I6_J,axiom,
% 190.77/191.58 ! [V_s1,V_s,V_P] :
% 190.77/191.58 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_s1))
% 190.77/191.58 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P))),V_s),V_s1)) ) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_evalc_OBody,axiom,
% 190.77/191.58 ! [V_s1,V_s0,V_pn] :
% 190.77/191.58 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_s0),V_s1))
% 190.77/191.58 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_pn)),V_s0),V_s1)) ) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_com__det,axiom,
% 190.77/191.58 ! [V_u,V_t,V_s,V_c] :
% 190.77/191.58 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t))
% 190.77/191.58 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_u))
% 190.77/191.58 => V_u = V_t ) ) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_evalc_Oequations_I9_J,axiom,
% 190.77/191.58 ! [V_a3_2,V_a2_2,V_a1_2] :
% 190.77/191.58 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),V_a3_2))
% 190.77/191.58 <=> 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)) ) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_evalc_Oequations_I2_J,axiom,
% 190.77/191.58 ! [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)))) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_Suc__neq__Zero,axiom,
% 190.77/191.58 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 190.77/191.58
% 190.77/191.58 fof(fact_Zero__neq__Suc,axiom,
% 190.77/191.58 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_nat_Osimps_I3_J,axiom,
% 190.77/191.59 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_Suc__not__Zero,axiom,
% 190.77/191.59 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_nat_Osimps_I2_J,axiom,
% 190.77/191.59 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_Zero__not__Suc,axiom,
% 190.77/191.59 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_eval__eq,axiom,
% 190.77/191.59 ! [V_t_2,V_s_2,V_ca_2] :
% 190.77/191.59 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),V_s_2),V_t_2))
% 190.77/191.59 <=> ? [B_n] : c_Natural_Oevaln(V_ca_2,V_s_2,B_n,V_t_2) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_evaln__evalc,axiom,
% 190.77/191.59 ! [V_t,V_n,V_s,V_c] :
% 190.77/191.59 ( c_Natural_Oevaln(V_c,V_s,V_n,V_t)
% 190.77/191.59 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_evalc_Oequations_I7_J,axiom,
% 190.77/191.59 ! [V_a2_2,V_a3_2,V_a1_2] :
% 190.77/191.59 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a2_2))
% 190.77/191.59 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 190.77/191.59 => ? [B_s1] :
% 190.77/191.59 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1))
% 190.77/191.59 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a2_2)) ) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_evalc_Oequations_I8_J,axiom,
% 190.77/191.59 ! [V_a5_2,V_a2_2,V_a3_2,V_a1_2] :
% 190.77/191.59 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a5_2))
% 190.77/191.59 <=> ( ( V_a5_2 = V_a2_2
% 190.77/191.59 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
% 190.77/191.59 | ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 190.77/191.59 & ? [B_s1] :
% 190.77/191.59 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1))
% 190.77/191.59 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a5_2)) ) ) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_evalc_Oequations_I5_J,axiom,
% 190.77/191.59 ! [V_a4_2,V_a2_2,V_a5_2,V_a3_2,V_a1_2] :
% 190.77/191.59 ( 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))
% 190.77/191.59 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 190.77/191.59 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) )
% 190.77/191.59 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 190.77/191.59 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) ) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_evalc_Oequations_I6_J,axiom,
% 190.77/191.59 ! [V_a4_2,V_a2_2,V_a3_2,V_a5_2,V_a1_2] :
% 190.77/191.59 ( 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))
% 190.77/191.59 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2))
% 190.77/191.59 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) )
% 190.77/191.59 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2))
% 190.77/191.59 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) ) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_evalc_Oequations_I4_J,axiom,
% 190.77/191.59 ! [V_a5_2,V_a2_2,V_a4_2,V_a1_2] :
% 190.77/191.59 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_a1_2,V_a4_2)),V_a2_2),V_a5_2))
% 190.77/191.59 <=> ? [B_s1] :
% 190.77/191.59 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a1_2),V_a2_2),B_s1))
% 190.77/191.59 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a4_2),B_s1),V_a5_2)) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_evalc_Oequations_I1_J,axiom,
% 190.77/191.59 ! [V_a] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_a),V_a)) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_nat__case__0,axiom,
% 190.77/191.59 ! [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 ).
% 190.77/191.59
% 190.77/191.59 fof(fact_triple_Osize_I1_J,axiom,
% 190.77/191.59 ! [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) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_triple_Osize_I2_J,axiom,
% 190.77/191.59 ! [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) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_evaln__elim__cases_I6_J,axiom,
% 190.77/191.59 ! [V_s1,V_n,V_s,V_P] :
% 190.77/191.59 ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_P),V_s,V_n,V_s1)
% 190.77/191.59 => ~ ! [B_n] :
% 190.77/191.59 ( V_n = hAPP(c_Nat_OSuc,B_n)
% 190.77/191.59 => ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P)),V_s,B_n,V_s1) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_evalc__elim__cases_I4_J,axiom,
% 190.77/191.59 ! [V_t,V_s,V_c2,V_c1] :
% 190.77/191.59 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1,V_c2)),V_s),V_t))
% 190.77/191.59 => ~ ! [B_s1] :
% 190.77/191.59 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s),B_s1))
% 190.77/191.59 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2),B_s1),V_t)) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_com_Osize_I1_J,axiom,
% 190.77/191.59 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_com_Osize_I8_J,axiom,
% 190.77/191.59 ! [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) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_com_Osize_I2_J,axiom,
% 190.77/191.59 ! [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) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_com_Osize_I7_J,axiom,
% 190.77/191.59 ! [V_pname] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_com_Osize_I9_J,axiom,
% 190.77/191.59 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_com_Osize_I16_J,axiom,
% 190.77/191.59 ! [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) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_com_Osize_I10_J,axiom,
% 190.77/191.59 ! [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) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_com_Osize_I15_J,axiom,
% 190.77/191.59 ! [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) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_com_Osize_I11_J,axiom,
% 190.77/191.59 ! [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))) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_com_Osize_I12_J,axiom,
% 190.77/191.59 ! [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))) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_com_Osize_I3_J,axiom,
% 190.77/191.59 ! [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))) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_com_Osize_I4_J,axiom,
% 190.77/191.59 ! [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))) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_com_Osize_I13_J,axiom,
% 190.77/191.59 ! [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))) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_com_Osize_I5_J,axiom,
% 190.77/191.59 ! [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))) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_com_Osize_I14_J,axiom,
% 190.77/191.59 ! [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))) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_com_Osize_I6_J,axiom,
% 190.77/191.59 ! [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))) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_WT_OBody,axiom,
% 190.77/191.59 ! [V_pn] :
% 190.77/191.59 ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_ONone(tc_Com_Ocom)
% 190.77/191.59 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn))) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_WT_Oequations_I7_J,axiom,
% 190.77/191.59 ! [V_a_2] :
% 190.77/191.59 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a_2)))
% 190.77/191.59 <=> ? [B_y] : hAPP(c_Com_Obody,V_a_2) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_add__right__imp__eq,axiom,
% 190.77/191.59 ! [V_c,V_a,V_b,T_a] :
% 190.77/191.59 ( class_Groups_Ocancel__semigroup__add(T_a)
% 190.77/191.59 => ( 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)
% 190.77/191.59 => V_b = V_c ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_add__imp__eq,axiom,
% 190.77/191.59 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.59 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 190.77/191.59 => ( 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)
% 190.77/191.59 => V_b = V_c ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_add__left__imp__eq,axiom,
% 190.77/191.59 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.59 ( class_Groups_Ocancel__semigroup__add(T_a)
% 190.77/191.59 => ( 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)
% 190.77/191.59 => V_b = V_c ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_add__right__cancel,axiom,
% 190.77/191.59 ! [V_ca_2,V_a_2,V_ba_2,T_b] :
% 190.77/191.59 ( class_Groups_Ocancel__semigroup__add(T_b)
% 190.77/191.59 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ba_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)
% 190.77/191.59 <=> V_ba_2 = V_ca_2 ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_add__left__cancel,axiom,
% 190.77/191.59 ! [V_ca_2,V_ba_2,V_a_2,T_b] :
% 190.77/191.59 ( class_Groups_Ocancel__semigroup__add(T_b)
% 190.77/191.59 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ba_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)
% 190.77/191.59 <=> V_ba_2 = V_ca_2 ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 190.77/191.59 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.59 ( class_Groups_Oab__semigroup__add(T_a)
% 190.77/191.59 => 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)) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_nat__add__commute,axiom,
% 190.77/191.59 ! [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) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_nat__add__left__commute,axiom,
% 190.77/191.59 ! [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)) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_nat__add__assoc,axiom,
% 190.77/191.59 ! [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)) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_nat__add__left__cancel,axiom,
% 190.77/191.59 ! [V_n_2,V_m_2,V_k_2] :
% 190.77/191.59 ( 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)
% 190.77/191.59 <=> V_m_2 = V_n_2 ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_nat__add__right__cancel,axiom,
% 190.77/191.59 ! [V_n_2,V_k_2,V_m_2] :
% 190.77/191.59 ( 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)
% 190.77/191.59 <=> V_m_2 = V_n_2 ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_add_Ocomm__neutral,axiom,
% 190.77/191.59 ! [V_a,T_a] :
% 190.77/191.59 ( class_Groups_Ocomm__monoid__add(T_a)
% 190.77/191.59 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_add__0__right,axiom,
% 190.77/191.59 ! [V_a,T_a] :
% 190.77/191.59 ( class_Groups_Omonoid__add(T_a)
% 190.77/191.59 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_double__zero__sym,axiom,
% 190.77/191.59 ! [V_a_2,T_b] :
% 190.77/191.59 ( class_Groups_Olinordered__ab__group__add(T_b)
% 190.77/191.59 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)
% 190.77/191.59 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_add__0,axiom,
% 190.77/191.59 ! [V_a,T_a] :
% 190.77/191.59 ( class_Groups_Ocomm__monoid__add(T_a)
% 190.77/191.59 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_add__0__left,axiom,
% 190.77/191.59 ! [V_a,T_a] :
% 190.77/191.59 ( class_Groups_Omonoid__add(T_a)
% 190.77/191.59 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_plus__nat_Oadd__0,axiom,
% 190.77/191.59 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 190.77/191.59
% 190.77/191.59 fof(fact_Nat_Oadd__0__right,axiom,
% 190.77/191.59 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 190.77/191.59
% 190.77/191.59 fof(fact_add__is__0,axiom,
% 190.77/191.59 ! [V_n_2,V_m_2] :
% 190.77/191.59 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.59 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.59 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_add__eq__self__zero,axiom,
% 190.77/191.59 ! [V_n,V_m] :
% 190.77/191.59 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m
% 190.77/191.59 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_add__Suc__shift,axiom,
% 190.77/191.59 ! [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)) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_add__Suc,axiom,
% 190.77/191.59 ! [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)) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_add__Suc__right,axiom,
% 190.77/191.59 ! [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)) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_one__is__add,axiom,
% 190.77/191.59 ! [V_n_2,V_m_2] :
% 190.77/191.59 ( 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)
% 190.77/191.59 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 190.77/191.59 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 190.77/191.59 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.59 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_add__is__1,axiom,
% 190.77/191.59 ! [V_n_2,V_m_2] :
% 190.77/191.59 ( 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))
% 190.77/191.59 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 190.77/191.59 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 190.77/191.59 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.59 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_zero__reorient,axiom,
% 190.77/191.59 ! [V_x_2,T_b] :
% 190.77/191.59 ( class_Groups_Ozero(T_b)
% 190.77/191.59 => ( c_Groups_Ozero__class_Ozero(T_b) = V_x_2
% 190.77/191.59 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_WT__bodiesD,axiom,
% 190.77/191.59 ! [V_b,V_pn] :
% 190.77/191.59 ( c_Com_OWT__bodies
% 190.77/191.59 => ( hAPP(c_Com_Obody,V_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b)
% 190.77/191.59 => hBOOL(hAPP(c_Com_OWT,V_b)) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_WTs__elim__cases_I7_J,axiom,
% 190.77/191.59 ! [V_P] :
% 190.77/191.59 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P)))
% 190.77/191.59 => ~ ! [B_y] : hAPP(c_Com_Obody,V_P) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_the_Osimps,axiom,
% 190.77/191.59 ! [V_x,T_a] : hAPP(c_Option_Othe(T_a),hAPP(c_Option_Ooption_OSome(T_a),V_x)) = V_x ).
% 190.77/191.59
% 190.77/191.59 fof(fact_not__None__eq,axiom,
% 190.77/191.59 ! [T_b,V_x_2] :
% 190.77/191.59 ( V_x_2 != c_Option_Ooption_ONone(T_b)
% 190.77/191.59 <=> ? [B_y] : V_x_2 = hAPP(c_Option_Ooption_OSome(T_b),B_y) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_not__Some__eq,axiom,
% 190.77/191.59 ! [T_b,V_x_2] :
% 190.77/191.59 ( ! [B_y] : V_x_2 != hAPP(c_Option_Ooption_OSome(T_b),B_y)
% 190.77/191.59 <=> V_x_2 = c_Option_Ooption_ONone(T_b) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_option_Osimps_I3_J,axiom,
% 190.77/191.59 ! [V_a_H,T_a] : hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_option_Osimps_I2_J,axiom,
% 190.77/191.59 ! [V_a_H,T_a] : c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_option_Osize_I2_J,axiom,
% 190.77/191.59 ! [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))) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_double__eq__0__iff,axiom,
% 190.77/191.59 ! [V_a_2,T_b] :
% 190.77/191.59 ( class_Groups_Olinordered__ab__group__add(T_b)
% 190.77/191.59 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 190.77/191.59 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_add__0__iff,axiom,
% 190.77/191.59 ! [V_a_2,V_ba_2,T_b] :
% 190.77/191.59 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 190.77/191.59 => ( V_ba_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ba_2),V_a_2)
% 190.77/191.59 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 190.77/191.59 ! [V_a,T_a] :
% 190.77/191.59 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.59 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 190.77/191.59 ! [V_c,V_a,T_a] :
% 190.77/191.59 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.59 => 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) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 190.77/191.59 ! [V_d,V_c,V_a,T_a] :
% 190.77/191.59 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.59 => 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)) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 190.77/191.59 ! [V_d,V_c,V_a,T_a] :
% 190.77/191.59 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.59 => 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) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 190.77/191.59 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.59 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.59 => 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)) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 190.77/191.59 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.59 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.59 => 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) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 190.77/191.59 ! [V_d,V_c,V_b,V_a,T_a] :
% 190.77/191.59 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.59 => 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)) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_option_Osize_I1_J,axiom,
% 190.77/191.59 ! [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) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_option_Oinject,axiom,
% 190.77/191.59 ! [V_a_H_2,V_a_2,T_b] :
% 190.77/191.59 ( hAPP(c_Option_Ooption_OSome(T_b),V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_a_H_2)
% 190.77/191.59 <=> V_a_2 = V_a_H_2 ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 190.77/191.59 ! [V_a,T_a] :
% 190.77/191.59 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.59 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_nat_Osize_I2_J,axiom,
% 190.77/191.59 ! [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))) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_nat_Osize_I4_J,axiom,
% 190.77/191.59 ! [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))) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_option_Osize_I4_J,axiom,
% 190.77/191.59 ! [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) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_option_Osize_I3_J,axiom,
% 190.77/191.59 ! [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) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_option_Orecs_I2_J,axiom,
% 190.77/191.59 ! [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) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_option_Osimps_I5_J,axiom,
% 190.77/191.59 ! [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) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_option_Orecs_I1_J,axiom,
% 190.77/191.59 ! [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 ).
% 190.77/191.59
% 190.77/191.59 fof(fact_option_Osimps_I4_J,axiom,
% 190.77/191.59 ! [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 ).
% 190.77/191.59
% 190.77/191.59 fof(fact_bool_Osize_I1_J,axiom,
% 190.77/191.59 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_bool_Osize_I2_J,axiom,
% 190.77/191.59 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_is__none__code_I2_J,axiom,
% 190.77/191.59 ! [V_x,T_b] : ~ c_Option_Ois__none(T_b,hAPP(c_Option_Ooption_OSome(T_b),V_x)) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_nat__size,axiom,
% 190.77/191.59 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ).
% 190.77/191.59
% 190.77/191.59 fof(fact_nat_Osize_I3_J,axiom,
% 190.77/191.59 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) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_nat_Osize_I1_J,axiom,
% 190.77/191.59 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_is__none__def,axiom,
% 190.77/191.59 ! [V_x_2,T_b] :
% 190.77/191.59 ( c_Option_Ois__none(T_b,V_x_2)
% 190.77/191.59 <=> V_x_2 = c_Option_Ooption_ONone(T_b) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_is__none__code_I1_J,axiom,
% 190.77/191.59 ! [T_a] : c_Option_Ois__none(T_a,c_Option_Ooption_ONone(T_a)) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_bool_Osize_I4_J,axiom,
% 190.77/191.59 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_bool_Osize_I3_J,axiom,
% 190.77/191.59 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_def__nat__rec__0,axiom,
% 190.77/191.59 ! [V_h_2,V_ca_2,T_b,V_f_2] :
% 190.77/191.59 ( ! [B_n] : hAPP(V_f_2,B_n) = hAPP(c_Nat_Onat_Onat__rec(T_b,V_ca_2,V_h_2),B_n)
% 190.77/191.59 => hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_ca_2 ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_evalc__WHILE__case,axiom,
% 190.77/191.59 ! [V_t_2,V_s_2,V_ca_2,V_ba_2] :
% 190.77/191.59 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_ba_2,V_ca_2)),V_s_2),V_t_2))
% 190.77/191.59 => ( ( V_t_2 = V_s_2
% 190.77/191.59 => hBOOL(hAPP(V_ba_2,V_s_2)) )
% 190.77/191.59 => ~ ( hBOOL(hAPP(V_ba_2,V_s_2))
% 190.77/191.59 => ! [B_s1] :
% 190.77/191.59 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),V_s_2),B_s1))
% 190.77/191.59 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_ba_2,V_ca_2)),B_s1),V_t_2)) ) ) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_pair__box_Osize_I1_J,axiom,
% 190.77/191.59 ! [V_ba_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_ba_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_ba_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_evalc__evaln,axiom,
% 190.77/191.59 ! [V_t,V_s,V_c] :
% 190.77/191.59 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t))
% 190.77/191.59 => ? [B_n] : c_Natural_Oevaln(V_c,V_s,B_n,V_t) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_sum_Osize_I1_J,axiom,
% 190.77/191.59 ! [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))) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_sum_Osize_I2_J,axiom,
% 190.77/191.59 ! [V_ba_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_ba_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fb_2,V_ba_2)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_option_Oexhaust,axiom,
% 190.77/191.59 ! [T_a,V_y] :
% 190.77/191.59 ( V_y != c_Option_Ooption_ONone(T_a)
% 190.77/191.59 => ~ ! [B_a] : V_y != hAPP(c_Option_Ooption_OSome(T_a),B_a) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_zero__less__Suc,axiom,
% 190.77/191.59 ! [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))) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_not0__implies__Suc,axiom,
% 190.77/191.59 ! [V_n] :
% 190.77/191.59 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.59 => ? [B_m] : V_n = hAPP(c_Nat_OSuc,B_m) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_less__zeroE,axiom,
% 190.77/191.59 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_lessI,axiom,
% 190.77/191.59 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_Suc__mono,axiom,
% 190.77/191.59 ! [V_n,V_m] :
% 190.77/191.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 190.77/191.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_nat__less__cases,axiom,
% 190.77/191.59 ! [V_Pa_2,V_n_2,V_m_2] :
% 190.77/191.59 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 190.77/191.59 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) )
% 190.77/191.59 => ( ( V_m_2 = V_n_2
% 190.77/191.59 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) )
% 190.77/191.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 190.77/191.59 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) )
% 190.77/191.59 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_less__not__refl3,axiom,
% 190.77/191.59 ! [V_t,V_s] :
% 190.77/191.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t))
% 190.77/191.59 => V_s != V_t ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_less__not__refl2,axiom,
% 190.77/191.59 ! [V_m,V_n] :
% 190.77/191.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 190.77/191.59 => V_m != V_n ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_less__irrefl__nat,axiom,
% 190.77/191.59 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_linorder__neqE__nat,axiom,
% 190.77/191.59 ! [V_y,V_x] :
% 190.77/191.59 ( V_x != V_y
% 190.77/191.59 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 190.77/191.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_nat__neq__iff,axiom,
% 190.77/191.59 ! [V_n_2,V_m_2] :
% 190.77/191.59 ( V_m_2 != V_n_2
% 190.77/191.59 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 190.77/191.59 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_less__not__refl,axiom,
% 190.77/191.59 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_pair__box_Oinject,axiom,
% 190.77/191.59 ! [V_b_H_2,V_a_H_2,V_ba_2,V_a_2,T_c,T_b] :
% 190.77/191.59 ( c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_ba_2) = c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_H_2,V_b_H_2)
% 190.77/191.59 <=> ( V_a_2 = V_a_H_2
% 190.77/191.59 & V_ba_2 = V_b_H_2 ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_add__less__cancel__right,axiom,
% 190.77/191.59 ! [V_ba_2,V_ca_2,V_a_2,T_b] :
% 190.77/191.59 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 190.77/191.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ba_2),V_ca_2)))
% 190.77/191.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_add__less__cancel__left,axiom,
% 190.77/191.59 ! [V_ba_2,V_a_2,V_ca_2,T_b] :
% 190.77/191.59 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 190.77/191.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_ba_2)))
% 190.77/191.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_add__strict__right__mono,axiom,
% 190.77/191.59 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.59 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 190.77/191.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 190.77/191.59 => 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))) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_add__strict__left__mono,axiom,
% 190.77/191.59 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.59 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 190.77/191.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 190.77/191.59 => 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))) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_add__strict__mono,axiom,
% 190.77/191.59 ! [V_d,V_c,V_b,V_a,T_a] :
% 190.77/191.59 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 190.77/191.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 190.77/191.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 190.77/191.59 => 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))) ) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_add__less__imp__less__right,axiom,
% 190.77/191.59 ! [V_b,V_c,V_a,T_a] :
% 190.77/191.59 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 190.77/191.59 => ( 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)))
% 190.77/191.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_add__less__imp__less__left,axiom,
% 190.77/191.59 ! [V_b,V_a,V_c,T_a] :
% 190.77/191.59 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 190.77/191.59 => ( 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)))
% 190.77/191.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_gr0I,axiom,
% 190.77/191.59 ! [V_n] :
% 190.77/191.59 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_gr__implies__not0,axiom,
% 190.77/191.59 ! [V_n,V_m] :
% 190.77/191.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 190.77/191.59 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_less__nat__zero__code,axiom,
% 190.77/191.59 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_neq0__conv,axiom,
% 190.77/191.59 ! [V_n_2] :
% 190.77/191.59 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_not__less0,axiom,
% 190.77/191.59 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_not__less__eq,axiom,
% 190.77/191.59 ! [V_n_2,V_m_2] :
% 190.77/191.59 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 190.77/191.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_less__Suc__eq,axiom,
% 190.77/191.59 ! [V_n_2,V_m_2] :
% 190.77/191.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 190.77/191.59 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 190.77/191.59 | V_m_2 = V_n_2 ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_Suc__less__eq,axiom,
% 190.77/191.59 ! [V_n_2,V_m_2] :
% 190.77/191.59 ( 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)))
% 190.77/191.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_not__less__less__Suc__eq,axiom,
% 190.77/191.59 ! [V_m_2,V_n_2] :
% 190.77/191.59 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 190.77/191.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 190.77/191.59 <=> V_n_2 = V_m_2 ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_less__antisym,axiom,
% 190.77/191.59 ! [V_m,V_n] :
% 190.77/191.59 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 190.77/191.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m)))
% 190.77/191.59 => V_m = V_n ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_less__SucI,axiom,
% 190.77/191.59 ! [V_n,V_m] :
% 190.77/191.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 190.77/191.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_Suc__lessI,axiom,
% 190.77/191.59 ! [V_n,V_m] :
% 190.77/191.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 190.77/191.59 => ( hAPP(c_Nat_OSuc,V_m) != V_n
% 190.77/191.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_less__trans__Suc,axiom,
% 190.77/191.59 ! [V_k,V_j,V_i] :
% 190.77/191.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 190.77/191.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 190.77/191.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_less__SucE,axiom,
% 190.77/191.59 ! [V_n,V_m] :
% 190.77/191.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 190.77/191.59 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 190.77/191.59 => V_m = V_n ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_Suc__lessD,axiom,
% 190.77/191.59 ! [V_n,V_m] :
% 190.77/191.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 190.77/191.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_Suc__less__SucD,axiom,
% 190.77/191.59 ! [V_n,V_m] :
% 190.77/191.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))
% 190.77/191.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_add__lessD1,axiom,
% 190.77/191.59 ! [V_k,V_j,V_i] :
% 190.77/191.59 ( 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))
% 190.77/191.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_less__add__eq__less,axiom,
% 190.77/191.59 ! [V_n,V_m,V_l,V_k] :
% 190.77/191.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 190.77/191.59 => ( 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)
% 190.77/191.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_add__less__mono,axiom,
% 190.77/191.59 ! [V_l,V_k,V_j,V_i] :
% 190.77/191.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 190.77/191.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 190.77/191.59 => 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))) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_add__less__mono1,axiom,
% 190.77/191.59 ! [V_k,V_j,V_i] :
% 190.77/191.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 190.77/191.59 => 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))) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_trans__less__add2,axiom,
% 190.77/191.59 ! [V_m,V_j,V_i] :
% 190.77/191.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 190.77/191.59 => 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))) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_trans__less__add1,axiom,
% 190.77/191.59 ! [V_m,V_j,V_i] :
% 190.77/191.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 190.77/191.59 => 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))) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_nat__add__left__cancel__less,axiom,
% 190.77/191.59 ! [V_n_2,V_m_2,V_k_2] :
% 190.77/191.59 ( 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)))
% 190.77/191.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_not__add__less2,axiom,
% 190.77/191.59 ! [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)) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_not__add__less1,axiom,
% 190.77/191.59 ! [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)) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_even__less__0__iff,axiom,
% 190.77/191.59 ! [V_a_2,T_b] :
% 190.77/191.59 ( class_Rings_Olinordered__idom(T_b)
% 190.77/191.59 => ( 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)))
% 190.77/191.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_add__neg__neg,axiom,
% 190.77/191.59 ! [V_b,V_a,T_a] :
% 190.77/191.59 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 190.77/191.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 190.77/191.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 190.77/191.59 => 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))) ) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_add__pos__pos,axiom,
% 190.77/191.59 ! [V_b,V_a,T_a] :
% 190.77/191.59 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 190.77/191.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 190.77/191.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 190.77/191.59 => 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))) ) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 190.77/191.59 ! [V_a_2,T_b] :
% 190.77/191.59 ( class_Groups_Olinordered__ab__group__add(T_b)
% 190.77/191.59 => ( 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)))
% 190.77/191.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 190.77/191.59 ! [V_a_2,T_b] :
% 190.77/191.59 ( class_Groups_Olinordered__ab__group__add(T_b)
% 190.77/191.59 => ( 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)))
% 190.77/191.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_less__Suc__eq__0__disj,axiom,
% 190.77/191.59 ! [V_n_2,V_m_2] :
% 190.77/191.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 190.77/191.59 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.59 | ? [B_j] :
% 190.77/191.59 ( V_m_2 = hAPP(c_Nat_OSuc,B_j)
% 190.77/191.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_less__Suc0,axiom,
% 190.77/191.59 ! [V_n_2] :
% 190.77/191.59 ( 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))))
% 190.77/191.59 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_gr0__conv__Suc,axiom,
% 190.77/191.59 ! [V_n_2] :
% 190.77/191.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 190.77/191.59 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_add__gr__0,axiom,
% 190.77/191.59 ! [V_n_2,V_m_2] :
% 190.77/191.59 ( 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)))
% 190.77/191.59 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 190.77/191.59 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_less__iff__Suc__add,axiom,
% 190.77/191.59 ! [V_n_2,V_m_2] :
% 190.77/191.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 190.77/191.59 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_less__add__Suc2,axiom,
% 190.77/191.59 ! [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)))) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_less__add__Suc1,axiom,
% 190.77/191.59 ! [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)))) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_pair__box_Osize_I2_J,axiom,
% 190.77/191.59 ! [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) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_pair__box_Orecs,axiom,
% 190.77/191.59 ! [V_ba_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_ba_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_ba_2) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_pair__box_Osimps_I2_J,axiom,
% 190.77/191.59 ! [V_ba_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_ba_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_ba_2) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_pos__add__strict,axiom,
% 190.77/191.59 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.59 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 190.77/191.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 190.77/191.59 => 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))) ) ) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_Inl__not__Inr,axiom,
% 190.77/191.59 ! [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) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_sum_Osimps_I3_J,axiom,
% 190.77/191.59 ! [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) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_Inr__not__Inl,axiom,
% 190.77/191.59 ! [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) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_sum_Osimps_I4_J,axiom,
% 190.77/191.59 ! [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) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_sum_Osize_I3_J,axiom,
% 190.77/191.59 ! [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) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_sum_Osize_I4_J,axiom,
% 190.77/191.59 ! [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) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_termination__basic__simps_I1_J,axiom,
% 190.77/191.59 ! [V_z,V_y,V_x] :
% 190.77/191.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 190.77/191.59 => 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))) ) ).
% 190.77/191.59
% 190.77/191.59 fof(fact_linorder__neqE__linordered__idom,axiom,
% 190.77/191.59 ! [V_y,V_x,T_a] :
% 190.77/191.59 ( class_Rings_Olinordered__idom(T_a)
% 190.77/191.59 => ( V_x != V_y
% 190.77/191.59 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 190.77/191.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 190.77/191.59
% 190.77/191.60 fof(fact_Inr__inject,axiom,
% 190.77/191.60 ! [V_y,V_x,T_a,T_b] :
% 190.77/191.60 ( hAPP(c_Sum__Type_OInr(T_b,T_a),V_x) = hAPP(c_Sum__Type_OInr(T_b,T_a),V_y)
% 190.77/191.60 => V_x = V_y ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_sum_Osimps_I2_J,axiom,
% 190.77/191.60 ! [V_b_H_2,V_ba_2,T_b,T_c] :
% 190.77/191.60 ( hAPP(c_Sum__Type_OInr(T_c,T_b),V_ba_2) = hAPP(c_Sum__Type_OInr(T_c,T_b),V_b_H_2)
% 190.77/191.60 <=> V_ba_2 = V_b_H_2 ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_Inl__inject,axiom,
% 190.77/191.60 ! [V_y,V_x,T_b,T_a] :
% 190.77/191.60 ( hAPP(c_Sum__Type_OInl(T_a,T_b),V_x) = hAPP(c_Sum__Type_OInl(T_a,T_b),V_y)
% 190.77/191.60 => V_x = V_y ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_sum_Osimps_I1_J,axiom,
% 190.77/191.60 ! [V_a_H_2,V_a_2,T_c,T_b] :
% 190.77/191.60 ( 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)
% 190.77/191.60 <=> V_a_2 = V_a_H_2 ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_termination__basic__simps_I2_J,axiom,
% 190.77/191.60 ! [V_y,V_z,V_x] :
% 190.77/191.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z))
% 190.77/191.60 => 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))) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_Projl_Osimps,axiom,
% 190.77/191.60 ! [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 ).
% 190.77/191.60
% 190.77/191.60 fof(fact_Projr_Osimps,axiom,
% 190.77/191.60 ! [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 ).
% 190.77/191.60
% 190.77/191.60 fof(fact_sum_Orecs_I1_J,axiom,
% 190.77/191.60 ! [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) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_sum_Orecs_I2_J,axiom,
% 190.77/191.60 ! [V_ba_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_ba_2)) = hAPP(V_f2_2,V_ba_2) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_Suml_Osimps,axiom,
% 190.77/191.60 ! [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) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_Sumr_Osimps,axiom,
% 190.77/191.60 ! [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) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_of__nat__0__less__iff,axiom,
% 190.77/191.60 ! [V_n_2,T_b] :
% 190.77/191.60 ( class_Rings_Olinordered__semidom(T_b)
% 190.77/191.60 => ( 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)))
% 190.77/191.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_less__imp__Suc__add,axiom,
% 190.77/191.60 ! [V_n,V_m] :
% 190.77/191.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 190.77/191.60 => ? [B_k] : V_n = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),B_k)) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_less__imp__add__positive,axiom,
% 190.77/191.60 ! [V_j,V_i] :
% 190.77/191.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 190.77/191.60 => ? [B_k] :
% 190.77/191.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_k))
% 190.77/191.60 & hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),B_k) = V_j ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_gr0__implies__Suc,axiom,
% 190.77/191.60 ! [V_n] :
% 190.77/191.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 190.77/191.60 => ? [B_m] : V_n = hAPP(c_Nat_OSuc,B_m) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_of__nat__eq__iff,axiom,
% 190.77/191.60 ! [V_n_2,V_m_2,T_b] :
% 190.77/191.60 ( class_Nat_Osemiring__char__0(T_b)
% 190.77/191.60 => ( 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)
% 190.77/191.60 <=> V_m_2 = V_n_2 ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_Suml__inject,axiom,
% 190.77/191.60 ! [V_g_2,V_f_2,T_c,T_d,T_b] :
% 190.77/191.60 ( 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)
% 190.77/191.60 => V_f_2 = V_g_2 ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_Sumr__inject,axiom,
% 190.77/191.60 ! [V_g_2,V_f_2,T_b,T_d,T_c] :
% 190.77/191.60 ( 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)
% 190.77/191.60 => V_f_2 = V_g_2 ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_int__eq__0__conv,axiom,
% 190.77/191.60 ! [V_n_2] :
% 190.77/191.60 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 190.77/191.60 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_int__0,axiom,
% 190.77/191.60 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) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_zless__iff__Suc__zadd,axiom,
% 190.77/191.60 ! [V_z_2,V_w_2] :
% 190.77/191.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 190.77/191.60 <=> ? [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))) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_zless__int,axiom,
% 190.77/191.60 ! [V_n_2,V_m_2] :
% 190.77/191.60 ( 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)))
% 190.77/191.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_zadd__int__left,axiom,
% 190.77/191.60 ! [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) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_zadd__int,axiom,
% 190.77/191.60 ! [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)) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_zero__less__int__conv,axiom,
% 190.77/191.60 ! [V_n_2] :
% 190.77/191.60 ( 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)))
% 190.77/191.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_of__nat__less__0__iff,axiom,
% 190.77/191.60 ! [V_m,T_a] :
% 190.77/191.60 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.60 => ~ 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))) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_of__nat__0,axiom,
% 190.77/191.60 ! [T_a] :
% 190.77/191.60 ( class_Rings_Osemiring__1(T_a)
% 190.77/191.60 => 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) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_of__nat__less__imp__less,axiom,
% 190.77/191.60 ! [V_n,V_m,T_a] :
% 190.77/191.60 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.60 => ( 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)))
% 190.77/191.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_less__imp__of__nat__less,axiom,
% 190.77/191.60 ! [V_n,V_m,T_a] :
% 190.77/191.60 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 190.77/191.60 => 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))) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_of__nat__less__iff,axiom,
% 190.77/191.60 ! [V_n_2,V_m_2,T_b] :
% 190.77/191.60 ( class_Rings_Olinordered__semidom(T_b)
% 190.77/191.60 => ( 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)))
% 190.77/191.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_of__nat__add,axiom,
% 190.77/191.60 ! [V_n,V_m,T_a] :
% 190.77/191.60 ( class_Rings_Osemiring__1(T_a)
% 190.77/191.60 => 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)) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_lift__Suc__mono__less__iff,axiom,
% 190.77/191.60 ! [V_m_2,V_n_2,V_f_2,T_b] :
% 190.77/191.60 ( class_Orderings_Oorder(T_b)
% 190.77/191.60 => ( ! [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))))
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_n_2)),hAPP(V_f_2,V_m_2)))
% 190.77/191.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_lift__Suc__mono__less,axiom,
% 190.77/191.60 ! [V_n_H_2,V_n_2,V_f_2,T_b] :
% 190.77/191.60 ( class_Orderings_Oorder(T_b)
% 190.77/191.60 => ( ! [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))))
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_n_H_2))
% 190.77/191.60 => 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))) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
% 190.77/191.60 ! [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)) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_transfer__int__nat__relations_I2_J,axiom,
% 190.77/191.60 ! [V_y_2,V_x_2] :
% 190.77/191.60 ( 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)))
% 190.77/191.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_transfer__int__nat__numerals_I1_J,axiom,
% 190.77/191.60 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)) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_order__less__irrefl,axiom,
% 190.77/191.60 ! [V_x,T_a] :
% 190.77/191.60 ( class_Orderings_Opreorder(T_a)
% 190.77/191.60 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_linorder__neq__iff,axiom,
% 190.77/191.60 ! [V_y_2,V_x_2,T_b] :
% 190.77/191.60 ( class_Orderings_Olinorder(T_b)
% 190.77/191.60 => ( V_x_2 != V_y_2
% 190.77/191.60 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 190.77/191.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_not__less__iff__gr__or__eq,axiom,
% 190.77/191.60 ! [V_y_2,V_x_2,T_b] :
% 190.77/191.60 ( class_Orderings_Olinorder(T_b)
% 190.77/191.60 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 190.77/191.60 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 190.77/191.60 | V_x_2 = V_y_2 ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_linorder__less__linear,axiom,
% 190.77/191.60 ! [V_y,V_x,T_a] :
% 190.77/191.60 ( class_Orderings_Olinorder(T_a)
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 190.77/191.60 | V_x = V_y
% 190.77/191.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_linorder__antisym__conv3,axiom,
% 190.77/191.60 ! [V_x_2,V_y_2,T_b] :
% 190.77/191.60 ( class_Orderings_Olinorder(T_b)
% 190.77/191.60 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 190.77/191.60 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 190.77/191.60 <=> V_x_2 = V_y_2 ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_int__less__0__conv,axiom,
% 190.77/191.60 ! [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))) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_transfer__int__nat__relations_I1_J,axiom,
% 190.77/191.60 ! [V_y_2,V_x_2] :
% 190.77/191.60 ( 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)
% 190.77/191.60 <=> V_x_2 = V_y_2 ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_int__int__eq,axiom,
% 190.77/191.60 ! [V_n_2,V_m_2] :
% 190.77/191.60 ( 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)
% 190.77/191.60 <=> V_m_2 = V_n_2 ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_zadd__assoc,axiom,
% 190.77/191.60 ! [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)) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_zadd__left__commute,axiom,
% 190.77/191.60 ! [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)) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_zadd__commute,axiom,
% 190.77/191.60 ! [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) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_zadd__0,axiom,
% 190.77/191.60 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ).
% 190.77/191.60
% 190.77/191.60 fof(fact_zadd__0__right,axiom,
% 190.77/191.60 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 190.77/191.60
% 190.77/191.60 fof(fact_zadd__strict__right__mono,axiom,
% 190.77/191.60 ! [V_k,V_j,V_i] :
% 190.77/191.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 190.77/191.60 => 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))) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_zless__linear,axiom,
% 190.77/191.60 ! [V_y,V_x] :
% 190.77/191.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y))
% 190.77/191.60 | V_x = V_y
% 190.77/191.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_linorder__cases,axiom,
% 190.77/191.60 ! [V_y,V_x,T_a] :
% 190.77/191.60 ( class_Orderings_Olinorder(T_a)
% 190.77/191.60 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 190.77/191.60 => ( V_x != V_y
% 190.77/191.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_order__less__asym,axiom,
% 190.77/191.60 ! [V_y,V_x,T_a] :
% 190.77/191.60 ( class_Orderings_Opreorder(T_a)
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 190.77/191.60 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_xt1_I10_J,axiom,
% 190.77/191.60 ! [V_z,V_x,V_y,T_a] :
% 190.77/191.60 ( class_Orderings_Oorder(T_a)
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 190.77/191.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_order__less__trans,axiom,
% 190.77/191.60 ! [V_z,V_y,V_x,T_a] :
% 190.77/191.60 ( class_Orderings_Opreorder(T_a)
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 190.77/191.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_xt1_I2_J,axiom,
% 190.77/191.60 ! [V_c,V_a,V_b,T_a] :
% 190.77/191.60 ( class_Orderings_Oorder(T_a)
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 190.77/191.60 => ( V_b = V_c
% 190.77/191.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_ord__less__eq__trans,axiom,
% 190.77/191.60 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.60 ( class_Orderings_Oord(T_a)
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 190.77/191.60 => ( V_b = V_c
% 190.77/191.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_xt1_I1_J,axiom,
% 190.77/191.60 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.60 ( class_Orderings_Oorder(T_a)
% 190.77/191.60 => ( V_a = V_b
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b))
% 190.77/191.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_ord__eq__less__trans,axiom,
% 190.77/191.60 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.60 ( class_Orderings_Oord(T_a)
% 190.77/191.60 => ( V_a = V_b
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 190.77/191.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_xt1_I9_J,axiom,
% 190.77/191.60 ! [V_a,V_b,T_a] :
% 190.77/191.60 ( class_Orderings_Oorder(T_a)
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 190.77/191.60 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_order__less__asym_H,axiom,
% 190.77/191.60 ! [V_b,V_a,T_a] :
% 190.77/191.60 ( class_Orderings_Opreorder(T_a)
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 190.77/191.60 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_order__less__imp__not__eq2,axiom,
% 190.77/191.60 ! [V_y,V_x,T_a] :
% 190.77/191.60 ( class_Orderings_Oorder(T_a)
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 190.77/191.60 => V_y != V_x ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_order__less__imp__not__eq,axiom,
% 190.77/191.60 ! [V_y,V_x,T_a] :
% 190.77/191.60 ( class_Orderings_Oorder(T_a)
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 190.77/191.60 => V_x != V_y ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_order__less__imp__not__less,axiom,
% 190.77/191.60 ! [V_y,V_x,T_a] :
% 190.77/191.60 ( class_Orderings_Opreorder(T_a)
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 190.77/191.60 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_order__less__not__sym,axiom,
% 190.77/191.60 ! [V_y,V_x,T_a] :
% 190.77/191.60 ( class_Orderings_Opreorder(T_a)
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 190.77/191.60 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_less__imp__neq,axiom,
% 190.77/191.60 ! [V_y,V_x,T_a] :
% 190.77/191.60 ( class_Orderings_Oorder(T_a)
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 190.77/191.60 => V_x != V_y ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_linorder__neqE,axiom,
% 190.77/191.60 ! [V_y,V_x,T_a] :
% 190.77/191.60 ( class_Orderings_Olinorder(T_a)
% 190.77/191.60 => ( V_x != V_y
% 190.77/191.60 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 190.77/191.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_zero__less__imp__eq__int,axiom,
% 190.77/191.60 ! [V_k] :
% 190.77/191.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 190.77/191.60 => ? [B_n] :
% 190.77/191.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 190.77/191.60 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_of__int__0__less__iff,axiom,
% 190.77/191.60 ! [V_z_2,T_b] :
% 190.77/191.60 ( class_Rings_Olinordered__idom(T_b)
% 190.77/191.60 => ( 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)))
% 190.77/191.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_of__int__less__0__iff,axiom,
% 190.77/191.60 ! [V_z_2,T_b] :
% 190.77/191.60 ( class_Rings_Olinordered__idom(T_b)
% 190.77/191.60 => ( 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)))
% 190.77/191.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_zmult__zless__mono2__lemma,axiom,
% 190.77/191.60 ! [V_k,V_j,V_i] :
% 190.77/191.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 190.77/191.60 => 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))) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_negative__zless__0,axiom,
% 190.77/191.60 ! [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))) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_split__nat,axiom,
% 190.77/191.60 ! [V_i_2,V_Pa_2] :
% 190.77/191.60 ( hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,V_i_2)))
% 190.77/191.60 <=> ( ! [B_n] :
% 190.77/191.60 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
% 190.77/191.60 => hBOOL(hAPP(V_Pa_2,B_n)) )
% 190.77/191.60 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 190.77/191.60 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_zero__less__nat__eq,axiom,
% 190.77/191.60 ! [V_z_2] :
% 190.77/191.60 ( 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)))
% 190.77/191.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_negative__zless,axiom,
% 190.77/191.60 ! [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))) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_int__Suc,axiom,
% 190.77/191.60 ! [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)) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_odd__less__0,axiom,
% 190.77/191.60 ! [V_z_2] :
% 190.77/191.60 ( 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)))
% 190.77/191.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 190.77/191.60 ! [V_m,V_a,T_a] :
% 190.77/191.60 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.60 => 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) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 190.77/191.60 ! [V_a,V_m,T_a] :
% 190.77/191.60 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.60 => 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) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 190.77/191.60 ! [V_m,T_a] :
% 190.77/191.60 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.60 => 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) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_less__1__mult,axiom,
% 190.77/191.60 ! [V_n,V_m,T_a] :
% 190.77/191.60 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m))
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n))
% 190.77/191.60 => 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))) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_square__eq__iff,axiom,
% 190.77/191.60 ! [V_ba_2,V_a_2,T_b] :
% 190.77/191.60 ( class_Rings_Oidom(T_b)
% 190.77/191.60 => ( 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_ba_2),V_ba_2)
% 190.77/191.60 <=> ( V_a_2 = V_ba_2
% 190.77/191.60 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_square__eq__1__iff,axiom,
% 190.77/191.60 ! [V_x_2,T_b] :
% 190.77/191.60 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 190.77/191.60 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 190.77/191.60 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_b)
% 190.77/191.60 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_minus__mult__minus,axiom,
% 190.77/191.60 ! [V_b,V_a,T_a] :
% 190.77/191.60 ( class_Rings_Oring(T_a)
% 190.77/191.60 => 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) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_minus__mult__commute,axiom,
% 190.77/191.60 ! [V_b,V_a,T_a] :
% 190.77/191.60 ( class_Rings_Oring(T_a)
% 190.77/191.60 => 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)) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_minus__mult__left,axiom,
% 190.77/191.60 ! [V_b,V_a,T_a] :
% 190.77/191.60 ( class_Rings_Oring(T_a)
% 190.77/191.60 => 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) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_minus__mult__right,axiom,
% 190.77/191.60 ! [V_b,V_a,T_a] :
% 190.77/191.60 ( class_Rings_Oring(T_a)
% 190.77/191.60 => 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)) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 190.77/191.60 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.60 ( class_Groups_Oab__semigroup__mult(T_a)
% 190.77/191.60 => 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)) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_neg__equal__iff__equal,axiom,
% 190.77/191.60 ! [V_ba_2,V_a_2,T_b] :
% 190.77/191.60 ( class_Groups_Ogroup__add(T_b)
% 190.77/191.60 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2)
% 190.77/191.60 <=> V_a_2 = V_ba_2 ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_minus__equation__iff,axiom,
% 190.77/191.60 ! [V_ba_2,V_a_2,T_b] :
% 190.77/191.60 ( class_Groups_Ogroup__add(T_b)
% 190.77/191.60 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_ba_2
% 190.77/191.60 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2) = V_a_2 ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_equation__minus__iff,axiom,
% 190.77/191.60 ! [V_ba_2,V_a_2,T_b] :
% 190.77/191.60 ( class_Groups_Ogroup__add(T_b)
% 190.77/191.60 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2)
% 190.77/191.60 <=> V_ba_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_mult_Ocomm__neutral,axiom,
% 190.77/191.60 ! [V_a,T_a] :
% 190.77/191.60 ( class_Groups_Ocomm__monoid__mult(T_a)
% 190.77/191.60 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_mult__1__right,axiom,
% 190.77/191.60 ! [V_a,T_a] :
% 190.77/191.60 ( class_Groups_Omonoid__mult(T_a)
% 190.77/191.60 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_one__reorient,axiom,
% 190.77/191.60 ! [V_x_2,T_b] :
% 190.77/191.60 ( class_Groups_Oone(T_b)
% 190.77/191.60 => ( c_Groups_Oone__class_Oone(T_b) = V_x_2
% 190.77/191.60 <=> V_x_2 = c_Groups_Oone__class_Oone(T_b) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_mult__1,axiom,
% 190.77/191.60 ! [V_a,T_a] :
% 190.77/191.60 ( class_Groups_Ocomm__monoid__mult(T_a)
% 190.77/191.60 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_mult__1__left,axiom,
% 190.77/191.60 ! [V_a,T_a] :
% 190.77/191.60 ( class_Groups_Omonoid__mult(T_a)
% 190.77/191.60 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_minus__minus,axiom,
% 190.77/191.60 ! [V_a,T_a] :
% 190.77/191.60 ( class_Groups_Ogroup__add(T_a)
% 190.77/191.60 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 190.77/191.60 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 190.77/191.60 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.60 => 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)) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 190.77/191.60 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 190.77/191.60 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.60 => 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)) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 190.77/191.60 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 190.77/191.60 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.60 => 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))) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 190.77/191.60 ! [V_rx,V_ly,V_lx,T_a] :
% 190.77/191.60 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.60 => 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) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_zmult__assoc,axiom,
% 190.77/191.60 ! [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)) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 190.77/191.60 ! [V_rx,V_ly,V_lx,T_a] :
% 190.77/191.60 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.60 => 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)) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_of__int__eq__iff,axiom,
% 190.77/191.60 ! [V_z_2,V_w_2,T_b] :
% 190.77/191.60 ( class_Int_Oring__char__0(T_b)
% 190.77/191.60 => ( 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)
% 190.77/191.60 <=> V_w_2 = V_z_2 ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_zmult__zminus,axiom,
% 190.77/191.60 ! [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)) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 190.77/191.60 ! [V_ry,V_rx,V_lx,T_a] :
% 190.77/191.60 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.60 => 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) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 190.77/191.60 ! [V_ry,V_rx,V_lx,T_a] :
% 190.77/191.60 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.60 => 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)) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_zmult__commute,axiom,
% 190.77/191.60 ! [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) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 190.77/191.60 ! [V_b,V_a,T_a] :
% 190.77/191.60 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.60 => 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) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_zmult__1__right,axiom,
% 190.77/191.60 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 190.77/191.60
% 190.77/191.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 190.77/191.60 ! [V_a,T_a] :
% 190.77/191.60 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.60 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_zmult__1,axiom,
% 190.77/191.60 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 190.77/191.60
% 190.77/191.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 190.77/191.60 ! [V_a,T_a] :
% 190.77/191.60 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.60 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_of__int__mult,axiom,
% 190.77/191.60 ! [V_z,V_w,T_a] :
% 190.77/191.60 ( class_Rings_Oring__1(T_a)
% 190.77/191.60 => 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)) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_of__int__minus,axiom,
% 190.77/191.60 ! [V_z,T_a] :
% 190.77/191.60 ( class_Rings_Oring__1(T_a)
% 190.77/191.60 => 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)) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_zminus__zminus,axiom,
% 190.77/191.60 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ).
% 190.77/191.60
% 190.77/191.60 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
% 190.77/191.60 ! [V_x,T_a] :
% 190.77/191.60 ( class_Rings_Ocomm__ring__1(T_a)
% 190.77/191.60 => 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) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_of__int__1,axiom,
% 190.77/191.60 ! [T_a] :
% 190.77/191.60 ( class_Rings_Oring__1(T_a)
% 190.77/191.60 => 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) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_of__nat__mult,axiom,
% 190.77/191.60 ! [V_n,V_m,T_a] :
% 190.77/191.60 ( class_Rings_Osemiring__1(T_a)
% 190.77/191.60 => 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)) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_of__nat__1,axiom,
% 190.77/191.60 ! [T_a] :
% 190.77/191.60 ( class_Rings_Osemiring__1(T_a)
% 190.77/191.60 => 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) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_of__int__of__nat,axiom,
% 190.77/191.60 ! [V_k,T_a] :
% 190.77/191.60 ( class_Rings_Oring__1(T_a)
% 190.77/191.60 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 190.77/191.60 => 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)))) )
% 190.77/191.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 190.77/191.60 => 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)) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_nat__zminus__int,axiom,
% 190.77/191.60 ! [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) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_nat__1,axiom,
% 190.77/191.60 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_pos__zmult__eq__1__iff,axiom,
% 190.77/191.60 ! [V_n_2,V_m_2] :
% 190.77/191.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2))
% 190.77/191.60 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 190.77/191.60 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 190.77/191.60 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_minus__zero,axiom,
% 190.77/191.60 ! [T_a] :
% 190.77/191.60 ( class_Groups_Ogroup__add(T_a)
% 190.77/191.60 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_neg__0__equal__iff__equal,axiom,
% 190.77/191.60 ! [V_a_2,T_b] :
% 190.77/191.60 ( class_Groups_Ogroup__add(T_b)
% 190.77/191.60 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 190.77/191.60 <=> c_Groups_Ozero__class_Ozero(T_b) = V_a_2 ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_equal__neg__zero,axiom,
% 190.77/191.60 ! [V_a_2,T_b] :
% 190.77/191.60 ( class_Groups_Olinordered__ab__group__add(T_b)
% 190.77/191.60 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 190.77/191.60 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_neg__equal__0__iff__equal,axiom,
% 190.77/191.60 ! [V_a_2,T_b] :
% 190.77/191.60 ( class_Groups_Ogroup__add(T_b)
% 190.77/191.60 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 190.77/191.60 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_neg__equal__zero,axiom,
% 190.77/191.60 ! [V_a_2,T_b] :
% 190.77/191.60 ( class_Groups_Olinordered__ab__group__add(T_b)
% 190.77/191.60 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_a_2
% 190.77/191.60 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_neg__less__iff__less,axiom,
% 190.77/191.60 ! [V_a_2,V_ba_2,T_b] :
% 190.77/191.60 ( class_Groups_Oordered__ab__group__add(T_b)
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 190.77/191.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_minus__less__iff,axiom,
% 190.77/191.60 ! [V_ba_2,V_a_2,T_b] :
% 190.77/191.60 ( class_Groups_Oordered__ab__group__add(T_b)
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_ba_2))
% 190.77/191.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2)),V_a_2)) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_less__minus__iff,axiom,
% 190.77/191.60 ! [V_ba_2,V_a_2,T_b] :
% 190.77/191.60 ( class_Groups_Oordered__ab__group__add(T_b)
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2)))
% 190.77/191.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_minus__add__distrib,axiom,
% 190.77/191.60 ! [V_b,V_a,T_a] :
% 190.77/191.60 ( class_Groups_Oab__group__add(T_a)
% 190.77/191.60 => 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)) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_minus__add,axiom,
% 190.77/191.60 ! [V_b,V_a,T_a] :
% 190.77/191.60 ( class_Groups_Ogroup__add(T_a)
% 190.77/191.60 => 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)) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_add__minus__cancel,axiom,
% 190.77/191.60 ! [V_b,V_a,T_a] :
% 190.77/191.60 ( class_Groups_Ogroup__add(T_a)
% 190.77/191.60 => 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 ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_minus__add__cancel,axiom,
% 190.77/191.60 ! [V_b,V_a,T_a] :
% 190.77/191.60 ( class_Groups_Ogroup__add(T_a)
% 190.77/191.60 => 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 ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 190.77/191.60 ! [V_a,T_a] :
% 190.77/191.60 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.60 => 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) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 190.77/191.60 ! [V_a,T_a] :
% 190.77/191.60 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.60 => 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) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_mult__zero__left,axiom,
% 190.77/191.60 ! [V_a,T_a] :
% 190.77/191.60 ( class_Rings_Omult__zero(T_a)
% 190.77/191.60 => 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) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_mult__zero__right,axiom,
% 190.77/191.60 ! [V_a,T_a] :
% 190.77/191.60 ( class_Rings_Omult__zero(T_a)
% 190.77/191.60 => 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) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_mult__eq__0__iff,axiom,
% 190.77/191.60 ! [V_ba_2,V_a_2,T_b] :
% 190.77/191.60 ( class_Rings_Oring__no__zero__divisors(T_b)
% 190.77/191.60 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ba_2) = c_Groups_Ozero__class_Ozero(T_b)
% 190.77/191.60 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 190.77/191.60 | V_ba_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_no__zero__divisors,axiom,
% 190.77/191.60 ! [V_b,V_a,T_a] :
% 190.77/191.60 ( class_Rings_Ono__zero__divisors(T_a)
% 190.77/191.60 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 190.77/191.60 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 190.77/191.60 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_divisors__zero,axiom,
% 190.77/191.60 ! [V_b,V_a,T_a] :
% 190.77/191.60 ( class_Rings_Ono__zero__divisors(T_a)
% 190.77/191.60 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 190.77/191.60 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 190.77/191.60 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_one__neq__zero,axiom,
% 190.77/191.60 ! [T_a] :
% 190.77/191.60 ( class_Rings_Ozero__neq__one(T_a)
% 190.77/191.60 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_zero__neq__one,axiom,
% 190.77/191.60 ! [T_a] :
% 190.77/191.60 ( class_Rings_Ozero__neq__one(T_a)
% 190.77/191.60 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_zminus__0,axiom,
% 190.77/191.60 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) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_nat__int,axiom,
% 190.77/191.60 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ).
% 190.77/191.60
% 190.77/191.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 190.77/191.60 ! [V_z,V_y,V_x,T_a] :
% 190.77/191.60 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.60 => 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)) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_crossproduct__noteq,axiom,
% 190.77/191.60 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] :
% 190.77/191.60 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 190.77/191.60 => ( ( V_a_2 != V_ba_2
% 190.77/191.60 & V_ca_2 != V_d_2 )
% 190.77/191.60 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ba_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_ba_2),V_ca_2)) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 190.77/191.60 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.60 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.60 => 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)) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 190.77/191.60 ! [V_b,V_m,V_a,T_a] :
% 190.77/191.60 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.60 => 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) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_crossproduct__eq,axiom,
% 190.77/191.60 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_b] :
% 190.77/191.60 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 190.77/191.60 => ( 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))
% 190.77/191.60 <=> ( V_w_2 = V_x_2
% 190.77/191.60 | V_y_2 = V_z_2 ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_comm__semiring__class_Odistrib,axiom,
% 190.77/191.60 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.60 ( class_Rings_Ocomm__semiring(T_a)
% 190.77/191.60 => 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)) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_combine__common__factor,axiom,
% 190.77/191.60 ! [V_c,V_b,V_e,V_a,T_a] :
% 190.77/191.60 ( class_Rings_Osemiring(T_a)
% 190.77/191.60 => 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) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_zminus__zadd__distrib,axiom,
% 190.77/191.60 ! [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)) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_zadd__zmult__distrib2,axiom,
% 190.77/191.60 ! [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)) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_zadd__zmult__distrib,axiom,
% 190.77/191.60 ! [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)) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_int__0__neq__1,axiom,
% 190.77/191.60 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_of__int__int__eq,axiom,
% 190.77/191.60 ! [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) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_one__less__nat__eq,axiom,
% 190.77/191.60 ! [V_z_2] :
% 190.77/191.60 ( 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)))
% 190.77/191.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_neg__less__nonneg,axiom,
% 190.77/191.60 ! [V_a_2,T_b] :
% 190.77/191.60 ( class_Groups_Olinordered__ab__group__add(T_b)
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
% 190.77/191.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_neg__less__0__iff__less,axiom,
% 190.77/191.60 ! [V_a_2,T_b] :
% 190.77/191.60 ( class_Groups_Oordered__ab__group__add(T_b)
% 190.77/191.60 => ( 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)))
% 190.77/191.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_neg__0__less__iff__less,axiom,
% 190.77/191.60 ! [V_a_2,T_b] :
% 190.77/191.60 ( class_Groups_Oordered__ab__group__add(T_b)
% 190.77/191.60 => ( 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)))
% 190.77/191.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_less__minus__self__iff,axiom,
% 190.77/191.60 ! [V_a_2,T_b] :
% 190.77/191.60 ( class_Rings_Olinordered__idom(T_b)
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 190.77/191.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_minus__unique,axiom,
% 190.77/191.60 ! [V_b,V_a,T_a] :
% 190.77/191.60 ( class_Groups_Ogroup__add(T_a)
% 190.77/191.60 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 190.77/191.60 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_ab__left__minus,axiom,
% 190.77/191.60 ! [V_a,T_a] :
% 190.77/191.60 ( class_Groups_Oab__group__add(T_a)
% 190.77/191.60 => 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) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_left__minus,axiom,
% 190.77/191.60 ! [V_a,T_a] :
% 190.77/191.60 ( class_Groups_Ogroup__add(T_a)
% 190.77/191.60 => 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) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_eq__neg__iff__add__eq__0,axiom,
% 190.77/191.60 ! [V_ba_2,V_a_2,T_b] :
% 190.77/191.60 ( class_Groups_Ogroup__add(T_b)
% 190.77/191.60 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2)
% 190.77/191.60 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ba_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_right__minus,axiom,
% 190.77/191.60 ! [V_a,T_a] :
% 190.77/191.60 ( class_Groups_Ogroup__add(T_a)
% 190.77/191.60 => 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) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_nat__0,axiom,
% 190.77/191.60 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_transfer__nat__int__numerals_I1_J,axiom,
% 190.77/191.60 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_not__square__less__zero,axiom,
% 190.77/191.60 ! [V_a,T_a] :
% 190.77/191.60 ( class_Rings_Olinordered__ring(T_a)
% 190.77/191.60 => ~ 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))) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_mult__less__cancel__right__disj,axiom,
% 190.77/191.60 ! [V_ba_2,V_ca_2,V_a_2,T_b] :
% 190.77/191.60 ( class_Rings_Olinordered__ring__strict(T_b)
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ba_2),V_ca_2)))
% 190.77/191.60 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 190.77/191.60 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) )
% 190.77/191.60 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 190.77/191.60 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),V_a_2)) ) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_mult__less__cancel__left__disj,axiom,
% 190.77/191.60 ! [V_ba_2,V_a_2,V_ca_2,T_b] :
% 190.77/191.60 ( class_Rings_Olinordered__ring__strict(T_b)
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_ba_2)))
% 190.77/191.60 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 190.77/191.60 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) )
% 190.77/191.60 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 190.77/191.60 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),V_a_2)) ) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_mult__less__cancel__left__pos,axiom,
% 190.77/191.60 ! [V_ba_2,V_a_2,V_ca_2,T_b] :
% 190.77/191.60 ( class_Rings_Olinordered__ring__strict(T_b)
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_ba_2)))
% 190.77/191.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_mult__pos__pos,axiom,
% 190.77/191.60 ! [V_b,V_a,T_a] :
% 190.77/191.60 ( class_Rings_Olinordered__semiring__strict(T_a)
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 190.77/191.60 => 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))) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_mult__pos__neg,axiom,
% 190.77/191.60 ! [V_b,V_a,T_a] :
% 190.77/191.60 ( class_Rings_Olinordered__semiring__strict(T_a)
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 190.77/191.60 => 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))) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_mult__pos__neg2,axiom,
% 190.77/191.60 ! [V_b,V_a,T_a] :
% 190.77/191.60 ( class_Rings_Olinordered__semiring__strict(T_a)
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 190.77/191.60 => 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))) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_zero__less__mult__pos,axiom,
% 190.77/191.60 ! [V_b,V_a,T_a] :
% 190.77/191.60 ( class_Rings_Olinordered__semiring__strict(T_a)
% 190.77/191.60 => ( 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)))
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 190.77/191.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_zero__less__mult__pos2,axiom,
% 190.77/191.60 ! [V_a,V_b,T_a] :
% 190.77/191.60 ( class_Rings_Olinordered__semiring__strict(T_a)
% 190.77/191.60 => ( 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)))
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 190.77/191.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_mult__less__cancel__left__neg,axiom,
% 190.77/191.60 ! [V_ba_2,V_a_2,V_ca_2,T_b] :
% 190.77/191.60 ( class_Rings_Olinordered__ring__strict(T_b)
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_ba_2)))
% 190.77/191.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),V_a_2)) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_mult__neg__pos,axiom,
% 190.77/191.60 ! [V_b,V_a,T_a] :
% 190.77/191.60 ( class_Rings_Olinordered__semiring__strict(T_a)
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 190.77/191.60 => 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))) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_mult__neg__neg,axiom,
% 190.77/191.60 ! [V_b,V_a,T_a] :
% 190.77/191.60 ( class_Rings_Olinordered__ring__strict(T_a)
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 190.77/191.60 => 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))) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_mult__strict__right__mono,axiom,
% 190.77/191.60 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.60 ( class_Rings_Olinordered__semiring__strict(T_a)
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 190.77/191.60 => 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))) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_mult__strict__left__mono,axiom,
% 190.77/191.60 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.60 ( class_Rings_Olinordered__semiring__strict(T_a)
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 190.77/191.60 => 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))) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_comm__mult__strict__left__mono,axiom,
% 190.77/191.60 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.60 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 190.77/191.60 => 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))) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_mult__strict__right__mono__neg,axiom,
% 190.77/191.60 ! [V_c,V_a,V_b,T_a] :
% 190.77/191.60 ( class_Rings_Olinordered__ring__strict(T_a)
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 190.77/191.60 => 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))) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_mult__strict__left__mono__neg,axiom,
% 190.77/191.60 ! [V_c,V_a,V_b,T_a] :
% 190.77/191.60 ( class_Rings_Olinordered__ring__strict(T_a)
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 190.77/191.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 190.77/191.60 => 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))) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_not__one__less__zero,axiom,
% 190.77/191.60 ! [T_a] :
% 190.77/191.60 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.60 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_zero__less__one,axiom,
% 190.77/191.60 ! [T_a] :
% 190.77/191.60 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_add__scale__eq__noteq,axiom,
% 190.77/191.60 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 190.77/191.60 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 190.77/191.60 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 190.77/191.60 => ( ( V_a = V_b
% 190.77/191.60 & V_c != V_d )
% 190.77/191.60 => 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)) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_sum__squares__eq__zero__iff,axiom,
% 190.77/191.60 ! [V_y_2,V_x_2,T_b] :
% 190.77/191.60 ( class_Rings_Olinordered__ring__strict(T_b)
% 190.77/191.60 => ( 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)
% 190.77/191.60 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 190.77/191.60 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_less__add__one,axiom,
% 190.77/191.60 ! [V_a,T_a] :
% 190.77/191.60 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.60 => 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)))) ) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_zadd__zminus__inverse2,axiom,
% 190.77/191.60 ! [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) ).
% 190.77/191.60
% 190.77/191.60 fof(fact_negative__eq__positive,axiom,
% 190.77/191.61 ! [V_m_2,V_n_2] :
% 190.77/191.61 ( 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)
% 190.77/191.61 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.61 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_not__int__zless__negative,axiom,
% 190.77/191.61 ! [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)))) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_zmult__zless__mono2,axiom,
% 190.77/191.61 ! [V_k,V_j,V_i] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 190.77/191.61 => 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))) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_int__0__less__1,axiom,
% 190.77/191.61 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))) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_odd__nonzero,axiom,
% 190.77/191.61 ! [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) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_zless__add1__eq,axiom,
% 190.77/191.61 ! [V_z_2,V_w_2] :
% 190.77/191.61 ( 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))))
% 190.77/191.61 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 190.77/191.61 | V_w_2 = V_z_2 ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_of__int__0,axiom,
% 190.77/191.61 ! [T_a] :
% 190.77/191.61 ( class_Rings_Oring__1(T_a)
% 190.77/191.61 => 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) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_of__int__0__eq__iff,axiom,
% 190.77/191.61 ! [V_z_2,T_b] :
% 190.77/191.61 ( class_Int_Oring__char__0(T_b)
% 190.77/191.61 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
% 190.77/191.61 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_of__int__eq__0__iff,axiom,
% 190.77/191.61 ! [V_z_2,T_b] :
% 190.77/191.61 ( class_Int_Oring__char__0(T_b)
% 190.77/191.61 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b)
% 190.77/191.61 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_of__int__less__iff,axiom,
% 190.77/191.61 ! [V_z_2,V_w_2,T_b] :
% 190.77/191.61 ( class_Rings_Olinordered__idom(T_b)
% 190.77/191.61 => ( 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)))
% 190.77/191.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_of__int__add,axiom,
% 190.77/191.61 ! [V_z,V_w,T_a] :
% 190.77/191.61 ( class_Rings_Oring__1(T_a)
% 190.77/191.61 => 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)) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_of__int__of__nat__eq,axiom,
% 190.77/191.61 ! [V_n,T_a] :
% 190.77/191.61 ( class_Rings_Oring__1(T_a)
% 190.77/191.61 => 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) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_nat__mono__iff,axiom,
% 190.77/191.61 ! [V_w_2,V_z_2] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 190.77/191.61 => ( 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)))
% 190.77/191.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_zless__nat__conj,axiom,
% 190.77/191.61 ! [V_z_2,V_w_2] :
% 190.77/191.61 ( 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)))
% 190.77/191.61 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 190.77/191.61 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_zless__nat__eq__int__zless,axiom,
% 190.77/191.61 ! [V_z_2,V_m_2] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2)))
% 190.77/191.61 <=> 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)) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_not__sum__squares__lt__zero,axiom,
% 190.77/191.61 ! [V_y,V_x,T_a] :
% 190.77/191.61 ( class_Rings_Olinordered__ring(T_a)
% 190.77/191.61 => ~ 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))) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_sum__squares__gt__zero__iff,axiom,
% 190.77/191.61 ! [V_y_2,V_x_2,T_b] :
% 190.77/191.61 ( class_Rings_Olinordered__ring__strict(T_b)
% 190.77/191.61 => ( 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))))
% 190.77/191.61 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 190.77/191.61 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_zero__less__two,axiom,
% 190.77/191.61 ! [T_a] :
% 190.77/191.61 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.61 => 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)))) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_of__nat__Suc,axiom,
% 190.77/191.61 ! [V_m,T_a] :
% 190.77/191.61 ( class_Rings_Osemiring__1(T_a)
% 190.77/191.61 => 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)) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_int__Suc0__eq__1,axiom,
% 190.77/191.61 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) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_nat__aux__def,axiom,
% 190.77/191.61 ! [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) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_negD,axiom,
% 190.77/191.61 ! [V_x] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 190.77/191.61 => ? [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))) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_sgn__if,axiom,
% 190.77/191.61 ! [V_x,T_a] :
% 190.77/191.61 ( class_Groups_Osgn__if(T_a)
% 190.77/191.61 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 190.77/191.61 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) )
% 190.77/191.61 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 190.77/191.61 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 190.77/191.61 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) )
% 190.77/191.61 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 190.77/191.61 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_sgn__neg,axiom,
% 190.77/191.61 ! [V_a,T_a] :
% 190.77/191.61 ( class_Rings_Olinordered__idom(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 190.77/191.61 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_sgn__1__neg,axiom,
% 190.77/191.61 ! [V_a_2,T_b] :
% 190.77/191.61 ( class_Rings_Olinordered__idom(T_b)
% 190.77/191.61 => ( 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))
% 190.77/191.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_zsgn__def,axiom,
% 190.77/191.61 ! [V_i] :
% 190.77/191.61 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 190.77/191.61 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 190.77/191.61 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 190.77/191.61 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 190.77/191.61 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 190.77/191.61 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 190.77/191.61 => 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)) ) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_Suc__nat__eq__nat__zadd1,axiom,
% 190.77/191.61 ! [V_z] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 190.77/191.61 => 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)) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_nat__less__iff,axiom,
% 190.77/191.61 ! [V_m_2,V_w_2] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2))
% 190.77/191.61 <=> 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))) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_convex__bound__lt,axiom,
% 190.77/191.61 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 190.77/191.61 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 190.77/191.61 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 190.77/191.61 => 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)) ) ) ) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_sgn__1__pos,axiom,
% 190.77/191.61 ! [V_a_2,T_b] :
% 190.77/191.61 ( class_Rings_Olinordered__idom(T_b)
% 190.77/191.61 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b)
% 190.77/191.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_order__refl,axiom,
% 190.77/191.61 ! [V_x,T_a] :
% 190.77/191.61 ( class_Orderings_Opreorder(T_a)
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_le0,axiom,
% 190.77/191.61 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_negative__zle,axiom,
% 190.77/191.61 ! [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))) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_mult__le__mono,axiom,
% 190.77/191.61 ! [V_l,V_k,V_j,V_i] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 190.77/191.61 => 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))) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_mult__le__mono2,axiom,
% 190.77/191.61 ! [V_k,V_j,V_i] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 190.77/191.61 => 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))) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_mult__le__mono1,axiom,
% 190.77/191.61 ! [V_k,V_j,V_i] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 190.77/191.61 => 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))) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_nat__mult__assoc,axiom,
% 190.77/191.61 ! [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)) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_nat__mult__eq__1__iff,axiom,
% 190.77/191.61 ! [V_n_2,V_m_2] :
% 190.77/191.61 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 190.77/191.61 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 190.77/191.61 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_nat__mult__commute,axiom,
% 190.77/191.61 ! [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) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_nat__mult__1__right,axiom,
% 190.77/191.61 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 190.77/191.61
% 190.77/191.61 fof(fact_nat__1__eq__mult__iff,axiom,
% 190.77/191.61 ! [V_n_2,V_m_2] :
% 190.77/191.61 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
% 190.77/191.61 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 190.77/191.61 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_nat__mult__1,axiom,
% 190.77/191.61 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 190.77/191.61
% 190.77/191.61 fof(fact_le__cube,axiom,
% 190.77/191.61 ! [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)))) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_le__square,axiom,
% 190.77/191.61 ! [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))) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_mult__eq__self__implies__10,axiom,
% 190.77/191.61 ! [V_n,V_m] :
% 190.77/191.61 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 190.77/191.61 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 190.77/191.61 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_Suc__mult__le__cancel1,axiom,
% 190.77/191.61 ! [V_n_2,V_m_2,V_k_2] :
% 190.77/191.61 ( 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)))
% 190.77/191.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_zle__refl,axiom,
% 190.77/191.61 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_zle__linear,axiom,
% 190.77/191.61 ! [V_w,V_z] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 190.77/191.61 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_zle__trans,axiom,
% 190.77/191.61 ! [V_k,V_j,V_i] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k))
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_zle__antisym,axiom,
% 190.77/191.61 ! [V_w,V_z] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
% 190.77/191.61 => V_z = V_w ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_sgn__sgn,axiom,
% 190.77/191.61 ! [V_a,T_a] :
% 190.77/191.61 ( class_Rings_Olinordered__idom(T_a)
% 190.77/191.61 => 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) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_le__fun__def,axiom,
% 190.77/191.61 ! [V_g_2,V_f_2,T_b,T_c] :
% 190.77/191.61 ( class_Orderings_Oord(T_c)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 190.77/191.61 <=> ! [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))) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_linorder__linear,axiom,
% 190.77/191.61 ! [V_y,V_x,T_a] :
% 190.77/191.61 ( class_Orderings_Olinorder(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 190.77/191.61 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_order__eq__iff,axiom,
% 190.77/191.61 ! [V_y_2,V_x_2,T_b] :
% 190.77/191.61 ( class_Orderings_Oorder(T_b)
% 190.77/191.61 => ( V_x_2 = V_y_2
% 190.77/191.61 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 190.77/191.61 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_order__eq__refl,axiom,
% 190.77/191.61 ! [V_y,V_x,T_a] :
% 190.77/191.61 ( class_Orderings_Opreorder(T_a)
% 190.77/191.61 => ( V_x = V_y
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_le__funD,axiom,
% 190.77/191.61 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 190.77/191.61 ( class_Orderings_Oord(T_c)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 190.77/191.61 => 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))) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_order__antisym__conv,axiom,
% 190.77/191.61 ! [V_x_2,V_y_2,T_b] :
% 190.77/191.61 ( class_Orderings_Oorder(T_b)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 190.77/191.61 <=> V_x_2 = V_y_2 ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_ord__eq__le__trans,axiom,
% 190.77/191.61 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.61 ( class_Orderings_Oord(T_a)
% 190.77/191.61 => ( V_a = V_b
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_xt1_I3_J,axiom,
% 190.77/191.61 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.61 ( class_Orderings_Oorder(T_a)
% 190.77/191.61 => ( V_a = V_b
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b))
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_ord__le__eq__trans,axiom,
% 190.77/191.61 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.61 ( class_Orderings_Oord(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 190.77/191.61 => ( V_b = V_c
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_xt1_I4_J,axiom,
% 190.77/191.61 ! [V_c,V_a,V_b,T_a] :
% 190.77/191.61 ( class_Orderings_Oorder(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 190.77/191.61 => ( V_b = V_c
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_order__antisym,axiom,
% 190.77/191.61 ! [V_y,V_x,T_a] :
% 190.77/191.61 ( class_Orderings_Oorder(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 190.77/191.61 => V_x = V_y ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_order__trans,axiom,
% 190.77/191.61 ! [V_z,V_y,V_x,T_a] :
% 190.77/191.61 ( class_Orderings_Opreorder(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_xt1_I5_J,axiom,
% 190.77/191.61 ! [V_x,V_y,T_a] :
% 190.77/191.61 ( class_Orderings_Oorder(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 190.77/191.61 => V_x = V_y ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_xt1_I6_J,axiom,
% 190.77/191.61 ! [V_z,V_x,V_y,T_a] :
% 190.77/191.61 ( class_Orderings_Oorder(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_le__funE,axiom,
% 190.77/191.61 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 190.77/191.61 ( class_Orderings_Oord(T_c)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 190.77/191.61 => 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))) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_linorder__le__cases,axiom,
% 190.77/191.61 ! [V_y,V_x,T_a] :
% 190.77/191.61 ( class_Orderings_Olinorder(T_a)
% 190.77/191.61 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_of__nat__le__iff,axiom,
% 190.77/191.61 ! [V_n_2,V_m_2,T_b] :
% 190.77/191.61 ( class_Rings_Olinordered__semidom(T_b)
% 190.77/191.61 => ( 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)))
% 190.77/191.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_transfer__int__nat__relations_I3_J,axiom,
% 190.77/191.61 ! [V_y_2,V_x_2] :
% 190.77/191.61 ( 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)))
% 190.77/191.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_zle__int,axiom,
% 190.77/191.61 ! [V_n_2,V_m_2] :
% 190.77/191.61 ( 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)))
% 190.77/191.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_of__int__le__iff,axiom,
% 190.77/191.61 ! [V_z_2,V_w_2,T_b] :
% 190.77/191.61 ( class_Rings_Olinordered__idom(T_b)
% 190.77/191.61 => ( 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)))
% 190.77/191.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_one__le__mult__iff,axiom,
% 190.77/191.61 ! [V_n_2,V_m_2] :
% 190.77/191.61 ( 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)))
% 190.77/191.61 <=> ( 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))
% 190.77/191.61 & 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)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_mult__le__cancel1,axiom,
% 190.77/191.61 ! [V_n_2,V_m_2,V_k_2] :
% 190.77/191.61 ( 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)))
% 190.77/191.61 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_mult__le__cancel2,axiom,
% 190.77/191.61 ! [V_n_2,V_k_2,V_m_2] :
% 190.77/191.61 ( 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)))
% 190.77/191.61 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_transfer__nat__int__relations_I3_J,axiom,
% 190.77/191.61 ! [V_y_2,V_x_2] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 190.77/191.61 => ( 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)))
% 190.77/191.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_xt1_I8_J,axiom,
% 190.77/191.61 ! [V_z,V_x,V_y,T_a] :
% 190.77/191.61 ( class_Orderings_Oorder(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_order__le__less__trans,axiom,
% 190.77/191.61 ! [V_z,V_y,V_x,T_a] :
% 190.77/191.61 ( class_Orderings_Opreorder(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_xt1_I7_J,axiom,
% 190.77/191.61 ! [V_z,V_x,V_y,T_a] :
% 190.77/191.61 ( class_Orderings_Oorder(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_order__less__le__trans,axiom,
% 190.77/191.61 ! [V_z,V_y,V_x,T_a] :
% 190.77/191.61 ( class_Orderings_Opreorder(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_xt1_I11_J,axiom,
% 190.77/191.61 ! [V_a,V_b,T_a] :
% 190.77/191.61 ( class_Orderings_Oorder(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 190.77/191.61 => ( V_a != V_b
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_order__le__neq__trans,axiom,
% 190.77/191.61 ! [V_b,V_a,T_a] :
% 190.77/191.61 ( class_Orderings_Oorder(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 190.77/191.61 => ( V_a != V_b
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_order__le__imp__less__or__eq,axiom,
% 190.77/191.61 ! [V_y,V_x,T_a] :
% 190.77/191.61 ( class_Orderings_Oorder(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 190.77/191.61 | V_x = V_y ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_linorder__antisym__conv2,axiom,
% 190.77/191.61 ! [V_y_2,V_x_2,T_b] :
% 190.77/191.61 ( class_Orderings_Olinorder(T_b)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 190.77/191.61 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 190.77/191.61 <=> V_x_2 = V_y_2 ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_order__less__imp__le,axiom,
% 190.77/191.61 ! [V_y,V_x,T_a] :
% 190.77/191.61 ( class_Orderings_Opreorder(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_leD,axiom,
% 190.77/191.61 ! [V_x,V_y,T_a] :
% 190.77/191.61 ( class_Orderings_Olinorder(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 190.77/191.61 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_xt1_I12_J,axiom,
% 190.77/191.61 ! [V_b,V_a,T_a] :
% 190.77/191.61 ( class_Orderings_Oorder(T_a)
% 190.77/191.61 => ( V_a != V_b
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_order__neq__le__trans,axiom,
% 190.77/191.61 ! [V_b,V_a,T_a] :
% 190.77/191.61 ( class_Orderings_Oorder(T_a)
% 190.77/191.61 => ( V_a != V_b
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_linorder__antisym__conv1,axiom,
% 190.77/191.61 ! [V_y_2,V_x_2,T_b] :
% 190.77/191.61 ( class_Orderings_Olinorder(T_b)
% 190.77/191.61 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 190.77/191.61 <=> V_x_2 = V_y_2 ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_not__leE,axiom,
% 190.77/191.61 ! [V_x,V_y,T_a] :
% 190.77/191.61 ( class_Orderings_Olinorder(T_a)
% 190.77/191.61 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_leI,axiom,
% 190.77/191.61 ! [V_y,V_x,T_a] :
% 190.77/191.61 ( class_Orderings_Olinorder(T_a)
% 190.77/191.61 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_order__le__less,axiom,
% 190.77/191.61 ! [V_y_2,V_x_2,T_b] :
% 190.77/191.61 ( class_Orderings_Oorder(T_b)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 190.77/191.61 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 190.77/191.61 | V_x_2 = V_y_2 ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_less__le__not__le,axiom,
% 190.77/191.61 ! [V_y_2,V_x_2,T_b] :
% 190.77/191.61 ( class_Orderings_Opreorder(T_b)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 190.77/191.61 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 190.77/191.61 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_order__less__le,axiom,
% 190.77/191.61 ! [V_y_2,V_x_2,T_b] :
% 190.77/191.61 ( class_Orderings_Oorder(T_b)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 190.77/191.61 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 190.77/191.61 & V_x_2 != V_y_2 ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_linorder__le__less__linear,axiom,
% 190.77/191.61 ! [V_y,V_x,T_a] :
% 190.77/191.61 ( class_Orderings_Olinorder(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 190.77/191.61 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_linorder__not__le,axiom,
% 190.77/191.61 ! [V_y_2,V_x_2,T_b] :
% 190.77/191.61 ( class_Orderings_Olinorder(T_b)
% 190.77/191.61 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 190.77/191.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_linorder__not__less,axiom,
% 190.77/191.61 ! [V_y_2,V_x_2,T_b] :
% 190.77/191.61 ( class_Orderings_Olinorder(T_b)
% 190.77/191.61 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 190.77/191.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_add__le__imp__le__left,axiom,
% 190.77/191.61 ! [V_b,V_a,V_c,T_a] :
% 190.77/191.61 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 190.77/191.61 => ( 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)))
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_add__le__imp__le__right,axiom,
% 190.77/191.61 ! [V_b,V_c,V_a,T_a] :
% 190.77/191.61 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 190.77/191.61 => ( 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)))
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_add__mono,axiom,
% 190.77/191.61 ! [V_d,V_c,V_b,V_a,T_a] :
% 190.77/191.61 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 190.77/191.61 => 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))) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_add__left__mono,axiom,
% 190.77/191.61 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.61 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 190.77/191.61 => 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))) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_add__right__mono,axiom,
% 190.77/191.61 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.61 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 190.77/191.61 => 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))) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_add__le__cancel__left,axiom,
% 190.77/191.61 ! [V_ba_2,V_a_2,V_ca_2,T_b] :
% 190.77/191.61 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_ba_2)))
% 190.77/191.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_add__le__cancel__right,axiom,
% 190.77/191.61 ! [V_ba_2,V_ca_2,V_a_2,T_b] :
% 190.77/191.61 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ba_2),V_ca_2)))
% 190.77/191.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_mult__0,axiom,
% 190.77/191.61 ! [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) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_mult__0__right,axiom,
% 190.77/191.61 ! [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) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_mult__is__0,axiom,
% 190.77/191.61 ! [V_n_2,V_m_2] :
% 190.77/191.61 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.61 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.61 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_mult__cancel1,axiom,
% 190.77/191.61 ! [V_n_2,V_m_2,V_k_2] :
% 190.77/191.61 ( 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)
% 190.77/191.61 <=> ( V_m_2 = V_n_2
% 190.77/191.61 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_mult__cancel2,axiom,
% 190.77/191.61 ! [V_n_2,V_k_2,V_m_2] :
% 190.77/191.61 ( 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)
% 190.77/191.61 <=> ( V_m_2 = V_n_2
% 190.77/191.61 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_Suc__mult__cancel1,axiom,
% 190.77/191.61 ! [V_n_2,V_m_2,V_k_2] :
% 190.77/191.61 ( 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)
% 190.77/191.61 <=> V_m_2 = V_n_2 ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 190.77/191.61 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_le__0__eq,axiom,
% 190.77/191.61 ! [V_n_2] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 190.77/191.61 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_le__minus__iff,axiom,
% 190.77/191.61 ! [V_ba_2,V_a_2,T_b] :
% 190.77/191.61 ( class_Groups_Oordered__ab__group__add(T_b)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2)))
% 190.77/191.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_minus__le__iff,axiom,
% 190.77/191.61 ! [V_ba_2,V_a_2,T_b] :
% 190.77/191.61 ( class_Groups_Oordered__ab__group__add(T_b)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_ba_2))
% 190.77/191.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2)),V_a_2)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_neg__le__iff__le,axiom,
% 190.77/191.61 ! [V_a_2,V_ba_2,T_b] :
% 190.77/191.61 ( class_Groups_Oordered__ab__group__add(T_b)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_ba_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 190.77/191.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_le__imp__neg__le,axiom,
% 190.77/191.61 ! [V_b,V_a,T_a] :
% 190.77/191.61 ( class_Groups_Oordered__ab__group__add(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 190.77/191.61 => 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))) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_add__mult__distrib2,axiom,
% 190.77/191.61 ! [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)) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_add__mult__distrib,axiom,
% 190.77/191.61 ! [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)) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_Suc__leD,axiom,
% 190.77/191.61 ! [V_n,V_m] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_le__SucE,axiom,
% 190.77/191.61 ! [V_n,V_m] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 190.77/191.61 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 190.77/191.61 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_le__SucI,axiom,
% 190.77/191.61 ! [V_n,V_m] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_Suc__le__mono,axiom,
% 190.77/191.61 ! [V_m_2,V_n_2] :
% 190.77/191.61 ( 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)))
% 190.77/191.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_le__Suc__eq,axiom,
% 190.77/191.61 ! [V_n_2,V_m_2] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 190.77/191.61 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 190.77/191.61 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_not__less__eq__eq,axiom,
% 190.77/191.61 ! [V_n_2,V_m_2] :
% 190.77/191.61 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 190.77/191.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_Suc__n__not__le__n,axiom,
% 190.77/191.61 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 190.77/191.61 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))) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_termination__basic__simps_I5_J,axiom,
% 190.77/191.61 ! [V_y,V_x] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_nat__less__le,axiom,
% 190.77/191.61 ! [V_n_2,V_m_2] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 190.77/191.61 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 190.77/191.61 & V_m_2 != V_n_2 ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_le__eq__less__or__eq,axiom,
% 190.77/191.61 ! [V_n_2,V_m_2] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 190.77/191.61 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 190.77/191.61 | V_m_2 = V_n_2 ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_less__imp__le__nat,axiom,
% 190.77/191.61 ! [V_n,V_m] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_le__neq__implies__less,axiom,
% 190.77/191.61 ! [V_n,V_m] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 190.77/191.61 => ( V_m != V_n
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_less__or__eq__imp__le,axiom,
% 190.77/191.61 ! [V_n,V_m] :
% 190.77/191.61 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 190.77/191.61 | V_m = V_n )
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_termination__basic__simps_I4_J,axiom,
% 190.77/191.61 ! [V_y,V_z,V_x] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z))
% 190.77/191.61 => 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))) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_termination__basic__simps_I3_J,axiom,
% 190.77/191.61 ! [V_z,V_y,V_x] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y))
% 190.77/191.61 => 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))) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_le__add2,axiom,
% 190.77/191.61 ! [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))) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_le__add1,axiom,
% 190.77/191.61 ! [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))) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_le__iff__add,axiom,
% 190.77/191.61 ! [V_n_2,V_m_2] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 190.77/191.61 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_nat__add__left__cancel__le,axiom,
% 190.77/191.61 ! [V_n_2,V_m_2,V_k_2] :
% 190.77/191.61 ( 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)))
% 190.77/191.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_trans__le__add1,axiom,
% 190.77/191.61 ! [V_m,V_j,V_i] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 190.77/191.61 => 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))) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_trans__le__add2,axiom,
% 190.77/191.61 ! [V_m,V_j,V_i] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 190.77/191.61 => 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))) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_add__le__mono1,axiom,
% 190.77/191.61 ! [V_k,V_j,V_i] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 190.77/191.61 => 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))) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_add__le__mono,axiom,
% 190.77/191.61 ! [V_l,V_k,V_j,V_i] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 190.77/191.61 => 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))) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_add__leD2,axiom,
% 190.77/191.61 ! [V_n,V_k,V_m] :
% 190.77/191.61 ( 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))
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_add__leD1,axiom,
% 190.77/191.61 ! [V_n,V_k,V_m] :
% 190.77/191.61 ( 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))
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_add__leE,axiom,
% 190.77/191.61 ! [V_n,V_k,V_m] :
% 190.77/191.61 ( 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))
% 190.77/191.61 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 190.77/191.61 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_zless__le,axiom,
% 190.77/191.61 ! [V_w_2,V_z_2] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2))
% 190.77/191.61 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2))
% 190.77/191.61 & V_z_2 != V_w_2 ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_zadd__left__mono,axiom,
% 190.77/191.61 ! [V_k,V_j,V_i] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 190.77/191.61 => 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))) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_evaln__nonstrict,axiom,
% 190.77/191.61 ! [V_m,V_t,V_n,V_s,V_c] :
% 190.77/191.61 ( c_Natural_Oevaln(V_c,V_s,V_n,V_t)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 190.77/191.61 => c_Natural_Oevaln(V_c,V_s,V_m,V_t) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_nat__le__eq__zle,axiom,
% 190.77/191.61 ! [V_z_2,V_w_2] :
% 190.77/191.61 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 190.77/191.61 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
% 190.77/191.61 => ( 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)))
% 190.77/191.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom,
% 190.77/191.61 ! [V_y,V_x] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 190.77/191.61 => 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)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_nat__mult__distrib,axiom,
% 190.77/191.61 ! [V_z_H,V_z] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 190.77/191.61 => 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)) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_of__int__0__le__iff,axiom,
% 190.77/191.61 ! [V_z_2,T_b] :
% 190.77/191.61 ( class_Rings_Olinordered__idom(T_b)
% 190.77/191.61 => ( 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)))
% 190.77/191.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_of__int__le__0__iff,axiom,
% 190.77/191.61 ! [V_z_2,T_b] :
% 190.77/191.61 ( class_Rings_Olinordered__idom(T_b)
% 190.77/191.61 => ( 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)))
% 190.77/191.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_sgn__0__0,axiom,
% 190.77/191.61 ! [V_a_2,T_b] :
% 190.77/191.61 ( class_Rings_Olinordered__idom(T_b)
% 190.77/191.61 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 190.77/191.61 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_sgn0,axiom,
% 190.77/191.61 ! [T_a] :
% 190.77/191.61 ( class_Groups_Osgn__if(T_a)
% 190.77/191.61 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_sgn__times,axiom,
% 190.77/191.61 ! [V_b,V_a,T_a] :
% 190.77/191.61 ( class_Rings_Olinordered__idom(T_a)
% 190.77/191.61 => 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)) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_nat__mult__distrib__neg,axiom,
% 190.77/191.61 ! [V_z_H,V_z] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 190.77/191.61 => 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))) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 190.77/191.61 ! [V_a_2,T_b] :
% 190.77/191.61 ( class_Groups_Olinordered__ab__group__add(T_b)
% 190.77/191.61 => ( 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)))
% 190.77/191.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 190.77/191.61 ! [V_a_2,T_b] :
% 190.77/191.61 ( class_Groups_Olinordered__ab__group__add(T_b)
% 190.77/191.61 => ( 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)))
% 190.77/191.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_add__nonneg__nonneg,axiom,
% 190.77/191.61 ! [V_b,V_a,T_a] :
% 190.77/191.61 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 190.77/191.61 => 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))) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_add__nonneg__eq__0__iff,axiom,
% 190.77/191.61 ! [V_y_2,V_x_2,T_b] :
% 190.77/191.61 ( class_Groups_Oordered__comm__monoid__add(T_b)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_x_2))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_y_2))
% 190.77/191.61 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b)
% 190.77/191.61 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 190.77/191.61 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_add__increasing,axiom,
% 190.77/191.61 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.61 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 190.77/191.61 => 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))) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_add__increasing2,axiom,
% 190.77/191.61 ! [V_a,V_b,V_c,T_a] :
% 190.77/191.61 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 190.77/191.61 => 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))) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_add__nonpos__nonpos,axiom,
% 190.77/191.61 ! [V_b,V_a,T_a] :
% 190.77/191.61 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 190.77/191.61 => 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))) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_split__mult__neg__le,axiom,
% 190.77/191.61 ! [V_b,V_a,T_a] :
% 190.77/191.61 ( class_Rings_Oordered__cancel__semiring(T_a)
% 190.77/191.61 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 190.77/191.61 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) )
% 190.77/191.61 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 190.77/191.61 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) )
% 190.77/191.61 => 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))) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_split__mult__pos__le,axiom,
% 190.77/191.61 ! [V_b,V_a,T_a] :
% 190.77/191.61 ( class_Rings_Oordered__ring(T_a)
% 190.77/191.61 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 190.77/191.61 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
% 190.77/191.61 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 190.77/191.61 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 190.77/191.61 => 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))) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_mult__mono,axiom,
% 190.77/191.61 ! [V_d,V_c,V_b,V_a,T_a] :
% 190.77/191.61 ( class_Rings_Oordered__semiring(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 190.77/191.61 => 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))) ) ) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_mult__mono_H,axiom,
% 190.77/191.61 ! [V_d,V_c,V_b,V_a,T_a] :
% 190.77/191.61 ( class_Rings_Oordered__semiring(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 190.77/191.61 => 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))) ) ) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_mult__left__mono__neg,axiom,
% 190.77/191.61 ! [V_c,V_a,V_b,T_a] :
% 190.77/191.61 ( class_Rings_Oordered__ring(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 190.77/191.61 => 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))) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_mult__right__mono__neg,axiom,
% 190.77/191.61 ! [V_c,V_a,V_b,T_a] :
% 190.77/191.61 ( class_Rings_Oordered__ring(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 190.77/191.61 => 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))) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_comm__mult__left__mono,axiom,
% 190.77/191.61 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.61 ( class_Rings_Oordered__comm__semiring(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 190.77/191.61 => 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))) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_mult__left__mono,axiom,
% 190.77/191.61 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.61 ( class_Rings_Oordered__semiring(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 190.77/191.61 => 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))) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_mult__right__mono,axiom,
% 190.77/191.61 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.61 ( class_Rings_Oordered__semiring(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 190.77/191.61 => 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))) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_mult__nonpos__nonpos,axiom,
% 190.77/191.61 ! [V_b,V_a,T_a] :
% 190.77/191.61 ( class_Rings_Oordered__ring(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 190.77/191.61 => 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))) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_mult__nonpos__nonneg,axiom,
% 190.77/191.61 ! [V_b,V_a,T_a] :
% 190.77/191.61 ( class_Rings_Oordered__cancel__semiring(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 190.77/191.61 => 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))) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_mult__nonneg__nonpos2,axiom,
% 190.77/191.61 ! [V_b,V_a,T_a] :
% 190.77/191.61 ( class_Rings_Oordered__cancel__semiring(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 190.77/191.61 => 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))) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_mult__nonneg__nonpos,axiom,
% 190.77/191.61 ! [V_b,V_a,T_a] :
% 190.77/191.61 ( class_Rings_Oordered__cancel__semiring(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 190.77/191.61 => 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))) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_mult__nonneg__nonneg,axiom,
% 190.77/191.61 ! [V_b,V_a,T_a] :
% 190.77/191.61 ( class_Rings_Oordered__cancel__semiring(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 190.77/191.61 => 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))) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_mult__le__0__iff,axiom,
% 190.77/191.61 ! [V_ba_2,V_a_2,T_b] :
% 190.77/191.61 ( class_Rings_Olinordered__ring__strict(T_b)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ba_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 190.77/191.61 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 190.77/191.61 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 190.77/191.61 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 190.77/191.61 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ba_2)) ) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_zero__le__mult__iff,axiom,
% 190.77/191.61 ! [V_ba_2,V_a_2,T_b] :
% 190.77/191.61 ( class_Rings_Olinordered__ring__strict(T_b)
% 190.77/191.61 => ( 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_ba_2)))
% 190.77/191.61 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 190.77/191.61 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ba_2)) )
% 190.77/191.61 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 190.77/191.61 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_zero__le__square,axiom,
% 190.77/191.61 ! [V_a,T_a] :
% 190.77/191.61 ( class_Rings_Olinordered__ring(T_a)
% 190.77/191.61 => 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))) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_add__le__less__mono,axiom,
% 190.77/191.61 ! [V_d,V_c,V_b,V_a,T_a] :
% 190.77/191.61 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 190.77/191.61 => 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))) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_add__less__le__mono,axiom,
% 190.77/191.61 ! [V_d,V_c,V_b,V_a,T_a] :
% 190.77/191.61 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 190.77/191.61 => 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))) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_zero__le__one,axiom,
% 190.77/191.61 ! [T_a] :
% 190.77/191.61 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.61 => 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))) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_not__one__le__zero,axiom,
% 190.77/191.61 ! [T_a] :
% 190.77/191.61 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.61 => ~ 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))) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_neg__0__le__iff__le,axiom,
% 190.77/191.61 ! [V_a_2,T_b] :
% 190.77/191.61 ( class_Groups_Oordered__ab__group__add(T_b)
% 190.77/191.61 => ( 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)))
% 190.77/191.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_le__minus__self__iff,axiom,
% 190.77/191.61 ! [V_a_2,T_b] :
% 190.77/191.61 ( class_Groups_Olinordered__ab__group__add(T_b)
% 190.77/191.61 => ( 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)))
% 190.77/191.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_neg__le__0__iff__le,axiom,
% 190.77/191.61 ! [V_a_2,T_b] :
% 190.77/191.61 ( class_Groups_Oordered__ab__group__add(T_b)
% 190.77/191.61 => ( 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)))
% 190.77/191.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_minus__le__self__iff,axiom,
% 190.77/191.61 ! [V_a_2,T_b] :
% 190.77/191.61 ( class_Groups_Olinordered__ab__group__add(T_b)
% 190.77/191.61 => ( 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))
% 190.77/191.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_mult__eq__1__iff,axiom,
% 190.77/191.61 ! [V_n_2,V_m_2] :
% 190.77/191.61 ( 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))
% 190.77/191.61 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 190.77/191.61 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_of__nat__0__le__iff,axiom,
% 190.77/191.61 ! [V_n,T_a] :
% 190.77/191.61 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.61 => 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))) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_zero__le__imp__of__nat,axiom,
% 190.77/191.61 ! [V_m,T_a] :
% 190.77/191.61 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.61 => 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))) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_nat__0__less__mult__iff,axiom,
% 190.77/191.61 ! [V_n_2,V_m_2] :
% 190.77/191.61 ( 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)))
% 190.77/191.61 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 190.77/191.61 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_mult__less__cancel1,axiom,
% 190.77/191.61 ! [V_n_2,V_m_2,V_k_2] :
% 190.77/191.61 ( 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)))
% 190.77/191.61 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 190.77/191.61 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_mult__less__cancel2,axiom,
% 190.77/191.61 ! [V_n_2,V_k_2,V_m_2] :
% 190.77/191.61 ( 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)))
% 190.77/191.61 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 190.77/191.61 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_mult__less__mono1,axiom,
% 190.77/191.61 ! [V_k,V_j,V_i] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 190.77/191.61 => 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))) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_mult__less__mono2,axiom,
% 190.77/191.61 ! [V_k,V_j,V_i] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 190.77/191.61 => 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))) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_Suc__mult__less__cancel1,axiom,
% 190.77/191.61 ! [V_n_2,V_m_2,V_k_2] :
% 190.77/191.61 ( 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)))
% 190.77/191.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_mult__Suc__right,axiom,
% 190.77/191.61 ! [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)) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_mult__Suc,axiom,
% 190.77/191.61 ! [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)) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_One__nat__def,axiom,
% 190.77/191.61 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_less__eq__Suc__le,axiom,
% 190.77/191.61 ! [V_m_2,V_n_2] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 190.77/191.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_less__Suc__eq__le,axiom,
% 190.77/191.61 ! [V_n_2,V_m_2] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 190.77/191.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_Suc__le__eq,axiom,
% 190.77/191.61 ! [V_n_2,V_m_2] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 190.77/191.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_le__imp__less__Suc,axiom,
% 190.77/191.61 ! [V_n,V_m] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_Suc__leI,axiom,
% 190.77/191.61 ! [V_n,V_m] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_le__less__Suc__eq,axiom,
% 190.77/191.61 ! [V_n_2,V_m_2] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 190.77/191.61 <=> V_n_2 = V_m_2 ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_Suc__le__lessD,axiom,
% 190.77/191.61 ! [V_n,V_m] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_Suc__eq__plus1__left,axiom,
% 190.77/191.61 ! [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) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_Suc__eq__plus1,axiom,
% 190.77/191.61 ! [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)) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 190.77/191.61 ! [V_y,V_x] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 190.77/191.61 => 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))) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
% 190.77/191.61 ! [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))) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
% 190.77/191.61 ! [V_Pa_2] :
% 190.77/191.61 ( ? [B_x] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 190.77/191.61 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 190.77/191.61 <=> ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
% 190.77/191.61 ! [V_Pa_2] :
% 190.77/191.61 ( ! [B_x] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 190.77/191.61 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 190.77/191.61 <=> ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_zero__zle__int,axiom,
% 190.77/191.61 ! [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))) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 190.77/191.61 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))) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_ex__nat,axiom,
% 190.77/191.61 ! [V_Pa_2] :
% 190.77/191.61 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 190.77/191.61 <=> ? [B_x] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 190.77/191.61 & hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_all__nat,axiom,
% 190.77/191.61 ! [V_Pa_2] :
% 190.77/191.61 ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 190.77/191.61 <=> ! [B_x] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 190.77/191.61 => hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_transfer__nat__int__relations_I1_J,axiom,
% 190.77/191.61 ! [V_y_2,V_x_2] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 190.77/191.61 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2)
% 190.77/191.61 <=> V_x_2 = V_y_2 ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_eq__nat__nat__iff,axiom,
% 190.77/191.61 ! [V_z_H_2,V_z_2] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2))
% 190.77/191.61 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2)
% 190.77/191.61 <=> V_z_2 = V_z_H_2 ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_zadd__zless__mono,axiom,
% 190.77/191.61 ! [V_z,V_z_H,V_w,V_w_H] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 190.77/191.61 => 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))) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 190.77/191.61 ! [V_y,V_x] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 190.77/191.61 => 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))) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
% 190.77/191.61 ! [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)) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_zmult__int,axiom,
% 190.77/191.61 ! [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)) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_int__mult,axiom,
% 190.77/191.61 ! [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)) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_zle__iff__zadd,axiom,
% 190.77/191.61 ! [V_z_2,V_w_2] :
% 190.77/191.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
% 190.77/191.61 <=> ? [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)) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_transfer__int__nat__numerals_I2_J,axiom,
% 190.77/191.61 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)) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_int__1,axiom,
% 190.77/191.61 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) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_transfer__nat__int__numerals_I2_J,axiom,
% 190.77/191.61 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_add__pos__nonneg,axiom,
% 190.77/191.61 ! [V_b,V_a,T_a] :
% 190.77/191.61 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 190.77/191.61 => 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))) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_add__nonneg__pos,axiom,
% 190.77/191.61 ! [V_b,V_a,T_a] :
% 190.77/191.61 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 190.77/191.61 => 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))) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_add__strict__increasing,axiom,
% 190.77/191.61 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.61 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 190.77/191.61 => 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))) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_add__strict__increasing2,axiom,
% 190.77/191.61 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.61 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 190.77/191.61 => 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))) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_add__neg__nonpos,axiom,
% 190.77/191.61 ! [V_b,V_a,T_a] :
% 190.77/191.61 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 190.77/191.61 => 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))) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_add__nonpos__neg,axiom,
% 190.77/191.61 ! [V_b,V_a,T_a] :
% 190.77/191.61 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 190.77/191.61 => 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))) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_mult__left__le__imp__le,axiom,
% 190.77/191.61 ! [V_b,V_a,V_c,T_a] :
% 190.77/191.61 ( class_Rings_Olinordered__semiring__strict(T_a)
% 190.77/191.61 => ( 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)))
% 190.77/191.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 190.77/191.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 190.77/191.61
% 190.77/191.61 fof(fact_mult__right__le__imp__le,axiom,
% 190.77/191.61 ! [V_b,V_c,V_a,T_a] :
% 190.77/191.61 ( class_Rings_Olinordered__semiring__strict(T_a)
% 190.77/191.61 => ( 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)))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 190.77/191.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mult__less__imp__less__left,axiom,
% 190.77/191.62 ! [V_b,V_a,V_c,T_a] :
% 190.77/191.62 ( class_Rings_Olinordered__semiring__strict(T_a)
% 190.77/191.62 => ( 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)))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 190.77/191.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mult__left__less__imp__less,axiom,
% 190.77/191.62 ! [V_b,V_a,V_c,T_a] :
% 190.77/191.62 ( class_Rings_Olinordered__semiring(T_a)
% 190.77/191.62 => ( 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)))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 190.77/191.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mult__less__imp__less__right,axiom,
% 190.77/191.62 ! [V_b,V_c,V_a,T_a] :
% 190.77/191.62 ( class_Rings_Olinordered__semiring__strict(T_a)
% 190.77/191.62 => ( 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)))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 190.77/191.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mult__right__less__imp__less,axiom,
% 190.77/191.62 ! [V_b,V_c,V_a,T_a] :
% 190.77/191.62 ( class_Rings_Olinordered__semiring(T_a)
% 190.77/191.62 => ( 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)))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 190.77/191.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mult__le__less__imp__less,axiom,
% 190.77/191.62 ! [V_d,V_c,V_b,V_a,T_a] :
% 190.77/191.62 ( class_Rings_Olinordered__semiring__strict(T_a)
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 190.77/191.62 => 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))) ) ) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mult__less__le__imp__less,axiom,
% 190.77/191.62 ! [V_d,V_c,V_b,V_a,T_a] :
% 190.77/191.62 ( class_Rings_Olinordered__semiring__strict(T_a)
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 190.77/191.62 => 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))) ) ) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mult__strict__mono_H,axiom,
% 190.77/191.62 ! [V_d,V_c,V_b,V_a,T_a] :
% 190.77/191.62 ( class_Rings_Olinordered__semiring__strict(T_a)
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 190.77/191.62 => 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))) ) ) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mult__strict__mono,axiom,
% 190.77/191.62 ! [V_d,V_c,V_b,V_a,T_a] :
% 190.77/191.62 ( class_Rings_Olinordered__semiring__strict(T_a)
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 190.77/191.62 => 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))) ) ) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mult__le__cancel__left__neg,axiom,
% 190.77/191.62 ! [V_ba_2,V_a_2,V_ca_2,T_b] :
% 190.77/191.62 ( class_Rings_Olinordered__ring__strict(T_b)
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_ba_2)))
% 190.77/191.62 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),V_a_2)) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mult__le__cancel__left__pos,axiom,
% 190.77/191.62 ! [V_ba_2,V_a_2,V_ca_2,T_b] :
% 190.77/191.62 ( class_Rings_Olinordered__ring__strict(T_b)
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_ba_2)))
% 190.77/191.62 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_sum__squares__le__zero__iff,axiom,
% 190.77/191.62 ! [V_y_2,V_x_2,T_b] :
% 190.77/191.62 ( class_Rings_Olinordered__ring__strict(T_b)
% 190.77/191.62 => ( 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)))
% 190.77/191.62 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 190.77/191.62 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_sum__squares__ge__zero,axiom,
% 190.77/191.62 ! [V_y,V_x,T_a] :
% 190.77/191.62 ( class_Rings_Olinordered__ring(T_a)
% 190.77/191.62 => 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)))) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mult__left__le__one__le,axiom,
% 190.77/191.62 ! [V_y,V_x,T_a] :
% 190.77/191.62 ( class_Rings_Olinordered__idom(T_a)
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 190.77/191.62 => 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)) ) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mult__right__le__one__le,axiom,
% 190.77/191.62 ! [V_y,V_x,T_a] :
% 190.77/191.62 ( class_Rings_Olinordered__idom(T_a)
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 190.77/191.62 => 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)) ) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_sgn__less,axiom,
% 190.77/191.62 ! [V_a_2,T_b] :
% 190.77/191.62 ( class_Rings_Olinordered__idom(T_b)
% 190.77/191.62 => ( 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)))
% 190.77/191.62 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_sgn__greater,axiom,
% 190.77/191.62 ! [V_a_2,T_b] :
% 190.77/191.62 ( class_Rings_Olinordered__idom(T_b)
% 190.77/191.62 => ( 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)))
% 190.77/191.62 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_one__less__mult,axiom,
% 190.77/191.62 ! [V_m,V_n] :
% 190.77/191.62 ( 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))
% 190.77/191.62 => ( 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))
% 190.77/191.62 => 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))) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_n__less__n__mult__m,axiom,
% 190.77/191.62 ! [V_m,V_n] :
% 190.77/191.62 ( 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))
% 190.77/191.62 => ( 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))
% 190.77/191.62 => 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))) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_n__less__m__mult__n,axiom,
% 190.77/191.62 ! [V_m,V_n] :
% 190.77/191.62 ( 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))
% 190.77/191.62 => ( 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))
% 190.77/191.62 => 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))) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_int__le__0__conv,axiom,
% 190.77/191.62 ! [V_n_2] :
% 190.77/191.62 ( 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)))
% 190.77/191.62 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_nat__0__iff,axiom,
% 190.77/191.62 ! [V_i_2] :
% 190.77/191.62 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.62 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_nat__le__0,axiom,
% 190.77/191.62 ! [V_z] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 190.77/191.62 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_int__one__le__iff__zero__less,axiom,
% 190.77/191.62 ! [V_z_2] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
% 190.77/191.62 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_nat__0__le,axiom,
% 190.77/191.62 ! [V_z] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 190.77/191.62 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_int__eq__iff,axiom,
% 190.77/191.62 ! [V_z_2,V_m_2] :
% 190.77/191.62 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2
% 190.77/191.62 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2)
% 190.77/191.62 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_int__nat__eq,axiom,
% 190.77/191.62 ! [V_z] :
% 190.77/191.62 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 190.77/191.62 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z )
% 190.77/191.62 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 190.77/191.62 => 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) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zless__imp__add1__zle,axiom,
% 190.77/191.62 ! [V_z,V_w] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z))
% 190.77/191.62 => 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)) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_add1__zle__eq,axiom,
% 190.77/191.62 ! [V_z_2,V_w_2] :
% 190.77/191.62 ( 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))
% 190.77/191.62 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zle__add1__eq__le,axiom,
% 190.77/191.62 ! [V_z_2,V_w_2] :
% 190.77/191.62 ( 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))))
% 190.77/191.62 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_int__zle__neg,axiom,
% 190.77/191.62 ! [V_m_2,V_n_2] :
% 190.77/191.62 ( 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))))
% 190.77/191.62 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.62 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_negative__zle__0,axiom,
% 190.77/191.62 ! [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))) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_convex__bound__le,axiom,
% 190.77/191.62 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 190.77/191.62 ( class_Rings_Olinordered__semiring__1(T_a)
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 190.77/191.62 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 190.77/191.62 => 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)) ) ) ) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_nat__less__eq__zless,axiom,
% 190.77/191.62 ! [V_z_2,V_w_2] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 190.77/191.62 => ( 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)))
% 190.77/191.62 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_transfer__nat__int__relations_I2_J,axiom,
% 190.77/191.62 ! [V_y_2,V_x_2] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 190.77/191.62 => ( 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)))
% 190.77/191.62 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_nat__eq__iff,axiom,
% 190.77/191.62 ! [V_m_2,V_w_2] :
% 190.77/191.62 ( hAPP(c_Int_Onat,V_w_2) = V_m_2
% 190.77/191.62 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 190.77/191.62 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 190.77/191.62 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 190.77/191.62 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_nat__eq__iff2,axiom,
% 190.77/191.62 ! [V_w_2,V_m_2] :
% 190.77/191.62 ( V_m_2 = hAPP(c_Int_Onat,V_w_2)
% 190.77/191.62 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 190.77/191.62 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 190.77/191.62 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 190.77/191.62 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_nat__add__distrib,axiom,
% 190.77/191.62 ! [V_z_H,V_z] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 190.77/191.62 => 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)) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom,
% 190.77/191.62 ! [V_y,V_x] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 190.77/191.62 => 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)) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_le__imp__0__less,axiom,
% 190.77/191.62 ! [V_z] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 190.77/191.62 => 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))) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_not__zle__0__negative,axiom,
% 190.77/191.62 ! [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))))) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_of__nat__nat,axiom,
% 190.77/191.62 ! [V_z,T_a] :
% 190.77/191.62 ( class_Rings_Oring__1(T_a)
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 190.77/191.62 => 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) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_sgn__pos,axiom,
% 190.77/191.62 ! [V_a,T_a] :
% 190.77/191.62 ( class_Rings_Olinordered__idom(T_a)
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 190.77/191.62 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_self__quotient__aux2,axiom,
% 190.77/191.62 ! [V_q,V_r,V_a] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 190.77/191.62 => ( 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))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 190.77/191.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_self__quotient__aux1,axiom,
% 190.77/191.62 ! [V_q,V_r,V_a] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 190.77/191.62 => ( 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))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a))
% 190.77/191.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_q__pos__lemma,axiom,
% 190.77/191.62 ! [V_r_H,V_q_H,V_b_H] :
% 190.77/191.62 ( 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)))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 190.77/191.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_q__neg__lemma,axiom,
% 190.77/191.62 ! [V_r_H,V_q_H,V_b_H] :
% 190.77/191.62 ( 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)))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 190.77/191.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_unique__quotient__lemma,axiom,
% 190.77/191.62 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 190.77/191.62 ( 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)))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 190.77/191.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zdiv__mono2__lemma,axiom,
% 190.77/191.62 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 190.77/191.62 ( 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)
% 190.77/191.62 => ( 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)))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 190.77/191.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_unique__quotient__lemma__neg,axiom,
% 190.77/191.62 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 190.77/191.62 ( 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)))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H))
% 190.77/191.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 190.77/191.62 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 190.77/191.62 ( 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)
% 190.77/191.62 => ( 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)))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 190.77/191.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_nat__mult__le__cancel1,axiom,
% 190.77/191.62 ! [V_n_2,V_m_2,V_k_2] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 190.77/191.62 => ( 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)))
% 190.77/191.62 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_le__refl,axiom,
% 190.77/191.62 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_nat__le__linear,axiom,
% 190.77/191.62 ! [V_n,V_m] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 190.77/191.62 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_eq__imp__le,axiom,
% 190.77/191.62 ! [V_n,V_m] :
% 190.77/191.62 ( V_m = V_n
% 190.77/191.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_le__trans,axiom,
% 190.77/191.62 ! [V_k,V_j,V_i] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k))
% 190.77/191.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_le__antisym,axiom,
% 190.77/191.62 ! [V_n,V_m] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 190.77/191.62 => V_m = V_n ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_less__fun__def,axiom,
% 190.77/191.62 ! [V_g_2,V_f_2,T_b,T_c] :
% 190.77/191.62 ( class_Orderings_Oord(T_c)
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 190.77/191.62 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 190.77/191.62 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2)) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 190.77/191.62 ! [V_n_2,V_m_2,V_k_2] :
% 190.77/191.62 ( 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)
% 190.77/191.62 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.62 | V_m_2 = V_n_2 ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_left__add__mult__distrib,axiom,
% 190.77/191.62 ! [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) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_nat__mult__eq__cancel1,axiom,
% 190.77/191.62 ! [V_n_2,V_m_2,V_k_2] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 190.77/191.62 => ( 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)
% 190.77/191.62 <=> V_m_2 = V_n_2 ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_nat__mult__less__cancel1,axiom,
% 190.77/191.62 ! [V_n_2,V_m_2,V_k_2] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 190.77/191.62 => ( 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)))
% 190.77/191.62 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_transfer__morphism__nat__int,axiom,
% 190.77/191.62 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))) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_compl__le__compl__iff,axiom,
% 190.77/191.62 ! [V_y_2,V_x_2,T_b] :
% 190.77/191.62 ( class_Lattices_Oboolean__algebra(T_b)
% 190.77/191.62 => ( 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)))
% 190.77/191.62 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_compl__mono,axiom,
% 190.77/191.62 ! [V_y,V_x,T_a] :
% 190.77/191.62 ( class_Lattices_Oboolean__algebra(T_a)
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 190.77/191.62 => 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))) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_ex__least__nat__less,axiom,
% 190.77/191.62 ! [V_n_2,V_Pa_2] :
% 190.77/191.62 ( ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 190.77/191.62 => ( hBOOL(hAPP(V_Pa_2,V_n_2))
% 190.77/191.62 => ? [B_k] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2))
% 190.77/191.62 & ! [B_i] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k))
% 190.77/191.62 => ~ hBOOL(hAPP(V_Pa_2,B_i)) )
% 190.77/191.62 & hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_divmod__int__rel__mod__eq,axiom,
% 190.77/191.62 ! [V_y,V_q_1,V_b_1,V_a_1] :
% 190.77/191.62 ( 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)
% 190.77/191.62 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 190.77/191.62 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) )
% 190.77/191.62 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y))
% 190.77/191.62 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 190.77/191.62 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 190.77/191.62 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zmult2__lemma__aux2,axiom,
% 190.77/191.62 ! [V_q,V_r,V_b,V_c] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 190.77/191.62 => 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))) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zmult2__lemma__aux1,axiom,
% 190.77/191.62 ! [V_q,V_r,V_b,V_c] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 190.77/191.62 => 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))) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zmult2__lemma__aux4,axiom,
% 190.77/191.62 ! [V_q,V_b,V_r,V_c] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 190.77/191.62 => 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))) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__mod__trivial,axiom,
% 190.77/191.62 ! [V_b,V_a,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__0,axiom,
% 190.77/191.62 ! [V_a,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__by__0,axiom,
% 190.77/191.62 ! [V_a,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__self,axiom,
% 190.77/191.62 ! [V_a,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__add__self2,axiom,
% 190.77/191.62 ! [V_b,V_a,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__add__self1,axiom,
% 190.77/191.62 ! [V_a,V_b,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__add__right__eq,axiom,
% 190.77/191.62 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__add__left__eq,axiom,
% 190.77/191.62 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__add__eq,axiom,
% 190.77/191.62 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zmod__simps_I2_J,axiom,
% 190.77/191.62 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zmod__simps_I1_J,axiom,
% 190.77/191.62 ! [V_b,V_c,V_a,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__add__cong,axiom,
% 190.77/191.62 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 190.77/191.62 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 190.77/191.62 => 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) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__mult__right__eq,axiom,
% 190.77/191.62 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__mult__left__eq,axiom,
% 190.77/191.62 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__mult__eq,axiom,
% 190.77/191.62 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__mult__mult1,axiom,
% 190.77/191.62 ! [V_b,V_a,V_c,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => 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)) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__mult__mult2,axiom,
% 190.77/191.62 ! [V_b,V_c,V_a,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zmod__simps_I4_J,axiom,
% 190.77/191.62 ! [V_b,V_c,V_a,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__mult__cong,axiom,
% 190.77/191.62 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 190.77/191.62 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 190.77/191.62 => 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) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__minus__eq,axiom,
% 190.77/191.62 ! [V_b,V_a,T_a] :
% 190.77/191.62 ( class_Divides_Oring__div(T_a)
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__minus__cong,axiom,
% 190.77/191.62 ! [V_a_H,V_b,V_a,T_a] :
% 190.77/191.62 ( class_Divides_Oring__div(T_a)
% 190.77/191.62 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)
% 190.77/191.62 => 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) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zmod__zero,axiom,
% 190.77/191.62 ! [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) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zmod__self,axiom,
% 190.77/191.62 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zmod__simps_I3_J,axiom,
% 190.77/191.62 ! [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) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zmod__zmult1__eq,axiom,
% 190.77/191.62 ! [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) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zminus__zmod,axiom,
% 190.77/191.62 ! [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) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zmod__zminus__zminus,axiom,
% 190.77/191.62 ! [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)) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zmod__zminus2,axiom,
% 190.77/191.62 ! [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)) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__mult__self2__is__0,axiom,
% 190.77/191.62 ! [V_b,V_a,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__mult__self1__is__0,axiom,
% 190.77/191.62 ! [V_a,V_b,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__mult__self2,axiom,
% 190.77/191.62 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__mult__self1,axiom,
% 190.77/191.62 ! [V_b,V_c,V_a,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__by__1,axiom,
% 190.77/191.62 ! [V_a,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zmod__le__nonneg__dividend,axiom,
% 190.77/191.62 ! [V_k,V_m] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 190.77/191.62 => 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)) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
% 190.77/191.62 ! [V_y,V_x] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 190.77/191.62 => 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))) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_neg__mod__bound,axiom,
% 190.77/191.62 ! [V_a,V_b] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 190.77/191.62 => 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))) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_pos__mod__bound,axiom,
% 190.77/191.62 ! [V_a,V_b] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 190.77/191.62 => 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)) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zmod__eq__0__iff,axiom,
% 190.77/191.62 ! [V_d_2,V_m_2] :
% 190.77/191.62 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 190.77/191.62 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zmod__zminus2__not__zero,axiom,
% 190.77/191.62 ! [V_l,V_k] :
% 190.77/191.62 ( 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)
% 190.77/191.62 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zmod__zminus1__not__zero,axiom,
% 190.77/191.62 ! [V_l,V_k] :
% 190.77/191.62 ( 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)
% 190.77/191.62 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__neg__neg__trivial,axiom,
% 190.77/191.62 ! [V_b,V_a] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 190.77/191.62 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_neg__mod__conj,axiom,
% 190.77/191.62 ! [V_a,V_b] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 190.77/191.62 => ( 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)))
% 190.77/191.62 & 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))) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_neg__mod__sign,axiom,
% 190.77/191.62 ! [V_a,V_b] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 190.77/191.62 => 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))) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__pos__pos__trivial,axiom,
% 190.77/191.62 ! [V_b,V_a] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 190.77/191.62 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_pos__mod__conj,axiom,
% 190.77/191.62 ! [V_a,V_b] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 190.77/191.62 => ( 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)))
% 190.77/191.62 & 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)) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_pos__mod__sign,axiom,
% 190.77/191.62 ! [V_a,V_b] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 190.77/191.62 => 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))) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mult__left__idem,axiom,
% 190.77/191.62 ! [V_b,V_a,T_a] :
% 190.77/191.62 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mult__idem,axiom,
% 190.77/191.62 ! [V_x,T_a] :
% 190.77/191.62 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 190.77/191.62 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_times_Oidem,axiom,
% 190.77/191.62 ! [V_a,T_a] :
% 190.77/191.62 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 190.77/191.62 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_compl__eq__compl__iff,axiom,
% 190.77/191.62 ! [V_y_2,V_x_2,T_b] :
% 190.77/191.62 ( class_Lattices_Oboolean__algebra(T_b)
% 190.77/191.62 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)
% 190.77/191.62 <=> V_x_2 = V_y_2 ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_uminus__apply,axiom,
% 190.77/191.62 ! [V_x_2,V_A_2,T_c,T_b] :
% 190.77/191.62 ( class_Groups_Ouminus(T_b)
% 190.77/191.62 => 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)) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_double__compl,axiom,
% 190.77/191.62 ! [V_x,T_a] :
% 190.77/191.62 ( class_Lattices_Oboolean__algebra(T_a)
% 190.77/191.62 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__pos__neg__trivial,axiom,
% 190.77/191.62 ! [V_b,V_a] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 190.77/191.62 => ( 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)))
% 190.77/191.62 => 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) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_split__zmod,axiom,
% 190.77/191.62 ! [V_k_2,V_n_2,V_Pa_2] :
% 190.77/191.62 ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 190.77/191.62 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 190.77/191.62 => hBOOL(hAPP(V_Pa_2,V_n_2)) )
% 190.77/191.62 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 190.77/191.62 => ! [B_i,B_j] :
% 190.77/191.62 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 190.77/191.62 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 190.77/191.62 & 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) )
% 190.77/191.62 => hBOOL(hAPP(V_Pa_2,B_j)) ) )
% 190.77/191.62 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 190.77/191.62 => ! [B_i,B_j] :
% 190.77/191.62 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 190.77/191.62 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 190.77/191.62 & 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) )
% 190.77/191.62 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zmult2__lemma__aux3,axiom,
% 190.77/191.62 ! [V_q,V_b,V_r,V_c] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 190.77/191.62 => 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))) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_z3mod__def,axiom,
% 190.77/191.62 ! [V_k,V_l] :
% 190.77/191.62 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 190.77/191.62 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) )
% 190.77/191.62 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 190.77/191.62 => 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)) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_split__pos__lemma,axiom,
% 190.77/191.62 ! [V_n_2,V_Pa_2,V_k_2] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 190.77/191.62 <=> ! [B_i,B_j] :
% 190.77/191.62 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 190.77/191.62 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 190.77/191.62 & 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) )
% 190.77/191.62 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_split__neg__lemma,axiom,
% 190.77/191.62 ! [V_n_2,V_Pa_2,V_k_2] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 190.77/191.62 <=> ! [B_i,B_j] :
% 190.77/191.62 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 190.77/191.62 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 190.77/191.62 & 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) )
% 190.77/191.62 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zmod__zmult2__eq,axiom,
% 190.77/191.62 ! [V_b,V_a,V_c] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 190.77/191.62 => 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)) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
% 190.77/191.62 ! [V_y,V_x] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 190.77/191.62 => 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))) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_split__zdiv,axiom,
% 190.77/191.62 ! [V_k_2,V_n_2,V_Pa_2] :
% 190.77/191.62 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)))
% 190.77/191.62 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 190.77/191.62 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 190.77/191.62 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 190.77/191.62 => ! [B_i] :
% 190.77/191.62 ( ? [B_j] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 190.77/191.62 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 190.77/191.62 & 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) )
% 190.77/191.62 => hBOOL(hAPP(V_Pa_2,B_i)) ) )
% 190.77/191.62 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 190.77/191.62 => ! [B_i] :
% 190.77/191.62 ( ? [B_j] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 190.77/191.62 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 190.77/191.62 & 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) )
% 190.77/191.62 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_divmod__int__rel__div__eq,axiom,
% 190.77/191.62 ! [V_r_1,V_y,V_b_1,V_a_1] :
% 190.77/191.62 ( 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)
% 190.77/191.62 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1))
% 190.77/191.62 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) )
% 190.77/191.62 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1))
% 190.77/191.62 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 190.77/191.62 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 190.77/191.62 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_split__div_H,axiom,
% 190.77/191.62 ! [V_n_2,V_m_2,V_Pa_2] :
% 190.77/191.62 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))
% 190.77/191.62 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.62 & hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 190.77/191.62 | ? [B_q] :
% 190.77/191.62 ( 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))
% 190.77/191.62 & 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))))
% 190.77/191.62 & hBOOL(hAPP(V_Pa_2,B_q)) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_div__add1__eq,axiom,
% 190.77/191.62 ! [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)) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
% 190.77/191.62 ! [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)) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zdiv__int,axiom,
% 190.77/191.62 ! [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)) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__mult2__eq,axiom,
% 190.77/191.62 ! [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)) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_div__mult1__eq,axiom,
% 190.77/191.62 ! [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)) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_div__le__mono,axiom,
% 190.77/191.62 ! [V_k,V_n,V_m] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 190.77/191.62 => 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))) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_div__le__dividend,axiom,
% 190.77/191.62 ! [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)) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zdiv__zero,axiom,
% 190.77/191.62 ! [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) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__Suc__eq__Suc__mod,axiom,
% 190.77/191.62 ! [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) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_div__mult2__eq,axiom,
% 190.77/191.62 ! [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) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__less,axiom,
% 190.77/191.62 ! [V_n,V_m] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 190.77/191.62 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__less__eq__dividend,axiom,
% 190.77/191.62 ! [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)) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__mult__distrib,axiom,
% 190.77/191.62 ! [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)) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__mult__distrib2,axiom,
% 190.77/191.62 ! [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)) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zdiv__zminus2,axiom,
% 190.77/191.62 ! [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) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zdiv__zminus__zminus,axiom,
% 190.77/191.62 ! [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) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_div__0,axiom,
% 190.77/191.62 ! [V_a,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_div__by__0,axiom,
% 190.77/191.62 ! [V_a,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_div__by__1,axiom,
% 190.77/191.62 ! [V_a,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_nat__div__distrib,axiom,
% 190.77/191.62 ! [V_y,V_x] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 190.77/191.62 => 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)) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom,
% 190.77/191.62 ! [V_y,V_x] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 190.77/191.62 => 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)) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_div__1,axiom,
% 190.77/191.62 ! [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 ).
% 190.77/191.62
% 190.77/191.62 fof(fact_div__less,axiom,
% 190.77/191.62 ! [V_n,V_m] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 190.77/191.62 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_nat__mult__div__cancel__disj,axiom,
% 190.77/191.62 ! [V_n,V_m,V_k] :
% 190.77/191.62 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.62 => 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) )
% 190.77/191.62 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.62 => 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) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__Suc,axiom,
% 190.77/191.62 ! [V_n,V_m] :
% 190.77/191.62 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n
% 190.77/191.62 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 190.77/191.62 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n
% 190.77/191.62 => 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)) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__1,axiom,
% 190.77/191.62 ! [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) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
% 190.77/191.62 ! [V_y,V_x] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 190.77/191.62 => 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))) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__less__divisor,axiom,
% 190.77/191.62 ! [V_m,V_n] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 190.77/191.62 => 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)) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_pos__imp__zdiv__neg__iff,axiom,
% 190.77/191.62 ! [V_a_2,V_ba_2] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_ba_2))
% 190.77/191.62 => ( 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_ba_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 190.77/191.62 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_neg__imp__zdiv__neg__iff,axiom,
% 190.77/191.62 ! [V_a_2,V_ba_2] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 190.77/191.62 => ( 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_ba_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 190.77/191.62 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_div__neg__pos__less0,axiom,
% 190.77/191.62 ! [V_b,V_a] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 190.77/191.62 => 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))) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zdiv__self,axiom,
% 190.77/191.62 ! [V_a] :
% 190.77/191.62 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 190.77/191.62 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__eq__0__iff,axiom,
% 190.77/191.62 ! [V_d_2,V_m_2] :
% 190.77/191.62 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.62 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_DIVISION__BY__ZERO,axiom,
% 190.77/191.62 ! [V_a] :
% 190.77/191.62 ( 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)
% 190.77/191.62 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zmod__zdiv__trivial,axiom,
% 190.77/191.62 ! [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) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__mult__self3,axiom,
% 190.77/191.62 ! [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) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zdiv__zadd1__eq,axiom,
% 190.77/191.62 ! [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)) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom,
% 190.77/191.62 ! [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)) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zmod__int,axiom,
% 190.77/191.62 ! [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)) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_div__mult__mult1,axiom,
% 190.77/191.62 ! [V_b,V_a,V_c,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 190.77/191.62 => 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) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_div__mult__mult2,axiom,
% 190.77/191.62 ! [V_b,V_a,V_c,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 190.77/191.62 => 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) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_div__mult__self1__is__id,axiom,
% 190.77/191.62 ! [V_a,V_b,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 190.77/191.62 => 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 ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_div__mult__self2__is__id,axiom,
% 190.77/191.62 ! [V_a,V_b,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 190.77/191.62 => 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 ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_div__mult__mult1__if,axiom,
% 190.77/191.62 ! [V_b,V_a,V_c,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a)
% 190.77/191.62 => 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) )
% 190.77/191.62 & ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 190.77/191.62 => 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) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_div__self,axiom,
% 190.77/191.62 ! [V_a,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 190.77/191.62 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__div__trivial,axiom,
% 190.77/191.62 ! [V_b,V_a,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_div__le__mono2,axiom,
% 190.77/191.62 ! [V_k,V_n,V_m] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 190.77/191.62 => 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))) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_div__mult__self__is__m,axiom,
% 190.77/191.62 ! [V_m,V_n] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 190.77/191.62 => 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 ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_div__mult__self1__is__m,axiom,
% 190.77/191.62 ! [V_m,V_n] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 190.77/191.62 => 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 ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_nat__mult__div__cancel1,axiom,
% 190.77/191.62 ! [V_n,V_m,V_k] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_div__less__dividend,axiom,
% 190.77/191.62 ! [V_m,V_n] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 190.77/191.62 => 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)) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zdiv__eq__0__iff,axiom,
% 190.77/191.62 ! [V_k_2,V_i_2] :
% 190.77/191.62 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 190.77/191.62 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 190.77/191.62 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2))
% 190.77/191.62 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) )
% 190.77/191.62 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 190.77/191.62 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
% 190.77/191.62 ! [V_a_2,V_ba_2] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_ba_2))
% 190.77/191.62 => ( 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_ba_2)))
% 190.77/191.62 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_pos__imp__zdiv__pos__iff,axiom,
% 190.77/191.62 ! [V_i_2,V_k_2] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 190.77/191.62 => ( 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)))
% 190.77/191.62 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
% 190.77/191.62 ! [V_ba_2,V_a_2] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
% 190.77/191.62 => ( 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_ba_2)))
% 190.77/191.62 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_ba_2),V_a_2))
% 190.77/191.62 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_ba_2)) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zdiv__mono2,axiom,
% 190.77/191.62 ! [V_b,V_b_H,V_a] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 190.77/191.62 => 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))) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_div__nonneg__neg__le0,axiom,
% 190.77/191.62 ! [V_b,V_a] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 190.77/191.62 => 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))) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_div__pos__pos__trivial,axiom,
% 190.77/191.62 ! [V_b,V_a] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 190.77/191.62 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
% 190.77/191.62 ! [V_a_2,V_ba_2] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 190.77/191.62 => ( 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_ba_2)))
% 190.77/191.62 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_div__nonpos__pos__le0,axiom,
% 190.77/191.62 ! [V_b,V_a] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 190.77/191.62 => 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))) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zdiv__mono2__neg,axiom,
% 190.77/191.62 ! [V_b,V_b_H,V_a] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 190.77/191.62 => 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))) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_div__neg__neg__trivial,axiom,
% 190.77/191.62 ! [V_b,V_a] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 190.77/191.62 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zdiv__mono1,axiom,
% 190.77/191.62 ! [V_b,V_a_H,V_a] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 190.77/191.62 => 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))) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zdiv__mono1__neg,axiom,
% 190.77/191.62 ! [V_b,V_a_H,V_a] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 190.77/191.62 => 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))) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__le__divisor,axiom,
% 190.77/191.62 ! [V_m,V_n] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 190.77/191.62 => 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)) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_int__div__less__self,axiom,
% 190.77/191.62 ! [V_k,V_x] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
% 190.77/191.62 => 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)) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zdiv__zmult2__eq,axiom,
% 190.77/191.62 ! [V_b,V_a,V_c] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__mult__self4,axiom,
% 190.77/191.62 ! [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) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zdiv__zmod__equality2,axiom,
% 190.77/191.62 ! [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) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zdiv__zmod__equality,axiom,
% 190.77/191.62 ! [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) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zdiv__zmult1__eq,axiom,
% 190.77/191.62 ! [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)) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zmod__zdiv__equality,axiom,
% 190.77/191.62 ! [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)) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_div__mult__self1,axiom,
% 190.77/191.62 ! [V_c,V_a,V_b,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 190.77/191.62 => 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)) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_div__mult__self2,axiom,
% 190.77/191.62 ! [V_c,V_a,V_b,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 190.77/191.62 => 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)) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_div__add__self1,axiom,
% 190.77/191.62 ! [V_a,V_b,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 190.77/191.62 => 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)) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_div__add__self2,axiom,
% 190.77/191.62 ! [V_a,V_b,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 190.77/191.62 => 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)) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_div__mod__equality,axiom,
% 190.77/191.62 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_div__mod__equality2,axiom,
% 190.77/191.62 ! [V_c,V_a,V_b,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__div__equality,axiom,
% 190.77/191.62 ! [V_b,V_a,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => 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 ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__div__equality2,axiom,
% 190.77/191.62 ! [V_a,V_b,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => 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 ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
% 190.77/191.62 ! [V_b,V_a,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => 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 ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_split__div,axiom,
% 190.77/191.62 ! [V_k_2,V_n_2,V_Pa_2] :
% 190.77/191.62 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2)))
% 190.77/191.62 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.62 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 190.77/191.62 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.62 => ! [B_i,B_j] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 190.77/191.62 => ( 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)
% 190.77/191.62 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__lemma,axiom,
% 190.77/191.62 ! [V_q,V_b,V_r,V_c] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b))
% 190.77/191.62 => 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))) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_split__mod,axiom,
% 190.77/191.62 ! [V_k_2,V_n_2,V_Pa_2] :
% 190.77/191.62 ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
% 190.77/191.62 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.62 => hBOOL(hAPP(V_Pa_2,V_n_2)) )
% 190.77/191.62 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.62 => ! [B_i,B_j] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 190.77/191.62 => ( 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)
% 190.77/191.62 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_Suc__times__mod__eq,axiom,
% 190.77/191.62 ! [V_m,V_k] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k))
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_nat__mod__distrib,axiom,
% 190.77/191.62 ! [V_y,V_x] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 190.77/191.62 => 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)) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom,
% 190.77/191.62 ! [V_y,V_x] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 190.77/191.62 => 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)) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_split__div__lemma,axiom,
% 190.77/191.62 ! [V_m_2,V_q_2,V_n_2] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 190.77/191.62 => ( ( 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))
% 190.77/191.62 & 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)))) )
% 190.77/191.62 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_z3div__def,axiom,
% 190.77/191.62 ! [V_k,V_l] :
% 190.77/191.62 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 190.77/191.62 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) )
% 190.77/191.62 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 190.77/191.62 => 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))) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zdiv__zminus1__eq__if,axiom,
% 190.77/191.62 ! [V_a,V_b] :
% 190.77/191.62 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 190.77/191.62 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 190.77/191.62 => 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)) )
% 190.77/191.62 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 190.77/191.62 => 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)) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zdiv__zminus2__eq__if,axiom,
% 190.77/191.62 ! [V_a,V_b] :
% 190.77/191.62 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 190.77/191.62 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 190.77/191.62 => 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)) )
% 190.77/191.62 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 190.77/191.62 => 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)) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_le__div__geq,axiom,
% 190.77/191.62 ! [V_m,V_n] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 190.77/191.62 => 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)) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__div__decomp,axiom,
% 190.77/191.62 ! [V_b,V_a,T_a] :
% 190.77/191.62 ( class_Divides_Osemiring__div(T_a)
% 190.77/191.62 => 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)) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom,
% 190.77/191.62 ! [V_y,V_x] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 190.77/191.62 => 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)) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_incr__mult__lemma,axiom,
% 190.77/191.62 ! [V_k_2,V_Pa_2,V_d_2] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 190.77/191.62 => ( ! [B_x] :
% 190.77/191.62 ( hBOOL(hAPP(V_Pa_2,B_x))
% 190.77/191.62 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) )
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 190.77/191.62 => ! [B_x] :
% 190.77/191.62 ( hBOOL(hAPP(V_Pa_2,B_x))
% 190.77/191.62 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_field__le__mult__one__interval,axiom,
% 190.77/191.62 ! [V_y,V_x,T_a] :
% 190.77/191.62 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 190.77/191.62 => ( ! [B_z] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a)))
% 190.77/191.62 => 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)) ) )
% 190.77/191.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__commute,axiom,
% 190.77/191.62 ! [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) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__eq__diff__eq,axiom,
% 190.77/191.62 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] :
% 190.77/191.62 ( class_Groups_Oab__group__add(T_b)
% 190.77/191.62 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_ba_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ca_2),V_d_2)
% 190.77/191.62 => ( V_a_2 = V_ba_2
% 190.77/191.62 <=> V_ca_2 = V_d_2 ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_of__int__diff,axiom,
% 190.77/191.62 ! [V_z,V_w,T_a] :
% 190.77/191.62 ( class_Rings_Oring__1(T_a)
% 190.77/191.62 => 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)) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_minus__apply,axiom,
% 190.77/191.62 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 190.77/191.62 ( class_Groups_Ominus(T_b)
% 190.77/191.62 => 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)) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_of__nat__diff,axiom,
% 190.77/191.62 ! [V_m,V_n,T_a] :
% 190.77/191.62 ( class_Rings_Oring__1(T_a)
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 190.77/191.62 => 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)) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zdiff__int,axiom,
% 190.77/191.62 ! [V_m,V_n] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 190.77/191.62 => 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)) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__eq__diff__less__eq,axiom,
% 190.77/191.62 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] :
% 190.77/191.62 ( class_Groups_Oordered__ab__group__add(T_b)
% 190.77/191.62 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_ba_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ca_2),V_d_2)
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2))
% 190.77/191.62 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_d_2)) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_right__minus__eq,axiom,
% 190.77/191.62 ! [V_ba_2,V_a_2,T_b] :
% 190.77/191.62 ( class_Groups_Ogroup__add(T_b)
% 190.77/191.62 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_ba_2) = c_Groups_Ozero__class_Ozero(T_b)
% 190.77/191.62 <=> V_a_2 = V_ba_2 ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_eq__iff__diff__eq__0,axiom,
% 190.77/191.62 ! [V_ba_2,V_a_2,T_b] :
% 190.77/191.62 ( class_Groups_Oab__group__add(T_b)
% 190.77/191.62 => ( V_a_2 = V_ba_2
% 190.77/191.62 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_ba_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__self,axiom,
% 190.77/191.62 ! [V_a,T_a] :
% 190.77/191.62 ( class_Groups_Ogroup__add(T_a)
% 190.77/191.62 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__0__right,axiom,
% 190.77/191.62 ! [V_a,T_a] :
% 190.77/191.62 ( class_Groups_Ogroup__add(T_a)
% 190.77/191.62 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__eq__diff__less,axiom,
% 190.77/191.62 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] :
% 190.77/191.62 ( class_Groups_Oordered__ab__group__add(T_b)
% 190.77/191.62 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_ba_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ca_2),V_d_2)
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2))
% 190.77/191.62 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2)) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_add__diff__cancel,axiom,
% 190.77/191.62 ! [V_b,V_a,T_a] :
% 190.77/191.62 ( class_Groups_Ogroup__add(T_a)
% 190.77/191.62 => 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 ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__add__cancel,axiom,
% 190.77/191.62 ! [V_b,V_a,T_a] :
% 190.77/191.62 ( class_Groups_Ogroup__add(T_a)
% 190.77/191.62 => 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 ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_minus__diff__eq,axiom,
% 190.77/191.62 ! [V_b,V_a,T_a] :
% 190.77/191.62 ( class_Groups_Oab__group__add(T_a)
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__diff__right__eq,axiom,
% 190.77/191.62 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.62 ( class_Divides_Oring__div(T_a)
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__diff__left__eq,axiom,
% 190.77/191.62 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.62 ( class_Divides_Oring__div(T_a)
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__diff__eq,axiom,
% 190.77/191.62 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.62 ( class_Divides_Oring__div(T_a)
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__diff__cong,axiom,
% 190.77/191.62 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 190.77/191.62 ( class_Divides_Oring__div(T_a)
% 190.77/191.62 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 190.77/191.62 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 190.77/191.62 => 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) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__0__eq__0,axiom,
% 190.77/191.62 ! [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) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_minus__nat_Odiff__0,axiom,
% 190.77/191.62 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__self__eq__0,axiom,
% 190.77/191.62 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diffs0__imp__equal,axiom,
% 190.77/191.62 ! [V_n,V_m] :
% 190.77/191.62 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.62 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.62 => V_m = V_n ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_Suc__diff__diff,axiom,
% 190.77/191.62 ! [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) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__Suc__Suc,axiom,
% 190.77/191.62 ! [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) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_less__imp__diff__less,axiom,
% 190.77/191.62 ! [V_n,V_k,V_j] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 190.77/191.62 => 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)) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__less__mono2,axiom,
% 190.77/191.62 ! [V_l,V_n,V_m] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l))
% 190.77/191.62 => 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))) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__if,axiom,
% 190.77/191.62 ! [V_n,V_m] :
% 190.77/191.62 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 190.77/191.62 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m )
% 190.77/191.62 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 190.77/191.62 => 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) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mod__geq,axiom,
% 190.77/191.62 ! [V_n,V_m] :
% 190.77/191.62 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__add__inverse2,axiom,
% 190.77/191.62 ! [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 ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__add__inverse,axiom,
% 190.77/191.62 ! [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 ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__diff__left,axiom,
% 190.77/191.62 ! [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)) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__cancel,axiom,
% 190.77/191.62 ! [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) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__cancel2,axiom,
% 190.77/191.62 ! [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) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_le__diff__iff,axiom,
% 190.77/191.62 ! [V_n_2,V_m_2,V_k_2] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 190.77/191.62 => ( 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)))
% 190.77/191.62 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_Nat_Odiff__diff__eq,axiom,
% 190.77/191.62 ! [V_n,V_m,V_k] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 190.77/191.62 => 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) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_eq__diff__iff,axiom,
% 190.77/191.62 ! [V_n_2,V_m_2,V_k_2] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 190.77/191.62 => ( 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)
% 190.77/191.62 <=> V_m_2 = V_n_2 ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__diff__cancel,axiom,
% 190.77/191.62 ! [V_n,V_i] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n))
% 190.77/191.62 => 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 ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__le__mono,axiom,
% 190.77/191.62 ! [V_l,V_n,V_m] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 190.77/191.62 => 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))) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__le__mono2,axiom,
% 190.77/191.62 ! [V_l,V_n,V_m] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 190.77/191.62 => 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))) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__le__self,axiom,
% 190.77/191.62 ! [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)) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_le__mod__geq,axiom,
% 190.77/191.62 ! [V_m,V_n] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zdiff__zmult__distrib2,axiom,
% 190.77/191.62 ! [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)) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zdiff__zmult__distrib,axiom,
% 190.77/191.62 ! [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)) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__mult__distrib,axiom,
% 190.77/191.62 ! [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)) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__mult__distrib2,axiom,
% 190.77/191.62 ! [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)) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zdiff__zmod__right,axiom,
% 190.77/191.62 ! [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) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zdiff__zmod__left,axiom,
% 190.77/191.62 ! [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) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_nat__diff__distrib,axiom,
% 190.77/191.62 ! [V_z,V_z_H] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 190.77/191.62 => 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)) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zdiff__int__split,axiom,
% 190.77/191.62 ! [V_y_2,V_x_2,V_Pa_2] :
% 190.77/191.62 ( hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2))))
% 190.77/191.62 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2))
% 190.77/191.62 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))) )
% 190.77/191.62 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 190.77/191.62 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_le__iff__diff__le__0,axiom,
% 190.77/191.62 ! [V_ba_2,V_a_2,T_b] :
% 190.77/191.62 ( class_Groups_Oordered__ab__group__add(T_b)
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2))
% 190.77/191.62 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_ba_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_less__iff__diff__less__0,axiom,
% 190.77/191.62 ! [V_ba_2,V_a_2,T_b] :
% 190.77/191.62 ( class_Groups_Oordered__ab__group__add(T_b)
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2))
% 190.77/191.62 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_ba_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_eq__add__iff1,axiom,
% 190.77/191.62 ! [V_d_2,V_ba_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 190.77/191.62 ( class_Rings_Oring(T_b)
% 190.77/191.62 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ba_2),V_e_2)),V_d_2)
% 190.77/191.62 <=> 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_ba_2)),V_e_2)),V_ca_2) = V_d_2 ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_eq__add__iff2,axiom,
% 190.77/191.62 ! [V_d_2,V_ba_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 190.77/191.62 ( class_Rings_Oring(T_b)
% 190.77/191.62 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ba_2),V_e_2)),V_d_2)
% 190.77/191.62 <=> V_ca_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ba_2),V_a_2)),V_e_2)),V_d_2) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__0,axiom,
% 190.77/191.62 ! [V_a,T_a] :
% 190.77/191.62 ( class_Groups_Ogroup__add(T_a)
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__minus__eq__add,axiom,
% 190.77/191.62 ! [V_b,V_a,T_a] :
% 190.77/191.62 ( class_Groups_Ogroup__add(T_a)
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_ab__diff__minus,axiom,
% 190.77/191.62 ! [V_b,V_a,T_a] :
% 190.77/191.62 ( class_Groups_Oab__group__add(T_a)
% 190.77/191.62 => 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)) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__def,axiom,
% 190.77/191.62 ! [V_b,V_a,T_a] :
% 190.77/191.62 ( class_Groups_Ogroup__add(T_a)
% 190.77/191.62 => 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)) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
% 190.77/191.62 ! [V_y,V_x,T_a] :
% 190.77/191.62 ( class_Rings_Ocomm__ring__1(T_a)
% 190.77/191.62 => 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)) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_less__bin__lemma,axiom,
% 190.77/191.62 ! [V_l_2,V_k_2] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
% 190.77/191.62 <=> 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))) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_zero__less__diff,axiom,
% 190.77/191.62 ! [V_m_2,V_n_2] :
% 190.77/191.62 ( 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)))
% 190.77/191.62 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__less,axiom,
% 190.77/191.62 ! [V_m,V_n] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 190.77/191.62 => 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)) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__less__Suc,axiom,
% 190.77/191.62 ! [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))) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__add__0,axiom,
% 190.77/191.62 ! [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) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__is__0__eq,axiom,
% 190.77/191.62 ! [V_n_2,V_m_2] :
% 190.77/191.62 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.62 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__is__0__eq_H,axiom,
% 190.77/191.62 ! [V_n,V_m] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 190.77/191.62 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_less__diff__conv,axiom,
% 190.77/191.62 ! [V_k_2,V_j_2,V_i_2] :
% 190.77/191.62 ( 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)))
% 190.77/191.62 <=> 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)) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_add__diff__inverse,axiom,
% 190.77/191.62 ! [V_n,V_m] :
% 190.77/191.62 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 190.77/191.62 => 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 ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_Suc__diff__le,axiom,
% 190.77/191.62 ! [V_m,V_n] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 190.77/191.62 => 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)) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_less__diff__iff,axiom,
% 190.77/191.62 ! [V_n_2,V_m_2,V_k_2] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 190.77/191.62 => ( 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)))
% 190.77/191.62 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__less__mono,axiom,
% 190.77/191.62 ! [V_c,V_b,V_a] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b))
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a))
% 190.77/191.62 => 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))) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__add__assoc2,axiom,
% 190.77/191.62 ! [V_i,V_j,V_k] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_add__diff__assoc2,axiom,
% 190.77/191.62 ! [V_i,V_j,V_k] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__add__assoc,axiom,
% 190.77/191.62 ! [V_i,V_j,V_k] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 190.77/191.62 => 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)) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_le__imp__diff__is__add,axiom,
% 190.77/191.62 ! [V_k_2,V_j_2,V_i_2] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 190.77/191.62 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2
% 190.77/191.62 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_le__add__diff__inverse2,axiom,
% 190.77/191.62 ! [V_m,V_n] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 190.77/191.62 => 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 ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_le__diff__conv2,axiom,
% 190.77/191.62 ! [V_i_2,V_j_2,V_k_2] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2))
% 190.77/191.62 => ( 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)))
% 190.77/191.62 <=> 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)) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_add__diff__assoc,axiom,
% 190.77/191.62 ! [V_i,V_j,V_k] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_le__add__diff__inverse,axiom,
% 190.77/191.62 ! [V_m,V_n] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 190.77/191.62 => 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 ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_le__add__diff,axiom,
% 190.77/191.62 ! [V_m,V_n,V_k] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 190.77/191.62 => 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))) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_le__diff__conv,axiom,
% 190.77/191.62 ! [V_i_2,V_k_2,V_j_2] :
% 190.77/191.62 ( 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))
% 190.77/191.62 <=> 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))) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__diff__right,axiom,
% 190.77/191.62 ! [V_i,V_j,V_k] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 190.77/191.62 => 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) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__int__def,axiom,
% 190.77/191.62 ! [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)) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__int__def__symmetric,axiom,
% 190.77/191.62 ! [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) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__Suc__eq__diff__pred,axiom,
% 190.77/191.62 ! [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) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__Suc__1,axiom,
% 190.77/191.62 ! [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 ).
% 190.77/191.62
% 190.77/191.62 fof(fact_div__mod__equality_H,axiom,
% 190.77/191.62 ! [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)) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_mult__div__cancel,axiom,
% 190.77/191.62 ! [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)) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_Divides_Omod__div__equality_H,axiom,
% 190.77/191.62 ! [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)) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_tsub__eq,axiom,
% 190.77/191.62 ! [V_x,V_y] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 190.77/191.62 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
% 190.77/191.62 ! [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)) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_le__add__iff1,axiom,
% 190.77/191.62 ! [V_d_2,V_ba_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 190.77/191.62 ( class_Rings_Oordered__ring(T_b)
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ba_2),V_e_2)),V_d_2)))
% 190.77/191.62 <=> 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_ba_2)),V_e_2)),V_ca_2)),V_d_2)) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_le__add__iff2,axiom,
% 190.77/191.62 ! [V_d_2,V_ba_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 190.77/191.62 ( class_Rings_Oordered__ring(T_b)
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ba_2),V_e_2)),V_d_2)))
% 190.77/191.62 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ba_2),V_a_2)),V_e_2)),V_d_2))) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_less__add__iff1,axiom,
% 190.77/191.62 ! [V_d_2,V_ba_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 190.77/191.62 ( class_Rings_Oordered__ring(T_b)
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ba_2),V_e_2)),V_d_2)))
% 190.77/191.62 <=> 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_ba_2)),V_e_2)),V_ca_2)),V_d_2)) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_less__add__iff2,axiom,
% 190.77/191.62 ! [V_d_2,V_ba_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 190.77/191.62 ( class_Rings_Oordered__ring(T_b)
% 190.77/191.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ba_2),V_e_2)),V_d_2)))
% 190.77/191.62 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ba_2),V_a_2)),V_e_2)),V_d_2))) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_diff__Suc__less,axiom,
% 190.77/191.62 ! [V_i,V_n] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 190.77/191.62 => 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)) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_Suc__pred,axiom,
% 190.77/191.62 ! [V_n] :
% 190.77/191.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 190.77/191.62 => 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 ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_nat__diff__split,axiom,
% 190.77/191.62 ! [V_ba_2,V_a_2,V_Pa_2] :
% 190.77/191.62 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_ba_2)))
% 190.77/191.62 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_ba_2))
% 190.77/191.62 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 190.77/191.62 & ! [B_d] :
% 190.77/191.62 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ba_2),B_d)
% 190.77/191.62 => hBOOL(hAPP(V_Pa_2,B_d)) ) ) ) ).
% 190.77/191.62
% 190.77/191.62 fof(fact_nat__diff__split__asm,axiom,
% 190.77/191.62 ! [V_ba_2,V_a_2,V_Pa_2] :
% 190.77/191.62 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_ba_2)))
% 190.77/191.62 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_ba_2))
% 190.77/191.62 & ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 190.77/191.63 | ? [B_d] :
% 190.77/191.63 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ba_2),B_d)
% 190.77/191.63 & ~ hBOOL(hAPP(V_Pa_2,B_d)) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_zle__diff1__eq,axiom,
% 190.77/191.63 ! [V_z_2,V_w_2] :
% 190.77/191.63 ( 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))))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_diff__Suc__diff__eq2,axiom,
% 190.77/191.63 ! [V_m,V_j,V_k] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_diff__Suc__diff__eq1,axiom,
% 190.77/191.63 ! [V_m,V_j,V_k] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_nat__le__add__iff1,axiom,
% 190.77/191.63 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 190.77/191.63 => ( 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)))
% 190.77/191.63 <=> 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)) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_nat__diff__add__eq1,axiom,
% 190.77/191.63 ! [V_n,V_m,V_u,V_i,V_j] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 190.77/191.63 => 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) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_nat__eq__add__iff1,axiom,
% 190.77/191.63 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 190.77/191.63 => ( 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)
% 190.77/191.63 <=> 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 ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_nat__le__add__iff2,axiom,
% 190.77/191.63 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 190.77/191.63 => ( 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)))
% 190.77/191.63 <=> 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))) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_nat__diff__add__eq2,axiom,
% 190.77/191.63 ! [V_n,V_m,V_u,V_j,V_i] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_nat__eq__add__iff2,axiom,
% 190.77/191.63 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 190.77/191.63 => ( 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)
% 190.77/191.63 <=> 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) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_zmod__zminus2__eq__if,axiom,
% 190.77/191.63 ! [V_b,V_a] :
% 190.77/191.63 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 190.77/191.63 => 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) )
% 190.77/191.63 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 190.77/191.63 => 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) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_zmod__zminus1__eq__if,axiom,
% 190.77/191.63 ! [V_b,V_a] :
% 190.77/191.63 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 190.77/191.63 => 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) )
% 190.77/191.63 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 190.77/191.63 => 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)) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_zmod__zdiv__equality_H,axiom,
% 190.77/191.63 ! [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)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_zmult__div__cancel,axiom,
% 190.77/191.63 ! [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)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_tsub__def,axiom,
% 190.77/191.63 ! [V_x,V_y] :
% 190.77/191.63 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 190.77/191.63 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) )
% 190.77/191.63 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 190.77/191.63 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_Suc__diff__1,axiom,
% 190.77/191.63 ! [V_n] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 190.77/191.63 => 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 ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_Suc__pred_H,axiom,
% 190.77/191.63 ! [V_n] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 190.77/191.63 => 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))) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_nat__less__add__iff1,axiom,
% 190.77/191.63 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 190.77/191.63 => ( 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)))
% 190.77/191.63 <=> 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)) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_nat__less__add__iff2,axiom,
% 190.77/191.63 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 190.77/191.63 => ( 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)))
% 190.77/191.63 <=> 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))) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_add__eq__if,axiom,
% 190.77/191.63 ! [V_n,V_m] :
% 190.77/191.63 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.63 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n )
% 190.77/191.63 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.63 => 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)) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_div__if,axiom,
% 190.77/191.63 ! [V_m,V_n] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 190.77/191.63 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 190.77/191.63 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 190.77/191.63 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 190.77/191.63 => 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)) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_div__geq,axiom,
% 190.77/191.63 ! [V_m,V_n] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 190.77/191.63 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 190.77/191.63 => 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)) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_mult__eq__if,axiom,
% 190.77/191.63 ! [V_n,V_m] :
% 190.77/191.63 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.63 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 190.77/191.63 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.63 => 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)) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_int__power__div__base,axiom,
% 190.77/191.63 ! [V_k,V_m] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 190.77/191.63 => 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)))) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_decr__mult__lemma,axiom,
% 190.77/191.63 ! [V_k_2,V_Pa_2,V_d_2] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 190.77/191.63 => ( ! [B_x] :
% 190.77/191.63 ( hBOOL(hAPP(V_Pa_2,B_x))
% 190.77/191.63 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) )
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 190.77/191.63 => ! [B_x] :
% 190.77/191.63 ( hBOOL(hAPP(V_Pa_2,B_x))
% 190.77/191.63 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_incr__lemma,axiom,
% 190.77/191.63 ! [V_x,V_z,V_d] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 190.77/191.63 => 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)))) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_decr__lemma,axiom,
% 190.77/191.63 ! [V_z,V_x,V_d] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_nat__mod__eq__lemma,axiom,
% 190.77/191.63 ! [V_y,V_n,V_x] :
% 190.77/191.63 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n)
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x))
% 190.77/191.63 => ? [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)) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_mod__induct__0,axiom,
% 190.77/191.63 ! [V_i_2,V_Pa_2,V_p_2] :
% 190.77/191.63 ( ! [B_i] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2))
% 190.77/191.63 => ( hBOOL(hAPP(V_Pa_2,B_i))
% 190.77/191.63 => hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) )
% 190.77/191.63 => ( hBOOL(hAPP(V_Pa_2,V_i_2))
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
% 190.77/191.63 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_expand__Suc,axiom,
% 190.77/191.63 ! [V_v] :
% 190.77/191.63 ( 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)))
% 190.77/191.63 => 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))) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_nat__gcd_Osimps,axiom,
% 190.77/191.63 ! [V_x,V_y] :
% 190.77/191.63 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.63 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x )
% 190.77/191.63 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.63 => 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)) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_of__int__power,axiom,
% 190.77/191.63 ! [V_n,V_z,T_a] :
% 190.77/191.63 ( class_Rings_Oring__1(T_a)
% 190.77/191.63 => 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) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_of__int__number__of__eq,axiom,
% 190.77/191.63 ! [V_v,T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => 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) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__idempotent,axiom,
% 190.77/191.63 ! [V_a,T_a] :
% 190.77/191.63 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 190.77/191.63 => 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) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_eq__number__of,axiom,
% 190.77/191.63 ! [V_y_2,V_x_2,T_b] :
% 190.77/191.63 ( ( class_Int_Onumber__ring(T_b)
% 190.77/191.63 & class_Int_Oring__char__0(T_b) )
% 190.77/191.63 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 190.77/191.63 <=> V_x_2 = V_y_2 ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_number__of__reorient,axiom,
% 190.77/191.63 ! [V_x_2,V_w_2,T_b] :
% 190.77/191.63 ( class_Int_Onumber(T_b)
% 190.77/191.63 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2
% 190.77/191.63 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_zero__le__zpower__abs,axiom,
% 190.77/191.63 ! [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))) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__le__D1,axiom,
% 190.77/191.63 ! [V_b,V_a,T_a] :
% 190.77/191.63 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 190.77/191.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__ge__self,axiom,
% 190.77/191.63 ! [V_a,T_a] :
% 190.77/191.63 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 190.77/191.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__zero,axiom,
% 190.77/191.63 ! [T_a] :
% 190.77/191.63 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 190.77/191.63 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__eq__0,axiom,
% 190.77/191.63 ! [V_a_2,T_b] :
% 190.77/191.63 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 190.77/191.63 => ( hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 190.77/191.63 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__add__abs,axiom,
% 190.77/191.63 ! [V_b,V_a,T_a] :
% 190.77/191.63 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__mult__self,axiom,
% 190.77/191.63 ! [V_a,T_a] :
% 190.77/191.63 ( class_Rings_Olinordered__idom(T_a)
% 190.77/191.63 => 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) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__mult,axiom,
% 190.77/191.63 ! [V_b,V_a,T_a] :
% 190.77/191.63 ( class_Rings_Olinordered__idom(T_a)
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__minus__commute,axiom,
% 190.77/191.63 ! [V_b,V_a,T_a] :
% 190.77/191.63 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__one,axiom,
% 190.77/191.63 ! [T_a] :
% 190.77/191.63 ( class_Rings_Olinordered__idom(T_a)
% 190.77/191.63 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__minus__cancel,axiom,
% 190.77/191.63 ! [V_a,T_a] :
% 190.77/191.63 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 190.77/191.63 => 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) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 190.77/191.63 ! [V_q,V_y,V_x,T_a] :
% 190.77/191.63 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__of__nat,axiom,
% 190.77/191.63 ! [V_n,T_a] :
% 190.77/191.63 ( class_Rings_Olinordered__idom(T_a)
% 190.77/191.63 => 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) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__int__eq,axiom,
% 190.77/191.63 ! [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) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 190.77/191.63 ! [V_q,V_p,V_x,T_a] :
% 190.77/191.63 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_zpower__zpower,axiom,
% 190.77/191.63 ! [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)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 190.77/191.63 ! [V_x,T_a] :
% 190.77/191.63 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.63 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_zpower__zmod,axiom,
% 190.77/191.63 ! [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) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_of__nat__number__of__lemma,axiom,
% 190.77/191.63 ! [V_v,T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => ( ( 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)))
% 190.77/191.63 => 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) )
% 190.77/191.63 & ( ~ 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)))
% 190.77/191.63 => 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) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_number__of__eq,axiom,
% 190.77/191.63 ! [V_k,T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__number__of,axiom,
% 190.77/191.63 ! [V_x,T_a] :
% 190.77/191.63 ( ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 & class_Rings_Olinordered__idom(T_a) )
% 190.77/191.63 => ( ( 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)))
% 190.77/191.63 => 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)) )
% 190.77/191.63 & ( ~ 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)))
% 190.77/191.63 => 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) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_zero__less__zpower__abs__iff,axiom,
% 190.77/191.63 ! [V_n_2,V_x_2] :
% 190.77/191.63 ( 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)))
% 190.77/191.63 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 190.77/191.63 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__of__nonneg,axiom,
% 190.77/191.63 ! [V_a,T_a] :
% 190.77/191.63 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 190.77/191.63 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__le__zero__iff,axiom,
% 190.77/191.63 ! [V_a_2,T_b] :
% 190.77/191.63 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 190.77/191.63 => ( 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)))
% 190.77/191.63 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__ge__zero,axiom,
% 190.77/191.63 ! [V_a,T_a] :
% 190.77/191.63 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 190.77/191.63 => 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))) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__not__less__zero,axiom,
% 190.77/191.63 ! [V_a,T_a] :
% 190.77/191.63 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 190.77/191.63 => ~ 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))) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_zero__less__abs__iff,axiom,
% 190.77/191.63 ! [V_a_2,T_b] :
% 190.77/191.63 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 190.77/191.63 => ( 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)))
% 190.77/191.63 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__of__pos,axiom,
% 190.77/191.63 ! [V_a,T_a] :
% 190.77/191.63 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 190.77/191.63 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__triangle__ineq,axiom,
% 190.77/191.63 ! [V_b,V_a,T_a] :
% 190.77/191.63 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 190.77/191.63 => 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)))) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__mult__less,axiom,
% 190.77/191.63 ! [V_d,V_b,V_c,V_a,T_a] :
% 190.77/191.63 ( class_Rings_Olinordered__idom(T_a)
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c))
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d))
% 190.77/191.63 => 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))) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__triangle__ineq2__sym,axiom,
% 190.77/191.63 ! [V_b,V_a,T_a] :
% 190.77/191.63 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 190.77/191.63 => 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)))) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__triangle__ineq2,axiom,
% 190.77/191.63 ! [V_b,V_a,T_a] :
% 190.77/191.63 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 190.77/191.63 => 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)))) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__triangle__ineq3,axiom,
% 190.77/191.63 ! [V_b,V_a,T_a] :
% 190.77/191.63 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 190.77/191.63 => 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)))) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__ge__minus__self,axiom,
% 190.77/191.63 ! [V_a,T_a] :
% 190.77/191.63 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 190.77/191.63 => 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))) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__le__iff,axiom,
% 190.77/191.63 ! [V_ba_2,V_a_2,T_b] :
% 190.77/191.63 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_ba_2))
% 190.77/191.63 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2))
% 190.77/191.63 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_ba_2)) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__leI,axiom,
% 190.77/191.63 ! [V_b,V_a,T_a] :
% 190.77/191.63 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))
% 190.77/191.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__le__D2,axiom,
% 190.77/191.63 ! [V_b,V_a,T_a] :
% 190.77/191.63 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 190.77/191.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__less__iff,axiom,
% 190.77/191.63 ! [V_ba_2,V_a_2,T_b] :
% 190.77/191.63 ( class_Rings_Olinordered__idom(T_b)
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_ba_2))
% 190.77/191.63 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2))
% 190.77/191.63 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_ba_2)) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_le__number__of__eq__not__less,axiom,
% 190.77/191.63 ! [V_w_2,V_v_2,T_b] :
% 190.77/191.63 ( ( class_Int_Onumber(T_b)
% 190.77/191.63 & class_Orderings_Olinorder(T_b) )
% 190.77/191.63 => ( 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)))
% 190.77/191.63 <=> ~ 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))) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_left__distrib__number__of,axiom,
% 190.77/191.63 ! [V_v,V_b,V_a,T_b] :
% 190.77/191.63 ( ( class_Int_Onumber(T_b)
% 190.77/191.63 & class_Rings_Osemiring(T_b) )
% 190.77/191.63 => 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))) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_right__distrib__number__of,axiom,
% 190.77/191.63 ! [V_c,V_b,V_v,T_b] :
% 190.77/191.63 ( ( class_Int_Onumber(T_b)
% 190.77/191.63 & class_Rings_Osemiring(T_b) )
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
% 190.77/191.63 ! [V_q,V_x,T_a] :
% 190.77/191.63 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
% 190.77/191.63 ! [V_q,V_x,T_a] :
% 190.77/191.63 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
% 190.77/191.63 ! [V_q,V_x,T_a] :
% 190.77/191.63 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_left__diff__distrib__number__of,axiom,
% 190.77/191.63 ! [V_v,V_b,V_a,T_b] :
% 190.77/191.63 ( ( class_Int_Onumber(T_b)
% 190.77/191.63 & class_Rings_Oring(T_b) )
% 190.77/191.63 => 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))) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_right__diff__distrib__number__of,axiom,
% 190.77/191.63 ! [V_c,V_b,V_v,T_b] :
% 190.77/191.63 ( ( class_Int_Onumber(T_b)
% 190.77/191.63 & class_Rings_Oring(T_b) )
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_le__number__of,axiom,
% 190.77/191.63 ! [V_y_2,V_x_2,T_b] :
% 190.77/191.63 ( ( class_Int_Onumber__ring(T_b)
% 190.77/191.63 & class_Rings_Olinordered__idom(T_b) )
% 190.77/191.63 => ( 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)))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 190.77/191.63 ! [V_x,T_a] :
% 190.77/191.63 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.63 => 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) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 190.77/191.63 ! [V_q,V_p,V_x,T_a] :
% 190.77/191.63 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_less__number__of,axiom,
% 190.77/191.63 ! [V_y_2,V_x_2,T_b] :
% 190.77/191.63 ( ( class_Int_Onumber__ring(T_b)
% 190.77/191.63 & class_Rings_Olinordered__idom(T_b) )
% 190.77/191.63 => ( 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)))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_number__of__add,axiom,
% 190.77/191.63 ! [V_w,V_v,T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_add__number__of__eq,axiom,
% 190.77/191.63 ! [V_w,V_v,T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_add__number__of__left,axiom,
% 190.77/191.63 ! [V_z,V_w,V_v,T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => 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) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 190.77/191.63 ! [V_n,V_x] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 190.77/191.63 => 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))) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_mult__number__of__left,axiom,
% 190.77/191.63 ! [V_z,V_w,V_v,T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => 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) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_arith__simps_I32_J,axiom,
% 190.77/191.63 ! [V_w,V_v,T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_number__of__mult,axiom,
% 190.77/191.63 ! [V_w,V_v,T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__zmult__eq__1,axiom,
% 190.77/191.63 ! [V_n,V_m] :
% 190.77/191.63 ( 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)
% 190.77/191.63 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_number__of__diff,axiom,
% 190.77/191.63 ! [V_w,V_v,T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_zpower__zadd__distrib,axiom,
% 190.77/191.63 ! [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)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_number__of__minus,axiom,
% 190.77/191.63 ! [V_w,T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_arith__simps_I30_J,axiom,
% 190.77/191.63 ! [V_w,T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_mult__sgn__abs,axiom,
% 190.77/191.63 ! [V_x,T_a] :
% 190.77/191.63 ( class_Rings_Olinordered__idom(T_a)
% 190.77/191.63 => 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 ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__sgn,axiom,
% 190.77/191.63 ! [V_k,T_a] :
% 190.77/191.63 ( class_Rings_Olinordered__idom(T_a)
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__mult__pos,axiom,
% 190.77/191.63 ! [V_y,V_x,T_a] :
% 190.77/191.63 ( class_Rings_Olinordered__idom(T_a)
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 190.77/191.63 => 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)) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__eq__mult,axiom,
% 190.77/191.63 ! [V_b,V_a,T_a] :
% 190.77/191.63 ( class_Rings_Oordered__ring__abs(T_a)
% 190.77/191.63 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 190.77/191.63 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
% 190.77/191.63 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 190.77/191.63 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 190.77/191.63 => 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)) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__diff__triangle__ineq,axiom,
% 190.77/191.63 ! [V_d,V_c,V_b,V_a,T_a] :
% 190.77/191.63 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 190.77/191.63 => 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))))) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__triangle__ineq4,axiom,
% 190.77/191.63 ! [V_b,V_a,T_a] :
% 190.77/191.63 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 190.77/191.63 => 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)))) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__of__nonpos,axiom,
% 190.77/191.63 ! [V_a,T_a] :
% 190.77/191.63 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 190.77/191.63 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__minus__le__zero,axiom,
% 190.77/191.63 ! [V_a,T_a] :
% 190.77/191.63 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 190.77/191.63 => 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))) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__if,axiom,
% 190.77/191.63 ! [V_a,T_a] :
% 190.77/191.63 ( class_Groups_Oabs__if(T_a)
% 190.77/191.63 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 190.77/191.63 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) )
% 190.77/191.63 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 190.77/191.63 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__of__neg,axiom,
% 190.77/191.63 ! [V_a,T_a] :
% 190.77/191.63 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 190.77/191.63 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_zabs__less__one__iff,axiom,
% 190.77/191.63 ! [V_z_2] :
% 190.77/191.63 ( 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)))
% 190.77/191.63 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_add__number__of__diff1,axiom,
% 190.77/191.63 ! [V_c,V_w,V_v,T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => 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) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_zabs__def,axiom,
% 190.77/191.63 ! [V_i] :
% 190.77/191.63 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 190.77/191.63 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) )
% 190.77/191.63 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 190.77/191.63 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_minus__number__of__mult,axiom,
% 190.77/191.63 ! [V_z,V_w,T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => 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) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_nat__abs__mult__distrib,axiom,
% 190.77/191.63 ! [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))) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_diff__number__of__eq,axiom,
% 190.77/191.63 ! [V_w,V_v,T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => 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))) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_add__number__of__diff2,axiom,
% 190.77/191.63 ! [V_w,V_c,V_v,T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => 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) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__strict__mono,axiom,
% 190.77/191.63 ! [V_n,V_b,V_a,T_a] :
% 190.77/191.63 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 190.77/191.63 => 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))) ) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_one__less__power,axiom,
% 190.77/191.63 ! [V_n,V_a,T_a] :
% 190.77/191.63 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 190.77/191.63 => 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))) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__increasing__iff,axiom,
% 190.77/191.63 ! [V_y_2,V_x_2,V_ba_2,T_b] :
% 190.77/191.63 ( class_Rings_Olinordered__semidom(T_b)
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_ba_2))
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_ba_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_ba_2),V_y_2)))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__le__imp__le__exp,axiom,
% 190.77/191.63 ! [V_n,V_m,V_a,T_a] :
% 190.77/191.63 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 190.77/191.63 => ( 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)))
% 190.77/191.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__decreasing,axiom,
% 190.77/191.63 ! [V_a,V_N,V_n,T_a] :
% 190.77/191.63 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 190.77/191.63 => 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))) ) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__strict__decreasing,axiom,
% 190.77/191.63 ! [V_a,V_N,V_n,T_a] :
% 190.77/191.63 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 190.77/191.63 => 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))) ) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__Suc__less__one,axiom,
% 190.77/191.63 ! [V_n,V_a,T_a] :
% 190.77/191.63 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 190.77/191.63 => 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))) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_number__of__is__id,axiom,
% 190.77/191.63 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ).
% 190.77/191.63
% 190.77/191.63 fof(fact_less__eq__number__of__int__code,axiom,
% 190.77/191.63 ! [V_l_2,V_k_2] :
% 190.77/191.63 ( 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)))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_less__number__of__int__code,axiom,
% 190.77/191.63 ! [V_l_2,V_k_2] :
% 190.77/191.63 ( 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)))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_plus__numeral__code_I9_J,axiom,
% 190.77/191.63 ! [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)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_times__numeral__code_I5_J,axiom,
% 190.77/191.63 ! [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)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_minus__numeral__code_I5_J,axiom,
% 190.77/191.63 ! [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)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__Suc__0,axiom,
% 190.77/191.63 ! [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)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_nat__power__eq__Suc__0__iff,axiom,
% 190.77/191.63 ! [V_m_2,V_x_2] :
% 190.77/191.63 ( 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))
% 190.77/191.63 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.63 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_nat__power__less__imp__less,axiom,
% 190.77/191.63 ! [V_n,V_m,V_i] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))
% 190.77/191.63 => ( 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)))
% 190.77/191.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_nat__zero__less__power__iff,axiom,
% 190.77/191.63 ! [V_n_2,V_x_2] :
% 190.77/191.63 ( 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)))
% 190.77/191.63 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))
% 190.77/191.63 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_int__number__of__def,axiom,
% 190.77/191.63 ! [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) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_nat__one__le__power,axiom,
% 190.77/191.63 ! [V_n,V_i] :
% 190.77/191.63 ( 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))
% 190.77/191.63 => 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))) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_nat__number__of,axiom,
% 190.77/191.63 ! [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) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_nat__number__of__def,axiom,
% 190.77/191.63 ! [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)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_int__power,axiom,
% 190.77/191.63 ! [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) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_zpower__int,axiom,
% 190.77/191.63 ! [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)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
% 190.77/191.63 ! [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)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_minus__numeral__code_I6_J,axiom,
% 190.77/191.63 ! [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))) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__eq__if,axiom,
% 190.77/191.63 ! [V_p,V_m] :
% 190.77/191.63 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.63 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 190.77/191.63 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.63 => 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)))) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_int__eq__iff__number__of,axiom,
% 190.77/191.63 ! [V_v_2,V_m_2] :
% 190.77/191.63 ( 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)
% 190.77/191.63 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))
% 190.77/191.63 & 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))) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom,
% 190.77/191.63 ! [V_n,V_x] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_nat__power__eq,axiom,
% 190.77/191.63 ! [V_n,V_z] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 190.77/191.63 => 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) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_field__power__not__zero,axiom,
% 190.77/191.63 ! [V_n,V_a,T_a] :
% 190.77/191.63 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 190.77/191.63 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 190.77/191.63 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__commutes,axiom,
% 190.77/191.63 ! [V_n,V_a,T_a] :
% 190.77/191.63 ( class_Groups_Omonoid__mult(T_a)
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__mult__distrib,axiom,
% 190.77/191.63 ! [V_n,V_b,V_a,T_a] :
% 190.77/191.63 ( class_Groups_Ocomm__monoid__mult(T_a)
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__one,axiom,
% 190.77/191.63 ! [V_n,T_a] :
% 190.77/191.63 ( class_Groups_Omonoid__mult(T_a)
% 190.77/191.63 => 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) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_of__nat__power,axiom,
% 190.77/191.63 ! [V_n,V_m,T_a] :
% 190.77/191.63 ( class_Rings_Osemiring__1(T_a)
% 190.77/191.63 => 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) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__mult,axiom,
% 190.77/191.63 ! [V_n,V_m,V_a,T_a] :
% 190.77/191.63 ( class_Groups_Omonoid__mult(T_a)
% 190.77/191.63 => 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) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_one__div__nat__number__of,axiom,
% 190.77/191.63 ! [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))) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__abs,axiom,
% 190.77/191.63 ! [V_n,V_a,T_a] :
% 190.77/191.63 ( class_Rings_Olinordered__idom(T_a)
% 190.77/191.63 => 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) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__one__right,axiom,
% 190.77/191.63 ! [V_a,T_a] :
% 190.77/191.63 ( class_Groups_Omonoid__mult(T_a)
% 190.77/191.63 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_zero__le__power,axiom,
% 190.77/191.63 ! [V_n,V_a,T_a] :
% 190.77/191.63 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 190.77/191.63 => 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))) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__mono,axiom,
% 190.77/191.63 ! [V_n,V_b,V_a,T_a] :
% 190.77/191.63 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 190.77/191.63 => 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))) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_zero__less__power,axiom,
% 190.77/191.63 ! [V_n,V_a,T_a] :
% 190.77/191.63 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 190.77/191.63 => 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))) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__eq__0__iff,axiom,
% 190.77/191.63 ! [V_n_2,V_a_2,T_b] :
% 190.77/191.63 ( ( class_Power_Opower(T_b)
% 190.77/191.63 & class_Rings_Omult__zero(T_b)
% 190.77/191.63 & class_Rings_Ono__zero__divisors(T_b)
% 190.77/191.63 & class_Rings_Ozero__neq__one(T_b) )
% 190.77/191.63 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_b)
% 190.77/191.63 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 190.77/191.63 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_one__le__power,axiom,
% 190.77/191.63 ! [V_n,V_a,T_a] :
% 190.77/191.63 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 190.77/191.63 => 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))) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__0__Suc,axiom,
% 190.77/191.63 ! [V_n,T_a] :
% 190.77/191.63 ( ( class_Power_Opower(T_a)
% 190.77/191.63 & class_Rings_Osemiring__0(T_a) )
% 190.77/191.63 => 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) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__inject__exp,axiom,
% 190.77/191.63 ! [V_n_2,V_m_2,V_a_2,T_b] :
% 190.77/191.63 ( class_Rings_Olinordered__semidom(T_b)
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2))
% 190.77/191.63 => ( 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)
% 190.77/191.63 <=> V_m_2 = V_n_2 ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__Suc,axiom,
% 190.77/191.63 ! [V_n,V_a,T_a] :
% 190.77/191.63 ( class_Power_Opower(T_a)
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__Suc2,axiom,
% 190.77/191.63 ! [V_n,V_a,T_a] :
% 190.77/191.63 ( class_Groups_Omonoid__mult(T_a)
% 190.77/191.63 => 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) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__0,axiom,
% 190.77/191.63 ! [V_a,T_a] :
% 190.77/191.63 ( class_Power_Opower(T_a)
% 190.77/191.63 => 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) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__add,axiom,
% 190.77/191.63 ! [V_n,V_m,V_a,T_a] :
% 190.77/191.63 ( class_Groups_Omonoid__mult(T_a)
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__power__minus,axiom,
% 190.77/191.63 ! [V_n,V_a,T_a] :
% 190.77/191.63 ( class_Rings_Olinordered__idom(T_a)
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__less__imp__less__base,axiom,
% 190.77/191.63 ! [V_b,V_n,V_a,T_a] :
% 190.77/191.63 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.63 => ( 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)))
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 190.77/191.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__le__imp__le__base,axiom,
% 190.77/191.63 ! [V_b,V_n,V_a,T_a] :
% 190.77/191.63 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.63 => ( 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))))
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 190.77/191.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__inject__base,axiom,
% 190.77/191.63 ! [V_b,V_n,V_a,T_a] :
% 190.77/191.63 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.63 => ( 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))
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 190.77/191.63 => V_a = V_b ) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__gt1__lemma,axiom,
% 190.77/191.63 ! [V_n,V_a,T_a] :
% 190.77/191.63 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 190.77/191.63 => 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)))) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__less__power__Suc,axiom,
% 190.77/191.63 ! [V_n,V_a,T_a] :
% 190.77/191.63 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 190.77/191.63 => 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)))) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__0__left,axiom,
% 190.77/191.63 ! [V_n,T_a] :
% 190.77/191.63 ( ( class_Power_Opower(T_a)
% 190.77/191.63 & class_Rings_Osemiring__0(T_a) )
% 190.77/191.63 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.63 => 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) )
% 190.77/191.63 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.63 => 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) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__gt1,axiom,
% 190.77/191.63 ! [V_n,V_a,T_a] :
% 190.77/191.63 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 190.77/191.63 => 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)))) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__strict__increasing,axiom,
% 190.77/191.63 ! [V_a,V_N,V_n,T_a] :
% 190.77/191.63 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 190.77/191.63 => 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))) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__less__imp__less__exp,axiom,
% 190.77/191.63 ! [V_n,V_m,V_a,T_a] :
% 190.77/191.63 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 190.77/191.63 => ( 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)))
% 190.77/191.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__strict__increasing__iff,axiom,
% 190.77/191.63 ! [V_y_2,V_x_2,V_ba_2,T_b] :
% 190.77/191.63 ( class_Rings_Olinordered__semidom(T_b)
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_ba_2))
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_ba_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_ba_2),V_y_2)))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_zero__le__power__abs,axiom,
% 190.77/191.63 ! [V_n,V_a,T_a] :
% 190.77/191.63 ( class_Rings_Olinordered__idom(T_a)
% 190.77/191.63 => 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))) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__increasing,axiom,
% 190.77/191.63 ! [V_a,V_N,V_n,T_a] :
% 190.77/191.63 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 190.77/191.63 => 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))) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__minus,axiom,
% 190.77/191.63 ! [V_n,V_a,T_a] :
% 190.77/191.63 ( class_Rings_Oring__1(T_a)
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__Suc__less,axiom,
% 190.77/191.63 ! [V_n,V_a,T_a] :
% 190.77/191.63 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 190.77/191.63 => 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))) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__eq__imp__eq__base,axiom,
% 190.77/191.63 ! [V_b,V_n,V_a,T_a] :
% 190.77/191.63 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.63 => ( 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)
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 190.77/191.63 => V_a = V_b ) ) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_Nitpick_Onat__lcm__def,axiom,
% 190.77/191.63 ! [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)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_Nitpick_Oint__gcd__def,axiom,
% 190.77/191.63 ! [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)))) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_one__mod__nat__number__of,axiom,
% 190.77/191.63 ! [V_v_H] :
% 190.77/191.63 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 190.77/191.63 => 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)) )
% 190.77/191.63 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 190.77/191.63 => 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))) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__power__power,axiom,
% 190.77/191.63 ! [T_b] :
% 190.77/191.63 ( class_Power_Opower(T_b)
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_div__nat__number__of,axiom,
% 190.77/191.63 ! [V_v_H,V_v] :
% 190.77/191.63 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 190.77/191.63 => 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) )
% 190.77/191.63 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 190.77/191.63 => 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))) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_mod__nat__number__of,axiom,
% 190.77/191.63 ! [V_v_H,V_v] :
% 190.77/191.63 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 190.77/191.63 => 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) )
% 190.77/191.63 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 190.77/191.63 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 190.77/191.63 => 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) )
% 190.77/191.63 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 190.77/191.63 => 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))) ) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_Nitpick_Oint__lcm__def,axiom,
% 190.77/191.63 ! [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)))) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_not__neg__0,axiom,
% 190.77/191.63 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_not__neg__int,axiom,
% 190.77/191.63 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_not__neg__1,axiom,
% 190.77/191.63 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_not__neg__eq__ge__0,axiom,
% 190.77/191.63 ! [V_x_2] :
% 190.77/191.63 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_neg__def,axiom,
% 190.77/191.63 ! [V_Z_2] :
% 190.77/191.63 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_neg__nat,axiom,
% 190.77/191.63 ! [V_z] :
% 190.77/191.63 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 190.77/191.63 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_not__neg__nat,axiom,
% 190.77/191.63 ! [V_z] :
% 190.77/191.63 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 190.77/191.63 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power_Opower_Opower__0,axiom,
% 190.77/191.63 ! [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 ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power_Opower_Opower__Suc,axiom,
% 190.77/191.63 ! [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)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_neg__imp__number__of__eq__0,axiom,
% 190.77/191.63 ! [V_v] :
% 190.77/191.63 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 190.77/191.63 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_neg__zminus__int,axiom,
% 190.77/191.63 ! [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))))) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_eq__nat__number__of,axiom,
% 190.77/191.63 ! [V_v_H_2,V_v_2] :
% 190.77/191.63 ( 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)
% 190.77/191.63 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 190.77/191.63 => 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))) )
% 190.77/191.63 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 190.77/191.63 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 190.77/191.63 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 190.77/191.63 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 190.77/191.63 => V_v_2 = V_v_H_2 ) ) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_nat__number__of__add__left,axiom,
% 190.77/191.63 ! [V_k,V_v_H,V_v] :
% 190.77/191.63 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 190.77/191.63 => 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) )
% 190.77/191.63 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 190.77/191.63 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 190.77/191.63 => 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) )
% 190.77/191.63 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 190.77/191.63 => 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) ) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_int__nat__number__of,axiom,
% 190.77/191.63 ! [V_v] :
% 190.77/191.63 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 190.77/191.63 => 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) )
% 190.77/191.63 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 190.77/191.63 => 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) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_of__nat__number__of__eq,axiom,
% 190.77/191.63 ! [V_v,T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 190.77/191.63 => 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) )
% 190.77/191.63 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 190.77/191.63 => 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) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__nat__number__of__number__of,axiom,
% 190.77/191.63 ! [V_w,V_v] :
% 190.77/191.63 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 190.77/191.63 => 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)) )
% 190.77/191.63 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 190.77/191.63 => 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))) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power__nat__number__of,axiom,
% 190.77/191.63 ! [V_n,V_v] :
% 190.77/191.63 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 190.77/191.63 => 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) )
% 190.77/191.63 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 190.77/191.63 => 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)) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_Suc__nat__number__of__add,axiom,
% 190.77/191.63 ! [V_n,V_v] :
% 190.77/191.63 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 190.77/191.63 => 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) )
% 190.77/191.63 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 190.77/191.63 => 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) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_Suc__nat__number__of,axiom,
% 190.77/191.63 ! [V_v] :
% 190.77/191.63 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 190.77/191.63 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 190.77/191.63 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 190.77/191.63 => 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)) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_zmod__minus1,axiom,
% 190.77/191.63 ! [V_b] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_div__pos__neg__trivial,axiom,
% 190.77/191.63 ! [V_b,V_a] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 190.77/191.63 => ( 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)))
% 190.77/191.63 => 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) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_nat0__intermed__int__val,axiom,
% 190.77/191.63 ! [V_k_2,V_f_2,V_n_2] :
% 190.77/191.63 ( ! [B_i] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 190.77/191.63 => 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))) )
% 190.77/191.63 => ( 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))
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 190.77/191.63 => ? [B_i] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 190.77/191.63 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_int__val__lemma,axiom,
% 190.77/191.63 ! [V_k_2,V_f_2,V_n_2] :
% 190.77/191.63 ( ! [B_i] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 190.77/191.63 => 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))) )
% 190.77/191.63 => ( 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))
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 190.77/191.63 => ? [B_i] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 190.77/191.63 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_eq__number__of__eq,axiom,
% 190.77/191.63 ! [V_y_2,V_x_2,T_b] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_b)
% 190.77/191.63 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 190.77/191.63 <=> 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)))) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_diff__bin__simps_I2_J,axiom,
% 190.77/191.63 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_nonzero__number__of__Min,axiom,
% 190.77/191.63 ! [T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I24_J,axiom,
% 190.77/191.63 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I7_J,axiom,
% 190.77/191.63 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_iszero__def,axiom,
% 190.77/191.63 ! [V_z_2,T_b] :
% 190.77/191.63 ( class_Rings_Osemiring__1(T_b)
% 190.77/191.63 => ( c_Int_Oiszero(T_b,V_z_2)
% 190.77/191.63 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_iszero__0,axiom,
% 190.77/191.63 ! [T_a] :
% 190.77/191.63 ( class_Rings_Osemiring__1(T_a)
% 190.77/191.63 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_not__iszero__1,axiom,
% 190.77/191.63 ! [T_a] :
% 190.77/191.63 ( class_Rings_Osemiring__1(T_a)
% 190.77/191.63 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_bin__less__0__simps_I2_J,axiom,
% 190.77/191.63 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_Int_OMin__def,axiom,
% 190.77/191.63 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_mult__Min,axiom,
% 190.77/191.63 ! [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) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_neg__number__of__Min,axiom,
% 190.77/191.63 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_mult__minus1__right,axiom,
% 190.77/191.63 ! [V_z,T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => 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) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_mult__minus1,axiom,
% 190.77/191.63 ! [V_z,T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => 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) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_arith__simps_I31_J,axiom,
% 190.77/191.63 ! [T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => 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) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_number__of__Min,axiom,
% 190.77/191.63 ! [T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__minus__one,axiom,
% 190.77/191.63 ! [T_a] :
% 190.77/191.63 ( ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 & class_Rings_Olinordered__idom(T_a) )
% 190.77/191.63 => 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) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_zmod__minus1__right,axiom,
% 190.77/191.63 ! [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) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_zmult__eq__1__iff,axiom,
% 190.77/191.63 ! [V_n_2,V_m_2] :
% 190.77/191.63 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 190.77/191.63 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 190.77/191.63 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 190.77/191.63 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
% 190.77/191.63 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
% 190.77/191.63 ! [V_n,V_m] :
% 190.77/191.63 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 190.77/191.63 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 190.77/191.63 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_of__int__m1,axiom,
% 190.77/191.63 ! [T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => 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) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_zdiv__minus1__right,axiom,
% 190.77/191.63 ! [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) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_succ__def,axiom,
% 190.77/191.63 ! [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)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_abs__power__minus__one,axiom,
% 190.77/191.63 ! [V_n,T_a] :
% 190.77/191.63 ( ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 & class_Rings_Olinordered__idom(T_a) )
% 190.77/191.63 => 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) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_div__eq__minus1,axiom,
% 190.77/191.63 ! [V_b] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 190.77/191.63 => 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) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_number__of__succ,axiom,
% 190.77/191.63 ! [V_k,T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_nat__1__add__number__of,axiom,
% 190.77/191.63 ! [V_v] :
% 190.77/191.63 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 190.77/191.63 => 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) )
% 190.77/191.63 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 190.77/191.63 => 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)) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_nat__number__of__add__1,axiom,
% 190.77/191.63 ! [V_v] :
% 190.77/191.63 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 190.77/191.63 => 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) )
% 190.77/191.63 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 190.77/191.63 => 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)) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_eq__special_I3_J,axiom,
% 190.77/191.63 ! [V_x_2,T_b] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_b)
% 190.77/191.63 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Ozero__class_Ozero(T_b)
% 190.77/191.63 <=> 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)))) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_eq__special_I1_J,axiom,
% 190.77/191.63 ! [V_y_2,T_b] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_b)
% 190.77/191.63 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 190.77/191.63 <=> 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)))) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_neg__number__of__pred__iff__0,axiom,
% 190.77/191.63 ! [V_v_2] :
% 190.77/191.63 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))))
% 190.77/191.63 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_nat__number__of__mult__left,axiom,
% 190.77/191.63 ! [V_k,V_v_H,V_v] :
% 190.77/191.63 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 190.77/191.63 => 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) )
% 190.77/191.63 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 190.77/191.63 => 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) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_mult__nat__number__of,axiom,
% 190.77/191.63 ! [V_v_H,V_v] :
% 190.77/191.63 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 190.77/191.63 => 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) )
% 190.77/191.63 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 190.77/191.63 => 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)) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_pred__Pls,axiom,
% 190.77/191.63 c_Int_Opred(c_Int_OPls) = c_Int_OMin ).
% 190.77/191.63
% 190.77/191.63 fof(fact_Pls__def,axiom,
% 190.77/191.63 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I19_J,axiom,
% 190.77/191.63 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I2_J,axiom,
% 190.77/191.63 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_add__Pls,axiom,
% 190.77/191.63 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ).
% 190.77/191.63
% 190.77/191.63 fof(fact_add__Pls__right,axiom,
% 190.77/191.63 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 190.77/191.63
% 190.77/191.63 fof(fact_mult__Pls,axiom,
% 190.77/191.63 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ).
% 190.77/191.63
% 190.77/191.63 fof(fact_diff__bin__simps_I1_J,axiom,
% 190.77/191.63 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 190.77/191.63
% 190.77/191.63 fof(fact_minus__Pls,axiom,
% 190.77/191.63 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I37_J,axiom,
% 190.77/191.63 c_Int_OPls != c_Int_OMin ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I40_J,axiom,
% 190.77/191.63 c_Int_OMin != c_Int_OPls ).
% 190.77/191.63
% 190.77/191.63 fof(fact_succ__pred,axiom,
% 190.77/191.63 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ).
% 190.77/191.63
% 190.77/191.63 fof(fact_number__of__Pls,axiom,
% 190.77/191.63 ! [T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_semiring__norm_I112_J,axiom,
% 190.77/191.63 ! [T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_add__numeral__0,axiom,
% 190.77/191.63 ! [V_a,T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => 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 ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_add__numeral__0__right,axiom,
% 190.77/191.63 ! [V_a,T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => 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 ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_bin__less__0__simps_I1_J,axiom,
% 190.77/191.63 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_nat__number__of__Pls,axiom,
% 190.77/191.63 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_semiring__norm_I113_J,axiom,
% 190.77/191.63 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_zero__is__num__zero,axiom,
% 190.77/191.63 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_Suc__diff__number__of,axiom,
% 190.77/191.63 ! [V_m,V_v] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v))
% 190.77/191.63 => 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))) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I20_J,axiom,
% 190.77/191.63 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I23_J,axiom,
% 190.77/191.63 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I3_J,axiom,
% 190.77/191.63 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I6_J,axiom,
% 190.77/191.63 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_eq__number__of__Pls__Min,axiom,
% 190.77/191.63 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) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_not__neg__number__of__Pls,axiom,
% 190.77/191.63 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_iszero__Numeral0,axiom,
% 190.77/191.63 ! [T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_succ__Min,axiom,
% 190.77/191.63 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ).
% 190.77/191.63
% 190.77/191.63 fof(fact_le__iff__pred__less,axiom,
% 190.77/191.63 ! [V_l_2,V_k_2] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_pred__def,axiom,
% 190.77/191.63 ! [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)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_add__Min__right,axiom,
% 190.77/191.63 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_add__Min,axiom,
% 190.77/191.63 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_nat__number__of__diff__1,axiom,
% 190.77/191.63 ! [V_v] :
% 190.77/191.63 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 190.77/191.63 => 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) )
% 190.77/191.63 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 190.77/191.63 => 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)) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_eq__0__number__of,axiom,
% 190.77/191.63 ! [V_v_2] :
% 190.77/191.63 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_eq__number__of__0,axiom,
% 190.77/191.63 ! [V_v_2] :
% 190.77/191.63 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_number__of2,axiom,
% 190.77/191.63 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))) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_less__nat__number__of,axiom,
% 190.77/191.63 ! [V_v_H_2,V_v_2] :
% 190.77/191.63 ( 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)))
% 190.77/191.63 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
% 190.77/191.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) )
% 190.77/191.63 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_le__nat__number__of,axiom,
% 190.77/191.63 ! [V_v_H_2,V_v_2] :
% 190.77/191.63 ( 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)))
% 190.77/191.63 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2))
% 190.77/191.63 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_le__special_I1_J,axiom,
% 190.77/191.63 ! [V_y_2,T_b] :
% 190.77/191.63 ( ( class_Int_Onumber__ring(T_b)
% 190.77/191.63 & class_Rings_Olinordered__idom(T_b) )
% 190.77/191.63 => ( 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)))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_le__special_I3_J,axiom,
% 190.77/191.63 ! [V_x_2,T_b] :
% 190.77/191.63 ( ( class_Int_Onumber__ring(T_b)
% 190.77/191.63 & class_Rings_Olinordered__idom(T_b) )
% 190.77/191.63 => ( 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)))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_less__special_I3_J,axiom,
% 190.77/191.63 ! [V_x_2,T_b] :
% 190.77/191.63 ( ( class_Int_Onumber__ring(T_b)
% 190.77/191.63 & class_Rings_Olinordered__idom(T_b) )
% 190.77/191.63 => ( 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)))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_less__special_I1_J,axiom,
% 190.77/191.63 ! [V_y_2,T_b] :
% 190.77/191.63 ( ( class_Int_Onumber__ring(T_b)
% 190.77/191.63 & class_Rings_Olinordered__idom(T_b) )
% 190.77/191.63 => ( 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)))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_less__0__number__of,axiom,
% 190.77/191.63 ! [V_v_2] :
% 190.77/191.63 ( 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)))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_add__nat__number__of,axiom,
% 190.77/191.63 ! [V_v_H,V_v] :
% 190.77/191.63 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 190.77/191.63 => 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) )
% 190.77/191.63 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 190.77/191.63 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 190.77/191.63 => 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) )
% 190.77/191.63 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 190.77/191.63 => 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)) ) ) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_number__of__pred,axiom,
% 190.77/191.63 ! [V_w,T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_eq__special_I4_J,axiom,
% 190.77/191.63 ! [V_x_2,T_b] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_b)
% 190.77/191.63 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 190.77/191.63 <=> 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))))) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_eq__special_I2_J,axiom,
% 190.77/191.63 ! [V_y_2,T_b] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_b)
% 190.77/191.63 => ( c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 190.77/191.63 <=> 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)))) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_diff__special_I2_J,axiom,
% 190.77/191.63 ! [V_v,T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => 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)))) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_diff__special_I1_J,axiom,
% 190.77/191.63 ! [V_w,T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => 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))) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_Suc__div__eq__add3__div__number__of,axiom,
% 190.77/191.63 ! [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)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_Suc__div__eq__add3__div,axiom,
% 190.77/191.63 ! [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) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I51_J,axiom,
% 190.77/191.63 ! [V_l_2,V_k_2] :
% 190.77/191.63 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
% 190.77/191.63 <=> V_k_2 = V_l_2 ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I34_J,axiom,
% 190.77/191.63 ! [V_l_2,V_k_2] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_less__eq__int__code_I16_J,axiom,
% 190.77/191.63 ! [V_k2_2,V_k1_2] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I17_J,axiom,
% 190.77/191.63 ! [V_l_2,V_k_2] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_less__int__code_I16_J,axiom,
% 190.77/191.63 ! [V_k2_2,V_k1_2] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I39_J,axiom,
% 190.77/191.63 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I46_J,axiom,
% 190.77/191.63 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ).
% 190.77/191.63
% 190.77/191.63 fof(fact_Bit1__Min,axiom,
% 190.77/191.63 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I43_J,axiom,
% 190.77/191.63 ! [V_l_2] :
% 190.77/191.63 ( c_Int_OMin = c_Int_OBit1(V_l_2)
% 190.77/191.63 <=> c_Int_OMin = V_l_2 ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I47_J,axiom,
% 190.77/191.63 ! [V_k_2] :
% 190.77/191.63 ( c_Int_OBit1(V_k_2) = c_Int_OMin
% 190.77/191.63 <=> V_k_2 = c_Int_OMin ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_bin__less__0__simps_I4_J,axiom,
% 190.77/191.63 ! [V_w_2] :
% 190.77/191.63 ( 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)))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I22_J,axiom,
% 190.77/191.63 ! [V_k_2] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I12_J,axiom,
% 190.77/191.63 ! [V_k_2] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_Bit1__def,axiom,
% 190.77/191.63 ! [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) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I26_J,axiom,
% 190.77/191.63 ! [V_k_2] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I30_J,axiom,
% 190.77/191.63 ! [V_k_2] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I9_J,axiom,
% 190.77/191.63 ! [V_k_2] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I13_J,axiom,
% 190.77/191.63 ! [V_k_2] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_neg__number__of__Bit1,axiom,
% 190.77/191.63 ! [V_w_2] :
% 190.77/191.63 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2))))
% 190.77/191.63 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_minus__Bit1,axiom,
% 190.77/191.63 ! [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))) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_iszero__number__of__Bit1,axiom,
% 190.77/191.63 ! [V_w,T_a] :
% 190.77/191.63 ( ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 & class_Int_Oring__char__0(T_a) )
% 190.77/191.63 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_succ__Pls,axiom,
% 190.77/191.63 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_number__of__Bit1,axiom,
% 190.77/191.63 ! [V_w,T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_mult__numeral__1__right,axiom,
% 190.77/191.63 ! [V_a,T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => 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 ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_mult__numeral__1,axiom,
% 190.77/191.63 ! [V_a,T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => 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 ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_numeral__1__eq__1,axiom,
% 190.77/191.63 ! [T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_semiring__norm_I110_J,axiom,
% 190.77/191.63 ! [T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I29_J,axiom,
% 190.77/191.63 ! [V_k_2] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I5_J,axiom,
% 190.77/191.63 ! [V_k_2] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_one__is__num__one,axiom,
% 190.77/191.63 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_Numeral1__eq1__nat,axiom,
% 190.77/191.63 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_nat__numeral__1__eq__1,axiom,
% 190.77/191.63 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_diff__bin__simps_I4_J,axiom,
% 190.77/191.63 ! [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)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_minus__Min,axiom,
% 190.77/191.63 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_not__iszero__Numeral1,axiom,
% 190.77/191.63 ! [T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_numeral__1__eq__Suc__0,axiom,
% 190.77/191.63 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)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_numeral__3__eq__3,axiom,
% 190.77/191.63 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)))) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_power3__eq__cube,axiom,
% 190.77/191.63 ! [V_a,T_a] :
% 190.77/191.63 ( class_Groups_Omonoid__mult(T_a)
% 190.77/191.63 => 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) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
% 190.77/191.63 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))))) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_Suc3__eq__add__3,axiom,
% 190.77/191.63 ! [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) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_transfer__int__nat__numerals_I4_J,axiom,
% 190.77/191.63 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)))) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_transfer__nat__int__numerals_I4_J,axiom,
% 190.77/191.63 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)))) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_le__special_I4_J,axiom,
% 190.77/191.63 ! [V_x_2,T_b] :
% 190.77/191.63 ( ( class_Int_Onumber__ring(T_b)
% 190.77/191.63 & class_Rings_Olinordered__idom(T_b) )
% 190.77/191.63 => ( 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)))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_le__special_I2_J,axiom,
% 190.77/191.63 ! [V_y_2,T_b] :
% 190.77/191.63 ( ( class_Int_Onumber__ring(T_b)
% 190.77/191.63 & class_Rings_Olinordered__idom(T_b) )
% 190.77/191.63 => ( 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)))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_less__special_I4_J,axiom,
% 190.77/191.63 ! [V_x_2,T_b] :
% 190.77/191.63 ( ( class_Int_Onumber__ring(T_b)
% 190.77/191.63 & class_Rings_Olinordered__idom(T_b) )
% 190.77/191.63 => ( 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)))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_less__special_I2_J,axiom,
% 190.77/191.63 ! [V_y_2,T_b] :
% 190.77/191.63 ( ( class_Int_Onumber__ring(T_b)
% 190.77/191.63 & class_Rings_Olinordered__idom(T_b) )
% 190.77/191.63 => ( 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)))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_add__special_I2_J,axiom,
% 190.77/191.63 ! [V_w,T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_add__special_I3_J,axiom,
% 190.77/191.63 ! [V_v,T_a] :
% 190.77/191.63 ( class_Int_Onumber__ring(T_a)
% 190.77/191.63 => 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))) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_Suc__diff__eq__diff__pred,axiom,
% 190.77/191.63 ! [V_m,V_n] :
% 190.77/191.63 ( 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))
% 190.77/191.63 => 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)))) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_mod__Suc__eq__mod__add3,axiom,
% 190.77/191.63 ! [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)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_Suc__mod__eq__add3__mod,axiom,
% 190.77/191.63 ! [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) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom,
% 190.77/191.63 ! [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)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_div__Suc__eq__div__add3,axiom,
% 190.77/191.63 ! [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)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_zmod__number__of__Bit1,axiom,
% 190.77/191.63 ! [V_v,V_w] :
% 190.77/191.63 ( ( 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)))
% 190.77/191.63 => 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)) )
% 190.77/191.63 & ( ~ 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)))
% 190.77/191.63 => 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)) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_neg__zmod__mult__2,axiom,
% 190.77/191.63 ! [V_b,V_a] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 190.77/191.63 => 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)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_pos__zdiv__mult__2,axiom,
% 190.77/191.63 ! [V_b,V_a] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 190.77/191.63 => 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) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_neg__zdiv__mult__2,axiom,
% 190.77/191.63 ! [V_b,V_a] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 190.77/191.63 => 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) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_pos__zmod__mult__2,axiom,
% 190.77/191.63 ! [V_b,V_a] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 190.77/191.63 => 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))) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_of__nat__double,axiom,
% 190.77/191.63 ! [V_x,T_a] :
% 190.77/191.63 ( class_Rings_Osemiring__1(T_a)
% 190.77/191.63 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 190.77/191.63 => 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))) ) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I48_J,axiom,
% 190.77/191.63 ! [V_l_2,V_k_2] :
% 190.77/191.63 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
% 190.77/191.63 <=> V_k_2 = V_l_2 ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_less__eq__int__code_I13_J,axiom,
% 190.77/191.63 ! [V_k2_2,V_k1_2] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I31_J,axiom,
% 190.77/191.63 ! [V_l_2,V_k_2] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_less__int__code_I13_J,axiom,
% 190.77/191.63 ! [V_k2_2,V_k1_2] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I14_J,axiom,
% 190.77/191.63 ! [V_l_2,V_k_2] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I44_J,axiom,
% 190.77/191.63 ! [V_k_2] :
% 190.77/191.63 ( c_Int_OBit0(V_k_2) = c_Int_OPls
% 190.77/191.63 <=> V_k_2 = c_Int_OPls ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I38_J,axiom,
% 190.77/191.63 ! [V_l_2] :
% 190.77/191.63 ( c_Int_OPls = c_Int_OBit0(V_l_2)
% 190.77/191.63 <=> c_Int_OPls = V_l_2 ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_Bit0__Pls,axiom,
% 190.77/191.63 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I50_J,axiom,
% 190.77/191.63 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I49_J,axiom,
% 190.77/191.63 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_Bit0__def,axiom,
% 190.77/191.63 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_add__Bit0__Bit0,axiom,
% 190.77/191.63 ! [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)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_mult__Bit0,axiom,
% 190.77/191.63 ! [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)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_diff__bin__simps_I7_J,axiom,
% 190.77/191.63 ! [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)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_minus__Bit0,axiom,
% 190.77/191.63 ! [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)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I45_J,axiom,
% 190.77/191.63 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I42_J,axiom,
% 190.77/191.63 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_bin__less__0__simps_I3_J,axiom,
% 190.77/191.63 ! [V_w_2] :
% 190.77/191.63 ( 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)))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I27_J,axiom,
% 190.77/191.63 ! [V_k_2] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I21_J,axiom,
% 190.77/191.63 ! [V_k_2] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_less__eq__int__code_I14_J,axiom,
% 190.77/191.63 ! [V_k2_2,V_k1_2] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I32_J,axiom,
% 190.77/191.63 ! [V_l_2,V_k_2] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I10_J,axiom,
% 190.77/191.63 ! [V_k_2] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I4_J,axiom,
% 190.77/191.63 ! [V_k_2] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_less__int__code_I15_J,axiom,
% 190.77/191.63 ! [V_k2_2,V_k1_2] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_rel__simps_I16_J,axiom,
% 190.77/191.63 ! [V_l_2,V_k_2] :
% 190.77/191.63 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 190.77/191.63 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_add__Bit1__Bit0,axiom,
% 190.77/191.63 ! [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)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_add__Bit0__Bit1,axiom,
% 190.77/191.63 ! [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)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_diff__bin__simps_I3_J,axiom,
% 190.77/191.63 ! [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)) ).
% 190.77/191.63
% 190.77/191.63 fof(fact_diff__bin__simps_I10_J,axiom,
% 190.77/191.63 ! [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)) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_diff__bin__simps_I9_J,axiom,
% 190.77/191.64 ! [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)) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_rel__simps_I28_J,axiom,
% 190.77/191.64 ! [V_k_2] :
% 190.77/191.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 190.77/191.64 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_rel__simps_I8_J,axiom,
% 190.77/191.64 ! [V_k_2] :
% 190.77/191.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 190.77/191.64 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_zdiv__number__of__Bit0,axiom,
% 190.77/191.64 ! [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)) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_neg__number__of__Bit0,axiom,
% 190.77/191.64 ! [V_w_2] :
% 190.77/191.64 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2))))
% 190.77/191.64 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_pred__Bit1,axiom,
% 190.77/191.64 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_pred__Bit0,axiom,
% 190.77/191.64 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_pred__Min,axiom,
% 190.77/191.64 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_iszero__number__of__Bit0,axiom,
% 190.77/191.64 ! [V_w_2,T_b] :
% 190.77/191.64 ( ( class_Int_Onumber__ring(T_b)
% 190.77/191.64 & class_Int_Oring__char__0(T_b) )
% 190.77/191.64 => ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2)))
% 190.77/191.64 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_succ__Bit0,axiom,
% 190.77/191.64 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_succ__Bit1,axiom,
% 190.77/191.64 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_number__of__Bit0,axiom,
% 190.77/191.64 ! [V_w,T_a] :
% 190.77/191.64 ( class_Int_Onumber__ring(T_a)
% 190.77/191.64 => 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)) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_rel__simps_I15_J,axiom,
% 190.77/191.64 ! [V_l_2,V_k_2] :
% 190.77/191.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 190.77/191.64 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_less__int__code_I14_J,axiom,
% 190.77/191.64 ! [V_k2_2,V_k1_2] :
% 190.77/191.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 190.77/191.64 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_rel__simps_I33_J,axiom,
% 190.77/191.64 ! [V_l_2,V_k_2] :
% 190.77/191.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 190.77/191.64 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_less__eq__int__code_I15_J,axiom,
% 190.77/191.64 ! [V_k2_2,V_k1_2] :
% 190.77/191.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 190.77/191.64 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_mult__Bit1,axiom,
% 190.77/191.64 ! [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) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_rel__simps_I25_J,axiom,
% 190.77/191.64 ! [V_k_2] :
% 190.77/191.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 190.77/191.64 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_rel__simps_I11_J,axiom,
% 190.77/191.64 ! [V_k_2] :
% 190.77/191.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 190.77/191.64 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_diff__bin__simps_I6_J,axiom,
% 190.77/191.64 ! [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)) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_diff__bin__simps_I5_J,axiom,
% 190.77/191.64 ! [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)) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_diff__bin__simps_I8_J,axiom,
% 190.77/191.64 ! [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)) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_add__Bit1__Bit1,axiom,
% 190.77/191.64 ! [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))) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_double__number__of__Bit0,axiom,
% 190.77/191.64 ! [V_w,T_a] :
% 190.77/191.64 ( class_Int_Onumber__ring(T_a)
% 190.77/191.64 => 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)) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_number__of1,axiom,
% 190.77/191.64 ! [V_n] :
% 190.77/191.64 ( 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)))
% 190.77/191.64 => ( 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))))
% 190.77/191.64 & 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)))) ) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_mult__2,axiom,
% 190.77/191.64 ! [V_z,T_a] :
% 190.77/191.64 ( class_Int_Onumber__ring(T_a)
% 190.77/191.64 => 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) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_mult__2__right,axiom,
% 190.77/191.64 ! [V_z,T_a] :
% 190.77/191.64 ( class_Int_Onumber__ring(T_a)
% 190.77/191.64 => 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) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_one__add__one__is__two,axiom,
% 190.77/191.64 ! [T_a] :
% 190.77/191.64 ( class_Int_Onumber__ring(T_a)
% 190.77/191.64 => 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))) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_zero__power2,axiom,
% 190.77/191.64 ! [T_a] :
% 190.77/191.64 ( class_Rings_Osemiring__1(T_a)
% 190.77/191.64 => 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) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_zero__eq__power2,axiom,
% 190.77/191.64 ! [V_a_2,T_b] :
% 190.77/191.64 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 190.77/191.64 => ( 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)
% 190.77/191.64 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_numeral__2__eq__2,axiom,
% 190.77/191.64 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))) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_semiring__norm_I115_J,axiom,
% 190.77/191.64 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))) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_power2__eq__square,axiom,
% 190.77/191.64 ! [V_a,T_a] :
% 190.77/191.64 ( class_Groups_Omonoid__mult(T_a)
% 190.77/191.64 => 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) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 190.77/191.64 ! [V_x,T_a] :
% 190.77/191.64 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.64 => 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)))) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
% 190.77/191.64 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))))) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_add__2__eq__Suc,axiom,
% 190.77/191.64 ! [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)) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_add__2__eq__Suc_H,axiom,
% 190.77/191.64 ! [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)) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_one__power2,axiom,
% 190.77/191.64 ! [T_a] :
% 190.77/191.64 ( class_Rings_Osemiring__1(T_a)
% 190.77/191.64 => 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) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_power2__minus,axiom,
% 190.77/191.64 ! [V_a,T_a] :
% 190.77/191.64 ( class_Rings_Oring__1(T_a)
% 190.77/191.64 => 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)))) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_nat__mult__2__right,axiom,
% 190.77/191.64 ! [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) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_nat__mult__2,axiom,
% 190.77/191.64 ! [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) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_power__even__eq,axiom,
% 190.77/191.64 ! [V_n,V_a,T_a] :
% 190.77/191.64 ( class_Groups_Omonoid__mult(T_a)
% 190.77/191.64 => 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)))) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_transfer__int__nat__numerals_I3_J,axiom,
% 190.77/191.64 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)))) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_transfer__nat__int__numerals_I3_J,axiom,
% 190.77/191.64 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)))) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_power2__abs,axiom,
% 190.77/191.64 ! [V_a,T_a] :
% 190.77/191.64 ( class_Rings_Olinordered__idom(T_a)
% 190.77/191.64 => 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)))) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_abs__power2,axiom,
% 190.77/191.64 ! [V_a,T_a] :
% 190.77/191.64 ( class_Rings_Olinordered__idom(T_a)
% 190.77/191.64 => 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)))) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_nat__1__add__1,axiom,
% 190.77/191.64 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))) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_mod2__Suc__Suc,axiom,
% 190.77/191.64 ! [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)))) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_div2__Suc__Suc,axiom,
% 190.77/191.64 ! [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))))) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_zmod__number__of__Bit0,axiom,
% 190.77/191.64 ! [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))) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_add__self__div__2,axiom,
% 190.77/191.64 ! [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 ).
% 190.77/191.64
% 190.77/191.64 fof(fact_zero__le__power2,axiom,
% 190.77/191.64 ! [V_a,T_a] :
% 190.77/191.64 ( class_Rings_Olinordered__idom(T_a)
% 190.77/191.64 => 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)))))) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_power2__le__imp__le,axiom,
% 190.77/191.64 ! [V_y,V_x,T_a] :
% 190.77/191.64 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.64 => ( 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))))))
% 190.77/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 190.77/191.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_power2__eq__imp__eq,axiom,
% 190.77/191.64 ! [V_y,V_x,T_a] :
% 190.77/191.64 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.64 => ( 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))))
% 190.77/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 190.77/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 190.77/191.64 => V_x = V_y ) ) ) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_zero__less__power2,axiom,
% 190.77/191.64 ! [V_a_2,T_b] :
% 190.77/191.64 ( class_Rings_Olinordered__idom(T_b)
% 190.77/191.64 => ( 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))))))
% 190.77/191.64 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_power2__less__0,axiom,
% 190.77/191.64 ! [V_a,T_a] :
% 190.77/191.64 ( class_Rings_Olinordered__idom(T_a)
% 190.77/191.64 => ~ 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))) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_sum__power2__eq__zero__iff,axiom,
% 190.77/191.64 ! [V_y_2,V_x_2,T_b] :
% 190.77/191.64 ( class_Rings_Olinordered__idom(T_b)
% 190.77/191.64 => ( 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)
% 190.77/191.64 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 190.77/191.64 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_power2__eq__square__number__of,axiom,
% 190.77/191.64 ! [V_w,T_b] :
% 190.77/191.64 ( ( class_Groups_Omonoid__mult(T_b)
% 190.77/191.64 & class_Int_Onumber(T_b) )
% 190.77/191.64 => 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)) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_less__2__cases,axiom,
% 190.77/191.64 ! [V_n] :
% 190.77/191.64 ( 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)))))
% 190.77/191.64 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 190.77/191.64 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_nat__2,axiom,
% 190.77/191.64 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))) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_power2__eq__1__iff,axiom,
% 190.77/191.64 ! [V_a_2,T_b] :
% 190.77/191.64 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 190.77/191.64 => ( 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)
% 190.77/191.64 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_b)
% 190.77/191.64 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 190.77/191.64 ! [V_n,V_x,T_a] :
% 190.77/191.64 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.64 => 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)) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_power__minus__even,axiom,
% 190.77/191.64 ! [V_n,V_a,T_a] :
% 190.77/191.64 ( class_Rings_Oring__1(T_a)
% 190.77/191.64 => 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)) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_power2__less__imp__less,axiom,
% 190.77/191.64 ! [V_y,V_x,T_a] :
% 190.77/191.64 ( class_Rings_Olinordered__semidom(T_a)
% 190.77/191.64 => ( 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))))))
% 190.77/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 190.77/191.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_sum__power2__le__zero__iff,axiom,
% 190.77/191.64 ! [V_y_2,V_x_2,T_b] :
% 190.77/191.64 ( class_Rings_Olinordered__idom(T_b)
% 190.77/191.64 => ( 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)))
% 190.77/191.64 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 190.77/191.64 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_sum__power2__ge__zero,axiom,
% 190.77/191.64 ! [V_y,V_x,T_a] :
% 190.77/191.64 ( class_Rings_Olinordered__idom(T_a)
% 190.77/191.64 => 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))))))) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_not__sum__power2__lt__zero,axiom,
% 190.77/191.64 ! [V_y,V_x,T_a] :
% 190.77/191.64 ( class_Rings_Olinordered__idom(T_a)
% 190.77/191.64 => ~ 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))) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_sum__power2__gt__zero__iff,axiom,
% 190.77/191.64 ! [V_y_2,V_x_2,T_b] :
% 190.77/191.64 ( class_Rings_Olinordered__idom(T_b)
% 190.77/191.64 => ( 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)))))))
% 190.77/191.64 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 190.77/191.64 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_power2__sum,axiom,
% 190.77/191.64 ! [V_y,V_x,T_a] :
% 190.77/191.64 ( class_Int_Onumber__ring(T_a)
% 190.77/191.64 => 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)) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_zero__le__even__power_H,axiom,
% 190.77/191.64 ! [V_n,V_a,T_a] :
% 190.77/191.64 ( class_Rings_Olinordered__idom(T_a)
% 190.77/191.64 => 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)))) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_power__odd__eq,axiom,
% 190.77/191.64 ! [V_n,V_a,T_a] :
% 190.77/191.64 ( class_Groups_Omonoid__mult(T_a)
% 190.77/191.64 => 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))))) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
% 190.77/191.64 ! [V_n,V_x,T_a] :
% 190.77/191.64 ( class_Rings_Ocomm__semiring__1(T_a)
% 190.77/191.64 => 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))) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_power__minus1__even,axiom,
% 190.77/191.64 ! [V_n,T_a] :
% 190.77/191.64 ( class_Rings_Oring__1(T_a)
% 190.77/191.64 => 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) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_zdiv__number__of__Bit1,axiom,
% 190.77/191.64 ! [V_v,V_w] :
% 190.77/191.64 ( ( 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)))
% 190.77/191.64 => 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)) )
% 190.77/191.64 & ( ~ 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)))
% 190.77/191.64 => 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)) ) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_mod2__gr__0,axiom,
% 190.77/191.64 ! [V_m_2] :
% 190.77/191.64 ( 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))))))
% 190.77/191.64 <=> 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) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_div__2__gt__zero,axiom,
% 190.77/191.64 ! [V_n] :
% 190.77/191.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 190.77/191.64 => 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)))))) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_power2__diff,axiom,
% 190.77/191.64 ! [V_y,V_x,T_a] :
% 190.77/191.64 ( class_Int_Onumber__ring(T_a)
% 190.77/191.64 => 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)) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_odd__0__le__power__imp__0__le,axiom,
% 190.77/191.64 ! [V_n,V_a,T_a] :
% 190.77/191.64 ( class_Rings_Olinordered__idom(T_a)
% 190.77/191.64 => ( 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)))))
% 190.77/191.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_odd__power__less__zero,axiom,
% 190.77/191.64 ! [V_n,V_a,T_a] :
% 190.77/191.64 ( class_Rings_Olinordered__idom(T_a)
% 190.77/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 190.77/191.64 => 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))) ) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_power__minus1__odd,axiom,
% 190.77/191.64 ! [V_n,T_a] :
% 190.77/191.64 ( class_Rings_Oring__1(T_a)
% 190.77/191.64 => 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)) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_power__m1__even,axiom,
% 190.77/191.64 ! [V_n,T_a] :
% 190.77/191.64 ( class_Int_Onumber__ring(T_a)
% 190.77/191.64 => 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) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_power__m1__odd,axiom,
% 190.77/191.64 ! [V_n,T_a] :
% 190.77/191.64 ( class_Int_Onumber__ring(T_a)
% 190.77/191.64 => 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) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_Suc__n__div__2__gt__zero,axiom,
% 190.77/191.64 ! [V_n] :
% 190.77/191.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 190.77/191.64 => 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)))))) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_int__of__code,axiom,
% 190.77/191.64 ! [V_k] :
% 190.77/191.64 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 190.77/191.64 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 190.77/191.64 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 190.77/191.64 => ( ( 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)
% 190.77/191.64 => 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)))))) )
% 190.77/191.64 & ( 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)
% 190.77/191.64 => 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)) ) ) ) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_one__code__numeral__code,axiom,
% 190.77/191.64 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)) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_half__gt__zero,axiom,
% 190.77/191.64 ! [V_r,T_a] :
% 190.77/191.64 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 190.77/191.64 & class_Int_Onumber__ring(T_a) )
% 190.77/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r))
% 190.77/191.64 => 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)))))) ) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_half__gt__zero__iff,axiom,
% 190.77/191.64 ! [V_r_2,T_b] :
% 190.77/191.64 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 190.77/191.64 & class_Int_Onumber__ring(T_b) )
% 190.77/191.64 => ( 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))))))
% 190.77/191.64 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2)) ) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom,
% 190.77/191.64 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_nat__intermed__int__val,axiom,
% 190.77/191.64 ! [V_k_2,V_f_2,V_n_2,V_m_2] :
% 190.77/191.64 ( ! [B_i] :
% 190.77/191.64 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 190.77/191.64 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) )
% 190.77/191.64 => 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))) )
% 190.77/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 190.77/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2))
% 190.77/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 190.77/191.64 => ? [B_i] :
% 190.77/191.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 190.77/191.64 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 190.77/191.64 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_code__numeral__zero__minus__one,axiom,
% 190.77/191.64 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) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_divide__zero,axiom,
% 190.77/191.64 ! [V_a,T_a] :
% 190.77/191.64 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 190.77/191.64 => 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) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_divide__zero__left,axiom,
% 190.77/191.64 ! [V_a,T_a] :
% 190.77/191.64 ( class_Rings_Odivision__ring(T_a)
% 190.77/191.64 => 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) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_add__divide__distrib,axiom,
% 190.77/191.64 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.64 ( class_Rings_Odivision__ring(T_a)
% 190.77/191.64 => 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)) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_times__divide__times__eq,axiom,
% 190.77/191.64 ! [V_w,V_z,V_y,V_x,T_a] :
% 190.77/191.64 ( class_Fields_Ofield__inverse__zero(T_a)
% 190.77/191.64 => 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)) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_times__divide__eq__right,axiom,
% 190.77/191.64 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.64 ( class_Rings_Odivision__ring(T_a)
% 190.77/191.64 => 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) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_diff__divide__distrib,axiom,
% 190.77/191.64 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.64 ( class_Rings_Odivision__ring(T_a)
% 190.77/191.64 => 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)) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_divide__1,axiom,
% 190.77/191.64 ! [V_a,T_a] :
% 190.77/191.64 ( class_Rings_Odivision__ring(T_a)
% 190.77/191.64 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_minus__divide__divide,axiom,
% 190.77/191.64 ! [V_b,V_a,T_a] :
% 190.77/191.64 ( class_Fields_Ofield__inverse__zero(T_a)
% 190.77/191.64 => 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) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_minus__divide__right,axiom,
% 190.77/191.64 ! [V_b,V_a,T_a] :
% 190.77/191.64 ( class_Fields_Ofield__inverse__zero(T_a)
% 190.77/191.64 => 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)) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_minus__divide__left,axiom,
% 190.77/191.64 ! [V_b,V_a,T_a] :
% 190.77/191.64 ( class_Rings_Odivision__ring(T_a)
% 190.77/191.64 => 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) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_power__divide,axiom,
% 190.77/191.64 ! [V_n,V_b,V_a,T_a] :
% 190.77/191.64 ( class_Fields_Ofield__inverse__zero(T_a)
% 190.77/191.64 => 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)) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_abs__divide,axiom,
% 190.77/191.64 ! [V_b,V_a,T_a] :
% 190.77/191.64 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 190.77/191.64 => 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)) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom,
% 190.77/191.64 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom,
% 190.77/191.64 ! [V_y,V_x] :
% 190.77/191.64 ( c_Nat__Transfer_Ois__nat(V_x)
% 190.77/191.64 => ( c_Nat__Transfer_Ois__nat(V_y)
% 190.77/191.64 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom,
% 190.77/191.64 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom,
% 190.77/191.64 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom,
% 190.77/191.64 ! [V_y,V_x] :
% 190.77/191.64 ( c_Nat__Transfer_Ois__nat(V_x)
% 190.77/191.64 => ( c_Nat__Transfer_Ois__nat(V_y)
% 190.77/191.64 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom,
% 190.77/191.64 ! [V_y,V_x] :
% 190.77/191.64 ( c_Nat__Transfer_Ois__nat(V_x)
% 190.77/191.64 => ( c_Nat__Transfer_Ois__nat(V_y)
% 190.77/191.64 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom,
% 190.77/191.64 ! [V_y,V_x] :
% 190.77/191.64 ( c_Nat__Transfer_Ois__nat(V_x)
% 190.77/191.64 => ( c_Nat__Transfer_Ois__nat(V_y)
% 190.77/191.64 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom,
% 190.77/191.64 ! [V_n,V_x] :
% 190.77/191.64 ( c_Nat__Transfer_Ois__nat(V_x)
% 190.77/191.64 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_zero__le__divide__iff,axiom,
% 190.77/191.64 ! [V_ba_2,V_a_2,T_b] :
% 190.77/191.64 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 190.77/191.64 => ( 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_ba_2)))
% 190.77/191.64 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 190.77/191.64 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ba_2)) )
% 190.77/191.64 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 190.77/191.64 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_divide__le__0__iff,axiom,
% 190.77/191.64 ! [V_ba_2,V_a_2,T_b] :
% 190.77/191.64 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 190.77/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_ba_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 190.77/191.64 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 190.77/191.64 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 190.77/191.64 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 190.77/191.64 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ba_2)) ) ) ) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_divide__right__mono,axiom,
% 190.77/191.64 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.64 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 190.77/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 190.77/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 190.77/191.64 => 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))) ) ) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_divide__right__mono__neg,axiom,
% 190.77/191.64 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.64 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 190.77/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 190.77/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 190.77/191.64 => 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))) ) ) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_divide__strict__right__mono__neg,axiom,
% 190.77/191.64 ! [V_c,V_a,V_b,T_a] :
% 190.77/191.64 ( class_Fields_Olinordered__field(T_a)
% 190.77/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 190.77/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 190.77/191.64 => 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))) ) ) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_divide__strict__right__mono,axiom,
% 190.77/191.64 ! [V_c,V_b,V_a,T_a] :
% 190.77/191.64 ( class_Fields_Olinordered__field(T_a)
% 190.77/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 190.77/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 190.77/191.64 => 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))) ) ) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_divide__neg__neg,axiom,
% 190.77/191.64 ! [V_y,V_x,T_a] :
% 190.77/191.64 ( class_Fields_Olinordered__field(T_a)
% 190.77/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 190.77/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 190.77/191.64 => 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))) ) ) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_divide__neg__pos,axiom,
% 190.77/191.64 ! [V_y,V_x,T_a] :
% 190.77/191.64 ( class_Fields_Olinordered__field(T_a)
% 190.77/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 190.77/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 190.77/191.64 => 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))) ) ) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_divide__pos__neg,axiom,
% 190.77/191.64 ! [V_y,V_x,T_a] :
% 190.77/191.64 ( class_Fields_Olinordered__field(T_a)
% 190.77/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 190.77/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 190.77/191.64 => 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))) ) ) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_divide__pos__pos,axiom,
% 190.77/191.64 ! [V_y,V_x,T_a] :
% 190.77/191.64 ( class_Fields_Olinordered__field(T_a)
% 190.77/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 190.77/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 190.77/191.64 => 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))) ) ) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_divide__less__0__iff,axiom,
% 190.77/191.64 ! [V_ba_2,V_a_2,T_b] :
% 190.77/191.64 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 190.77/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_ba_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 190.77/191.64 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 190.77/191.64 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 190.77/191.64 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 190.77/191.64 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ba_2)) ) ) ) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_zero__less__divide__iff,axiom,
% 190.77/191.64 ! [V_ba_2,V_a_2,T_b] :
% 190.77/191.64 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 190.77/191.64 => ( 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_ba_2)))
% 190.77/191.64 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 190.77/191.64 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ba_2)) )
% 190.77/191.64 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 190.77/191.64 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 190.77/191.64
% 190.77/191.64 fof(fact_eq__divide__eq,axiom,
% 190.77/191.64 ! [V_ca_2,V_ba_2,V_a_2,T_b] :
% 191.04/191.64 ( class_Fields_Ofield__inverse__zero(T_b)
% 191.04/191.64 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2)
% 191.04/191.64 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 191.04/191.64 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) = V_ba_2 )
% 191.04/191.64 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
% 191.04/191.64 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divide__eq__eq,axiom,
% 191.04/191.64 ! [V_a_2,V_ca_2,V_ba_2,T_b] :
% 191.04/191.64 ( class_Fields_Ofield__inverse__zero(T_b)
% 191.04/191.64 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2) = V_a_2
% 191.04/191.64 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 191.04/191.64 => V_ba_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) )
% 191.04/191.64 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
% 191.04/191.64 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_mult__divide__mult__cancel__right,axiom,
% 191.04/191.64 ! [V_b,V_a,V_c,T_a] :
% 191.04/191.64 ( class_Fields_Ofield__inverse__zero(T_a)
% 191.04/191.64 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 191.04/191.64 => 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) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_mult__divide__mult__cancel__left,axiom,
% 191.04/191.64 ! [V_b,V_a,V_c,T_a] :
% 191.04/191.64 ( class_Fields_Ofield__inverse__zero(T_a)
% 191.04/191.64 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 191.04/191.64 => 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) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_frac__eq__eq,axiom,
% 191.04/191.64 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] :
% 191.04/191.64 ( class_Fields_Ofield(T_b)
% 191.04/191.64 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
% 191.04/191.64 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_b)
% 191.04/191.64 => ( 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)
% 191.04/191.64 <=> 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) ) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_eq__divide__imp,axiom,
% 191.04/191.64 ! [V_b,V_a,V_c,T_a] :
% 191.04/191.64 ( class_Rings_Odivision__ring(T_a)
% 191.04/191.64 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 191.04/191.64 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b
% 191.04/191.64 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divide__eq__imp,axiom,
% 191.04/191.64 ! [V_a,V_b,V_c,T_a] :
% 191.04/191.64 ( class_Rings_Odivision__ring(T_a)
% 191.04/191.64 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 191.04/191.64 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
% 191.04/191.64 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_nonzero__divide__eq__eq,axiom,
% 191.04/191.64 ! [V_a_2,V_ba_2,V_ca_2,T_b] :
% 191.04/191.64 ( class_Rings_Odivision__ring(T_b)
% 191.04/191.64 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 191.04/191.64 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2) = V_a_2
% 191.04/191.64 <=> V_ba_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_nonzero__eq__divide__eq,axiom,
% 191.04/191.64 ! [V_ba_2,V_a_2,V_ca_2,T_b] :
% 191.04/191.64 ( class_Rings_Odivision__ring(T_b)
% 191.04/191.64 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 191.04/191.64 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2)
% 191.04/191.64 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) = V_ba_2 ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_right__inverse__eq,axiom,
% 191.04/191.64 ! [V_a_2,V_ba_2,T_b] :
% 191.04/191.64 ( class_Rings_Odivision__ring(T_b)
% 191.04/191.64 => ( V_ba_2 != c_Groups_Ozero__class_Ozero(T_b)
% 191.04/191.64 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_ba_2) = c_Groups_Oone__class_Oone(T_b)
% 191.04/191.64 <=> V_a_2 = V_ba_2 ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divide__self,axiom,
% 191.04/191.64 ! [V_a,T_a] :
% 191.04/191.64 ( class_Rings_Odivision__ring(T_a)
% 191.04/191.64 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 191.04/191.64 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divide__self__if,axiom,
% 191.04/191.64 ! [V_a,T_a] :
% 191.04/191.64 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 191.04/191.64 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 191.04/191.64 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) )
% 191.04/191.64 & ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 191.04/191.64 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_nonzero__minus__divide__divide,axiom,
% 191.04/191.64 ! [V_a,V_b,T_a] :
% 191.04/191.64 ( class_Rings_Odivision__ring(T_a)
% 191.04/191.64 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 191.04/191.64 => 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) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_nonzero__minus__divide__right,axiom,
% 191.04/191.64 ! [V_a,V_b,T_a] :
% 191.04/191.64 ( class_Rings_Odivision__ring(T_a)
% 191.04/191.64 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 191.04/191.64 => 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)) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_nonzero__power__divide,axiom,
% 191.04/191.64 ! [V_n,V_a,V_b,T_a] :
% 191.04/191.64 ( class_Fields_Ofield(T_a)
% 191.04/191.64 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 191.04/191.64 => 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)) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_nonzero__abs__divide,axiom,
% 191.04/191.64 ! [V_a,V_b,T_a] :
% 191.04/191.64 ( class_Fields_Olinordered__field(T_a)
% 191.04/191.64 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 191.04/191.64 => 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)) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_power__one__over,axiom,
% 191.04/191.64 ! [V_n,V_a,T_a] :
% 191.04/191.64 ( class_Fields_Ofield__inverse__zero(T_a)
% 191.04/191.64 => 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) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom,
% 191.04/191.64 ! [V_y,V_x] :
% 191.04/191.64 ( c_Nat__Transfer_Ois__nat(V_x)
% 191.04/191.64 => ( c_Nat__Transfer_Ois__nat(V_y)
% 191.04/191.64 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divide__nonpos__neg,axiom,
% 191.04/191.64 ! [V_y,V_x,T_a] :
% 191.04/191.64 ( class_Fields_Olinordered__field(T_a)
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 191.04/191.64 => 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))) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divide__nonpos__pos,axiom,
% 191.04/191.64 ! [V_y,V_x,T_a] :
% 191.04/191.64 ( class_Fields_Olinordered__field(T_a)
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 191.04/191.64 => 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))) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_frac__le,axiom,
% 191.04/191.64 ! [V_z,V_w,V_y,V_x,T_a] :
% 191.04/191.64 ( class_Fields_Olinordered__field(T_a)
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 191.04/191.64 => 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))) ) ) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_frac__less,axiom,
% 191.04/191.64 ! [V_z,V_w,V_y,V_x,T_a] :
% 191.04/191.64 ( class_Fields_Olinordered__field(T_a)
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 191.04/191.64 => 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))) ) ) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_frac__less2,axiom,
% 191.04/191.64 ! [V_z,V_w,V_y,V_x,T_a] :
% 191.04/191.64 ( class_Fields_Olinordered__field(T_a)
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z))
% 191.04/191.64 => 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))) ) ) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divide__nonneg__neg,axiom,
% 191.04/191.64 ! [V_y,V_x,T_a] :
% 191.04/191.64 ( class_Fields_Olinordered__field(T_a)
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 191.04/191.64 => 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))) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divide__nonneg__pos,axiom,
% 191.04/191.64 ! [V_y,V_x,T_a] :
% 191.04/191.64 ( class_Fields_Olinordered__field(T_a)
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 191.04/191.64 => 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))) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divide__strict__left__mono__neg,axiom,
% 191.04/191.64 ! [V_c,V_b,V_a,T_a] :
% 191.04/191.64 ( class_Fields_Olinordered__field(T_a)
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 191.04/191.64 => ( 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)))
% 191.04/191.64 => 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))) ) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divide__strict__left__mono,axiom,
% 191.04/191.64 ! [V_c,V_a,V_b,T_a] :
% 191.04/191.64 ( class_Fields_Olinordered__field(T_a)
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 191.04/191.64 => ( 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)))
% 191.04/191.64 => 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))) ) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_neg__divide__less__eq,axiom,
% 191.04/191.64 ! [V_a_2,V_ba_2,V_ca_2,T_b] :
% 191.04/191.64 ( class_Fields_Olinordered__field(T_b)
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2)),V_a_2))
% 191.04/191.64 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_ba_2)) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_neg__less__divide__eq,axiom,
% 191.04/191.64 ! [V_ba_2,V_a_2,V_ca_2,T_b] :
% 191.04/191.64 ( class_Fields_Olinordered__field(T_b)
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2)))
% 191.04/191.64 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_mult__imp__less__div__pos,axiom,
% 191.04/191.64 ! [V_x,V_z,V_y,T_a] :
% 191.04/191.64 ( class_Fields_Olinordered__field(T_a)
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 191.04/191.64 => ( 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))
% 191.04/191.64 => 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))) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_mult__imp__div__pos__less,axiom,
% 191.04/191.64 ! [V_z,V_x,V_y,T_a] :
% 191.04/191.64 ( class_Fields_Olinordered__field(T_a)
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 191.04/191.64 => ( 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)))
% 191.04/191.64 => 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)) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_pos__divide__less__eq,axiom,
% 191.04/191.64 ! [V_a_2,V_ba_2,V_ca_2,T_b] :
% 191.04/191.64 ( class_Fields_Olinordered__field(T_b)
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2)),V_a_2))
% 191.04/191.64 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_pos__less__divide__eq,axiom,
% 191.04/191.64 ! [V_ba_2,V_a_2,V_ca_2,T_b] :
% 191.04/191.64 ( class_Fields_Olinordered__field(T_b)
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2)))
% 191.04/191.64 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_ba_2)) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divide__less__eq,axiom,
% 191.04/191.64 ! [V_a_2,V_ca_2,V_ba_2,T_b] :
% 191.04/191.64 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2)),V_a_2))
% 191.04/191.64 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 191.04/191.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) )
% 191.04/191.64 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 191.04/191.64 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 191.04/191.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_ba_2)) )
% 191.04/191.64 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 191.04/191.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_less__divide__eq,axiom,
% 191.04/191.64 ! [V_ca_2,V_ba_2,V_a_2,T_b] :
% 191.04/191.64 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2)))
% 191.04/191.64 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 191.04/191.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_ba_2)) )
% 191.04/191.64 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 191.04/191.64 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 191.04/191.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) )
% 191.04/191.64 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 191.04/191.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_is__nat__def,axiom,
% 191.04/191.64 ! [V_x_2] :
% 191.04/191.64 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 191.04/191.64 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_add__num__frac,axiom,
% 191.04/191.64 ! [V_x,V_z,V_y,T_a] :
% 191.04/191.64 ( class_Fields_Ofield__inverse__zero(T_a)
% 191.04/191.64 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 191.04/191.64 => 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) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_add__divide__eq__iff,axiom,
% 191.04/191.64 ! [V_y,V_x,V_z,T_a] :
% 191.04/191.64 ( class_Fields_Ofield(T_a)
% 191.04/191.64 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 191.04/191.64 => 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) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_add__frac__num,axiom,
% 191.04/191.64 ! [V_z,V_x,V_y,T_a] :
% 191.04/191.64 ( class_Fields_Ofield__inverse__zero(T_a)
% 191.04/191.64 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 191.04/191.64 => 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) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divide__add__eq__iff,axiom,
% 191.04/191.64 ! [V_y,V_x,V_z,T_a] :
% 191.04/191.64 ( class_Fields_Ofield(T_a)
% 191.04/191.64 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 191.04/191.64 => 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) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_add__frac__eq,axiom,
% 191.04/191.64 ! [V_w,V_x,V_z,V_y,T_a] :
% 191.04/191.64 ( class_Fields_Ofield(T_a)
% 191.04/191.64 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 191.04/191.64 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 191.04/191.64 => 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)) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_diff__frac__eq,axiom,
% 191.04/191.64 ! [V_w,V_x,V_z,V_y,T_a] :
% 191.04/191.64 ( class_Fields_Ofield(T_a)
% 191.04/191.64 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 191.04/191.64 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 191.04/191.64 => 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)) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divide__diff__eq__iff,axiom,
% 191.04/191.64 ! [V_y,V_x,V_z,T_a] :
% 191.04/191.64 ( class_Fields_Ofield(T_a)
% 191.04/191.64 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 191.04/191.64 => 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) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_diff__divide__eq__iff,axiom,
% 191.04/191.64 ! [V_y,V_x,V_z,T_a] :
% 191.04/191.64 ( class_Fields_Ofield(T_a)
% 191.04/191.64 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 191.04/191.64 => 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) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divide__eq__eq__number__of1,axiom,
% 191.04/191.64 ! [V_a_2,V_w_2,V_ba_2,T_b] :
% 191.04/191.64 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 191.04/191.64 & class_Int_Onumber(T_b) )
% 191.04/191.64 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) = V_a_2
% 191.04/191.64 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 191.04/191.64 => V_ba_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)) )
% 191.04/191.64 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 191.04/191.64 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divide__eq__eq__number__of,axiom,
% 191.04/191.64 ! [V_w_2,V_ca_2,V_ba_2,T_b] :
% 191.04/191.64 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 191.04/191.64 & class_Int_Onumber(T_b) )
% 191.04/191.64 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)
% 191.04/191.64 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 191.04/191.64 => V_ba_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2) )
% 191.04/191.64 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
% 191.04/191.64 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_eq__divide__eq__number__of,axiom,
% 191.04/191.64 ! [V_ca_2,V_ba_2,V_w_2,T_b] :
% 191.04/191.64 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 191.04/191.64 & class_Int_Onumber(T_b) )
% 191.04/191.64 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2)
% 191.04/191.64 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 191.04/191.64 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2) = V_ba_2 )
% 191.04/191.64 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
% 191.04/191.64 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_eq__divide__eq__number__of1,axiom,
% 191.04/191.64 ! [V_w_2,V_ba_2,V_a_2,T_b] :
% 191.04/191.64 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 191.04/191.64 & class_Int_Onumber(T_b) )
% 191.04/191.64 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))
% 191.04/191.64 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 191.04/191.64 => 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_ba_2 )
% 191.04/191.64 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 191.04/191.64 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_gt__half__sum,axiom,
% 191.04/191.64 ! [V_b,V_a,T_a] :
% 191.04/191.64 ( class_Fields_Olinordered__field(T_a)
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 191.04/191.64 => 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)) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_less__half__sum,axiom,
% 191.04/191.64 ! [V_b,V_a,T_a] :
% 191.04/191.64 ( class_Fields_Olinordered__field(T_a)
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 191.04/191.64 => 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))))) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divide__Numeral0,axiom,
% 191.04/191.64 ! [V_x,T_a] :
% 191.04/191.64 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 191.04/191.64 & class_Int_Onumber__ring(T_a) )
% 191.04/191.64 => 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) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_abs__div__pos,axiom,
% 191.04/191.64 ! [V_x,V_y,T_a] :
% 191.04/191.64 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 191.04/191.64 => 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)) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divide__numeral__1,axiom,
% 191.04/191.64 ! [V_a,T_a] :
% 191.04/191.64 ( ( class_Fields_Ofield(T_a)
% 191.04/191.64 & class_Int_Onumber__ring(T_a) )
% 191.04/191.64 => 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 ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divide__Numeral1,axiom,
% 191.04/191.64 ! [V_x,T_a] :
% 191.04/191.64 ( ( class_Fields_Ofield(T_a)
% 191.04/191.64 & class_Int_Onumber__ring(T_a) )
% 191.04/191.64 => 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 ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divide__minus1,axiom,
% 191.04/191.64 ! [V_x,T_a] :
% 191.04/191.64 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 191.04/191.64 & class_Int_Onumber__ring(T_a) )
% 191.04/191.64 => 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) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_zero__code__numeral__code,axiom,
% 191.04/191.64 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) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_le__divide__eq,axiom,
% 191.04/191.64 ! [V_ca_2,V_ba_2,V_a_2,T_b] :
% 191.04/191.64 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2)))
% 191.04/191.64 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 191.04/191.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_ba_2)) )
% 191.04/191.64 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 191.04/191.64 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 191.04/191.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) )
% 191.04/191.64 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 191.04/191.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divide__le__eq,axiom,
% 191.04/191.64 ! [V_a_2,V_ca_2,V_ba_2,T_b] :
% 191.04/191.64 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2)),V_a_2))
% 191.04/191.64 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 191.04/191.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) )
% 191.04/191.64 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 191.04/191.64 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 191.04/191.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_ba_2)) )
% 191.04/191.64 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 191.04/191.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_pos__le__divide__eq,axiom,
% 191.04/191.64 ! [V_ba_2,V_a_2,V_ca_2,T_b] :
% 191.04/191.64 ( class_Fields_Olinordered__field(T_b)
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2)))
% 191.04/191.64 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_ba_2)) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_pos__divide__le__eq,axiom,
% 191.04/191.64 ! [V_a_2,V_ba_2,V_ca_2,T_b] :
% 191.04/191.64 ( class_Fields_Olinordered__field(T_b)
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2)),V_a_2))
% 191.04/191.64 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_mult__imp__div__pos__le,axiom,
% 191.04/191.64 ! [V_z,V_x,V_y,T_a] :
% 191.04/191.64 ( class_Fields_Olinordered__field(T_a)
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 191.04/191.64 => ( 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)))
% 191.04/191.64 => 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)) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_mult__imp__le__div__pos,axiom,
% 191.04/191.64 ! [V_x,V_z,V_y,T_a] :
% 191.04/191.64 ( class_Fields_Olinordered__field(T_a)
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 191.04/191.64 => ( 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))
% 191.04/191.64 => 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))) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_neg__le__divide__eq,axiom,
% 191.04/191.64 ! [V_ba_2,V_a_2,V_ca_2,T_b] :
% 191.04/191.64 ( class_Fields_Olinordered__field(T_b)
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2)))
% 191.04/191.64 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_neg__divide__le__eq,axiom,
% 191.04/191.64 ! [V_a_2,V_ba_2,V_ca_2,T_b] :
% 191.04/191.64 ( class_Fields_Olinordered__field(T_b)
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2)),V_a_2))
% 191.04/191.64 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_ba_2)) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divide__left__mono,axiom,
% 191.04/191.64 ! [V_c,V_a,V_b,T_a] :
% 191.04/191.64 ( class_Fields_Olinordered__field(T_a)
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 191.04/191.64 => ( 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)))
% 191.04/191.64 => 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))) ) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divide__left__mono__neg,axiom,
% 191.04/191.64 ! [V_c,V_b,V_a,T_a] :
% 191.04/191.64 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 191.04/191.64 => ( 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)))
% 191.04/191.64 => 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))) ) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_less__divide__eq__number__of1,axiom,
% 191.04/191.64 ! [V_w_2,V_ba_2,V_a_2,T_b] :
% 191.04/191.64 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 191.04/191.64 & class_Int_Onumber(T_b) )
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
% 191.04/191.64 <=> ( ( 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)))
% 191.04/191.64 => 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_ba_2)) )
% 191.04/191.64 & ( ~ 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)))
% 191.04/191.64 => ( ( 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)))
% 191.04/191.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_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)))) )
% 191.04/191.64 & ( ~ 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)))
% 191.04/191.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_less__divide__eq__number__of,axiom,
% 191.04/191.64 ! [V_ca_2,V_ba_2,V_w_2,T_b] :
% 191.04/191.64 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 191.04/191.64 & class_Int_Onumber(T_b) )
% 191.04/191.64 => ( 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_ba_2),V_ca_2)))
% 191.04/191.64 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 191.04/191.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)),V_ba_2)) )
% 191.04/191.64 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 191.04/191.64 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 191.04/191.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2))) )
% 191.04/191.64 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 191.04/191.64 => 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))) ) ) ) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divide__less__eq__number__of,axiom,
% 191.04/191.64 ! [V_w_2,V_ca_2,V_ba_2,T_b] :
% 191.04/191.64 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 191.04/191.64 & class_Int_Onumber(T_b) )
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 191.04/191.64 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 191.04/191.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2))) )
% 191.04/191.64 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 191.04/191.64 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 191.04/191.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)),V_ba_2)) )
% 191.04/191.64 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 191.04/191.64 => 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))) ) ) ) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divide__less__eq__number__of1,axiom,
% 191.04/191.64 ! [V_a_2,V_w_2,V_ba_2,T_b] :
% 191.04/191.64 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 191.04/191.64 & class_Int_Onumber(T_b) )
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2))
% 191.04/191.64 <=> ( ( 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)))
% 191.04/191.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_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)))) )
% 191.04/191.64 & ( ~ 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)))
% 191.04/191.64 => ( ( 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)))
% 191.04/191.64 => 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_ba_2)) )
% 191.04/191.64 & ( ~ 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)))
% 191.04/191.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_power__diff,axiom,
% 191.04/191.64 ! [V_m,V_n,V_a,T_a] :
% 191.04/191.64 ( class_Fields_Ofield(T_a)
% 191.04/191.64 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 191.04/191.64 => 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)) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_minus1__divide,axiom,
% 191.04/191.64 ! [V_x,T_a] :
% 191.04/191.64 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 191.04/191.64 & class_Int_Onumber__ring(T_a) )
% 191.04/191.64 => 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)) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom,
% 191.04/191.64 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divide__le__eq__number__of1,axiom,
% 191.04/191.64 ! [V_a_2,V_w_2,V_ba_2,T_b] :
% 191.04/191.64 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 191.04/191.64 & class_Int_Onumber(T_b) )
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2))
% 191.04/191.64 <=> ( ( 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)))
% 191.04/191.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_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)))) )
% 191.04/191.64 & ( ~ 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)))
% 191.04/191.64 => ( ( 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)))
% 191.04/191.64 => 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_ba_2)) )
% 191.04/191.64 & ( ~ 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)))
% 191.04/191.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divide__le__eq__number__of,axiom,
% 191.04/191.64 ! [V_w_2,V_ca_2,V_ba_2,T_b] :
% 191.04/191.64 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 191.04/191.64 & class_Int_Onumber(T_b) )
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),V_ca_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 191.04/191.64 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 191.04/191.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2))) )
% 191.04/191.64 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 191.04/191.64 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 191.04/191.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)),V_ba_2)) )
% 191.04/191.64 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 191.04/191.64 => 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))) ) ) ) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_le__divide__eq__number__of,axiom,
% 191.04/191.64 ! [V_ca_2,V_ba_2,V_w_2,T_b] :
% 191.04/191.64 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 191.04/191.64 & class_Int_Onumber(T_b) )
% 191.04/191.64 => ( 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_ba_2),V_ca_2)))
% 191.04/191.64 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 191.04/191.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)),V_ba_2)) )
% 191.04/191.64 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 191.04/191.64 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 191.04/191.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2))) )
% 191.04/191.64 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 191.04/191.64 => 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))) ) ) ) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_le__divide__eq__number__of1,axiom,
% 191.04/191.64 ! [V_w_2,V_ba_2,V_a_2,T_b] :
% 191.04/191.64 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 191.04/191.64 & class_Int_Onumber(T_b) )
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_ba_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
% 191.04/191.64 <=> ( ( 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)))
% 191.04/191.64 => 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_ba_2)) )
% 191.04/191.64 & ( ~ 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)))
% 191.04/191.64 => ( ( 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)))
% 191.04/191.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_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)))) )
% 191.04/191.64 & ( ~ 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)))
% 191.04/191.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_nat__of__aux__code,axiom,
% 191.04/191.64 ! [V_n,V_i] :
% 191.04/191.64 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 191.04/191.64 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n )
% 191.04/191.64 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 191.04/191.64 => 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)) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_code__numeral_Osize_I1_J,axiom,
% 191.04/191.64 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) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_code__numeral_Osize_I3_J,axiom,
% 191.04/191.64 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) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_code__numeral_Osimps_I4_J,axiom,
% 191.04/191.64 ! [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 ).
% 191.04/191.64
% 191.04/191.64 fof(fact_log_Osimps,axiom,
% 191.04/191.64 ! [V_i,V_b] :
% 191.04/191.64 ( ( ( 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)))
% 191.04/191.64 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 191.04/191.64 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 191.04/191.64 & ( ~ ( 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)))
% 191.04/191.64 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 191.04/191.64 => 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))) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_field__le__epsilon,axiom,
% 191.04/191.64 ! [V_y,V_x,T_a] :
% 191.04/191.64 ( class_Fields_Olinordered__field(T_a)
% 191.04/191.64 => ( ! [B_e] :
% 191.04/191.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e))
% 191.04/191.64 => 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))) )
% 191.04/191.64 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_minus__shift__def,axiom,
% 191.04/191.64 ! [V_r,V_l,V_k] :
% 191.04/191.64 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 191.04/191.64 => 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) )
% 191.04/191.64 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 191.04/191.64 => 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) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_inc__shift__def,axiom,
% 191.04/191.64 ! [V_k,V_v] :
% 191.04/191.64 ( ( V_v = V_k
% 191.04/191.64 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 191.04/191.64 & ( V_v != V_k
% 191.04/191.64 => 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)) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_code__numeral_Osize_I4_J,axiom,
% 191.04/191.64 ! [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))) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_code__numeral_Osize_I2_J,axiom,
% 191.04/191.64 ! [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))) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_minus__code__numeral__code,axiom,
% 191.04/191.64 ! [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) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_subtract__code__numeral__def,axiom,
% 191.04/191.64 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_code__numeral_Oinject,axiom,
% 191.04/191.64 ! [V_code__numeral_H_2,V_code__numeral_2] :
% 191.04/191.64 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2)
% 191.04/191.64 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_code__numeral_Osimps_I2_J,axiom,
% 191.04/191.64 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_code__numeral_Osimps_I3_J,axiom,
% 191.04/191.64 ! [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) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_code__numeral_Osimps_I5_J,axiom,
% 191.04/191.64 ! [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) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_Suc__code__numeral__minus__one,axiom,
% 191.04/191.64 ! [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 ).
% 191.04/191.64
% 191.04/191.64 fof(fact_negDivAlg__eqn__1__number__of,axiom,
% 191.04/191.64 ! [V_w] :
% 191.04/191.64 ( 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)))
% 191.04/191.64 => ( ( 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))))
% 191.04/191.64 => 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))) )
% 191.04/191.64 & ( ~ 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))))
% 191.04/191.64 => 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)))) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_diff__nat__number__of,axiom,
% 191.04/191.64 ! [V_v_2,V_v_H_2] :
% 191.04/191.64 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 191.04/191.64 => 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) )
% 191.04/191.64 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 191.04/191.64 => 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)) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_code__numeral_Orecs_I2_J,axiom,
% 191.04/191.64 ! [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)) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divmod__nat__step,axiom,
% 191.04/191.64 ! [V_m,V_n] :
% 191.04/191.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 191.04/191.64 => 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)) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_code__numeral__not__eq__zero,axiom,
% 191.04/191.64 ! [V_i_2] :
% 191.04/191.64 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 191.04/191.64 <=> 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)) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_beyond__def,axiom,
% 191.04/191.64 ! [V_l,V_k] :
% 191.04/191.64 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 191.04/191.64 => c_Quickcheck_Obeyond(V_k,V_l) = V_l )
% 191.04/191.64 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 191.04/191.64 => c_Quickcheck_Obeyond(V_k,V_l) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divmod__nat__zero,axiom,
% 191.04/191.64 ! [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) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_Code__Numeral_Oof__nat__inject,axiom,
% 191.04/191.64 ! [V_m_2,V_n_2] :
% 191.04/191.64 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2)
% 191.04/191.64 <=> V_n_2 = V_m_2 ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_Code__Numeral_Oof__nat__code,axiom,
% 191.04/191.64 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_fun__Compl__def,axiom,
% 191.04/191.64 ! [V_x_2,V_A_2,T_c,T_b] :
% 191.04/191.64 ( class_Groups_Ouminus(T_b)
% 191.04/191.64 => 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)) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_fun__diff__def,axiom,
% 191.04/191.64 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 191.04/191.64 ( class_Groups_Ominus(T_b)
% 191.04/191.64 => 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)) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_less__eq__nat_Osimps_I2_J,axiom,
% 191.04/191.64 ! [V_n_2,V_m_2] :
% 191.04/191.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 191.04/191.64 <=> 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)) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divmod__nat__base,axiom,
% 191.04/191.64 ! [V_n,V_m] :
% 191.04/191.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 191.04/191.64 => 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) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_less__eq__Suc__le__raw,axiom,
% 191.04/191.64 ! [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)) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_diff__Suc,axiom,
% 191.04/191.64 ! [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)) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_nat__number__of__Bit0,axiom,
% 191.04/191.64 ! [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))) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_times__code__numeral__code,axiom,
% 191.04/191.64 ! [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)) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divmod__nat__div__mod,axiom,
% 191.04/191.64 ! [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)) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_power__number__of__even,axiom,
% 191.04/191.64 ! [V_w_2,V_z_2,T_b] :
% 191.04/191.64 ( class_Int_Onumber__ring(T_b)
% 191.04/191.64 => 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))) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_zpower__number__of__even,axiom,
% 191.04/191.64 ! [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))) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_beyond__zero,axiom,
% 191.04/191.64 ! [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) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_power__number__of__even__number__of,axiom,
% 191.04/191.64 ! [V_w_2,V_v_2,T_b] :
% 191.04/191.64 ( class_Int_Onumber__ring(T_b)
% 191.04/191.64 => 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))) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_diff__nat__eq__if,axiom,
% 191.04/191.64 ! [V_z_2,V_z_H_2] :
% 191.04/191.64 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 191.04/191.64 => 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) )
% 191.04/191.64 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 191.04/191.64 => 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)) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_negDivAlg__div__mod,axiom,
% 191.04/191.64 ! [V_l,V_k] :
% 191.04/191.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 191.04/191.64 => 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)) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_negDivAlg__minus1,axiom,
% 191.04/191.64 ! [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))) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_semiring__1__class_Oof__nat__code,axiom,
% 191.04/191.64 ! [V_n_2,T_b] :
% 191.04/191.64 ( class_Rings_Osemiring__1(T_b)
% 191.04/191.64 => 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)) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_adjust__eq,axiom,
% 191.04/191.64 ! [V_r_2,V_q_2,V_ba_2] : hAPP(c_Divides_Oadjust(V_ba_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_ba_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))) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_zero__code__numeral__def,axiom,
% 191.04/191.64 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_one__code__numeral__def,axiom,
% 191.04/191.64 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_less__code__numeral__code,axiom,
% 191.04/191.64 ! [V_m_2,V_n_2] :
% 191.04/191.64 ( 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)))
% 191.04/191.64 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_Suc__eq__number__of,axiom,
% 191.04/191.64 ! [V_v_2,V_n_2] :
% 191.04/191.64 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 191.04/191.64 <=> 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))))) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_eq__number__of__Suc,axiom,
% 191.04/191.64 ! [V_n_2,V_v_2] :
% 191.04/191.64 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2)
% 191.04/191.64 <=> 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))))) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_nat__case__number__of,axiom,
% 191.04/191.64 ! [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))) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_nat__rec__number__of,axiom,
% 191.04/191.64 ! [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)))) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_plus__code__numeral__code,axiom,
% 191.04/191.64 ! [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)) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_less__eq__code__numeral__code,axiom,
% 191.04/191.64 ! [V_m_2,V_n_2] :
% 191.04/191.64 ( 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)))
% 191.04/191.64 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_nat__number__of__Bit1,axiom,
% 191.04/191.64 ! [V_w_2] :
% 191.04/191.64 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 191.04/191.64 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 191.04/191.64 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 191.04/191.64 => 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)))) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_less__Suc__number__of,axiom,
% 191.04/191.64 ! [V_v_2,V_n_2] :
% 191.04/191.64 ( 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)))
% 191.04/191.64 <=> 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))))) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_less__number__of__Suc,axiom,
% 191.04/191.64 ! [V_n_2,V_v_2] :
% 191.04/191.64 ( 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)))
% 191.04/191.64 <=> 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)))) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_le__Suc__number__of,axiom,
% 191.04/191.64 ! [V_v_2,V_n_2] :
% 191.04/191.64 ( 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)))
% 191.04/191.64 <=> 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))))) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_le__number__of__Suc,axiom,
% 191.04/191.64 ! [V_n_2,V_v_2] :
% 191.04/191.64 ( 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)))
% 191.04/191.64 <=> 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)))) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_subtract__code__numeral__code,axiom,
% 191.04/191.64 ! [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)) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_nat__case__add__eq__if,axiom,
% 191.04/191.64 ! [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)))) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_nat__rec__add__eq__if,axiom,
% 191.04/191.64 ! [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))))) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_power__number__of__odd,axiom,
% 191.04/191.64 ! [V_z_2,V_w_2,T_b] :
% 191.04/191.64 ( class_Int_Onumber__ring(T_b)
% 191.04/191.64 => ( ( 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)))
% 191.04/191.64 => 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))) )
% 191.04/191.64 & ( ~ 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)))
% 191.04/191.64 => 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) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_zpower__number__of__odd,axiom,
% 191.04/191.64 ! [V_z_2,V_w_2] :
% 191.04/191.64 ( ( 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)))
% 191.04/191.64 => 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))) )
% 191.04/191.64 & ( ~ 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)))
% 191.04/191.64 => 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) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_negDivAlg_Osimps,axiom,
% 191.04/191.64 ! [V_b,V_a] :
% 191.04/191.64 ( ( ( 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)))
% 191.04/191.64 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 191.04/191.64 => 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)) )
% 191.04/191.64 & ( ~ ( 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)))
% 191.04/191.64 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 191.04/191.64 => 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))) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_power__number__of__odd__number__of,axiom,
% 191.04/191.64 ! [V_v_2,V_w_2,T_b] :
% 191.04/191.64 ( class_Int_Onumber__ring(T_b)
% 191.04/191.64 => ( ( 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)))
% 191.04/191.64 => 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))) )
% 191.04/191.64 & ( ~ 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)))
% 191.04/191.64 => 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) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_code__numeral_Orecs_I1_J,axiom,
% 191.04/191.64 ! [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 ).
% 191.04/191.64
% 191.04/191.64 fof(fact_negDivAlg__eqn,axiom,
% 191.04/191.64 ! [V_a,V_b] :
% 191.04/191.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 191.04/191.64 => ( ( 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)))
% 191.04/191.64 => 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)) )
% 191.04/191.64 & ( ~ 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)))
% 191.04/191.64 => 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))) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_negDivAlg__eqn__number__of,axiom,
% 191.04/191.64 ! [V_w,V_v] :
% 191.04/191.64 ( 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)))
% 191.04/191.64 => ( ( 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))))
% 191.04/191.64 => 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))) )
% 191.04/191.64 & ( ~ 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))))
% 191.04/191.64 => 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)))) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_norm__frac_Osimps,axiom,
% 191.04/191.64 ! [V_a_2,V_ba_2] :
% 191.04/191.64 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 191.04/191.64 => c_Nitpick_Onorm__frac(V_a_2,V_ba_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_ba_2)) )
% 191.04/191.64 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 191.04/191.64 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 191.04/191.64 | V_ba_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 191.04/191.64 => c_Nitpick_Onorm__frac(V_a_2,V_ba_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)) )
% 191.04/191.64 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 191.04/191.64 | V_ba_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 191.04/191.64 => c_Nitpick_Onorm__frac(V_a_2,V_ba_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_ba_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_ba_2))) ) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_posDivAlg__eqn__1__number__of,axiom,
% 191.04/191.64 ! [V_w] :
% 191.04/191.64 ( 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)))
% 191.04/191.64 => ( ( 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)))
% 191.04/191.64 => 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)) )
% 191.04/191.64 & ( ~ 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)))
% 191.04/191.64 => 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)))) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_posDivAlg_Osimps,axiom,
% 191.04/191.64 ! [V_b,V_a] :
% 191.04/191.64 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 191.04/191.64 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 191.04/191.64 => 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) )
% 191.04/191.64 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 191.04/191.64 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 191.04/191.64 => 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))) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_adjust__def,axiom,
% 191.04/191.64 ! [V_ba_2] : c_Divides_Oadjust(V_ba_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_ba_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_ba_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))))))) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_posDivAlg__eqn__number__of,axiom,
% 191.04/191.64 ! [V_w,V_v] :
% 191.04/191.64 ( 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)))
% 191.04/191.64 => ( ( 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)))
% 191.04/191.64 => 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)) )
% 191.04/191.64 & ( ~ 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)))
% 191.04/191.64 => 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)))) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_posDivAlg__eqn,axiom,
% 191.04/191.64 ! [V_a,V_b] :
% 191.04/191.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 191.04/191.64 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 191.04/191.64 => 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) )
% 191.04/191.64 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 191.04/191.64 => 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))) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_posDivAlg__0,axiom,
% 191.04/191.64 ! [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)) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_posDivAlg__div__mod,axiom,
% 191.04/191.64 ! [V_l,V_k] :
% 191.04/191.64 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 191.04/191.64 => 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)) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_of__int__num,axiom,
% 191.04/191.64 ! [V_k_2,T_b] :
% 191.04/191.64 ( class_Rings_Oring__1(T_b)
% 191.04/191.64 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 191.04/191.64 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b) )
% 191.04/191.64 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 191.04/191.64 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 191.04/191.64 => 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))) )
% 191.04/191.64 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 191.04/191.64 => 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))))) ) ) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_MGT__def,axiom,
% 191.04/191.64 ! [V_ca_2] : c_Hoare__Mirabelle_OMGT(V_ca_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),V_ca_2),c_Natural_Oevalc(V_ca_2)) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divmod__nat__rel__mult1__eq,axiom,
% 191.04/191.64 ! [V_a,V_r,V_q,V_c,V_b] :
% 191.04/191.64 ( 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)))
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 191.04/191.64 => 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)))) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divmod__nat__rel__mult2__eq,axiom,
% 191.04/191.64 ! [V_c,V_r,V_q,V_b,V_a] :
% 191.04/191.64 ( 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)))
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b))
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 191.04/191.64 => 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)))) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_negDivAlg_Opsimps,axiom,
% 191.04/191.64 ! [V_ba_2,V_a_2] :
% 191.04/191.64 ( 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_ba_2)))
% 191.04/191.64 => ( ( ( 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_ba_2)))
% 191.04/191.64 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 191.04/191.64 => c_Divides_OnegDivAlg(V_a_2,V_ba_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_ba_2)) )
% 191.04/191.64 & ( ~ ( 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_ba_2)))
% 191.04/191.64 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 191.04/191.64 => c_Divides_OnegDivAlg(V_a_2,V_ba_2) = hAPP(c_Divides_Oadjust(V_ba_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_ba_2))) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_accp__downward,axiom,
% 191.04/191.64 ! [V_a_2,V_ba_2,V_r_2,T_b] :
% 191.04/191.64 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_ba_2))
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_ba_2))
% 191.04/191.64 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_accp_Oequations,axiom,
% 191.04/191.64 ! [V_a_2,V_r_2,T_b] :
% 191.04/191.64 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 191.04/191.64 <=> ! [B_x] :
% 191.04/191.64 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 191.04/191.64 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_accp_Osimps,axiom,
% 191.04/191.64 ! [V_a_2,V_r_2,T_b] :
% 191.04/191.64 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 191.04/191.64 <=> ! [B_x] :
% 191.04/191.64 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 191.04/191.64 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divmod__nat__rel__unique,axiom,
% 191.04/191.64 ! [V_qr_H,V_qr,V_n,V_m] :
% 191.04/191.64 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 191.04/191.64 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H))
% 191.04/191.64 => V_qr = V_qr_H ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_accp__subset,axiom,
% 191.04/191.64 ! [V_R2_2,V_R1_2,T_b] :
% 191.04/191.64 ( 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))
% 191.04/191.64 => 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))) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divmod__nat__eq,axiom,
% 191.04/191.64 ! [V_qr,V_n,V_m] :
% 191.04/191.64 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 191.04/191.64 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divmod__nat__rel__divmod__nat,axiom,
% 191.04/191.64 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_mod__eq,axiom,
% 191.04/191.64 ! [V_r,V_q,V_n,V_m] :
% 191.04/191.64 ( 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)))
% 191.04/191.64 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_div__eq,axiom,
% 191.04/191.64 ! [V_r,V_q,V_n,V_m] :
% 191.04/191.64 ( 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)))
% 191.04/191.64 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divmod__nat__rel,axiom,
% 191.04/191.64 ! [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)))) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divmod__int__mod__div,axiom,
% 191.04/191.64 ! [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)) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divmod__nat__rel__add1__eq,axiom,
% 191.04/191.64 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 191.04/191.64 ( 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)))
% 191.04/191.64 => ( 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)))
% 191.04/191.64 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 191.04/191.64 => 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)))) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_posDivAlg_Opsimps,axiom,
% 191.04/191.64 ! [V_ba_2,V_a_2] :
% 191.04/191.64 ( 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_ba_2)))
% 191.04/191.64 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_ba_2))
% 191.04/191.64 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 191.04/191.64 => c_Divides_OposDivAlg(V_a_2,V_ba_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2) )
% 191.04/191.64 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_ba_2))
% 191.04/191.64 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 191.04/191.64 => c_Divides_OposDivAlg(V_a_2,V_ba_2) = hAPP(c_Divides_Oadjust(V_ba_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_ba_2))) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_norm__frac_Opsimps,axiom,
% 191.04/191.64 ! [V_ba_2,V_a_2] :
% 191.04/191.64 ( 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_ba_2)))
% 191.04/191.64 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 191.04/191.64 => c_Nitpick_Onorm__frac(V_a_2,V_ba_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_ba_2)) )
% 191.04/191.64 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_ba_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 191.04/191.64 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 191.04/191.64 | V_ba_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 191.04/191.64 => c_Nitpick_Onorm__frac(V_a_2,V_ba_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)) )
% 191.04/191.64 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 191.04/191.64 | V_ba_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 191.04/191.64 => c_Nitpick_Onorm__frac(V_a_2,V_ba_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_ba_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_ba_2))) ) ) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_Nitpick_OFrac__def,axiom,
% 191.04/191.64 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)))) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divmod__int__def,axiom,
% 191.04/191.64 ! [V_b,V_a] :
% 191.04/191.64 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 191.04/191.64 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 191.04/191.64 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) )
% 191.04/191.64 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 191.04/191.64 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 191.04/191.64 => 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)) )
% 191.04/191.64 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 191.04/191.64 => 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))) ) ) ) ) )
% 191.04/191.64 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 191.04/191.64 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 191.04/191.64 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) )
% 191.04/191.64 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 191.04/191.64 => 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))) ) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_negDivAlg_Opinduct,axiom,
% 191.04/191.64 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 191.04/191.64 ( 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)))
% 191.04/191.64 => ( ! [B_a,B_b] :
% 191.04/191.64 ( 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)))
% 191.04/191.64 => ( ( ~ ( 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)))
% 191.04/191.64 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 191.04/191.64 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) )
% 191.04/191.64 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) )
% 191.04/191.64 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_negateSnd__eq,axiom,
% 191.04/191.64 ! [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)) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_splitI,axiom,
% 191.04/191.64 ! [T_c,T_b,V_ba_2,V_a_2,V_f_2] :
% 191.04/191.64 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_ba_2))
% 191.04/191.64 => 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_ba_2))) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_prod__caseI,axiom,
% 191.04/191.64 ! [T_c,T_b,V_ba_2,V_a_2,V_f1_2] :
% 191.04/191.64 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_ba_2))
% 191.04/191.64 => 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_ba_2))) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_posDivAlg_Opinduct,axiom,
% 191.04/191.64 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 191.04/191.64 ( 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)))
% 191.04/191.64 => ( ! [B_a,B_b] :
% 191.04/191.64 ( 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)))
% 191.04/191.64 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b))
% 191.04/191.64 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 191.04/191.64 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) )
% 191.04/191.64 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) )
% 191.04/191.64 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_nat__gcd_Opsimps,axiom,
% 191.04/191.64 ! [V_y_2,V_x_2] :
% 191.04/191.64 ( 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)))
% 191.04/191.64 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 191.04/191.64 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 )
% 191.04/191.64 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 191.04/191.64 => 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)) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_divmod__int__pdivmod,axiom,
% 191.04/191.64 ! [V_l_2,V_k_2] :
% 191.04/191.64 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 191.04/191.64 => 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)) )
% 191.04/191.64 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 191.04/191.64 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 191.04/191.64 => 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) )
% 191.04/191.64 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 191.04/191.64 => 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)))) ) ) ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_apsnd__conv,axiom,
% 191.04/191.64 ! [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)) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_split__paired__All,axiom,
% 191.04/191.64 ! [T_c,T_b,V_Pa_2] :
% 191.04/191.64 ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 191.04/191.64 <=> ! [B_a,B_b] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_Pair__eq,axiom,
% 191.04/191.64 ! [V_b_H_2,V_a_H_2,V_ba_2,V_a_2,T_c,T_b] :
% 191.04/191.64 ( hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2)
% 191.04/191.64 <=> ( V_a_2 = V_a_H_2
% 191.04/191.64 & V_ba_2 = V_b_H_2 ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_Pair__inject,axiom,
% 191.04/191.64 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] :
% 191.04/191.64 ( 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)
% 191.04/191.64 => ~ ( V_a = V_a_H
% 191.04/191.64 => V_b != V_b_H ) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_negateSnd__def,axiom,
% 191.04/191.64 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_split__weak__cong,axiom,
% 191.04/191.64 ! [V_ca_2,T_d,T_c,T_b,V_q_2,V_p_2] :
% 191.04/191.64 ( V_p_2 = V_q_2
% 191.04/191.64 => hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_ca_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_ca_2),V_q_2) ) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_prod_Osimps_I2_J,axiom,
% 191.04/191.64 ! [V_ba_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_ba_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_ba_2) ).
% 191.04/191.64
% 191.04/191.64 fof(fact_split__conv,axiom,
% 191.04/191.65 ! [V_ba_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_ba_2)) = hAPP(hAPP(V_f_2,V_a_2),V_ba_2) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_splitD,axiom,
% 191.04/191.65 ! [V_ba_2,V_a_2,V_f_2,T_c,T_b] :
% 191.04/191.65 ( 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_ba_2)))
% 191.04/191.65 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_ba_2)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_split__eta,axiom,
% 191.04/191.65 ! [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 ).
% 191.04/191.65
% 191.04/191.65 fof(fact_split__twice,axiom,
% 191.04/191.65 ! [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) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_pdivmod__def,axiom,
% 191.04/191.65 ! [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))) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_pdivmod__posDivAlg,axiom,
% 191.04/191.65 ! [V_k,V_l] :
% 191.04/191.65 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 191.04/191.65 => 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)) )
% 191.04/191.65 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 191.04/191.65 => 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)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_divmod__int__code,axiom,
% 191.04/191.65 ! [V_l_2,V_k_2] :
% 191.04/191.65 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 191.04/191.65 => 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)) )
% 191.04/191.65 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 191.04/191.65 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 191.04/191.65 => 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) )
% 191.04/191.65 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 191.04/191.65 => 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)))) ) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_div__mod__code__numeral__def,axiom,
% 191.04/191.65 ! [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)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_zmult2__lemma,axiom,
% 191.04/191.65 ! [V_c,V_r,V_q,V_b,V_a] :
% 191.04/191.65 ( 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)))
% 191.04/191.65 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 191.04/191.65 => 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)))) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_mod__pos__neg__1__number__of,axiom,
% 191.04/191.65 ! [V_w] :
% 191.04/191.65 ( 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)))
% 191.04/191.65 => 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))))) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_divmod__int__rel__def,axiom,
% 191.04/191.65 ! [V_ba_2,V_a_2] : c_Divides_Odivmod__int__rel(V_a_2,V_ba_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_ba_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_ba_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_ba_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_ba_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_ba_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))))))) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_norm__frac_Opinduct,axiom,
% 191.04/191.65 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 191.04/191.65 ( 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)))
% 191.04/191.65 => ( ! [B_a,B_b] :
% 191.04/191.65 ( 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)))
% 191.04/191.65 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 191.04/191.65 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_b))) )
% 191.04/191.65 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) )
% 191.04/191.65 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_splitD_H,axiom,
% 191.04/191.65 ! [V_ca_2,V_ba_2,V_a_2,V_R_2,T_d,T_c,T_b] :
% 191.04/191.65 ( 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_ba_2)),V_ca_2))
% 191.04/191.65 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_ba_2),V_ca_2)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_snd__conv,axiom,
% 191.04/191.65 ! [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 ).
% 191.04/191.65
% 191.04/191.65 fof(fact_snd__eqD,axiom,
% 191.04/191.65 ! [V_a,V_y,V_x,T_a,T_b] :
% 191.04/191.65 ( 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
% 191.04/191.65 => V_y = V_a ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_apsnd__eq__conv,axiom,
% 191.04/191.65 ! [V_g_2,V_x_2,V_f_2,T_b,T_c,T_d] :
% 191.04/191.65 ( 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)
% 191.04/191.65 <=> 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)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_snd__apsnd,axiom,
% 191.04/191.65 ! [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)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_snd__def,axiom,
% 191.04/191.65 ! [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) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_mod__int__def,axiom,
% 191.04/191.65 ! [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)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_divmod__int__rel__0,axiom,
% 191.04/191.65 ! [V_b] :
% 191.04/191.65 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 191.04/191.65 => 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)))) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_self__remainder,axiom,
% 191.04/191.65 ! [V_r,V_q,V_a] :
% 191.04/191.65 ( 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)))
% 191.04/191.65 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 191.04/191.65 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_unique__quotient,axiom,
% 191.04/191.65 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 191.04/191.65 ( 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)))
% 191.04/191.65 => ( 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)))
% 191.04/191.65 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 191.04/191.65 => V_q = V_q_H ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_unique__remainder,axiom,
% 191.04/191.65 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 191.04/191.65 ( 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)))
% 191.04/191.65 => ( 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)))
% 191.04/191.65 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 191.04/191.65 => V_r = V_r_H ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_divmod__int__rel__neg,axiom,
% 191.04/191.65 ! [V_qr,V_b,V_a] :
% 191.04/191.65 ( 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))
% 191.04/191.65 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_divmod__int__correct,axiom,
% 191.04/191.65 ! [V_a,V_b] :
% 191.04/191.65 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 191.04/191.65 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_self__quotient,axiom,
% 191.04/191.65 ! [V_r,V_q,V_a] :
% 191.04/191.65 ( 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)))
% 191.04/191.65 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 191.04/191.65 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_divmod__int__rel__mod,axiom,
% 191.04/191.65 ! [V_r,V_q,V_b,V_a] :
% 191.04/191.65 ( 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)))
% 191.04/191.65 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 191.04/191.65 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_divmod__int__rel__div,axiom,
% 191.04/191.65 ! [V_r,V_q,V_b,V_a] :
% 191.04/191.65 ( 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)))
% 191.04/191.65 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 191.04/191.65 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_negDivAlg__correct,axiom,
% 191.04/191.65 ! [V_b,V_a] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 191.04/191.65 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_mod__neg__pos,axiom,
% 191.04/191.65 ! [V_b,V_a] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 191.04/191.65 => 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)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_divmod__int__rel__div__mod,axiom,
% 191.04/191.65 ! [V_a,V_b] :
% 191.04/191.65 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 191.04/191.65 => 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)))) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_posDivAlg__correct,axiom,
% 191.04/191.65 ! [V_b,V_a] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 191.04/191.65 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_mod__pos__pos,axiom,
% 191.04/191.65 ! [V_b,V_a] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 191.04/191.65 => 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)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_mod__pos__pos__1__number__of,axiom,
% 191.04/191.65 ! [V_w] :
% 191.04/191.65 ( 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)))
% 191.04/191.65 => 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))) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_zadd1__lemma,axiom,
% 191.04/191.65 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 191.04/191.65 ( 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)))
% 191.04/191.65 => ( 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)))
% 191.04/191.65 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 191.04/191.65 => 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)))) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_zminus1__lemma,axiom,
% 191.04/191.65 ! [V_r_2,V_q_2,V_ba_2,V_a_2] :
% 191.04/191.65 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a_2,V_ba_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_2),V_r_2)))
% 191.04/191.65 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),V_ba_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_ba_2),V_r_2))))) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_mod__pos__neg,axiom,
% 191.04/191.65 ! [V_b,V_a] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 191.04/191.65 => 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)))) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_divmod__nat__if,axiom,
% 191.04/191.65 ! [V_m_2,V_n_2] :
% 191.04/191.65 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 191.04/191.65 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 191.04/191.65 => 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) )
% 191.04/191.65 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 191.04/191.65 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 191.04/191.65 => 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)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_divmod__int__relI,axiom,
% 191.04/191.65 ! [V_r,V_q,V_b,V_a] :
% 191.04/191.65 ( 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)
% 191.04/191.65 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 191.04/191.65 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) )
% 191.04/191.65 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 191.04/191.65 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 191.04/191.65 => 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))) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_mod__neg__neg,axiom,
% 191.04/191.65 ! [V_b,V_a] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 191.04/191.65 => 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)))) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_zmult1__lemma,axiom,
% 191.04/191.65 ! [V_a,V_r,V_q,V_c,V_b] :
% 191.04/191.65 ( 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)))
% 191.04/191.65 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 191.04/191.65 => 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)))) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_equalityI,axiom,
% 191.04/191.65 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 191.04/191.65 => V_A_2 = V_B_2 ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_div__pos__neg__1__number__of,axiom,
% 191.04/191.65 ! [V_w] :
% 191.04/191.65 ( 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)))
% 191.04/191.65 => 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))))) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_nat__gcd_Opinduct,axiom,
% 191.04/191.65 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 191.04/191.65 ( 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)))
% 191.04/191.65 => ( ! [B_x,B_y] :
% 191.04/191.65 ( 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)))
% 191.04/191.65 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 191.04/191.65 => hBOOL(hAPP(hAPP(V_Pa_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) )
% 191.04/191.65 => hBOOL(hAPP(hAPP(V_Pa_2,B_x),B_y)) ) )
% 191.04/191.65 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_div__neg__neg,axiom,
% 191.04/191.65 ! [V_b,V_a] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 191.04/191.65 => 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)))) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__number__of__Suc,axiom,
% 191.04/191.65 ! [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)))) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__0L,axiom,
% 191.04/191.65 ! [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) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__0R,axiom,
% 191.04/191.65 ! [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) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__Suc__Suc,axiom,
% 191.04/191.65 ! [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)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__le__iff__disj,axiom,
% 191.04/191.65 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_b)
% 191.04/191.65 => ( 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))
% 191.04/191.65 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 191.04/191.65 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Oinf__le1,axiom,
% 191.04/191.65 ! [V_y,V_x,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => 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)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Oinf__le2,axiom,
% 191.04/191.65 ! [V_y,V_x,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => 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)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Ole__iff__inf,axiom,
% 191.04/191.65 ! [V_y_2,V_x_2,T_b] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_b)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 191.04/191.65 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Ole__inf__iff,axiom,
% 191.04/191.65 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_b)
% 191.04/191.65 => ( 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)))
% 191.04/191.65 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 191.04/191.65 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Ole__infI1,axiom,
% 191.04/191.65 ! [V_b,V_x,V_a,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 191.04/191.65 => 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)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Ole__infI2,axiom,
% 191.04/191.65 ! [V_a,V_x,V_b,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 191.04/191.65 => 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)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Oinf__absorb1,axiom,
% 191.04/191.65 ! [V_y,V_x,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 191.04/191.65 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Oinf__absorb2,axiom,
% 191.04/191.65 ! [V_x,V_y,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 191.04/191.65 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Ole__infI,axiom,
% 191.04/191.65 ! [V_b,V_a,V_x,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 191.04/191.65 => 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))) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Oinf__greatest,axiom,
% 191.04/191.65 ! [V_z,V_y,V_x,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 191.04/191.65 => 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))) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Oinf__mono,axiom,
% 191.04/191.65 ! [V_d,V_b,V_c,V_a,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 191.04/191.65 => 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))) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Ole__infE,axiom,
% 191.04/191.65 ! [V_b,V_a,V_x,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => ( 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)))
% 191.04/191.65 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 191.04/191.65 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__diff__distrib__left,axiom,
% 191.04/191.65 ! [V_z,V_y,V_x,T_a] :
% 191.04/191.65 ( class_Groups_Oordered__ab__group__add(T_a)
% 191.04/191.65 => 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)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Oless__infI1,axiom,
% 191.04/191.65 ! [V_b,V_x,V_a,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 191.04/191.65 => 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)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Oless__infI2,axiom,
% 191.04/191.65 ! [V_a,V_x,V_b,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 191.04/191.65 => 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)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__less__iff__disj,axiom,
% 191.04/191.65 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_b)
% 191.04/191.65 => ( 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))
% 191.04/191.65 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 191.04/191.65 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__less__iff__conj,axiom,
% 191.04/191.65 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_b)
% 191.04/191.65 => ( 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)))
% 191.04/191.65 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 191.04/191.65 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__add__distrib__left,axiom,
% 191.04/191.65 ! [V_z,V_y,V_x,T_a] :
% 191.04/191.65 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 191.04/191.65 => 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)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Oinf__assoc,axiom,
% 191.04/191.65 ! [V_z,V_y,V_x,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => 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)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Oinf_Oassoc,axiom,
% 191.04/191.65 ! [V_c,V_b,V_a,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => 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)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Oinf__left__commute,axiom,
% 191.04/191.65 ! [V_z,V_y,V_x,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => 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)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Oinf_Oleft__commute,axiom,
% 191.04/191.65 ! [V_c,V_a,V_b,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => 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)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Oinf__left__idem,axiom,
% 191.04/191.65 ! [V_y,V_x,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => 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) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Oinf_Oleft__idem,axiom,
% 191.04/191.65 ! [V_b,V_a,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => 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) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Oinf__commute,axiom,
% 191.04/191.65 ! [V_y,V_x,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => 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) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Oinf_Ocommute,axiom,
% 191.04/191.65 ! [V_b,V_a,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => 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) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Oinf_Oidem,axiom,
% 191.04/191.65 ! [V_a,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__diff,axiom,
% 191.04/191.65 ! [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) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_fst__eqD,axiom,
% 191.04/191.65 ! [V_a,V_y,V_x,T_b,T_a] :
% 191.04/191.65 ( 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
% 191.04/191.65 => V_x = V_a ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_fst__conv,axiom,
% 191.04/191.65 ! [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 ).
% 191.04/191.65
% 191.04/191.65 fof(fact_prod__eqI,axiom,
% 191.04/191.65 ! [V_q,V_p,T_b,T_a] :
% 191.04/191.65 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q)
% 191.04/191.65 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q)
% 191.04/191.65 => V_p = V_q ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_Pair__fst__snd__eq,axiom,
% 191.04/191.65 ! [T_c,T_b,V_t_2,V_s_2] :
% 191.04/191.65 ( V_s_2 = V_t_2
% 191.04/191.65 <=> ( hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2)
% 191.04/191.65 & hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_fst__apsnd,axiom,
% 191.04/191.65 ! [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) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_fst__def,axiom,
% 191.04/191.65 ! [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) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__number__of,axiom,
% 191.04/191.65 ! [V_v,V_u,T_b] :
% 191.04/191.65 ( ( class_Int_Onumber(T_b)
% 191.04/191.65 & class_Orderings_Oord(T_b) )
% 191.04/191.65 => ( ( 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)))
% 191.04/191.65 => 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) )
% 191.04/191.65 & ( ~ 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)))
% 191.04/191.65 => 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) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_surjective__pairing,axiom,
% 191.04/191.65 ! [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)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_pair__collapse,axiom,
% 191.04/191.65 ! [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 ).
% 191.04/191.65
% 191.04/191.65 fof(fact_prod__case__beta,axiom,
% 191.04/191.65 ! [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)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_div__int__def,axiom,
% 191.04/191.65 ! [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)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_mod__nat__def,axiom,
% 191.04/191.65 ! [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)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_split__beta,axiom,
% 191.04/191.65 ! [V_z_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_Pa_2),V_z_2) = hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_z_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_z_2)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_split__comp__eq,axiom,
% 191.04/191.65 ! [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)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_split__def,axiom,
% 191.04/191.65 ! [V_p_2,V_ca_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_ca_2),V_p_2) = hAPP(hAPP(V_ca_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_double__diff,axiom,
% 191.04/191.65 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 191.04/191.65 => 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 ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_Diff__mono,axiom,
% 191.04/191.65 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_b] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2))
% 191.04/191.65 => 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))) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_Diff__subset,axiom,
% 191.04/191.65 ! [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)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_Compl__anti__mono,axiom,
% 191.04/191.65 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.65 => 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))) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_Compl__subset__Compl__iff,axiom,
% 191.04/191.65 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.65 ( 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)))
% 191.04/191.65 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_equalityE,axiom,
% 191.04/191.65 ! [T_b,V_B_2,V_A_2] :
% 191.04/191.65 ( V_A_2 = V_B_2
% 191.04/191.65 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.65 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_subset__trans,axiom,
% 191.04/191.65 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 191.04/191.65 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_equalityD2,axiom,
% 191.04/191.65 ! [T_b,V_B_2,V_A_2] :
% 191.04/191.65 ( V_A_2 = V_B_2
% 191.04/191.65 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_equalityD1,axiom,
% 191.04/191.65 ! [T_b,V_B_2,V_A_2] :
% 191.04/191.65 ( V_A_2 = V_B_2
% 191.04/191.65 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_set__eq__subset,axiom,
% 191.04/191.65 ! [T_b,V_B_2,V_A_2] :
% 191.04/191.65 ( V_A_2 = V_B_2
% 191.04/191.65 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.65 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_subset__refl,axiom,
% 191.04/191.65 ! [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)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_subset__psubset__trans,axiom,
% 191.04/191.65 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 191.04/191.65 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_psubset__subset__trans,axiom,
% 191.04/191.65 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 191.04/191.65 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_psubset__imp__subset,axiom,
% 191.04/191.65 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.65 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_subset__iff__psubset__eq,axiom,
% 191.04/191.65 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.65 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.65 | V_A_2 = V_B_2 ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_psubset__eq,axiom,
% 191.04/191.65 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.65 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.65 & V_A_2 != V_B_2 ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__Suc1,axiom,
% 191.04/191.65 ! [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) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__Suc2,axiom,
% 191.04/191.65 ! [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) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_div__neg__pos,axiom,
% 191.04/191.65 ! [V_b,V_a] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 191.04/191.65 => 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)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_div__pos__pos,axiom,
% 191.04/191.65 ! [V_b,V_a] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 191.04/191.65 => 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)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_div__pos__pos__1__number__of,axiom,
% 191.04/191.65 ! [V_w] :
% 191.04/191.65 ( 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)))
% 191.04/191.65 => 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))) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_div__pos__neg,axiom,
% 191.04/191.65 ! [V_b,V_a] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 191.04/191.65 => 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)))) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__Suc__number__of,axiom,
% 191.04/191.65 ! [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)))) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_prod__size__simp,axiom,
% 191.04/191.65 ! [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))) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_conjI__realizer,axiom,
% 191.04/191.65 ! [T_c,T_b,V_q_2,V_Q_2,V_p_2,V_Pa_2] :
% 191.04/191.65 ( hBOOL(hAPP(V_Pa_2,V_p_2))
% 191.04/191.65 => ( hBOOL(hAPP(V_Q_2,V_q_2))
% 191.04/191.65 => ( hBOOL(hAPP(V_Pa_2,hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2))))
% 191.04/191.65 & 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)))) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_exI__realizer,axiom,
% 191.04/191.65 ! [T_b,T_c,V_x_2,V_y_2,V_Pa_2] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(V_Pa_2,V_y_2),V_x_2))
% 191.04/191.65 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2))),hAPP(c_Product__Type_Ofst(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)))) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__ord__min,axiom,
% 191.04/191.65 ! [T_b] :
% 191.04/191.65 ( class_Orderings_Oord(T_b)
% 191.04/191.65 => c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_prod_Orecs,axiom,
% 191.04/191.65 ! [V_ba_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_ba_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_ba_2) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_Compl__eq__Compl__iff,axiom,
% 191.04/191.65 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.65 ( 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)
% 191.04/191.65 <=> V_A_2 = V_B_2 ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_double__complement,axiom,
% 191.04/191.65 ! [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 ).
% 191.04/191.65
% 191.04/191.65 fof(fact_Diff__idemp,axiom,
% 191.04/191.65 ! [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) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_psubset__trans,axiom,
% 191.04/191.65 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 191.04/191.65 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_div__nat__def,axiom,
% 191.04/191.65 ! [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)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_divmod__nat__rel__def,axiom,
% 191.04/191.65 ! [V_qr_2,V_n_2,V_m_2] :
% 191.04/191.65 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2))
% 191.04/191.65 <=> ( 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))
% 191.04/191.65 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 191.04/191.65 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 191.04/191.65 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 191.04/191.65 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 191.04/191.65 => ( 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)))
% 191.04/191.65 & 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)) ) )
% 191.04/191.65 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 191.04/191.65 => ( 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)))
% 191.04/191.65 & 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))) ) ) ) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_range,axiom,
% 191.04/191.65 ! [V_s,V_k] :
% 191.04/191.65 ( 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))
% 191.04/191.65 => 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)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_New__DSequence_Opos__not__seq__def,axiom,
% 191.04/191.65 ! [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))) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_max__number__of__Suc,axiom,
% 191.04/191.65 ! [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)))) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_max__Suc__number__of,axiom,
% 191.04/191.65 ! [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)))) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_apsnd__apfst,axiom,
% 191.04/191.65 ! [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))) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_max__diff__distrib__left,axiom,
% 191.04/191.65 ! [V_z,V_y,V_x,T_a] :
% 191.04/191.65 ( class_Groups_Oordered__ab__group__add(T_a)
% 191.04/191.65 => 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)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_less__max__iff__disj,axiom,
% 191.04/191.65 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_b)
% 191.04/191.65 => ( 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)))
% 191.04/191.65 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 191.04/191.65 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_max__less__iff__conj,axiom,
% 191.04/191.65 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_b)
% 191.04/191.65 => ( 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))
% 191.04/191.65 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 191.04/191.65 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Oless__supI2,axiom,
% 191.04/191.65 ! [V_a,V_b,V_x,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 191.04/191.65 => 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))) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Oless__supI1,axiom,
% 191.04/191.65 ! [V_b,V_a,V_x,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 191.04/191.65 => 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))) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Osup__inf__absorb,axiom,
% 191.04/191.65 ! [V_y,V_x,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => 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 ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Oinf__sup__absorb,axiom,
% 191.04/191.65 ! [V_y,V_x,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => 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 ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Osup__inf__distrib1,axiom,
% 191.04/191.65 ! [V_z,V_y,V_x,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => 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)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Oinf__sup__distrib1,axiom,
% 191.04/191.65 ! [V_z,V_y,V_x,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => 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)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Osup__inf__distrib2,axiom,
% 191.04/191.65 ! [V_x,V_z,V_y,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => 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)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Oinf__sup__distrib2,axiom,
% 191.04/191.65 ! [V_x,V_z,V_y,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => 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)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_max__0L,axiom,
% 191.04/191.65 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 191.04/191.65
% 191.04/191.65 fof(fact_max__0R,axiom,
% 191.04/191.65 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ).
% 191.04/191.65
% 191.04/191.65 fof(fact_max__Suc__Suc,axiom,
% 191.04/191.65 ! [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)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_le__max__iff__disj,axiom,
% 191.04/191.65 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_b)
% 191.04/191.65 => ( 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)))
% 191.04/191.65 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2))
% 191.04/191.65 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2)) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_le__maxI1,axiom,
% 191.04/191.65 ! [V_y,V_x,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => 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))) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_le__maxI2,axiom,
% 191.04/191.65 ! [V_x,V_y,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => 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))) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Ole__iff__sup,axiom,
% 191.04/191.65 ! [V_y_2,V_x_2,T_b] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_b)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 191.04/191.65 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Ole__sup__iff,axiom,
% 191.04/191.65 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_b)
% 191.04/191.65 => ( 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))
% 191.04/191.65 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 191.04/191.65 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Ole__supI1,axiom,
% 191.04/191.65 ! [V_b,V_a,V_x,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 191.04/191.65 => 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))) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Ole__supI2,axiom,
% 191.04/191.65 ! [V_a,V_b,V_x,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 191.04/191.65 => 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))) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Osup__absorb2,axiom,
% 191.04/191.65 ! [V_y,V_x,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 191.04/191.65 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Osup__absorb1,axiom,
% 191.04/191.65 ! [V_x,V_y,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 191.04/191.65 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Ole__supI,axiom,
% 191.04/191.65 ! [V_b,V_x,V_a,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 191.04/191.65 => 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)) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Osup__least,axiom,
% 191.04/191.65 ! [V_z,V_x,V_y,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 191.04/191.65 => 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)) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Osup__mono,axiom,
% 191.04/191.65 ! [V_d,V_b,V_c,V_a,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 191.04/191.65 => 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))) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Ole__supE,axiom,
% 191.04/191.65 ! [V_x,V_b,V_a,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => ( 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))
% 191.04/191.65 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 191.04/191.65 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_max__add__distrib__left,axiom,
% 191.04/191.65 ! [V_z,V_y,V_x,T_a] :
% 191.04/191.65 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 191.04/191.65 => 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)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Osup__assoc,axiom,
% 191.04/191.65 ! [V_z,V_y,V_x,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => 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)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Osup_Oassoc,axiom,
% 191.04/191.65 ! [V_c,V_b,V_a,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => 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)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Osup__left__commute,axiom,
% 191.04/191.65 ! [V_z,V_y,V_x,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => 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)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Osup_Oleft__commute,axiom,
% 191.04/191.65 ! [V_c,V_a,V_b,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => 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)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Osup__left__idem,axiom,
% 191.04/191.65 ! [V_y,V_x,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => 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) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Osup_Oleft__idem,axiom,
% 191.04/191.65 ! [V_b,V_a,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => 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) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Osup__commute,axiom,
% 191.04/191.65 ! [V_y,V_x,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => 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) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Osup_Ocommute,axiom,
% 191.04/191.65 ! [V_b,V_a,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => 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) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Osup_Oidem,axiom,
% 191.04/191.65 ! [V_a,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_apfst__conv,axiom,
% 191.04/191.65 ! [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) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_apfst__eq__conv,axiom,
% 191.04/191.65 ! [V_g_2,V_x_2,V_f_2,T_c,T_b,T_d] :
% 191.04/191.65 ( 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)
% 191.04/191.65 <=> 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)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_fst__apfst,axiom,
% 191.04/191.65 ! [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)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_snd__apfst,axiom,
% 191.04/191.65 ! [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) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_max__number__of,axiom,
% 191.04/191.65 ! [V_v,V_u,T_b] :
% 191.04/191.65 ( ( class_Int_Onumber(T_b)
% 191.04/191.65 & class_Orderings_Oord(T_b) )
% 191.04/191.65 => ( ( 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)))
% 191.04/191.65 => 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) )
% 191.04/191.65 & ( ~ 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)))
% 191.04/191.65 => 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) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Odistrib__inf__le,axiom,
% 191.04/191.65 ! [V_z,V_y,V_x,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => 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)))) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_min__max_Odistrib__sup__le,axiom,
% 191.04/191.65 ! [V_z,V_y,V_x,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => 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)))) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_minus__max__eq__min,axiom,
% 191.04/191.65 ! [V_y,V_x,T_a] :
% 191.04/191.65 ( class_Groups_Olinordered__ab__group__add(T_a)
% 191.04/191.65 => 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)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_minus__min__eq__max,axiom,
% 191.04/191.65 ! [V_y,V_x,T_a] :
% 191.04/191.65 ( class_Groups_Olinordered__ab__group__add(T_a)
% 191.04/191.65 => 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)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_nat__minus__add__max,axiom,
% 191.04/191.65 ! [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) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_apsnd__apfst__commute,axiom,
% 191.04/191.65 ! [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)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_max__Suc1,axiom,
% 191.04/191.65 ! [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) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_max__Suc2,axiom,
% 191.04/191.65 ! [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) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_apfst__apsnd,axiom,
% 191.04/191.65 ! [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))) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dual__min,axiom,
% 191.04/191.65 ! [T_b] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_b)
% 191.04/191.65 => 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) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_max__ord__max,axiom,
% 191.04/191.65 ! [T_b] :
% 191.04/191.65 ( class_Orderings_Oord(T_b)
% 191.04/191.65 => c_Orderings_Oord__class_Omax(T_b) = c_Orderings_Oord_Omax(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_code__numeral__decr,axiom,
% 191.04/191.65 ! [V_k] :
% 191.04/191.65 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 191.04/191.65 => 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))) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_Nitpick_Ozero__frac__def,axiom,
% 191.04/191.65 ! [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))) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_pos__not__random__dseq__def,axiom,
% 191.04/191.65 ! [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)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_Code__Numeral_Onat__of__inject,axiom,
% 191.04/191.65 ! [V_l_2,V_k_2] :
% 191.04/191.65 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2)
% 191.04/191.65 <=> V_k_2 = V_l_2 ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_code__numeral_Onat__of__inject,axiom,
% 191.04/191.65 ! [V_y_2,V_x_2] :
% 191.04/191.65 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2)
% 191.04/191.65 <=> V_x_2 = V_y_2 ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_nat__of__of__nat,axiom,
% 191.04/191.65 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ).
% 191.04/191.65
% 191.04/191.65 fof(fact_of__nat__nat__of,axiom,
% 191.04/191.65 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ).
% 191.04/191.65
% 191.04/191.65 fof(fact_nat__of__inverse,axiom,
% 191.04/191.65 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ).
% 191.04/191.65
% 191.04/191.65 fof(fact_less__code__numeral__def,axiom,
% 191.04/191.65 ! [V_m_2,V_n_2] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 191.04/191.65 <=> 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))) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_nat__of__number,axiom,
% 191.04/191.65 ! [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) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_less__eq__code__numeral__def,axiom,
% 191.04/191.65 ! [V_m_2,V_n_2] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 191.04/191.65 <=> 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))) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_nat__of__code,axiom,
% 191.04/191.65 ! [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)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_nat__of__aux__def,axiom,
% 191.04/191.65 ! [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) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_Min_Oidem,axiom,
% 191.04/191.65 ! [V_x,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_Max_Oidem,axiom,
% 191.04/191.65 ! [V_x,T_a] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_a)
% 191.04/191.65 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dual__max,axiom,
% 191.04/191.65 ! [T_b] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_b)
% 191.04/191.65 => 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) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_Suc__code__numeral__def,axiom,
% 191.04/191.65 ! [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))) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_minus__code__numeral__def,axiom,
% 191.04/191.65 ! [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))) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_plus__code__numeral__def,axiom,
% 191.04/191.65 ! [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))) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_div__code__numeral__def,axiom,
% 191.04/191.65 ! [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))) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_times__code__numeral__def,axiom,
% 191.04/191.65 ! [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))) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_mod__code__numeral__def,axiom,
% 191.04/191.65 ! [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))) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_Nitpick_Oone__frac__def,axiom,
% 191.04/191.65 ! [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))) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_Nitpick_Onumber__of__frac__def,axiom,
% 191.04/191.65 ! [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))) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_Nitpick_Ofrac__def,axiom,
% 191.04/191.65 ! [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)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_surjective__sum,axiom,
% 191.04/191.65 ! [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 ).
% 191.04/191.65
% 191.04/191.65 fof(fact_iterate_Osimps,axiom,
% 191.04/191.65 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 191.04/191.65 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 191.04/191.65 => 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) )
% 191.04/191.65 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 191.04/191.65 => 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)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_sum__case__KK,axiom,
% 191.04/191.65 ! [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 ).
% 191.04/191.65
% 191.04/191.65 fof(fact_scomp__scomp,axiom,
% 191.04/191.65 ! [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)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_sum__case__inject,axiom,
% 191.04/191.65 ! [V_g2_2,V_g1_2,V_f2_2,V_f1_2,T_c,T_d,T_b] :
% 191.04/191.65 ( 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)
% 191.04/191.65 => ~ ( V_f1_2 = V_g1_2
% 191.04/191.65 => V_f2_2 != V_g2_2 ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_sum__case__weak__cong,axiom,
% 191.04/191.65 ! [V_g_2,V_f_2,T_c,T_d,T_b,V_t_2,V_s_2] :
% 191.04/191.65 ( V_s_2 = V_t_2
% 191.04/191.65 => 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) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_scomp__Pair,axiom,
% 191.04/191.65 ! [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 ).
% 191.04/191.65
% 191.04/191.65 fof(fact_Pair__scomp,axiom,
% 191.04/191.65 ! [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) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_scomp__apply,axiom,
% 191.04/191.65 ! [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)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_sum_Osimps_I6_J,axiom,
% 191.04/191.65 ! [V_ba_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_ba_2)) = hAPP(V_f2_2,V_ba_2) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_sum_Osimps_I5_J,axiom,
% 191.04/191.65 ! [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) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_scomp__def,axiom,
% 191.04/191.65 ! [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)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_scomp__unfold,axiom,
% 191.04/191.65 ! [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))) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_Nitpick_Oplus__frac__def,axiom,
% 191.04/191.65 ! [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))) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_internal__split__def,axiom,
% 191.04/191.65 ! [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) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_transfer__morphism__int__nat,axiom,
% 191.04/191.65 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)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_New__DSequence_Opos__decr__bind__def,axiom,
% 191.04/191.65 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 191.04/191.65 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 191.04/191.65 => 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) )
% 191.04/191.65 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 191.04/191.65 => 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)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom,
% 191.04/191.65 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 191.04/191.65 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 191.04/191.65 => 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) )
% 191.04/191.65 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 191.04/191.65 => 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)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_internal__split__conv,axiom,
% 191.04/191.65 ! [V_ba_2,V_a_2,V_ca_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_c,T_d,T_b),V_ca_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_ba_2)) = hAPP(hAPP(V_ca_2,V_a_2),V_ba_2) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_Nitpick_Otimes__frac__def,axiom,
% 191.04/191.65 ! [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))) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_Nitpick_Oof__frac__def,axiom,
% 191.04/191.65 ! [V_q,T_a,T_b] :
% 191.04/191.65 ( ( class_Rings_Oinverse(T_b)
% 191.04/191.65 & class_Rings_Oring__1(T_b) )
% 191.04/191.65 => 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))) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_Nitpick_Oinverse__frac__def,axiom,
% 191.04/191.65 ! [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)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_Nitpick_Ouminus__frac__def,axiom,
% 191.04/191.65 ! [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))) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom,
% 191.04/191.65 ! [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)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_Nitpick_Oless__frac__def,axiom,
% 191.04/191.65 ! [V_r_2,V_q_2,T_b] :
% 191.04/191.65 ( c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2)
% 191.04/191.65 <=> 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))) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_Nitpick_Oless__eq__frac__def,axiom,
% 191.04/191.65 ! [V_r_2,V_q_2,T_b] :
% 191.04/191.65 ( c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2)
% 191.04/191.65 <=> 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))) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom,
% 191.04/191.65 ! [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)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_New__DSequence_Oneg__bind__def,axiom,
% 191.04/191.65 ! [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)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_New__DSequence_Opos__empty__def,axiom,
% 191.04/191.65 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_pos__empty__def,axiom,
% 191.04/191.65 ! [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) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_neg__bind__def,axiom,
% 191.04/191.65 ! [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)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_New__DSequence_Opos__bind__def,axiom,
% 191.04/191.65 ! [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)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_predicate2D,axiom,
% 191.04/191.65 ! [V_y_2,V_x_2,V_Q_2,V_Pa_2,T_c,T_b] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_Pa_2),V_Q_2))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 191.04/191.65 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_rev__predicate2D,axiom,
% 191.04/191.65 ! [V_Q_2,T_c,T_b,V_y_2,V_x_2,V_Pa_2] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_Pa_2),V_Q_2))
% 191.04/191.65 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_predicate1D,axiom,
% 191.04/191.65 ! [V_x_2,V_Q_2,V_Pa_2,T_b] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Q_2))
% 191.04/191.65 => ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 191.04/191.65 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_rev__predicate1D,axiom,
% 191.04/191.65 ! [V_Q_2,T_b,V_x_2,V_Pa_2] :
% 191.04/191.65 ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Q_2))
% 191.04/191.65 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_pos__bind__def,axiom,
% 191.04/191.65 ! [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)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_The__split,axiom,
% 191.04/191.65 ! [V_Pa_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2)) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_Pa_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_Random_Osimps,axiom,
% 191.04/191.65 ! [V_size_2,V_g_2,T_b,V_nrandom_2] :
% 191.04/191.65 ( ( 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)))
% 191.04/191.65 => 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)) )
% 191.04/191.65 & ( ~ 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)))
% 191.04/191.65 => 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))))))) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_exE__realizer,axiom,
% 191.04/191.65 ! [T_d,V_f_2,V_Q_2,V_p_2,T_b,T_c,V_Pa_2] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2)),hAPP(c_Product__Type_Ofst(T_c,T_b),V_p_2)))
% 191.04/191.65 => ( ! [B_x,B_y] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(V_Pa_2,B_y),B_x))
% 191.04/191.65 => hBOOL(hAPP(V_Q_2,hAPP(hAPP(V_f_2,B_x),B_y))) )
% 191.04/191.65 => 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))) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_curry__def,axiom,
% 191.04/191.65 ! [V_y_2,V_x_2,V_ca_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_ca_2),V_x_2),V_y_2) = hAPP(V_ca_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_curryI,axiom,
% 191.04/191.65 ! [V_ba_2,V_a_2,T_c,T_b,V_f_2] :
% 191.04/191.65 ( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2)))
% 191.04/191.65 => hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_ba_2)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_curryD,axiom,
% 191.04/191.65 ! [V_ba_2,V_a_2,V_f_2,T_c,T_b] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_ba_2))
% 191.04/191.65 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2))) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_curryE,axiom,
% 191.04/191.65 ! [V_ba_2,V_a_2,V_f_2,T_c,T_b] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_ba_2))
% 191.04/191.65 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_ba_2))) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_curry__conv,axiom,
% 191.04/191.65 ! [V_ba_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_ba_2) = hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_ba_2)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_split__curry,axiom,
% 191.04/191.65 ! [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 ).
% 191.04/191.65
% 191.04/191.65 fof(fact_curry__split,axiom,
% 191.04/191.65 ! [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 ).
% 191.04/191.65
% 191.04/191.65 fof(fact_split__paired__The,axiom,
% 191.04/191.65 ! [V_Pa_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),V_Pa_2) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_Pa_2)),c_Product__Type_OPair(T_b,T_c)))) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_The__split__eq,axiom,
% 191.04/191.65 ! [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) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_divmod__nat__def,axiom,
% 191.04/191.65 ! [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)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_Random__Sequence_Oempty__def,axiom,
% 191.04/191.65 ! [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)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_Random__Sequence_Osingle__def,axiom,
% 191.04/191.65 ! [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)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_the__eq__trivial,axiom,
% 191.04/191.65 ! [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 ).
% 191.04/191.65
% 191.04/191.65 fof(fact_the__sym__eq__trivial,axiom,
% 191.04/191.65 ! [V_x_2,T_b] : c_HOL_OThe(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 191.04/191.65
% 191.04/191.65 fof(fact_Powp__def,axiom,
% 191.04/191.65 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.65 ( hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2))
% 191.04/191.65 <=> ! [B_x] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 191.04/191.65 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_Powp__mono,axiom,
% 191.04/191.65 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.65 => 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))) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_power__dvd__imp__le,axiom,
% 191.04/191.65 ! [V_n,V_m,V_i] :
% 191.04/191.65 ( 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)))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_i))
% 191.04/191.65 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd__mult__cancel2,axiom,
% 191.04/191.65 ! [V_n_2,V_m_2] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 191.04/191.65 => ( 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))
% 191.04/191.65 <=> V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd__mult__cancel1,axiom,
% 191.04/191.65 ! [V_n_2,V_m_2] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 191.04/191.65 => ( 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))
% 191.04/191.65 <=> V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_zdvd__mult__cancel1,axiom,
% 191.04/191.65 ! [V_n_2,V_m_2] :
% 191.04/191.65 ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 191.04/191.65 => ( 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))
% 191.04/191.65 <=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_arith__series__int,axiom,
% 191.04/191.65 ! [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)))) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd_Oorder__refl,axiom,
% 191.04/191.65 ! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd__0__right,axiom,
% 191.04/191.65 ! [V_a,T_a] :
% 191.04/191.65 ( class_Rings_Ocomm__semiring__1(T_a)
% 191.04/191.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd__1__left,axiom,
% 191.04/191.65 ! [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)) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_setsum__abs,axiom,
% 191.04/191.65 ! [V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.65 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 191.04/191.65 => 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))) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_setsum__abs__ge__zero,axiom,
% 191.04/191.65 ! [V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.65 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 191.04/191.65 => 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))) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_zdvd__antisym__abs,axiom,
% 191.04/191.65 ! [V_b,V_a] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a),V_b))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_b),V_a))
% 191.04/191.65 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_a) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_b) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_nat__dvd__1__iff__1,axiom,
% 191.04/191.65 ! [V_m_2] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
% 191.04/191.65 <=> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd__if__abs__eq,axiom,
% 191.04/191.65 ! [V_k,V_l,T_a] :
% 191.04/191.65 ( class_Rings_Olinordered__idom(T_a)
% 191.04/191.65 => ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_l) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k)
% 191.04/191.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_l),V_k)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_abs__dvd__iff,axiom,
% 191.04/191.65 ! [V_k_2,V_m_2,T_b] :
% 191.04/191.65 ( class_Rings_Olinordered__idom(T_b)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_m_2)),V_k_2))
% 191.04/191.65 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd__abs__iff,axiom,
% 191.04/191.65 ! [V_k_2,V_m_2,T_b] :
% 191.04/191.65 ( class_Rings_Olinordered__idom(T_b)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_k_2)))
% 191.04/191.65 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd__power__same,axiom,
% 191.04/191.65 ! [V_n,V_y,V_x,T_a] :
% 191.04/191.65 ( class_Rings_Ocomm__semiring__1(T_a)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
% 191.04/191.65 => 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))) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_one__dvd,axiom,
% 191.04/191.65 ! [V_a,T_a] :
% 191.04/191.65 ( class_Rings_Ocomm__semiring__1(T_a)
% 191.04/191.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd__0__left,axiom,
% 191.04/191.65 ! [V_a,T_a] :
% 191.04/191.65 ( class_Rings_Ocomm__semiring__1(T_a)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 191.04/191.65 => V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd__add,axiom,
% 191.04/191.65 ! [V_c,V_b,V_a,T_a] :
% 191.04/191.65 ( class_Rings_Ocomm__semiring__1(T_a)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
% 191.04/191.65 => 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))) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_lessThan__eq__iff,axiom,
% 191.04/191.65 ! [V_y_2,V_x_2,T_b] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_b)
% 191.04/191.65 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)
% 191.04/191.65 <=> V_x_2 = V_y_2 ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd_Oeq__iff,axiom,
% 191.04/191.65 ! [V_y_2,V_x_2] :
% 191.04/191.65 ( V_x_2 = V_y_2
% 191.04/191.65 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 191.04/191.65 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd_Ole__less,axiom,
% 191.04/191.65 ! [V_y_2,V_x_2] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 191.04/191.65 <=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 191.04/191.65 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) )
% 191.04/191.65 | V_x_2 = V_y_2 ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd_Oless__le,axiom,
% 191.04/191.65 ! [V_y_2,V_x_2] :
% 191.04/191.65 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 191.04/191.65 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) )
% 191.04/191.65 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 191.04/191.65 & V_x_2 != V_y_2 ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd_Oneq__le__trans,axiom,
% 191.04/191.65 ! [V_b,V_a] :
% 191.04/191.65 ( V_a != V_b
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 191.04/191.65 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd_Oeq__refl,axiom,
% 191.04/191.65 ! [V_y,V_x] :
% 191.04/191.65 ( V_x = V_y
% 191.04/191.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd_Oantisym__conv,axiom,
% 191.04/191.65 ! [V_x_2,V_y_2] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 191.04/191.65 <=> V_x_2 = V_y_2 ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd_Ole__imp__less__or__eq,axiom,
% 191.04/191.65 ! [V_y,V_x] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 191.04/191.65 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 191.04/191.65 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 191.04/191.65 | V_x = V_y ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd_Ole__neq__trans,axiom,
% 191.04/191.65 ! [V_b,V_a] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 191.04/191.65 => ( V_a != V_b
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 191.04/191.65 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd_Oord__eq__le__trans,axiom,
% 191.04/191.65 ! [V_c,V_b,V_a] :
% 191.04/191.65 ( V_a = V_b
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))
% 191.04/191.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd_Oord__le__eq__trans,axiom,
% 191.04/191.65 ! [V_c,V_b,V_a] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 191.04/191.65 => ( V_b = V_c
% 191.04/191.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd__antisym,axiom,
% 191.04/191.65 ! [V_n,V_m] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m))
% 191.04/191.65 => V_m = V_n ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd_Oantisym,axiom,
% 191.04/191.65 ! [V_y,V_x] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 191.04/191.65 => V_x = V_y ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd_Oorder__trans,axiom,
% 191.04/191.65 ! [V_z,V_y,V_x] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 191.04/191.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd_Oord__eq__less__trans,axiom,
% 191.04/191.65 ! [V_c,V_b,V_a] :
% 191.04/191.65 ( V_a = V_b
% 191.04/191.65 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))
% 191.04/191.65 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_b)) )
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c))
% 191.04/191.65 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd_Ole__less__trans,axiom,
% 191.04/191.65 ! [V_z,V_y,V_x] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 191.04/191.65 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 191.04/191.65 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y)) )
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
% 191.04/191.65 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd_Oless__imp__neq,axiom,
% 191.04/191.65 ! [V_y,V_x] :
% 191.04/191.65 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 191.04/191.65 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 191.04/191.65 => V_x != V_y ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd_Oless__not__sym,axiom,
% 191.04/191.65 ! [V_y,V_x] :
% 191.04/191.65 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 191.04/191.65 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 191.04/191.65 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 191.04/191.65 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd_Oless__imp__le,axiom,
% 191.04/191.65 ! [V_y,V_x] :
% 191.04/191.65 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 191.04/191.65 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 191.04/191.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd_Oless__imp__not__less,axiom,
% 191.04/191.65 ! [V_y,V_x] :
% 191.04/191.65 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 191.04/191.65 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 191.04/191.65 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 191.04/191.65 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd_Oless__imp__not__eq,axiom,
% 191.04/191.65 ! [V_y,V_x] :
% 191.04/191.65 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 191.04/191.65 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 191.04/191.65 => V_x != V_y ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd_Oless__imp__not__eq2,axiom,
% 191.04/191.65 ! [V_y,V_x] :
% 191.04/191.65 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 191.04/191.65 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 191.04/191.65 => V_y != V_x ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd_Oord__less__eq__trans,axiom,
% 191.04/191.65 ! [V_c,V_b,V_a] :
% 191.04/191.65 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 191.04/191.65 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) )
% 191.04/191.65 => ( V_b = V_c
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c))
% 191.04/191.65 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd_Oless__le__trans,axiom,
% 191.04/191.65 ! [V_z,V_y,V_x] :
% 191.04/191.65 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 191.04/191.65 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
% 191.04/191.65 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd_Oless__asym_H,axiom,
% 191.04/191.65 ! [V_b,V_a] :
% 191.04/191.65 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 191.04/191.65 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) )
% 191.04/191.65 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
% 191.04/191.65 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd_Oless__trans,axiom,
% 191.04/191.65 ! [V_z,V_y,V_x] :
% 191.04/191.65 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 191.04/191.65 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 191.04/191.65 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 191.04/191.65 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y)) )
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
% 191.04/191.65 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd_Oless__asym,axiom,
% 191.04/191.65 ! [V_y,V_x] :
% 191.04/191.65 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 191.04/191.65 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 191.04/191.65 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 191.04/191.65 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd__refl,axiom,
% 191.04/191.65 ! [V_a,T_a] :
% 191.04/191.65 ( class_Rings_Ocomm__semiring__1(T_a)
% 191.04/191.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_a)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd__trans,axiom,
% 191.04/191.65 ! [V_c,V_b,V_a,T_a] :
% 191.04/191.65 ( class_Rings_Ocomm__semiring__1(T_a)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c))
% 191.04/191.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd__mod__imp__dvd,axiom,
% 191.04/191.65 ! [V_n,V_m,V_k,T_a] :
% 191.04/191.65 ( class_Divides_Osemiring__div(T_a)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n)))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))
% 191.04/191.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m)) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd__mod,axiom,
% 191.04/191.65 ! [V_n,V_m,V_k,T_a] :
% 191.04/191.65 ( class_Divides_Osemiring__div(T_a)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))
% 191.04/191.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n))) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_mod__mod__cancel,axiom,
% 191.04/191.65 ! [V_a,V_b,V_c,T_a] :
% 191.04/191.65 ( class_Divides_Osemiring__div(T_a)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
% 191.04/191.65 => 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) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd__mod__iff,axiom,
% 191.04/191.65 ! [V_m_2,V_n_2,V_k_2,T_b] :
% 191.04/191.65 ( class_Divides_Osemiring__div(T_b)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_n_2))
% 191.04/191.65 => ( 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)))
% 191.04/191.65 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_m_2)) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_transfer__int__nat__relations_I4_J,axiom,
% 191.04/191.65 ! [V_y_2,V_x_2] :
% 191.04/191.65 ( 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)))
% 191.04/191.65 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_zdvd__int,axiom,
% 191.04/191.65 ! [V_y_2,V_x_2] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 191.04/191.65 <=> 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))) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd__triv__left,axiom,
% 191.04/191.65 ! [V_b,V_a,T_a] :
% 191.04/191.65 ( class_Rings_Ocomm__semiring__1(T_a)
% 191.04/191.65 => 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))) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd__triv__right,axiom,
% 191.04/191.65 ! [V_b,V_a,T_a] :
% 191.04/191.65 ( class_Rings_Ocomm__semiring__1(T_a)
% 191.04/191.65 => 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))) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd__mult2,axiom,
% 191.04/191.65 ! [V_c,V_b,V_a,T_a] :
% 191.04/191.65 ( class_Rings_Ocomm__semiring__1(T_a)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 191.04/191.65 => 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))) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd__mult,axiom,
% 191.04/191.65 ! [V_b,V_c,V_a,T_a] :
% 191.04/191.65 ( class_Rings_Ocomm__semiring__1(T_a)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
% 191.04/191.65 => 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))) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_mult__dvd__mono,axiom,
% 191.04/191.65 ! [V_d,V_c,V_b,V_a,T_a] :
% 191.04/191.65 ( class_Rings_Ocomm__semiring__1(T_a)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_d))
% 191.04/191.65 => 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))) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvdI,axiom,
% 191.04/191.65 ! [V_k,V_b,V_a,T_a] :
% 191.04/191.65 ( class_Rings_Odvd(T_a)
% 191.04/191.65 => ( V_a = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k)
% 191.04/191.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_a)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd__mult__left,axiom,
% 191.04/191.65 ! [V_c,V_b,V_a,T_a] :
% 191.04/191.65 ( class_Rings_Ocomm__semiring__1(T_a)
% 191.04/191.65 => ( 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))
% 191.04/191.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd__mult__right,axiom,
% 191.04/191.65 ! [V_c,V_b,V_a,T_a] :
% 191.04/191.65 ( class_Rings_Ocomm__semiring__1(T_a)
% 191.04/191.65 => ( 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))
% 191.04/191.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_div__dvd__div,axiom,
% 191.04/191.65 ! [V_ca_2,V_ba_2,V_a_2,T_b] :
% 191.04/191.65 ( class_Divides_Osemiring__div(T_b)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_ba_2))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_ca_2))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_ba_2),V_a_2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_ca_2),V_a_2)))
% 191.04/191.65 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_ba_2),V_ca_2)) ) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_zdvd__zmod__imp__zdvd,axiom,
% 191.04/191.65 ! [V_n,V_m,V_k] :
% 191.04/191.65 ( 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)))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n))
% 191.04/191.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_zdvd__zmod,axiom,
% 191.04/191.65 ! [V_n,V_m,V_f] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),V_m))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),V_n))
% 191.04/191.65 => 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))) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_uminus__dvd__conv_I2_J,axiom,
% 191.04/191.65 ! [V_t_2,V_d_2] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))
% 191.04/191.65 <=> 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))) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_uminus__dvd__conv_I1_J,axiom,
% 191.04/191.65 ! [V_t_2,V_d_2] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))
% 191.04/191.65 <=> 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)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_zdvd__zdiffD,axiom,
% 191.04/191.65 ! [V_n,V_m,V_k] :
% 191.04/191.65 ( 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)))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n))
% 191.04/191.65 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd__reduce,axiom,
% 191.04/191.65 ! [V_n_2,V_k_2] :
% 191.04/191.65 ( 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)))
% 191.04/191.65 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_n_2)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_of__nat__setsum,axiom,
% 191.04/191.65 ! [V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.65 ( class_Rings_Osemiring__1(T_b)
% 191.04/191.65 => 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) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd__minus__iff,axiom,
% 191.04/191.65 ! [V_y_2,V_x_2,T_b] :
% 191.04/191.65 ( class_Rings_Ocomm__ring__1(T_b)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)))
% 191.04/191.65 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_minus__dvd__iff,axiom,
% 191.04/191.65 ! [V_y_2,V_x_2,T_b] :
% 191.04/191.65 ( class_Rings_Ocomm__ring__1(T_b)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),V_y_2))
% 191.04/191.65 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd__diff,axiom,
% 191.04/191.65 ! [V_z,V_y,V_x,T_a] :
% 191.04/191.65 ( class_Rings_Ocomm__ring__1(T_a)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_z))
% 191.04/191.65 => 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))) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_setsum__lessThan__Suc,axiom,
% 191.04/191.65 ! [V_n_2,V_f_2,T_b] :
% 191.04/191.65 ( class_Groups_Ocomm__monoid__add(T_b)
% 191.04/191.65 => 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)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_of__int__setsum,axiom,
% 191.04/191.65 ! [V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.65 ( class_Rings_Oring__1(T_b)
% 191.04/191.65 => 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) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd__diff__nat,axiom,
% 191.04/191.65 ! [V_n,V_m,V_k] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
% 191.04/191.65 => 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))) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_setsum__commute,axiom,
% 191.04/191.65 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 191.04/191.65 ( class_Groups_Ocomm__monoid__add(T_b)
% 191.04/191.65 => 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) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_setsum__0,axiom,
% 191.04/191.65 ! [V_A_2,T_c,T_b] :
% 191.04/191.65 ( class_Groups_Ocomm__monoid__add(T_b)
% 191.04/191.65 => 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) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_setsum__addf,axiom,
% 191.04/191.65 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 191.04/191.65 ( class_Groups_Ocomm__monoid__add(T_b)
% 191.04/191.65 => 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)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_setsum__right__distrib,axiom,
% 191.04/191.65 ! [V_A_2,V_f_2,T_c,V_r_2,T_b] :
% 191.04/191.65 ( class_Rings_Osemiring__0(T_b)
% 191.04/191.65 => 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) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_setsum__left__distrib,axiom,
% 191.04/191.65 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.65 ( class_Rings_Osemiring__0(T_b)
% 191.04/191.65 => 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) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_setsum__product,axiom,
% 191.04/191.65 ! [V_B_2,V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.65 ( class_Rings_Osemiring__0(T_b)
% 191.04/191.65 => 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) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_setsum__subtractf,axiom,
% 191.04/191.65 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 191.04/191.65 ( class_Groups_Oab__group__add(T_b)
% 191.04/191.65 => 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)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_setsum__negf,axiom,
% 191.04/191.65 ! [V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.65 ( class_Groups_Oab__group__add(T_b)
% 191.04/191.65 => 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)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_setsum__divide__distrib,axiom,
% 191.04/191.65 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.65 ( class_Fields_Ofield(T_b)
% 191.04/191.65 => 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) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_abs__setsum__abs,axiom,
% 191.04/191.65 ! [V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.65 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 191.04/191.65 => 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) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_transfer__nat__int__relations_I4_J,axiom,
% 191.04/191.65 ! [V_y_2,V_x_2] :
% 191.04/191.65 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 191.04/191.65 => ( 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)))
% 191.04/191.65 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_int__dvd__iff,axiom,
% 191.04/191.65 ! [V_z_2,V_m_2] :
% 191.04/191.65 ( 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))
% 191.04/191.65 <=> 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)))) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd__int__iff,axiom,
% 191.04/191.65 ! [V_m_2,V_z_2] :
% 191.04/191.65 ( 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)))
% 191.04/191.65 <=> 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)) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_lessThan__subset__iff,axiom,
% 191.04/191.65 ! [V_y_2,V_x_2,T_b] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_b)
% 191.04/191.65 => ( 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)))
% 191.04/191.65 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd__mult__cancel__left,axiom,
% 191.04/191.65 ! [V_ba_2,V_a_2,V_ca_2,T_b] :
% 191.04/191.65 ( class_Rings_Oidom(T_b)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_ba_2)))
% 191.04/191.65 <=> ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
% 191.04/191.65 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_ba_2)) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd__mult__cancel__right,axiom,
% 191.04/191.65 ! [V_ba_2,V_ca_2,V_a_2,T_b] :
% 191.04/191.65 ( class_Rings_Oidom(T_b)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ba_2),V_ca_2)))
% 191.04/191.65 <=> ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
% 191.04/191.65 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_ba_2)) ) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd__imp__mod__0,axiom,
% 191.04/191.65 ! [V_b,V_a,T_a] :
% 191.04/191.65 ( class_Divides_Osemiring__div(T_a)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 191.04/191.65 => c_Divides_Odiv__class_Omod(T_a,V_b,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_dvd__eq__mod__eq__0,axiom,
% 191.04/191.65 ! [V_ba_2,V_a_2,T_b] :
% 191.04/191.65 ( class_Divides_Osemiring__div(T_b)
% 191.04/191.65 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_ba_2))
% 191.04/191.65 <=> c_Divides_Odiv__class_Omod(T_b,V_ba_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 191.04/191.65
% 191.04/191.65 fof(fact_lessThan__strict__subset__iff,axiom,
% 191.04/191.65 ! [V_n_2,V_m_2,T_b] :
% 191.04/191.65 ( class_Orderings_Olinorder(T_b)
% 191.04/191.66 => ( 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)))
% 191.04/191.66 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_n_2)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_div__add,axiom,
% 191.04/191.66 ! [V_y,V_x,V_z,T_a] :
% 191.04/191.66 ( class_Divides_Osemiring__div(T_a)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_x))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_y))
% 191.04/191.66 => 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)) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_dvd__mult__div__cancel,axiom,
% 191.04/191.66 ! [V_b,V_a,T_a] :
% 191.04/191.66 ( class_Divides_Osemiring__div(T_a)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 191.04/191.66 => 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 ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_div__mult__swap,axiom,
% 191.04/191.66 ! [V_a,V_b,V_c,T_a] :
% 191.04/191.66 ( class_Divides_Osemiring__div(T_a)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
% 191.04/191.66 => 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) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_dvd__div__mult__self,axiom,
% 191.04/191.66 ! [V_b,V_a,T_a] :
% 191.04/191.66 ( class_Divides_Osemiring__div(T_a)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 191.04/191.66 => 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 ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_dvd__div__mult,axiom,
% 191.04/191.66 ! [V_c,V_b,V_a,T_a] :
% 191.04/191.66 ( class_Divides_Osemiring__div(T_a)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 191.04/191.66 => 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) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_div__mult__div__if__dvd,axiom,
% 191.04/191.66 ! [V_w,V_z,V_x,V_y,T_a] :
% 191.04/191.66 ( class_Divides_Osemiring__div(T_a)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_w))
% 191.04/191.66 => 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)) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_dvd__div__neg,axiom,
% 191.04/191.66 ! [V_x,V_y,T_a] :
% 191.04/191.66 ( class_Divides_Oring__div(T_a)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 191.04/191.66 => 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)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_dvd__neg__div,axiom,
% 191.04/191.66 ! [V_x,V_y,T_a] :
% 191.04/191.66 ( class_Divides_Oring__div(T_a)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 191.04/191.66 => 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)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_power__le__dvd,axiom,
% 191.04/191.66 ! [V_m,V_b,V_n,V_a,T_a] :
% 191.04/191.66 ( class_Rings_Ocomm__semiring__1(T_a)
% 191.04/191.66 => ( 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))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 191.04/191.66 => 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)) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_dvd__power__le,axiom,
% 191.04/191.66 ! [V_m,V_n,V_y,V_x,T_a] :
% 191.04/191.66 ( class_Rings_Ocomm__semiring__1(T_a)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 191.04/191.66 => 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))) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_le__imp__power__dvd,axiom,
% 191.04/191.66 ! [V_a,V_n,V_m,T_a] :
% 191.04/191.66 ( class_Rings_Ocomm__semiring__1(T_a)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 191.04/191.66 => 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))) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_div__power,axiom,
% 191.04/191.66 ! [V_n,V_x,V_y,T_a] :
% 191.04/191.66 ( class_Divides_Osemiring__div(T_a)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 191.04/191.66 => 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)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_zdvd__antisym__nonneg,axiom,
% 191.04/191.66 ! [V_n,V_m] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_n))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m))
% 191.04/191.66 => V_m = V_n ) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_zdvd__not__zless,axiom,
% 191.04/191.66 ! [V_n,V_m] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_m),V_n))
% 191.04/191.66 => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_zdvd__mono,axiom,
% 191.04/191.66 ! [V_t_2,V_m_2,V_k_2] :
% 191.04/191.66 ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m_2),V_t_2))
% 191.04/191.66 <=> 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))) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_zdvd__mult__cancel,axiom,
% 191.04/191.66 ! [V_n,V_m,V_k] :
% 191.04/191.66 ( 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)))
% 191.04/191.66 => ( V_k != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 191.04/191.66 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_zdvd__reduce,axiom,
% 191.04/191.66 ! [V_m_2,V_n_2,V_k_2] :
% 191.04/191.66 ( 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))))
% 191.04/191.66 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),V_n_2)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_zdvd__period,axiom,
% 191.04/191.66 ! [V_ca_2,V_t_2,V_x_2,V_d_2,V_a_2] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),V_d_2))
% 191.04/191.66 => ( 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)))
% 191.04/191.66 <=> 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_ca_2),V_d_2))),V_t_2))) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_dvd__1__iff__1,axiom,
% 191.04/191.66 ! [V_m_2] :
% 191.04/191.66 ( 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))))
% 191.04/191.66 <=> V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_nat__dvd__not__less,axiom,
% 191.04/191.66 ! [V_n,V_m] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 191.04/191.66 => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_nat__mult__dvd__cancel__disj,axiom,
% 191.04/191.66 ! [V_n_2,V_m_2,V_k_2] :
% 191.04/191.66 ( 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)))
% 191.04/191.66 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 191.04/191.66 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_zdvd__mult__div__cancel,axiom,
% 191.04/191.66 ! [V_m,V_n] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m))
% 191.04/191.66 => 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 ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_zmod__eq__dvd__iff,axiom,
% 191.04/191.66 ! [V_y_2,V_n_2,V_x_2] :
% 191.04/191.66 ( 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)
% 191.04/191.66 <=> 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))) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_dvd__diffD1,axiom,
% 191.04/191.66 ! [V_n,V_m,V_k] :
% 191.04/191.66 ( 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)))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 191.04/191.66 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_dvd__diffD,axiom,
% 191.04/191.66 ! [V_n,V_m,V_k] :
% 191.04/191.66 ( 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)))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 191.04/191.66 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_zdvd1__eq,axiom,
% 191.04/191.66 ! [V_x_2] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_x_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))
% 191.04/191.66 <=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_abs__div,axiom,
% 191.04/191.66 ! [V_x,V_y] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_y),V_x))
% 191.04/191.66 => 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)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_nat__dvd__iff,axiom,
% 191.04/191.66 ! [V_m_2,V_z_2] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),V_m_2))
% 191.04/191.66 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 191.04/191.66 => 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))) )
% 191.04/191.66 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 191.04/191.66 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_arith__series__general,axiom,
% 191.04/191.66 ! [V_n_2,V_d_2,V_a_2,T_b] :
% 191.04/191.66 ( class_Rings_Ocomm__semiring__1(T_b)
% 191.04/191.66 => 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)))) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_unity__coeff__ex,axiom,
% 191.04/191.66 ! [V_l_2,V_Pa_2,T_b] :
% 191.04/191.66 ( ( class_Rings_Odvd(T_b)
% 191.04/191.66 & class_Rings_Osemiring__0(T_b) )
% 191.04/191.66 => ( ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x)))
% 191.04/191.66 <=> ? [B_x] :
% 191.04/191.66 ( 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))))
% 191.04/191.66 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_inf__period_I3_J,axiom,
% 191.04/191.66 ! [V_t_2,V_D_2,V_d_2,T_b] :
% 191.04/191.66 ( ( class_Rings_Ocomm__ring(T_b)
% 191.04/191.66 & class_Rings_Odvd(T_b) )
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
% 191.04/191.66 => ! [B_x,B_k] :
% 191.04/191.66 ( 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)))
% 191.04/191.66 <=> 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))) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_inf__period_I4_J,axiom,
% 191.04/191.66 ! [V_t_2,V_D_2,V_d_2,T_b] :
% 191.04/191.66 ( ( class_Rings_Ocomm__ring(T_b)
% 191.04/191.66 & class_Rings_Odvd(T_b) )
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
% 191.04/191.66 => ! [B_x,B_k] :
% 191.04/191.66 ( 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)))
% 191.04/191.66 <=> 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))) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_dvd__eq__mod__eq__0__number__of,axiom,
% 191.04/191.66 ! [V_y_2,V_x_2,T_b] :
% 191.04/191.66 ( ( class_Divides_Osemiring__div(T_b)
% 191.04/191.66 & class_Int_Onumber(T_b) )
% 191.04/191.66 => ( 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)))
% 191.04/191.66 <=> 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) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_dvd__div__div__eq__mult,axiom,
% 191.04/191.66 ! [V_d_2,V_ba_2,V_ca_2,V_a_2,T_b] :
% 191.04/191.66 ( class_Divides_Osemiring__div(T_b)
% 191.04/191.66 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
% 191.04/191.66 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_ba_2))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_ca_2),V_d_2))
% 191.04/191.66 => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_ba_2),V_a_2) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_d_2),V_ca_2)
% 191.04/191.66 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ba_2),V_ca_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2) ) ) ) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_dvd__div__eq__mult,axiom,
% 191.04/191.66 ! [V_ca_2,V_ba_2,V_a_2,T_b] :
% 191.04/191.66 ( class_Divides_Osemiring__div(T_b)
% 191.04/191.66 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_ba_2))
% 191.04/191.66 => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_ba_2),V_a_2) = V_ca_2
% 191.04/191.66 <=> V_ba_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2) ) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_zdvd__imp__le,axiom,
% 191.04/191.66 ! [V_n,V_z] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z),V_n))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_n))
% 191.04/191.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_n)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_zdvd__iff__zmod__eq__0__number__of,axiom,
% 191.04/191.66 ! [V_y_2,V_x_2] :
% 191.04/191.66 ( 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)))
% 191.04/191.66 <=> 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) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_dvd__imp__le,axiom,
% 191.04/191.66 ! [V_n,V_k] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 191.04/191.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_dvd__mult__cancel,axiom,
% 191.04/191.66 ! [V_n,V_m,V_k] :
% 191.04/191.66 ( 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)))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 191.04/191.66 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_nat__mult__dvd__cancel1,axiom,
% 191.04/191.66 ! [V_n_2,V_m_2,V_k_2] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 191.04/191.66 => ( 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)))
% 191.04/191.66 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_dvd__imp__le__int,axiom,
% 191.04/191.66 ! [V_d,V_i] :
% 191.04/191.66 ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d),V_i))
% 191.04/191.66 => 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))) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_dvd__power,axiom,
% 191.04/191.66 ! [V_x,V_n,T_a] :
% 191.04/191.66 ( class_Rings_Ocomm__semiring__1(T_a)
% 191.04/191.66 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 191.04/191.66 | V_x = c_Groups_Oone__class_Oone(T_a) )
% 191.04/191.66 => 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))) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_dvd_Ostrict__monoD,axiom,
% 191.04/191.66 ! [V_y_2,V_x_2,V_f_2,T_b] :
% 191.04/191.66 ( class_Orderings_Oorder(T_b)
% 191.04/191.66 => ( 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)
% 191.04/191.66 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 191.04/191.66 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) )
% 191.04/191.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_arith__series__nat,axiom,
% 191.04/191.66 ! [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)))) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_dvd_OmonoD,axiom,
% 191.04/191.66 ! [V_y_2,V_x_2,V_f_2,T_b] :
% 191.04/191.66 ( class_Orderings_Oorder(T_b)
% 191.04/191.66 => ( c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 191.04/191.66 => 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))) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_setsum__natinterval__difff,axiom,
% 191.04/191.66 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 191.04/191.66 ( class_Groups_Oab__group__add(T_b)
% 191.04/191.66 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 191.04/191.66 => 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)))) )
% 191.04/191.66 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 191.04/191.66 => 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) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_gauss__sum,axiom,
% 191.04/191.66 ! [V_n_2,T_b] :
% 191.04/191.66 ( class_Rings_Ocomm__semiring__1(T_b)
% 191.04/191.66 => 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))) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_setsum__shift__lb__Suc0__0,axiom,
% 191.04/191.66 ! [V_k_2,V_f_2] :
% 191.04/191.66 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 191.04/191.66 => 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)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_dvd_Ostrict__mono__mono,axiom,
% 191.04/191.66 ! [V_f_2,T_b] :
% 191.04/191.66 ( class_Orderings_Oorder(T_b)
% 191.04/191.66 => ( 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)
% 191.04/191.66 => c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_atLeastatMost__subset__iff,axiom,
% 191.04/191.66 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] :
% 191.04/191.66 ( class_Orderings_Oorder(T_b)
% 191.04/191.66 => ( 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_ba_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2)))
% 191.04/191.66 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2))
% 191.04/191.66 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2))
% 191.04/191.66 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),V_d_2)) ) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom,
% 191.04/191.66 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 191.04/191.66 ( class_Groups_Ocomm__monoid__add(T_b)
% 191.04/191.66 => 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)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom,
% 191.04/191.66 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
% 191.04/191.66 ( class_Groups_Ocomm__monoid__add(T_b)
% 191.04/191.66 => 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)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_int__setsum,axiom,
% 191.04/191.66 ! [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) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom,
% 191.04/191.66 ! [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)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_atLeastatMost__psubset__iff,axiom,
% 191.04/191.66 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] :
% 191.04/191.66 ( class_Orderings_Oorder(T_b)
% 191.04/191.66 => ( 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_ba_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2)))
% 191.04/191.66 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2))
% 191.04/191.66 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2))
% 191.04/191.66 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),V_d_2))
% 191.04/191.66 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_a_2))
% 191.04/191.66 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),V_d_2)) ) ) )
% 191.04/191.66 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_d_2)) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_setsum__head__Suc,axiom,
% 191.04/191.66 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 191.04/191.66 ( class_Groups_Ocomm__monoid__add(T_b)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 191.04/191.66 => 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))) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_setsum__cl__ivl__Suc,axiom,
% 191.04/191.66 ! [V_f_2,V_m_2,V_n_2,T_b] :
% 191.04/191.66 ( class_Groups_Ocomm__monoid__add(T_b)
% 191.04/191.66 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 191.04/191.66 => 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) )
% 191.04/191.66 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 191.04/191.66 => 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))) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_setsum__ub__add__nat,axiom,
% 191.04/191.66 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_b] :
% 191.04/191.66 ( class_Groups_Ocomm__monoid__add(T_b)
% 191.04/191.66 => ( 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))))
% 191.04/191.66 => 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)))) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_all__nat__less,axiom,
% 191.04/191.66 ! [V_Pa_2,V_n_2] :
% 191.04/191.66 ( ! [B_m] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 191.04/191.66 => hBOOL(hAPP(V_Pa_2,B_m)) )
% 191.04/191.66 <=> ! [B_x] :
% 191.04/191.66 ( 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)))
% 191.04/191.66 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_ex__nat__less,axiom,
% 191.04/191.66 ! [V_Pa_2,V_n_2] :
% 191.04/191.66 ( ? [B_m] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 191.04/191.66 & hBOOL(hAPP(V_Pa_2,B_m)) )
% 191.04/191.66 <=> ? [B_x] :
% 191.04/191.66 ( 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)))
% 191.04/191.66 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_sum__diff__distrib,axiom,
% 191.04/191.66 ! [V_n_2,V_Pa_2,V_Q_2] :
% 191.04/191.66 ( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_Q_2,B_x)),hAPP(V_Pa_2,B_x)))
% 191.04/191.66 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_Pa_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_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_Pa_2)),V_Q_2)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_geometric__sum,axiom,
% 191.04/191.66 ! [V_n_2,V_x_2,T_b] :
% 191.04/191.66 ( class_Fields_Ofield(T_b)
% 191.04/191.66 => ( V_x_2 != c_Groups_Oone__class_Oone(T_b)
% 191.04/191.66 => 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))) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_ex__nat__less__eq,axiom,
% 191.04/191.66 ! [V_Pa_2,V_n_2] :
% 191.04/191.66 ( ? [B_m] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 191.04/191.66 & hBOOL(hAPP(V_Pa_2,B_m)) )
% 191.04/191.66 <=> ? [B_x] :
% 191.04/191.66 ( 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)))
% 191.04/191.66 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_all__nat__less__eq,axiom,
% 191.04/191.66 ! [V_Pa_2,V_n_2] :
% 191.04/191.66 ( ! [B_m] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 191.04/191.66 => hBOOL(hAPP(V_Pa_2,B_m)) )
% 191.04/191.66 <=> ! [B_x] :
% 191.04/191.66 ( 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)))
% 191.04/191.66 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_atLeastLessThan__inj_I2_J,axiom,
% 191.04/191.66 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] :
% 191.04/191.66 ( class_Orderings_Olinorder(T_b)
% 191.04/191.66 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_ba_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2))
% 191.04/191.66 => V_ba_2 = V_d_2 ) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_atLeastLessThan__inj_I1_J,axiom,
% 191.04/191.66 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] :
% 191.04/191.66 ( class_Orderings_Olinorder(T_b)
% 191.04/191.66 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_ba_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2))
% 191.04/191.66 => V_a_2 = V_ca_2 ) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_atLeastLessThan__eq__iff,axiom,
% 191.04/191.66 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] :
% 191.04/191.66 ( class_Orderings_Olinorder(T_b)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2))
% 191.04/191.66 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_ba_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)
% 191.04/191.66 <=> ( V_a_2 = V_ca_2
% 191.04/191.66 & V_ba_2 = V_d_2 ) ) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
% 191.04/191.66 ! [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) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_atLeast0LessThan,axiom,
% 191.04/191.66 ! [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) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_atLeastLessThan__subset__iff,axiom,
% 191.04/191.66 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] :
% 191.04/191.66 ( class_Orderings_Olinorder(T_b)
% 191.04/191.66 => ( 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_ba_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),V_a_2))
% 191.04/191.66 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2))
% 191.04/191.66 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),V_d_2)) ) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
% 191.04/191.66 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 191.04/191.66 ( class_Groups_Ocomm__monoid__add(T_b)
% 191.04/191.66 => 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)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_setsum__shift__bounds__nat__ivl,axiom,
% 191.04/191.66 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
% 191.04/191.66 ( class_Groups_Ocomm__monoid__add(T_b)
% 191.04/191.66 => 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)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_ivl__diff,axiom,
% 191.04/191.66 ! [V_m_2,V_n_2,V_i_2,T_b] :
% 191.04/191.66 ( class_Orderings_Olinorder(T_b)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_n_2))
% 191.04/191.66 => 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) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_setsum__add__nat__ivl,axiom,
% 191.04/191.66 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
% 191.04/191.66 ( class_Groups_Ocomm__monoid__add(T_b)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 191.04/191.66 => 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)) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_setsum__diff__nat__ivl,axiom,
% 191.04/191.66 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
% 191.04/191.66 ( class_Groups_Oab__group__add(T_b)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 191.04/191.66 => 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)) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
% 191.04/191.66 ! [V_k_2,V_f_2,T_b] :
% 191.04/191.66 ( class_Groups_Ocomm__monoid__add(T_b)
% 191.04/191.66 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_b)
% 191.04/191.66 => 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)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_setsum__head__upt__Suc,axiom,
% 191.04/191.66 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 191.04/191.66 ( class_Groups_Ocomm__monoid__add(T_b)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 191.04/191.66 => 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))) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_setsum__op__ivl__Suc,axiom,
% 191.04/191.66 ! [V_f_2,V_m_2,V_n_2,T_b] :
% 191.04/191.66 ( class_Groups_Ocomm__monoid__add(T_b)
% 191.04/191.66 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 191.04/191.66 => 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) )
% 191.04/191.66 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 191.04/191.66 => 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)) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_bset_I6_J,axiom,
% 191.04/191.66 ! [V_t_2,V_B_2,V_D_2] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 191.04/191.66 => ! [B_x] :
% 191.04/191.66 ( ! [B_xa] :
% 191.04/191.66 ( 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)))
% 191.04/191.66 => ! [B_xb] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 191.04/191.66 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 191.04/191.66 => 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)) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_aset_I8_J,axiom,
% 191.04/191.66 ! [V_t_2,V_A_2,V_D_2] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 191.04/191.66 => ! [B_x] :
% 191.04/191.66 ( ! [B_xa] :
% 191.04/191.66 ( 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)))
% 191.04/191.66 => ! [B_xb] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 191.04/191.66 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 191.04/191.66 => 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))) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_periodic__finite__ex,axiom,
% 191.04/191.66 ! [V_Pa_2,V_d_2] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 191.04/191.66 => ( ! [B_x,B_k] :
% 191.04/191.66 ( hBOOL(hAPP(V_Pa_2,B_x))
% 191.04/191.66 <=> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B_k),V_d_2)))) )
% 191.04/191.66 => ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 191.04/191.66 <=> ? [B_x] :
% 191.04/191.66 ( 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)))
% 191.04/191.66 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_aset_I7_J,axiom,
% 191.04/191.66 ! [V_t_2,V_A_2,V_D_2] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 191.04/191.66 => ! [B_x] :
% 191.04/191.66 ( ! [B_xa] :
% 191.04/191.66 ( 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)))
% 191.04/191.66 => ! [B_xb] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 191.04/191.66 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 191.04/191.66 => 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))) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 191.04/191.66 ! [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) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_bset_I5_J,axiom,
% 191.04/191.66 ! [V_t_2,V_B_2,V_D_2] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 191.04/191.66 => ! [B_x] :
% 191.04/191.66 ( ! [B_xa] :
% 191.04/191.66 ( 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)))
% 191.04/191.66 => ! [B_xb] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 191.04/191.66 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 191.04/191.66 => 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)) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_aset_I10_J,axiom,
% 191.04/191.66 ! [V_t_2,V_A_2,V_D_2,V_d_2] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2))
% 191.04/191.66 => ! [B_x] :
% 191.04/191.66 ( ! [B_xa] :
% 191.04/191.66 ( 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)))
% 191.04/191.66 => ! [B_xb] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 191.04/191.66 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 191.04/191.66 => ( ~ 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)))
% 191.04/191.66 => ~ 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))) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_bset_I10_J,axiom,
% 191.04/191.66 ! [V_t_2,V_B_2,V_D_2,V_d_2] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2))
% 191.04/191.66 => ! [B_x] :
% 191.04/191.66 ( ! [B_xa] :
% 191.04/191.66 ( 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)))
% 191.04/191.66 => ! [B_xb] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 191.04/191.66 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 191.04/191.66 => ( ~ 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)))
% 191.04/191.66 => ~ 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))) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_aset_I9_J,axiom,
% 191.04/191.66 ! [V_t_2,V_A_2,V_D_2,V_d_2] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2))
% 191.04/191.66 => ! [B_x] :
% 191.04/191.66 ( ! [B_xa] :
% 191.04/191.66 ( 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)))
% 191.04/191.66 => ! [B_xb] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 191.04/191.66 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 191.04/191.66 => ( 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)))
% 191.04/191.66 => 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))) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_bset_I9_J,axiom,
% 191.04/191.66 ! [V_t_2,V_B_2,V_D_2,V_d_2] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2))
% 191.04/191.66 => ! [B_x] :
% 191.04/191.66 ( ! [B_xa] :
% 191.04/191.66 ( 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)))
% 191.04/191.66 => ! [B_xb] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 191.04/191.66 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 191.04/191.66 => ( 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)))
% 191.04/191.66 => 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))) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_image__atLeastZeroLessThan__int,axiom,
% 191.04/191.66 ! [V_u_2] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))
% 191.04/191.66 => 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))) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_setsum__head,axiom,
% 191.04/191.66 ! [V_Pa_2,V_n_2,V_m_2,T_b] :
% 191.04/191.66 ( class_Groups_Ocomm__monoid__add(T_b)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 191.04/191.66 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_Pa_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_Pa_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_Pa_2),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_m_2,V_n_2))) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_dvd_Ostrict__monoI,axiom,
% 191.04/191.66 ! [V_f_2,T_b] :
% 191.04/191.66 ( class_Orderings_Oorder(T_b)
% 191.04/191.66 => ( ! [B_x,B_y] :
% 191.04/191.66 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_x),B_y))
% 191.04/191.66 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_y),B_x)) )
% 191.04/191.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),hAPP(V_f_2,B_y))) )
% 191.04/191.66 => 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) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_image__uminus__atLeastLessThan,axiom,
% 191.04/191.66 ! [V_y_2,V_x_2,T_b] :
% 191.04/191.66 ( class_Groups_Oordered__ab__group__add(T_b)
% 191.04/191.66 => 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)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_image__uminus__greaterThanAtMost,axiom,
% 191.04/191.66 ! [V_y_2,V_x_2,T_b] :
% 191.04/191.66 ( class_Groups_Oordered__ab__group__add(T_b)
% 191.04/191.66 => 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)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_subset__image__iff,axiom,
% 191.04/191.66 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
% 191.04/191.66 ( 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)))
% 191.04/191.66 <=> ? [B_AA] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2))
% 191.04/191.66 & V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_image__mono,axiom,
% 191.04/191.66 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.66 => 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))) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_transfer__nat__int__set__relations_I5_J,axiom,
% 191.04/191.66 ! [V_B_2,V_A_2] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.66 <=> 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))) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_image__image,axiom,
% 191.04/191.66 ! [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) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_transfer__nat__int__set__relations_I4_J,axiom,
% 191.04/191.66 ! [V_B_2,V_A_2] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.66 <=> 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))) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_transfer__nat__int__set__relations_I3_J,axiom,
% 191.04/191.66 ! [V_B_2,V_A_2] :
% 191.04/191.66 ( V_A_2 = V_B_2
% 191.04/191.66 <=> 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) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_image__diff__subset,axiom,
% 191.04/191.66 ! [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)))) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_image__uminus__atLeastAtMost,axiom,
% 191.04/191.66 ! [V_y_2,V_x_2,T_b] :
% 191.04/191.66 ( class_Groups_Oordered__ab__group__add(T_b)
% 191.04/191.66 => 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)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom,
% 191.04/191.66 ! [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) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom,
% 191.04/191.66 ! [V_A_2,V_f_2,T_b] :
% 191.04/191.66 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 191.04/191.66 & class_Groups_Ocomm__monoid__mult(T_b) )
% 191.04/191.66 => 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)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom,
% 191.04/191.66 ! [V_n_2,V_m_2] :
% 191.04/191.66 ( c_Nat__Transfer_Ois__nat(V_m_2)
% 191.04/191.66 => ( c_Nat__Transfer_Ois__nat(V_n_2)
% 191.04/191.66 => 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))) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_setsum__SucD,axiom,
% 191.04/191.66 ! [V_n_2,V_A_2,V_f_2,T_b] :
% 191.04/191.66 ( 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)
% 191.04/191.66 => ? [B_x] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.04/191.66 & 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))) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_setsum__ivl__cong,axiom,
% 191.04/191.66 ! [V_g_2,V_f_2,V_d_2,V_ba_2,V_ca_2,V_a_2,T_b,T_c] :
% 191.04/191.66 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 191.04/191.66 & class_Orderings_Oord(T_b) )
% 191.04/191.66 => ( V_a_2 = V_ca_2
% 191.04/191.66 => ( V_ba_2 = V_d_2
% 191.04/191.66 => ( ! [B_x] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),B_x))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2))
% 191.04/191.66 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) )
% 191.04/191.66 => 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_ba_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)) ) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_card__atLeastAtMost__int,axiom,
% 191.04/191.66 ! [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))) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_image__uminus__lessThan,axiom,
% 191.04/191.66 ! [V_x_2,T_b] :
% 191.04/191.66 ( class_Groups_Oordered__ab__group__add(T_b)
% 191.04/191.66 => 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)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_card__greaterThanAtMost__int,axiom,
% 191.04/191.66 ! [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)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_greaterThan__eq__iff,axiom,
% 191.04/191.66 ! [V_y_2,V_x_2,T_b] :
% 191.04/191.66 ( class_Orderings_Olinorder(T_b)
% 191.04/191.66 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)
% 191.04/191.66 <=> V_x_2 = V_y_2 ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_image__Suc__atLeastLessThan,axiom,
% 191.04/191.66 ! [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)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_image__Suc__atLeastAtMost,axiom,
% 191.04/191.66 ! [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)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_image__add__atLeastLessThan,axiom,
% 191.04/191.66 ! [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)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_image__add__atLeastAtMost,axiom,
% 191.04/191.66 ! [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)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_card__eq__setsum,axiom,
% 191.04/191.66 ! [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) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_transfer__int__nat__set__return__embed,axiom,
% 191.04/191.66 ! [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 ).
% 191.04/191.66
% 191.04/191.66 fof(fact_greaterThan__subset__iff,axiom,
% 191.04/191.66 ! [V_y_2,V_x_2,T_b] :
% 191.04/191.66 ( class_Orderings_Olinorder(T_b)
% 191.04/191.66 => ( 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)))
% 191.04/191.66 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_setsum__constant,axiom,
% 191.04/191.66 ! [V_A_2,V_y_2,T_c,T_b] :
% 191.04/191.66 ( class_Rings_Osemiring__1(T_b)
% 191.04/191.66 => 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) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_card__atLeastZeroLessThan__int,axiom,
% 191.04/191.66 ! [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) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_card__atLeastLessThan__int,axiom,
% 191.04/191.66 ! [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)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom,
% 191.04/191.66 ! [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))) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 191.04/191.66 ! [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) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_image__add__int__atLeastLessThan,axiom,
% 191.04/191.66 ! [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) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_image__uminus__greaterThan,axiom,
% 191.04/191.66 ! [V_x_2,T_b] :
% 191.04/191.66 ( class_Groups_Oordered__ab__group__add(T_b)
% 191.04/191.66 => 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)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_card__greaterThanLessThan__int,axiom,
% 191.04/191.66 ! [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)))) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom,
% 191.04/191.66 ! [V_f_2,V_A_2,T_b] :
% 191.04/191.66 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 191.04/191.66 & class_Groups_Ocomm__monoid__mult(T_b) )
% 191.04/191.66 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 191.04/191.66 => 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)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_transfer__int__nat__set__relations_I4_J,axiom,
% 191.04/191.66 ! [V_B_2,V_A_2] :
% 191.04/191.66 ( c_Nat__Transfer_Onat__set(V_A_2)
% 191.04/191.66 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.66 <=> 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))) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_transfer__int__nat__set__relations_I5_J,axiom,
% 191.04/191.66 ! [V_B_2,V_A_2] :
% 191.04/191.66 ( c_Nat__Transfer_Onat__set(V_A_2)
% 191.04/191.66 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.66 <=> 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))) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom,
% 191.04/191.66 ! [V_A_2] :
% 191.04/191.66 ( c_Nat__Transfer_Onat__set(V_A_2)
% 191.04/191.66 => 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)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_card__lessThan,axiom,
% 191.04/191.66 ! [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 ).
% 191.04/191.66
% 191.04/191.66 fof(fact_transfer__int__nat__set__relations_I3_J,axiom,
% 191.04/191.66 ! [V_B_2,V_A_2] :
% 191.04/191.66 ( c_Nat__Transfer_Onat__set(V_A_2)
% 191.04/191.66 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 191.04/191.66 => ( V_A_2 = V_B_2
% 191.04/191.66 <=> 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) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_card__atLeastLessThan,axiom,
% 191.04/191.66 ! [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) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_card__greaterThanAtMost,axiom,
% 191.04/191.66 ! [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) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_nat__set__def,axiom,
% 191.04/191.66 ! [V_S_2] :
% 191.04/191.66 ( c_Nat__Transfer_Onat__set(V_S_2)
% 191.04/191.66 <=> ! [B_x] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2))
% 191.04/191.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_image__uminus__greaterThanLessThan,axiom,
% 191.04/191.66 ! [V_y_2,V_x_2,T_b] :
% 191.04/191.66 ( class_Groups_Oordered__ab__group__add(T_b)
% 191.04/191.66 => 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)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom,
% 191.04/191.66 ! [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)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom,
% 191.04/191.66 ! [V_y_2,V_x_2] :
% 191.04/191.66 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 191.04/191.66 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_card__atLeastAtMost,axiom,
% 191.04/191.66 ! [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) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
% 191.04/191.66 ! [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)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_subset__card__intvl__is__intvl,axiom,
% 191.04/191.66 ! [V_k_2,V_A_2] :
% 191.04/191.66 ( 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)))))
% 191.04/191.66 => 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))) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom,
% 191.04/191.66 ! [V_y_2,V_x_2] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 191.04/191.66 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_transfer__nat__int__set__return__embed,axiom,
% 191.04/191.66 ! [V_A_2] :
% 191.04/191.66 ( c_Nat__Transfer_Onat__set(V_A_2)
% 191.04/191.66 => 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 ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 191.04/191.66 ! [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) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom,
% 191.04/191.66 ! [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))) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom,
% 191.04/191.66 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 191.04/191.66 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 191.04/191.66 & class_Groups_Ocomm__monoid__mult(T_b) )
% 191.04/191.66 => ( V_A_2 = V_B_2
% 191.04/191.66 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 191.04/191.66 => ( ! [B_x] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 191.04/191.66 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 191.04/191.66 => 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) ) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_ivl__disj__un_I19_J,axiom,
% 191.04/191.66 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 191.04/191.66 ( class_Orderings_Olinorder(T_b)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 191.04/191.66 => 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) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_ivl__disj__un_I18_J,axiom,
% 191.04/191.66 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 191.04/191.66 ( class_Orderings_Olinorder(T_b)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 191.04/191.66 => 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) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_sup1E,axiom,
% 191.04/191.66 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 191.04/191.66 ( 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))
% 191.04/191.66 => ( ~ hBOOL(hAPP(V_A_2,V_x_2))
% 191.04/191.66 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_sup1CI,axiom,
% 191.04/191.66 ! [T_b,V_A_2,V_x_2,V_B_2] :
% 191.04/191.66 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2))
% 191.04/191.66 => hBOOL(hAPP(V_A_2,V_x_2)) )
% 191.04/191.66 => 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)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_ivl__disj__un_I9_J,axiom,
% 191.04/191.66 ! [V_u_2,V_l_2,T_b] :
% 191.04/191.66 ( class_Orderings_Olinorder(T_b)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 191.04/191.66 => 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) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_image__Un,axiom,
% 191.04/191.66 ! [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)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom,
% 191.04/191.66 ! [V_B_2,V_A_2] :
% 191.04/191.66 ( c_Nat__Transfer_Onat__set(V_A_2)
% 191.04/191.66 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 191.04/191.66 => 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)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_sup1I1,axiom,
% 191.04/191.66 ! [V_B_2,T_b,V_x_2,V_A_2] :
% 191.04/191.66 ( hBOOL(hAPP(V_A_2,V_x_2))
% 191.04/191.66 => 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)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_sup1I2,axiom,
% 191.04/191.66 ! [V_A_2,T_b,V_x_2,V_B_2] :
% 191.04/191.66 ( hBOOL(hAPP(V_B_2,V_x_2))
% 191.04/191.66 => 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)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_Un__absorb,axiom,
% 191.04/191.66 ! [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 ).
% 191.04/191.66
% 191.04/191.66 fof(fact_Un__commute,axiom,
% 191.04/191.66 ! [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) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_Un__left__absorb,axiom,
% 191.04/191.66 ! [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) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_Un__left__commute,axiom,
% 191.04/191.66 ! [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)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_Un__assoc,axiom,
% 191.04/191.66 ! [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)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_bex__Un,axiom,
% 191.04/191.66 ! [V_Pa_2,V_B_2,V_A_2,T_b] :
% 191.04/191.66 ( ? [B_x] :
% 191.04/191.66 ( 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)))
% 191.04/191.66 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 191.04/191.66 <=> ( ? [B_x] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.04/191.66 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 191.04/191.66 | ? [B_x] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 191.04/191.66 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_ball__Un,axiom,
% 191.04/191.66 ! [V_Pa_2,V_B_2,V_A_2,T_b] :
% 191.04/191.66 ( ! [B_x] :
% 191.04/191.66 ( 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)))
% 191.04/191.66 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 191.04/191.66 <=> ( ! [B_x] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.04/191.66 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 191.04/191.66 & ! [B_x] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 191.04/191.66 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_sup_Oidem,axiom,
% 191.04/191.66 ! [V_a,T_a] :
% 191.04/191.66 ( class_Lattices_Osemilattice__sup(T_a)
% 191.04/191.66 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_sup__idem,axiom,
% 191.04/191.66 ! [V_x,T_a] :
% 191.04/191.66 ( class_Lattices_Osemilattice__sup(T_a)
% 191.04/191.66 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_sup_Ocommute,axiom,
% 191.04/191.66 ! [V_b,V_a,T_a] :
% 191.04/191.66 ( class_Lattices_Osemilattice__sup(T_a)
% 191.04/191.66 => 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) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_inf__sup__aci_I5_J,axiom,
% 191.04/191.66 ! [V_y,V_x,T_a] :
% 191.04/191.66 ( class_Lattices_Olattice(T_a)
% 191.04/191.66 => 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) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_sup__commute,axiom,
% 191.04/191.66 ! [V_y,V_x,T_a] :
% 191.04/191.66 ( class_Lattices_Osemilattice__sup(T_a)
% 191.04/191.66 => 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) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_sup_Oleft__idem,axiom,
% 191.04/191.66 ! [V_b,V_a,T_a] :
% 191.04/191.66 ( class_Lattices_Osemilattice__sup(T_a)
% 191.04/191.66 => 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) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_inf__sup__aci_I8_J,axiom,
% 191.04/191.66 ! [V_y,V_x,T_a] :
% 191.04/191.66 ( class_Lattices_Olattice(T_a)
% 191.04/191.66 => 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) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_sup__left__idem,axiom,
% 191.04/191.66 ! [V_y,V_x,T_a] :
% 191.04/191.66 ( class_Lattices_Osemilattice__sup(T_a)
% 191.04/191.66 => 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) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_sup_Oleft__commute,axiom,
% 191.04/191.66 ! [V_c,V_a,V_b,T_a] :
% 191.04/191.66 ( class_Lattices_Osemilattice__sup(T_a)
% 191.04/191.66 => 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)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_inf__sup__aci_I7_J,axiom,
% 191.04/191.66 ! [V_z,V_y,V_x,T_a] :
% 191.04/191.66 ( class_Lattices_Olattice(T_a)
% 191.04/191.66 => 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)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_sup__left__commute,axiom,
% 191.04/191.66 ! [V_z,V_y,V_x,T_a] :
% 191.04/191.66 ( class_Lattices_Osemilattice__sup(T_a)
% 191.04/191.66 => 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)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_sup_Oassoc,axiom,
% 191.04/191.66 ! [V_c,V_b,V_a,T_a] :
% 191.04/191.66 ( class_Lattices_Osemilattice__sup(T_a)
% 191.04/191.66 => 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)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_inf__sup__aci_I6_J,axiom,
% 191.04/191.66 ! [V_z,V_y,V_x,T_a] :
% 191.04/191.66 ( class_Lattices_Olattice(T_a)
% 191.04/191.66 => 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)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_sup__assoc,axiom,
% 191.04/191.66 ! [V_z,V_y,V_x,T_a] :
% 191.04/191.66 ( class_Lattices_Osemilattice__sup(T_a)
% 191.04/191.66 => 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)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_sup__apply,axiom,
% 191.04/191.66 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 191.04/191.66 ( class_Lattices_Olattice(T_b)
% 191.04/191.66 => 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)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_sup__fun__def,axiom,
% 191.04/191.66 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 191.04/191.66 ( class_Lattices_Olattice(T_b)
% 191.04/191.66 => 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)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_Un__Diff__cancel,axiom,
% 191.04/191.66 ! [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) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_Un__Diff__cancel2,axiom,
% 191.04/191.66 ! [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) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_Un__Diff,axiom,
% 191.04/191.66 ! [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)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_Sup__fin_Oidem,axiom,
% 191.04/191.66 ! [V_x,T_a] :
% 191.04/191.66 ( class_Lattices_Olattice(T_a)
% 191.04/191.66 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_sup__max,axiom,
% 191.04/191.66 ! [T_b] :
% 191.04/191.66 ( ( class_Lattices_Osemilattice__sup(T_b)
% 191.04/191.66 & class_Orderings_Olinorder(T_b) )
% 191.04/191.66 => c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_atMost__eq__iff,axiom,
% 191.04/191.66 ! [V_y_2,V_x_2,T_b] :
% 191.04/191.66 ( class_Orderings_Olinorder(T_b)
% 191.04/191.66 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)
% 191.04/191.66 <=> V_x_2 = V_y_2 ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_le__supE,axiom,
% 191.04/191.66 ! [V_x,V_b,V_a,T_a] :
% 191.04/191.66 ( class_Lattices_Osemilattice__sup(T_a)
% 191.04/191.66 => ( 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))
% 191.04/191.66 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 191.04/191.66 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_sup__mono,axiom,
% 191.04/191.66 ! [V_d,V_b,V_c,V_a,T_a] :
% 191.04/191.66 ( class_Lattices_Osemilattice__sup(T_a)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 191.04/191.66 => 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))) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_sup__least,axiom,
% 191.04/191.66 ! [V_z,V_x,V_y,T_a] :
% 191.04/191.66 ( class_Lattices_Osemilattice__sup(T_a)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 191.04/191.66 => 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)) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_le__supI,axiom,
% 191.04/191.66 ! [V_b,V_x,V_a,T_a] :
% 191.04/191.66 ( class_Lattices_Osemilattice__sup(T_a)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 191.04/191.66 => 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)) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_sup__absorb1,axiom,
% 191.04/191.66 ! [V_x,V_y,T_a] :
% 191.04/191.66 ( class_Lattices_Osemilattice__sup(T_a)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 191.04/191.66 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_sup__absorb2,axiom,
% 191.04/191.66 ! [V_y,V_x,T_a] :
% 191.04/191.66 ( class_Lattices_Osemilattice__sup(T_a)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 191.04/191.66 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_le__supI2,axiom,
% 191.04/191.66 ! [V_a,V_b,V_x,T_a] :
% 191.04/191.66 ( class_Lattices_Osemilattice__sup(T_a)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 191.04/191.66 => 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))) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_le__supI1,axiom,
% 191.04/191.66 ! [V_b,V_a,V_x,T_a] :
% 191.04/191.66 ( class_Lattices_Osemilattice__sup(T_a)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 191.04/191.66 => 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))) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_le__sup__iff,axiom,
% 191.04/191.66 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 191.04/191.66 ( class_Lattices_Osemilattice__sup(T_b)
% 191.04/191.66 => ( 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))
% 191.04/191.66 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 191.04/191.66 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_le__iff__sup,axiom,
% 191.04/191.66 ! [V_y_2,V_x_2,T_b] :
% 191.04/191.66 ( class_Lattices_Osemilattice__sup(T_b)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 191.04/191.66 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_sup__ge2,axiom,
% 191.04/191.66 ! [V_x,V_y,T_a] :
% 191.04/191.66 ( class_Lattices_Osemilattice__sup(T_a)
% 191.04/191.66 => 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))) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_inf__sup__ord_I4_J,axiom,
% 191.04/191.66 ! [V_x,V_y,T_a] :
% 191.04/191.66 ( class_Lattices_Olattice(T_a)
% 191.04/191.66 => 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))) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_sup__ge1,axiom,
% 191.04/191.66 ! [V_y,V_x,T_a] :
% 191.04/191.66 ( class_Lattices_Osemilattice__sup(T_a)
% 191.04/191.66 => 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))) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_inf__sup__ord_I3_J,axiom,
% 191.04/191.66 ! [V_y,V_x,T_a] :
% 191.04/191.66 ( class_Lattices_Olattice(T_a)
% 191.04/191.66 => 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))) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_Un__upper1,axiom,
% 191.04/191.66 ! [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))) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_Un__upper2,axiom,
% 191.04/191.66 ! [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))) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_subset__Un__eq,axiom,
% 191.04/191.66 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.66 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_Un__absorb1,axiom,
% 191.04/191.66 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.66 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_Un__absorb2,axiom,
% 191.04/191.66 ! [V_A_2,V_B_2,T_b] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 191.04/191.66 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_Un__least,axiom,
% 191.04/191.66 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 191.04/191.66 => 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)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_Un__mono,axiom,
% 191.04/191.66 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 191.04/191.66 => 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))) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_less__supI2,axiom,
% 191.04/191.66 ! [V_a,V_b,V_x,T_a] :
% 191.04/191.66 ( class_Lattices_Osemilattice__sup(T_a)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 191.04/191.66 => 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))) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_less__supI1,axiom,
% 191.04/191.66 ! [V_b,V_a,V_x,T_a] :
% 191.04/191.66 ( class_Lattices_Osemilattice__sup(T_a)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 191.04/191.66 => 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))) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_card__atMost,axiom,
% 191.04/191.66 ! [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) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_ivl__disj__un_I10_J,axiom,
% 191.04/191.66 ! [V_u_2,V_l_2,T_b] :
% 191.04/191.66 ( class_Orderings_Olinorder(T_b)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 191.04/191.66 => 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) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_ivl__disj__un_I7_J,axiom,
% 191.04/191.66 ! [V_u_2,V_l_2,T_b] :
% 191.04/191.66 ( class_Orderings_Olinorder(T_b)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 191.04/191.66 => 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) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_ivl__disj__un_I17_J,axiom,
% 191.04/191.66 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 191.04/191.66 ( class_Orderings_Olinorder(T_b)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 191.04/191.66 => 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) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_Diff__partition,axiom,
% 191.04/191.66 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.66 => 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 ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_Diff__subset__conv,axiom,
% 191.04/191.66 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 191.04/191.66 ( 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))
% 191.04/191.66 <=> 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))) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom,
% 191.04/191.66 ! [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))) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_ivl__disj__un_I20_J,axiom,
% 191.04/191.66 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 191.04/191.66 ( class_Orderings_Olinorder(T_b)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 191.04/191.66 => 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) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_Compl__Diff__eq,axiom,
% 191.04/191.66 ! [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) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom,
% 191.04/191.66 ! [V_B_2,V_A_2] :
% 191.04/191.66 ( c_Nat__Transfer_Onat__set(V_A_2)
% 191.04/191.66 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 191.04/191.66 => 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))) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_atLeast0AtMost,axiom,
% 191.04/191.66 ! [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) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_card__greaterThanLessThan,axiom,
% 191.04/191.66 ! [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)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_lessThan__Suc__atMost,axiom,
% 191.04/191.66 ! [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) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom,
% 191.04/191.66 ! [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) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_atMost__subset__iff,axiom,
% 191.04/191.66 ! [V_y_2,V_x_2,T_b] :
% 191.04/191.66 ( class_Orderings_Oorder(T_b)
% 191.04/191.66 => ( 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)))
% 191.04/191.66 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_ivl__disj__un_I21_J,axiom,
% 191.04/191.66 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 191.04/191.66 ( class_Orderings_Olinorder(T_b)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 191.04/191.66 => 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) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_atLeastLessThan__add__Un,axiom,
% 191.04/191.66 ! [V_k_2,V_j_2,V_i_2] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 191.04/191.66 => 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))) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_ivl__disj__un_I8_J,axiom,
% 191.04/191.66 ! [V_u_2,V_l_2,T_b] :
% 191.04/191.66 ( class_Orderings_Olinorder(T_b)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 191.04/191.66 => 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) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_ivl__disj__un_I22_J,axiom,
% 191.04/191.66 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 191.04/191.66 ( class_Orderings_Olinorder(T_b)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 191.04/191.66 => 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) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_ivl__disj__un_I11_J,axiom,
% 191.04/191.66 ! [V_u_2,V_l_2,T_b] :
% 191.04/191.66 ( class_Orderings_Olinorder(T_b)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 191.04/191.66 => 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) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_Compl__atMost,axiom,
% 191.04/191.66 ! [V_k_2,T_b] :
% 191.04/191.66 ( class_Orderings_Olinorder(T_b)
% 191.04/191.66 => 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) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_Compl__greaterThan,axiom,
% 191.04/191.66 ! [V_k_2,T_b] :
% 191.04/191.66 ( class_Orderings_Olinorder(T_b)
% 191.04/191.66 => 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) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_ivl__disj__un_I15_J,axiom,
% 191.04/191.66 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 191.04/191.66 ( class_Orderings_Olinorder(T_b)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 191.04/191.66 => 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) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_ivl__disj__un_I16_J,axiom,
% 191.04/191.66 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 191.04/191.66 ( class_Orderings_Olinorder(T_b)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 191.04/191.66 => 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) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_setsum__atMost__Suc,axiom,
% 191.04/191.66 ! [V_n_2,V_f_2,T_b] :
% 191.04/191.66 ( class_Groups_Ocomm__monoid__add(T_b)
% 191.04/191.66 => 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))) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_ivl__disj__un_I12_J,axiom,
% 191.04/191.66 ! [V_u_2,V_l_2,T_b] :
% 191.04/191.66 ( class_Orderings_Olinorder(T_b)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 191.04/191.66 => 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) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_ivl__disj__un_I13_J,axiom,
% 191.04/191.66 ! [V_u_2,V_l_2,T_b] :
% 191.04/191.66 ( class_Orderings_Olinorder(T_b)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 191.04/191.66 => 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) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_hoare__derivs_OBody,axiom,
% 191.04/191.66 ! [V_Procs_2,V_Q_2,V_Pa_2,V_Ga_2,T_b] :
% 191.04/191.66 ( 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_Pa_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_Pa_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))
% 191.04/191.66 => 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_Pa_2)),c_Com_Ocom_OBODY)),V_Q_2)),V_Procs_2)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_UN__le__eq__Un0,axiom,
% 191.04/191.66 ! [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))) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_sup__nat__def,axiom,
% 191.04/191.66 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_asm,axiom,
% 191.04/191.66 ! [V_Ga_2,V_ts_2,T_b] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_ts_2),V_Ga_2))
% 191.04/191.66 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_weaken,axiom,
% 191.04/191.66 ! [V_ts_2,V_ts_H_2,V_Ga_2,T_b] :
% 191.04/191.66 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_H_2)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_ts_2),V_ts_H_2))
% 191.04/191.66 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_thin,axiom,
% 191.04/191.66 ! [V_Ga_2,V_ts_2,V_G_H_2,T_b] :
% 191.04/191.66 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
% 191.04/191.66 => ( 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))
% 191.04/191.66 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_atLeast__eq__iff,axiom,
% 191.04/191.66 ! [V_y_2,V_x_2,T_b] :
% 191.04/191.66 ( class_Orderings_Olinorder(T_b)
% 191.04/191.66 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)
% 191.04/191.66 <=> V_x_2 = V_y_2 ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_cut,axiom,
% 191.04/191.66 ! [V_Ga_2,V_ts_2,V_G_H_2,T_b] :
% 191.04/191.66 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_2)
% 191.04/191.66 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_G_H_2)
% 191.04/191.66 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_SUP1__iff,axiom,
% 191.04/191.66 ! [V_ba_2,V_B_2,V_A_2,T_c,T_b] :
% 191.04/191.66 ( 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_ba_2))
% 191.04/191.66 <=> ? [B_x] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.04/191.66 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_ba_2)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_atLeast__Suc__greaterThan,axiom,
% 191.04/191.66 ! [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) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_atLeast__subset__iff,axiom,
% 191.04/191.66 ! [V_y_2,V_x_2,T_b] :
% 191.04/191.66 ( class_Orderings_Oorder(T_b)
% 191.04/191.66 => ( 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)))
% 191.04/191.66 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_Compl__atLeast,axiom,
% 191.04/191.66 ! [V_k_2,T_b] :
% 191.04/191.66 ( class_Orderings_Olinorder(T_b)
% 191.04/191.66 => 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) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_Compl__lessThan,axiom,
% 191.04/191.66 ! [V_k_2,T_b] :
% 191.04/191.66 ( class_Orderings_Olinorder(T_b)
% 191.04/191.66 => 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) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_UN__le__add__shift,axiom,
% 191.04/191.66 ! [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) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_ivl__disj__un_I14_J,axiom,
% 191.04/191.66 ! [V_u_2,V_l_2,T_b] :
% 191.04/191.66 ( class_Orderings_Olinorder(T_b)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 191.04/191.66 => 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) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_image__uminus__atLeast,axiom,
% 191.04/191.66 ! [V_x_2,T_b] :
% 191.04/191.66 ( class_Groups_Oordered__ab__group__add(T_b)
% 191.04/191.66 => 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)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_image__uminus__atMost,axiom,
% 191.04/191.66 ! [V_x_2,T_b] :
% 191.04/191.66 ( class_Groups_Oordered__ab__group__add(T_b)
% 191.04/191.66 => 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)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_SUP__subset,axiom,
% 191.04/191.66 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 191.04/191.66 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.66 => 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))) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_UN__extend__simps_I6_J,axiom,
% 191.04/191.66 ! [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)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_UN__simps_I6_J,axiom,
% 191.04/191.66 ! [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) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_SUPR__apply,axiom,
% 191.04/191.66 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 191.04/191.66 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 191.04/191.66 => 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)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_ball__UN,axiom,
% 191.04/191.66 ! [V_Pa_2,V_B_2,V_A_2,T_c,T_b] :
% 191.04/191.66 ( ! [B_x] :
% 191.04/191.66 ( 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)))
% 191.04/191.66 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 191.04/191.66 <=> ! [B_x] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 191.04/191.66 => ! [B_xa] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x)))
% 191.04/191.66 => hBOOL(hAPP(V_Pa_2,B_xa)) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_SUP__commute,axiom,
% 191.04/191.66 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 191.04/191.66 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 191.04/191.66 => 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))) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_UN__UN__flatten,axiom,
% 191.04/191.66 ! [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)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_UN__simps_I9_J,axiom,
% 191.04/191.66 ! [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)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_UN__extend__simps_I9_J,axiom,
% 191.04/191.66 ! [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) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_SUP__le__iff,axiom,
% 191.04/191.66 ! [V_u_2,V_M_2,V_A_2,T_c,T_b] :
% 191.04/191.66 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 191.04/191.66 => ( 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))
% 191.04/191.66 <=> ! [B_x] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 191.04/191.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_less__SUP__iff,axiom,
% 191.04/191.66 ! [V_f_2,V_A_2,T_c,V_a_2,T_b] :
% 191.04/191.66 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 191.04/191.66 & class_Orderings_Olinorder(T_b) )
% 191.04/191.66 => ( 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)))
% 191.04/191.66 <=> ? [B_x] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 191.04/191.66 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_UN__subset__iff,axiom,
% 191.04/191.66 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] :
% 191.04/191.66 ( 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))
% 191.04/191.66 <=> ! [B_x] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 191.04/191.66 => 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)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_UN__extend__simps_I10_J,axiom,
% 191.04/191.66 ! [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) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_image__UN,axiom,
% 191.04/191.66 ! [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)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_UN__simps_I10_J,axiom,
% 191.04/191.66 ! [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)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_UN__Un__distrib,axiom,
% 191.04/191.66 ! [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)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_UN__Un,axiom,
% 191.04/191.66 ! [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)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_greaterThan__0,axiom,
% 191.04/191.66 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))) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_dvd_OatLeastatMost__psubset__iff,axiom,
% 191.04/191.66 ! [V_d_2,V_ca_2,V_ba_2,V_a_2] :
% 191.04/191.66 ( 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_ba_2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ca_2,V_d_2)))
% 191.04/191.66 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_ba_2))
% 191.04/191.66 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ca_2),V_a_2))
% 191.04/191.66 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ba_2),V_d_2))
% 191.04/191.66 & ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ca_2),V_a_2))
% 191.04/191.66 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_ca_2)) )
% 191.04/191.66 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ba_2),V_d_2))
% 191.04/191.66 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_d_2),V_ba_2)) ) ) ) )
% 191.04/191.66 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ca_2),V_d_2)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_dvd_OmonoI,axiom,
% 191.04/191.66 ! [V_f_2,T_b] :
% 191.04/191.66 ( class_Orderings_Oorder(T_b)
% 191.04/191.66 => ( ! [B_x,B_y] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_x),B_y))
% 191.04/191.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_f_2,B_y))) )
% 191.04/191.66 => c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_upto_Opinduct,axiom,
% 191.04/191.66 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 191.04/191.66 ( 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)))
% 191.04/191.66 => ( ! [B_i,B_j] :
% 191.04/191.66 ( 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)))
% 191.04/191.66 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j))
% 191.04/191.66 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint))),B_j)) )
% 191.04/191.66 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) )
% 191.04/191.66 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_top1I,axiom,
% 191.04/191.66 ! [V_x_2,T_b] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_Un__UNIV__left,axiom,
% 191.04/191.66 ! [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)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_Un__UNIV__right,axiom,
% 191.04/191.66 ! [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)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_subset__UNIV,axiom,
% 191.04/191.66 ! [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)))) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_top__apply,axiom,
% 191.04/191.66 ! [V_x_2,T_c,T_b] :
% 191.04/191.66 ( class_Orderings_Otop(T_b)
% 191.04/191.66 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_range__composition,axiom,
% 191.04/191.66 ! [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)))) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_top__greatest,axiom,
% 191.04/191.66 ! [V_x,T_a] :
% 191.04/191.66 ( class_Orderings_Otop(T_a)
% 191.04/191.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_sup__top__right,axiom,
% 191.04/191.66 ! [V_x,T_a] :
% 191.04/191.66 ( class_Lattices_Obounded__lattice__top(T_a)
% 191.04/191.66 => 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) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_sup__top__left,axiom,
% 191.04/191.66 ! [V_x,T_a] :
% 191.04/191.66 ( class_Lattices_Obounded__lattice__top(T_a)
% 191.04/191.66 => 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) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_UN__lessThan__UNIV,axiom,
% 191.04/191.66 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)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_UN__atMost__UNIV,axiom,
% 191.04/191.66 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)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_UN__atLeast__UNIV,axiom,
% 191.04/191.66 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)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_Compl__partition2,axiom,
% 191.04/191.66 ! [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)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_Compl__partition,axiom,
% 191.04/191.66 ! [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)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_Compl__eq__Diff__UNIV,axiom,
% 191.04/191.66 ! [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) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_atLeast__0,axiom,
% 191.04/191.66 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)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_compl__sup__top,axiom,
% 191.04/191.66 ! [V_x,T_a] :
% 191.04/191.66 ( class_Lattices_Oboolean__algebra(T_a)
% 191.04/191.66 => 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) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_sup__compl__top,axiom,
% 191.04/191.66 ! [V_x,T_a] :
% 191.04/191.66 ( class_Lattices_Oboolean__algebra(T_a)
% 191.04/191.66 => 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) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_UN__UN__finite__eq,axiom,
% 191.04/191.66 ! [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) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_dvd_OatLeastatMost__subset__iff,axiom,
% 191.04/191.66 ! [V_d_2,V_ca_2,V_ba_2,V_a_2] :
% 191.04/191.66 ( 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_ba_2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ca_2,V_d_2)))
% 191.04/191.66 <=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_ba_2))
% 191.04/191.66 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ca_2),V_a_2))
% 191.04/191.66 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ba_2),V_d_2)) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_surj__Compl__image__subset,axiom,
% 191.04/191.66 ! [V_A_2,V_f_2,T_b,T_c] :
% 191.04/191.66 ( 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))
% 191.04/191.66 => 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)))) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_UN__finite2__subset,axiom,
% 191.04/191.66 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 191.04/191.66 ( ! [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)))
% 191.04/191.66 => 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))) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_UN__finite2__eq,axiom,
% 191.04/191.66 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 191.04/191.66 ( ! [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)
% 191.04/191.66 => 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) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_UN__finite__subset,axiom,
% 191.04/191.66 ! [V_C_2,V_A_2,T_b] :
% 191.04/191.66 ( ! [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))
% 191.04/191.66 => 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)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_card__UNIV__bool,axiom,
% 191.04/191.66 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))) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_image__ident,axiom,
% 191.04/191.66 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 191.04/191.66
% 191.04/191.66 fof(fact_type__definition__code__numeral,axiom,
% 191.04/191.66 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))) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_lessThan__Suc__eq__insert__0,axiom,
% 191.04/191.66 ! [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))) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_setsum__diff__nat,axiom,
% 191.04/191.66 ! [V_f_2,V_A_2,V_B_2,T_b] :
% 191.04/191.66 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 191.04/191.66 => 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)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_setsum__diff,axiom,
% 191.04/191.66 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 191.04/191.66 ( class_Groups_Oab__group__add(T_c)
% 191.04/191.66 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 191.04/191.66 => 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)) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_finite__atLeastLessThan,axiom,
% 191.04/191.66 ! [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))) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_finite__atLeastAtMost__int,axiom,
% 191.04/191.66 ! [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))) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_finite__atLeastAtMost,axiom,
% 191.04/191.66 ! [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))) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_finite__lessThan,axiom,
% 191.04/191.66 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_finite__atMost,axiom,
% 191.04/191.66 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_finite__atLeastLessThan__int,axiom,
% 191.04/191.66 ! [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))) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_finite__greaterThanAtMost,axiom,
% 191.04/191.66 ! [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))) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_finite__greaterThanAtMost__int,axiom,
% 191.04/191.66 ! [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))) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_finite__greaterThanLessThan__int,axiom,
% 191.04/191.66 ! [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))) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_finite__greaterThanLessThan,axiom,
% 191.04/191.66 ! [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))) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_Un__insert__right,axiom,
% 191.04/191.66 ! [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)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_Un__insert__left,axiom,
% 191.04/191.66 ! [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)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_subset__insertI,axiom,
% 191.04/191.66 ! [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))) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_subset__insertI2,axiom,
% 191.04/191.66 ! [V_ba_2,V_B_2,V_A_2,T_b] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.66 => 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_ba_2),V_B_2))) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_insert__mono,axiom,
% 191.04/191.66 ! [V_a_2,V_D_2,V_C_2,T_b] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))
% 191.04/191.66 => 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))) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_finite__nat__set__iff__bounded__le,axiom,
% 191.04/191.66 ! [V_N_2] :
% 191.04/191.66 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 191.04/191.66 <=> ? [B_m] :
% 191.04/191.66 ! [B_x] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 191.04/191.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_finite__nat__set__iff__bounded,axiom,
% 191.04/191.66 ! [V_N_2] :
% 191.04/191.66 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 191.04/191.66 <=> ? [B_m] :
% 191.04/191.66 ! [B_x] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 191.04/191.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_insert__code,axiom,
% 191.04/191.66 ! [V_x_2,V_A_2,V_y_2,T_b] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2))
% 191.04/191.66 <=> ( V_y_2 = V_x_2
% 191.04/191.66 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_insert__commute,axiom,
% 191.04/191.66 ! [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)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_insert__absorb2,axiom,
% 191.04/191.66 ! [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) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_transfer__nat__int__set__relations_I1_J,axiom,
% 191.04/191.66 ! [V_A_2] :
% 191.04/191.66 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2))
% 191.04/191.66 <=> 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))) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_image__insert,axiom,
% 191.04/191.66 ! [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)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_transfer__int__nat__set__relations_I1_J,axiom,
% 191.04/191.66 ! [V_A_2] :
% 191.04/191.66 ( c_Nat__Transfer_Onat__set(V_A_2)
% 191.04/191.66 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2))
% 191.04/191.66 <=> 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))) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_setsum_Oinfinite,axiom,
% 191.04/191.66 ! [V_g_2,V_A_2,T_b,T_c] :
% 191.04/191.66 ( class_Groups_Ocomm__monoid__add(T_c)
% 191.04/191.66 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.66 => 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) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_setsum__infinite,axiom,
% 191.04/191.66 ! [V_f_2,V_A_2,T_b,T_c] :
% 191.04/191.66 ( class_Groups_Ocomm__monoid__add(T_c)
% 191.04/191.66 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.66 => 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) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_lessThan__Suc,axiom,
% 191.04/191.66 ! [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)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_atMost__Suc,axiom,
% 191.04/191.66 ! [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)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_setsum__eq__0__iff,axiom,
% 191.04/191.66 ! [V_f_2,V_F_2,T_b] :
% 191.04/191.66 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 191.04/191.66 => ( 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)
% 191.04/191.66 <=> ! [B_x] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 191.04/191.66 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_UN__insert,axiom,
% 191.04/191.66 ! [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)) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_setsum_Odistrib,axiom,
% 191.04/191.66 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 191.04/191.66 ( class_Groups_Ocomm__monoid__add(T_c)
% 191.04/191.66 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.66 => 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)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_finite__atLeastZeroLessThan__int,axiom,
% 191.04/191.66 ! [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))) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_atLeastAtMostSuc__conv,axiom,
% 191.04/191.66 ! [V_n_2,V_m_2] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 191.04/191.66 => 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)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_setsum__eq__Suc0__iff,axiom,
% 191.04/191.66 ! [V_f_2,V_A_2,T_b] :
% 191.04/191.66 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.66 => ( 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))
% 191.04/191.66 <=> ? [B_x] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.04/191.66 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 191.04/191.66 & ! [B_xa] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 191.04/191.66 => ( B_x != B_xa
% 191.04/191.66 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_setsum__eq__1__iff,axiom,
% 191.04/191.66 ! [V_f_2,V_A_2,T_b] :
% 191.04/191.66 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.66 => ( 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)
% 191.04/191.66 <=> ? [B_x] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.04/191.66 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 191.04/191.66 & ! [B_xa] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 191.04/191.66 => ( B_x != B_xa
% 191.04/191.66 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_card__psubset,axiom,
% 191.04/191.66 ! [V_A_2,V_B_2,T_b] :
% 191.04/191.66 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.66 => ( 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)))
% 191.04/191.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_diff__card__le__card__Diff,axiom,
% 191.04/191.66 ! [V_A_2,V_B_2,T_b] :
% 191.04/191.66 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.66 => 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)))) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_card__Diff__subset,axiom,
% 191.04/191.66 ! [V_A_2,V_B_2,T_b] :
% 191.04/191.66 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 191.04/191.66 => 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)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_finite__Diff,axiom,
% 191.04/191.66 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.66 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.66 => 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))) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_finite_OinsertI,axiom,
% 191.04/191.66 ! [V_a_2,V_A_2,T_b] :
% 191.04/191.66 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.66 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_finite__imageI,axiom,
% 191.04/191.66 ! [V_h_2,T_c,V_F_2,T_b] :
% 191.04/191.66 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 191.04/191.66 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2))) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_infinite__UNIV__int,axiom,
% 191.04/191.66 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_UNIV__option__conv,axiom,
% 191.04/191.66 ! [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)))) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_finite__code,axiom,
% 191.04/191.66 ! [V_A_2,T_b] :
% 191.04/191.66 ( class_Finite__Set_Ofinite(T_b)
% 191.04/191.66 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_finite,axiom,
% 191.04/191.66 ! [V_A_2,T_b] :
% 191.04/191.66 ( class_Finite__Set_Ofinite(T_b)
% 191.04/191.66 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_card__UNIV__unit,axiom,
% 191.04/191.66 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) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_infinite__UNIV__nat,axiom,
% 191.04/191.66 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_finite__insert,axiom,
% 191.04/191.66 ! [V_A_2,V_a_2,T_b] :
% 191.04/191.66 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)))
% 191.04/191.66 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_rev__finite__subset,axiom,
% 191.04/191.66 ! [V_A_2,V_B_2,T_b] :
% 191.04/191.66 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.66 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_finite__subset,axiom,
% 191.04/191.66 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.66 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.66 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_finite__Prod__UNIV,axiom,
% 191.04/191.66 ! [T_c,T_b] :
% 191.04/191.66 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 191.04/191.66 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
% 191.04/191.66 => 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)))) ) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_finite__fun__UNIVD2,axiom,
% 191.04/191.66 ! [T_c,T_b] :
% 191.04/191.66 ( 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))))
% 191.04/191.66 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ).
% 191.04/191.66
% 191.04/191.66 fof(fact_finite__Plus__UNIV__iff,axiom,
% 191.04/191.66 ! [T_c,T_b] :
% 191.04/191.66 ( 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))))
% 191.04/191.66 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 191.04/191.66 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_finite__option__UNIV,axiom,
% 191.04/191.67 ! [T_b] :
% 191.04/191.67 ( 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))))
% 191.04/191.67 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_finite__UNIV,axiom,
% 191.04/191.67 ! [T_b] :
% 191.04/191.67 ( class_Finite__Set_Ofinite(T_b)
% 191.04/191.67 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_finite__Un,axiom,
% 191.04/191.67 ! [V_Ga_2,V_F_2,T_b] :
% 191.04/191.67 ( 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)))
% 191.04/191.67 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 191.04/191.67 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_finite__UnI,axiom,
% 191.04/191.67 ! [V_Ga_2,V_F_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2))
% 191.04/191.67 => 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))) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_finite__Diff2,axiom,
% 191.04/191.67 ! [V_A_2,V_B_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.67 => ( 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)))
% 191.04/191.67 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_finite__UN,axiom,
% 191.04/191.67 ! [V_B_2,T_c,V_A_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( 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)))
% 191.04/191.67 <=> ! [B_x] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.04/191.67 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_finite__surj,axiom,
% 191.04/191.67 ! [V_f_2,V_B_2,T_c,V_A_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( 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)))
% 191.04/191.67 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_finite__Diff__insert,axiom,
% 191.04/191.67 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 191.04/191.67 ( 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))))
% 191.04/191.67 <=> 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))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_card__infinite,axiom,
% 191.04/191.67 ! [V_A_2,T_b] :
% 191.04/191.67 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
% 191.04/191.67 ! [V_A_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 191.04/191.67 => ( 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)))
% 191.04/191.67 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_finite__compl,axiom,
% 191.04/191.67 ! [V_A_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 191.04/191.67 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_finite__range__imageI,axiom,
% 191.04/191.67 ! [V_f_2,T_d,V_g_2,T_c,T_b] :
% 191.04/191.67 ( 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)))))
% 191.04/191.67 => 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))))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_card__ge__0__finite,axiom,
% 191.04/191.67 ! [V_A_2,T_b] :
% 191.04/191.67 ( 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)))
% 191.04/191.67 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_card__insert__le,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => 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)))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_card__mono,axiom,
% 191.04/191.67 ! [V_A_2,V_B_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.67 => 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))) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_card__seteq,axiom,
% 191.04/191.67 ! [V_A_2,V_B_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.67 => ( 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)))
% 191.04/191.67 => V_A_2 = V_B_2 ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_card__image__le,axiom,
% 191.04/191.67 ! [V_f_2,T_c,V_A_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => 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))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_psubset__card__mono,axiom,
% 191.04/191.67 ! [V_A_2,V_B_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.67 => 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))) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_finite__UNIV__card__ge__0,axiom,
% 191.04/191.67 ! [T_b] :
% 191.04/191.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 191.04/191.67 => 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))))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_finite__fun__UNIVD1,axiom,
% 191.04/191.67 ! [T_c,T_b] :
% 191.04/191.67 ( 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))))
% 191.04/191.67 => ( 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))
% 191.04/191.67 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_type__definition_OAbs__image,axiom,
% 191.04/191.67 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 191.04/191.67 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 191.04/191.67 => 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)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_type__definition_ORep__range,axiom,
% 191.04/191.67 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 191.04/191.67 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 191.04/191.67 => 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 ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
% 191.04/191.67 ! [V_x_2,V_y_2,V_ca_2] :
% 191.04/191.67 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2))
% 191.04/191.67 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_ca_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_ca_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_ca_2)) )
% 191.04/191.67 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2))
% 191.04/191.67 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 191.04/191.67 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_ca_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) )
% 191.04/191.67 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 191.04/191.67 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_ca_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_finite_OemptyI,axiom,
% 191.04/191.67 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_empty__subsetI,axiom,
% 191.04/191.67 ! [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)) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_finite_Oequations_I1_J,axiom,
% 191.04/191.67 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_singleton__inject,axiom,
% 191.04/191.67 ! [V_ba_2,V_a_2,T_b] :
% 191.04/191.67 ( 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_ba_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
% 191.04/191.67 => V_a_2 = V_ba_2 ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_doubleton__eq__iff,axiom,
% 191.04/191.67 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] :
% 191.04/191.67 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_ca_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 191.04/191.67 <=> ( ( V_a_2 = V_ca_2
% 191.04/191.67 & V_ba_2 = V_d_2 )
% 191.04/191.67 | ( V_a_2 = V_d_2
% 191.04/191.67 & V_ba_2 = V_ca_2 ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_insert__not__empty,axiom,
% 191.04/191.67 ! [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)) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_empty__not__insert,axiom,
% 191.04/191.67 ! [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) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Un__empty__left,axiom,
% 191.04/191.67 ! [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 ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Un__empty__right,axiom,
% 191.04/191.67 ! [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 ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Un__empty,axiom,
% 191.04/191.67 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.67 ( 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))
% 191.04/191.67 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_subset__empty,axiom,
% 191.04/191.67 ! [V_A_2,T_b] :
% 191.04/191.67 ( 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))))
% 191.04/191.67 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_not__psubset__empty,axiom,
% 191.04/191.67 ! [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)))) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_bot__fun__def,axiom,
% 191.04/191.67 ! [V_x_2,T_c,T_b] :
% 191.04/191.67 ( class_Orderings_Obot(T_b)
% 191.04/191.67 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_bot__apply,axiom,
% 191.04/191.67 ! [V_x_2,T_c,T_b] :
% 191.04/191.67 ( class_Orderings_Obot(T_b)
% 191.04/191.67 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Diff__cancel,axiom,
% 191.04/191.67 ! [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)) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Diff__empty,axiom,
% 191.04/191.67 ! [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 ).
% 191.04/191.67
% 191.04/191.67 fof(fact_empty__Diff,axiom,
% 191.04/191.67 ! [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)) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_ball__empty,axiom,
% 191.04/191.67 ! [V_Pa_2,T_b,B_x] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 191.04/191.67 => hBOOL(hAPP(V_Pa_2,B_x)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_image__is__empty,axiom,
% 191.04/191.67 ! [V_A_2,V_f_2,T_b,T_c] :
% 191.04/191.67 ( 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))
% 191.04/191.67 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_image__empty,axiom,
% 191.04/191.67 ! [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)) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_empty__is__image,axiom,
% 191.04/191.67 ! [V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.67 ( 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)
% 191.04/191.67 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_UNIV__not__empty,axiom,
% 191.04/191.67 ! [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)) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_bot__least,axiom,
% 191.04/191.67 ! [V_x,T_a] :
% 191.04/191.67 ( class_Orderings_Obot(T_a)
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_SUP__const,axiom,
% 191.04/191.67 ! [V_M_2,T_b,V_A_2,T_c] :
% 191.04/191.67 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 191.04/191.67 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => 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 ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_UNION__empty__conv_I2_J,axiom,
% 191.04/191.67 ! [V_B_2,V_A_2,T_b,T_c] :
% 191.04/191.67 ( 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))
% 191.04/191.67 <=> ! [B_x] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 191.04/191.67 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_UN__constant,axiom,
% 191.04/191.67 ! [V_ca_2,T_c,T_b,V_A_2] :
% 191.04/191.67 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_ca_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 191.04/191.67 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_ca_2)) = V_ca_2 ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_UN__empty2,axiom,
% 191.04/191.67 ! [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)) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_UNION__empty__conv_I1_J,axiom,
% 191.04/191.67 ! [V_B_2,V_A_2,T_c,T_b] :
% 191.04/191.67 ( 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)
% 191.04/191.67 <=> ! [B_x] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 191.04/191.67 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_sup__eq__bot__iff,axiom,
% 191.04/191.67 ! [V_y_2,V_x_2,T_b] :
% 191.04/191.67 ( class_Lattices_Obounded__lattice__bot(T_b)
% 191.04/191.67 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_b)
% 191.04/191.67 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_b)
% 191.04/191.67 & V_y_2 = c_Orderings_Obot__class_Obot(T_b) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_sup__bot__right,axiom,
% 191.04/191.67 ! [V_x,T_a] :
% 191.04/191.67 ( class_Lattices_Obounded__lattice__bot(T_a)
% 191.04/191.67 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_sup__bot__left,axiom,
% 191.04/191.67 ! [V_x,T_a] :
% 191.04/191.67 ( class_Lattices_Obounded__lattice__bot(T_a)
% 191.04/191.67 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_setsum_Oempty,axiom,
% 191.04/191.67 ! [V_g_2,T_c,T_b] :
% 191.04/191.67 ( class_Groups_Ocomm__monoid__add(T_b)
% 191.04/191.67 => 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) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_setsum__empty,axiom,
% 191.04/191.67 ! [V_f_2,T_c,T_b] :
% 191.04/191.67 ( class_Groups_Ocomm__monoid__add(T_b)
% 191.04/191.67 => 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) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_subset__singletonD,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( 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)))))
% 191.04/191.67 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 | V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_insert__is__Un,axiom,
% 191.04/191.67 ! [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) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_atLeastatMost__empty__iff,axiom,
% 191.04/191.67 ! [V_ba_2,V_a_2,T_b] :
% 191.04/191.67 ( class_Orderings_Oorder(T_b)
% 191.04/191.67 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_ba_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_atLeastatMost__empty__iff2,axiom,
% 191.04/191.67 ! [V_ba_2,V_a_2,T_b] :
% 191.04/191.67 ( class_Orderings_Oorder(T_b)
% 191.04/191.67 => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_ba_2)
% 191.04/191.67 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_ba_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_atLeastatMost__empty,axiom,
% 191.04/191.67 ! [V_a_2,V_ba_2,T_b] :
% 191.04/191.67 ( class_Orderings_Oorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ba_2),V_a_2))
% 191.04/191.67 => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_ba_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_insert__Diff__single,axiom,
% 191.04/191.67 ! [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) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Diff__insert2,axiom,
% 191.04/191.67 ! [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) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Diff__insert,axiom,
% 191.04/191.67 ! [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)))) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_atLeastLessThan__empty,axiom,
% 191.04/191.67 ! [V_a_2,V_ba_2,T_b] :
% 191.04/191.67 ( class_Orderings_Oorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),V_a_2))
% 191.04/191.67 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_ba_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_card_Oempty,axiom,
% 191.04/191.67 ! [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) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_atLeastLessThan__empty__iff,axiom,
% 191.04/191.67 ! [V_ba_2,V_a_2,T_b] :
% 191.04/191.67 ( class_Orderings_Oorder(T_b)
% 191.04/191.67 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_ba_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_atLeastLessThan__empty__iff2,axiom,
% 191.04/191.67 ! [V_ba_2,V_a_2,T_b] :
% 191.04/191.67 ( class_Orderings_Oorder(T_b)
% 191.04/191.67 => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_ba_2)
% 191.04/191.67 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_ba_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Diff__UNIV,axiom,
% 191.04/191.67 ! [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)) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_atLeastAtMost__singleton,axiom,
% 191.04/191.67 ! [V_a_2,T_b] :
% 191.04/191.67 ( class_Orderings_Oorder(T_b)
% 191.04/191.67 => 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))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_atLeastAtMost__singleton__iff,axiom,
% 191.04/191.67 ! [V_ca_2,V_ba_2,V_a_2,T_b] :
% 191.04/191.67 ( class_Orderings_Oorder(T_b)
% 191.04/191.67 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_ba_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
% 191.04/191.67 <=> ( V_a_2 = V_ba_2
% 191.04/191.67 & V_ba_2 = V_ca_2 ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_atLeastAtMost__singleton_H,axiom,
% 191.04/191.67 ! [V_ba_2,V_a_2,T_b] :
% 191.04/191.67 ( class_Orderings_Oorder(T_b)
% 191.04/191.67 => ( V_a_2 = V_ba_2
% 191.04/191.67 => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_ba_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_subset__Compl__self__eq,axiom,
% 191.04/191.67 ! [V_A_2,T_b] :
% 191.04/191.67 ( 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)))
% 191.04/191.67 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Compl__UNIV__eq,axiom,
% 191.04/191.67 ! [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)) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Compl__empty__eq,axiom,
% 191.04/191.67 ! [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)) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_atLeastLessThan0,axiom,
% 191.04/191.67 ! [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)) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_greaterThanAtMost__empty,axiom,
% 191.04/191.67 ! [V_k_2,V_l_2,T_b] :
% 191.04/191.67 ( class_Orderings_Oorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 191.04/191.67 => 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)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_greaterThanAtMost__empty__iff,axiom,
% 191.04/191.67 ! [V_l_2,V_k_2,T_b] :
% 191.04/191.67 ( class_Orderings_Oorder(T_b)
% 191.04/191.67 => ( 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))
% 191.04/191.67 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_greaterThanAtMost__empty__iff2,axiom,
% 191.04/191.67 ! [V_l_2,V_k_2,T_b] :
% 191.04/191.67 ( class_Orderings_Oorder(T_b)
% 191.04/191.67 => ( 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)
% 191.04/191.67 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_greaterThanLessThan__empty,axiom,
% 191.04/191.67 ! [V_k_2,V_l_2,T_b] :
% 191.04/191.67 ( class_Orderings_Oorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 191.04/191.67 => 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)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_lessThan__0,axiom,
% 191.04/191.67 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)) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_image__constant__conv,axiom,
% 191.04/191.67 ! [V_ca_2,T_c,T_b,V_A_2] :
% 191.04/191.67 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_ca_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 191.04/191.67 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_ca_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_UN__extend__simps_I1_J,axiom,
% 191.04/191.67 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 191.04/191.67 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => 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))) )
% 191.04/191.67 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => 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)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_UN__singleton,axiom,
% 191.04/191.67 ! [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 ).
% 191.04/191.67
% 191.04/191.67 fof(fact_UN__simps_I1_J,axiom,
% 191.04/191.67 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 191.04/191.67 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => 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)) )
% 191.04/191.67 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => 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)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_dvd_OatLeastatMost__empty__iff2,axiom,
% 191.04/191.67 ! [V_ba_2,V_a_2] :
% 191.04/191.67 ( 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_ba_2)
% 191.04/191.67 <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_ba_2)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_dvd_OatLeastatMost__empty__iff,axiom,
% 191.04/191.67 ! [V_ba_2,V_a_2] :
% 191.04/191.67 ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_ba_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
% 191.04/191.67 <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_ba_2)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_dvd_OatLeastatMost__empty,axiom,
% 191.04/191.67 ! [V_a_2,V_ba_2] :
% 191.04/191.67 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ba_2),V_a_2))
% 191.04/191.67 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_ba_2)) )
% 191.04/191.67 => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_ba_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_UN__extend__simps_I2_J,axiom,
% 191.04/191.67 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 191.04/191.67 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => 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 )
% 191.04/191.67 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => 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)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_UN__extend__simps_I3_J,axiom,
% 191.04/191.67 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 191.04/191.67 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => 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 )
% 191.04/191.67 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => 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)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_UN__simps_I2_J,axiom,
% 191.04/191.67 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 191.04/191.67 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => 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)) )
% 191.04/191.67 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => 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) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_UN__simps_I3_J,axiom,
% 191.04/191.67 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 191.04/191.67 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => 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)) )
% 191.04/191.67 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => 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)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_compl__bot__eq,axiom,
% 191.04/191.67 ! [T_a] :
% 191.04/191.67 ( class_Lattices_Oboolean__algebra(T_a)
% 191.04/191.67 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_compl__top__eq,axiom,
% 191.04/191.67 ! [T_a] :
% 191.04/191.67 ( class_Lattices_Oboolean__algebra(T_a)
% 191.04/191.67 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_card__eq__0__iff,axiom,
% 191.04/191.67 ! [V_A_2,T_b] :
% 191.04/191.67 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 191.04/191.67 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_single__Diff__lessThan,axiom,
% 191.04/191.67 ! [V_k_2,T_b] :
% 191.04/191.67 ( class_Orderings_Oorder(T_b)
% 191.04/191.67 => 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))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_image__eq__UN,axiom,
% 191.04/191.67 ! [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)))) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_atLeastLessThan__singleton,axiom,
% 191.04/191.67 ! [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))) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_atMost__0,axiom,
% 191.04/191.67 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))) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_type__definition_ORep__inverse,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 191.04/191.67 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 191.04/191.67 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_type__definition_ORep__inject,axiom,
% 191.04/191.67 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 191.04/191.67 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 191.04/191.67 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2)
% 191.04/191.67 <=> V_x_2 = V_y_2 ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_dvd_OatLeastAtMost__singleton_H,axiom,
% 191.04/191.67 ! [V_ba_2,V_a_2] :
% 191.04/191.67 ( V_a_2 = V_ba_2
% 191.04/191.67 => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_ba_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))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_dvd_OatLeastAtMost__singleton,axiom,
% 191.04/191.67 ! [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))) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_dvd_OatLeastAtMost__singleton__iff,axiom,
% 191.04/191.67 ! [V_ca_2,V_ba_2,V_a_2] :
% 191.04/191.67 ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_ba_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
% 191.04/191.67 <=> ( V_a_2 = V_ba_2
% 191.04/191.67 & V_ba_2 = V_ca_2 ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_atLeast__Suc,axiom,
% 191.04/191.67 ! [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)))) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_greaterThan__Suc,axiom,
% 191.04/191.67 ! [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)))) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_card__gt__0__iff,axiom,
% 191.04/191.67 ! [V_A_2,T_b] :
% 191.04/191.67 ( 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)))
% 191.04/191.67 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_ivl__disj__un_I2_J,axiom,
% 191.04/191.67 ! [V_u_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => 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) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_atLeastLessThanSuc,axiom,
% 191.04/191.67 ! [V_n_2,V_m_2] :
% 191.04/191.67 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 191.04/191.67 => 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)) )
% 191.04/191.67 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 191.04/191.67 => 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)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_ivl__disj__un_I1_J,axiom,
% 191.04/191.67 ! [V_l_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => 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) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_setsum_Oinsert__remove,axiom,
% 191.04/191.67 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 191.04/191.67 ( class_Groups_Ocomm__monoid__add(T_c)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => 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)))))) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_card__insert,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => 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)))))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_card__Diff1__le,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => 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))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_ivl__disj__un_I6_J,axiom,
% 191.04/191.67 ! [V_u_2,V_l_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 191.04/191.67 => 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) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_ivl__disj__un_I5_J,axiom,
% 191.04/191.67 ! [V_u_2,V_l_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 191.04/191.67 => 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) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_ivl__disj__un_I3_J,axiom,
% 191.04/191.67 ! [V_u_2,V_l_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 191.04/191.67 => 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) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_ivl__disj__un_I4_J,axiom,
% 191.04/191.67 ! [V_u_2,V_l_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 191.04/191.67 => 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) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_card_Oinsert__remove,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => 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)))))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_the__elem__def,axiom,
% 191.04/191.67 ! [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))))) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_dvd_OgreaterThanLessThan__empty,axiom,
% 191.04/191.67 ! [V_k_2,V_l_2] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
% 191.04/191.67 => 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)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_the__elem__eq,axiom,
% 191.04/191.67 ! [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 ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Option_Oset_Osimps_I2_J,axiom,
% 191.04/191.67 ! [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))) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_derivs__insertD,axiom,
% 191.04/191.67 ! [V_ts_2,V_t_2,V_Ga_2,T_b] :
% 191.04/191.67 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),V_ts_2))
% 191.04/191.67 => ( 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))))
% 191.04/191.67 & c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_hoare__derivs_Oinsert,axiom,
% 191.04/191.67 ! [V_ts_2,V_t_2,V_Ga_2,T_b] :
% 191.04/191.67 ( 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))))
% 191.04/191.67 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
% 191.04/191.67 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),V_ts_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom,
% 191.04/191.67 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_hoare__derivs_Oequations_I1_J,axiom,
% 191.04/191.67 ! [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))) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_empty,axiom,
% 191.04/191.67 ! [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))) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_bot__nat__def,axiom,
% 191.04/191.67 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Comp,axiom,
% 191.04/191.67 ! [V_R_2,V_d_2,V_Q_2,V_ca_2,V_Pa_2,V_Ga_2,T_b] :
% 191.04/191.67 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 191.04/191.67 => ( 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))))
% 191.04/191.67 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),c_Com_Ocom_OSemi(V_ca_2,V_d_2)),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_hoare__derivs_Oequations_I7_J,axiom,
% 191.04/191.67 ! [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)))) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_hoare__derivs_OSkip,axiom,
% 191.04/191.67 ! [V_Pa_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),c_Com_Ocom_OSKIP),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
% 191.04/191.67 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))) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom,
% 191.04/191.67 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))) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_LoopF,axiom,
% 191.04/191.67 ! [V_ca_2,V_ba_2,V_Pa_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),V_Pa_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),V_ba_2))),c_Com_Ocom_OWhile(V_ba_2,V_ca_2)),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_simp__from__to,axiom,
% 191.04/191.67 ! [V_i_2,V_j_2] :
% 191.04/191.67 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 191.04/191.67 => 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)) )
% 191.04/191.67 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 191.04/191.67 => 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)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_hoare__derivs_Oequations_I8_J,axiom,
% 191.04/191.67 ! [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)))) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Ass,axiom,
% 191.04/191.67 ! [V_a_2,V_X_2,V_Pa_2,V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_fun(tc_Com_Ostate,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_b),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),V_Pa_2)),hAPP(hAPP(c_COMBS(tc_Com_Ostate,tc_Nat_Onat,tc_Com_Ostate),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ovname,tc_fun(tc_Nat_Onat,tc_Com_Ostate)),c_Natural_Oupdate),V_X_2)),V_a_2))),c_Com_Ocom_OAss(V_X_2,V_a_2)),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Option_Oset_Osimps_I1_J,axiom,
% 191.04/191.67 ! [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)) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_set__empty__eq,axiom,
% 191.04/191.67 ! [V_xo_2,T_b] :
% 191.04/191.67 ( c_Option_Oset(T_b,V_xo_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 <=> V_xo_2 = c_Option_Ooption_ONone(T_b) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_weak__Body,axiom,
% 191.04/191.67 ! [V_Q_2,V_pn_2,V_Pa_2,V_Ga_2,T_b] :
% 191.04/191.67 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),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))))
% 191.04/191.67 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),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)))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_BodyN,axiom,
% 191.04/191.67 ! [V_Ga_2,V_Q_2,V_pn_2,V_Pa_2,T_b] :
% 191.04/191.67 ( 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_Pa_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_Pa_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))))
% 191.04/191.67 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),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)))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Body1,axiom,
% 191.04/191.67 ! [V_pn_2,V_Procs_2,V_Q_2,V_Pa_2,V_Ga_2,T_b] :
% 191.04/191.67 ( 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_Pa_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_Pa_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))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),V_pn_2),V_Procs_2))
% 191.04/191.67 => 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_Pa_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)))) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_nat__def,axiom,
% 191.04/191.67 ! [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)))))) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_setsum__mono3,axiom,
% 191.04/191.67 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 191.04/191.67 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 191.04/191.67 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.67 => ( ! [B_x] :
% 191.04/191.67 ( 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)))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 191.04/191.67 => 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))) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_card__Diff__singleton,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => 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)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_equalityCE,axiom,
% 191.04/191.67 ! [V_ca_2,T_b,V_B_2,V_A_2] :
% 191.04/191.67 ( V_A_2 = V_B_2
% 191.04/191.67 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 191.04/191.67 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) )
% 191.04/191.67 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_SUP2__I,axiom,
% 191.04/191.67 ! [T_d,T_c,V_ca_2,V_ba_2,V_B_2,V_A_2,V_a_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_ba_2),V_ca_2))
% 191.04/191.67 => 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_ba_2),V_ca_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_emptyE,axiom,
% 191.04/191.67 ! [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)))) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_insertE,axiom,
% 191.04/191.67 ! [V_A_2,V_ba_2,V_a_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),V_A_2)))
% 191.04/191.67 => ( V_a_2 != V_ba_2
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_insertCI,axiom,
% 191.04/191.67 ! [V_ba_2,V_B_2,V_a_2,T_b] :
% 191.04/191.67 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 191.04/191.67 => V_a_2 = V_ba_2 )
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),V_B_2))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_subsetD,axiom,
% 191.04/191.67 ! [V_ca_2,V_B_2,V_A_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_UNIV__I,axiom,
% 191.04/191.67 ! [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)))) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_image__eqI,axiom,
% 191.04/191.67 ! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_ba_2] :
% 191.04/191.67 ( V_ba_2 = hAPP(V_f_2,V_x_2)
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_UnE,axiom,
% 191.04/191.67 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 191.04/191.67 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_UnCI,axiom,
% 191.04/191.67 ! [V_A_2,V_B_2,V_ca_2,T_b] :
% 191.04/191.67 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) )
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_DiffI,axiom,
% 191.04/191.67 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 191.04/191.67 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_DiffE,axiom,
% 191.04/191.67 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 191.04/191.67 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_ComplI,axiom,
% 191.04/191.67 ! [V_A_2,V_ca_2,T_b] :
% 191.04/191.67 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_SUP1__I,axiom,
% 191.04/191.67 ! [T_c,V_ba_2,V_B_2,V_A_2,V_a_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_ba_2))
% 191.04/191.67 => 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_ba_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_UN__I,axiom,
% 191.04/191.67 ! [V_B_2,V_ba_2,T_c,V_A_2,V_a_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(V_B_2,V_a_2)))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_c),V_ba_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))) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_mem__splitI,axiom,
% 191.04/191.67 ! [T_d,T_c,V_ba_2,V_a_2,V_ca_2,V_z_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_ca_2,V_a_2),V_ba_2)))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_ca_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_ba_2)))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_pair__imageI,axiom,
% 191.04/191.67 ! [V_f_2,T_d,V_A_2,V_ba_2,V_a_2,T_c,T_b] :
% 191.04/191.67 ( 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_ba_2)),V_A_2))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_d),hAPP(hAPP(V_f_2,V_a_2),V_ba_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))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_bot__empty__eq2,axiom,
% 191.04/191.67 ! [V_y_2,V_x_2,T_c,T_b] :
% 191.04/191.67 ( 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))
% 191.04/191.67 <=> 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)))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_equals0D,axiom,
% 191.04/191.67 ! [V_a_2,T_b,V_A_2] :
% 191.04/191.67 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_empty__iff,axiom,
% 191.04/191.67 ! [V_ca_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_ex__in__conv,axiom,
% 191.04/191.67 ! [V_A_2,T_b] :
% 191.04/191.67 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.04/191.67 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_all__not__in__conv,axiom,
% 191.04/191.67 ! [V_A_2,T_b] :
% 191.04/191.67 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.04/191.67 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Diff__iff,axiom,
% 191.04/191.67 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 191.04/191.67 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 191.04/191.67 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_DiffD1,axiom,
% 191.04/191.67 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_DiffD2,axiom,
% 191.04/191.67 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 191.04/191.67 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_bot__empty__eq,axiom,
% 191.04/191.67 ! [V_x_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2))
% 191.04/191.67 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_ord_OatLeastAtMost__iff,axiom,
% 191.04/191.67 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_b] :
% 191.04/191.67 ( 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)))
% 191.04/191.67 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 191.04/191.67 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_pred__equals__eq2,axiom,
% 191.04/191.67 ! [V_S_2,V_R_2,T_c,T_b] :
% 191.04/191.67 ( 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)
% 191.04/191.67 <=> V_R_2 = V_S_2 ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_sup__Un__eq2,axiom,
% 191.04/191.67 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 191.04/191.67 ( 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))
% 191.04/191.67 <=> 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))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_pred__subset__eq,axiom,
% 191.04/191.67 ! [V_S_2,V_R_2,T_b] :
% 191.04/191.67 ( 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)))
% 191.04/191.67 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Un__iff,axiom,
% 191.04/191.67 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 191.04/191.67 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 191.04/191.67 | hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_UnI1,axiom,
% 191.04/191.67 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_UnI2,axiom,
% 191.04/191.67 ! [V_A_2,V_B_2,V_ca_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_in__mono,axiom,
% 191.04/191.67 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_set__rev__mp,axiom,
% 191.04/191.67 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_set__mp,axiom,
% 191.04/191.67 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_psubsetD,axiom,
% 191.04/191.67 ! [V_ca_2,V_B_2,V_A_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Rep__Integ__inject,axiom,
% 191.04/191.67 ! [V_y_2,V_x_2] :
% 191.04/191.67 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2)
% 191.04/191.67 <=> V_x_2 = V_y_2 ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_eq__mem__trans,axiom,
% 191.04/191.67 ! [V_A_2,T_b,V_ba_2,V_a_2] :
% 191.04/191.67 ( V_a_2 = V_ba_2
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),V_A_2))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_eqelem__imp__iff,axiom,
% 191.04/191.67 ! [V_A_2,T_b,V_y_2,V_x_2] :
% 191.04/191.67 ( V_x_2 = V_y_2
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_eqset__imp__iff,axiom,
% 191.04/191.67 ! [V_x_2,T_b,V_B_2,V_A_2] :
% 191.04/191.67 ( V_A_2 = V_B_2
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_mem__def,axiom,
% 191.04/191.67 ! [V_A_2,V_x_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_eq__mem,axiom,
% 191.04/191.67 ! [V_y_2,V_x_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2)))
% 191.04/191.67 <=> V_x_2 = V_y_2 ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_pred__equals__eq,axiom,
% 191.04/191.67 ! [V_S_2,V_R_2,T_b] :
% 191.04/191.67 ( 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)
% 191.04/191.67 <=> V_R_2 = V_S_2 ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_ComplE,axiom,
% 191.04/191.67 ! [V_A_2,V_ca_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 191.04/191.67 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_ComplD,axiom,
% 191.04/191.67 ! [V_A_2,V_ca_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 191.04/191.67 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Compl__iff,axiom,
% 191.04/191.67 ! [V_A_2,V_ca_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 191.04/191.67 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_type__definition_ORep,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 191.04/191.67 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_type__definition_OAbs__inverse,axiom,
% 191.04/191.67 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 191.04/191.67 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 191.04/191.67 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_type__definition_OAbs__inject,axiom,
% 191.04/191.67 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 191.04/191.67 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 191.04/191.67 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2)
% 191.04/191.67 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_image__iff,axiom,
% 191.04/191.67 ! [V_A_2,V_f_2,T_c,V_z_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 191.04/191.67 <=> ? [B_x] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 191.04/191.67 & V_z_2 = hAPP(V_f_2,B_x) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_imageI,axiom,
% 191.04/191.67 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => 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))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_rev__image__eqI,axiom,
% 191.04/191.67 ! [T_c,V_f_2,V_ba_2,V_A_2,V_x_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => ( V_ba_2 = hAPP(V_f_2,V_x_2)
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_transfer__nat__int__set__relations_I2_J,axiom,
% 191.04/191.67 ! [V_A_2,V_x_2] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2))
% 191.04/191.67 <=> 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))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_insertI1,axiom,
% 191.04/191.67 ! [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))) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_insert__iff,axiom,
% 191.04/191.67 ! [V_A_2,V_ba_2,V_a_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),V_A_2)))
% 191.04/191.67 <=> ( V_a_2 = V_ba_2
% 191.04/191.67 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_insert__ident,axiom,
% 191.04/191.67 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 191.04/191.67 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 191.04/191.67 => ( 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)
% 191.04/191.67 <=> V_A_2 = V_B_2 ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_insertI2,axiom,
% 191.04/191.67 ! [V_ba_2,V_B_2,V_a_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),V_B_2))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_insert__absorb,axiom,
% 191.04/191.67 ! [V_A_2,V_a_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.67 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_sup__Un__eq,axiom,
% 191.04/191.67 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 191.04/191.67 ( 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))
% 191.04/191.67 <=> 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))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_UN__iff,axiom,
% 191.04/191.67 ! [V_B_2,V_A_2,T_c,V_ba_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_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)))
% 191.04/191.67 <=> ? [B_x] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 191.04/191.67 & hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(V_B_2,B_x))) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_singletonE,axiom,
% 191.04/191.67 ! [V_a_2,V_ba_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
% 191.04/191.67 => V_ba_2 = V_a_2 ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_singleton__iff,axiom,
% 191.04/191.67 ! [V_a_2,V_ba_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
% 191.04/191.67 <=> V_ba_2 = V_a_2 ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_insert__subset,axiom,
% 191.04/191.67 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 191.04/191.67 ( 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))
% 191.04/191.67 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 191.04/191.67 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_subset__insert,axiom,
% 191.04/191.67 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 191.04/191.67 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => ( 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)))
% 191.04/191.67 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_insert__image,axiom,
% 191.04/191.67 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => 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) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_range__eqI,axiom,
% 191.04/191.67 ! [T_c,T_b,V_x_2,V_f_2,V_ba_2] :
% 191.04/191.67 ( V_ba_2 = hAPP(V_f_2,V_x_2)
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_rangeI,axiom,
% 191.04/191.67 ! [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))))) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_insert__Diff1,axiom,
% 191.04/191.67 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 191.04/191.67 => 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) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_insert__Diff__if,axiom,
% 191.04/191.67 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 191.04/191.67 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 191.04/191.67 => 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) )
% 191.04/191.67 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 191.04/191.67 => 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)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_lessThan__iff,axiom,
% 191.04/191.67 ! [V_k_2,V_i_2,T_b] :
% 191.04/191.67 ( class_Orderings_Oord(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)))
% 191.04/191.67 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_ord_OgreaterThanLessThan__iff,axiom,
% 191.04/191.67 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_b] :
% 191.04/191.67 ( 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)))
% 191.04/191.67 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 191.04/191.67 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_transfer__int__nat__set__relations_I2_J,axiom,
% 191.04/191.67 ! [V_A_2,V_x_2] :
% 191.04/191.67 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 191.04/191.67 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 191.04/191.67 <=> 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))) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_atMost__iff,axiom,
% 191.04/191.67 ! [V_k_2,V_i_2,T_b] :
% 191.04/191.67 ( class_Orderings_Oord(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)))
% 191.04/191.67 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_atLeast__iff,axiom,
% 191.04/191.67 ! [V_k_2,V_i_2,T_b] :
% 191.04/191.67 ( class_Orderings_Oord(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)))
% 191.04/191.67 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_greaterThan__iff,axiom,
% 191.04/191.67 ! [V_k_2,V_i_2,T_b] :
% 191.04/191.67 ( class_Orderings_Oord(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)))
% 191.04/191.67 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_code__numeral_Oof__nat__inject,axiom,
% 191.04/191.67 ! [V_y_2,V_x_2] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 191.04/191.67 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2)
% 191.04/191.67 <=> V_x_2 = V_y_2 ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_le__SUPI,axiom,
% 191.04/191.67 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 191.04/191.67 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 191.04/191.67 => 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))) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_nat__of,axiom,
% 191.04/191.67 ! [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)))) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2] :
% 191.04/191.67 ( c_Nat__Transfer_Onat__set(V_A_2)
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 191.04/191.67 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_SUP__UN__eq2,axiom,
% 191.04/191.67 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 191.04/191.67 ( 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))
% 191.04/191.67 <=> 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))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_UN__insert__distrib,axiom,
% 191.04/191.67 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 191.04/191.67 => 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)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_UN__upper,axiom,
% 191.04/191.67 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.67 => 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))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_SUP__UN__eq,axiom,
% 191.04/191.67 ! [V_x_2,V_r_2,T_c,T_b] :
% 191.04/191.67 ( 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))
% 191.04/191.67 <=> 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))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_UN__absorb,axiom,
% 191.04/191.67 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 191.04/191.67 => 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) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_elem__set,axiom,
% 191.04/191.67 ! [V_xo_2,V_x_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Option_Oset(T_b,V_xo_2)))
% 191.04/191.67 <=> V_xo_2 = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_pred__subset__eq2,axiom,
% 191.04/191.67 ! [V_S_2,V_R_2,T_c,T_b] :
% 191.04/191.67 ( 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)))
% 191.04/191.67 <=> 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)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_insert__Diff,axiom,
% 191.04/191.67 ! [V_A_2,V_a_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.67 => 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 ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Diff__insert__absorb,axiom,
% 191.04/191.67 ! [V_A_2,V_x_2,T_b] :
% 191.04/191.67 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => 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 ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2] :
% 191.04/191.67 ( c_Nat__Transfer_Onat__set(V_A_2)
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_setsum__delta_H,axiom,
% 191.04/191.67 ! [V_ba_2,V_a_2,V_S_2,T_b,T_c] :
% 191.04/191.67 ( class_Groups_Ocomm__monoid__add(T_c)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 191.04/191.67 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 191.04/191.67 => 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_ba_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_ba_2,V_a_2) )
% 191.04/191.67 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 191.04/191.67 => 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_ba_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_setsum__delta,axiom,
% 191.04/191.67 ! [V_ba_2,V_a_2,V_S_2,T_b,T_c] :
% 191.04/191.67 ( class_Groups_Ocomm__monoid__add(T_c)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 191.04/191.67 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 191.04/191.67 => 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_ba_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_ba_2,V_a_2) )
% 191.04/191.67 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 191.04/191.67 => 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_ba_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_image__constant,axiom,
% 191.04/191.67 ! [V_ca_2,T_c,V_A_2,V_x_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_ca_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_of__nat__inverse,axiom,
% 191.04/191.67 ! [V_y_2] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 191.04/191.67 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_setsum_Oinsert,axiom,
% 191.04/191.67 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 191.04/191.67 ( class_Groups_Ocomm__monoid__add(T_c)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => 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)) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_setsum__insert,axiom,
% 191.04/191.67 ! [V_f_2,V_a_2,V_F_2,T_b,T_c] :
% 191.04/191.67 ( class_Groups_Ocomm__monoid__add(T_c)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 191.04/191.67 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2))
% 191.04/191.67 => 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)) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_diff__single__insert,axiom,
% 191.04/191.67 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( 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))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => 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))) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_subset__insert__iff,axiom,
% 191.04/191.67 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( 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)))
% 191.04/191.67 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => 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)) )
% 191.04/191.67 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_card__insert__if,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => 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) )
% 191.04/191.67 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => 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)) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_card__insert__disjoint,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => 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)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_card_Oinsert,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => 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)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_psubset__insert__iff,axiom,
% 191.04/191.67 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( 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)))
% 191.04/191.67 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
% 191.04/191.67 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 191.04/191.67 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => 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)) )
% 191.04/191.67 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_setsum__diff1__nat,axiom,
% 191.04/191.67 ! [V_f_2,V_A_2,V_a_2,T_b] :
% 191.04/191.67 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.67 => 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)) )
% 191.04/191.67 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.67 => 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) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_setsum_Oremove,axiom,
% 191.04/191.67 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 191.04/191.67 ( class_Groups_Ocomm__monoid__add(T_c)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => 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)))))) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_setsum__diff1_H,axiom,
% 191.04/191.67 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 191.04/191.67 ( class_Groups_Ocomm__monoid__add(T_c)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.67 => 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)))))) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_setsum__diff1,axiom,
% 191.04/191.67 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 191.04/191.67 ( class_Groups_Oab__group__add(T_c)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.67 => 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)) )
% 191.04/191.67 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.67 => 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) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_setsum__diff1__ring,axiom,
% 191.04/191.67 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 191.04/191.67 ( class_Rings_Oring(T_c)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.67 => 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)) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_card__Suc__Diff1,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => 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) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_card__Diff2__less,axiom,
% 191.04/191.67 ! [V_y_2,V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 191.04/191.67 => 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))) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_card__Diff1__less,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => 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))) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_card__Diff__insert,axiom,
% 191.04/191.67 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.67 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 191.04/191.67 => 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)) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_card_Oremove,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => 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)))))) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_card__Diff__singleton__if,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => 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)) )
% 191.04/191.67 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => 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) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_in__rel__def,axiom,
% 191.04/191.67 ! [V_y_2,V_x_2,V_R_2,T_c,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2))
% 191.04/191.67 <=> 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)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_finite__pointwise,axiom,
% 191.04/191.67 ! [V_Q_2,V_Pa_2,V_Q_H_2,V_c0_2,V_P_H_2,V_Ga_2,T_c,V_U_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_U_2))
% 191.04/191.67 => ( ! [B_p] :
% 191.04/191.67 ( 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))))
% 191.04/191.67 => c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_c),hAPP(V_Pa_2,B_p)),hAPP(V_c0_2,B_p)),hAPP(V_Q_2,B_p))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_c),tc_HOL_Obool)))) )
% 191.04/191.67 => ( 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))
% 191.04/191.67 => c_Hoare__Mirabelle_Ohoare__derivs(T_c,V_Ga_2,hAPP(c_Set_Oimage(T_b,tc_Hoare__Mirabelle_Otriple(T_c),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c)),hAPP(hAPP(c_COMBS(T_b,tc_Com_Ocom,tc_fun(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(T_c,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(T_c))),T_b),c_Hoare__Mirabelle_Otriple_Otriple(T_c)),V_Pa_2)),V_c0_2)),V_Q_2)),V_U_2)) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom,
% 191.04/191.67 ! [V_f_2,V_A_2,T_b] :
% 191.04/191.67 ( ! [B_x] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.04/191.67 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 191.04/191.67 => 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)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_bset_I8_J,axiom,
% 191.04/191.67 ! [V_B_2,V_t_2,V_D_2] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 191.04/191.67 => ( 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))
% 191.04/191.67 => ! [B_x] :
% 191.04/191.67 ( ! [B_xa] :
% 191.04/191.67 ( 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)))
% 191.04/191.67 => ! [B_xb] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 191.04/191.67 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 191.04/191.67 => 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))) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_sup2CI,axiom,
% 191.04/191.67 ! [T_c,T_b,V_A_2,V_y_2,V_x_2,V_B_2] :
% 191.04/191.67 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 191.04/191.67 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) )
% 191.04/191.67 => 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)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_sup2E,axiom,
% 191.04/191.67 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 191.04/191.67 ( 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))
% 191.04/191.67 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 191.04/191.67 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_bot2E,axiom,
% 191.04/191.67 ! [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)) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_less__by__empty,axiom,
% 191.04/191.67 ! [V_B_2,T_b,V_A_2] :
% 191.04/191.67 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 191.04/191.67 => 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)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_SUP2__iff,axiom,
% 191.04/191.67 ! [V_ca_2,V_ba_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 191.04/191.67 ( 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_ba_2),V_ca_2))
% 191.04/191.67 <=> ? [B_x] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.04/191.67 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_ba_2),V_ca_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_sup2I2,axiom,
% 191.04/191.67 ! [V_A_2,T_c,T_b,V_y_2,V_x_2,V_B_2] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 191.04/191.67 => 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)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_sup2I1,axiom,
% 191.04/191.67 ! [V_B_2,T_c,T_b,V_y_2,V_x_2,V_A_2] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 191.04/191.67 => 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)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Nitpick_Orefl_H__def,axiom,
% 191.04/191.67 ! [V_r_2,T_b] :
% 191.04/191.67 ( c_Nitpick_Orefl_H(T_b,V_r_2)
% 191.04/191.67 <=> ! [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)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_aset_I6_J,axiom,
% 191.04/191.67 ! [V_A_2,V_t_2,V_D_2] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 191.04/191.67 => ( 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))
% 191.04/191.67 => ! [B_x] :
% 191.04/191.67 ( ! [B_xa] :
% 191.04/191.67 ( 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)))
% 191.04/191.67 => ! [B_xb] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 191.04/191.67 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 191.04/191.67 => 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)) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_dvd_OgreaterThan__iff,axiom,
% 191.04/191.67 ! [V_k_2,V_i_2] :
% 191.04/191.67 ( 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)))
% 191.04/191.67 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2))
% 191.04/191.67 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_ord_OgreaterThan__iff,axiom,
% 191.04/191.67 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2)))
% 191.04/191.67 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_dvd_OlessThan__iff,axiom,
% 191.04/191.67 ! [V_k_2,V_i_2] :
% 191.04/191.67 ( 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)))
% 191.04/191.67 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2))
% 191.04/191.67 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_aset_I4_J,axiom,
% 191.04/191.67 ! [V_A_2,V_t_2,V_D_2] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 191.04/191.67 => ! [B_x] :
% 191.04/191.67 ( ! [B_xa] :
% 191.04/191.67 ( 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)))
% 191.04/191.67 => ! [B_xb] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 191.04/191.67 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 191.04/191.67 => ( B_x != V_t_2
% 191.04/191.67 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_bset_I4_J,axiom,
% 191.04/191.67 ! [V_B_2,V_t_2,V_D_2] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 191.04/191.67 => ! [B_x] :
% 191.04/191.67 ( ! [B_xa] :
% 191.04/191.67 ( 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)))
% 191.04/191.67 => ! [B_xb] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 191.04/191.67 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 191.04/191.67 => ( B_x != V_t_2
% 191.04/191.67 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_ord_OlessThan__iff,axiom,
% 191.04/191.67 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2)))
% 191.04/191.67 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_bset_I3_J,axiom,
% 191.04/191.67 ! [V_B_2,V_t_2,V_D_2] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 191.04/191.67 => ( 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))
% 191.04/191.67 => ( ! [B_x] :
% 191.04/191.67 ( 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)))
% 191.04/191.67 => ! [B_xa] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2))
% 191.04/191.67 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) )
% 191.04/191.67 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_aset_I3_J,axiom,
% 191.04/191.67 ! [V_A_2,V_t_2,V_D_2] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 191.04/191.67 => ( 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))
% 191.04/191.67 => ( ! [B_x] :
% 191.04/191.67 ( 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)))
% 191.04/191.67 => ! [B_xa] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2))
% 191.04/191.67 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) )
% 191.04/191.67 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_aset_I5_J,axiom,
% 191.04/191.67 ! [V_A_2,V_t_2,V_D_2] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 191.04/191.67 => ! [B_x] :
% 191.04/191.67 ( ! [B_xa] :
% 191.04/191.67 ( 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)))
% 191.04/191.67 => ! [B_xb] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 191.04/191.67 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 191.04/191.67 => 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)) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_bset_I7_J,axiom,
% 191.04/191.67 ! [V_B_2,V_t_2,V_D_2] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 191.04/191.67 => ! [B_x] :
% 191.04/191.67 ( ! [B_xa] :
% 191.04/191.67 ( 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)))
% 191.04/191.67 => ! [B_xb] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 191.04/191.67 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 191.04/191.67 => 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))) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_in__measure,axiom,
% 191.04/191.67 ! [V_f_2,V_y_2,V_x_2,T_b] :
% 191.04/191.67 ( hBOOL(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)))
% 191.04/191.67 <=> 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))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_dvd_OatMost__iff,axiom,
% 191.04/191.67 ! [V_k_2,V_i_2] :
% 191.04/191.67 ( 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)))
% 191.04/191.67 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_ord_OatMost__iff,axiom,
% 191.04/191.67 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2)))
% 191.04/191.67 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_dvd_OatLeast__iff,axiom,
% 191.04/191.67 ! [V_k_2,V_i_2] :
% 191.04/191.67 ( 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)))
% 191.04/191.67 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_folding__image__simple_Oremove,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 191.04/191.67 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 191.04/191.67 => 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)))))) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_folding__one_Oremove,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 191.04/191.67 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 191.04/191.67 => hAPP(V_F_2,V_A_2) = V_x_2 )
% 191.04/191.67 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 191.04/191.67 => 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)))))) ) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_folding__image__simple_Oempty,axiom,
% 191.04/191.67 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 191.04/191.67 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 191.04/191.67 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_folding__one_Osingleton,axiom,
% 191.04/191.67 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 191.04/191.67 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 191.04/191.67 => 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 ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_folding__image__simple_Oinsert,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 191.04/191.67 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 191.04/191.67 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 191.04/191.67 => 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)) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_folding__one_Oinsert,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 191.04/191.67 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => 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)) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_folding__image__simple_Oinsert__remove,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 191.04/191.67 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 191.04/191.67 => 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)))))) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_folding__one_Oinsert__remove,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 191.04/191.67 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 191.04/191.67 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 191.04/191.67 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 191.04/191.67 => 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)))))) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_ord_OatLeast__iff,axiom,
% 191.04/191.67 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2)))
% 191.04/191.67 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_fold__graph_H_Ointros_I2_J,axiom,
% 191.04/191.67 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => ( 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)
% 191.04/191.67 => 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)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_setsum__mono2,axiom,
% 191.04/191.67 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 191.04/191.67 ( class_Groups_Oordered__comm__monoid__add(T_c)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.67 => ( ! [B_b] :
% 191.04/191.67 ( 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)))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_b))) )
% 191.04/191.67 => 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))) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_flat__lub__def,axiom,
% 191.04/191.67 ! [V_ba_2,V_A_2,T_b] :
% 191.04/191.67 ( ( 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_ba_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
% 191.04/191.67 => c_Partial__Function_Oflat__lub(T_b,V_ba_2,V_A_2) = V_ba_2 )
% 191.04/191.67 & ( ~ 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_ba_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
% 191.04/191.67 => c_Partial__Function_Oflat__lub(T_b,V_ba_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_ba_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_fold__graph_H_Oequations_I1_J,axiom,
% 191.04/191.67 ! [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) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_fold__graph_H_Ointros_I1_J,axiom,
% 191.04/191.67 ! [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) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_mlex__leq,axiom,
% 191.04/191.67 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 191.04/191.67 ( 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)))
% 191.04/191.67 => ( hBOOL(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))
% 191.04/191.67 => hBOOL(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))) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_mlex__less,axiom,
% 191.04/191.67 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 191.04/191.67 ( 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)))
% 191.04/191.67 => hBOOL(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))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_setsum__bounded,axiom,
% 191.04/191.67 ! [V_K_2,V_f_2,V_A_2,T_b,T_c] :
% 191.04/191.67 ( ( class_Groups_Oordered__ab__semigroup__add(T_c)
% 191.04/191.67 & class_Rings_Osemiring__1(T_c) )
% 191.04/191.67 => ( ! [B_i] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2)) )
% 191.04/191.67 => 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))) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_card__Suc__eq,axiom,
% 191.04/191.67 ! [V_k_2,V_A_2,T_b] :
% 191.04/191.67 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Nat_OSuc,V_k_2)
% 191.04/191.67 <=> ? [B_b,B_B] :
% 191.04/191.67 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B)
% 191.04/191.67 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B))
% 191.04/191.67 & hAPP(c_Finite__Set_Ocard(T_b),B_B) = V_k_2
% 191.04/191.67 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 191.04/191.67 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_ord_OgreaterThanAtMost__iff,axiom,
% 191.04/191.67 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 191.04/191.67 ( 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)))
% 191.04/191.67 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 191.04/191.67 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_ord_OatLeastLessThan__iff,axiom,
% 191.04/191.67 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 191.04/191.67 ( 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)))
% 191.04/191.67 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 191.04/191.67 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_dvd_OgreaterThanAtMost__empty,axiom,
% 191.04/191.67 ! [V_k_2,V_l_2] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
% 191.04/191.67 => 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)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_dvd_OatLeastLessThan__empty,axiom,
% 191.04/191.67 ! [V_a_2,V_ba_2] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ba_2),V_a_2))
% 191.04/191.67 => 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_ba_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_dvd_OgreaterThanAtMost__empty__iff,axiom,
% 191.04/191.67 ! [V_l_2,V_k_2] :
% 191.04/191.67 ( 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))
% 191.04/191.67 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2))
% 191.04/191.67 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_dvd_OatLeastLessThan__empty__iff,axiom,
% 191.04/191.67 ! [V_ba_2,V_a_2] :
% 191.04/191.67 ( 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_ba_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
% 191.04/191.67 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_ba_2))
% 191.04/191.67 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ba_2),V_a_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_dvd_OgreaterThanAtMost__empty__iff2,axiom,
% 191.04/191.67 ! [V_l_2,V_k_2] :
% 191.04/191.67 ( 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)
% 191.04/191.67 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2))
% 191.04/191.67 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_dvd_OatLeastLessThan__empty__iff2,axiom,
% 191.04/191.67 ! [V_ba_2,V_a_2] :
% 191.04/191.67 ( 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_ba_2)
% 191.04/191.67 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_ba_2))
% 191.04/191.67 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ba_2),V_a_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Nats__number__of,axiom,
% 191.04/191.67 ! [V_w_2,T_b] :
% 191.04/191.67 ( class_Int_Onumber__ring(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
% 191.04/191.67 => 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))) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Ints__odd__less__0,axiom,
% 191.04/191.67 ! [V_a_2,T_b] :
% 191.04/191.67 ( class_Rings_Olinordered__idom(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 191.04/191.67 => ( 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)))
% 191.04/191.67 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Sup__fin_Oremove,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( class_Lattices_Olattice(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 191.04/191.67 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_2 )
% 191.04/191.67 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 191.04/191.67 => 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)))))) ) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Sup__fin_Osingleton,axiom,
% 191.04/191.67 ! [V_x_2,T_b] :
% 191.04/191.67 ( class_Lattices_Olattice(T_b)
% 191.04/191.67 => 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 ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Ints__0,axiom,
% 191.04/191.67 ! [T_b] :
% 191.04/191.67 ( class_Rings_Oring__1(T_b)
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Ints__add,axiom,
% 191.04/191.67 ! [V_ba_2,V_a_2,T_b] :
% 191.04/191.67 ( class_Rings_Oring__1(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Int_Oring__1__class_OInts(T_b)))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ba_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Ints__mult,axiom,
% 191.04/191.67 ! [V_ba_2,V_a_2,T_b] :
% 191.04/191.67 ( class_Rings_Oring__1(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Int_Oring__1__class_OInts(T_b)))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ba_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Ints__diff,axiom,
% 191.04/191.67 ! [V_ba_2,V_a_2,T_b] :
% 191.04/191.67 ( class_Rings_Oring__1(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Int_Oring__1__class_OInts(T_b)))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_ba_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Ints__number__of,axiom,
% 191.04/191.67 ! [V_w_2,T_b] :
% 191.04/191.67 ( class_Int_Onumber__ring(T_b)
% 191.04/191.67 => 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))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Ints__1,axiom,
% 191.04/191.67 ! [T_b] :
% 191.04/191.67 ( class_Rings_Oring__1(T_b)
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Ints__minus,axiom,
% 191.04/191.67 ! [V_a_2,T_b] :
% 191.04/191.67 ( class_Rings_Oring__1(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 191.04/191.67 => 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))) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Ints__of__nat,axiom,
% 191.04/191.67 ! [V_n_2,T_b] :
% 191.04/191.67 ( class_Rings_Oring__1(T_b)
% 191.04/191.67 => 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))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Ints__power,axiom,
% 191.04/191.67 ! [V_n_2,V_a_2,T_b] :
% 191.04/191.67 ( class_Rings_Oring__1(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 191.04/191.67 => 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))) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Ints__of__int,axiom,
% 191.04/191.67 ! [V_z_2,T_b] :
% 191.04/191.67 ( class_Rings_Oring__1(T_b)
% 191.04/191.67 => 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))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Sup__fin_Oin__idem,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( class_Lattices_Olattice(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => 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) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Nats__0,axiom,
% 191.04/191.67 ! [T_b] :
% 191.04/191.67 ( class_Rings_Osemiring__1(T_b)
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Nats__add,axiom,
% 191.04/191.67 ! [V_ba_2,V_a_2,T_b] :
% 191.04/191.67 ( class_Rings_Osemiring__1(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ba_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Nats__mult,axiom,
% 191.04/191.67 ! [V_ba_2,V_a_2,T_b] :
% 191.04/191.67 ( class_Rings_Osemiring__1(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ba_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Nats__1,axiom,
% 191.04/191.67 ! [T_b] :
% 191.04/191.67 ( class_Rings_Osemiring__1(T_b)
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_of__nat__in__Nats,axiom,
% 191.04/191.67 ! [V_n_2,T_b] :
% 191.04/191.67 ( class_Rings_Osemiring__1(T_b)
% 191.04/191.67 => 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))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Ints__double__eq__0__iff,axiom,
% 191.04/191.67 ! [V_a_2,T_b] :
% 191.04/191.67 ( class_Int_Oring__char__0(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 191.04/191.67 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 191.04/191.67 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Sup__fin_Oinsert__idem,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( class_Lattices_Olattice(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => 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)) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Sup__fin_Osubset__idem,axiom,
% 191.04/191.67 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.67 ( class_Lattices_Olattice(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 191.04/191.67 => 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) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Sup__fin_Ounion__idem,axiom,
% 191.04/191.67 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.67 ( class_Lattices_Olattice(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.67 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => 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)) ) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Ints__odd__nonzero,axiom,
% 191.04/191.67 ! [V_a_2,T_b] :
% 191.04/191.67 ( class_Int_Oring__char__0(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 191.04/191.67 => 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) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Sup__fin_Oinsert,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( class_Lattices_Olattice(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => 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)) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Sup__fin_Oinsert__remove,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( class_Lattices_Olattice(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 191.04/191.67 => 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 )
% 191.04/191.67 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 191.04/191.67 => 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)))))) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Sup__fin_Oclosed,axiom,
% 191.04/191.67 ! [V_A_2,T_b] :
% 191.04/191.67 ( class_Lattices_Olattice(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => ( ! [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))))))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Max_Oremove,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 191.04/191.67 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 )
% 191.04/191.67 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 191.04/191.67 => 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)))))) ) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Min_Oremove,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 191.04/191.67 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 )
% 191.04/191.67 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 191.04/191.67 => 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)))))) ) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_minus__Max__eq__Min,axiom,
% 191.04/191.67 ! [V_S_2,T_b] :
% 191.04/191.67 ( class_Groups_Olinordered__ab__group__add(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 191.04/191.67 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => 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)) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_minus__Min__eq__Max,axiom,
% 191.04/191.67 ! [V_S_2,T_b] :
% 191.04/191.67 ( class_Groups_Olinordered__ab__group__add(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 191.04/191.67 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => 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)) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Max_Osingleton,axiom,
% 191.04/191.67 ! [V_x_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => 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 ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Min_Osingleton,axiom,
% 191.04/191.67 ! [V_x_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => 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 ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Max__ge,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => 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))) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Min__le,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => 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)) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Max__in,axiom,
% 191.04/191.67 ! [V_A_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Min__in,axiom,
% 191.04/191.67 ! [V_A_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Min_Oin__idem,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => 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) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Max_Oin__idem,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => 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) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Min__antimono,axiom,
% 191.04/191.67 ! [V_N_2,V_M_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 191.04/191.67 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 191.04/191.67 => 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))) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Max__mono,axiom,
% 191.04/191.67 ! [V_N_2,V_M_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 191.04/191.67 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 191.04/191.67 => 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))) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Min__insert,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => 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)) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Max__insert,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => 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)) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Min_Osubset__idem,axiom,
% 191.04/191.67 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 191.04/191.67 => 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) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Max_Osubset__idem,axiom,
% 191.04/191.67 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 191.04/191.67 => 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) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Min__Un,axiom,
% 191.04/191.67 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.67 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => 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)) ) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Max__Un,axiom,
% 191.04/191.67 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.67 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => 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)) ) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Min_Oinsert,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => 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)) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Max_Oinsert,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => 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)) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Min_Oinsert__remove,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 191.04/191.67 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 191.04/191.67 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 191.04/191.67 => 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)))))) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Max_Oinsert__remove,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 191.04/191.67 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 191.04/191.67 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 191.04/191.67 => 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)))))) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Max_Oclosed,axiom,
% 191.04/191.67 ! [V_A_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => ( ! [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))))))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Min_Oclosed,axiom,
% 191.04/191.67 ! [V_A_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => ( ! [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))))))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_iso__tuple__UNIV__I,axiom,
% 191.04/191.67 ! [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)))) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_fold__graph_H_Oequations_I2_J,axiom,
% 191.04/191.67 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_c,T_b] :
% 191.04/191.67 ( 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))
% 191.04/191.67 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 )
% 191.04/191.67 | ? [B_x,B_y] :
% 191.04/191.67 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y)
% 191.04/191.67 & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2))
% 191.04/191.67 & 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) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_in__lex__prod,axiom,
% 191.04/191.67 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_ba_2,V_a_2,T_c,T_b] :
% 191.04/191.67 ( 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_ba_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)))
% 191.04/191.67 <=> ( 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))
% 191.04/191.67 | ( V_a_2 = V_a_H_2
% 191.04/191.67 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_ba_2),V_b_H_2)),V_s_2)) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_card__Plus__conv__if,axiom,
% 191.04/191.67 ! [V_B_2,T_c,V_A_2,T_b] :
% 191.04/191.67 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 191.04/191.67 => 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)) )
% 191.04/191.67 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 191.04/191.67 => 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) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_InrI,axiom,
% 191.04/191.67 ! [V_A_2,T_c,V_B_2,V_ba_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),V_B_2))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(tc_sum(T_c,T_b)),hAPP(c_Sum__Type_OInr(T_b,T_c),V_ba_2)),c_Sum__Type_OPlus(T_c,T_b,V_A_2,V_B_2))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_InlI,axiom,
% 191.04/191.67 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.67 => 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))) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Plus__eq__empty__conv,axiom,
% 191.04/191.67 ! [V_B_2,V_A_2,T_c,T_b] :
% 191.04/191.67 ( 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))
% 191.04/191.67 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_Plus__def,axiom,
% 191.04/191.67 ! [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)) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_finite__Plus__iff,axiom,
% 191.04/191.67 ! [V_B_2,V_A_2,T_c,T_b] :
% 191.04/191.67 ( 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)))
% 191.04/191.67 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_finite__Plus,axiom,
% 191.04/191.67 ! [V_B_2,T_c,V_A_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 191.04/191.67 => 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))) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_finite__PlusD_I1_J,axiom,
% 191.04/191.67 ! [V_B_2,V_A_2,T_c,T_b] :
% 191.04/191.67 ( 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)))
% 191.04/191.67 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_finite__PlusD_I2_J,axiom,
% 191.04/191.67 ! [V_B_2,V_A_2,T_c,T_b] :
% 191.04/191.67 ( 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)))
% 191.04/191.67 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_UNIV__Plus__UNIV,axiom,
% 191.04/191.67 ! [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)) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_card__Plus,axiom,
% 191.04/191.67 ! [V_B_2,T_c,V_A_2,T_b] :
% 191.04/191.67 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 191.04/191.67 => 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)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_same__fstI,axiom,
% 191.04/191.67 ! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_Pa_2] :
% 191.04/191.67 ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 191.04/191.67 => ( 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)))
% 191.04/191.67 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_b,T_c,V_Pa_2,V_R_2))) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_in__finite__psubset,axiom,
% 191.04/191.67 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.67 ( 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)))
% 191.04/191.67 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.67 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_min__max_OSup__fin_Oremove,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 191.04/191.67 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = V_x_2 )
% 191.04/191.67 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 191.04/191.67 => 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)))))) ) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_min__max_OSup__fin_Oin__idem,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => 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) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_min__max_OSup__fin_Osingleton,axiom,
% 191.04/191.67 ! [V_x_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => 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 ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => 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)) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
% 191.04/191.67 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 191.04/191.67 => 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) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_min__max_Oinf__Sup__absorb,axiom,
% 191.04/191.67 ! [V_a_2,V_A_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.67 => 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 ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
% 191.04/191.67 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.67 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => 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)) ) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_min__max_OSup__fin_Oinsert,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => 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)) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 191.04/191.67 => 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 )
% 191.04/191.67 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 191.04/191.67 => 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)))))) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_min__max_OSup__fin_Oclosed,axiom,
% 191.04/191.67 ! [V_A_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => ( ! [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))))))
% 191.04/191.67 => 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)) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_min__max_OInf__le__Sup,axiom,
% 191.04/191.67 ! [V_A_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.67 => 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))) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_min__max_OInf__fin_Oremove,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 191.04/191.67 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = V_x_2 )
% 191.04/191.67 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 191.04/191.67 => 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)))))) ) ) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_min__max_OInf__fin_Oin__idem,axiom,
% 191.04/191.67 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.67 ( class_Orderings_Olinorder(T_b)
% 191.04/191.67 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.67 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.67 => 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) ) ) ) ).
% 191.04/191.67
% 191.04/191.67 fof(fact_min__max_OInf__fin_Osingleton,axiom,
% 191.04/191.67 ! [V_x_2,T_b] :
% 191.04/191.68 ( class_Orderings_Olinorder(T_b)
% 191.04/191.68 => 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 ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
% 191.04/191.68 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.68 ( class_Orderings_Olinorder(T_b)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.68 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.68 => 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)) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
% 191.04/191.68 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.68 ( class_Orderings_Olinorder(T_b)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.68 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 191.04/191.68 => 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) ) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_min__max_Osup__Inf__absorb,axiom,
% 191.04/191.68 ! [V_a_2,V_A_2,T_b] :
% 191.04/191.68 ( class_Orderings_Olinorder(T_b)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.68 => 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 ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
% 191.04/191.68 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.68 ( class_Orderings_Olinorder(T_b)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.68 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.68 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.68 => 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)) ) ) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_min__max_OInf__fin_Oinsert,axiom,
% 191.04/191.68 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.68 ( class_Orderings_Olinorder(T_b)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.68 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.68 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.68 => 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)) ) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom,
% 191.04/191.68 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.68 ( class_Orderings_Olinorder(T_b)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.68 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 191.04/191.68 => 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 )
% 191.04/191.68 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 191.04/191.68 => 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)))))) ) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_min__max_OInf__fin_Oclosed,axiom,
% 191.04/191.68 ! [V_A_2,T_b] :
% 191.04/191.68 ( class_Orderings_Olinorder(T_b)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.68 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.68 => ( ! [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))))))
% 191.04/191.68 => 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)) ) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_folding__one_Oclosed,axiom,
% 191.04/191.68 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 191.04/191.68 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.68 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.68 => ( ! [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))))))
% 191.04/191.68 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_fun__upd__image,axiom,
% 191.04/191.68 ! [V_y_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 191.04/191.68 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.68 => 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)))))) )
% 191.04/191.68 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.68 => 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) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_fun__upd__triv,axiom,
% 191.04/191.68 ! [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 ).
% 191.04/191.68
% 191.04/191.68 fof(fact_fun__upd__idem,axiom,
% 191.04/191.68 ! [T_b,T_c,V_y_2,V_x_2,V_f_2] :
% 191.04/191.68 ( hAPP(V_f_2,V_x_2) = V_y_2
% 191.04/191.68 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,T_b),V_f_2),V_x_2),V_y_2) = V_f_2 ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_fun__upd__other,axiom,
% 191.04/191.68 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 191.04/191.68 ( V_z_2 != V_x_2
% 191.04/191.68 => 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) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_fun__upd__twist,axiom,
% 191.04/191.68 ! [V_d_2,V_ba_2,V_m_2,T_c,T_b,V_ca_2,V_a_2] :
% 191.04/191.68 ( V_a_2 != V_ca_2
% 191.04/191.68 => 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_ba_2)),V_ca_2),V_d_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_m_2),V_ca_2),V_d_2)),V_a_2),V_ba_2) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_fun__upd__apply,axiom,
% 191.04/191.68 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 191.04/191.68 ( ( V_z_2 = V_x_2
% 191.04/191.68 => 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 )
% 191.04/191.68 & ( V_z_2 != V_x_2
% 191.04/191.68 => 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) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_fun__upd__same,axiom,
% 191.04/191.68 ! [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 ).
% 191.04/191.68
% 191.04/191.68 fof(fact_fun__upd__upd,axiom,
% 191.04/191.68 ! [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) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_fun__upd__idem__iff,axiom,
% 191.04/191.68 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 191.04/191.68 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2) = V_f_2
% 191.04/191.68 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_fun__upd__def,axiom,
% 191.04/191.68 ! [V_ba_2,V_f_2,T_c,T_b,V_a_2,V_x_2] :
% 191.04/191.68 ( ( V_x_2 = V_a_2
% 191.04/191.68 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_a_2),V_ba_2),V_x_2) = V_ba_2 )
% 191.04/191.68 & ( V_x_2 != V_a_2
% 191.04/191.68 => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_a_2),V_ba_2),V_x_2) = hAPP(V_f_2,V_x_2) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_finite__range__updI,axiom,
% 191.04/191.68 ! [V_ba_2,V_a_2,V_f_2,T_c,T_b] :
% 191.04/191.68 ( 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)))))
% 191.04/191.68 => 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_ba_2))),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_image__map__upd,axiom,
% 191.04/191.68 ! [V_y_2,V_m_2,T_c,V_A_2,V_x_2,T_b] :
% 191.04/191.68 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.68 => 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) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_map__upd__nonempty,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_map__upd__Some__unfold,axiom,
% 191.04/191.68 ! [V_y_2,V_x_2,V_ba_2,V_a_2,V_m_2,T_b,T_c] :
% 191.04/191.68 ( 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_ba_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
% 191.04/191.68 <=> ( ( V_x_2 = V_a_2
% 191.04/191.68 & V_ba_2 = V_y_2 )
% 191.04/191.68 | ( V_x_2 != V_a_2
% 191.04/191.68 & hAPP(V_m_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_map__upd__triv,axiom,
% 191.04/191.68 ! [T_c,V_x_2,T_b,V_k_2,V_t_2] :
% 191.04/191.68 ( hAPP(V_t_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
% 191.04/191.68 => 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 ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_map__upd__eqD1,axiom,
% 191.04/191.68 ! [V_y_2,V_n_2,V_x_2,V_a_2,V_m_2,T_c,T_b] :
% 191.04/191.68 ( 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))
% 191.04/191.68 => V_x_2 = V_y_2 ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_empty__upd__none,axiom,
% 191.04/191.68 ! [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) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_ran__map__upd,axiom,
% 191.04/191.68 ! [V_ba_2,T_c,T_b,V_a_2,V_m_2] :
% 191.04/191.68 ( hAPP(V_m_2,V_a_2) = c_Option_Ooption_ONone(T_b)
% 191.04/191.68 => 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_ba_2))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),c_Map_Oran(T_c,T_b,V_m_2)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_fun__upd__None__restrict,axiom,
% 191.04/191.68 ! [V_m_2,T_c,V_D_2,V_x_2,T_b] :
% 191.04/191.68 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 191.04/191.68 => 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))))) )
% 191.04/191.68 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 191.04/191.68 => 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) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_setprod__gen__delta,axiom,
% 191.04/191.68 ! [V_ca_2,V_ba_2,V_a_2,V_S_2,T_b,T_c] :
% 191.04/191.68 ( class_Groups_Ocomm__monoid__mult(T_c)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 191.04/191.68 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 191.04/191.68 => 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_ba_2)),V_ca_2)),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_ba_2,V_a_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
% 191.04/191.68 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 191.04/191.68 => 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_ba_2)),V_ca_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_ca_2),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)) ) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_restrict__in,axiom,
% 191.04/191.68 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.68 => 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) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_setprod__1,axiom,
% 191.04/191.68 ! [V_A_2,T_c,T_b] :
% 191.04/191.68 ( class_Groups_Ocomm__monoid__mult(T_b)
% 191.04/191.68 => 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) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_of__int__setprod,axiom,
% 191.04/191.68 ! [V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.68 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 191.04/191.68 & class_Rings_Oring__1(T_b) )
% 191.04/191.68 => 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) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_of__nat__setprod,axiom,
% 191.04/191.68 ! [V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.68 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 191.04/191.68 & class_Rings_Osemiring__1(T_b) )
% 191.04/191.68 => 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) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_int__setprod,axiom,
% 191.04/191.68 ! [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) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_setprod__timesf,axiom,
% 191.04/191.68 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 191.04/191.68 ( class_Groups_Ocomm__monoid__mult(T_b)
% 191.04/191.68 => 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)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_abs__setprod,axiom,
% 191.04/191.68 ! [V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.68 ( class_Fields_Olinordered__field(T_b)
% 191.04/191.68 => 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) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom,
% 191.04/191.68 ! [V_A_2,V_f_2,T_b] :
% 191.04/191.68 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 191.04/191.68 & class_Groups_Ocomm__monoid__mult(T_b) )
% 191.04/191.68 => 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)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_setprod__zero,axiom,
% 191.04/191.68 ! [V_f_2,V_A_2,T_b,T_c] :
% 191.04/191.68 ( class_Rings_Ocomm__semiring__1(T_c)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.68 => ( ? [B_x] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.04/191.68 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 191.04/191.68 => 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) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_setprod__zero__iff,axiom,
% 191.04/191.68 ! [V_f_2,V_A_2,T_b,T_c] :
% 191.04/191.68 ( ( class_Rings_Ocomm__semiring__1(T_c)
% 191.04/191.68 & class_Rings_Ono__zero__divisors(T_c) )
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.68 => ( 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)
% 191.04/191.68 <=> ? [B_x] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.04/191.68 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_setprod__empty,axiom,
% 191.04/191.68 ! [V_f_2,T_c,T_b] :
% 191.04/191.68 ( class_Groups_Ocomm__monoid__mult(T_b)
% 191.04/191.68 => 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) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_setprod_Oempty,axiom,
% 191.04/191.68 ! [V_g_2,T_c,T_b] :
% 191.04/191.68 ( class_Groups_Ocomm__monoid__mult(T_b)
% 191.04/191.68 => 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) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_setprod__infinite,axiom,
% 191.04/191.68 ! [V_f_2,V_A_2,T_b,T_c] :
% 191.04/191.68 ( class_Groups_Ocomm__monoid__mult(T_c)
% 191.04/191.68 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.68 => 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) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_setprod_Oinfinite,axiom,
% 191.04/191.68 ! [V_g_2,V_A_2,T_b,T_c] :
% 191.04/191.68 ( class_Groups_Ocomm__monoid__mult(T_c)
% 191.04/191.68 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.68 => 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) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_setprod__eq__1__iff,axiom,
% 191.04/191.68 ! [V_f_2,V_F_2,T_b] :
% 191.04/191.68 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 191.04/191.68 => ( 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)
% 191.04/191.68 <=> ! [B_x] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 191.04/191.68 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_restrict__map__empty,axiom,
% 191.04/191.68 ! [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) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom,
% 191.04/191.68 ! [V_f_2,V_A_2,T_b] :
% 191.04/191.68 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 191.04/191.68 & class_Groups_Ocomm__monoid__mult(T_b) )
% 191.04/191.68 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 191.04/191.68 => 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)) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_setprod_Odistrib,axiom,
% 191.04/191.68 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 191.04/191.68 ( class_Groups_Ocomm__monoid__mult(T_c)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.68 => 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)) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_setprod__dividef,axiom,
% 191.04/191.68 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 191.04/191.68 ( class_Fields_Ofield__inverse__zero(T_c)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.68 => 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)) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_restrict__out,axiom,
% 191.04/191.68 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] :
% 191.04/191.68 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.68 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_c) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_dvd__setprod,axiom,
% 191.04/191.68 ! [V_f_2,V_i_2,V_A_2,T_b,T_c] :
% 191.04/191.68 ( class_Rings_Ocomm__semiring__1(T_c)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 191.04/191.68 => 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))) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_setprod__pos__nat__iff,axiom,
% 191.04/191.68 ! [V_f_2,V_S_2,T_b] :
% 191.04/191.68 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 191.04/191.68 => ( 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)))
% 191.04/191.68 <=> ! [B_x] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 191.04/191.68 => 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))) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_setprod__dvd__setprod__subset,axiom,
% 191.04/191.68 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 191.04/191.68 ( ( class_Groups_Ocomm__monoid__mult(T_c)
% 191.04/191.68 & class_Rings_Odvd(T_c) )
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.68 => 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))) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_restrict__map__insert,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_setprod__delta,axiom,
% 191.04/191.68 ! [V_ba_2,V_a_2,V_S_2,T_b,T_c] :
% 191.04/191.68 ( class_Groups_Ocomm__monoid__mult(T_c)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 191.04/191.68 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 191.04/191.68 => 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_ba_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_ba_2,V_a_2) )
% 191.04/191.68 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 191.04/191.68 => 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_ba_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_setprod__delta_H,axiom,
% 191.04/191.68 ! [V_ba_2,V_a_2,V_S_2,T_b,T_c] :
% 191.04/191.68 ( class_Groups_Ocomm__monoid__mult(T_c)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 191.04/191.68 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 191.04/191.68 => 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_ba_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_ba_2,V_a_2) )
% 191.04/191.68 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 191.04/191.68 => 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_ba_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_restrict__map__def,axiom,
% 191.04/191.68 ! [V_m_2,T_c,V_A_2,V_x_2,T_b] :
% 191.04/191.68 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.68 => 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) )
% 191.04/191.68 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.68 => hAPP(c_Map_Orestrict__map(T_b,T_c,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_c) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_restrict__map__to__empty,axiom,
% 191.04/191.68 ! [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) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_setprod__constant,axiom,
% 191.04/191.68 ! [V_y_2,V_A_2,T_b,T_c] :
% 191.04/191.68 ( class_Groups_Ocomm__monoid__mult(T_c)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.68 => 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)) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_setprod_Oinsert,axiom,
% 191.04/191.68 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 191.04/191.68 ( class_Groups_Ocomm__monoid__mult(T_c)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.68 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.68 => 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)) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_setprod__insert,axiom,
% 191.04/191.68 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 191.04/191.68 ( class_Groups_Ocomm__monoid__mult(T_c)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.68 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.68 => 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)) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_ranI,axiom,
% 191.04/191.68 ! [T_c,V_ba_2,T_b,V_a_2,V_m_2] :
% 191.04/191.68 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_ba_2)
% 191.04/191.68 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Map_Oran(T_c,T_b,V_m_2))) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_setprod_Oinsert__remove,axiom,
% 191.04/191.68 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 191.04/191.68 ( class_Groups_Ocomm__monoid__mult(T_c)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.68 => 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)))))) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_fun__upd__restrict,axiom,
% 191.04/191.68 ! [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) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_ran__empty,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_setprod_Oremove,axiom,
% 191.04/191.68 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 191.04/191.68 ( class_Groups_Ocomm__monoid__mult(T_c)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.68 => 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)))))) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_setprod__diff1,axiom,
% 191.04/191.68 ! [V_a_2,V_f_2,V_A_2,T_b,T_c] :
% 191.04/191.68 ( class_Fields_Ofield(T_c)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.68 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_c)
% 191.04/191.68 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.68 => 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)) )
% 191.04/191.68 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.68 => 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) ) ) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_fun__upd__restrict__conv,axiom,
% 191.04/191.68 ! [V_y_2,V_m_2,T_c,V_D_2,V_x_2,T_b] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 191.04/191.68 => 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) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_restrict__fun__upd,axiom,
% 191.04/191.68 ! [V_y_2,V_m_2,T_c,V_D_2,V_x_2,T_b] :
% 191.04/191.68 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 191.04/191.68 => 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) )
% 191.04/191.68 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_D_2))
% 191.04/191.68 => 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) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_restrict__complement__singleton__eq,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_restrict__upd__same,axiom,
% 191.04/191.68 ! [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))))) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_setsum__nonneg__leq__bound,axiom,
% 191.04/191.68 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_b,T_c] :
% 191.04/191.68 ( class_Groups_Oordered__ab__group__add(T_c)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 191.04/191.68 => ( ! [B_i] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 191.04/191.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 191.04/191.68 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = V_B_2
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 191.04/191.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_setsum__nonneg__0,axiom,
% 191.04/191.68 ! [V_i_2,V_f_2,V_s_2,T_b,T_c] :
% 191.04/191.68 ( class_Groups_Oordered__ab__group__add(T_c)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 191.04/191.68 => ( ! [B_i] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 191.04/191.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 191.04/191.68 => ( 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)
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 191.04/191.68 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_pair__lessI2,axiom,
% 191.04/191.68 ! [V_t_2,V_s_2,V_ba_2,V_a_2] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_ba_2))
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2))
% 191.04/191.68 => 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_ba_2),V_t_2))),c_FunDef_Opair__less)) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_pair__lessI1,axiom,
% 191.04/191.68 ! [V_t_2,V_s_2,V_ba_2,V_a_2] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_ba_2))
% 191.04/191.68 => 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_ba_2),V_t_2))),c_FunDef_Opair__less)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_pair__leqI2,axiom,
% 191.04/191.68 ! [V_t_2,V_s_2,V_ba_2,V_a_2] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_ba_2))
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2))
% 191.04/191.68 => 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_ba_2),V_t_2))),c_FunDef_Opair__leq)) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_smax__insertI,axiom,
% 191.04/191.68 ! [V_X_2,V_x_2,V_Y_2,V_y_2] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2))
% 191.04/191.68 => ( 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))
% 191.04/191.68 => ( 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))
% 191.04/191.68 => 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)) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_smin__insertI,axiom,
% 191.04/191.68 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 191.04/191.68 => ( 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))
% 191.04/191.68 => ( 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))
% 191.04/191.68 => 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)) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_smin__emptyI,axiom,
% 191.04/191.68 ! [V_X_2] :
% 191.04/191.68 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 191.04/191.68 => 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)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_smax__emptyI,axiom,
% 191.04/191.68 ! [V_Y_2] :
% 191.04/191.68 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2))
% 191.04/191.68 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 191.04/191.68 => 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)) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_pair__leqI1,axiom,
% 191.04/191.68 ! [V_t_2,V_s_2,V_ba_2,V_a_2] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_ba_2))
% 191.04/191.68 => 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_ba_2),V_t_2))),c_FunDef_Opair__leq)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_wmin__insertI,axiom,
% 191.04/191.68 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 191.04/191.68 => ( 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))
% 191.04/191.68 => ( 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))
% 191.04/191.68 => 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)) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_wmax__insertI,axiom,
% 191.04/191.68 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))
% 191.04/191.68 => ( 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))
% 191.04/191.68 => ( 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))
% 191.04/191.68 => 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)) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom,
% 191.04/191.68 ! [V_f_2,V_A_2,T_b] :
% 191.04/191.68 ( ! [B_x] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.04/191.68 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 191.04/191.68 => 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)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_wmax__emptyI,axiom,
% 191.04/191.68 ! [V_X_2] :
% 191.04/191.68 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2))
% 191.04/191.68 => 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)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_wmin__emptyI,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_min__weak__def,axiom,
% 191.04/191.68 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)))) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_max__weak__def,axiom,
% 191.04/191.68 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)))) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_min__rpair__set,axiom,
% 191.04/191.68 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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_max__strict__def,axiom,
% 191.04/191.68 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_max__ext__additive,axiom,
% 191.04/191.68 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_b] :
% 191.04/191.68 ( 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)))
% 191.04/191.68 => ( 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)))
% 191.04/191.68 => 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))) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_min__strict__def,axiom,
% 191.04/191.68 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_max__rpair__set,axiom,
% 191.04/191.68 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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_max__extp__max__ext__eq,axiom,
% 191.04/191.68 ! [V_xa_2,V_x_2,V_R_2,T_b] :
% 191.04/191.68 ( 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)
% 191.04/191.68 <=> 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))) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_less__than__iff,axiom,
% 191.04/191.68 ! [V_y_2,V_x_2] :
% 191.04/191.68 ( 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))
% 191.04/191.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_intrel__iff,axiom,
% 191.04/191.68 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 191.04/191.68 ( 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))
% 191.04/191.68 <=> 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) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_pair__less__def,axiom,
% 191.04/191.68 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_mlex__prod__def,axiom,
% 191.04/191.68 ! [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))) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_rp__inv__image__rp,axiom,
% 191.04/191.68 ! [V_f_2,T_c,V_Pa_2,T_b] :
% 191.04/191.68 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2)
% 191.04/191.68 => c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_Pa_2),V_f_2)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_min__max_OSup__fin_Ohom__commute,axiom,
% 191.04/191.68 ! [V_N_2,V_h_2,T_b] :
% 191.04/191.68 ( class_Orderings_Olinorder(T_b)
% 191.04/191.68 => ( ! [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))
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 191.04/191.68 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.68 => 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)) ) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_rp__inv__image__def,axiom,
% 191.04/191.68 ! [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))) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_in__inv__image,axiom,
% 191.04/191.68 ! [V_f_2,V_r_2,T_c,V_y_2,V_x_2,T_b] :
% 191.04/191.68 ( hBOOL(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)))
% 191.04/191.68 <=> 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)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_min__max_OInf__fin_Ohom__commute,axiom,
% 191.04/191.68 ! [V_N_2,V_h_2,T_b] :
% 191.04/191.68 ( class_Orderings_Olinorder(T_b)
% 191.04/191.68 => ( ! [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))
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 191.04/191.68 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.68 => 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)) ) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Max_Ohom__commute,axiom,
% 191.04/191.68 ! [V_N_2,V_h_2,T_b] :
% 191.04/191.68 ( class_Orderings_Olinorder(T_b)
% 191.04/191.68 => ( ! [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))
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 191.04/191.68 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.68 => 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)) ) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_measure__def,axiom,
% 191.04/191.68 ! [T_b] : c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_irrefl__def,axiom,
% 191.04/191.68 ! [V_r_2,T_b] :
% 191.04/191.68 ( c_Relation_Oirrefl(T_b,V_r_2)
% 191.04/191.68 <=> ! [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)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Field__insert,axiom,
% 191.04/191.68 ! [V_r_2,V_ba_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_ba_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_ba_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OField(T_b),V_r_2)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Id__on__def,axiom,
% 191.04/191.68 ! [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)))) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Id__on__def_H,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Id__on__empty,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Field__empty,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_mono__Field,axiom,
% 191.04/191.68 ! [V_s_2,V_r_2,T_b] :
% 191.04/191.68 ( 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))
% 191.04/191.68 => 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))) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Field__Un,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_finite__Field,axiom,
% 191.04/191.68 ! [V_r_2,T_b] :
% 191.04/191.68 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 191.04/191.68 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_OField(T_b),V_r_2))) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Id__on__eqI,axiom,
% 191.04/191.68 ! [V_A_2,T_b,V_ba_2,V_a_2] :
% 191.04/191.68 ( V_a_2 = V_ba_2
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.68 => 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_ba_2)),c_Relation_OId__on(T_b,V_A_2))) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Id__on__iff,axiom,
% 191.04/191.68 ! [V_A_2,V_y_2,V_x_2,T_b] :
% 191.04/191.68 ( hBOOL(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)))
% 191.04/191.68 <=> ( V_x_2 = V_y_2
% 191.04/191.68 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Id__onE,axiom,
% 191.04/191.68 ! [V_A_2,V_ca_2,T_b] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_ca_2),c_Relation_OId__on(T_b,V_A_2)))
% 191.04/191.68 => ~ ! [B_x] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.04/191.68 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Min_Ohom__commute,axiom,
% 191.04/191.68 ! [V_N_2,V_h_2,T_b] :
% 191.04/191.68 ( class_Orderings_Olinorder(T_b)
% 191.04/191.68 => ( ! [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))
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 191.04/191.68 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.68 => 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)) ) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Sup__fin_Ohom__commute,axiom,
% 191.04/191.68 ! [V_N_2,V_h_2,T_b] :
% 191.04/191.68 ( class_Lattices_Olattice(T_b)
% 191.04/191.68 => ( ! [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))
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 191.04/191.68 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.68 => 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)) ) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_setprod__mono__one__left,axiom,
% 191.04/191.68 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 191.04/191.68 ( class_Groups_Ocomm__monoid__mult(T_c)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 191.04/191.68 => ( ! [B_x] :
% 191.04/191.68 ( 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)))
% 191.04/191.68 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 191.04/191.68 => 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) ) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_setprod__mono__one__right,axiom,
% 191.04/191.68 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 191.04/191.68 ( class_Groups_Ocomm__monoid__mult(T_c)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 191.04/191.68 => ( ! [B_x] :
% 191.04/191.68 ( 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)))
% 191.04/191.68 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 191.04/191.68 => 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) ) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_setsum__mono__zero__right,axiom,
% 191.04/191.68 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 191.04/191.68 ( class_Groups_Ocomm__monoid__add(T_c)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 191.04/191.68 => ( ! [B_x] :
% 191.04/191.68 ( 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)))
% 191.04/191.68 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 191.04/191.68 => 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) ) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_setsum__mono__zero__left,axiom,
% 191.04/191.68 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 191.04/191.68 ( class_Groups_Ocomm__monoid__add(T_c)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 191.04/191.68 => ( ! [B_x] :
% 191.04/191.68 ( 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)))
% 191.04/191.68 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 191.04/191.68 => 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) ) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_escape,axiom,
% 191.04/191.68 ! [V_Q_2,V_ca_2,V_Ga_2,T_b,V_Pa_2] :
% 191.04/191.68 ( ! [B_Z,B_s] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s))
% 191.04/191.68 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),B_s))),V_ca_2),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_b),hAPP(V_Q_2,B_Z)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) )
% 191.04/191.68 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_card__Pow,axiom,
% 191.04/191.68 ! [V_A_2,T_b] :
% 191.04/191.68 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.68 => 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)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_PowI,axiom,
% 191.04/191.68 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.68 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Pow__insert,axiom,
% 191.04/191.68 ! [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))) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Pow__empty,axiom,
% 191.04/191.68 ! [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))) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Pow__bottom,axiom,
% 191.04/191.68 ! [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))) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Pow__not__empty,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Pow__top,axiom,
% 191.04/191.68 ! [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))) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_PowD,axiom,
% 191.04/191.68 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 191.04/191.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Pow__iff,axiom,
% 191.04/191.68 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 191.04/191.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Cantors__paradox,axiom,
% 191.04/191.68 ! [V_A_2,T_b] :
% 191.04/191.68 ~ ? [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) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_image__Pow__surj,axiom,
% 191.04/191.68 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 191.04/191.68 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_B_2
% 191.04/191.68 => 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) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Pow__UNIV,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_finite__Pow__iff,axiom,
% 191.04/191.68 ! [V_A_2,T_b] :
% 191.04/191.68 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)))
% 191.04/191.68 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Pow__mono,axiom,
% 191.04/191.68 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.68 => 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))) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Un__Pow__subset,axiom,
% 191.04/191.68 ! [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)))) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_UN__Pow__subset,axiom,
% 191.04/191.68 ! [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)))) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Powp__Pow__eq,axiom,
% 191.04/191.68 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.68 ( 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))
% 191.04/191.68 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_image__Pow__mono,axiom,
% 191.04/191.68 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.68 ( 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))
% 191.04/191.68 => 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))) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_finite__empty__induct,axiom,
% 191.04/191.68 ! [V_Pa_2,V_A_2,T_b] :
% 191.04/191.68 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.68 => ( hBOOL(hAPP(V_Pa_2,V_A_2))
% 191.04/191.68 => ( ! [B_a,B_A] :
% 191.04/191.68 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A))
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
% 191.04/191.68 => ( hBOOL(hAPP(V_Pa_2,B_A))
% 191.04/191.68 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(hAPP(c_Set_Oinsert(T_b),B_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) )
% 191.04/191.68 => hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_folding__one__idem_Ounion__idem,axiom,
% 191.04/191.68 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 191.04/191.68 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.68 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.68 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.68 => 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)) ) ) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_finite__subset__induct,axiom,
% 191.04/191.68 ! [V_Pa_2,V_A_2,V_F_2,T_b] :
% 191.04/191.68 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2))
% 191.04/191.68 => ( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 191.04/191.68 => ( ! [B_a,B_F] :
% 191.04/191.68 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 191.04/191.68 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F))
% 191.04/191.68 => ( hBOOL(hAPP(V_Pa_2,B_F))
% 191.04/191.68 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F))) ) ) ) )
% 191.04/191.68 => hBOOL(hAPP(V_Pa_2,V_F_2)) ) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_folding__one__idem_Oidem,axiom,
% 191.04/191.68 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 191.04/191.68 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 191.04/191.68 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_folding__one__idem_Oin__idem,axiom,
% 191.04/191.68 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 191.04/191.68 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.68 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_folding__one__idem_Oinsert__idem,axiom,
% 191.04/191.68 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 191.04/191.68 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.68 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.68 => 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)) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_folding__one__idem_Osubset__idem,axiom,
% 191.04/191.68 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 191.04/191.68 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.68 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 191.04/191.68 => 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) ) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_setsum__strict__mono,axiom,
% 191.04/191.68 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 191.04/191.68 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 191.04/191.68 & class_Groups_Oordered__cancel__ab__semigroup__add(T_c) )
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.68 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.68 => ( ! [B_x] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.04/191.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 191.04/191.68 => 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))) ) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_equiv__intrel__iff,axiom,
% 191.04/191.68 ! [V_y_2,V_x_2] :
% 191.04/191.68 ( 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))))
% 191.04/191.68 <=> 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)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_setsum__Plus,axiom,
% 191.04/191.68 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 191.04/191.68 ( class_Groups_Ocomm__monoid__add(T_d)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 191.04/191.68 => 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)) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Image__empty,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Image__Un,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Image__UN,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_image__compose,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_K__record__comp,axiom,
% 191.04/191.68 ! [V_x_2,V_f_2,V_ca_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,hAPP(c_COMBK(T_b,T_c),V_ca_2)),V_f_2),V_x_2) = V_ca_2 ).
% 191.04/191.68
% 191.04/191.68 fof(fact_o__eq__dest__lhs,axiom,
% 191.04/191.68 ! [V_v_2,V_ca_2,V_ba_2,V_a_2,T_b,T_c,T_d] :
% 191.04/191.68 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_ba_2) = V_ca_2
% 191.04/191.68 => hAPP(V_a_2,hAPP(V_ba_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_apfst__compose,axiom,
% 191.04/191.68 ! [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) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_apsnd__compose,axiom,
% 191.04/191.68 ! [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) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_comp__cong,axiom,
% 191.04/191.68 ! [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] :
% 191.04/191.68 ( 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))
% 191.04/191.68 => 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) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_o__def,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_o__assoc,axiom,
% 191.04/191.68 ! [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) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_o__apply,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_o__eq__dest,axiom,
% 191.04/191.68 ! [V_v_2,V_d_2,V_ca_2,T_e,V_ba_2,V_a_2,T_b,T_c,T_d] :
% 191.04/191.68 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_ba_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_ca_2),V_d_2)
% 191.04/191.68 => hAPP(V_a_2,hAPP(V_ba_2,V_v_2)) = hAPP(V_ca_2,hAPP(V_d_2,V_v_2)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_o__eq__elim,axiom,
% 191.04/191.68 ! [V_d_2,V_ca_2,T_e,V_ba_2,V_a_2,T_b,T_c,T_d] :
% 191.04/191.68 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_ba_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_ca_2),V_d_2)
% 191.04/191.68 => ! [B_v] : hAPP(V_a_2,hAPP(V_ba_2,B_v)) = hAPP(V_ca_2,hAPP(V_d_2,B_v)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_fun__upd__comp,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_comp__surj,axiom,
% 191.04/191.68 ! [V_g_2,T_d,V_f_2,T_b,T_c] :
% 191.04/191.68 ( 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))
% 191.04/191.68 => ( 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))
% 191.04/191.68 => 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)) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Image__mono,axiom,
% 191.04/191.68 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_c,T_b] :
% 191.04/191.68 ( 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))
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2))
% 191.04/191.68 => 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))) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Un__Image,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Image__iff,axiom,
% 191.04/191.68 ! [V_A_2,V_r_2,T_c,V_ba_2,T_b] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 191.04/191.68 <=> ? [B_x] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 191.04/191.68 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_ba_2)),V_r_2)) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_rev__ImageI,axiom,
% 191.04/191.68 ! [V_r_2,V_ba_2,T_c,V_A_2,V_a_2,T_b] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.68 => ( 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_ba_2)),V_r_2))
% 191.04/191.68 => hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Image__eq__UN,axiom,
% 191.04/191.68 ! [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))))) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Image__singleton__iff,axiom,
% 191.04/191.68 ! [V_a_2,V_r_2,T_c,V_ba_2,T_b] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_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))))))
% 191.04/191.68 <=> 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_ba_2)),V_r_2)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_of__int,axiom,
% 191.04/191.68 ! [V_j_2,V_i_2,T_b] :
% 191.04/191.68 ( class_Rings_Oring__1(T_b)
% 191.04/191.68 => 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)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_One__int__def,axiom,
% 191.04/191.68 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))))) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_mult,axiom,
% 191.04/191.68 ! [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))))) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_UN__o,axiom,
% 191.04/191.68 ! [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) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Rep__Integ__inverse,axiom,
% 191.04/191.68 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ).
% 191.04/191.68
% 191.04/191.68 fof(fact_split__comp,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_number__of__code__numeral__def,axiom,
% 191.04/191.68 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) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_int__of__def,axiom,
% 191.04/191.68 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) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_minus,axiom,
% 191.04/191.68 ! [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))))) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Zero__int__def,axiom,
% 191.04/191.68 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))))) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_int__def,axiom,
% 191.04/191.68 ! [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))))) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_add,axiom,
% 191.04/191.68 ! [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))))) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_nat,axiom,
% 191.04/191.68 ! [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) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_minus__int__def,axiom,
% 191.04/191.68 ! [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))))))) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_less,axiom,
% 191.04/191.68 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 191.04/191.68 ( 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)))))))
% 191.04/191.68 <=> 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))) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_le,axiom,
% 191.04/191.68 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 191.04/191.68 ( 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)))))))
% 191.04/191.68 <=> 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))) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_hoare__derivs_OIf,axiom,
% 191.04/191.68 ! [V_d_2,V_Q_2,V_ca_2,V_ba_2,V_Pa_2,V_Ga_2,T_b] :
% 191.04/191.68 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_ba_2)),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 191.04/191.68 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_ba_2))),V_d_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 191.04/191.68 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),c_Com_Ocom_OCond(V_ba_2,V_ca_2,V_d_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Loop,axiom,
% 191.04/191.68 ! [V_ca_2,V_ba_2,V_Pa_2,V_Ga_2,T_b] :
% 191.04/191.68 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_ba_2)),V_ca_2),V_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 191.04/191.68 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),c_Com_Ocom_OWhile(V_ba_2,V_ca_2)),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_ba_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Nitpick_Odenom__def,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_peek__and__def,axiom,
% 191.04/191.68 ! [V_s_2,V_Z_2,V_p_2,V_Pa_2,T_b] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_p_2),V_Z_2),V_s_2))
% 191.04/191.68 <=> ( hBOOL(hAPP(hAPP(V_Pa_2,V_Z_2),V_s_2))
% 191.04/191.68 & hBOOL(hAPP(V_p_2,V_s_2)) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Nitpick_Onum__def,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_folding_Oremove,axiom,
% 191.04/191.68 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 191.04/191.68 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.68 => 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)) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_eq__Abs__Integ,axiom,
% 191.04/191.68 ! [V_z_2] :
% 191.04/191.68 ~ ! [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))))) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_folding_Oinsert__remove,axiom,
% 191.04/191.68 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 191.04/191.68 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.68 => 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)) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_folding_Ocommute__comps_I1_J,axiom,
% 191.04/191.68 ! [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] :
% 191.04/191.68 ( c_Finite__Set_Ofolding(T_b,T_c,V_fa_2,V_F_2)
% 191.04/191.68 => 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) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_folding_Ocommute__comp,axiom,
% 191.04/191.68 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_c,T_b] :
% 191.04/191.68 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 191.04/191.68 => 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)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_folding_Ocommute__left__comp,axiom,
% 191.04/191.68 ! [V_g_2,V_x_2,V_y_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 191.04/191.68 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 191.04/191.68 => 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)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_folding_Ocommute__left__comp_H_H,axiom,
% 191.04/191.68 ! [V_g_2,T_d,V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 191.04/191.68 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.68 => 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)) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_folding_Ocommute__comp_H_H,axiom,
% 191.04/191.68 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 191.04/191.68 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.68 => 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)) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_folding_Ocommute__left__comp_H,axiom,
% 191.04/191.68 ! [V_g_2,V_x_2,T_d,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 191.04/191.68 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.68 => 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)) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_folding_Ocommute__comp_H,axiom,
% 191.04/191.68 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 191.04/191.68 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.68 => 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)) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_folding_Oinsert,axiom,
% 191.04/191.68 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 191.04/191.68 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.68 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.68 => 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)) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_setsum__reindex__nonzero,axiom,
% 191.04/191.68 ! [T_c,V_h_2,V_f_2,V_S_2,T_b,T_d] :
% 191.04/191.68 ( class_Groups_Ocomm__monoid__add(T_d)
% 191.04/191.68 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 191.04/191.68 => ( ! [B_x] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 191.04/191.68 => ! [B_y] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2))
% 191.04/191.68 => ( B_x != B_y
% 191.04/191.68 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 191.04/191.68 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) )
% 191.04/191.68 => 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) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Random__Sequence_Omap__def,axiom,
% 191.04/191.68 ! [V_Pa_2,V_f_2,T_b,T_c] : c_Random__Sequence_Omap(T_c,T_b,V_f_2,V_Pa_2) = c_Random__Sequence_Obind(T_c,T_b,V_Pa_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),T_c,c_Random__Sequence_Osingle(T_b)),V_f_2)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_quotient__def,axiom,
% 191.04/191.68 ! [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)))) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_quotient__is__empty,axiom,
% 191.04/191.68 ! [V_r_2,V_A_2,T_b] :
% 191.04/191.68 ( 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))
% 191.04/191.68 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_quotient__is__empty2,axiom,
% 191.04/191.68 ! [V_r_2,V_A_2,T_b] :
% 191.04/191.68 ( 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)
% 191.04/191.68 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_quotient__empty,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_quotientI,axiom,
% 191.04/191.68 ! [V_r_2,V_A_2,V_x_2,T_b] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.68 => 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))) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_singleton__quotient,axiom,
% 191.04/191.68 ! [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))) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_subset__equiv__class,axiom,
% 191.04/191.68 ! [V_a_2,V_ba_2,V_r_2,V_A_2,T_b] :
% 191.04/191.68 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 191.04/191.68 => ( 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_ba_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))))))
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),V_A_2))
% 191.04/191.68 => 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_ba_2)),V_r_2)) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_quotientE,axiom,
% 191.04/191.68 ! [V_r_2,V_A_2,V_X_2,T_b] :
% 191.04/191.68 ( 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)))
% 191.04/191.68 => ~ ! [B_x] :
% 191.04/191.68 ( 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))))
% 191.04/191.68 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_eq__equiv__class__iff2,axiom,
% 191.04/191.68 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 191.04/191.68 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 191.04/191.68 => ( 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)
% 191.04/191.68 <=> hBOOL(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)) ) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_equiv__intrel,axiom,
% 191.04/191.68 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) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_equiv__class__self,axiom,
% 191.04/191.68 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 191.04/191.68 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.68 => 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)))))) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_equiv__class__eq,axiom,
% 191.04/191.68 ! [V_ba_2,V_a_2,V_r_2,V_A_2,T_b] :
% 191.04/191.68 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 191.04/191.68 => ( 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_ba_2)),V_r_2))
% 191.04/191.68 => 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_ba_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_quotient__eq__iff,axiom,
% 191.04/191.68 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 191.04/191.68 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 191.04/191.68 => ( 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)))
% 191.04/191.68 => ( 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)))
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 191.04/191.68 => ( V_X_2 = V_Y_2
% 191.04/191.68 <=> hBOOL(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)) ) ) ) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_quotient__eqI,axiom,
% 191.04/191.68 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 191.04/191.68 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 191.04/191.68 => ( 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)))
% 191.04/191.68 => ( 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)))
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 191.04/191.68 => ( hBOOL(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))
% 191.04/191.68 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_eq__equiv__class__iff,axiom,
% 191.04/191.68 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 191.04/191.68 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 191.04/191.68 => ( 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))))
% 191.04/191.68 <=> hBOOL(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)) ) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_eq__equiv__class,axiom,
% 191.04/191.68 ! [V_A_2,V_ba_2,V_a_2,V_r_2,T_b] :
% 191.04/191.68 ( 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_ba_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 191.04/191.68 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),V_A_2))
% 191.04/191.68 => 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_ba_2)),V_r_2)) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_equiv__class__eq__iff,axiom,
% 191.04/191.68 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 191.04/191.68 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 191.04/191.68 => ( hBOOL(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))
% 191.04/191.68 <=> ( 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))))
% 191.04/191.68 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.68 & hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_equiv__class__subset,axiom,
% 191.04/191.68 ! [V_ba_2,V_a_2,V_r_2,V_A_2,T_b] :
% 191.04/191.68 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 191.04/191.68 => ( 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_ba_2)),V_r_2))
% 191.04/191.68 => 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_ba_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_UN__equiv__class2,axiom,
% 191.04/191.68 ! [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] :
% 191.04/191.68 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 191.04/191.68 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 191.04/191.68 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a1_2),V_A1_2))
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a2_2),V_A2_2))
% 191.04/191.68 => 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) ) ) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_UN__equiv__class,axiom,
% 191.04/191.68 ! [V_a_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 191.04/191.68 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 191.04/191.68 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.68 => 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) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_equiv__class__nondisjoint,axiom,
% 191.04/191.68 ! [V_ba_2,V_a_2,V_x_2,V_r_2,V_A_2,T_b] :
% 191.04/191.68 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 191.04/191.68 => ( 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_ba_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))
% 191.04/191.68 => 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_ba_2)),V_r_2)) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf1I,axiom,
% 191.04/191.68 ! [T_b,V_B_2,V_x_2,V_A_2] :
% 191.04/191.68 ( hBOOL(hAPP(V_A_2,V_x_2))
% 191.04/191.68 => ( hBOOL(hAPP(V_B_2,V_x_2))
% 191.04/191.68 => 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)) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf1E,axiom,
% 191.04/191.68 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 191.04/191.68 ( 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))
% 191.04/191.68 => ~ ( hBOOL(hAPP(V_A_2,V_x_2))
% 191.04/191.68 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_IntE,axiom,
% 191.04/191.68 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 191.04/191.68 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 191.04/191.68 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_IntI,axiom,
% 191.04/191.68 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
% 191.04/191.68 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_finite__Int,axiom,
% 191.04/191.68 ! [V_Ga_2,V_F_2,T_b] :
% 191.04/191.68 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 191.04/191.68 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) )
% 191.04/191.68 => 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))) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf__eq__top__iff,axiom,
% 191.04/191.68 ! [V_y_2,V_x_2,T_b] :
% 191.04/191.68 ( class_Lattices_Obounded__lattice__top(T_b)
% 191.04/191.68 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b)
% 191.04/191.68 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_b)
% 191.04/191.68 & V_y_2 = c_Orderings_Otop__class_Otop(T_b) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf__top__right,axiom,
% 191.04/191.68 ! [V_x,T_a] :
% 191.04/191.68 ( class_Lattices_Obounded__lattice__top(T_a)
% 191.04/191.68 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf__top__left,axiom,
% 191.04/191.68 ! [V_x,T_a] :
% 191.04/191.68 ( class_Lattices_Obounded__lattice__top(T_a)
% 191.04/191.68 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Int__UNIV__right,axiom,
% 191.04/191.68 ! [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 ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Int__UNIV__left,axiom,
% 191.04/191.68 ! [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 ).
% 191.04/191.68
% 191.04/191.68 fof(fact_IntD2,axiom,
% 191.04/191.68 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 191.04/191.68 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_IntD1,axiom,
% 191.04/191.68 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 191.04/191.68 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Int__iff,axiom,
% 191.04/191.68 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 191.04/191.68 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 191.04/191.68 & hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf__Int__eq,axiom,
% 191.04/191.68 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 191.04/191.68 ( 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))
% 191.04/191.68 <=> 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))) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_sup__inf__distrib2,axiom,
% 191.04/191.68 ! [V_x,V_z,V_y,T_a] :
% 191.04/191.68 ( class_Lattices_Odistrib__lattice(T_a)
% 191.04/191.68 => 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)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf__sup__distrib2,axiom,
% 191.04/191.68 ! [V_x,V_z,V_y,T_a] :
% 191.04/191.68 ( class_Lattices_Odistrib__lattice(T_a)
% 191.04/191.68 => 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)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_sup__inf__distrib1,axiom,
% 191.04/191.68 ! [V_z,V_y,V_x,T_a] :
% 191.04/191.68 ( class_Lattices_Odistrib__lattice(T_a)
% 191.04/191.68 => 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)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf__sup__distrib1,axiom,
% 191.04/191.68 ! [V_z,V_y,V_x,T_a] :
% 191.04/191.68 ( class_Lattices_Odistrib__lattice(T_a)
% 191.04/191.68 => 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)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_sup__inf__absorb,axiom,
% 191.04/191.68 ! [V_y,V_x,T_a] :
% 191.04/191.68 ( class_Lattices_Olattice(T_a)
% 191.04/191.68 => 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 ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf__sup__absorb,axiom,
% 191.04/191.68 ! [V_y,V_x,T_a] :
% 191.04/191.68 ( class_Lattices_Olattice(T_a)
% 191.04/191.68 => 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 ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Un__Int__crazy,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Un__Int__distrib2,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Int__Un__distrib2,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Un__Int__distrib,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Int__Un__distrib,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Int__empty__left,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Int__empty__right,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_disjoint__iff__not__equal,axiom,
% 191.04/191.68 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.68 ( 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))
% 191.04/191.68 <=> ! [B_x] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.04/191.68 => ! [B_xa] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2))
% 191.04/191.68 => B_x != B_xa ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf__bot__left,axiom,
% 191.04/191.68 ! [V_x,T_a] :
% 191.04/191.68 ( class_Lattices_Obounded__lattice__bot(T_a)
% 191.04/191.68 => 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) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf__bot__right,axiom,
% 191.04/191.68 ! [V_x,T_a] :
% 191.04/191.68 ( class_Lattices_Obounded__lattice__bot(T_a)
% 191.04/191.68 => 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) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_insert__inter__insert,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_restrict__restrict,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom,
% 191.04/191.68 ! [V_B_2,V_A_2] :
% 191.04/191.68 ( c_Nat__Transfer_Onat__set(V_A_2)
% 191.04/191.68 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 191.04/191.68 => 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)) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf1D1,axiom,
% 191.04/191.68 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 191.04/191.68 ( 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))
% 191.04/191.68 => hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf1D2,axiom,
% 191.04/191.68 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 191.04/191.68 ( 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))
% 191.04/191.68 => hBOOL(hAPP(V_B_2,V_x_2)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Int__absorb,axiom,
% 191.04/191.68 ! [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 ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Int__commute,axiom,
% 191.04/191.68 ! [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) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Int__left__absorb,axiom,
% 191.04/191.68 ! [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) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Int__left__commute,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Int__assoc,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf_Oidem,axiom,
% 191.04/191.68 ! [V_a,T_a] :
% 191.04/191.68 ( class_Lattices_Osemilattice__inf(T_a)
% 191.04/191.68 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf__idem,axiom,
% 191.04/191.68 ! [V_x,T_a] :
% 191.04/191.68 ( class_Lattices_Osemilattice__inf(T_a)
% 191.04/191.68 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf_Ocommute,axiom,
% 191.04/191.68 ! [V_b,V_a,T_a] :
% 191.04/191.68 ( class_Lattices_Osemilattice__inf(T_a)
% 191.04/191.68 => 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) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf__sup__aci_I1_J,axiom,
% 191.04/191.68 ! [V_y,V_x,T_a] :
% 191.04/191.68 ( class_Lattices_Olattice(T_a)
% 191.04/191.68 => 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) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf__commute,axiom,
% 191.04/191.68 ! [V_y,V_x,T_a] :
% 191.04/191.68 ( class_Lattices_Osemilattice__inf(T_a)
% 191.04/191.68 => 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) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf_Oleft__idem,axiom,
% 191.04/191.68 ! [V_b,V_a,T_a] :
% 191.04/191.68 ( class_Lattices_Osemilattice__inf(T_a)
% 191.04/191.68 => 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) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf__sup__aci_I4_J,axiom,
% 191.04/191.68 ! [V_y,V_x,T_a] :
% 191.04/191.68 ( class_Lattices_Olattice(T_a)
% 191.04/191.68 => 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) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf__left__idem,axiom,
% 191.04/191.68 ! [V_y,V_x,T_a] :
% 191.04/191.68 ( class_Lattices_Osemilattice__inf(T_a)
% 191.04/191.68 => 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) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf_Oleft__commute,axiom,
% 191.04/191.68 ! [V_c,V_a,V_b,T_a] :
% 191.04/191.68 ( class_Lattices_Osemilattice__inf(T_a)
% 191.04/191.68 => 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)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf__sup__aci_I3_J,axiom,
% 191.04/191.68 ! [V_z,V_y,V_x,T_a] :
% 191.04/191.68 ( class_Lattices_Olattice(T_a)
% 191.04/191.68 => 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)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf__left__commute,axiom,
% 191.04/191.68 ! [V_z,V_y,V_x,T_a] :
% 191.04/191.68 ( class_Lattices_Osemilattice__inf(T_a)
% 191.04/191.68 => 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)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf_Oassoc,axiom,
% 191.04/191.68 ! [V_c,V_b,V_a,T_a] :
% 191.04/191.68 ( class_Lattices_Osemilattice__inf(T_a)
% 191.04/191.68 => 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)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf__sup__aci_I2_J,axiom,
% 191.04/191.68 ! [V_z,V_y,V_x,T_a] :
% 191.04/191.68 ( class_Lattices_Olattice(T_a)
% 191.04/191.68 => 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)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf__assoc,axiom,
% 191.04/191.68 ! [V_z,V_y,V_x,T_a] :
% 191.04/191.68 ( class_Lattices_Osemilattice__inf(T_a)
% 191.04/191.68 => 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)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf__apply,axiom,
% 191.04/191.68 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 191.04/191.68 ( class_Lattices_Olattice(T_b)
% 191.04/191.68 => 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)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf__fun__def,axiom,
% 191.04/191.68 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 191.04/191.68 ( class_Lattices_Olattice(T_b)
% 191.04/191.68 => 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)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf__min,axiom,
% 191.04/191.68 ! [T_b] :
% 191.04/191.68 ( ( class_Lattices_Osemilattice__inf(T_b)
% 191.04/191.68 & class_Orderings_Olinorder(T_b) )
% 191.04/191.68 => c_Lattices_Osemilattice__inf__class_Oinf(T_b) = c_Orderings_Oord__class_Omin(T_b) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Inf__fin_Oidem,axiom,
% 191.04/191.68 ! [V_x,T_a] :
% 191.04/191.68 ( class_Lattices_Olattice(T_a)
% 191.04/191.68 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_less__infI2,axiom,
% 191.04/191.68 ! [V_a,V_x,V_b,T_a] :
% 191.04/191.68 ( class_Lattices_Osemilattice__inf(T_a)
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 191.04/191.68 => 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)) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_less__infI1,axiom,
% 191.04/191.68 ! [V_b,V_x,V_a,T_a] :
% 191.04/191.68 ( class_Lattices_Osemilattice__inf(T_a)
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 191.04/191.68 => 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)) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Diff__Int2,axiom,
% 191.04/191.68 ! [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) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Diff__Int__distrib2,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Int__Diff,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Diff__Int__distrib,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_le__infE,axiom,
% 191.04/191.68 ! [V_b,V_a,V_x,T_a] :
% 191.04/191.68 ( class_Lattices_Osemilattice__inf(T_a)
% 191.04/191.68 => ( 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)))
% 191.04/191.68 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 191.04/191.68 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf__mono,axiom,
% 191.04/191.68 ! [V_d,V_b,V_c,V_a,T_a] :
% 191.04/191.68 ( class_Lattices_Osemilattice__inf(T_a)
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 191.04/191.68 => 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))) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf__greatest,axiom,
% 191.04/191.68 ! [V_z,V_y,V_x,T_a] :
% 191.04/191.68 ( class_Lattices_Osemilattice__inf(T_a)
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 191.04/191.68 => 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))) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_le__infI,axiom,
% 191.04/191.68 ! [V_b,V_a,V_x,T_a] :
% 191.04/191.68 ( class_Lattices_Osemilattice__inf(T_a)
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 191.04/191.68 => 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))) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf__absorb2,axiom,
% 191.04/191.68 ! [V_x,V_y,T_a] :
% 191.04/191.68 ( class_Lattices_Osemilattice__inf(T_a)
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 191.04/191.68 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf__absorb1,axiom,
% 191.04/191.68 ! [V_y,V_x,T_a] :
% 191.04/191.68 ( class_Lattices_Osemilattice__inf(T_a)
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 191.04/191.68 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_le__infI2,axiom,
% 191.04/191.68 ! [V_a,V_x,V_b,T_a] :
% 191.04/191.68 ( class_Lattices_Osemilattice__inf(T_a)
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 191.04/191.68 => 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)) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_le__infI1,axiom,
% 191.04/191.68 ! [V_b,V_x,V_a,T_a] :
% 191.04/191.68 ( class_Lattices_Osemilattice__inf(T_a)
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 191.04/191.68 => 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)) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_le__inf__iff,axiom,
% 191.04/191.68 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 191.04/191.68 ( class_Lattices_Osemilattice__inf(T_b)
% 191.04/191.68 => ( 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)))
% 191.04/191.68 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 191.04/191.68 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_le__iff__inf,axiom,
% 191.04/191.68 ! [V_y_2,V_x_2,T_b] :
% 191.04/191.68 ( class_Lattices_Osemilattice__inf(T_b)
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 191.04/191.68 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf__le2,axiom,
% 191.04/191.68 ! [V_y,V_x,T_a] :
% 191.04/191.68 ( class_Lattices_Osemilattice__inf(T_a)
% 191.04/191.68 => 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)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf__sup__ord_I2_J,axiom,
% 191.04/191.68 ! [V_y,V_x,T_a] :
% 191.04/191.68 ( class_Lattices_Olattice(T_a)
% 191.04/191.68 => 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)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf__le1,axiom,
% 191.04/191.68 ! [V_y,V_x,T_a] :
% 191.04/191.68 ( class_Lattices_Osemilattice__inf(T_a)
% 191.04/191.68 => 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)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf__sup__ord_I1_J,axiom,
% 191.04/191.68 ! [V_y,V_x,T_a] :
% 191.04/191.68 ( class_Lattices_Olattice(T_a)
% 191.04/191.68 => 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)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Int__lower1,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Int__lower2,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Int__absorb2,axiom,
% 191.04/191.68 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.68 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Int__absorb1,axiom,
% 191.04/191.68 ! [V_A_2,V_B_2,T_b] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 191.04/191.68 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Int__greatest,axiom,
% 191.04/191.68 ! [V_B_2,V_A_2,V_C_2,T_b] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2))
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2))
% 191.04/191.68 => 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))) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Int__mono,axiom,
% 191.04/191.68 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 191.04/191.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 191.04/191.68 => 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))) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Pow__Int__eq,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Int__UN__distrib2,axiom,
% 191.04/191.68 ! [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))) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_UN__extend__simps_I4_J,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Int__UN__distrib,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_UN__extend__simps_I5_J,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_UN__simps_I4_J,axiom,
% 191.04/191.68 ! [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) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_UN__simps_I5_J,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_distrib__sup__le,axiom,
% 191.04/191.68 ! [V_z,V_y,V_x,T_a] :
% 191.04/191.68 ( class_Lattices_Olattice(T_a)
% 191.04/191.68 => 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)))) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_distrib__inf__le,axiom,
% 191.04/191.68 ! [V_z,V_y,V_x,T_a] :
% 191.04/191.68 ( class_Lattices_Olattice(T_a)
% 191.04/191.68 => 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)))) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_inf__compl__bot,axiom,
% 191.04/191.68 ! [V_x,T_a] :
% 191.04/191.68 ( class_Lattices_Oboolean__algebra(T_a)
% 191.04/191.68 => 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) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_compl__inf__bot,axiom,
% 191.04/191.68 ! [V_x,T_a] :
% 191.04/191.68 ( class_Lattices_Oboolean__algebra(T_a)
% 191.04/191.68 => 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) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_diff__eq,axiom,
% 191.04/191.68 ! [V_y,V_x,T_a] :
% 191.04/191.68 ( class_Lattices_Oboolean__algebra(T_a)
% 191.04/191.68 => 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)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_compl__inf,axiom,
% 191.04/191.68 ! [V_y,V_x,T_a] :
% 191.04/191.68 ( class_Lattices_Oboolean__algebra(T_a)
% 191.04/191.68 => 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)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_compl__sup,axiom,
% 191.04/191.68 ! [V_y,V_x,T_a] :
% 191.04/191.68 ( class_Lattices_Oboolean__algebra(T_a)
% 191.04/191.68 => 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)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Int__insert__left__if1,axiom,
% 191.04/191.68 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 191.04/191.68 => 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)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Int__insert__right__if1,axiom,
% 191.04/191.68 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 191.04/191.68 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.68 => 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)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Int__insert__left__if0,axiom,
% 191.04/191.68 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 191.04/191.68 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 191.04/191.68 => 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) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Int__insert__right__if0,axiom,
% 191.04/191.68 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 191.04/191.68 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.68 => 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) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Int__insert__left,axiom,
% 191.04/191.68 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 191.04/191.68 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 191.04/191.68 => 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)) )
% 191.04/191.68 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 191.04/191.68 => 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) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Int__insert__right,axiom,
% 191.04/191.68 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 191.04/191.68 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.68 => 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)) )
% 191.04/191.68 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.68 => 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) ) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_image__Int__subset,axiom,
% 191.04/191.68 ! [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)))) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Diff__disjoint,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Diff__triv,axiom,
% 191.04/191.68 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.68 ( 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))
% 191.04/191.68 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Un__Int__assoc__eq,axiom,
% 191.04/191.68 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 191.04/191.68 ( 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))
% 191.04/191.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Diff__Int,axiom,
% 191.04/191.68 ! [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)) ).
% 191.04/191.68
% 191.04/191.68 fof(fact_Diff__Un,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Un__Diff__Int,axiom,
% 191.04/191.69 ! [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 ).
% 191.04/191.69
% 191.04/191.69 fof(fact_ivl__disj__int_I11_J,axiom,
% 191.04/191.69 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 191.04/191.69 ( class_Orderings_Oorder(T_b)
% 191.04/191.69 => 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)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom,
% 191.04/191.69 ! [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))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Compl__disjoint,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Compl__disjoint2,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Image__Int__subset,axiom,
% 191.04/191.69 ! [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)))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Compl__Int,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Compl__Un,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Diff__eq,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Diff__Compl,axiom,
% 191.04/191.69 ! [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) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_ivl__disj__int_I14_J,axiom,
% 191.04/191.69 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 191.04/191.69 ( class_Orderings_Oorder(T_b)
% 191.04/191.69 => 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)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Image__Id__on,axiom,
% 191.04/191.69 ! [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) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2] :
% 191.04/191.69 ( c_Nat__Transfer_Onat__set(V_A_2)
% 191.04/191.69 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 191.04/191.69 => 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))) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_congruent2__implies__congruent,axiom,
% 191.04/191.69 ! [V_a_2,V_f_2,V_r2_2,T_d,T_c,V_r1_2,V_A_2,T_b] :
% 191.04/191.69 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r1_2)
% 191.04/191.69 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.69 => c_Equiv__Relations_Ocongruent(T_c,T_d,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inf__Sup__absorb,axiom,
% 191.04/191.69 ! [V_a_2,V_A_2,T_b] :
% 191.04/191.69 ( class_Lattices_Olattice(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.69 => 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 ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_disjoint__eq__subset__Compl,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.69 ( 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))
% 191.04/191.69 <=> 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))) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_ivl__disj__int_I15_J,axiom,
% 191.04/191.69 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 191.04/191.69 ( class_Orderings_Oorder(T_b)
% 191.04/191.69 => 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)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Int__atLeastAtMost,axiom,
% 191.04/191.69 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] :
% 191.04/191.69 ( class_Orderings_Olinorder(T_b)
% 191.04/191.69 => 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_ba_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_ba_2),V_d_2)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Int__atLeastLessThan,axiom,
% 191.04/191.69 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] :
% 191.04/191.69 ( class_Orderings_Olinorder(T_b)
% 191.04/191.69 => 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_ba_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_ba_2),V_d_2)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_ivl__disj__int_I4_J,axiom,
% 191.04/191.69 ! [V_u_2,V_l_2,T_b] :
% 191.04/191.69 ( class_Orderings_Oorder(T_b)
% 191.04/191.69 => 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)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_ivl__disj__int_I2_J,axiom,
% 191.04/191.69 ! [V_u_2,V_l_2,T_b] :
% 191.04/191.69 ( class_Orderings_Oorder(T_b)
% 191.04/191.69 => 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)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_ivl__disj__int_I16_J,axiom,
% 191.04/191.69 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 191.04/191.69 ( class_Orderings_Oorder(T_b)
% 191.04/191.69 => 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)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_ivl__disj__int_I12_J,axiom,
% 191.04/191.69 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 191.04/191.69 ( class_Orderings_Oorder(T_b)
% 191.04/191.69 => 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)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_ivl__disj__int_I13_J,axiom,
% 191.04/191.69 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 191.04/191.69 ( class_Orderings_Oorder(T_b)
% 191.04/191.69 => 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)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Int__greaterThanAtMost,axiom,
% 191.04/191.69 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] :
% 191.04/191.69 ( class_Orderings_Olinorder(T_b)
% 191.04/191.69 => 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_ba_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_ba_2),V_d_2)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_ivl__disj__int_I9_J,axiom,
% 191.04/191.69 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 191.04/191.69 ( class_Orderings_Oorder(T_b)
% 191.04/191.69 => 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)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Int__greaterThanLessThan,axiom,
% 191.04/191.69 ! [V_d_2,V_ca_2,V_ba_2,V_a_2,T_b] :
% 191.04/191.69 ( class_Orderings_Olinorder(T_b)
% 191.04/191.69 => 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_ba_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_ba_2),V_d_2)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Int__atLeastAtMostL1,axiom,
% 191.04/191.69 ! [V_d_2,V_ba_2,V_a_2,T_b] :
% 191.04/191.69 ( class_Orderings_Olinorder(T_b)
% 191.04/191.69 => 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_ba_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_ba_2),V_d_2)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Int__atLeastAtMostR1,axiom,
% 191.04/191.69 ! [V_d_2,V_ca_2,V_ba_2,T_b] :
% 191.04/191.69 ( class_Orderings_Olinorder(T_b)
% 191.04/191.69 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_ba_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_ba_2),V_d_2)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_ivl__disj__int_I8_J,axiom,
% 191.04/191.69 ! [V_u_2,V_l_2,T_b] :
% 191.04/191.69 ( class_Orderings_Oorder(T_b)
% 191.04/191.69 => 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)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_ivl__disj__int_I7_J,axiom,
% 191.04/191.69 ! [V_u_2,V_l_2,T_b] :
% 191.04/191.69 ( class_Orderings_Oorder(T_b)
% 191.04/191.69 => 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)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Int__atLeastAtMostL2,axiom,
% 191.04/191.69 ! [V_ca_2,V_ba_2,V_a_2,T_b] :
% 191.04/191.69 ( class_Orderings_Olinorder(T_b)
% 191.04/191.69 => 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_ba_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_ca_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),V_ba_2) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Int__atLeastAtMostR2,axiom,
% 191.04/191.69 ! [V_d_2,V_ca_2,V_a_2,T_b] :
% 191.04/191.69 ( class_Orderings_Olinorder(T_b)
% 191.04/191.69 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),V_d_2) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_ivl__disj__int_I3_J,axiom,
% 191.04/191.69 ! [V_u_2,V_l_2,T_b] :
% 191.04/191.69 ( class_Orderings_Oorder(T_b)
% 191.04/191.69 => 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)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_ivl__disj__int_I10_J,axiom,
% 191.04/191.69 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 191.04/191.69 ( class_Orderings_Oorder(T_b)
% 191.04/191.69 => 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)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_ivl__disj__int_I1_J,axiom,
% 191.04/191.69 ! [V_u_2,V_l_2,T_b] :
% 191.04/191.69 ( class_Orderings_Oorder(T_b)
% 191.04/191.69 => 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)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_ivl__disj__int_I6_J,axiom,
% 191.04/191.69 ! [V_u_2,V_l_2,T_b] :
% 191.04/191.69 ( class_Orderings_Oorder(T_b)
% 191.04/191.69 => 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)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_ivl__disj__int_I5_J,axiom,
% 191.04/191.69 ! [V_u_2,V_l_2,T_b] :
% 191.04/191.69 ( class_Orderings_Oorder(T_b)
% 191.04/191.69 => 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)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_folding__image__simple_Ounion__inter,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 191.04/191.69 => 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)) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_compl__unique,axiom,
% 191.04/191.69 ! [V_y,V_x,T_a] :
% 191.04/191.69 ( class_Lattices_Oboolean__algebra(T_a)
% 191.04/191.69 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a)
% 191.04/191.69 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a)
% 191.04/191.69 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_setsum__Un__Int,axiom,
% 191.04/191.69 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 191.04/191.69 ( class_Groups_Ocomm__monoid__add(T_c)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => 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)) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_setprod_Ounion__inter,axiom,
% 191.04/191.69 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 191.04/191.69 ( class_Groups_Ocomm__monoid__mult(T_c)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => 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)) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_setprod__Un__Int,axiom,
% 191.04/191.69 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 191.04/191.69 ( class_Groups_Ocomm__monoid__mult(T_c)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => 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)) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_card__Un__Int,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => 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))) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_card_Ounion__inter,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => 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)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_card__Diff__subset__Int,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.69 ( 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)))
% 191.04/191.69 => 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))) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_setsum__restrict__set,axiom,
% 191.04/191.69 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 191.04/191.69 ( class_Groups_Ocomm__monoid__add(T_c)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => 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) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_folding_Ounion__inter,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => 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)) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_quotient__disj,axiom,
% 191.04/191.69 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 191.04/191.69 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 191.04/191.69 => ( 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)))
% 191.04/191.69 => ( 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)))
% 191.04/191.69 => ( V_X_2 = V_Y_2
% 191.04/191.69 | 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)) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_atMost__Int__atLeast,axiom,
% 191.04/191.69 ! [V_n_2,T_b] :
% 191.04/191.69 ( class_Orderings_Oorder(T_b)
% 191.04/191.69 => 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))) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_folding__one_Ounion__inter,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 191.04/191.69 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => ( 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))
% 191.04/191.69 => 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)) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_folding__one_Ounion__disjoint,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 191.04/191.69 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => ( 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))
% 191.04/191.69 => 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)) ) ) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_folding__image__simple_Ounion__disjoint,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 191.04/191.69 => ( 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))
% 191.04/191.69 => 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)) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_congruent__def,axiom,
% 191.04/191.69 ! [V_f_2,V_r_2,T_c,T_b] :
% 191.04/191.69 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 191.04/191.69 <=> ! [B_x] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 191.04/191.69 => 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)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_setsum__Un__disjoint,axiom,
% 191.04/191.69 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 191.04/191.69 ( class_Groups_Ocomm__monoid__add(T_c)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => ( 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))
% 191.04/191.69 => 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)) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_setsum__Un,axiom,
% 191.04/191.69 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 191.04/191.69 ( class_Groups_Oab__group__add(T_c)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => 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))) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_setprod__Un__disjoint,axiom,
% 191.04/191.69 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 191.04/191.69 ( class_Groups_Ocomm__monoid__mult(T_c)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => ( 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))
% 191.04/191.69 => 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)) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_setprod_Ounion__disjoint,axiom,
% 191.04/191.69 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 191.04/191.69 ( class_Groups_Ocomm__monoid__mult(T_c)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => ( 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))
% 191.04/191.69 => 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)) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_card__Un__disjoint,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => ( 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))
% 191.04/191.69 => 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)) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Sup__fin_Ounion__disjoint,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.69 ( class_Lattices_Olattice(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => ( 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))
% 191.04/191.69 => 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)) ) ) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Sup__fin_Ounion__inter,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.69 ( class_Lattices_Olattice(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => ( 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))
% 191.04/191.69 => 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)) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Min_Ounion__disjoint,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.69 ( class_Orderings_Olinorder(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => ( 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))
% 191.04/191.69 => 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)) ) ) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Min_Ounion__inter,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.69 ( class_Orderings_Olinorder(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => ( 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))
% 191.04/191.69 => 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)) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Max_Ounion__inter,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.69 ( class_Orderings_Olinorder(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => ( 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))
% 191.04/191.69 => 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)) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Max_Ounion__disjoint,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.69 ( class_Orderings_Olinorder(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => ( 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))
% 191.04/191.69 => 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)) ) ) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.69 ( class_Orderings_Olinorder(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => ( 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))
% 191.04/191.69 => 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)) ) ) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.69 ( class_Orderings_Olinorder(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => ( 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))
% 191.04/191.69 => 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)) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_min__max_OSup__fin_Ounion__inter,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.69 ( class_Orderings_Olinorder(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => ( 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))
% 191.04/191.69 => 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)) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.69 ( class_Orderings_Olinorder(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => ( 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))
% 191.04/191.69 => 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)) ) ) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_congruent2D,axiom,
% 191.04/191.69 ! [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] :
% 191.04/191.69 ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 191.04/191.69 => ( 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))
% 191.04/191.69 => ( 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))
% 191.04/191.69 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_setsum__Un__nat,axiom,
% 191.04/191.69 ! [V_f_2,V_B_2,V_A_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => 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))) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_folding_Ounion,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => ( 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))
% 191.04/191.69 => 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)) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_congruentD,axiom,
% 191.04/191.69 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_c,T_b] :
% 191.04/191.69 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 191.04/191.69 => ( 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))
% 191.04/191.69 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_congruent2__implies__congruent__UN,axiom,
% 191.04/191.69 ! [V_a_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
% 191.04/191.69 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 191.04/191.69 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 191.04/191.69 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A2_2))
% 191.04/191.69 => 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)) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_UN__equiv__class__inject,axiom,
% 191.04/191.69 ! [V_Y_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 191.04/191.69 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 191.04/191.69 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 191.04/191.69 => ( 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)
% 191.04/191.69 => ( 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)))
% 191.04/191.69 => ( 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)))
% 191.04/191.69 => ( ! [B_x] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.04/191.69 => ! [B_y] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 191.04/191.69 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 191.04/191.69 => 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)) ) ) )
% 191.04/191.69 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_UN__equiv__class__type2,axiom,
% 191.04/191.69 ! [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] :
% 191.04/191.69 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 191.04/191.69 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 191.04/191.69 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 191.04/191.69 => ( 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)))
% 191.04/191.69 => ( 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)))
% 191.04/191.69 => ( ! [B_x1] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x1),V_A1_2))
% 191.04/191.69 => ! [B_x2] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x2),V_A2_2))
% 191.04/191.69 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) )
% 191.04/191.69 => 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)) ) ) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_UN__equiv__class__type,axiom,
% 191.04/191.69 ! [V_B_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 191.04/191.69 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 191.04/191.69 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 191.04/191.69 => ( 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)))
% 191.04/191.69 => ( ! [B_x] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.04/191.69 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) )
% 191.04/191.69 => 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)) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inf__nat__def,axiom,
% 191.04/191.69 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inf__Int__eq2,axiom,
% 191.04/191.69 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 191.04/191.69 ( 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))
% 191.04/191.69 <=> 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))) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_card_Ounion__inter__neutral,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => ( ( ? [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)))
% 191.04/191.69 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 191.04/191.69 => 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)) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_setprod__Un,axiom,
% 191.04/191.69 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 191.04/191.69 ( class_Fields_Ofield(T_c)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => ( ! [B_x] :
% 191.04/191.69 ( 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)))
% 191.04/191.69 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c) )
% 191.04/191.69 => 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))) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Integ__def,axiom,
% 191.04/191.69 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) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inf2I,axiom,
% 191.04/191.69 ! [T_c,T_b,V_B_2,V_y_2,V_x_2,V_A_2] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 191.04/191.69 => 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)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inf2E,axiom,
% 191.04/191.69 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 191.04/191.69 ( 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))
% 191.04/191.69 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 191.04/191.69 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inf2D1,axiom,
% 191.04/191.69 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 191.04/191.69 ( 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))
% 191.04/191.69 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inf2D2,axiom,
% 191.04/191.69 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 191.04/191.69 ( 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))
% 191.04/191.69 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Rep__Integ,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_type__definition__Integ,axiom,
% 191.04/191.69 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) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_setprod_Ounion__inter__neutral,axiom,
% 191.04/191.69 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 191.04/191.69 ( class_Groups_Ocomm__monoid__mult(T_c)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => ( ! [B_x] :
% 191.04/191.69 ( 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)))
% 191.04/191.69 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 191.04/191.69 => 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)) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_setprod__Un__one,axiom,
% 191.04/191.69 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 191.04/191.69 ( class_Groups_Ocomm__monoid__mult(T_c)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 191.04/191.69 => ( ! [B_x] :
% 191.04/191.69 ( 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)))
% 191.04/191.69 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 191.04/191.69 => 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)) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_setsum_Ounion__inter__neutral,axiom,
% 191.04/191.69 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 191.04/191.69 ( class_Groups_Ocomm__monoid__add(T_c)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => ( ! [B_x] :
% 191.04/191.69 ( 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)))
% 191.04/191.69 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 191.04/191.69 => 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)) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_setsum__Un__zero,axiom,
% 191.04/191.69 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 191.04/191.69 ( class_Groups_Ocomm__monoid__add(T_c)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 191.04/191.69 => ( ! [B_x] :
% 191.04/191.69 ( 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)))
% 191.04/191.69 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 191.04/191.69 => 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)) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_refl__on__def_H,axiom,
% 191.04/191.69 ! [V_r_2,V_A_2,T_b] :
% 191.04/191.69 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 191.04/191.69 <=> ( ! [B_x] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 191.04/191.69 => 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)) )
% 191.04/191.69 & ! [B_x] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.04/191.69 => 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)) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Inf__fin_Oremove,axiom,
% 191.04/191.69 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.69 ( class_Lattices_Olattice(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.69 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 191.04/191.69 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_2 )
% 191.04/191.69 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 191.04/191.69 => 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)))))) ) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_refl__on__Id__on,axiom,
% 191.04/191.69 ! [V_A_2,T_b] : c_Relation_Orefl__on(T_b,V_A_2,c_Relation_OId__on(T_b,V_A_2)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Inf__fin_Osingleton,axiom,
% 191.04/191.69 ! [V_x_2,T_b] :
% 191.04/191.69 ( class_Lattices_Olattice(T_b)
% 191.04/191.69 => 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 ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_refl__on__empty,axiom,
% 191.04/191.69 ! [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))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_refl__on__Un,axiom,
% 191.04/191.69 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 191.04/191.69 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 191.04/191.69 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 191.04/191.69 => 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)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_refl__on__Int,axiom,
% 191.04/191.69 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 191.04/191.69 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 191.04/191.69 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 191.04/191.69 => 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)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_sup__Inf__absorb,axiom,
% 191.04/191.69 ! [V_a_2,V_A_2,T_b] :
% 191.04/191.69 ( class_Lattices_Olattice(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.69 => 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 ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Inf__fin_Oin__idem,axiom,
% 191.04/191.69 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.69 ( class_Lattices_Olattice(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.69 => 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) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_refl__onD,axiom,
% 191.04/191.69 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 191.04/191.69 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.69 => 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)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_refl__onD1,axiom,
% 191.04/191.69 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 191.04/191.69 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 191.04/191.69 => ( hBOOL(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))
% 191.04/191.69 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_refl__onD2,axiom,
% 191.04/191.69 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 191.04/191.69 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 191.04/191.69 => ( hBOOL(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))
% 191.04/191.69 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Inf__fin_Oinsert__idem,axiom,
% 191.04/191.69 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.69 ( class_Lattices_Olattice(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => 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)) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Inf__fin_Osubset__idem,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.69 ( class_Lattices_Olattice(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 191.04/191.69 => 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) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Inf__fin_Ounion__idem,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.69 ( class_Lattices_Olattice(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => 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)) ) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Inf__le__Sup,axiom,
% 191.04/191.69 ! [V_A_2,T_b] :
% 191.04/191.69 ( class_Lattices_Olattice(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => 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))) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Inf__fin_Oinsert,axiom,
% 191.04/191.69 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.69 ( class_Lattices_Olattice(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => 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)) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Inf__fin_Oinsert__remove,axiom,
% 191.04/191.69 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.69 ( class_Lattices_Olattice(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 191.04/191.69 => 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 )
% 191.04/191.69 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 191.04/191.69 => 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)))))) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Inf__fin_Ounion__disjoint,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.69 ( class_Lattices_Olattice(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => ( 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))
% 191.04/191.69 => 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)) ) ) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Inf__fin_Ounion__inter,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.69 ( class_Lattices_Olattice(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => ( 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))
% 191.04/191.69 => 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)) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Inf__fin_Oclosed,axiom,
% 191.04/191.69 ! [V_A_2,T_b] :
% 191.04/191.69 ( class_Lattices_Olattice(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => ( ! [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))))))
% 191.04/191.69 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_equiv__imp__dvd__card,axiom,
% 191.04/191.69 ! [V_k_2,V_r_2,V_A_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 191.04/191.69 => ( ! [B_x] :
% 191.04/191.69 ( 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)))
% 191.04/191.69 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_b),B_x))) )
% 191.04/191.69 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_folding__idem_Ounion__idem,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => 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)) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_folding__idem_Oidem__left__comp,axiom,
% 191.04/191.69 ! [V_g_2,V_x_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 191.04/191.69 => 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) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_folding__idem_Oidem__comp,axiom,
% 191.04/191.69 ! [V_x_2,V_F_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 191.04/191.69 => 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) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_folding__idem_Oin__comp__idem,axiom,
% 191.04/191.69 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.69 => 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) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_folding__idem_Oinsert__idem,axiom,
% 191.04/191.69 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => 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)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_folding__idem_Osubset__comp__idem,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 191.04/191.69 => 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) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_equivp__equiv,axiom,
% 191.04/191.69 ! [V_A_2,T_b] :
% 191.04/191.69 ( c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2)
% 191.04/191.69 <=> 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)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_card__quotient__disjoint,axiom,
% 191.04/191.69 ! [V_r_2,V_A_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( 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)
% 191.04/191.69 => 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) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fold__Un__disjoint,axiom,
% 191.04/191.69 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 191.04/191.69 ( class_Groups_Ocomm__monoid__mult(T_c)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => ( 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))
% 191.04/191.69 => 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)) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__on__empty,axiom,
% 191.04/191.69 ! [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))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__uminus,axiom,
% 191.04/191.69 ! [V_A_2,T_b] :
% 191.04/191.69 ( class_Groups_Oordered__ab__group__add(T_b)
% 191.04/191.69 => c_Fun_Oinj__on(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b),V_A_2) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__on__strict__subset,axiom,
% 191.04/191.69 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.69 => 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))) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__on__contraD,axiom,
% 191.04/191.69 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 191.04/191.69 => ( V_x_2 != V_y_2
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 191.04/191.69 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__on__iff,axiom,
% 191.04/191.69 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 191.04/191.69 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 191.04/191.69 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__onD,axiom,
% 191.04/191.69 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 191.04/191.69 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 191.04/191.69 => V_x_2 = V_y_2 ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__on__Un__image__eq__iff,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( 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))
% 191.04/191.69 => ( 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)
% 191.04/191.69 <=> V_A_2 = V_B_2 ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__comp,axiom,
% 191.04/191.69 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 191.04/191.69 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
% 191.04/191.69 => 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))) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__on__imageI,axiom,
% 191.04/191.69 ! [V_A_2,V_f_2,V_g_2,T_d,T_c,T_b] :
% 191.04/191.69 ( 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)
% 191.04/191.69 => 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)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_comp__inj__on,axiom,
% 191.04/191.69 ! [V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 191.04/191.69 => ( 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))
% 191.04/191.69 => 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) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_comp__inj__on__iff,axiom,
% 191.04/191.69 ! [V_f_H_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 191.04/191.69 => ( 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))
% 191.04/191.69 <=> 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) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_card__image,axiom,
% 191.04/191.69 ! [V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 191.04/191.69 => 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) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fold__image__reindex,axiom,
% 191.04/191.69 ! [V_z_2,V_g_2,V_h_2,T_c,V_A_2,T_b,T_d] :
% 191.04/191.69 ( class_Groups_Oab__semigroup__mult(T_d)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2)
% 191.04/191.69 => 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) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fold__image__empty,axiom,
% 191.04/191.69 ! [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 ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__on__id2,axiom,
% 191.04/191.69 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_COMBI(T_b),V_A_2) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__on__def,axiom,
% 191.04/191.69 ! [V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 191.04/191.69 <=> ! [B_x] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.04/191.69 => ! [B_xa] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 191.04/191.69 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
% 191.04/191.69 => B_x = B_xa ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__on__diff,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 191.04/191.69 => 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)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_subset__inj__on,axiom,
% 191.04/191.69 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.69 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_finite__imageD,axiom,
% 191.04/191.69 ! [V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 191.04/191.69 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2)
% 191.04/191.69 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__on__imageI2,axiom,
% 191.04/191.69 ! [V_A_2,V_f_2,V_f_H_2,T_d,T_c,T_b] :
% 191.04/191.69 ( 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)
% 191.04/191.69 => c_Fun_Oinj__on(T_b,T_d,V_f_2,V_A_2) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_identity__equivp,axiom,
% 191.04/191.69 ! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_equivp__def,axiom,
% 191.04/191.69 ! [V_R_2,T_b] :
% 191.04/191.69 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 191.04/191.69 <=> ! [B_x,B_y] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
% 191.04/191.69 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_equivp__reflp,axiom,
% 191.04/191.69 ! [V_x_2,V_R_2,T_b] :
% 191.04/191.69 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 191.04/191.69 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_equivp__symp,axiom,
% 191.04/191.69 ! [V_y_2,V_x_2,V_R_2,T_b] :
% 191.04/191.69 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 191.04/191.69 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_equivp__transp,axiom,
% 191.04/191.69 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
% 191.04/191.69 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
% 191.04/191.69 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__image__eq__iff,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 191.04/191.69 => ( 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)
% 191.04/191.69 <=> V_A_2 = V_B_2 ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_injD,axiom,
% 191.04/191.69 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 191.04/191.69 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 191.04/191.69 => V_x_2 = V_y_2 ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__eq,axiom,
% 191.04/191.69 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 191.04/191.69 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 191.04/191.69 <=> V_x_2 = V_y_2 ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__fun,axiom,
% 191.04/191.69 ! [T_d,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 191.04/191.69 => 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))) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__on__Int,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 191.04/191.69 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 191.04/191.69 => 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)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__image__mem__iff,axiom,
% 191.04/191.69 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 191.04/191.69 => ( 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)))
% 191.04/191.69 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_range__ex1__eq,axiom,
% 191.04/191.69 ! [V_ba_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
% 191.04/191.69 <=> ? [B_x] :
% 191.04/191.69 ( V_ba_2 = hAPP(V_f_2,B_x)
% 191.04/191.69 & ! [B_y] :
% 191.04/191.69 ( V_ba_2 = hAPP(V_f_2,B_y)
% 191.04/191.69 => B_y = B_x ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_folding__image__simple_Oeq__fold__g,axiom,
% 191.04/191.69 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 191.04/191.69 => 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) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__on__iff__surj,axiom,
% 191.04/191.69 ! [V_A_H_2,T_c,T_b,V_A_2] :
% 191.04/191.69 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => ( ? [B_f] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 191.04/191.69 & 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)) )
% 191.04/191.69 <=> ? [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) = V_A_2 ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_endo__inj__surj,axiom,
% 191.04/191.69 ! [V_f_2,V_A_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( 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))
% 191.04/191.69 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2)
% 191.04/191.69 => hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2) = V_A_2 ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_finite__surj__inj,axiom,
% 191.04/191.69 ! [V_f_2,V_A_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( 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)))
% 191.04/191.69 => c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_finite__UNIV__surj__inj,axiom,
% 191.04/191.69 ! [V_f_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 191.04/191.69 => ( 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))
% 191.04/191.69 => c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_finite__UNIV__inj__surj,axiom,
% 191.04/191.69 ! [V_f_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 191.04/191.69 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 191.04/191.69 => 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)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__image__subset__iff,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 191.04/191.69 => ( 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)))
% 191.04/191.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__on__image__Int,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 191.04/191.69 => 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)) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_image__Int,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 191.04/191.69 => 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)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__on__iff__eq__card,axiom,
% 191.04/191.69 ! [V_f_2,T_c,V_A_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 191.04/191.69 <=> 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) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_eq__card__imp__inj__on,axiom,
% 191.04/191.69 ! [V_f_2,T_c,V_A_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( 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)
% 191.04/191.69 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__on__image__set__diff,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 191.04/191.69 => 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)) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_image__set__diff,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 191.04/191.69 => 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)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_setsum__reindex,axiom,
% 191.04/191.69 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 191.04/191.69 ( class_Groups_Ocomm__monoid__add(T_d)
% 191.04/191.69 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 191.04/191.69 => 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) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_pigeonhole,axiom,
% 191.04/191.69 ! [V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( 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)))
% 191.04/191.69 => ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__on__fun__updI,axiom,
% 191.04/191.69 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 191.04/191.69 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 191.04/191.69 => 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) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_setprod__reindex,axiom,
% 191.04/191.69 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 191.04/191.69 ( class_Groups_Ocomm__monoid__mult(T_d)
% 191.04/191.69 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 191.04/191.69 => 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) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_setprod__reindex__cong,axiom,
% 191.04/191.69 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 191.04/191.69 ( class_Groups_Ocomm__monoid__mult(T_d)
% 191.04/191.69 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 191.04/191.69 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 191.04/191.69 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)
% 191.04/191.69 => 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) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__singleton,axiom,
% 191.04/191.69 ! [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))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_setsum_Oreindex,axiom,
% 191.04/191.69 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 191.04/191.69 ( class_Groups_Ocomm__monoid__add(T_c)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 191.04/191.69 => 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) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_card__bij__eq,axiom,
% 191.04/191.69 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 191.04/191.69 => ( 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))
% 191.04/191.69 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
% 191.04/191.69 => ( 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))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 191.04/191.69 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_setprod_Oreindex,axiom,
% 191.04/191.69 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 191.04/191.69 ( class_Groups_Ocomm__monoid__mult(T_c)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 191.04/191.69 => 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) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fold__image__distrib,axiom,
% 191.04/191.69 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 191.04/191.69 ( class_Groups_Ocomm__monoid__mult(T_c)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => 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)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__image__Compl__subset,axiom,
% 191.04/191.69 ! [V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 191.04/191.69 => 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)))) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fold__image__insert,axiom,
% 191.04/191.69 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_b,T_c] :
% 191.04/191.69 ( class_Groups_Oab__semigroup__mult(T_c)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.69 => 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)) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_setsum_OF__eq,axiom,
% 191.04/191.69 ! [V_g_2,V_A_2,T_b,T_c] :
% 191.04/191.69 ( class_Groups_Ocomm__monoid__add(T_c)
% 191.04/191.69 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => 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) )
% 191.04/191.69 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => 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) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_setsum_Oeq__fold,axiom,
% 191.04/191.69 ! [V_g_2,V_A_2,T_b,T_c] :
% 191.04/191.69 ( class_Groups_Ocomm__monoid__add(T_c)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => 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) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_setprod_Oeq__fold,axiom,
% 191.04/191.69 ! [V_g_2,V_A_2,T_b,T_c] :
% 191.04/191.69 ( class_Groups_Ocomm__monoid__mult(T_c)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => 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) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_setprod_OF__eq,axiom,
% 191.04/191.69 ! [V_g_2,V_A_2,T_b,T_c] :
% 191.04/191.69 ( class_Groups_Ocomm__monoid__mult(T_c)
% 191.04/191.69 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => 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) )
% 191.04/191.69 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => 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) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__on__insert,axiom,
% 191.04/191.69 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))
% 191.04/191.69 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 191.04/191.69 & ~ 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))))))) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__on__Un,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( 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))
% 191.04/191.69 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 191.04/191.69 & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 191.04/191.69 & 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)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_card__inj__on__le,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 191.04/191.69 => ( 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))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 191.04/191.69 => 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))) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__on__iff__card__le,axiom,
% 191.04/191.69 ! [V_B_2,T_c,V_A_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 191.04/191.69 => ( ? [B_f] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 191.04/191.69 & 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)) )
% 191.04/191.69 <=> 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))) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_quotient__diff1,axiom,
% 191.04/191.69 ! [V_a_2,V_A_2,V_r_2,T_b] :
% 191.04/191.69 ( 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)
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.69 => 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)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fold__image__Un__Int,axiom,
% 191.04/191.69 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 191.04/191.69 ( class_Groups_Ocomm__monoid__mult(T_c)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => 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))) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_image__eq__fold__image,axiom,
% 191.04/191.69 ! [V_f_2,T_c,V_A_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => 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) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_card_Oeq__fold__g,axiom,
% 191.04/191.69 ! [V_A_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => 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) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_card__def,axiom,
% 191.04/191.69 ! [V_A_2,T_b] :
% 191.04/191.69 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => 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) )
% 191.04/191.69 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_comm__monoid__big_OF__eq,axiom,
% 191.04/191.69 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 191.04/191.69 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 191.04/191.69 => 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) )
% 191.04/191.69 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 191.04/191.69 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_folding__image_Oreindex,axiom,
% 191.04/191.69 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 191.04/191.69 => ( c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2)
% 191.04/191.69 => 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) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fold__image__Un__one,axiom,
% 191.04/191.69 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 191.04/191.69 ( class_Groups_Ocomm__monoid__mult(T_c)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 191.04/191.69 => ( ! [B_x] :
% 191.04/191.69 ( 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)))
% 191.04/191.69 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 191.04/191.69 => 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)) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__Inr,axiom,
% 191.04/191.69 ! [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) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__Suc,axiom,
% 191.04/191.69 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__Some,axiom,
% 191.04/191.69 ! [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) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__Inl,axiom,
% 191.04/191.69 ! [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) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__on__add__nat,axiom,
% 191.04/191.69 ! [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) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__of__nat,axiom,
% 191.04/191.69 ! [T_b] :
% 191.04/191.69 ( class_Nat_Osemiring__char__0(T_b)
% 191.04/191.69 => 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))) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__int,axiom,
% 191.04/191.69 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))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_swap__inj__on,axiom,
% 191.04/191.69 ! [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) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_folding__image_Odistrib,axiom,
% 191.04/191.69 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 191.04/191.69 => 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)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_folding__image_Oeq__fold,axiom,
% 191.04/191.69 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 191.04/191.69 => 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) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_comm__monoid__big_Oinfinite,axiom,
% 191.04/191.69 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 191.04/191.69 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 191.04/191.69 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_the__inv__into__comp,axiom,
% 191.04/191.69 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
% 191.04/191.69 ( 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))
% 191.04/191.69 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
% 191.04/191.69 => ( 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))))
% 191.04/191.69 => 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) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_the__inv__into__into,axiom,
% 191.04/191.69 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.69 => 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)) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__vimage__singleton,axiom,
% 191.04/191.69 ! [V_a_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 191.04/191.69 => 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))))) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_vimageI,axiom,
% 191.04/191.69 ! [T_c,V_B_2,T_b,V_ba_2,V_a_2,V_f_2] :
% 191.04/191.69 ( hAPP(V_f_2,V_a_2) = V_ba_2
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),V_B_2))
% 191.04/191.69 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_vimage__Diff,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_image__vimage__subset,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_surj__image__vimage__eq,axiom,
% 191.04/191.69 ! [V_A_2,V_f_2,T_b,T_c] :
% 191.04/191.69 ( 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))
% 191.04/191.69 => 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 ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_vimage__eq,axiom,
% 191.04/191.69 ! [V_B_2,V_f_2,T_c,V_a_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)))
% 191.04/191.69 <=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_vimageD,axiom,
% 191.04/191.69 ! [V_A_2,V_f_2,T_c,V_a_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)))
% 191.04/191.69 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_vimageI2,axiom,
% 191.04/191.69 ! [T_c,V_A_2,V_a_2,V_f_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2))
% 191.04/191.69 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_vimage__Un,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_vimage__empty,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_vimage__Compl,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_vimage__code,axiom,
% 191.04/191.69 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2))
% 191.04/191.69 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_vimage__ident,axiom,
% 191.04/191.69 ! [V_Y_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 191.04/191.69
% 191.04/191.69 fof(fact_vimage__mono,axiom,
% 191.04/191.69 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.69 => 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))) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_vimage__UN,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_vimage__compose,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_vimage__UNIV,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_vimage__Int,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_vimage__singleton__eq,axiom,
% 191.04/191.69 ! [V_ba_2,V_f_2,T_c,V_a_2,T_b] :
% 191.04/191.69 ( 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_ba_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
% 191.04/191.69 <=> hAPP(V_f_2,V_a_2) = V_ba_2 ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_vimage__insert,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_finite__vimageD,axiom,
% 191.04/191.69 ! [V_F_2,V_h_2,T_c,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
% 191.04/191.69 => ( 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))
% 191.04/191.69 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_vimage__subsetD,axiom,
% 191.04/191.69 ! [V_A_2,V_B_2,V_f_2,T_b,T_c] :
% 191.04/191.69 ( 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))
% 191.04/191.69 => ( 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))
% 191.04/191.69 => 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))) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_image__vimage__eq,axiom,
% 191.04/191.69 ! [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)))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_finite__vimageI,axiom,
% 191.04/191.69 ! [V_h_2,T_c,V_F_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 191.04/191.69 => ( c_Fun_Oinj__on(T_c,T_b,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 191.04/191.69 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_b,V_h_2),V_F_2))) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__vimage__image__eq,axiom,
% 191.04/191.69 ! [V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 191.04/191.69 => 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 ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_vimage__const,axiom,
% 191.04/191.69 ! [T_c,V_A_2,V_ca_2,T_b] :
% 191.04/191.69 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 191.04/191.69 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_ca_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 191.04/191.69 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 191.04/191.69 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_ca_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_vimage__eq__UN,axiom,
% 191.04/191.69 ! [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))))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_the__inv__into__f__f,axiom,
% 191.04/191.69 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.69 => 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 ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_the__inv__into__f__eq,axiom,
% 191.04/191.69 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 191.04/191.69 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.69 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_the__inv__f__f,axiom,
% 191.04/191.69 ! [V_x_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 191.04/191.69 => 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 ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__on__the__inv__into,axiom,
% 191.04/191.69 ! [V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 191.04/191.69 => 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)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_the__inv__into__onto,axiom,
% 191.04/191.69 ! [V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 191.04/191.69 => 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 ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_vimage__subsetI,axiom,
% 191.04/191.69 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 191.04/191.69 => ( 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)))
% 191.04/191.69 => 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)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_the__inv__into__def,axiom,
% 191.04/191.69 ! [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))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_vimage__if,axiom,
% 191.04/191.69 ! [V_B_2,T_c,V_d_2,V_A_2,V_ca_2,T_b] :
% 191.04/191.69 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 191.04/191.69 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 191.04/191.69 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 191.04/191.69 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 191.04/191.69 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = V_B_2 ) ) )
% 191.04/191.69 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 191.04/191.69 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 191.04/191.69 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2) )
% 191.04/191.69 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 191.04/191.69 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_f__the__inv__into__f,axiom,
% 191.04/191.69 ! [V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 191.04/191.69 => 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 ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Inf__fin_Ohom__commute,axiom,
% 191.04/191.69 ! [V_N_2,V_h_2,T_b] :
% 191.04/191.69 ( class_Lattices_Olattice(T_b)
% 191.04/191.69 => ( ! [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))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 191.04/191.69 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => 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)) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_ImageE,axiom,
% 191.04/191.69 ! [V_A_2,V_r_2,T_c,V_ba_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 191.04/191.69 => ~ ! [B_x] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_ba_2)),V_r_2))
% 191.04/191.69 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_strong__setprod__reindex__cong,axiom,
% 191.04/191.69 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 191.04/191.69 ( class_Groups_Ocomm__monoid__mult(T_d)
% 191.04/191.69 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 191.04/191.69 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 191.04/191.69 => ( ! [B_x] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.04/191.69 => 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) )
% 191.04/191.69 => 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) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom,
% 191.04/191.69 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 191.04/191.69 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 191.04/191.69 & class_Groups_Ocomm__monoid__mult(T_b) )
% 191.04/191.69 => ( V_A_2 = V_B_2
% 191.04/191.69 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 191.04/191.69 => ( ! [B_x] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 191.04/191.69 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 191.04/191.69 => 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) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_dom__eq__singleton__conv,axiom,
% 191.04/191.69 ! [V_x_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( 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)))
% 191.04/191.69 <=> ? [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)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fold__graph__permute__diff,axiom,
% 191.04/191.69 ! [V_a_2,V_x_2,V_A_2,V_ba_2,T_b] :
% 191.04/191.69 ( class_Groups_Oab__semigroup__mult(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_ba_2,V_A_2),V_x_2))
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.69 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),V_A_2))
% 191.04/191.69 => 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_ba_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)) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fold__graph__imp__finite,axiom,
% 191.04/191.69 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 191.04/191.69 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_finite__dom__body,axiom,
% 191.04/191.69 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fold__graph_Oequations_I1_J,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fold__graph_OemptyI,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_empty__fold__graphE,axiom,
% 191.04/191.69 ! [V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( 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))
% 191.04/191.69 => V_x_2 = V_z_2 ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_domIff,axiom,
% 191.04/191.69 ! [V_m_2,T_c,V_a_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_c,V_m_2)))
% 191.04/191.69 <=> hAPP(V_m_2,V_a_2) != c_Option_Ooption_ONone(T_c) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_domI,axiom,
% 191.04/191.69 ! [T_c,V_ba_2,T_b,V_a_2,V_m_2] :
% 191.04/191.69 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_b),V_ba_2)
% 191.04/191.69 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),c_Map_Odom(T_c,T_b,V_m_2))) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_insert__dom,axiom,
% 191.04/191.69 ! [T_c,V_y_2,T_b,V_x_2,V_f_2] :
% 191.04/191.69 ( hAPP(V_f_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
% 191.04/191.69 => 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) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_dom__restrict,axiom,
% 191.04/191.69 ! [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) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fold__graph_OinsertI,axiom,
% 191.04/191.69 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 191.04/191.69 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 191.04/191.69 => 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))) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_dom__empty,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_dom__eq__empty__conv,axiom,
% 191.04/191.69 ! [V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Map_Odom(T_b,T_c,V_f_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 <=> V_f_2 = hAPP(c_COMBK(tc_Option_Ooption(T_c),T_b),c_Option_Ooption_ONone(T_c)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_dom__const,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_dom__minus,axiom,
% 191.04/191.69 ! [V_A_2,T_c,T_b,V_x_2,V_f_2] :
% 191.04/191.69 ( hAPP(V_f_2,V_x_2) = c_Option_Ooption_ONone(T_b)
% 191.04/191.69 => 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) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fold__graph__insert__swap,axiom,
% 191.04/191.69 ! [V_z_2,V_y_2,V_A_2,V_ba_2,T_b] :
% 191.04/191.69 ( class_Groups_Oab__semigroup__mult(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_ba_2,V_A_2),V_y_2))
% 191.04/191.69 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),V_A_2))
% 191.04/191.69 => 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_ba_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2),V_y_2))) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Diff1__fold__graph,axiom,
% 191.04/191.69 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( 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))
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.69 => 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))) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_dom__fun__upd,axiom,
% 191.04/191.69 ! [V_x_2,V_f_2,T_c,T_b,V_y_2] :
% 191.04/191.69 ( ( V_y_2 = c_Option_Ooption_ONone(T_b)
% 191.04/191.69 => 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)))) )
% 191.04/191.69 & ( V_y_2 != c_Option_Ooption_ONone(T_b)
% 191.04/191.69 => 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)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fold1Set_Ointros,axiom,
% 191.04/191.69 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2))
% 191.04/191.69 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.69 => 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)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_ran__restrictD,axiom,
% 191.04/191.69 ! [V_A_2,V_m_2,T_c,V_y_2,T_b] :
% 191.04/191.69 ( 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))))
% 191.04/191.69 => ? [B_x] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 191.04/191.69 & hAPP(V_m_2,B_x) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_accp__acc__eq,axiom,
% 191.04/191.69 ! [V_x_2,V_r_2,T_b] :
% 191.04/191.69 ( 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))
% 191.04/191.69 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_empty__fold1SetE,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fold1Set__nonempty,axiom,
% 191.04/191.69 ! [V_x_2,V_A_2,V_f_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2))
% 191.04/191.69 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_acc__subset,axiom,
% 191.04/191.69 ! [V_R2_2,V_R1_2,T_b] :
% 191.04/191.69 ( 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))
% 191.04/191.69 => 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))) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fold1Set__sing,axiom,
% 191.04/191.69 ! [V_ba_2,V_a_2,V_f_2,T_b] :
% 191.04/191.69 ( 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_ba_2))
% 191.04/191.69 <=> V_a_2 = V_ba_2 ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_acc__downward,axiom,
% 191.04/191.69 ! [V_a_2,V_r_2,V_ba_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 191.04/191.69 => ( 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_ba_2)),V_r_2))
% 191.04/191.69 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_acc_Osimps,axiom,
% 191.04/191.69 ! [V_r_2,V_a_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 191.04/191.69 <=> ! [B_x] :
% 191.04/191.69 ( 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))
% 191.04/191.69 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_max__extp_Oequations,axiom,
% 191.04/191.69 ! [V_a2_2,V_a1_2,V_R_2,T_b] :
% 191.04/191.69 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
% 191.04/191.69 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 191.04/191.69 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 191.04/191.69 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 & ! [B_x] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 191.04/191.69 => ? [B_xa] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 191.04/191.69 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_max__ext_Ointros,axiom,
% 191.04/191.69 ! [V_R_2,V_Y_2,V_X_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
% 191.04/191.69 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => ( ! [B_x] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2))
% 191.04/191.69 => ? [B_xa] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2))
% 191.04/191.69 & 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)) ) )
% 191.04/191.69 => 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))) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_conseq2,axiom,
% 191.04/191.69 ! [V_Q_2,V_Q_H_2,V_ca_2,V_Pa_2,V_Ga_2,T_b] :
% 191.04/191.69 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_ca_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 191.04/191.69 => ( ! [B_Z,B_s] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s))
% 191.04/191.69 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s)) )
% 191.04/191.69 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_conseq1,axiom,
% 191.04/191.69 ! [V_Pa_2,V_Q_2,V_ca_2,V_P_H_2,V_Ga_2,T_b] :
% 191.04/191.69 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_P_H_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 191.04/191.69 => ( ! [B_Z,B_s] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s))
% 191.04/191.69 => hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s)) )
% 191.04/191.69 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fold1Set_Oequations,axiom,
% 191.04/191.69 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_b] :
% 191.04/191.69 ( 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))
% 191.04/191.69 <=> ? [B_a,B_A] :
% 191.04/191.69 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 191.04/191.69 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2))
% 191.04/191.69 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_insert__fold1SetE,axiom,
% 191.04/191.69 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_b] :
% 191.04/191.69 ( 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))
% 191.04/191.69 => ~ ! [B_a,B_A] :
% 191.04/191.69 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2))
% 191.04/191.69 => hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_image__split__eq__Sigma,axiom,
% 191.04/191.69 ! [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))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fold1__Un,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.69 ( class_Groups_Oab__semigroup__mult(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => ( 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))
% 191.04/191.69 => 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)) ) ) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fold1__antimono,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.69 ( class_Orderings_Olinorder(T_b)
% 191.04/191.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => 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))) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_SigmaI,axiom,
% 191.04/191.69 ! [V_B_2,V_ba_2,T_c,V_A_2,V_a_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(V_B_2,V_a_2)))
% 191.04/191.69 => 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_ba_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Sigma__Diff__distrib1,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Times__Diff__distrib1,axiom,
% 191.04/191.69 ! [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))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Sigma__Diff__distrib2,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Times__eq__cancel2,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 191.04/191.69 => ( 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))
% 191.04/191.69 <=> V_A_2 = V_B_2 ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Sigma__empty1,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_card__cartesian__product,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_setsum__cartesian__product,axiom,
% 191.04/191.69 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 191.04/191.69 ( class_Groups_Ocomm__monoid__add(T_b)
% 191.04/191.69 => 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))) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Times__empty,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,T_c,T_b] :
% 191.04/191.69 ( 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))
% 191.04/191.69 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Sigma__empty2,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Compl__Times__UNIV2,axiom,
% 191.04/191.69 ! [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)))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Compl__Times__UNIV1,axiom,
% 191.04/191.69 ! [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))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_setprod__cartesian__product,axiom,
% 191.04/191.69 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 191.04/191.69 ( class_Groups_Ocomm__monoid__mult(T_b)
% 191.04/191.69 => 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))) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Sigma__Un__distrib1,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Times__Un__distrib1,axiom,
% 191.04/191.69 ! [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))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Sigma__Un__distrib2,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_swap__product,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fold1__singleton__def,axiom,
% 191.04/191.69 ! [V_a_2,V_f_2,T_b,V_g_2] :
% 191.04/191.69 ( V_g_2 = c_Finite__Set_Ofold1(T_b,V_f_2)
% 191.04/191.69 => 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 ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fold1__singleton,axiom,
% 191.04/191.69 ! [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 ).
% 191.04/191.69
% 191.04/191.69 fof(fact_finite__cartesian__product,axiom,
% 191.04/191.69 ! [V_B_2,T_c,V_A_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 191.04/191.69 => 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)))) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_equiv__type,axiom,
% 191.04/191.69 ! [V_r_2,V_A_2,T_b] :
% 191.04/191.69 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 191.04/191.69 => 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)))) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Sigma__Int__distrib2,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Times__Int__distrib1,axiom,
% 191.04/191.69 ! [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))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Sigma__Int__distrib1,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Id__on__subset__Times,axiom,
% 191.04/191.69 ! [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)))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_UNIV__Times__UNIV,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_SigmaE2,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,V_ba_2,V_a_2,T_c,T_b] :
% 191.04/191.69 ( 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_ba_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 191.04/191.69 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.69 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_SigmaD2,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,V_ba_2,V_a_2,T_c,T_b] :
% 191.04/191.69 ( 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_ba_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 191.04/191.69 => hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(V_B_2,V_a_2))) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_SigmaD1,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,V_ba_2,V_a_2,T_c,T_b] :
% 191.04/191.69 ( 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_ba_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 191.04/191.69 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_mem__Sigma__iff,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,V_ba_2,V_a_2,T_c,T_b] :
% 191.04/191.69 ( 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_ba_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 191.04/191.69 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.69 & hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_folding__one_Oeq__fold,axiom,
% 191.04/191.69 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 191.04/191.69 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_card__cartesian__product__singleton,axiom,
% 191.04/191.69 ! [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) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Times__subset__cancel2,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 191.04/191.69 => ( 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))))
% 191.04/191.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Image__subset,axiom,
% 191.04/191.69 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 191.04/191.69 ( 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))))
% 191.04/191.69 => 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)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_finite__cartesian__productD1,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,T_c,T_b] :
% 191.04/191.69 ( 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))))
% 191.04/191.69 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 191.04/191.69 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_finite__cartesian__productD2,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,T_c,T_b] :
% 191.04/191.69 ( 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))))
% 191.04/191.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fst__image__times,axiom,
% 191.04/191.69 ! [V_A_2,T_c,T_b,V_B_2] :
% 191.04/191.69 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => 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)) )
% 191.04/191.69 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => 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 ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_snd__image__times,axiom,
% 191.04/191.69 ! [V_B_2,T_c,T_b,V_A_2] :
% 191.04/191.69 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => 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)) )
% 191.04/191.69 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => 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 ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fold1__def,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Sup__fin_OF__eq,axiom,
% 191.04/191.69 ! [V_A_2,T_b] :
% 191.04/191.69 ( class_Lattices_Olattice(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => 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) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Inf__fin_OF__eq,axiom,
% 191.04/191.69 ! [V_A_2,T_b] :
% 191.04/191.69 ( class_Lattices_Olattice(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => 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) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Min_OF__eq,axiom,
% 191.04/191.69 ! [V_A_2,T_b] :
% 191.04/191.69 ( class_Orderings_Olinorder(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => 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) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Max_OF__eq,axiom,
% 191.04/191.69 ! [V_A_2,T_b] :
% 191.04/191.69 ( class_Orderings_Olinorder(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => 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) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_min__max_OInf__fin_OF__eq,axiom,
% 191.04/191.69 ! [V_A_2,T_b] :
% 191.04/191.69 ( class_Orderings_Olinorder(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => 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) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_min__max_OSup__fin_OF__eq,axiom,
% 191.04/191.69 ! [V_A_2,T_b] :
% 191.04/191.69 ( class_Orderings_Olinorder(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => 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) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_refl__on__def,axiom,
% 191.04/191.69 ! [V_r_2,V_A_2,T_b] :
% 191.04/191.69 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 191.04/191.69 <=> ( 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))))
% 191.04/191.69 & ! [B_x] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.04/191.69 => 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)) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_insert__times__insert,axiom,
% 191.04/191.69 ! [V_B_2,V_ba_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_ba_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_ba_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_ba_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)))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_finite__equiv__class,axiom,
% 191.04/191.69 ! [V_X_2,V_r_2,V_A_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( 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))))
% 191.04/191.69 => ( 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)))
% 191.04/191.69 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_UN__Times__distrib,axiom,
% 191.04/191.69 ! [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))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Sigma__def,axiom,
% 191.04/191.69 ! [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))))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fold1__belowI,axiom,
% 191.04/191.69 ! [V_a_2,V_A_2,T_b] :
% 191.04/191.69 ( class_Lattices_Osemilattice__inf(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.69 => 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)) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_finite__quotient,axiom,
% 191.04/191.69 ! [V_r_2,V_A_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( 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))))
% 191.04/191.69 => 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))) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_below__fold1__iff,axiom,
% 191.04/191.69 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.69 ( class_Lattices_Osemilattice__inf(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => ( 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)))
% 191.04/191.69 <=> ! [B_x] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.04/191.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_min__max_Ofold1__belowI,axiom,
% 191.04/191.69 ! [V_a_2,V_A_2,T_b] :
% 191.04/191.69 ( class_Orderings_Olinorder(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.69 => 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)) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fold1__insert__idem,axiom,
% 191.04/191.69 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.69 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 191.04/191.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => 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)) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fold1__below__iff,axiom,
% 191.04/191.69 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.69 ( class_Orderings_Olinorder(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => ( 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))
% 191.04/191.69 <=> ? [B_x] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.04/191.69 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_min__max_Obelow__fold1__iff,axiom,
% 191.04/191.69 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.69 ( class_Orderings_Olinorder(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => ( 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)))
% 191.04/191.69 <=> ! [B_x] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.04/191.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fold1__Un2,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.69 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.69 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => 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)) ) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_strict__below__fold1__iff,axiom,
% 191.04/191.69 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.69 ( class_Orderings_Olinorder(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => ( 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)))
% 191.04/191.69 <=> ! [B_x] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.04/191.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fold1__strict__below__iff,axiom,
% 191.04/191.69 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.69 ( class_Orderings_Olinorder(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => ( 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))
% 191.04/191.69 <=> ? [B_x] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.04/191.69 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_vimage__Times,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fold1__insert,axiom,
% 191.04/191.69 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.69 ( class_Groups_Oab__semigroup__mult(T_b)
% 191.04/191.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.69 => 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)) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_semilattice__big_OF__eq,axiom,
% 191.04/191.69 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 191.04/191.69 ( c_Big__Operators_Osemilattice__big(T_b,V_f_2,V_F_2)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Ex__inj__on__UNION__Sigma,axiom,
% 191.04/191.69 ! [V_A_2,V_I_2,T_c,T_b] :
% 191.04/191.69 ? [B_f] :
% 191.04/191.69 ( 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))
% 191.04/191.69 & 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))) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_refl__onI,axiom,
% 191.04/191.69 ! [V_A_2,V_r_2,T_b] :
% 191.04/191.69 ( 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))))
% 191.04/191.69 => ( ! [B_x] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.04/191.69 => 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)) )
% 191.04/191.69 => c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_setprod__Sigma,axiom,
% 191.04/191.69 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 191.04/191.69 ( class_Groups_Ocomm__monoid__mult(T_d)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( ! [B_x] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.04/191.69 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 191.04/191.69 => 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)) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_setsum__Sigma,axiom,
% 191.04/191.69 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 191.04/191.69 ( class_Groups_Ocomm__monoid__add(T_d)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( ! [B_x] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.04/191.69 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 191.04/191.69 => 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)) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fold__image__Sigma,axiom,
% 191.04/191.69 ! [V_g_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 191.04/191.69 ( class_Groups_Ocomm__monoid__mult(T_d)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( ! [B_x] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.04/191.69 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 191.04/191.69 => 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)) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_card__SigmaI,axiom,
% 191.04/191.69 ! [V_B_2,T_c,V_A_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( ! [B_x] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.04/191.69 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 191.04/191.69 => 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) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fold1__in,axiom,
% 191.04/191.69 ! [V_A_2,T_b] :
% 191.04/191.69 ( class_Groups_Oab__semigroup__mult(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => ( ! [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))))))
% 191.04/191.69 => 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)) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_finite__SigmaI,axiom,
% 191.04/191.69 ! [V_B_2,T_c,V_A_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => ( ! [B_a] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 191.04/191.69 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 191.04/191.69 => 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))) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_hom__fold1__commute,axiom,
% 191.04/191.69 ! [V_N_2,V_h_2,T_b] :
% 191.04/191.69 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 191.04/191.69 => ( ! [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))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 191.04/191.69 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => 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)) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_SigmaE,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,V_ca_2,T_c,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_ca_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 191.04/191.69 => ~ ! [B_x] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.04/191.69 => ! [B_y] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x)))
% 191.04/191.69 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_map__pair__surj,axiom,
% 191.04/191.69 ! [V_g_2,T_d,T_e,V_f_2,T_b,T_c] :
% 191.04/191.69 ( 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))
% 191.04/191.69 => ( 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))
% 191.04/191.69 => 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)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_map__pair__inj__on,axiom,
% 191.04/191.69 ! [V_B_2,V_g_2,T_e,T_d,V_A_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 191.04/191.69 => ( c_Fun_Oinj__on(T_d,T_e,V_g_2,V_B_2)
% 191.04/191.69 => 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))) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_map__pair__imageI,axiom,
% 191.04/191.69 ! [V_g_2,V_f_2,T_e,T_d,V_R_2,V_ba_2,V_a_2,T_c,T_b] :
% 191.04/191.69 ( 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_ba_2)),V_R_2))
% 191.04/191.69 => 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_ba_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))) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fst__comp__map__pair,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_snd__comp__map__pair,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_map__pair_Ocompositionality,axiom,
% 191.04/191.69 ! [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) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_map__pair__compose,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_map__pair_Ocomp,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_snd__prod__fun,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_map__pair__ident,axiom,
% 191.04/191.69 ! [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 ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fst__map__pair,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_map__pair__simp,axiom,
% 191.04/191.69 ! [V_ba_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_ba_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_ba_2)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_map__pair__def,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_map__pair__surj__on,axiom,
% 191.04/191.69 ! [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] :
% 191.04/191.69 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
% 191.04/191.69 => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_B_2) = V_B_H_2
% 191.04/191.69 => 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)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_prod__fun__imageE,axiom,
% 191.04/191.69 ! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_ca_2,T_c,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_ca_2),hAPP(c_Set_Oimage(tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2)),V_R_2)))
% 191.04/191.69 => ~ ! [B_x,B_y] :
% 191.04/191.69 ( V_ca_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y))
% 191.04/191.69 => ~ 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)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_setprod__pos__nat,axiom,
% 191.04/191.69 ! [V_f_2,V_S_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 191.04/191.69 => ( ! [B_x] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 191.04/191.69 => 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))) )
% 191.04/191.69 => 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))) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_folding__one__idem_Ohom__commute,axiom,
% 191.04/191.69 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_b] :
% 191.04/191.69 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 191.04/191.69 => ( ! [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))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 191.04/191.69 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 => 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)) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Rep__Integ__induct,axiom,
% 191.04/191.69 ! [V_Pa_2,V_y_2] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 191.04/191.69 => ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Int_ORep__Integ,B_x)))
% 191.04/191.69 => hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Rep__Integ__cases,axiom,
% 191.04/191.69 ! [V_y_2] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 191.04/191.69 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 191.04/191.69 => ( ! [B_x] :
% 191.04/191.69 ( 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)))
% 191.04/191.69 => hAPP(V_g_2,B_x) = V_z_2 )
% 191.04/191.69 => 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)) ) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fun__left__comm__idem__remove,axiom,
% 191.04/191.69 ! [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))))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_card__less__Suc,axiom,
% 191.04/191.69 ! [V_i_2,V_M_2] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 191.04/191.69 => 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))))) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_CollectI,axiom,
% 191.04/191.69 ! [T_b,V_a_2,V_Pa_2] :
% 191.04/191.69 ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 191.04/191.69 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_finite__Collect__conjI,axiom,
% 191.04/191.69 ! [V_Q_2,V_Pa_2,T_b] :
% 191.04/191.69 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 191.04/191.69 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2))) )
% 191.04/191.69 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2)),V_Q_2)))) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_finite__Collect__less__nat,axiom,
% 191.04/191.69 ! [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)))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_finite__Collect__le__nat,axiom,
% 191.04/191.69 ! [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)))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom,
% 191.04/191.69 ! [V_x_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 191.04/191.69 => 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) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Collect__split,axiom,
% 191.04/191.69 ! [V_Q_2,V_Pa_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_OCollect(T_c),V_Q_2))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_SetCompr__Sigma__eq,axiom,
% 191.04/191.69 ! [V_Q_2,V_Pa_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),V_Q_2)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_vimage__Collect__eq,axiom,
% 191.04/191.69 ! [V_Pa_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_c),V_Pa_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),V_Pa_2),V_f_2)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Collect__neg__eq,axiom,
% 191.04/191.69 ! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_finite__Collect__disjI,axiom,
% 191.04/191.69 ! [V_Q_2,V_Pa_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_Pa_2)),V_Q_2))))
% 191.04/191.69 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 191.04/191.69 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2))) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom,
% 191.04/191.69 ! [T_b] :
% 191.04/191.69 ( class_Orderings_Olinorder(T_b)
% 191.04/191.69 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom,
% 191.04/191.69 ! [T_b] :
% 191.04/191.69 ( class_Orderings_Olinorder(T_b)
% 191.04/191.69 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Collect__mem__eq,axiom,
% 191.04/191.69 ! [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 ).
% 191.04/191.69
% 191.04/191.69 fof(fact_mem__Collect__eq,axiom,
% 191.04/191.69 ! [V_Pa_2,V_a_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 191.04/191.69 <=> hBOOL(hAPP(V_Pa_2,V_a_2)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_CollectD,axiom,
% 191.04/191.69 ! [V_Pa_2,V_a_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 191.04/191.69 => hBOOL(hAPP(V_Pa_2,V_a_2)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_CollectE,axiom,
% 191.04/191.69 ! [V_Pa_2,V_a_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 191.04/191.69 => hBOOL(hAPP(V_Pa_2,V_a_2)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fun__left__comm__idem,axiom,
% 191.04/191.69 ! [T_b] :
% 191.04/191.69 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 191.04/191.69 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fun__left__comm__idem__sup,axiom,
% 191.04/191.69 ! [T_b] :
% 191.04/191.69 ( class_Lattices_Osemilattice__sup(T_b)
% 191.04/191.69 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Collect__disj__eq,axiom,
% 191.04/191.69 ! [V_Q_2,V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_Pa_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_Set_OCollect(T_b),V_Q_2)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_empty__Collect__eq,axiom,
% 191.04/191.69 ! [V_Pa_2,T_b] :
% 191.04/191.69 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_Pa_2)
% 191.04/191.69 <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Collect__empty__eq,axiom,
% 191.04/191.69 ! [V_Pa_2,T_b] :
% 191.04/191.69 ( hAPP(c_Set_OCollect(T_b),V_Pa_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.69 <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_empty__def,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_insert__Collect,axiom,
% 191.04/191.69 ! [V_Pa_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)))),V_Pa_2)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Collect__def,axiom,
% 191.04/191.69 ! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),V_Pa_2) = V_Pa_2 ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom,
% 191.04/191.69 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 191.04/191.69 => 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)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom,
% 191.04/191.69 ! [V_z_2,V_x_2,V_f_2,T_c,T_b] :
% 191.04/191.69 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 191.04/191.69 => 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) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fun__left__comm__idem__insert,axiom,
% 191.04/191.69 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_UNIV__def,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_fun__left__comm__idem__inf,axiom,
% 191.04/191.69 ! [T_b] :
% 191.04/191.69 ( class_Lattices_Osemilattice__inf(T_b)
% 191.04/191.69 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Collect__conj__eq,axiom,
% 191.04/191.69 ! [V_Q_2,V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_Set_OCollect(T_b),V_Q_2)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_insert__compr,axiom,
% 191.04/191.69 ! [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))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_insert__compr__raw,axiom,
% 191.04/191.69 ! [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))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Un__def,axiom,
% 191.04/191.69 ! [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))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Int__Collect,axiom,
% 191.04/191.69 ! [V_Pa_2,V_A_2,V_x_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))))
% 191.04/191.69 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.04/191.69 & hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Int__def,axiom,
% 191.04/191.69 ! [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))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_singleton__conv2,axiom,
% 191.04/191.69 ! [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))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_singleton__conv,axiom,
% 191.04/191.69 ! [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))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Collect__conv__if2,axiom,
% 191.04/191.69 ! [T_b,V_a_2,V_Pa_2] :
% 191.04/191.69 ( ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 191.04/191.69 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_Pa_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) )
% 191.04/191.69 & ( ~ hBOOL(hAPP(V_Pa_2,V_a_2))
% 191.04/191.69 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Collect__conv__if,axiom,
% 191.04/191.69 ! [T_b,V_a_2,V_Pa_2] :
% 191.04/191.69 ( ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 191.04/191.69 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_Pa_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) )
% 191.04/191.69 & ( ~ hBOOL(hAPP(V_Pa_2,V_a_2))
% 191.04/191.69 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_set__diff__eq,axiom,
% 191.04/191.69 ! [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)))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_finite__Collect__not,axiom,
% 191.04/191.69 ! [V_Pa_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2))))
% 191.04/191.69 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_insert__def,axiom,
% 191.04/191.69 ! [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) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Compl__eq,axiom,
% 191.04/191.69 ! [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))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_vimage__def,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Collect__imp__eq,axiom,
% 191.04/191.69 ! [V_Q_2,V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),V_Pa_2)),V_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_Pa_2))),hAPP(c_Set_OCollect(T_b),V_Q_2)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_dom__def,axiom,
% 191.04/191.69 ! [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)))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_finite__M__bounded__by__nat,axiom,
% 191.04/191.69 ! [V_i_2,V_Pa_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),V_Pa_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2))))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_setsum__setsum__restrict,axiom,
% 191.04/191.69 ! [V_R_2,V_f_2,V_T_2,T_c,V_S_2,T_b,T_d] :
% 191.04/191.69 ( class_Groups_Ocomm__monoid__add(T_d)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 191.04/191.69 => 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) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_if__image__distrib,axiom,
% 191.04/191.69 ! [V_S_2,V_g_2,V_f_2,V_Pa_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),V_Pa_2)),V_f_2)),V_g_2)),V_S_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),V_Pa_2)))),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),V_Pa_2))))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_dom__if,axiom,
% 191.04/191.69 ! [V_g_2,V_f_2,V_Pa_2,T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(hAPP(c_COMBS(T_b,tc_Option_Ooption(T_c),tc_Option_Ooption(T_c)),hAPP(hAPP(c_COMBS(T_b,tc_Option_Ooption(T_c),tc_fun(tc_Option_Ooption(T_c),tc_Option_Ooption(T_c))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(T_c),tc_fun(tc_Option_Ooption(T_c),tc_Option_Ooption(T_c))),T_b),c_If(tc_Option_Ooption(T_c))),V_Pa_2)),V_f_2)),V_g_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_f_2)),hAPP(c_Set_OCollect(T_b),V_Pa_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_g_2)),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2)))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_nat__seg__image__imp__finite,axiom,
% 191.04/191.69 ! [V_n_2,V_f_2,T_b,V_A_2] :
% 191.04/191.69 ( 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)))
% 191.04/191.69 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_setsum__restrict__set_H,axiom,
% 191.04/191.69 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 191.04/191.69 ( class_Groups_Ocomm__monoid__add(T_c)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => 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) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_setsum__image__gen,axiom,
% 191.04/191.69 ! [V_f_2,T_d,V_g_2,V_S_2,T_b,T_c] :
% 191.04/191.69 ( class_Groups_Ocomm__monoid__add(T_c)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 191.04/191.69 => 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)) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Image__singleton,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_setsum__cases,axiom,
% 191.04/191.69 ! [V_g_2,V_f_2,V_Pa_2,V_A_2,T_b,T_c] :
% 191.04/191.69 ( class_Groups_Ocomm__monoid__add(T_c)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),V_Pa_2)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2))))) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_card__less__Suc2,axiom,
% 191.04/191.69 ! [V_i_2,V_M_2] :
% 191.04/191.69 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 191.04/191.69 => 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))))) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_card__less,axiom,
% 191.04/191.69 ! [V_i_2,V_M_2] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 191.04/191.69 => 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) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_dom__override__on,axiom,
% 191.04/191.69 ! [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))))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_setsum__multicount,axiom,
% 191.04/191.69 ! [V_k_2,V_R_2,V_T_2,T_c,V_S_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 191.04/191.69 => ( ! [B_x] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2))
% 191.04/191.69 => 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 )
% 191.04/191.69 => 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)) ) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_finite__Collect__subsets,axiom,
% 191.04/191.69 ! [V_A_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.69 => 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)))) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Pow__def,axiom,
% 191.04/191.69 ! [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)) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_override__on__apply__in,axiom,
% 191.04/191.69 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 191.04/191.69 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.69 => 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) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_override__on__apply__notin,axiom,
% 191.04/191.69 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 191.04/191.69 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.69 => 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) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_override__on__emptyset,axiom,
% 191.04/191.69 ! [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 ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inj__graph,axiom,
% 191.04/191.69 ! [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))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
% 191.04/191.69 ! [V_Pa_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_Pa_2))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_override__on__def,axiom,
% 191.04/191.69 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 191.04/191.69 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.69 => 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) )
% 191.04/191.69 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.04/191.69 => 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) ) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_finite__psubset__def,axiom,
% 191.04/191.69 ! [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)))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_inv__image__def,axiom,
% 191.04/191.69 ! [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))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
% 191.04/191.69 ! [V_Pa_2] : hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_Pa_2)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),V_Pa_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom,
% 191.04/191.69 ! [V_Pa_2] : hAPP(c_Set_OCollect(tc_Nat_Onat),V_Pa_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),V_Pa_2),c_Int_Onat)))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_Nitpick_Oprod__def,axiom,
% 191.04/191.69 ! [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)))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_int__ge__less__than__def,axiom,
% 191.04/191.69 ! [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)))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_int__ge__less__than2__def,axiom,
% 191.04/191.69 ! [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)))) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_reflp__def,axiom,
% 191.04/191.69 ! [V_r_2,T_b] :
% 191.04/191.69 ( c_Predicate_Oreflp(T_b,V_r_2)
% 191.04/191.69 <=> 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))) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_reflpE,axiom,
% 191.04/191.69 ! [V_x_2,V_r_2,T_b] :
% 191.04/191.69 ( c_Predicate_Oreflp(T_b,V_r_2)
% 191.04/191.69 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ).
% 191.04/191.69
% 191.04/191.69 fof(fact_min__max_Oinf__Sup2__distrib,axiom,
% 191.04/191.69 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.69 ( class_Orderings_Olinorder(T_b)
% 191.04/191.69 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.70 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.70 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.70 => 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))))))) ) ) ) ) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_min__max_Oinf__Sup1__distrib,axiom,
% 191.04/191.70 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.70 ( class_Orderings_Olinorder(T_b)
% 191.04/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.70 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.70 => 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))))) ) ) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_finite__Collect__bounded__ex,axiom,
% 191.04/191.70 ! [V_Q_2,T_c,V_Pa_2,T_b] :
% 191.04/191.70 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 191.04/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),V_Q_2)))))
% 191.04/191.70 <=> ! [B_y] :
% 191.04/191.70 ( hBOOL(hAPP(V_Pa_2,B_y))
% 191.04/191.70 => 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)))) ) ) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_finite__image__set,axiom,
% 191.04/191.70 ! [V_f_2,T_c,V_Pa_2,T_b] :
% 191.04/191.70 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 191.04/191.70 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_b)),c_fequal)),V_f_2)))),V_Pa_2))))) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_ran__def,axiom,
% 191.04/191.70 ! [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)))) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_Pow__Compl,axiom,
% 191.04/191.70 ! [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))))) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_add__Max__commute,axiom,
% 191.04/191.70 ! [V_k_2,V_N_2,T_b] :
% 191.04/191.70 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 191.04/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 191.04/191.70 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.70 => 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))))) ) ) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_add__Min__commute,axiom,
% 191.04/191.70 ! [V_k_2,V_N_2,T_b] :
% 191.04/191.70 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 191.04/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 191.04/191.70 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.70 => 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))))) ) ) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_sup__Inf2__distrib,axiom,
% 191.04/191.70 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.70 ( class_Lattices_Odistrib__lattice(T_b)
% 191.04/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.70 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.70 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.70 => 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))))))) ) ) ) ) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_sup__Inf1__distrib,axiom,
% 191.04/191.70 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.70 ( class_Lattices_Odistrib__lattice(T_b)
% 191.04/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.70 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.70 => 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))))) ) ) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_inf__Sup1__distrib,axiom,
% 191.04/191.70 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.70 ( class_Lattices_Odistrib__lattice(T_b)
% 191.04/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.70 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.70 => 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))))) ) ) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_inf__Sup2__distrib,axiom,
% 191.04/191.70 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.70 ( class_Lattices_Odistrib__lattice(T_b)
% 191.04/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.70 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.70 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.70 => 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))))))) ) ) ) ) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_min__max_Osup__Inf2__distrib,axiom,
% 191.04/191.70 ! [V_B_2,V_A_2,T_b] :
% 191.04/191.70 ( class_Orderings_Olinorder(T_b)
% 191.04/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.70 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.04/191.70 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.70 => 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))))))) ) ) ) ) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_min__max_Osup__Inf1__distrib,axiom,
% 191.04/191.70 ! [V_x_2,V_A_2,T_b] :
% 191.04/191.70 ( class_Orderings_Olinorder(T_b)
% 191.04/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.70 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.70 => 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))))) ) ) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_setsum__mult__setsum__if__inj,axiom,
% 191.04/191.70 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] :
% 191.04/191.70 ( class_Rings_Osemiring__0(T_d)
% 191.04/191.70 => ( 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)))
% 191.04/191.70 => 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))))))) ) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_setsum__multicount__gen,axiom,
% 191.04/191.70 ! [V_k_2,V_R_2,V_t_2,T_c,V_s_2,T_b] :
% 191.04/191.70 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 191.04/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2))
% 191.04/191.70 => ( ! [B_x] :
% 191.04/191.70 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2))
% 191.04/191.70 => 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) )
% 191.04/191.70 => 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) ) ) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_inj__on__id,axiom,
% 191.04/191.70 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_Fun_Oid(T_b),V_A_2) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_map__pair_Oid,axiom,
% 191.04/191.70 ! [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)) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_map__pair_Oidentity,axiom,
% 191.04/191.70 ! [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)) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_id__apply,axiom,
% 191.04/191.70 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ).
% 191.04/191.70
% 191.04/191.70 fof(fact_id__def,axiom,
% 191.04/191.70 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ).
% 191.04/191.70
% 191.04/191.70 fof(fact_apsnd__id,axiom,
% 191.04/191.70 ! [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)) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_apfst__id,axiom,
% 191.04/191.70 ! [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)) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_of__int__eq__id,axiom,
% 191.04/191.70 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_vimage__id,axiom,
% 191.04/191.70 ! [V_A_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_Fun_Oid(T_b)),V_A_2) = V_A_2 ).
% 191.04/191.70
% 191.04/191.70 fof(fact_o__id,axiom,
% 191.04/191.70 ! [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 ).
% 191.04/191.70
% 191.04/191.70 fof(fact_id__o,axiom,
% 191.04/191.70 ! [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 ).
% 191.04/191.70
% 191.04/191.70 fof(fact_o__eq__id__dest,axiom,
% 191.04/191.70 ! [V_v_2,V_ca_2,V_ba_2,V_a_2,T_b,T_c,T_d] :
% 191.04/191.70 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_ba_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_ca_2)
% 191.04/191.70 => hAPP(V_a_2,hAPP(V_ba_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_surj__id,axiom,
% 191.04/191.70 ! [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)) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_image__id,axiom,
% 191.04/191.70 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),V_Y_2) = V_Y_2 ).
% 191.04/191.70
% 191.04/191.70 fof(fact_folding_Oempty,axiom,
% 191.04/191.70 ! [V_F_2,V_f_2,T_c,T_b] :
% 191.04/191.70 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 191.04/191.70 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_apsnd__def,axiom,
% 191.04/191.70 ! [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) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_apfst__def,axiom,
% 191.04/191.70 ! [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)) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_split__Pair,axiom,
% 191.04/191.70 ! [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)) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_setsum__reindex__id,axiom,
% 191.04/191.70 ! [V_B_2,V_f_2,T_b,T_c] :
% 191.04/191.70 ( class_Groups_Ocomm__monoid__add(T_c)
% 191.04/191.70 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 191.04/191.70 => 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)) ) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_setprod__reindex__id,axiom,
% 191.04/191.70 ! [V_B_2,V_f_2,T_b,T_c] :
% 191.04/191.70 ( class_Groups_Ocomm__monoid__mult(T_c)
% 191.04/191.70 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 191.04/191.70 => 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)) ) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_finite__conv__nat__seg__image,axiom,
% 191.04/191.70 ! [V_A_2,T_b] :
% 191.04/191.70 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.04/191.70 <=> ? [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))) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_rel__comp__def,axiom,
% 191.04/191.70 ! [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))))) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_rel__compI,axiom,
% 191.04/191.70 ! [V_s_2,V_ca_2,T_d,V_r_2,V_ba_2,V_a_2,T_c,T_b] :
% 191.04/191.70 ( 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_ba_2)),V_r_2))
% 191.04/191.70 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_ba_2),V_ca_2)),V_s_2))
% 191.04/191.70 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_a_2),V_ca_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_rel__comp__UNION__distrib,axiom,
% 191.04/191.70 ! [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)) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_rel__comp__UNION__distrib2,axiom,
% 191.04/191.70 ! [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)) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_rel__comp__empty1,axiom,
% 191.04/191.70 ! [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)) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_rel__comp__empty2,axiom,
% 191.04/191.70 ! [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)) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_rel__comp__distrib2,axiom,
% 191.04/191.70 ! [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)) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_rel__comp__distrib,axiom,
% 191.04/191.70 ! [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)) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_rel__comp__mono,axiom,
% 191.04/191.70 ! [V_s_2,V_s_H_2,T_d,V_r_2,V_r_H_2,T_c,T_b] :
% 191.04/191.70 ( 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))
% 191.04/191.70 => ( 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))
% 191.04/191.70 => 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))) ) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_O__assoc,axiom,
% 191.04/191.70 ! [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)) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_union__comp__emptyR,axiom,
% 191.04/191.70 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 191.04/191.70 ( 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))
% 191.04/191.70 => ( 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))
% 191.04/191.70 => 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)) ) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_union__comp__emptyL,axiom,
% 191.04/191.70 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 191.04/191.70 ( 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))
% 191.04/191.70 => ( 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))
% 191.04/191.70 => 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)) ) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_rel__comp__subset__Sigma,axiom,
% 191.04/191.70 ! [V_C_2,V_s_2,T_d,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 191.04/191.70 ( 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))))
% 191.04/191.70 => ( 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))))
% 191.04/191.70 => 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)))) ) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_max__ext__compat,axiom,
% 191.04/191.70 ! [V_S_2,V_R_2,T_b] :
% 191.04/191.70 ( 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))
% 191.04/191.70 => 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))) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_min__ext__compat,axiom,
% 191.04/191.70 ! [V_S_2,V_R_2,T_b] :
% 191.04/191.70 ( 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))
% 191.04/191.70 => 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))) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_pred__comp__rel__comp__eq,axiom,
% 191.04/191.70 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 191.04/191.70 ( 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)
% 191.04/191.70 <=> 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))) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_reduction__pairI,axiom,
% 191.04/191.70 ! [V_S_2,V_R_2,T_b] :
% 191.04/191.70 ( c_Wellfounded_Owf(T_b,V_R_2)
% 191.04/191.70 => ( 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))
% 191.04/191.70 => 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)) ) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wf__less__than,axiom,
% 191.04/191.70 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_pred__comp_Ointros,axiom,
% 191.04/191.70 ! [T_d,T_c,T_b,V_ca_2,V_s_2,V_ba_2,V_a_2,V_r_2] :
% 191.04/191.70 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_ba_2))
% 191.04/191.70 => ( hBOOL(hAPP(hAPP(V_s_2,V_ba_2),V_ca_2))
% 191.04/191.70 => c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2,V_a_2,V_ca_2) ) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wf__empty,axiom,
% 191.04/191.70 ! [T_b] : c_Wellfounded_Owf(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wf__inv__image,axiom,
% 191.04/191.70 ! [V_f_2,T_c,V_r_2,T_b] :
% 191.04/191.70 ( c_Wellfounded_Owf(T_b,V_r_2)
% 191.04/191.70 => c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wf__lex__prod,axiom,
% 191.04/191.70 ! [V_rb_2,T_c,V_ra_2,T_b] :
% 191.04/191.70 ( c_Wellfounded_Owf(T_b,V_ra_2)
% 191.04/191.70 => ( c_Wellfounded_Owf(T_c,V_rb_2)
% 191.04/191.70 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2)) ) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wf__measure,axiom,
% 191.04/191.70 ! [V_f_2,T_b] : c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wf__union__merge,axiom,
% 191.04/191.70 ! [V_S_2,V_R_2,T_b] :
% 191.04/191.70 ( 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))
% 191.04/191.70 <=> 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)) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wf__no__loop,axiom,
% 191.04/191.70 ! [V_R_2,T_b] :
% 191.04/191.70 ( 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))
% 191.04/191.70 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wf__comp__self,axiom,
% 191.04/191.70 ! [V_R_2,T_b] :
% 191.04/191.70 ( c_Wellfounded_Owf(T_b,V_R_2)
% 191.04/191.70 <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wf__less,axiom,
% 191.04/191.70 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)))) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wf__int__ge__less__than,axiom,
% 191.04/191.70 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wf__irrefl,axiom,
% 191.04/191.70 ! [V_a_2,V_r_2,T_b] :
% 191.04/191.70 ( c_Wellfounded_Owf(T_b,V_r_2)
% 191.04/191.70 => ~ 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)) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wf__asym,axiom,
% 191.04/191.70 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 191.04/191.70 ( c_Wellfounded_Owf(T_b,V_r_2)
% 191.04/191.70 => ( 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))
% 191.04/191.70 => ~ hBOOL(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)) ) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wf__not__sym,axiom,
% 191.04/191.70 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 191.04/191.70 ( c_Wellfounded_Owf(T_b,V_r_2)
% 191.04/191.70 => ( 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))
% 191.04/191.70 => ~ hBOOL(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)) ) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wf__not__refl,axiom,
% 191.04/191.70 ! [V_a_2,V_r_2,T_b] :
% 191.04/191.70 ( c_Wellfounded_Owf(T_b,V_r_2)
% 191.04/191.70 => ~ 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)) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wf__Int1,axiom,
% 191.04/191.70 ! [V_r_H_2,V_r_2,T_b] :
% 191.04/191.70 ( c_Wellfounded_Owf(T_b,V_r_2)
% 191.04/191.70 => 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)) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wf__Int2,axiom,
% 191.04/191.70 ! [V_r_H_2,V_r_2,T_b] :
% 191.04/191.70 ( c_Wellfounded_Owf(T_b,V_r_2)
% 191.04/191.70 => 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)) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_max__ext__wf,axiom,
% 191.04/191.70 ! [V_r_2,T_b] :
% 191.04/191.70 ( c_Wellfounded_Owf(T_b,V_r_2)
% 191.04/191.70 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_b,V_r_2)) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wf__pair__less,axiom,
% 191.04/191.70 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wf__subset,axiom,
% 191.04/191.70 ! [V_p_2,V_r_2,T_b] :
% 191.04/191.70 ( c_Wellfounded_Owf(T_b,V_r_2)
% 191.04/191.70 => ( 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))
% 191.04/191.70 => c_Wellfounded_Owf(T_b,V_p_2) ) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_pred__comp_Oequations,axiom,
% 191.04/191.70 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 191.04/191.70 ( c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2,V_a1_2,V_a3_2)
% 191.04/191.70 <=> ? [B_b] :
% 191.04/191.70 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b))
% 191.04/191.70 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wf__finite__psubset,axiom,
% 191.04/191.70 ! [T_b] : c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_min__ext__wf,axiom,
% 191.04/191.70 ! [V_r_2,T_b] :
% 191.04/191.70 ( c_Wellfounded_Owf(T_b,V_r_2)
% 191.04/191.70 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_b,V_r_2)) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wf__mlex,axiom,
% 191.04/191.70 ! [V_f_2,V_R_2,T_b] :
% 191.04/191.70 ( c_Wellfounded_Owf(T_b,V_R_2)
% 191.04/191.70 => c_Wellfounded_Owf(T_b,c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wf__acc__iff,axiom,
% 191.04/191.70 ! [V_r_2,T_b] :
% 191.04/191.70 ( c_Wellfounded_Owf(T_b,V_r_2)
% 191.04/191.70 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_acc__wfD,axiom,
% 191.04/191.70 ! [V_x_2,V_r_2,T_b] :
% 191.04/191.70 ( c_Wellfounded_Owf(T_b,V_r_2)
% 191.04/191.70 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wf__int__ge__less__than2,axiom,
% 191.04/191.70 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wf__iff__no__infinite__down__chain,axiom,
% 191.04/191.70 ! [V_r_2,T_b] :
% 191.04/191.70 ( c_Wellfounded_Owf(T_b,V_r_2)
% 191.04/191.70 <=> ~ ? [B_f] :
% 191.04/191.70 ! [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)) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wfE__pf,axiom,
% 191.04/191.70 ! [V_A_2,V_R_2,T_b] :
% 191.04/191.70 ( c_Wellfounded_Owf(T_b,V_R_2)
% 191.04/191.70 => ( 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)))
% 191.04/191.70 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wf__union__compatible,axiom,
% 191.04/191.70 ! [V_S_2,V_R_2,T_b] :
% 191.04/191.70 ( c_Wellfounded_Owf(T_b,V_R_2)
% 191.04/191.70 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 191.04/191.70 => ( 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))
% 191.04/191.70 => 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)) ) ) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wf,axiom,
% 191.04/191.70 ! [T_b] :
% 191.04/191.70 ( class_Orderings_Owellorder(T_b)
% 191.04/191.70 => 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)))) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_reduction__pair__def,axiom,
% 191.04/191.70 ! [V_Pa_2,T_b] :
% 191.04/191.70 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2)
% 191.04/191.70 <=> ( c_Wellfounded_Owf(T_b,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))
% 191.04/191.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))) ) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_reduction__pair__lemma,axiom,
% 191.04/191.70 ! [V_S_2,V_R_2,V_Pa_2,T_b] :
% 191.04/191.70 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2)
% 191.04/191.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2)))
% 191.04/191.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2)))
% 191.04/191.70 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 191.04/191.70 => 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)) ) ) ) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wf__map__pair__image,axiom,
% 191.04/191.70 ! [V_f_2,T_c,V_r_2,T_b] :
% 191.04/191.70 ( c_Wellfounded_Owf(T_b,V_r_2)
% 191.04/191.70 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 191.04/191.70 => 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)) ) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wf__lenlex,axiom,
% 191.04/191.70 ! [V_r_2,T_b] :
% 191.04/191.70 ( c_Wellfounded_Owf(T_b,V_r_2)
% 191.04/191.70 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olenlex(T_b,V_r_2)) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wf__if__measure,axiom,
% 191.04/191.70 ! [T_b,V_g_2,V_f_2,V_Pa_2] :
% 191.04/191.70 ( ! [B_x] :
% 191.04/191.70 ( hBOOL(hAPP(V_Pa_2,B_x))
% 191.04/191.70 => 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))) )
% 191.04/191.70 => c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),V_g_2))))) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_pred__nat__def,axiom,
% 191.04/191.70 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))) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wf__lex,axiom,
% 191.04/191.70 ! [V_r_2,T_b] :
% 191.04/191.70 ( c_Wellfounded_Owf(T_b,V_r_2)
% 191.04/191.70 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olex(T_b,V_r_2)) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wf__pred__nat,axiom,
% 191.04/191.70 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_lex__def,axiom,
% 191.04/191.70 ! [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)) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wf__lexn,axiom,
% 191.04/191.70 ! [V_n_2,V_r_2,T_b] :
% 191.04/191.70 ( c_Wellfounded_Owf(T_b,V_r_2)
% 191.04/191.70 => c_Wellfounded_Owf(tc_List_Olist(T_b),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_lexn_Osimps_I1_J,axiom,
% 191.04/191.70 ! [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)) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wf__same__fst,axiom,
% 191.04/191.70 ! [T_b,V_R_2,T_c,V_Pa_2] :
% 191.04/191.70 ( ! [B_x] :
% 191.04/191.70 ( hBOOL(hAPP(V_Pa_2,B_x))
% 191.04/191.70 => c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x)) )
% 191.04/191.70 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_Pa_2,V_R_2)) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_Range__Collect__split,axiom,
% 191.04/191.70 ! [V_Pa_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Set_OCollect(tc_prod(T_c,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_Pa_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Pa_2))) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_RangeI,axiom,
% 191.04/191.70 ! [V_r_2,V_ba_2,V_a_2,T_c,T_b] :
% 191.04/191.70 ( 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_ba_2)),V_r_2))
% 191.04/191.70 => hBOOL(hAPP(hAPP(c_member(T_c),V_ba_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_Range__Id__on,axiom,
% 191.04/191.70 ! [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 ).
% 191.04/191.70
% 191.04/191.70 fof(fact_Range__empty__iff,axiom,
% 191.04/191.70 ! [V_r_2,T_b,T_c] :
% 191.04/191.70 ( hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.70 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_Range__empty,axiom,
% 191.04/191.70 ! [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)) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_Range__Un__eq,axiom,
% 191.04/191.70 ! [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)) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_finite__Range,axiom,
% 191.04/191.70 ! [V_r_2,T_c,T_b] :
% 191.04/191.70 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 191.04/191.70 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_snd__eq__Range,axiom,
% 191.04/191.70 ! [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) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_Range__iff,axiom,
% 191.04/191.70 ! [V_r_2,T_c,V_a_2,T_b] :
% 191.04/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 191.04/191.70 <=> ? [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)) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_Range__insert,axiom,
% 191.04/191.70 ! [V_r_2,V_ba_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_ba_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_ba_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_Range__Int__subset,axiom,
% 191.04/191.70 ! [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)))) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_Range__Diff__subset,axiom,
% 191.04/191.70 ! [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)))) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_RangeP__Range__eq,axiom,
% 191.04/191.70 ! [V_x_2,V_r_2,T_c,T_b] :
% 191.04/191.70 ( 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))
% 191.04/191.70 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_RangeE,axiom,
% 191.04/191.70 ! [V_r_2,T_c,V_ba_2,T_b] :
% 191.04/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 191.04/191.70 => ~ ! [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_ba_2)),V_r_2)) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_RangeP_Ointros,axiom,
% 191.04/191.70 ! [T_c,T_b,V_ba_2,V_a_2,V_r_2] :
% 191.04/191.70 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_ba_2))
% 191.04/191.70 => hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_ba_2)) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_RangeP_Oequations,axiom,
% 191.04/191.70 ! [V_a2_2,V_r_2,T_c,T_b] :
% 191.04/191.70 ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2))
% 191.04/191.70 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wf__Un,axiom,
% 191.04/191.70 ! [V_s_2,V_r_2,T_b] :
% 191.04/191.70 ( c_Wellfounded_Owf(T_b,V_r_2)
% 191.04/191.70 => ( c_Wellfounded_Owf(T_b,V_s_2)
% 191.04/191.70 => ( 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))
% 191.04/191.70 => 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)) ) ) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wfP__def,axiom,
% 191.04/191.70 ! [V_r_2,T_b] :
% 191.04/191.70 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 191.04/191.70 <=> 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))) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wfP__empty,axiom,
% 191.04/191.70 ! [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))) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_DomainI,axiom,
% 191.04/191.70 ! [V_r_2,V_ba_2,V_a_2,T_c,T_b] :
% 191.04/191.70 ( 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_ba_2)),V_r_2))
% 191.04/191.70 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_Domain__Id__on,axiom,
% 191.04/191.70 ! [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 ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wfP__accp__iff,axiom,
% 191.04/191.70 ! [V_r_2,T_b] :
% 191.04/191.70 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 191.04/191.70 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1)) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_accp__wfPD,axiom,
% 191.04/191.70 ! [V_x_2,V_r_2,T_b] :
% 191.04/191.70 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 191.04/191.70 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_x_2)) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_wfP__subset,axiom,
% 191.04/191.70 ! [V_p_2,V_r_2,T_b] :
% 191.04/191.70 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 191.04/191.70 => ( 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))
% 191.04/191.70 => c_Wellfounded_OwfP(T_b,V_p_2) ) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_Domain__empty__iff,axiom,
% 191.04/191.70 ! [V_r_2,T_c,T_b] :
% 191.04/191.70 ( hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.04/191.70 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_Domain__empty,axiom,
% 191.04/191.70 ! [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)) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_Domain__mono,axiom,
% 191.04/191.70 ! [V_s_2,V_r_2,T_c,T_b] :
% 191.04/191.70 ( 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))
% 191.04/191.70 => 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))) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_Domain__Un__eq,axiom,
% 191.04/191.70 ! [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)) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_finite__Domain,axiom,
% 191.04/191.70 ! [V_r_2,T_c,T_b] :
% 191.04/191.70 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 191.04/191.70 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_fst__eq__Domain,axiom,
% 191.04/191.70 ! [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) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_Domain__iff,axiom,
% 191.04/191.70 ! [V_r_2,T_c,V_a_2,T_b] :
% 191.04/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 191.04/191.70 <=> ? [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)) ) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_Domain__insert,axiom,
% 191.04/191.70 ! [V_r_2,V_ba_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_ba_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)) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_Domain__Int__subset,axiom,
% 191.04/191.70 ! [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)))) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_Domain__Diff__subset,axiom,
% 191.04/191.70 ! [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)))) ).
% 191.04/191.70
% 191.04/191.70 fof(fact_Field__def,axiom,
% 191.04/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_wf__in__rel,axiom,
% 191.21/191.70 ! [V_R_2,T_b] :
% 191.21/191.70 ( c_Wellfounded_Owf(T_b,V_R_2)
% 191.21/191.70 => c_Wellfounded_OwfP(T_b,c_FunDef_Oin__rel(T_b,T_b,V_R_2)) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_wfP__wf__eq,axiom,
% 191.21/191.70 ! [V_r_2,T_b] :
% 191.21/191.70 ( 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))
% 191.21/191.70 <=> c_Wellfounded_Owf(T_b,V_r_2) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Domain__Collect__split,axiom,
% 191.21/191.70 ! [V_Pa_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),V_Pa_2)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_DomainP__Domain__eq,axiom,
% 191.21/191.70 ! [V_x_2,V_r_2,T_c,T_b] :
% 191.21/191.70 ( 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))
% 191.21/191.70 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_DomainE,axiom,
% 191.21/191.70 ! [V_r_2,T_c,V_a_2,T_b] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 191.21/191.70 => ~ ! [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)) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_DomainP_Ointros,axiom,
% 191.21/191.70 ! [T_c,T_b,V_ba_2,V_a_2,V_r_2] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_ba_2))
% 191.21/191.70 => hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a_2)) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_DomainP_Oequations,axiom,
% 191.21/191.70 ! [V_a1_2,V_r_2,T_c,T_b] :
% 191.21/191.70 ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2))
% 191.21/191.70 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_wfP__acyclicP,axiom,
% 191.21/191.70 ! [V_r_2,T_b] :
% 191.21/191.70 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 191.21/191.70 => 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))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_neg__map__def,axiom,
% 191.21/191.70 ! [V_Pa_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Oneg__map(T_c,T_b,V_f_2,V_Pa_2) = c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_Pa_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),T_c,c_New__Random__Sequence_Oneg__single(T_b)),V_f_2)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_wf__acyclic,axiom,
% 191.21/191.70 ! [V_r_2,T_b] :
% 191.21/191.70 ( c_Wellfounded_Owf(T_b,V_r_2)
% 191.21/191.70 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_acyclic__subset,axiom,
% 191.21/191.70 ! [V_r_2,V_s_2,T_b] :
% 191.21/191.70 ( c_Wellfounded_Oacyclic(T_b,V_s_2)
% 191.21/191.70 => ( 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))
% 191.21/191.70 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_finite__acyclic__wf,axiom,
% 191.21/191.70 ! [V_r_2,T_b] :
% 191.21/191.70 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 191.21/191.70 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 191.21/191.70 => c_Wellfounded_Owf(T_b,V_r_2) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_wf__iff__acyclic__if__finite,axiom,
% 191.21/191.70 ! [V_r_2,T_b] :
% 191.21/191.70 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 191.21/191.70 => ( c_Wellfounded_Owf(T_b,V_r_2)
% 191.21/191.70 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_neg__single__def,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_pos__map__def,axiom,
% 191.21/191.70 ! [V_Pa_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Opos__map(T_c,T_b,V_f_2,V_Pa_2) = c_New__Random__Sequence_Opos__bind(T_c,T_b,V_Pa_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),T_c,c_New__Random__Sequence_Opos__single(T_b)),V_f_2)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_New__DSequence_Oneg__single__def,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_pos__single__def,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_New__DSequence_Opos__single__def,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Nitpick_Owf_H__def,axiom,
% 191.21/191.70 ! [V_r_2,T_b] :
% 191.21/191.70 ( c_Nitpick_Owf_H(T_b,V_r_2)
% 191.21/191.70 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 191.21/191.70 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 191.21/191.70 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_pigeonhole__infinite,axiom,
% 191.21/191.70 ! [V_f_2,T_c,V_A_2,T_b] :
% 191.21/191.70 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 191.21/191.70 => ? [B_x] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.21/191.70 & ~ 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)))))) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Abs__Integ__cases,axiom,
% 191.21/191.70 ! [V_x_2] :
% 191.21/191.70 ~ ! [B_y] :
% 191.21/191.70 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y)
% 191.21/191.70 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Abs__Integ__induct,axiom,
% 191.21/191.70 ! [V_x_2,V_Pa_2] :
% 191.21/191.70 ( ! [B_y] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg))
% 191.21/191.70 => hBOOL(hAPP(V_Pa_2,hAPP(c_Int_OAbs__Integ,B_y))) )
% 191.21/191.70 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_finite__UN__I,axiom,
% 191.21/191.70 ! [V_B_2,T_c,V_A_2,T_b] :
% 191.21/191.70 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => ( ! [B_a] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 191.21/191.70 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 191.21/191.70 => 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))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_inj__on__diff__nat,axiom,
% 191.21/191.70 ! [V_k_2,V_N_2] :
% 191.21/191.70 ( ! [B_x] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) )
% 191.21/191.70 => 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) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_wfP__SUP,axiom,
% 191.21/191.70 ! [T_b,V_r_2,T_c] :
% 191.21/191.70 ( ! [B_i] : c_Wellfounded_OwfP(T_c,hAPP(V_r_2,B_i))
% 191.21/191.70 => ( ! [B_i,B_j] :
% 191.21/191.70 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j)
% 191.21/191.70 => 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)) )
% 191.21/191.70 => 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)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_finite__map__freshness,axiom,
% 191.21/191.70 ! [V_f_2,T_c,T_b] :
% 191.21/191.70 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Map_Odom(T_b,T_c,V_f_2)))
% 191.21/191.70 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 191.21/191.70 => ? [B_x] : hAPP(V_f_2,B_x) = c_Option_Ooption_ONone(T_c) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_mem__splitE,axiom,
% 191.21/191.70 ! [V_p_2,V_ca_2,T_d,T_c,V_z_2,T_b] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_ca_2),V_p_2)))
% 191.21/191.70 => ~ ! [B_x,B_y] :
% 191.21/191.70 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y)
% 191.21/191.70 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_ca_2,B_x),B_y))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_mem__splitI2,axiom,
% 191.21/191.70 ! [V_ca_2,V_z_2,T_d,T_c,T_b,V_p_2] :
% 191.21/191.70 ( ! [B_a,B_b] :
% 191.21/191.70 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_ca_2,B_a),B_b))) )
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_ca_2),V_p_2))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Eps__split,axiom,
% 191.21/191.70 ! [V_Pa_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2)) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_Pa_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_someI,axiom,
% 191.21/191.70 ! [T_b,V_x_2,V_Pa_2] :
% 191.21/191.70 ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 191.21/191.70 => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_tfl__some,axiom,
% 191.21/191.70 ! [T_b,B_P] :
% 191.21/191.70 ( ? [B_x] : hBOOL(hAPP(B_P,B_x))
% 191.21/191.70 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_b,B_P))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_someI__ex,axiom,
% 191.21/191.70 ! [T_b,V_Pa_2] :
% 191.21/191.70 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 191.21/191.70 => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_some__eq__ex,axiom,
% 191.21/191.70 ! [T_b,V_Pa_2] :
% 191.21/191.70 ( hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2)))
% 191.21/191.70 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_some__eq__trivial,axiom,
% 191.21/191.70 ! [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 ).
% 191.21/191.70
% 191.21/191.70 fof(fact_some__sym__eq__trivial,axiom,
% 191.21/191.70 ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 191.21/191.70
% 191.21/191.70 fof(fact_exE__some,axiom,
% 191.21/191.70 ! [T_b,V_ca_2,V_Pa_2] :
% 191.21/191.70 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 191.21/191.70 => ( V_ca_2 = c_Hilbert__Choice_OEps(T_b,V_Pa_2)
% 191.21/191.70 => hBOOL(hAPP(V_Pa_2,V_ca_2)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Eps__split__eq,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_split__paired__Eps,axiom,
% 191.21/191.70 ! [V_Pa_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),V_Pa_2) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_Pa_2)),c_Product__Type_OPair(T_b,T_c)))) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_wfI__pf,axiom,
% 191.21/191.70 ! [V_R_2,T_b] :
% 191.21/191.70 ( ! [B_A] :
% 191.21/191.70 ( 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)))
% 191.21/191.70 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 191.21/191.70 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Sigma__mono,axiom,
% 191.21/191.70 ! [V_D_2,V_B_2,T_c,V_C_2,V_A_2,T_b] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 191.21/191.70 => ( ! [B_x] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.21/191.70 => 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))) )
% 191.21/191.70 => 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))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_acc_OaccI,axiom,
% 191.21/191.70 ! [V_r_2,V_x_2,T_b] :
% 191.21/191.70 ( ! [B_y] :
% 191.21/191.70 ( 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))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_member(T_b),B_y),c_Wellfounded_Oacc(T_b,V_r_2))) )
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_not__acc__down,axiom,
% 191.21/191.70 ! [V_R_2,V_x_2,T_b] :
% 191.21/191.70 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_R_2)))
% 191.21/191.70 => ~ ! [B_z] :
% 191.21/191.70 ( 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))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_member(T_b),B_z),c_Wellfounded_Oacc(T_b,V_R_2))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_fold__image__1,axiom,
% 191.21/191.70 ! [V_f_2,V_S_2,T_b,T_c] :
% 191.21/191.70 ( class_Groups_Ocomm__monoid__mult(T_c)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 191.21/191.70 => ( ! [B_x] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 191.21/191.70 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 191.21/191.70 => 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) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_card_Oneutral,axiom,
% 191.21/191.70 ! [V_A_2,T_b] :
% 191.21/191.70 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.21/191.70 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 191.21/191.70 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_max__ext_Osimps,axiom,
% 191.21/191.70 ! [V_R_2,V_a2_2,V_a1_2,T_b] :
% 191.21/191.70 ( 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)))
% 191.21/191.70 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 191.21/191.70 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 191.21/191.70 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.21/191.70 & ! [B_x] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 191.21/191.70 => ? [B_xa] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 191.21/191.70 & 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)) ) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_fold__image__cong,axiom,
% 191.21/191.70 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 191.21/191.70 ( class_Groups_Oab__semigroup__mult(T_c)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => ( ! [B_x] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.21/191.70 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
% 191.21/191.70 => 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) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_setprod__dvd__setprod__subset2,axiom,
% 191.21/191.70 ! [V_g_2,V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 191.21/191.70 ( class_Rings_Ocomm__semiring__1(T_c)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.21/191.70 => ( ! [B_x] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 191.21/191.70 => 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))) ) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Min__eqI,axiom,
% 191.21/191.70 ! [V_x_2,V_A_2,T_b] :
% 191.21/191.70 ( class_Orderings_Olinorder(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => ( ! [B_y] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y)) )
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.21/191.70 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Max__eqI,axiom,
% 191.21/191.70 ! [V_x_2,V_A_2,T_b] :
% 191.21/191.70 ( class_Orderings_Olinorder(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => ( ! [B_y] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_y),V_x_2)) )
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.21/191.70 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_wf__no__infinite__down__chainE,axiom,
% 191.21/191.70 ! [V_f_2,V_r_2,T_b] :
% 191.21/191.70 ( c_Wellfounded_Owf(T_b,V_r_2)
% 191.21/191.70 => ~ ! [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)) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_setsum__reindex__cong,axiom,
% 191.21/191.70 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 191.21/191.70 ( class_Groups_Ocomm__monoid__add(T_d)
% 191.21/191.70 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 191.21/191.70 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 191.21/191.70 => ( ! [B_a] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 191.21/191.70 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) )
% 191.21/191.70 => 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) ) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_less__eq,axiom,
% 191.21/191.70 ! [V_n_2,V_m_2] :
% 191.21/191.70 ( 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)))
% 191.21/191.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_wf__trancl,axiom,
% 191.21/191.70 ! [V_r_2,T_b] :
% 191.21/191.70 ( c_Wellfounded_Owf(T_b,V_r_2)
% 191.21/191.70 => c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_less__than__def,axiom,
% 191.21/191.70 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_acyclic__def,axiom,
% 191.21/191.70 ! [V_r_2,T_b] :
% 191.21/191.70 ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 191.21/191.70 <=> ! [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))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_trancl_Or__into__trancl,axiom,
% 191.21/191.70 ! [V_r_2,V_ba_2,V_a_2,T_b] :
% 191.21/191.70 ( 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_ba_2)),V_r_2))
% 191.21/191.70 => 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_ba_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_trancl__subset__Field2,axiom,
% 191.21/191.70 ! [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))))) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_r__into__trancl_H,axiom,
% 191.21/191.70 ! [V_r_2,V_p_2,T_b] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_trancl__empty,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_trancl__domain,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_trancl__range,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_finite__trancl,axiom,
% 191.21/191.70 ! [V_r_2,T_b] :
% 191.21/191.70 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 191.21/191.70 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_trancl__trans,axiom,
% 191.21/191.70 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] :
% 191.21/191.70 ( 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_ba_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
% 191.21/191.70 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] :
% 191.21/191.70 ( 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_ba_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_ca_2)),V_r_2))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_trancl__into__trancl2,axiom,
% 191.21/191.70 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] :
% 191.21/191.70 ( 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_ba_2)),V_r_2))
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_r__r__into__trancl,axiom,
% 191.21/191.70 ! [V_ca_2,V_R_2,V_ba_2,V_a_2,T_b] :
% 191.21/191.70 ( 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_ba_2)),V_R_2))
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_ca_2)),V_R_2))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_trancl__mono,axiom,
% 191.21/191.70 ! [V_s_2,V_r_2,V_p_2,T_b] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 191.21/191.70 => ( 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))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_s_2))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_trancl__unfold,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_trancl__subset__Sigma,axiom,
% 191.21/191.70 ! [V_A_2,V_r_2,T_b] :
% 191.21/191.70 ( 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))))
% 191.21/191.70 => 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)))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_trancl__Int__subset,axiom,
% 191.21/191.70 ! [V_s_2,V_r_2,T_b] :
% 191.21/191.70 ( 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))
% 191.21/191.70 => ( 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))
% 191.21/191.70 => 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)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_trancl__insert,axiom,
% 191.21/191.70 ! [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)))))) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_reflcl__set__eq,axiom,
% 191.21/191.70 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 191.21/191.70 ( 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))
% 191.21/191.70 <=> hBOOL(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)))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_r__into__rtrancl,axiom,
% 191.21/191.70 ! [V_r_2,V_p_2,T_b] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rtrancl_Ortrancl__refl,axiom,
% 191.21/191.70 ! [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))) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_IdI,axiom,
% 191.21/191.70 ! [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))) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_trancl__into__rtrancl,axiom,
% 191.21/191.70 ! [V_r_2,V_ba_2,V_a_2,T_b] :
% 191.21/191.70 ( 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_ba_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 191.21/191.70 => 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_ba_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_trancl__unfold__right,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_trancl__unfold__left,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_reflcl__trancl,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_trancl__reflcl,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_trancl__rtrancl__absorb,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rtrancl__trancl__absorb,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_refl__rtrancl,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rtrancl__idemp,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rtrancl__trans,axiom,
% 191.21/191.70 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] :
% 191.21/191.70 ( 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_ba_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
% 191.21/191.70 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] :
% 191.21/191.70 ( 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_ba_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_ca_2)),V_r_2))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_converse__rtrancl__into__rtrancl,axiom,
% 191.21/191.70 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] :
% 191.21/191.70 ( 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_ba_2)),V_r_2))
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rtrancl__r__diff__Id,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_in__rtrancl__UnI,axiom,
% 191.21/191.70 ! [V_S_2,V_R_2,V_x_2,T_b] :
% 191.21/191.70 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 191.21/191.70 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) )
% 191.21/191.70 => 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)))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Image__closed__trancl,axiom,
% 191.21/191.70 ! [V_X_2,V_r_2,T_b] :
% 191.21/191.70 ( 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))
% 191.21/191.70 => hAPP(c_Relation_OImage(T_b,T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_X_2) = V_X_2 ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rtrancl__Un__subset,axiom,
% 191.21/191.70 ! [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)))) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rtrancl__reflcl,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rtrancl__Un__rtrancl,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rtrancl__reflcl__absorb,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rtrancl__subset__rtrancl,axiom,
% 191.21/191.70 ! [V_s_2,V_r_2,T_b] :
% 191.21/191.70 ( 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)))
% 191.21/191.70 => 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))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rtrancl__subset,axiom,
% 191.21/191.70 ! [V_S_2,V_R_2,T_b] :
% 191.21/191.70 ( 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))
% 191.21/191.70 => ( 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)))
% 191.21/191.70 => c_Transitive__Closure_Ortrancl(T_b,V_S_2) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rtrancl__mono,axiom,
% 191.21/191.70 ! [V_s_2,V_r_2,T_b] :
% 191.21/191.70 ( 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))
% 191.21/191.70 => 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))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rtrancl__Int__subset,axiom,
% 191.21/191.70 ! [V_r_2,V_s_2,T_b] :
% 191.21/191.70 ( 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))
% 191.21/191.70 => ( 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))
% 191.21/191.70 => 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)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_r__comp__rtrancl__eq,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rtrancl__idemp__self__comp,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rtrancl__unfold,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rtrancl__empty,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Range__rtrancl,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Domain__rtrancl,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Id__O__R,axiom,
% 191.21/191.70 ! [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 ).
% 191.21/191.70
% 191.21/191.70 fof(fact_R__O__Id,axiom,
% 191.21/191.70 ! [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 ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Image__Id,axiom,
% 191.21/191.70 ! [V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId(T_b)),V_A_2) = V_A_2 ).
% 191.21/191.70
% 191.21/191.70 fof(fact_pair__in__Id__conv,axiom,
% 191.21/191.70 ! [V_ba_2,V_a_2,T_b] :
% 191.21/191.70 ( 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_ba_2)),c_Relation_OId(T_b)))
% 191.21/191.70 <=> V_a_2 = V_ba_2 ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rtrancl__trancl__trancl,axiom,
% 191.21/191.70 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
% 191.21/191.70 ( hBOOL(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)))
% 191.21/191.70 => ( 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)))
% 191.21/191.70 => hBOOL(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))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_trancl__rtrancl__trancl,axiom,
% 191.21/191.70 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] :
% 191.21/191.70 ( 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_ba_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rtrancl__into__trancl1,axiom,
% 191.21/191.70 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] :
% 191.21/191.70 ( 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_ba_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_ca_2)),V_r_2))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rtranclD,axiom,
% 191.21/191.70 ! [V_R_2,V_ba_2,V_a_2,T_b] :
% 191.21/191.70 ( 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_ba_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 191.21/191.70 => ( V_a_2 = V_ba_2
% 191.21/191.70 | ( V_a_2 != V_ba_2
% 191.21/191.70 & 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_ba_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rtrancl__into__trancl2,axiom,
% 191.21/191.70 ! [V_ca_2,V_r_2,V_ba_2,V_a_2,T_b] :
% 191.21/191.70 ( 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_ba_2)),V_r_2))
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rtrancl__eq__or__trancl,axiom,
% 191.21/191.70 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 191.21/191.70 ( hBOOL(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)))
% 191.21/191.70 <=> ( V_x_2 = V_y_2
% 191.21/191.70 | ( V_x_2 != V_y_2
% 191.21/191.70 & hBOOL(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))) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Domain__Id,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Range__Id,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_refl__Id,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_pair__leq__def,axiom,
% 191.21/191.70 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))) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Not__Domain__rtrancl,axiom,
% 191.21/191.70 ! [V_y_2,V_R_2,V_x_2,T_b] :
% 191.21/191.70 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_b),V_R_2)))
% 191.21/191.70 => ( hBOOL(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)))
% 191.21/191.70 <=> V_x_2 = V_y_2 ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_acc__downwards__aux,axiom,
% 191.21/191.70 ! [V_r_2,V_a_2,V_ba_2,T_b] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_acc__downwards,axiom,
% 191.21/191.70 ! [V_ba_2,V_r_2,V_a_2,T_b] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_ba_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_wf__insert,axiom,
% 191.21/191.70 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 191.21/191.70 ( 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))
% 191.21/191.70 <=> ( c_Wellfounded_Owf(T_b,V_r_2)
% 191.21/191.70 & ~ hBOOL(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))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_acyclic__insert,axiom,
% 191.21/191.70 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 191.21/191.70 ( 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))
% 191.21/191.70 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 191.21/191.70 & ~ hBOOL(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))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_refl__reflcl,axiom,
% 191.21/191.70 ! [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))) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Id__def,axiom,
% 191.21/191.70 ! [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))))) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_irrefl__diff__Id,axiom,
% 191.21/191.70 ! [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))) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_pred__nat__trancl__eq__le,axiom,
% 191.21/191.70 ! [V_n_2,V_m_2] :
% 191.21/191.70 ( 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)))
% 191.21/191.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_trancl__subset__Sigma__aux,axiom,
% 191.21/191.70 ! [V_A_2,V_r_2,V_ba_2,V_a_2,T_b] :
% 191.21/191.70 ( 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_ba_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 191.21/191.70 => ( 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))))
% 191.21/191.70 => ( V_a_2 = V_ba_2
% 191.21/191.70 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_irrefl__tranclI,axiom,
% 191.21/191.70 ! [V_x_2,V_r_2,T_b] :
% 191.21/191.70 ( 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))
% 191.21/191.70 => ~ hBOOL(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))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_sequence__trans,axiom,
% 191.21/191.70 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_b] :
% 191.21/191.70 ( ! [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)))
% 191.21/191.70 => 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))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rtrancl__converse,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_converse__Id,axiom,
% 191.21/191.70 ! [T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId(T_b)) = c_Relation_OId(T_b) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Range__def,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Domain__converse,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Range__converse,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_equiv__comp__eq,axiom,
% 191.21/191.70 ! [V_r_2,V_A_2,T_b] :
% 191.21/191.70 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 191.21/191.70 => 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 ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_converse__UNION,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_converseD,axiom,
% 191.21/191.70 ! [V_r_2,V_ba_2,V_a_2,T_c,T_b] :
% 191.21/191.70 ( 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_ba_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_ba_2),V_a_2)),V_r_2)) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_converseI,axiom,
% 191.21/191.70 ! [V_r_2,V_ba_2,V_a_2,T_c,T_b] :
% 191.21/191.70 ( 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_ba_2)),V_r_2))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_ba_2),V_a_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_converse__iff,axiom,
% 191.21/191.70 ! [V_r_2,V_ba_2,V_a_2,T_c,T_b] :
% 191.21/191.70 ( 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_ba_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 191.21/191.70 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_ba_2),V_a_2)),V_r_2)) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_refl__on__converse,axiom,
% 191.21/191.70 ! [V_r_2,V_A_2,T_b] :
% 191.21/191.70 ( c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 191.21/191.70 <=> c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_converse__Int,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_converse__converse,axiom,
% 191.21/191.70 ! [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 ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Field__converse,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_converse__Id__on,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_converse__inv__image,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_finite__converse,axiom,
% 191.21/191.70 ! [V_r_2,T_c,T_b] :
% 191.21/191.70 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 191.21/191.70 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2)) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_converse__Un,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_converse__rel__comp,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_acyclic__converse,axiom,
% 191.21/191.70 ! [V_r_2,T_b] :
% 191.21/191.70 ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 191.21/191.70 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_wf__converse__trancl,axiom,
% 191.21/191.70 ! [V_r_2,T_b] :
% 191.21/191.70 ( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 191.21/191.70 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_trancl__converse,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rtrancl__converseI,axiom,
% 191.21/191.70 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 191.21/191.70 ( 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)))
% 191.21/191.70 => hBOOL(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)))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rtrancl__converseD,axiom,
% 191.21/191.70 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 191.21/191.70 ( hBOOL(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))))
% 191.21/191.70 => 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))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_trancl__converseI,axiom,
% 191.21/191.70 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 191.21/191.70 ( hBOOL(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))))
% 191.21/191.70 => hBOOL(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)))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_trancl__converseD,axiom,
% 191.21/191.70 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 191.21/191.70 ( hBOOL(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))))
% 191.21/191.70 => hBOOL(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)))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Image__subset__eq,axiom,
% 191.21/191.70 ! [V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 191.21/191.70 ( 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))
% 191.21/191.70 <=> 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))))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_refl__on__comp__subset,axiom,
% 191.21/191.70 ! [V_r_2,V_A_2,T_b] :
% 191.21/191.70 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 191.21/191.70 => 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))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_comp__equivI,axiom,
% 191.21/191.70 ! [V_A_2,V_r_2,T_b] :
% 191.21/191.70 ( 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
% 191.21/191.70 => ( hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) = V_A_2
% 191.21/191.70 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_finite__acyclic__wf__converse,axiom,
% 191.21/191.70 ! [V_r_2,T_b] :
% 191.21/191.70 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 191.21/191.70 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 191.21/191.70 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_converse__def,axiom,
% 191.21/191.70 ! [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))) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_total__on__diff__Id,axiom,
% 191.21/191.70 ! [V_r_2,V_A_2,T_b] :
% 191.21/191.70 ( 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)))
% 191.21/191.70 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rtrancl__imp__UN__rel__pow,axiom,
% 191.21/191.70 ! [V_R_2,V_p_2,T_b] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 191.21/191.70 => 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)))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_relpow_Osimps_I1_J,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rtrancl__power,axiom,
% 191.21/191.70 ! [V_R_2,V_p_2,T_b] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 191.21/191.70 <=> ? [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))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rel__pow__imp__rtrancl,axiom,
% 191.21/191.70 ! [V_R_2,V_n_2,V_p_2,T_b] :
% 191.21/191.70 ( 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)))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rel__pow__1,axiom,
% 191.21/191.70 ! [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 ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rel__pow__commute,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_relpow_Osimps_I2_J,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rel__pow__add,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_funpow__mult,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_funpow__swap1,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_wf__exp,axiom,
% 191.21/191.70 ! [V_R_2,V_n_2,T_b] :
% 191.21/191.70 ( 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))
% 191.21/191.70 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_comp__funpow,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_total__on__empty,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_total__on__converse,axiom,
% 191.21/191.70 ! [V_r_2,V_A_2,T_b] :
% 191.21/191.70 ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 191.21/191.70 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rel__pow__0__E,axiom,
% 191.21/191.70 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 191.21/191.70 ( hBOOL(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)))
% 191.21/191.70 => V_x_2 = V_y_2 ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rel__pow__0__I,axiom,
% 191.21/191.70 ! [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))) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rel__pow__Suc__I2,axiom,
% 191.21/191.70 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_b] :
% 191.21/191.70 ( hBOOL(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))
% 191.21/191.70 => ( 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)))
% 191.21/191.70 => hBOOL(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))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rel__pow__Suc__I,axiom,
% 191.21/191.70 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_b] :
% 191.21/191.70 ( hBOOL(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)))
% 191.21/191.70 => ( 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))
% 191.21/191.70 => hBOOL(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))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_funpow_Osimps_I2_J,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_funpow__add,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_funpow_Osimps_I1_J,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_trancl__power,axiom,
% 191.21/191.70 ! [V_R_2,V_p_2,T_b] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
% 191.21/191.70 <=> ? [B_n] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 191.21/191.70 & 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))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_total__on__def,axiom,
% 191.21/191.70 ! [V_r_2,V_A_2,T_b] :
% 191.21/191.70 ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2)
% 191.21/191.70 <=> ! [B_x] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.21/191.70 => ! [B_xa] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 191.21/191.70 => ( B_x != B_xa
% 191.21/191.70 => ( 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))
% 191.21/191.70 | 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)) ) ) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rtrancl__is__UN__rel__pow,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_funpow__code__def,axiom,
% 191.21/191.70 ! [T_b] : c_Nat_Ofunpow(T_b) = c_Nat_Ocompow(T_b,T_b) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rel__pow__E2,axiom,
% 191.21/191.70 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 191.21/191.70 ( hBOOL(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)))
% 191.21/191.70 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 191.21/191.70 => V_x_2 != V_z_2 )
% 191.21/191.70 => ~ ! [B_y,B_m] :
% 191.21/191.70 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 191.21/191.70 => ( 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))
% 191.21/191.70 => ~ 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))) ) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rel__pow__E,axiom,
% 191.21/191.70 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 191.21/191.70 ( hBOOL(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)))
% 191.21/191.70 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 191.21/191.70 => V_x_2 != V_z_2 )
% 191.21/191.70 => ~ ! [B_y,B_m] :
% 191.21/191.70 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 191.21/191.70 => ( 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)))
% 191.21/191.70 => ~ 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)) ) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_acyclicI,axiom,
% 191.21/191.70 ! [V_r_2,T_b] :
% 191.21/191.70 ( ! [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)))
% 191.21/191.70 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Image__Int__eq,axiom,
% 191.21/191.70 ! [V_B_2,V_A_2,V_R_2,T_c,T_b] :
% 191.21/191.70 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_R_2))
% 191.21/191.70 => 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)) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rtrancl__Un__separator__converseE,axiom,
% 191.21/191.70 ! [V_Q_2,V_Pa_2,V_ba_2,V_a_2,T_b] :
% 191.21/191.70 ( 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_ba_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2),V_Q_2))))
% 191.21/191.70 => ( ! [B_x] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_ba_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2)))
% 191.21/191.70 => ! [B_y] :
% 191.21/191.70 ( 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))
% 191.21/191.70 => B_y = B_x ) )
% 191.21/191.70 => 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_ba_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_single__valued__Id__on,axiom,
% 191.21/191.70 ! [V_A_2,T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_single__valued__subset,axiom,
% 191.21/191.70 ! [V_s_2,V_r_2,T_c,T_b] :
% 191.21/191.70 ( 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))
% 191.21/191.70 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2)
% 191.21/191.70 => c_Relation_Osingle__valued(T_b,T_c,V_r_2) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_single__valued__rel__comp,axiom,
% 191.21/191.70 ! [V_s_2,T_d,V_r_2,T_c,T_b] :
% 191.21/191.70 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 191.21/191.70 => ( c_Relation_Osingle__valued(T_c,T_d,V_s_2)
% 191.21/191.70 => 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)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_single__valued__Id,axiom,
% 191.21/191.70 ! [T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId(T_b)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_single__valued__rel__pow,axiom,
% 191.21/191.70 ! [V_n_2,V_R_2,T_b] :
% 191.21/191.70 ( c_Relation_Osingle__valued(T_b,T_b,V_R_2)
% 191.21/191.70 => 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)) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_single__valuedD,axiom,
% 191.21/191.70 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_c,T_b] :
% 191.21/191.70 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 191.21/191.70 => ( 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))
% 191.21/191.70 => ( 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))
% 191.21/191.70 => V_y_2 = V_z_2 ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_single__valued__def,axiom,
% 191.21/191.70 ! [V_r_2,T_c,T_b] :
% 191.21/191.70 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 191.21/191.70 <=> ! [B_x,B_y] :
% 191.21/191.70 ( 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))
% 191.21/191.70 => ! [B_z] :
% 191.21/191.70 ( 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))
% 191.21/191.70 => B_y = B_z ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_single__valued__confluent,axiom,
% 191.21/191.70 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
% 191.21/191.70 ( c_Relation_Osingle__valued(T_b,T_b,V_r_2)
% 191.21/191.70 => ( hBOOL(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)))
% 191.21/191.70 => ( hBOOL(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)))
% 191.21/191.70 => ( 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)))
% 191.21/191.70 | 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))) ) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rtrancl__Un__separatorE,axiom,
% 191.21/191.70 ! [V_Q_2,V_Pa_2,V_ba_2,V_a_2,T_b] :
% 191.21/191.70 ( 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_ba_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2),V_Q_2))))
% 191.21/191.70 => ( ! [B_x] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),B_x)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2)))
% 191.21/191.70 => ! [B_y] :
% 191.21/191.70 ( 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))
% 191.21/191.70 => B_x = B_y ) )
% 191.21/191.70 => 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_ba_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rel__pow__Suc__E,axiom,
% 191.21/191.70 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 191.21/191.70 ( hBOOL(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)))
% 191.21/191.70 => ~ ! [B_y] :
% 191.21/191.70 ( 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)))
% 191.21/191.70 => ~ 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)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rel__pow__Suc__D2,axiom,
% 191.21/191.70 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 191.21/191.70 ( hBOOL(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)))
% 191.21/191.70 => ? [B_y] :
% 191.21/191.70 ( 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))
% 191.21/191.70 & 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))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_rel__pow__Suc__E2,axiom,
% 191.21/191.70 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 191.21/191.70 ( hBOOL(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)))
% 191.21/191.70 => ~ ! [B_y] :
% 191.21/191.70 ( 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))
% 191.21/191.70 => ~ 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))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_tranclD2,axiom,
% 191.21/191.70 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 191.21/191.70 ( hBOOL(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)))
% 191.21/191.70 => ? [B_z] :
% 191.21/191.70 ( 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)))
% 191.21/191.70 & 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)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_tranclD,axiom,
% 191.21/191.70 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 191.21/191.70 ( hBOOL(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)))
% 191.21/191.70 => ? [B_z] :
% 191.21/191.70 ( 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))
% 191.21/191.70 & 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))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_IdE,axiom,
% 191.21/191.70 ! [V_p_2,T_b] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Relation_OId(T_b)))
% 191.21/191.70 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom,
% 191.21/191.70 ! [V_x_2,V_A_2,T_b] :
% 191.21/191.70 ( class_Orderings_Olinorder(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.21/191.70 => 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) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_folding_Oeq__fold,axiom,
% 191.21/191.70 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 191.21/191.70 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => 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) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_fold__image__def,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_fold__empty,axiom,
% 191.21/191.70 ! [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 ).
% 191.21/191.70
% 191.21/191.70 fof(fact_fold__def,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_union__fold__insert,axiom,
% 191.21/191.70 ! [V_B_2,V_A_2,T_b] :
% 191.21/191.70 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => 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) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_fold__sup__insert,axiom,
% 191.21/191.70 ! [V_a_2,V_ba_2,V_A_2,T_b] :
% 191.21/191.70 ( class_Lattices_Osemilattice__sup(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_ba_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_ba_2),V_A_2)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_fold__inf__insert,axiom,
% 191.21/191.70 ! [V_a_2,V_ba_2,V_A_2,T_b] :
% 191.21/191.70 ( class_Lattices_Osemilattice__inf(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_ba_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_ba_2),V_A_2)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_min__max_Ofold__inf__insert,axiom,
% 191.21/191.70 ! [V_a_2,V_ba_2,V_A_2,T_b] :
% 191.21/191.70 ( class_Orderings_Olinorder(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_ba_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_ba_2),V_A_2)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_min__max_Ofold__sup__insert,axiom,
% 191.21/191.70 ! [V_a_2,V_ba_2,V_A_2,T_b] :
% 191.21/191.70 ( class_Orderings_Olinorder(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_ba_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_ba_2),V_A_2)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom,
% 191.21/191.70 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 191.21/191.70 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => 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)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom,
% 191.21/191.70 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 191.21/191.70 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => 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) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_sup__SUPR__fold__sup,axiom,
% 191.21/191.70 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 191.21/191.70 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => 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) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom,
% 191.21/191.70 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_b] :
% 191.21/191.70 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => 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) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_sup__le__fold__sup,axiom,
% 191.21/191.70 ! [V_ba_2,V_a_2,V_A_2,T_b] :
% 191.21/191.70 ( class_Lattices_Osemilattice__sup(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.21/191.70 => 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_ba_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_ba_2),V_A_2))) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_fold__inf__le__inf,axiom,
% 191.21/191.70 ! [V_ba_2,V_a_2,V_A_2,T_b] :
% 191.21/191.70 ( class_Lattices_Osemilattice__inf(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.21/191.70 => 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_ba_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_ba_2))) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_min__max_Ofold__inf__le__inf,axiom,
% 191.21/191.70 ! [V_ba_2,V_a_2,V_A_2,T_b] :
% 191.21/191.70 ( class_Orderings_Olinorder(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.21/191.70 => 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_ba_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),V_ba_2))) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_min__max_Osup__le__fold__sup,axiom,
% 191.21/191.70 ! [V_ba_2,V_a_2,V_A_2,T_b] :
% 191.21/191.70 ( class_Orderings_Olinorder(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ba_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_ba_2),V_A_2))) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_fold1__eq__fold__idem,axiom,
% 191.21/191.70 ! [V_a_2,V_A_2,T_b] :
% 191.21/191.70 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => 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) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom,
% 191.21/191.70 ! [V_a_2,V_A_2,T_b] :
% 191.21/191.70 ( class_Lattices_Olattice(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => 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) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom,
% 191.21/191.70 ! [V_a_2,V_A_2,T_b] :
% 191.21/191.70 ( class_Lattices_Olattice(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => 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) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Min_Oeq__fold__idem_H,axiom,
% 191.21/191.70 ! [V_a_2,V_A_2,T_b] :
% 191.21/191.70 ( class_Orderings_Olinorder(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => 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) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Max_Oeq__fold__idem_H,axiom,
% 191.21/191.70 ! [V_a_2,V_A_2,T_b] :
% 191.21/191.70 ( class_Orderings_Olinorder(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => 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) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom,
% 191.21/191.70 ! [V_a_2,V_A_2,T_b] :
% 191.21/191.70 ( class_Orderings_Olinorder(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => 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) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom,
% 191.21/191.70 ! [V_a_2,V_A_2,T_b] :
% 191.21/191.70 ( class_Orderings_Olinorder(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => 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) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_minus__fold__remove,axiom,
% 191.21/191.70 ! [V_B_2,V_A_2,T_b] :
% 191.21/191.70 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => 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) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_folding__one_Oeq__fold_H,axiom,
% 191.21/191.70 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 191.21/191.70 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.21/191.70 => 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) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_SUPR__fold__sup,axiom,
% 191.21/191.70 ! [V_f_2,V_A_2,T_b,T_c] :
% 191.21/191.70 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => 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) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_fold1__eq__fold,axiom,
% 191.21/191.70 ! [V_a_2,V_A_2,T_b] :
% 191.21/191.70 ( class_Groups_Oab__semigroup__mult(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.21/191.70 => 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) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Sup__fin_Oeq__fold_H,axiom,
% 191.21/191.70 ! [V_x_2,V_A_2,T_b] :
% 191.21/191.70 ( class_Lattices_Olattice(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.21/191.70 => 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) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Inf__fin_Oeq__fold_H,axiom,
% 191.21/191.70 ! [V_x_2,V_A_2,T_b] :
% 191.21/191.70 ( class_Lattices_Olattice(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.21/191.70 => 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) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Min_Oeq__fold_H,axiom,
% 191.21/191.70 ! [V_x_2,V_A_2,T_b] :
% 191.21/191.70 ( class_Orderings_Olinorder(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.21/191.70 => 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) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Max_Oeq__fold_H,axiom,
% 191.21/191.70 ! [V_x_2,V_A_2,T_b] :
% 191.21/191.70 ( class_Orderings_Olinorder(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.21/191.70 => 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) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom,
% 191.21/191.70 ! [V_x_2,V_A_2,T_b] :
% 191.21/191.70 ( class_Orderings_Olinorder(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.21/191.70 => 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) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_fun__left__comm_Ofold__rec,axiom,
% 191.21/191.70 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 191.21/191.70 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.21/191.70 => 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)))))) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_fun__left__comm_Ofold__insert__remove,axiom,
% 191.21/191.70 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 191.21/191.70 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => 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)))))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom,
% 191.21/191.70 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 191.21/191.70 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 191.21/191.70 => 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)) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_fun__left__comm_Ofun__left__comm,axiom,
% 191.21/191.70 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 191.21/191.70 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 191.21/191.70 => 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)) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_fun__left__comm,axiom,
% 191.21/191.70 ! [T_b] :
% 191.21/191.70 ( class_Groups_Oab__semigroup__mult(T_b)
% 191.21/191.70 => c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_fun__left__comm_Ofold__graph__determ,axiom,
% 191.21/191.70 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 191.21/191.70 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 191.21/191.70 => V_y_2 = V_x_2 ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_fun__left__comm_Ofun__comp__comm,axiom,
% 191.21/191.70 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 191.21/191.70 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 191.21/191.70 => 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)) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_fun__left__comm_Ofold__fun__comm,axiom,
% 191.21/191.70 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 191.21/191.70 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => 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) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_fun__left__comm_Ofold__equality,axiom,
% 191.21/191.70 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 191.21/191.70 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 191.21/191.70 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_fun__left__comm_Ofold__graph__fold,axiom,
% 191.21/191.70 ! [V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 191.21/191.70 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => 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))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_fun__left__comm_Ofold__insert,axiom,
% 191.21/191.70 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 191.21/191.70 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.21/191.70 => 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)) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_fun__left__comm_Ofold__insert2,axiom,
% 191.21/191.70 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 191.21/191.70 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.21/191.70 => 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) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom,
% 191.21/191.70 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 191.21/191.70 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.21/191.70 => ? [B_y_H] :
% 191.21/191.70 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H)
% 191.21/191.70 & 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)) ) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INFI__fold__inf,axiom,
% 191.21/191.70 ! [V_f_2,V_A_2,T_b,T_c] :
% 191.21/191.70 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => 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) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INT__E,axiom,
% 191.21/191.70 ! [V_a_2,V_B_2,V_A_2,T_c,V_ba_2,T_b] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_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)))
% 191.21/191.70 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(V_B_2,V_a_2)))
% 191.21/191.70 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INT__D,axiom,
% 191.21/191.70 ! [V_a_2,V_B_2,V_A_2,T_c,V_ba_2,T_b] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_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)))
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INF1__E,axiom,
% 191.21/191.70 ! [V_a_2,V_ba_2,V_B_2,V_A_2,T_c,T_b] :
% 191.21/191.70 ( 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_ba_2))
% 191.21/191.70 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_ba_2))
% 191.21/191.70 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INF1__D,axiom,
% 191.21/191.70 ! [V_a_2,V_ba_2,V_B_2,V_A_2,T_c,T_b] :
% 191.21/191.70 ( 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_ba_2))
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.21/191.70 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_ba_2)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INF2__D,axiom,
% 191.21/191.70 ! [V_a_2,V_ca_2,V_ba_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 191.21/191.70 ( 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_ba_2),V_ca_2))
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.21/191.70 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_ba_2),V_ca_2)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INF2__E,axiom,
% 191.21/191.70 ! [V_a_2,V_ca_2,V_ba_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 191.21/191.70 ( 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_ba_2),V_ca_2))
% 191.21/191.70 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_ba_2),V_ca_2))
% 191.21/191.70 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_finite__INT,axiom,
% 191.21/191.70 ! [V_A_2,T_c,V_I_2,T_b] :
% 191.21/191.70 ( ? [B_x] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 191.21/191.70 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) )
% 191.21/191.70 => 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))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_UN__simps_I7_J,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_UN__extend__simps_I7_J,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INT__extend__simps_I9_J,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INT__simps_I9_J,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Compl__INT,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Compl__UN,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Collect__ball__eq,axiom,
% 191.21/191.70 ! [V_Pa_2,V_A_2,T_c,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),V_Pa_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_Pa_2))) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INF__less__iff,axiom,
% 191.21/191.70 ! [V_a_2,V_f_2,V_A_2,T_c,T_b] :
% 191.21/191.70 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 191.21/191.70 & class_Orderings_Olinorder(T_b) )
% 191.21/191.70 => ( 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))
% 191.21/191.70 <=> ? [B_x] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 191.21/191.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INT__Int__distrib,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INTER__UNIV__conv_I2_J,axiom,
% 191.21/191.70 ! [V_B_2,V_A_2,T_b,T_c] :
% 191.21/191.70 ( 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))
% 191.21/191.70 <=> ! [B_x] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 191.21/191.70 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INTER__UNIV__conv_I1_J,axiom,
% 191.21/191.70 ! [V_B_2,V_A_2,T_c,T_b] :
% 191.21/191.70 ( 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)
% 191.21/191.70 <=> ! [B_x] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 191.21/191.70 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Pow__INT__eq,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INFI__apply,axiom,
% 191.21/191.70 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 191.21/191.70 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 191.21/191.70 => 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)) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INF__commute,axiom,
% 191.21/191.70 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 191.21/191.70 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 191.21/191.70 => 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))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INFI__bool__eq,axiom,
% 191.21/191.70 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_HOL_Obool) = c_Set_OBall(T_b) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INT__iff,axiom,
% 191.21/191.70 ! [V_B_2,V_A_2,T_c,V_ba_2,T_b] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ba_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)))
% 191.21/191.70 <=> ! [B_x] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_member(T_b),V_ba_2),hAPP(V_B_2,B_x))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INF__INT__eq2,axiom,
% 191.21/191.70 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 191.21/191.70 ( 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))
% 191.21/191.70 <=> 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))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INT__absorb,axiom,
% 191.21/191.70 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 191.21/191.70 => 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) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INF__INT__eq,axiom,
% 191.21/191.70 ! [V_x_2,V_r_2,T_c,T_b] :
% 191.21/191.70 ( 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))
% 191.21/191.70 <=> 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))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_vimage__INT,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INT__extend__simps_I10_J,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INT__simps_I10_J,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Image__INT__subset,axiom,
% 191.21/191.70 ! [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)))) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INT__lower,axiom,
% 191.21/191.70 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 191.21/191.70 => 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))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_le__INF__iff,axiom,
% 191.21/191.70 ! [V_M_2,V_A_2,T_c,V_u_2,T_b] :
% 191.21/191.70 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 191.21/191.70 => ( 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)))
% 191.21/191.70 <=> ! [B_x] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INT__simps_I5_J,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INT__extend__simps_I5_J,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INT__subset__iff,axiom,
% 191.21/191.70 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] :
% 191.21/191.70 ( 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)))
% 191.21/191.70 <=> ! [B_x] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 191.21/191.70 => 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))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INT__insert__distrib,axiom,
% 191.21/191.70 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 191.21/191.70 => 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)) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INT__insert,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INF__const,axiom,
% 191.21/191.70 ! [V_M_2,T_b,V_A_2,T_c] :
% 191.21/191.70 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 191.21/191.70 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.21/191.70 => 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 ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INT__extend__simps_I2_J,axiom,
% 191.21/191.70 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 191.21/191.70 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.21/191.70 => 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 )
% 191.21/191.70 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.21/191.70 => 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)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INT__extend__simps_I1_J,axiom,
% 191.21/191.70 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 191.21/191.70 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.21/191.70 => 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 )
% 191.21/191.70 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.21/191.70 => 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)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INT__constant,axiom,
% 191.21/191.70 ! [V_ca_2,T_c,T_b,V_A_2] :
% 191.21/191.70 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.21/191.70 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_ca_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 191.21/191.70 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.21/191.70 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_ca_2)) = V_ca_2 ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INT__empty,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Un__INT__distrib2,axiom,
% 191.21/191.70 ! [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))) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INT__extend__simps_I6_J,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Un__INT__distrib,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INT__extend__simps_I7_J,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INT__simps_I6_J,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INT__simps_I7_J,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INT__Un,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_converse__INTER,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INF__subset,axiom,
% 191.21/191.70 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 191.21/191.70 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.21/191.70 => 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))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INTER__def,axiom,
% 191.21/191.70 ! [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)))) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INT__simps_I2_J,axiom,
% 191.21/191.70 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 191.21/191.70 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.21/191.70 => 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)) )
% 191.21/191.70 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.21/191.70 => 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)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INT__simps_I1_J,axiom,
% 191.21/191.70 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 191.21/191.70 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.21/191.70 => 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)) )
% 191.21/191.70 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.21/191.70 => 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) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INT__extend__simps_I3_J,axiom,
% 191.21/191.70 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 191.21/191.70 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.21/191.70 => 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) )
% 191.21/191.70 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.21/191.70 => 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)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INT__simps_I3_J,axiom,
% 191.21/191.70 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 191.21/191.70 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.21/191.70 => 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)) )
% 191.21/191.70 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.21/191.70 => 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) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INT__extend__simps_I4_J,axiom,
% 191.21/191.70 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 191.21/191.70 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.21/191.70 => 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 )
% 191.21/191.70 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.21/191.70 => 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)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INF__leI,axiom,
% 191.21/191.70 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 191.21/191.70 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 191.21/191.70 => 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))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INT__greaterThan__UNIV,axiom,
% 191.21/191.70 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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INT__simps_I4_J,axiom,
% 191.21/191.70 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 191.21/191.70 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.21/191.70 => 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)) )
% 191.21/191.70 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.21/191.70 => 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)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Image__INT__eq,axiom,
% 191.21/191.70 ! [V_B_2,T_d,V_A_2,V_r_2,T_c,T_b] :
% 191.21/191.70 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))
% 191.21/191.70 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
% 191.21/191.70 => 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)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_inf__INFI__fold__inf,axiom,
% 191.21/191.70 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 191.21/191.70 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => 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) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Inf__fold__inf,axiom,
% 191.21/191.70 ! [V_A_2,T_b] :
% 191.21/191.70 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => 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) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Sup__fold__sup,axiom,
% 191.21/191.70 ! [V_A_2,T_b] :
% 191.21/191.70 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => 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) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_finite__Inter,axiom,
% 191.21/191.70 ! [V_M_2,T_b] :
% 191.21/191.70 ( ? [B_x] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2))
% 191.21/191.70 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) )
% 191.21/191.70 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_UnionI,axiom,
% 191.21/191.70 ! [V_A_2,V_C_2,V_X_2,T_b] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
% 191.21/191.70 => 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))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_InterD,axiom,
% 191.21/191.70 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 191.21/191.70 ( 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)))
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_InterE,axiom,
% 191.21/191.70 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 191.21/191.70 ( 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)))
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INT__simps_I8_J,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INT__extend__simps_I8_J,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INF2__iff,axiom,
% 191.21/191.70 ! [V_ca_2,V_ba_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 191.21/191.70 ( 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_ba_2),V_ca_2))
% 191.21/191.70 <=> ! [B_x] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.21/191.70 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_ba_2),V_ca_2)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INF1__iff,axiom,
% 191.21/191.70 ! [V_ba_2,V_B_2,V_A_2,T_c,T_b] :
% 191.21/191.70 ( 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_ba_2))
% 191.21/191.70 <=> ! [B_x] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.21/191.70 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_ba_2)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Inter__image__eq,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_INTER__eq__Inter__image,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Un__Inter,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Inter__anti__mono,axiom,
% 191.21/191.70 ! [V_A_2,V_B_2,T_b] :
% 191.21/191.70 ( 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))
% 191.21/191.70 => 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))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Inter__empty,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Union__insert,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_subset__Pow__Union,axiom,
% 191.21/191.70 ! [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)))) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Union__disjoint,axiom,
% 191.21/191.70 ! [V_A_2,V_C_2,T_b] :
% 191.21/191.70 ( 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))
% 191.21/191.70 <=> ! [B_x] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2))
% 191.21/191.70 => 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)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Union__empty,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Sup__le__iff,axiom,
% 191.21/191.70 ! [V_ba_2,V_A_2,T_b] :
% 191.21/191.70 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)),V_ba_2))
% 191.21/191.70 <=> ! [B_x] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_ba_2)) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_le__Inf__iff,axiom,
% 191.21/191.70 ! [V_A_2,V_ba_2,T_b] :
% 191.21/191.70 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)))
% 191.21/191.70 <=> ! [B_x] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),B_x)) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Union__upper,axiom,
% 191.21/191.70 ! [V_A_2,V_B_2,T_b] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 191.21/191.70 => 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))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Inter__lower,axiom,
% 191.21/191.70 ! [V_A_2,V_B_2,T_b] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 191.21/191.70 => 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)) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Union__mono,axiom,
% 191.21/191.70 ! [V_B_2,V_A_2,T_b] :
% 191.21/191.70 ( 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))
% 191.21/191.70 => 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))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Field__Union,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Inf__less__iff,axiom,
% 191.21/191.70 ! [V_a_2,V_S_2,T_b] :
% 191.21/191.70 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 191.21/191.70 & class_Orderings_Olinorder(T_b) )
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2))
% 191.21/191.70 <=> ? [B_x] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 191.21/191.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2)) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_less__Sup__iff,axiom,
% 191.21/191.70 ! [V_S_2,V_a_2,T_b] :
% 191.21/191.70 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 191.21/191.70 & class_Orderings_Olinorder(T_b) )
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2)))
% 191.21/191.70 <=> ? [B_x] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 191.21/191.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x)) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Union__Pow__eq,axiom,
% 191.21/191.70 ! [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 ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Union__quotient,axiom,
% 191.21/191.70 ! [V_r_2,V_A_2,T_b] :
% 191.21/191.70 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 191.21/191.70 => 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 ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Inf__Sup,axiom,
% 191.21/191.70 ! [V_A_2,T_b] :
% 191.21/191.70 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 191.21/191.70 => 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))))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Sup__Inf,axiom,
% 191.21/191.70 ! [V_A_2,T_b] :
% 191.21/191.70 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 191.21/191.70 => 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)))))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_finite__UnionD,axiom,
% 191.21/191.70 ! [V_A_2,T_b] :
% 191.21/191.70 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))
% 191.21/191.70 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_image__Union,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Sigma__Union,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_vimage__Union,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Int__Union,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Int__Union2,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_UN__extend__simps_I8_J,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_UN__simps_I8_J,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Range__Union,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Domain__Union,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Inter__eq,axiom,
% 191.21/191.70 ! [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)))) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Inter__insert,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Union__Un__distrib,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Union__UNIV,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_UNION__eq__Union__image,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Union__image__eq,axiom,
% 191.21/191.70 ! [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) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Sup__upper,axiom,
% 191.21/191.70 ! [V_A_2,V_x_2,T_b] :
% 191.21/191.70 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.21/191.70 => 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))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Inter__UNIV,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Inf__lower,axiom,
% 191.21/191.70 ! [V_A_2,V_x_2,T_b] :
% 191.21/191.70 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.21/191.70 => 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)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Inter__Un__distrib,axiom,
% 191.21/191.70 ! [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)) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Sup__empty,axiom,
% 191.21/191.70 ! [T_b] :
% 191.21/191.70 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 191.21/191.70 => 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) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Sup__singleton,axiom,
% 191.21/191.70 ! [V_a_2,T_b] :
% 191.21/191.70 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 191.21/191.70 => 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 ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Sup__insert,axiom,
% 191.21/191.70 ! [V_A_2,V_a_2,T_b] :
% 191.21/191.70 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 191.21/191.70 => 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)) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Int__Inter__image,axiom,
% 191.21/191.70 ! [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))) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Inf__singleton,axiom,
% 191.21/191.70 ! [V_a_2,T_b] :
% 191.21/191.70 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 191.21/191.70 => 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 ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Sup__UNIV,axiom,
% 191.21/191.70 ! [T_b] :
% 191.21/191.70 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 191.21/191.70 => 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) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Inf__empty,axiom,
% 191.21/191.70 ! [T_b] :
% 191.21/191.70 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 191.21/191.70 => 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) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Inf__UNIV,axiom,
% 191.21/191.70 ! [T_b] :
% 191.21/191.70 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 191.21/191.70 => 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) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Inf__insert,axiom,
% 191.21/191.70 ! [V_A_2,V_a_2,T_b] :
% 191.21/191.70 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 191.21/191.70 => 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)) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Un__eq__Union,axiom,
% 191.21/191.70 ! [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))))) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Un__Union__image,axiom,
% 191.21/191.70 ! [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))) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Union__Int__subset,axiom,
% 191.21/191.70 ! [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)))) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Int__eq__Inter,axiom,
% 191.21/191.70 ! [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))))) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Inter__Un__subset,axiom,
% 191.21/191.70 ! [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)))) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Sup__binary,axiom,
% 191.21/191.70 ! [V_ba_2,V_a_2,T_b] :
% 191.21/191.70 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 191.21/191.70 => 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_ba_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_ba_2) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Inf__binary,axiom,
% 191.21/191.70 ! [V_ba_2,V_a_2,T_b] :
% 191.21/191.70 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 191.21/191.70 => 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_ba_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_ba_2) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_sup__Sup__fold__sup,axiom,
% 191.21/191.70 ! [V_B_2,V_A_2,T_b] :
% 191.21/191.70 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => 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) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Sup__fin__Sup,axiom,
% 191.21/191.70 ! [V_A_2,T_b] :
% 191.21/191.70 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.21/191.70 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_inf__Inf__fold__inf,axiom,
% 191.21/191.70 ! [V_B_2,V_A_2,T_b] :
% 191.21/191.70 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => 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) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Inf__fin__Inf,axiom,
% 191.21/191.70 ! [V_A_2,T_b] :
% 191.21/191.70 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.21/191.70 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_image__INT,axiom,
% 191.21/191.70 ! [V_j_2,V_B_2,V_A_2,T_d,V_C_2,V_f_2,T_c,T_b] :
% 191.21/191.70 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 191.21/191.70 => ( ! [B_x] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2))
% 191.21/191.70 => 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)) )
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_j_2),V_A_2))
% 191.21/191.70 => 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)) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_card__partition,axiom,
% 191.21/191.70 ! [V_k_2,V_C_2,T_b] :
% 191.21/191.70 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_C_2))
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
% 191.21/191.70 => ( ! [B_c] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c),V_C_2))
% 191.21/191.70 => hAPP(c_Finite__Set_Ocard(T_b),B_c) = V_k_2 )
% 191.21/191.70 => ( ! [B_c1] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c1),V_C_2))
% 191.21/191.70 => ! [B_c2] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c2),V_C_2))
% 191.21/191.70 => ( B_c1 != B_c2
% 191.21/191.70 => 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)) ) ) )
% 191.21/191.70 => 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)) ) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Inter__def,axiom,
% 191.21/191.70 ! [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))) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Union__def,axiom,
% 191.21/191.70 ! [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))) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_finite__Union,axiom,
% 191.21/191.70 ! [V_A_2,T_b] :
% 191.21/191.70 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2))
% 191.21/191.70 => ( ! [B_M] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2))
% 191.21/191.70 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M)) )
% 191.21/191.70 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_insert__partition,axiom,
% 191.21/191.70 ! [V_F_2,V_x_2,T_b] :
% 191.21/191.70 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))
% 191.21/191.70 => ( ! [B_x] :
% 191.21/191.70 ( 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)))
% 191.21/191.70 => ! [B_xa] :
% 191.21/191.70 ( 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)))
% 191.21/191.70 => ( B_x != B_xa
% 191.21/191.70 => 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)) ) ) )
% 191.21/191.70 => 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)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_inj__on__Inter,axiom,
% 191.21/191.70 ! [V_f_2,T_c,T_b,V_S_2] :
% 191.21/191.70 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 191.21/191.70 => ( ! [B_A] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_A),V_S_2))
% 191.21/191.70 => c_Fun_Oinj__on(T_b,T_c,V_f_2,B_A) )
% 191.21/191.70 => 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)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_Inter__subset,axiom,
% 191.21/191.70 ! [V_B_2,V_A_2,T_b] :
% 191.21/191.70 ( ! [B_X] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_B_2)) )
% 191.21/191.70 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 191.21/191.70 => 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)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_inj__on__INTER,axiom,
% 191.21/191.70 ! [V_A_2,V_f_2,T_d,T_c,T_b,V_I_2] :
% 191.21/191.70 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.21/191.70 => ( ! [B_i] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_I_2))
% 191.21/191.70 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(V_A_2,B_i)) )
% 191.21/191.70 => 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)) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom,
% 191.21/191.70 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 191.21/191.70 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 191.21/191.70 => ( 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))
% 191.21/191.70 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.21/191.70 => ~ ! [B_y] :
% 191.21/191.70 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y)
% 191.21/191.70 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_min__max_Ofold__sup__le__sup,axiom,
% 191.21/191.70 ! [V_ca_2,V_ba_2,V_A_2,T_b] :
% 191.21/191.70 ( class_Orderings_Olinorder(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => ( ! [B_x] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_ba_2)) )
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_ca_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_ba_2),V_ca_2))) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_min__max_Oinf__le__fold__inf,axiom,
% 191.21/191.70 ! [V_ca_2,V_ba_2,V_A_2,T_b] :
% 191.21/191.70 ( class_Orderings_Olinorder(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => ( ! [B_x] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),B_x)) )
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_ba_2),V_ca_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_ca_2),V_A_2))) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_InterI,axiom,
% 191.21/191.70 ! [V_A_2,V_C_2,T_b] :
% 191.21/191.70 ( ! [B_X] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) )
% 191.21/191.70 => 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))) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_inf__le__fold__inf,axiom,
% 191.21/191.70 ! [V_ca_2,V_ba_2,V_A_2,T_b] :
% 191.21/191.70 ( class_Lattices_Osemilattice__inf(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => ( ! [B_x] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ba_2),B_x)) )
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_ba_2),V_ca_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_ca_2),V_A_2))) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_fold__sup__le__sup,axiom,
% 191.21/191.70 ! [V_ca_2,V_ba_2,V_A_2,T_b] :
% 191.21/191.70 ( class_Lattices_Osemilattice__sup(T_b)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.70 => ( ! [B_x] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_ba_2)) )
% 191.21/191.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_ca_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_ba_2),V_ca_2))) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_wf__eq__minimal,axiom,
% 191.21/191.70 ! [V_r_2,T_b] :
% 191.21/191.70 ( c_Wellfounded_Owf(T_b,V_r_2)
% 191.21/191.70 <=> ! [B_Q] :
% 191.21/191.70 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 191.21/191.70 => ? [B_x] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 191.21/191.70 & ! [B_y] :
% 191.21/191.70 ( 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))
% 191.21/191.70 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q)) ) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_folding__image__simple__idem_Ounion__idem,axiom,
% 191.21/191.70 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 191.21/191.70 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 191.21/191.70 => 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)) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_transfer__nat__int__set__cong,axiom,
% 191.21/191.70 ! [V_P_H_2,V_Pa_2] :
% 191.21/191.70 ( ! [B_x] :
% 191.21/191.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 191.21/191.70 => ( hBOOL(hAPP(V_Pa_2,B_x))
% 191.21/191.70 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) )
% 191.21/191.70 => hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_Pa_2)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_H_2)) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_folding__image__simple__idem_Oidem,axiom,
% 191.21/191.70 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 191.21/191.70 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 191.21/191.70 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_folding__image__simple__idem_Oin__idem,axiom,
% 191.21/191.70 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 191.21/191.70 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 191.21/191.70 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 191.21/191.70 => 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) ) ) ) ).
% 191.21/191.70
% 191.21/191.70 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
% 191.21/191.70 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 191.21/191.70 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 191.21/191.70 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 191.21/191.70 => 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)) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
% 191.21/191.71 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 191.21/191.71 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 191.21/191.71 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 191.21/191.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
% 191.21/191.71 => 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) ) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_Int__Collect__mono,axiom,
% 191.21/191.71 ! [V_Q_2,V_Pa_2,V_B_2,V_A_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.21/191.71 => ( ! [B_x] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 191.21/191.71 => ( hBOOL(hAPP(V_Pa_2,B_x))
% 191.21/191.71 => hBOOL(hAPP(V_Q_2,B_x)) ) )
% 191.21/191.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_OCollect(T_b),V_Q_2)))) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_UnionE,axiom,
% 191.21/191.71 ! [V_C_2,V_A_2,T_b] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => ~ ! [B_X] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X))
% 191.21/191.71 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__add__upd__left,axiom,
% 191.21/191.71 ! [V_u1_2,V_e1_2,V_e2_2,T_c,V_m_2,T_b] :
% 191.21/191.71 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_e2_2)))
% 191.21/191.71 => 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)) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_converseE,axiom,
% 191.21/191.71 ! [V_r_2,V_yx_2,T_c,T_b] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => ~ ! [B_x,B_y] :
% 191.21/191.71 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_y),B_x)
% 191.21/191.71 => ~ 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)) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__add__None,axiom,
% 191.21/191.71 ! [V_k_2,V_n_2,V_m_2,T_b,T_c] :
% 191.21/191.71 ( hAPP(c_Map_Omap__add(T_c,T_b,V_m_2,V_n_2),V_k_2) = c_Option_Ooption_ONone(T_b)
% 191.21/191.71 <=> ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 191.21/191.71 & hAPP(V_m_2,V_k_2) = c_Option_Ooption_ONone(T_b) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__add__find__right,axiom,
% 191.21/191.71 ! [V_m_2,T_c,V_xx_2,T_b,V_k_2,V_n_2] :
% 191.21/191.71 ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_xx_2)
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__add__assoc,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__add__empty,axiom,
% 191.21/191.71 ! [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 ).
% 191.21/191.71
% 191.21/191.71 fof(fact_empty__map__add,axiom,
% 191.21/191.71 ! [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 ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__add__def,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__add__dom__app__simps_I1_J,axiom,
% 191.21/191.71 ! [V_l1_2,V_l2_2,T_c,V_m_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l2_2)))
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__add__dom__app__simps_I3_J,axiom,
% 191.21/191.71 ! [V_l1_2,V_l2_2,T_c,V_m_2,T_b] :
% 191.21/191.71 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l2_2)))
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__add__dom__app__simps_I2_J,axiom,
% 191.21/191.71 ! [V_l2_2,V_l1_2,T_c,V_m_2,T_b] :
% 191.21/191.71 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l1_2)))
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_dom__map__add,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__add__SomeD,axiom,
% 191.21/191.71 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_b,T_c] :
% 191.21/191.71 ( 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)
% 191.21/191.71 => ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
% 191.21/191.71 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 191.21/191.71 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__add__Some__iff,axiom,
% 191.21/191.71 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_b,T_c] :
% 191.21/191.71 ( 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)
% 191.21/191.71 <=> ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
% 191.21/191.71 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 191.21/191.71 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2) ) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__add__upd,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_inj__on__map__add__dom,axiom,
% 191.21/191.71 ! [V_m_H_2,V_m_2,T_c,T_b] :
% 191.21/191.71 ( 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))
% 191.21/191.71 <=> 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)) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__add__comm,axiom,
% 191.21/191.71 ! [V_m2_2,V_m1_2,T_c,T_b] :
% 191.21/191.71 ( 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))
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_finite__range__map__of__map__add,axiom,
% 191.21/191.71 ! [V_l_2,V_f_2,T_c,T_b] :
% 191.21/191.71 ( 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)))))
% 191.21/191.71 => 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))))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_rel__compE,axiom,
% 191.21/191.71 ! [V_s_2,V_r_2,T_d,V_xz_2,T_c,T_b] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => ~ ! [B_x,B_y,B_z] :
% 191.21/191.71 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)
% 191.21/191.71 => ( 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))
% 191.21/191.71 => ~ 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)) ) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_finite__dom__map__of,axiom,
% 191.21/191.71 ! [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)))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_finite__range__map__of,axiom,
% 191.21/191.71 ! [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))))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__add__map__of__foldr,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_full__small__int__def,axiom,
% 191.21/191.71 ! [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))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_small_H_Osimps,axiom,
% 191.21/191.71 ! [V_f_2,V_i_2,V_d_2] :
% 191.21/191.71 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 191.21/191.71 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
% 191.21/191.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 191.21/191.71 => 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)) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_small_H_Opsimps,axiom,
% 191.21/191.71 ! [V_i_2,V_d_2,V_f_2] :
% 191.21/191.71 ( 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))))
% 191.21/191.71 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 191.21/191.71 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) )
% 191.21/191.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 191.21/191.71 => 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)) ) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_small__int__def,axiom,
% 191.21/191.71 ! [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))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_small__prod__def,axiom,
% 191.21/191.71 ! [V_d_2,V_f_2,T_b,T_c] :
% 191.21/191.71 ( ( class_Smallcheck_Osmall(T_c)
% 191.21/191.71 & class_Smallcheck_Osmall(T_b) )
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_small_H_Opinduct,axiom,
% 191.21/191.71 ! [V_Pa_2,V_a2_2,V_a1_2,V_a0_2] :
% 191.21/191.71 ( 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))))
% 191.21/191.71 => ( ! [B_f,B_d,B_i] :
% 191.21/191.71 ( 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))))
% 191.21/191.71 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i))
% 191.21/191.71 => ( hAPP(B_f,B_i) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
% 191.21/191.71 => hBOOL(hAPP(hAPP(hAPP(V_Pa_2,B_f),B_d),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) )
% 191.21/191.71 => hBOOL(hAPP(hAPP(hAPP(V_Pa_2,B_f),B_d),B_i)) ) )
% 191.21/191.71 => hBOOL(hAPP(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2),V_a2_2)) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_body__def,axiom,
% 191.21/191.71 c_Com_Obody = c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom,c_Com_Obodies) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__of__mapk__SomeI,axiom,
% 191.21/191.71 ! [V_x_2,V_k_2,V_t_2,T_d,V_f_2,T_c,T_b] :
% 191.21/191.71 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 191.21/191.71 => ( 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)
% 191.21/191.71 => 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) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__comp__def,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_inj__mapI,axiom,
% 191.21/191.71 ! [V_f_2,T_c,T_b] :
% 191.21/191.71 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 191.21/191.71 => 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))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__comp__Some__iff,axiom,
% 191.21/191.71 ! [V_v_2,V_k_2,V_m2_2,V_m1_2,T_d,T_b,T_c] :
% 191.21/191.71 ( 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)
% 191.21/191.71 <=> ? [B_k_H] :
% 191.21/191.71 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_k_H)
% 191.21/191.71 & hAPP(V_m1_2,B_k_H) = hAPP(c_Option_Ooption_OSome(T_b),V_v_2) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__comp__simps_I2_J,axiom,
% 191.21/191.71 ! [V_m1_2,T_c,T_d,V_k_H_2,T_b,V_k_2,V_m2_2] :
% 191.21/191.71 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_k_H_2)
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__comp__simps_I1_J,axiom,
% 191.21/191.71 ! [V_m1_2,T_c,T_d,T_b,V_k_2,V_m2_2] :
% 191.21/191.71 ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b)
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_inj__map,axiom,
% 191.21/191.71 ! [V_f_2,T_c,T_b] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 <=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_inj__map__eq__map,axiom,
% 191.21/191.71 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 191.21/191.71 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 191.21/191.71 => ( 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)
% 191.21/191.71 <=> V_xs_2 = V_ys_2 ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_inj__mapD,axiom,
% 191.21/191.71 ! [V_f_2,T_c,T_b] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__injective,axiom,
% 191.21/191.71 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 191.21/191.71 ( 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)
% 191.21/191.71 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 191.21/191.71 => V_xs_2 = V_ys_2 ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__ident,axiom,
% 191.21/191.71 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)),V_xs_2) = V_xs_2 ).
% 191.21/191.71
% 191.21/191.71 fof(fact_List_Omap_Oidentity,axiom,
% 191.21/191.71 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_List_Omap_Oid,axiom,
% 191.21/191.71 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__map,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_List_Omap_Ocompositionality,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__comp__map,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_List_Omap_Ocomp,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_foldr__map,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__comp__empty_I1_J,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__comp__empty_I2_J,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__comp__None__iff,axiom,
% 191.21/191.71 ! [V_k_2,V_m2_2,V_m1_2,T_d,T_b,T_c] :
% 191.21/191.71 ( 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)
% 191.21/191.71 <=> ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_c)
% 191.21/191.71 | ? [B_k_H] :
% 191.21/191.71 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_c),B_k_H)
% 191.21/191.71 & hAPP(V_m1_2,B_k_H) = c_Option_Ooption_ONone(T_b) ) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__of__map,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__of__map__keys,axiom,
% 191.21/191.71 ! [V_m_2,T_c,V_xs_2,T_b] :
% 191.21/191.71 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Map_Odom(T_b,T_c,V_m_2)
% 191.21/191.71 => 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 ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_finite__set,axiom,
% 191.21/191.71 ! [V_xs_2,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_set__map,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__eq__conv,axiom,
% 191.21/191.71 ! [V_g_2,V_xs_2,V_f_2,T_b,T_c] :
% 191.21/191.71 ( 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)
% 191.21/191.71 <=> ! [B_x] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
% 191.21/191.71 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_Option_Omap_Ocomp,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_Option_Omap_Ocompositionality,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_option__map__comp,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_option__map__o__sum__case,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_Option_Omap_Oidentity,axiom,
% 191.21/191.71 ! [T_b] : hAPP(c_Option_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_Option_Ooption(T_b)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_Option_Omap_Oid,axiom,
% 191.21/191.71 ! [T_b] : hAPP(c_Option_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_Option_Ooption(T_b)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_infinite__UNIV__listI,axiom,
% 191.21/191.71 ! [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)))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_dom__option__map,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_option__map__Some,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_option__map__eq__Some,axiom,
% 191.21/191.71 ! [V_y_2,V_xo_2,V_f_2,T_b,T_c] :
% 191.21/191.71 ( 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)
% 191.21/191.71 <=> ? [B_z] :
% 191.21/191.71 ( V_xo_2 = hAPP(c_Option_Ooption_OSome(T_c),B_z)
% 191.21/191.71 & hAPP(V_f_2,B_z) = V_y_2 ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_option__map__None,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_option__map__is__None,axiom,
% 191.21/191.71 ! [V_opt_2,V_f_2,T_b,T_c] :
% 191.21/191.71 ( hAPP(hAPP(c_Option_Omap(T_c,T_b),V_f_2),V_opt_2) = c_Option_Ooption_ONone(T_b)
% 191.21/191.71 <=> V_opt_2 = c_Option_Ooption_ONone(T_c) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_option__map__o__empty,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_option__map__o__map__upd,axiom,
% 191.21/191.71 ! [V_ba_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_ba_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_ba_2))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_inj__on__map__eq__map,axiom,
% 191.21/191.71 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => ( 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)
% 191.21/191.71 <=> V_xs_2 = V_ys_2 ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__inj__on,axiom,
% 191.21/191.71 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 191.21/191.71 ( 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)
% 191.21/191.71 => ( 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)))
% 191.21/191.71 => V_xs_2 = V_ys_2 ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__fun__upd,axiom,
% 191.21/191.71 ! [V_v_2,V_f_2,T_c,V_xs_2,V_y_2,T_b] :
% 191.21/191.71 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_inj__on__mapI,axiom,
% 191.21/191.71 ! [V_A_2,V_f_2,T_c,T_b] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__of__eq__dom,axiom,
% 191.21/191.71 ! [V_ys_2,V_xs_2,T_c,T_b] :
% 191.21/191.71 ( c_Map_Omap__of(T_b,T_c,V_xs_2) = c_Map_Omap__of(T_b,T_c,V_ys_2)
% 191.21/191.71 => 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)) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__of__SomeD,axiom,
% 191.21/191.71 ! [V_y_2,V_k_2,V_xs_2,T_b,T_c] :
% 191.21/191.71 ( 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)
% 191.21/191.71 => 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))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__of__is__SomeD,axiom,
% 191.21/191.71 ! [V_y_2,V_x_2,V_xys_2,T_b,T_c] :
% 191.21/191.71 ( 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)
% 191.21/191.71 => 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))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_dom__map__of__conv__image__fst,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__of__eq__None__iff,axiom,
% 191.21/191.71 ! [V_x_2,V_xys_2,T_b,T_c] :
% 191.21/191.71 ( hAPP(c_Map_Omap__of(T_c,T_b,V_xys_2),V_x_2) = c_Option_Ooption_ONone(T_b)
% 191.21/191.71 <=> ~ 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)))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_Option_Omap__def,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_WT__bodies__def,axiom,
% 191.21/191.71 ( c_Com_OWT__bodies
% 191.21/191.71 <=> ! [B_x] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => 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)) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__of__map__restrict,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_ran__distinct,axiom,
% 191.21/191.71 ! [V_al_2,T_c,T_b] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => 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)) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_set__map__of__compr,axiom,
% 191.21/191.71 ! [V_xs_2,T_c,T_b] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => 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)))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_distinct__map,axiom,
% 191.21/191.71 ! [V_xs_2,V_f_2,T_c,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
% 191.21/191.71 <=> ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
% 191.21/191.71 & c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2)) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__of__inject__set,axiom,
% 191.21/191.71 ! [V_ys_2,V_xs_2,T_c,T_b] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => ( 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)))
% 191.21/191.71 => ( c_Map_Omap__of(T_b,T_c,V_xs_2) = c_Map_Omap__of(T_b,T_c,V_ys_2)
% 191.21/191.71 <=> 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) ) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__of__is__SomeI,axiom,
% 191.21/191.71 ! [V_y_2,V_x_2,V_xys_2,T_c,T_b] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => ( 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)))
% 191.21/191.71 => 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) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__of__eq__Some__iff,axiom,
% 191.21/191.71 ! [V_y_2,V_x_2,V_xys_2,T_c,T_b] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => ( 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)
% 191.21/191.71 <=> 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))) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_Some__eq__map__of__iff,axiom,
% 191.21/191.71 ! [V_x_2,V_y_2,V_xys_2,T_c,T_b] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => ( 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)
% 191.21/191.71 <=> 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))) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_greaterThanLessThan__upto,axiom,
% 191.21/191.71 ! [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)))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_weak__map__of__SomeI,axiom,
% 191.21/191.71 ! [V_l_2,V_x_2,V_k_2,T_c,T_b] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => ? [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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_atLeastAtMost__upto,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_set__upto,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_distinct__upto,axiom,
% 191.21/191.71 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_atLeastLessThan__upto,axiom,
% 191.21/191.71 ! [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)))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_greaterThanAtMost__upto,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_nat__list__def,axiom,
% 191.21/191.71 ! [V_l_2] :
% 191.21/191.71 ( c_List_Onat__list(V_l_2)
% 191.21/191.71 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_set__remove1__eq,axiom,
% 191.21/191.71 ! [V_x_2,V_xs_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 191.21/191.71 => 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)))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_remove1__idem,axiom,
% 191.21/191.71 ! [V_xs_2,V_x_2,T_b] :
% 191.21/191.71 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.71 => c_List_Oremove1(T_b,V_x_2,V_xs_2) = V_xs_2 ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_notin__set__remove1,axiom,
% 191.21/191.71 ! [V_y_2,V_xs_2,V_x_2,T_b] :
% 191.21/191.71 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.71 => ~ 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)))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_in__set__remove1,axiom,
% 191.21/191.71 ! [V_xs_2,T_b,V_ba_2,V_a_2] :
% 191.21/191.71 ( V_a_2 != V_ba_2
% 191.21/191.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_ba_2,V_xs_2))))
% 191.21/191.71 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_set__remove1__subset,axiom,
% 191.21/191.71 ! [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))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_remove1__commute,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_distinct__remove1,axiom,
% 191.21/191.71 ! [V_x,V_xs,T_a] :
% 191.21/191.71 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 191.21/191.71 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_sorted__list__of__set__remove,axiom,
% 191.21/191.71 ! [V_x_2,V_A_2,T_b] :
% 191.21/191.71 ( class_Orderings_Olinorder(T_b)
% 191.21/191.71 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.71 => 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)) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__of__zip__map,axiom,
% 191.21/191.71 ! [V_f_2,T_c,V_xs_2,V_x_2,T_b] :
% 191.21/191.71 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.71 => 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)) )
% 191.21/191.71 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.71 => 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) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_distinct__zipI2,axiom,
% 191.21/191.71 ! [V_xs,T_b,V_ys,T_a] :
% 191.21/191.71 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys))
% 191.21/191.71 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_distinct__zipI1,axiom,
% 191.21/191.71 ! [V_ys,T_b,V_xs,T_a] :
% 191.21/191.71 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 191.21/191.71 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_zip__same__conv__map,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_zip__map__fst__snd,axiom,
% 191.21/191.71 ! [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 ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__zip__map2,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__zip__map,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_in__set__zipE,axiom,
% 191.21/191.71 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 191.21/191.71 ( 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))))
% 191.21/191.71 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.71 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_set__zip__rightD,axiom,
% 191.21/191.71 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 191.21/191.71 ( 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))))
% 191.21/191.71 => hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_set__zip__leftD,axiom,
% 191.21/191.71 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 191.21/191.71 ( 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))))
% 191.21/191.71 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_zip__same,axiom,
% 191.21/191.71 ! [V_xs_2,V_ba_2,V_a_2,T_b] :
% 191.21/191.71 ( 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_ba_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))))
% 191.21/191.71 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.71 & V_a_2 = V_ba_2 ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_zip__map2,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_zip__map1,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_zip__map__map,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_sorted__list__of__set__insert,axiom,
% 191.21/191.71 ! [V_x_2,V_A_2,T_b] :
% 191.21/191.71 ( class_Orderings_Olinorder(T_b)
% 191.21/191.71 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.71 => 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)))))) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__of__zip__upd,axiom,
% 191.21/191.71 ! [V_z_2,V_y_2,V_x_2,V_zs_2,V_xs_2,T_c,V_ys_2,T_b] :
% 191.21/191.71 ( 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)
% 191.21/191.71 => ( 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)
% 191.21/191.71 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_List_Oset(T_c),V_xs_2)))
% 191.21/191.71 => ( 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))
% 191.21/191.71 => 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)) ) ) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_length__zip,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_set__insort,axiom,
% 191.21/191.71 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 191.21/191.71 ( class_Orderings_Olinorder(T_c)
% 191.21/191.71 => 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)) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_insort__left__comm,axiom,
% 191.21/191.71 ! [V_xs_2,V_y_2,V_x_2,T_b] :
% 191.21/191.71 ( class_Orderings_Olinorder(T_b)
% 191.21/191.71 => 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)) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_insort__key__left__comm,axiom,
% 191.21/191.71 ! [V_xs_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 191.21/191.71 ( class_Orderings_Olinorder(T_b)
% 191.21/191.71 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
% 191.21/191.71 => 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)) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_length__insort,axiom,
% 191.21/191.71 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 191.21/191.71 ( class_Orderings_Olinorder(T_c)
% 191.21/191.71 => 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)) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_neq__if__length__neq,axiom,
% 191.21/191.71 ! [V_ys,V_xs,T_a] :
% 191.21/191.71 ( 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)
% 191.21/191.71 => V_xs != V_ys ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_fun__left__comm__insort,axiom,
% 191.21/191.71 ! [T_b] :
% 191.21/191.71 ( class_Orderings_Olinorder(T_b)
% 191.21/191.71 => 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))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_lexn__length,axiom,
% 191.21/191.71 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 191.21/191.71 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_n_2
% 191.21/191.71 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_length__map,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__eq__imp__length__eq,axiom,
% 191.21/191.71 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_b,T_c] :
% 191.21/191.71 ( 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)
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_remove1__insort,axiom,
% 191.21/191.71 ! [V_xs_2,V_x_2,T_b] :
% 191.21/191.71 ( class_Orderings_Olinorder(T_b)
% 191.21/191.71 => 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 ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_card__length,axiom,
% 191.21/191.71 ! [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))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_distinct__card,axiom,
% 191.21/191.71 ! [V_xs_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_card__distinct,axiom,
% 191.21/191.71 ! [V_xs_2,T_b] :
% 191.21/191.71 ( 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)
% 191.21/191.71 => hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__of__zip__inject,axiom,
% 191.21/191.71 ! [V_zs_2,V_xs_2,T_c,V_ys_2,T_b] :
% 191.21/191.71 ( 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)
% 191.21/191.71 => ( 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)
% 191.21/191.71 => ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
% 191.21/191.71 => ( 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))
% 191.21/191.71 => V_ys_2 = V_zs_2 ) ) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__fst__zip,axiom,
% 191.21/191.71 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 191.21/191.71 ( 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)
% 191.21/191.71 => 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 ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__snd__zip,axiom,
% 191.21/191.71 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 191.21/191.71 ( 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)
% 191.21/191.71 => 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 ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_distinct__insort,axiom,
% 191.21/191.71 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 191.21/191.71 ( class_Orderings_Olinorder(T_c)
% 191.21/191.71 => ( 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)))
% 191.21/191.71 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.71 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_length__pos__if__in__set,axiom,
% 191.21/191.71 ! [V_xs_2,V_x_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.71 => 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))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_zip__eq__conv,axiom,
% 191.21/191.71 ! [V_zs_2,V_ys_2,T_c,V_xs_2,T_b] :
% 191.21/191.71 ( 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)
% 191.21/191.71 => ( hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) = V_zs_2
% 191.21/191.71 <=> ( 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
% 191.21/191.71 & 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 ) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_lenlex__conv,axiom,
% 191.21/191.71 ! [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)))))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_lenlex__def,axiom,
% 191.21/191.71 ! [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)))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_finite__lists__length__eq,axiom,
% 191.21/191.71 ! [V_n_2,V_A_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.71 => 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))))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_list__eq__iff__zip__eq,axiom,
% 191.21/191.71 ! [T_b,V_ys_2,V_xs_2] :
% 191.21/191.71 ( V_xs_2 = V_ys_2
% 191.21/191.71 <=> ( 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)
% 191.21/191.71 & ! [B_x] :
% 191.21/191.71 ( 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))))
% 191.21/191.71 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__of__zip__is__None,axiom,
% 191.21/191.71 ! [V_x_2,V_ys_2,T_c,V_xs_2,T_b] :
% 191.21/191.71 ( 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)
% 191.21/191.71 => ( 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)
% 191.21/191.71 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__of__zip__is__Some,axiom,
% 191.21/191.71 ! [V_x_2,V_ys_2,T_c,V_xs_2,T_b] :
% 191.21/191.71 ( 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)
% 191.21/191.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.71 <=> ? [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) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_length__remove1,axiom,
% 191.21/191.71 ! [V_xs_2,V_x_2,T_b] :
% 191.21/191.71 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.71 => 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)) )
% 191.21/191.71 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.71 => 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) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_dom__map__of__zip,axiom,
% 191.21/191.71 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 191.21/191.71 ( 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)
% 191.21/191.71 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 191.21/191.71 => 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) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_finite__lists__length__le,axiom,
% 191.21/191.71 ! [V_n_2,V_A_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.71 => 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))))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_Nitpick_Ocard_H__def,axiom,
% 191.21/191.71 ! [V_A_2,T_b] :
% 191.21/191.71 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.71 => 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)))) )
% 191.21/191.71 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.71 => c_Nitpick_Ocard_H(T_b,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listrel__iff__zip,axiom,
% 191.21/191.71 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 191.21/191.71 <=> ( 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)
% 191.21/191.71 & ! [B_x] :
% 191.21/191.71 ( 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))))
% 191.21/191.71 => 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)) ) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listrel__rtrancl__refl,axiom,
% 191.21/191.71 ! [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)))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listrel__eq__len,axiom,
% 191.21/191.71 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listrel__rtrancl__trans,axiom,
% 191.21/191.71 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 191.21/191.71 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 191.21/191.71 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listrel__mono,axiom,
% 191.21/191.71 ! [V_s_2,V_r_2,T_b] :
% 191.21/191.71 ( 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))
% 191.21/191.71 => 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))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listrelp__listrel__eq,axiom,
% 191.21/191.71 ! [V_xa_2,V_x_2,V_r_2,T_b] :
% 191.21/191.71 ( 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)
% 191.21/191.71 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_lexn_Osimps_I2_J,axiom,
% 191.21/191.71 ! [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)))))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_impossible__Cons,axiom,
% 191.21/191.71 ! [V_x,V_ys,V_xs,T_a] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_set__ConsD,axiom,
% 191.21/191.71 ! [V_xs_2,V_x_2,V_y_2,T_b] :
% 191.21/191.71 ( 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))))
% 191.21/191.71 => ( V_y_2 = V_x_2
% 191.21/191.71 | hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_zip__Cons__Cons,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_List_Oset_Osimps_I2_J,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_set__subset__Cons,axiom,
% 191.21/191.71 ! [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)))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_foldr_Osimps_I2_J,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_not__Cons__self,axiom,
% 191.21/191.71 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_not__Cons__self2,axiom,
% 191.21/191.71 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ).
% 191.21/191.71
% 191.21/191.71 fof(fact_list_Oinject,axiom,
% 191.21/191.71 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_b] :
% 191.21/191.71 ( 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)
% 191.21/191.71 <=> ( V_a_2 = V_a_H_2
% 191.21/191.71 & V_list_2 = V_list_H_2 ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listrelp_Oequations_I2_J,axiom,
% 191.21/191.71 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_b] :
% 191.21/191.71 ( 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))
% 191.21/191.71 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2))
% 191.21/191.71 & c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listrelp_OCons,axiom,
% 191.21/191.71 ! [V_ys_2,V_xs_2,T_b,V_y_2,V_x_2,V_r_2] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 191.21/191.71 => ( c_List_Olistrelp(T_b,V_r_2,V_xs_2,V_ys_2)
% 191.21/191.71 => 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)) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map_Osimps_I2_J,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_remove1_Osimps_I2_J,axiom,
% 191.21/191.71 ! [V_xs,T_a,V_y,V_x] :
% 191.21/191.71 ( ( V_x = V_y
% 191.21/191.71 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs )
% 191.21/191.71 & ( V_x != V_y
% 191.21/191.71 => 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)) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_insort__key_Osimps_I2_J,axiom,
% 191.21/191.71 ! [V_ys_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 191.21/191.71 ( class_Orderings_Olinorder(T_b)
% 191.21/191.71 => ( ( 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)))
% 191.21/191.71 => 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)) )
% 191.21/191.71 & ( ~ 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)))
% 191.21/191.71 => 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)) ) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_distinct_Osimps_I2_J,axiom,
% 191.21/191.71 ! [V_xs_2,V_x_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))
% 191.21/191.71 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.71 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__of__Cons__code_I2_J,axiom,
% 191.21/191.71 ! [V_ps,V_v,T_c,T_b,V_k,V_l] :
% 191.21/191.71 ( ( V_l = V_k
% 191.21/191.71 => 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) )
% 191.21/191.71 & ( V_l != V_k
% 191.21/191.71 => 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) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_list_Osize_I4_J,axiom,
% 191.21/191.71 ! [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))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listrel_OCons,axiom,
% 191.21/191.71 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 191.21/191.71 ( hBOOL(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))
% 191.21/191.71 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 191.21/191.71 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__of_Osimps_I2_J,axiom,
% 191.21/191.71 ! [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))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_Cons__in__lex,axiom,
% 191.21/191.71 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 191.21/191.71 <=> ( ( hBOOL(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))
% 191.21/191.71 & 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) )
% 191.21/191.71 | ( V_x_2 = V_y_2
% 191.21/191.71 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listrel__Cons,axiom,
% 191.21/191.71 ! [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))))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_set__Cons__def,axiom,
% 191.21/191.71 ! [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)))))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listrel__Cons1,axiom,
% 191.21/191.71 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 191.21/191.71 => ~ ! [B_y,B_ys] :
% 191.21/191.71 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys)
% 191.21/191.71 => ( 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))
% 191.21/191.71 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listrel__Cons2,axiom,
% 191.21/191.71 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 191.21/191.71 => ~ ! [B_x,B_xs] :
% 191.21/191.71 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
% 191.21/191.71 => ( 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))
% 191.21/191.71 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_length__sublist,axiom,
% 191.21/191.71 ! [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)))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_pick_Osimps,axiom,
% 191.21/191.71 ! [V_xs,V_x,T_a,V_i] :
% 191.21/191.71 ( ( 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)))
% 191.21/191.71 => 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) )
% 191.21/191.71 & ( ~ 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)))
% 191.21/191.71 => 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))) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_distinct__sublistI,axiom,
% 191.21/191.71 ! [V_I_2,V_xs_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 191.21/191.71 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_in__set__sublistD,axiom,
% 191.21/191.71 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 191.21/191.71 ( 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))))
% 191.21/191.71 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_notin__set__sublistI,axiom,
% 191.21/191.71 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 191.21/191.71 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.71 => ~ 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)))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_set__sublist__subset,axiom,
% 191.21/191.71 ! [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))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_select__weight__cons__zero,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_pick__member,axiom,
% 191.21/191.71 ! [V_xs_2,T_b,V_i_2] :
% 191.21/191.71 ( 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))))
% 191.21/191.71 => 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)))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listsum__simps_I2_J,axiom,
% 191.21/191.71 ! [V_xs,V_x,T_a] :
% 191.21/191.71 ( class_Groups_Omonoid__add(T_a)
% 191.21/191.71 => 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)) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listsum__subtractf,axiom,
% 191.21/191.71 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 191.21/191.71 ( class_Groups_Oab__group__add(T_b)
% 191.21/191.71 => 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))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listsum__const__mult,axiom,
% 191.21/191.71 ! [V_xs_2,V_f_2,V_ca_2,T_c,T_b] :
% 191.21/191.71 ( class_Rings_Osemiring__0(T_b)
% 191.21/191.71 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listsum__mult__const,axiom,
% 191.21/191.71 ! [V_xs_2,V_ca_2,V_f_2,T_c,T_b] :
% 191.21/191.71 ( class_Rings_Osemiring__0(T_b)
% 191.21/191.71 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_ca_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),V_ca_2) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listsum__addf,axiom,
% 191.21/191.71 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 191.21/191.71 ( class_Groups_Ocomm__monoid__add(T_b)
% 191.21/191.71 => 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))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listsum__0,axiom,
% 191.21/191.71 ! [V_xs_2,T_c,T_b] :
% 191.21/191.71 ( class_Groups_Omonoid__add(T_b)
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listsum__abs,axiom,
% 191.21/191.71 ! [V_xs_2,T_b] :
% 191.21/191.71 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 191.21/191.71 => 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)))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_uminus__listsum__map,axiom,
% 191.21/191.71 ! [V_xs_2,V_f_2,T_c,T_b] :
% 191.21/191.71 ( class_Groups_Oab__group__add(T_b)
% 191.21/191.71 => 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)) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_distinct__listsum__conv__Setsum,axiom,
% 191.21/191.71 ! [V_xs_2,T_b] :
% 191.21/191.71 ( class_Groups_Ocomm__monoid__add(T_b)
% 191.21/191.71 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 191.21/191.71 => 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)) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_select__weight__def,axiom,
% 191.21/191.71 ! [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))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listsum__distinct__conv__setsum__set,axiom,
% 191.21/191.71 ! [V_f_2,V_xs_2,T_b,T_c] :
% 191.21/191.71 ( class_Groups_Ocomm__monoid__add(T_c)
% 191.21/191.71 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 191.21/191.71 => 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)) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_interv__listsum__conv__setsum__set__int,axiom,
% 191.21/191.71 ! [V_l_2,V_k_2,V_f_2,T_b] :
% 191.21/191.71 ( class_Groups_Ocomm__monoid__add(T_b)
% 191.21/191.71 => 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))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_setsum__set__upto__conv__listsum__int,axiom,
% 191.21/191.71 ! [V_j_2,V_i_2,V_f_2,T_b] :
% 191.21/191.71 ( class_Groups_Ocomm__monoid__add(T_b)
% 191.21/191.71 => 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))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listsum__triv,axiom,
% 191.21/191.71 ! [V_xs_2,V_r_2,T_c,T_b] :
% 191.21/191.71 ( class_Rings_Osemiring__1(T_b)
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listsum__map__remove1,axiom,
% 191.21/191.71 ! [V_f_2,V_xs_2,V_x_2,T_b,T_c] :
% 191.21/191.71 ( class_Groups_Ocomm__monoid__add(T_c)
% 191.21/191.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.71 => 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)))) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_select__weight__member,axiom,
% 191.21/191.71 ! [V_s_2,V_xs_2,T_b] :
% 191.21/191.71 ( 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))))
% 191.21/191.71 => 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)))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_Nitpick_Osetsum_H__def,axiom,
% 191.21/191.71 ! [V_f_2,V_A_2,T_b,T_c] :
% 191.21/191.71 ( class_Groups_Ocomm__monoid__add(T_c)
% 191.21/191.71 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.71 => 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))))) )
% 191.21/191.71 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.71 => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_upto_Opsimps,axiom,
% 191.21/191.71 ! [V_j_2,V_i_2] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 191.21/191.71 => 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)) )
% 191.21/191.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 191.21/191.71 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listrel__Nil2,axiom,
% 191.21/191.71 ! [V_r_2,V_xs_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 191.21/191.71 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listrel__Nil1,axiom,
% 191.21/191.71 ! [V_r_2,V_xs_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 191.21/191.71 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listsum__eq__0__nat__iff__nat,axiom,
% 191.21/191.71 ! [V_ns_2] :
% 191.21/191.71 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 191.21/191.71 <=> ! [B_x] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 191.21/191.71 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listsum__simps_I1_J,axiom,
% 191.21/191.71 ! [T_a] :
% 191.21/191.71 ( class_Groups_Omonoid__add(T_a)
% 191.21/191.71 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__is__Nil__conv,axiom,
% 191.21/191.71 ! [V_xs_2,V_f_2,T_b,T_c] :
% 191.21/191.71 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 191.21/191.71 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map_Osimps_I1_J,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_Nil__is__map__conv,axiom,
% 191.21/191.71 ! [V_xs_2,V_f_2,T_c,T_b] :
% 191.21/191.71 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)
% 191.21/191.71 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listrelp_Oequations_I1_J,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listrelp_ONil,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_insort__not__Nil,axiom,
% 191.21/191.71 ! [V_xs_2,V_a_2,V_f_2,T_b,T_c] :
% 191.21/191.71 ( class_Orderings_Olinorder(T_c)
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_distinct_Osimps_I1_J,axiom,
% 191.21/191.71 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_remove1_Osimps_I1_J,axiom,
% 191.21/191.71 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_foldr_Osimps_I1_J,axiom,
% 191.21/191.71 ! [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 ).
% 191.21/191.71
% 191.21/191.71 fof(fact_upto__empty,axiom,
% 191.21/191.71 ! [V_i,V_j] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i))
% 191.21/191.71 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_zip__Nil,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_zip_Osimps_I1_J,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_list_Osize_I3_J,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_length__0__conv,axiom,
% 191.21/191.71 ! [V_xs_2,T_b] :
% 191.21/191.71 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 191.21/191.71 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_sorted__list__of__set__empty,axiom,
% 191.21/191.71 ! [T_b] :
% 191.21/191.71 ( class_Orderings_Olinorder(T_b)
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_set__empty,axiom,
% 191.21/191.71 ! [V_xs_2,T_b] :
% 191.21/191.71 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 191.21/191.71 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_set__empty2,axiom,
% 191.21/191.71 ! [V_xs_2,T_b] :
% 191.21/191.71 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),V_xs_2)
% 191.21/191.71 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_List_Oset_Osimps_I1_J,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_list_Osimps_I2_J,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_list_Osimps_I3_J,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_insort__key_Osimps_I1_J,axiom,
% 191.21/191.71 ! [V_x_2,V_f_2,T_b,T_c] :
% 191.21/191.71 ( class_Orderings_Olinorder(T_c)
% 191.21/191.71 => 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)) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_sublist__empty,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_sublist__nil,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_length__greater__0__conv,axiom,
% 191.21/191.71 ! [V_xs_2,T_b] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 <=> V_xs_2 != c_List_Olist_ONil(T_b) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listrel_ONil,axiom,
% 191.21/191.71 ! [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))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_Nil__notin__lex,axiom,
% 191.21/191.71 ! [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))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_Nil2__notin__lex,axiom,
% 191.21/191.71 ! [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))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_upto_Osimps,axiom,
% 191.21/191.71 ! [V_j,V_i] :
% 191.21/191.71 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 191.21/191.71 => 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)) )
% 191.21/191.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 191.21/191.71 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_sublist__singleton,axiom,
% 191.21/191.71 ! [V_x_2,T_b,V_A_2] :
% 191.21/191.71 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 191.21/191.71 => 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)) )
% 191.21/191.71 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 191.21/191.71 => 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) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_upto__rec__number__of,axiom,
% 191.21/191.71 ! [V_n,V_m] :
% 191.21/191.71 ( ( 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)))
% 191.21/191.71 => 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))) )
% 191.21/191.71 & ( ~ 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)))
% 191.21/191.71 => 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) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listrel__Nil,axiom,
% 191.21/191.71 ! [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))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_set__Cons__sing__Nil,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_select__weigth__select,axiom,
% 191.21/191.71 ! [T_b,V_xs_2] :
% 191.21/191.71 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_select,axiom,
% 191.21/191.71 ! [V_s_2,T_b,V_xs_2] :
% 191.21/191.71 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 191.21/191.71 => 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))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__of_Osimps_I1_J,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__of__Cons__code_I1_J,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_anamorph_Osimps,axiom,
% 191.21/191.71 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 191.21/191.71 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 191.21/191.71 => 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) )
% 191.21/191.71 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 191.21/191.71 => 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)) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listset_Osimps_I1_J,axiom,
% 191.21/191.71 ! [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))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listset_Osimps_I2_J,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_zip__Cons1,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_zip__Cons,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_list_Osimps_I5_J,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_list_Osimps_I4_J,axiom,
% 191.21/191.71 ! [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 ).
% 191.21/191.71
% 191.21/191.71 fof(fact_select__def,axiom,
% 191.21/191.71 ! [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))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_pick__same,axiom,
% 191.21/191.71 ! [V_xs_2,T_b,V_l_2] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_nth_Osimps,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_nth__Cons__0,axiom,
% 191.21/191.71 ! [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 ).
% 191.21/191.71
% 191.21/191.71 fof(fact_nth__Cons__Suc,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_nth__map,axiom,
% 191.21/191.71 ! [V_f_2,T_c,V_xs_2,T_b,V_n_2] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => 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)) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_all__set__conv__all__nth,axiom,
% 191.21/191.71 ! [V_Pa_2,V_xs_2,T_b] :
% 191.21/191.71 ( ! [B_x] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.71 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 191.21/191.71 <=> ! [B_i] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_distinct__conv__nth,axiom,
% 191.21/191.71 ! [V_xs_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 191.21/191.71 <=> ! [B_i] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => ! [B_j] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => ( B_i != B_j
% 191.21/191.71 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j) ) ) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_nth__eq__iff__index__eq,axiom,
% 191.21/191.71 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 191.21/191.71 => ( 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)))
% 191.21/191.71 => ( 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)))
% 191.21/191.71 => ( 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)
% 191.21/191.71 <=> V_i_2 = V_j_2 ) ) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_list__eq__iff__nth__eq,axiom,
% 191.21/191.71 ! [T_b,V_ys_2,V_xs_2] :
% 191.21/191.71 ( V_xs_2 = V_ys_2
% 191.21/191.71 <=> ( 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)
% 191.21/191.71 & ! [B_i] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i) ) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_nth__zip,axiom,
% 191.21/191.71 ! [V_ys,T_b,V_xs,T_a,V_i] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => ( 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)))
% 191.21/191.71 => 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)) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_elem__le__listsum__nat,axiom,
% 191.21/191.71 ! [V_ns,V_k] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => 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))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_nth__mem,axiom,
% 191.21/191.71 ! [V_xs_2,T_b,V_n_2] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => 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))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_in__set__conv__nth,axiom,
% 191.21/191.71 ! [V_xs_2,V_x_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.71 <=> ? [B_i] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 & hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = V_x_2 ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_nth__Cons_H,axiom,
% 191.21/191.71 ! [V_xs,V_x,T_a,V_n] :
% 191.21/191.71 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 191.21/191.71 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x )
% 191.21/191.71 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 191.21/191.71 => 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))) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_set__conv__nth,axiom,
% 191.21/191.71 ! [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))))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_nth__Cons__number__of,axiom,
% 191.21/191.71 ! [V_xs,V_x,T_a,V_v] :
% 191.21/191.71 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 191.21/191.71 => 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 )
% 191.21/191.71 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 191.21/191.71 => 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))) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listsum__setsum__nth,axiom,
% 191.21/191.71 ! [V_xs_2,T_b] :
% 191.21/191.71 ( class_Groups_Ocomm__monoid__add(T_b)
% 191.21/191.71 => 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))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_set__sublist,axiom,
% 191.21/191.71 ! [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))))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listrel__iff__nth,axiom,
% 191.21/191.71 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 191.21/191.71 <=> ( 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)
% 191.21/191.71 & ! [B_n] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => 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)) ) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_set__zip,axiom,
% 191.21/191.71 ! [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)))))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_insort__insert__insort__key,axiom,
% 191.21/191.71 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 191.21/191.71 ( class_Orderings_Olinorder(T_b)
% 191.21/191.71 => ( ~ 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))))
% 191.21/191.71 => 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) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_distinct__list__update,axiom,
% 191.21/191.71 ! [V_i_2,V_a_2,V_xs_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 191.21/191.71 => ( ~ 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))))))
% 191.21/191.71 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_a_2))) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_nth__list__update__neq,axiom,
% 191.21/191.71 ! [V_x,V_xs,T_a,V_j,V_i] :
% 191.21/191.71 ( V_i != V_j
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_list__update__id,axiom,
% 191.21/191.71 ! [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 ).
% 191.21/191.71
% 191.21/191.71 fof(fact_list__update__code_I1_J,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_list__update_Osimps_I1_J,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_list__update__nonempty,axiom,
% 191.21/191.71 ! [V_x_2,V_k_2,V_xs_2,T_b] :
% 191.21/191.71 ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_b)
% 191.21/191.71 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_zip__update,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_update__zip,axiom,
% 191.21/191.71 ! [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))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_length__list__update,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_list__update__overwrite,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_list__update__swap,axiom,
% 191.21/191.71 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] :
% 191.21/191.71 ( V_i != V_i_H
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_distinct__insort__insert,axiom,
% 191.21/191.71 ! [V_x_2,V_f_2,V_xs_2,T_b,T_c] :
% 191.21/191.71 ( class_Orderings_Olinorder(T_c)
% 191.21/191.71 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 191.21/191.71 => 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))) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_list__update__beyond,axiom,
% 191.21/191.71 ! [V_x,V_i,V_xs,T_a] :
% 191.21/191.71 ( 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))
% 191.21/191.71 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__update,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_list__update__code_I3_J,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_list__update__code_I2_J,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_list__update_Osimps_I2_J,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_set__update__subsetI,axiom,
% 191.21/191.71 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_b] :
% 191.21/191.71 ( 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))
% 191.21/191.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.21/191.71 => 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)) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_set__update__subset__insert,axiom,
% 191.21/191.71 ! [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)))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_nth__list__update,axiom,
% 191.21/191.71 ! [V_x,V_j,V_xs,T_a,V_i] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => ( ( V_i = V_j
% 191.21/191.71 => 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 )
% 191.21/191.71 & ( V_i != V_j
% 191.21/191.71 => 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) ) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_list__update__same__conv,axiom,
% 191.21/191.71 ! [V_x_2,V_xs_2,T_b,V_i_2] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) = V_xs_2
% 191.21/191.71 <=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = V_x_2 ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_nth__list__update__eq,axiom,
% 191.21/191.71 ! [V_x,V_xs,T_a,V_i] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => 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 ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_set__update__memI,axiom,
% 191.21/191.71 ! [V_x_2,V_xs_2,T_b,V_n_2] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => 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)))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_insort__insert__triv,axiom,
% 191.21/191.71 ! [V_xs_2,V_x_2,T_b] :
% 191.21/191.71 ( class_Orderings_Olinorder(T_b)
% 191.21/191.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.71 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_set__insort__insert,axiom,
% 191.21/191.71 ! [V_xs_2,V_x_2,T_b] :
% 191.21/191.71 ( class_Orderings_Olinorder(T_b)
% 191.21/191.71 => 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)) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listsum__update__nat,axiom,
% 191.21/191.71 ! [V_n,V_ns,V_k] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => 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)) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_insort__insert__key__triv,axiom,
% 191.21/191.71 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 191.21/191.71 ( class_Orderings_Olinorder(T_b)
% 191.21/191.71 => ( 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))))
% 191.21/191.71 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_insort__insert__insort,axiom,
% 191.21/191.71 ! [V_xs_2,V_x_2,T_b] :
% 191.21/191.71 ( class_Orderings_Olinorder(T_b)
% 191.21/191.71 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.71 => 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) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_sublist__Cons,axiom,
% 191.21/191.71 ! [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)))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_lexord__cons__cons,axiom,
% 191.21/191.71 ! [V_r_2,V_y_2,V_ba_2,V_x_2,V_a_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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_ba_2),V_y_2))),c_List_Olexord(T_b,V_r_2)))
% 191.21/191.71 <=> ( 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_ba_2)),V_r_2))
% 191.21/191.71 | ( V_a_2 = V_ba_2
% 191.21/191.71 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_nth__append__length,axiom,
% 191.21/191.71 ! [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 ).
% 191.21/191.71
% 191.21/191.71 fof(fact_nth__append__length__plus,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_zip__append,axiom,
% 191.21/191.71 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] :
% 191.21/191.71 ( 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)
% 191.21/191.71 => ( 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)
% 191.21/191.71 => 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)) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_length__append,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_list__update__append1,axiom,
% 191.21/191.71 ! [V_x,V_ys,V_xs,T_a,V_i] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_list__update__length,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_remove1__append,axiom,
% 191.21/191.71 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 191.21/191.71 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.71 => 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) )
% 191.21/191.71 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.71 => 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)) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_append__eq__Cons__conv,axiom,
% 191.21/191.71 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_b] :
% 191.21/191.71 ( 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)
% 191.21/191.71 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 191.21/191.71 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) )
% 191.21/191.71 | ? [B_ys_H] :
% 191.21/191.71 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H)
% 191.21/191.71 & hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_Cons__eq__append__conv,axiom,
% 191.21/191.71 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_b] :
% 191.21/191.71 ( 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)
% 191.21/191.71 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 191.21/191.71 & hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = V_zs_2 )
% 191.21/191.71 | ? [B_ys_H] :
% 191.21/191.71 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) = V_ys_2
% 191.21/191.71 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) ) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_append1__eq__conv,axiom,
% 191.21/191.71 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 <=> ( V_xs_2 = V_ys_2
% 191.21/191.71 & V_x_2 = V_y_2 ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_lexord__append__left__rightI,axiom,
% 191.21/191.71 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_ba_2,V_a_2,T_b] :
% 191.21/191.71 ( 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_ba_2)),V_r_2))
% 191.21/191.71 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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_ba_2),V_y_2)))),c_List_Olexord(T_b,V_r_2))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_append__Cons,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_Cons__eq__appendI,axiom,
% 191.21/191.71 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] :
% 191.21/191.71 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys
% 191.21/191.71 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs)
% 191.21/191.71 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listsum__append,axiom,
% 191.21/191.71 ! [V_ys,V_xs,T_a] :
% 191.21/191.71 ( class_Groups_Omonoid__add(T_a)
% 191.21/191.71 => 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)) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__append,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_set__append,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_append__eq__appendI,axiom,
% 191.21/191.71 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] :
% 191.21/191.71 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs
% 191.21/191.71 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us)
% 191.21/191.71 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_append__same__eq,axiom,
% 191.21/191.71 ! [V_zs_2,V_xs_2,V_ys_2,T_b] :
% 191.21/191.71 ( 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)
% 191.21/191.71 <=> V_ys_2 = V_zs_2 ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_same__append__eq,axiom,
% 191.21/191.71 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 191.21/191.71 ( 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)
% 191.21/191.71 <=> V_ys_2 = V_zs_2 ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_append__eq__append__conv2,axiom,
% 191.21/191.71 ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_b] :
% 191.21/191.71 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_ts_2)
% 191.21/191.71 <=> ? [B_us] :
% 191.21/191.71 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us)
% 191.21/191.71 & hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) = V_ts_2 )
% 191.21/191.71 | ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) = V_zs_2
% 191.21/191.71 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ts_2) ) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_append__assoc,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__of__append,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_foldr__append,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_lexord__append__leftI,axiom,
% 191.21/191.71 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 191.21/191.71 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_append__Nil,axiom,
% 191.21/191.71 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ).
% 191.21/191.71
% 191.21/191.71 fof(fact_Nil__is__append__conv,axiom,
% 191.21/191.71 ! [V_ys_2,V_xs_2,T_b] :
% 191.21/191.71 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 191.21/191.71 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 191.21/191.71 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_append__Nil2,axiom,
% 191.21/191.71 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ).
% 191.21/191.71
% 191.21/191.71 fof(fact_self__append__conv,axiom,
% 191.21/191.71 ! [V_ys_2,T_b,V_xs_2] :
% 191.21/191.71 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 191.21/191.71 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_self__append__conv2,axiom,
% 191.21/191.71 ! [V_xs_2,T_b,V_ys_2] :
% 191.21/191.71 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 191.21/191.71 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_append__is__Nil__conv,axiom,
% 191.21/191.71 ! [V_ys_2,V_xs_2,T_b] :
% 191.21/191.71 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_b)
% 191.21/191.71 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 191.21/191.71 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_append__self__conv,axiom,
% 191.21/191.71 ! [V_ys_2,V_xs_2,T_b] :
% 191.21/191.71 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_xs_2
% 191.21/191.71 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_append__self__conv2,axiom,
% 191.21/191.71 ! [V_ys_2,V_xs_2,T_b] :
% 191.21/191.71 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_ys_2
% 191.21/191.71 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_eq__Nil__appendI,axiom,
% 191.21/191.71 ! [T_a,V_ys,V_xs] :
% 191.21/191.71 ( V_xs = V_ys
% 191.21/191.71 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_distinct__append,axiom,
% 191.21/191.71 ! [V_ys_2,V_xs_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
% 191.21/191.71 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 191.21/191.71 & hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 191.21/191.71 & 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)) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_nth__append,axiom,
% 191.21/191.71 ! [V_ys,V_xs,T_a,V_n] :
% 191.21/191.71 ( ( 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)))
% 191.21/191.71 => 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) )
% 191.21/191.71 & ( ~ 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)))
% 191.21/191.71 => 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))) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_list__update__append,axiom,
% 191.21/191.71 ! [V_x,V_ys,V_xs,T_a,V_n] :
% 191.21/191.71 ( ( 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)))
% 191.21/191.71 => 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) )
% 191.21/191.71 & ( ~ 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)))
% 191.21/191.71 => 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)) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_lexord__Nil__right,axiom,
% 191.21/191.71 ! [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))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_sublist__append,axiom,
% 191.21/191.71 ! [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)))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_lexord__lex,axiom,
% 191.21/191.71 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 191.21/191.71 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 191.21/191.71 & 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) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__upds__append1,axiom,
% 191.21/191.71 ! [V_x_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => 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)))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_lexord__take__index__conv,axiom,
% 191.21/191.71 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 191.21/191.71 <=> ( ( 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)))
% 191.21/191.71 & 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 )
% 191.21/191.71 | ? [B_i] :
% 191.21/191.71 ( 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))))
% 191.21/191.71 & hAPP(hAPP(c_List_Otake(T_b),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_b),B_i),V_y_2)
% 191.21/191.71 & 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)) ) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_take__append,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_fun__upds__append__drop,axiom,
% 191.21/191.71 ! [V_zs_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] :
% 191.21/191.71 ( 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)
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_fun__upds__append2__drop,axiom,
% 191.21/191.71 ! [V_zs_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] :
% 191.21/191.71 ( 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)
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__upds__Nil2,axiom,
% 191.21/191.71 ! [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 ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__upds__Nil1,axiom,
% 191.21/191.71 ! [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 ).
% 191.21/191.71
% 191.21/191.71 fof(fact_take__Nil,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_take__eq__Nil,axiom,
% 191.21/191.71 ! [V_xs_2,V_n_2,T_b] :
% 191.21/191.71 ( hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 191.21/191.71 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 191.21/191.71 | V_xs_2 = c_List_Olist_ONil(T_b) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_take__0,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_sublist__upt__eq__take,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_take__zip,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_take__take,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__add__upds,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_distinct__take,axiom,
% 191.21/191.71 ! [V_i,V_xs,T_a] :
% 191.21/191.71 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 191.21/191.71 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_set__take__subset,axiom,
% 191.21/191.71 ! [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))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_set__take__subset__set__take,axiom,
% 191.21/191.71 ! [V_xs_2,T_b,V_n_2,V_m_2] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 191.21/191.71 => 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)))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_in__set__takeD,axiom,
% 191.21/191.71 ! [V_xs_2,V_n_2,V_x_2,T_b] :
% 191.21/191.71 ( 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))))
% 191.21/191.71 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__upds__apply__nontin,axiom,
% 191.21/191.71 ! [V_ys_2,V_f_2,T_c,V_xs_2,V_x_2,T_b] :
% 191.21/191.71 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_take__map,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_take__Suc__Cons,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_take__1__Cons,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__upd__upds__conv__if,axiom,
% 191.21/191.71 ! [V_y_2,V_f_2,V_xs_2,V_ys_2,T_c,V_x_2,T_b] :
% 191.21/191.71 ( ( 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))))
% 191.21/191.71 => 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) )
% 191.21/191.71 & ( ~ 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))))
% 191.21/191.71 => 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)) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_dom__map__upds,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_take__all,axiom,
% 191.21/191.71 ! [V_n,V_xs,T_a] :
% 191.21/191.71 ( 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))
% 191.21/191.71 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_length__take,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_nth__take,axiom,
% 191.21/191.71 ! [V_xs,T_a,V_n,V_i] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__upds__Cons,axiom,
% 191.21/191.71 ! [V_bs_2,V_ba_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_ba_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_ba_2)),V_as_2,V_bs_2) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_take__Cons,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_take__Cons_H,axiom,
% 191.21/191.71 ! [V_xs,V_x,T_a,V_n] :
% 191.21/191.71 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 191.21/191.71 => 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) )
% 191.21/191.71 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 191.21/191.71 => 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)) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__upds__list__update2__drop,axiom,
% 191.21/191.71 ! [V_y_2,V_m_2,V_ys_2,T_c,V_i_2,V_xs_2,T_b] :
% 191.21/191.71 ( 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))
% 191.21/191.71 => ( 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)))
% 191.21/191.71 => 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) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__upds__twist,axiom,
% 191.21/191.71 ! [V_bs_2,V_ba_2,V_m_2,T_c,V_as_2,V_a_2,T_b] :
% 191.21/191.71 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_as_2)))
% 191.21/191.71 => 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_ba_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_ba_2)) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_take__Cons__number__of,axiom,
% 191.21/191.71 ! [V_xs,V_x,T_a,V_v] :
% 191.21/191.71 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 191.21/191.71 => 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) )
% 191.21/191.71 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 191.21/191.71 => 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)) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_restrict__map__upds,axiom,
% 191.21/191.71 ! [V_m_2,V_D_2,V_ys_2,T_c,V_xs_2,T_b] :
% 191.21/191.71 ( 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)
% 191.21/191.71 => ( 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))
% 191.21/191.71 => 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) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_take__Suc__conv__app__nth,axiom,
% 191.21/191.71 ! [V_xs,T_a,V_i] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => 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))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_snoc__listrel1__snoc__iff,axiom,
% 191.21/191.71 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 191.21/191.71 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 191.21/191.71 & V_x_2 = V_y_2 )
% 191.21/191.71 | ( V_xs_2 = V_ys_2
% 191.21/191.71 & hBOOL(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)) ) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_lexord__append__leftD,axiom,
% 191.21/191.71 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 191.21/191.71 => ( ! [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))
% 191.21/191.71 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_Cons__acc__listrel1I,axiom,
% 191.21/191.71 ! [V_xs_2,V_r_2,V_x_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 191.21/191.71 => ( 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))))
% 191.21/191.71 => 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)))) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listrel1__mono,axiom,
% 191.21/191.71 ! [V_s_2,V_r_2,T_b] :
% 191.21/191.71 ( 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))
% 191.21/191.71 => 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))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
% 191.21/191.71 ! [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)))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listrel1__converse,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listrel__subset__rtrancl__listrel1,axiom,
% 191.21/191.71 ! [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)))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listrel1I2,axiom,
% 191.21/191.71 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 191.21/191.71 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_rtrancl__listrel1__ConsI1,axiom,
% 191.21/191.71 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 191.21/191.71 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listrel1__eq__len,axiom,
% 191.21/191.71 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_rtrancl__listrel1__eq__len,axiom,
% 191.21/191.71 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_not__Nil__listrel1,axiom,
% 191.21/191.71 ! [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))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_not__listrel1__Nil,axiom,
% 191.21/191.71 ! [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))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_append__listrel1I,axiom,
% 191.21/191.71 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 191.21/191.71 ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 191.21/191.71 & V_us_2 = V_vs_2 )
% 191.21/191.71 | ( V_xs_2 = V_ys_2
% 191.21/191.71 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) )
% 191.21/191.71 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_in__listrel1__converse,axiom,
% 191.21/191.71 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 191.21/191.71 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_rtrancl__listrel1__if__listrel,axiom,
% 191.21/191.71 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 191.21/191.71 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listrel__reflcl__if__listrel1,axiom,
% 191.21/191.71 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 191.21/191.71 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_Cons__listrel1__Cons,axiom,
% 191.21/191.71 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 191.21/191.71 <=> ( ( hBOOL(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))
% 191.21/191.71 & V_xs_2 = V_ys_2 )
% 191.21/191.71 | ( V_x_2 = V_y_2
% 191.21/191.71 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listrel1I1,axiom,
% 191.21/191.71 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 191.21/191.71 ( hBOOL(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))
% 191.21/191.71 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listrel1__subset__listrel,axiom,
% 191.21/191.71 ! [V_r_H_2,V_r_2,T_b] :
% 191.21/191.71 ( 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))
% 191.21/191.71 => ( c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_r_H_2)
% 191.21/191.71 => 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))) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listrel1I,axiom,
% 191.21/191.71 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 191.21/191.71 ( hBOOL(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))
% 191.21/191.71 => ( 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))
% 191.21/191.71 => ( 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))
% 191.21/191.71 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_rtrancl__listrel1__ConsI2,axiom,
% 191.21/191.71 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 191.21/191.71 ( hBOOL(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)))
% 191.21/191.71 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 191.21/191.71 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listrel1__iff__update,axiom,
% 191.21/191.71 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 191.21/191.71 <=> ? [B_y,B_n] :
% 191.21/191.71 ( 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))
% 191.21/191.71 & 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)))
% 191.21/191.71 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listrel1E,axiom,
% 191.21/191.71 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 191.21/191.71 => ~ ! [B_x,B_y] :
% 191.21/191.71 ( 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))
% 191.21/191.71 => ! [B_us,B_vs] :
% 191.21/191.71 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_vs))
% 191.21/191.71 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_vs)) ) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_rotate1__def,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_upd__conv__take__nth__drop,axiom,
% 191.21/191.71 ! [V_a,V_xs,T_a,V_i] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => 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))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_set__drop__subset__set__drop,axiom,
% 191.21/191.71 ! [V_xs_2,T_b,V_m_2,V_n_2] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2))
% 191.21/191.71 => 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)))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_drop__eq__Nil,axiom,
% 191.21/191.71 ! [V_xs_2,V_n_2,T_b] :
% 191.21/191.71 ( hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 191.21/191.71 <=> 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)) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_drop__all,axiom,
% 191.21/191.71 ! [V_n,V_xs,T_a] :
% 191.21/191.71 ( 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))
% 191.21/191.71 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_nth__via__drop,axiom,
% 191.21/191.71 ! [V_ys,V_y,V_xs,V_n,T_a] :
% 191.21/191.71 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)
% 191.21/191.71 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_length__drop,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_length__rotate1,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_drop__1__Cons,axiom,
% 191.21/191.71 ! [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 ).
% 191.21/191.71
% 191.21/191.71 fof(fact_drop__Suc__Cons,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_drop__map,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_in__set__dropD,axiom,
% 191.21/191.71 ! [V_xs_2,V_n_2,V_x_2,T_b] :
% 191.21/191.71 ( 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))))
% 191.21/191.71 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_set__rotate1,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_set__drop__subset,axiom,
% 191.21/191.71 ! [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))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_distinct1__rotate,axiom,
% 191.21/191.71 ! [V_xs_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)))
% 191.21/191.71 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_distinct__drop,axiom,
% 191.21/191.71 ! [V_i,V_xs,T_a] :
% 191.21/191.71 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 191.21/191.71 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_drop__drop,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_drop__0,axiom,
% 191.21/191.71 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ).
% 191.21/191.71
% 191.21/191.71 fof(fact_drop__zip,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_drop__Nil,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_rotate1__is__Nil__conv,axiom,
% 191.21/191.71 ! [V_xs_2,T_b] :
% 191.21/191.71 ( hAPP(c_List_Orotate1(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 191.21/191.71 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_drop__append,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_take__drop,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_drop__take,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_append__take__drop__id,axiom,
% 191.21/191.71 ! [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 ).
% 191.21/191.71
% 191.21/191.71 fof(fact_append__eq__conv__conj,axiom,
% 191.21/191.71 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 191.21/191.71 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_zs_2
% 191.21/191.71 <=> ( 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)
% 191.21/191.71 & 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) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_drop__Cons,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_drop__Cons_H,axiom,
% 191.21/191.71 ! [V_xs,V_x,T_a,V_n] :
% 191.21/191.71 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 191.21/191.71 => 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) )
% 191.21/191.71 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 191.21/191.71 => 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) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_nth__drop,axiom,
% 191.21/191.71 ! [V_xs,T_a,V_i,V_n] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => 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)) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_append__eq__append__conv__if,axiom,
% 191.21/191.71 ! [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] :
% 191.21/191.71 ( 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)
% 191.21/191.71 <=> ( ( 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)))
% 191.21/191.71 => ( 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)
% 191.21/191.71 & 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) ) )
% 191.21/191.71 & ( ~ 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)))
% 191.21/191.71 => ( 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
% 191.21/191.71 & 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 ) ) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_nth__drop_H,axiom,
% 191.21/191.71 ! [V_xs,T_a,V_i] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_rotate__simps,axiom,
% 191.21/191.71 ! [V_xs,V_x,T_b,T_a] :
% 191.21/191.71 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a)
% 191.21/191.71 & 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))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_drop__Cons__number__of,axiom,
% 191.21/191.71 ! [V_xs,V_x,T_a,V_v] :
% 191.21/191.71 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 191.21/191.71 => 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) )
% 191.21/191.71 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 191.21/191.71 => 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) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_take__add,axiom,
% 191.21/191.71 ! [V_xs,T_a,V_j,V_i] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => 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))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_rotate1__length01,axiom,
% 191.21/191.71 ! [V_xs,T_a] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_zip__append1,axiom,
% 191.21/191.71 ! [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))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_zip__append2,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_id__take__nth__drop,axiom,
% 191.21/191.71 ! [V_xs,T_a,V_i] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => 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))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_take__hd__drop,axiom,
% 191.21/191.71 ! [V_xs,T_a,V_n] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_hd__drop__conv__nth,axiom,
% 191.21/191.71 ! [V_n,T_a,V_xs] :
% 191.21/191.71 ( V_xs != c_List_Olist_ONil(T_a)
% 191.21/191.71 => ( 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)))
% 191.21/191.71 => 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) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_hd__map,axiom,
% 191.21/191.71 ! [V_f_2,T_c,T_b,V_xs_2] :
% 191.21/191.71 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 191.21/191.71 => 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)) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_hd_Osimps,axiom,
% 191.21/191.71 ! [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 ).
% 191.21/191.71
% 191.21/191.71 fof(fact_hd__append2,axiom,
% 191.21/191.71 ! [V_ys,T_a,V_xs] :
% 191.21/191.71 ( V_xs != c_List_Olist_ONil(T_a)
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_hd__append,axiom,
% 191.21/191.71 ! [V_ys,T_a,V_xs] :
% 191.21/191.71 ( ( V_xs = c_List_Olist_ONil(T_a)
% 191.21/191.71 => 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) )
% 191.21/191.71 & ( V_xs != c_List_Olist_ONil(T_a)
% 191.21/191.71 => 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) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_hd__in__set,axiom,
% 191.21/191.71 ! [T_b,V_xs_2] :
% 191.21/191.71 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 191.21/191.71 => 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))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_hd__conv__nth,axiom,
% 191.21/191.71 ! [T_a,V_xs] :
% 191.21/191.71 ( V_xs != c_List_Olist_ONil(T_a)
% 191.21/191.71 => 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)) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_rotate1__hd__tl,axiom,
% 191.21/191.71 ! [T_a,V_xs] :
% 191.21/191.71 ( V_xs != c_List_Olist_ONil(T_a)
% 191.21/191.71 => 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))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_hd__rotate__conv__nth,axiom,
% 191.21/191.71 ! [V_n,T_a,V_xs] :
% 191.21/191.71 ( V_xs != c_List_Olist_ONil(T_a)
% 191.21/191.71 => 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))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_drop__Suc,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_drop__tl,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_tl__drop,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_tl__append2,axiom,
% 191.21/191.71 ! [V_ys,T_a,V_xs] :
% 191.21/191.71 ( V_xs != c_List_Olist_ONil(T_a)
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_length__rotate,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_rotate__conv__mod,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_tl_Osimps_I2_J,axiom,
% 191.21/191.71 ! [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 ).
% 191.21/191.71
% 191.21/191.71 fof(fact_rotate__map,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__tl,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_set__rotate,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_distinct__rotate,axiom,
% 191.21/191.71 ! [V_xs_2,V_n_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)))
% 191.21/191.71 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_distinct__tl,axiom,
% 191.21/191.71 ! [V_xs,T_a] :
% 191.21/191.71 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 191.21/191.71 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_rotate__rotate,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_tl_Osimps_I1_J,axiom,
% 191.21/191.71 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_rotate__is__Nil__conv,axiom,
% 191.21/191.71 ! [V_xs_2,V_n_2,T_b] :
% 191.21/191.71 ( hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 191.21/191.71 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_take__tl,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_rotate__def,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_rotate__Suc,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_rotate1__rotate__swap,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_tl__append,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_rotate0,axiom,
% 191.21/191.71 ! [T_b] : c_List_Orotate(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_rotate__add,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_rotate__id,axiom,
% 191.21/191.71 ! [V_xs,T_a,V_n] :
% 191.21/191.71 ( 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)
% 191.21/191.71 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_rotate__length01,axiom,
% 191.21/191.71 ! [V_n,V_xs,T_a] :
% 191.21/191.71 ( 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)))
% 191.21/191.71 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_length__tl,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_tl__take,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_take__Suc,axiom,
% 191.21/191.71 ! [V_n,T_a,V_xs] :
% 191.21/191.71 ( V_xs != c_List_Olist_ONil(T_a)
% 191.21/191.71 => 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))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_rotate__drop__take,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_fold1__set,axiom,
% 191.21/191.71 ! [V_xs_2,T_b] :
% 191.21/191.71 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 191.21/191.71 => ( V_xs_2 != c_List_Olist_ONil(T_b)
% 191.21/191.71 => 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)) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_list_Osize_I2_J,axiom,
% 191.21/191.71 ! [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))) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_foldl__Nil,axiom,
% 191.21/191.71 ! [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 ).
% 191.21/191.71
% 191.21/191.71 fof(fact_foldr__conv__foldl,axiom,
% 191.21/191.71 ! [V_a_2,V_xs_2,T_b] :
% 191.21/191.71 ( class_Groups_Oab__semigroup__add(T_b)
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_foldl__absorb0,axiom,
% 191.21/191.71 ! [V_zs_2,V_x_2,T_b] :
% 191.21/191.71 ( class_Groups_Omonoid__add(T_b)
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_foldl__assoc,axiom,
% 191.21/191.71 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 191.21/191.71 ( class_Groups_Osemigroup__add(T_b)
% 191.21/191.71 => 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)) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_start__le__sum,axiom,
% 191.21/191.71 ! [V_ns_2,V_n_2,V_m_2] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 191.21/191.71 => 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))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_foldl__map,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_list__size__map,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_foldl__Cons,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_foldl__append,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_listsum__foldl,axiom,
% 191.21/191.71 ! [T_b] :
% 191.21/191.71 ( class_Groups_Omonoid__add(T_b)
% 191.21/191.71 => 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)) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_foldl__foldr1,axiom,
% 191.21/191.71 ! [V_xs_2,T_b] :
% 191.21/191.71 ( class_Groups_Omonoid__add(T_b)
% 191.21/191.71 => 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)) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_foldl__foldr1__lemma,axiom,
% 191.21/191.71 ! [V_xs_2,V_a_2,T_b] :
% 191.21/191.71 ( class_Groups_Omonoid__add(T_b)
% 191.21/191.71 => 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))) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_sum__eq__0__conv,axiom,
% 191.21/191.71 ! [V_ns_2,V_m_2] :
% 191.21/191.71 ( 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)
% 191.21/191.71 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 191.21/191.71 & ! [B_x] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 191.21/191.71 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_list_Osize_I1_J,axiom,
% 191.21/191.71 ! [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) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_fun__left__comm__idem_Ofold__set,axiom,
% 191.21/191.71 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
% 191.21/191.71 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_Sup__set__fold,axiom,
% 191.21/191.71 ! [V_xs_2,T_b] :
% 191.21/191.71 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_Inf__set__fold,axiom,
% 191.21/191.71 ! [V_xs_2,T_b] :
% 191.21/191.71 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_Sup__fin__set__fold,axiom,
% 191.21/191.71 ! [V_xs_2,V_x_2,T_b] :
% 191.21/191.71 ( class_Lattices_Olattice(T_b)
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_Inf__fin__set__fold,axiom,
% 191.21/191.71 ! [V_xs_2,V_x_2,T_b] :
% 191.21/191.71 ( class_Lattices_Olattice(T_b)
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_Min__fin__set__fold,axiom,
% 191.21/191.71 ! [V_xs_2,V_x_2,T_b] :
% 191.21/191.71 ( class_Orderings_Olinorder(T_b)
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_Max__fin__set__fold,axiom,
% 191.21/191.71 ! [V_xs_2,V_x_2,T_b] :
% 191.21/191.71 ( class_Orderings_Olinorder(T_b)
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_min__max_OInf__fin__set__fold,axiom,
% 191.21/191.71 ! [V_xs_2,V_x_2,T_b] :
% 191.21/191.71 ( class_Orderings_Olinorder(T_b)
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_min__max_OSup__fin__set__fold,axiom,
% 191.21/191.71 ! [V_xs_2,V_x_2,T_b] :
% 191.21/191.71 ( class_Orderings_Olinorder(T_b)
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_SUPR__set__fold,axiom,
% 191.21/191.71 ! [V_f_2,V_xs_2,T_c,T_b] :
% 191.21/191.71 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_INFI__set__fold,axiom,
% 191.21/191.71 ! [V_f_2,V_xs_2,T_c,T_b] :
% 191.21/191.71 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 191.21/191.71 => 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) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_list__size__estimation,axiom,
% 191.21/191.71 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 191.21/191.71 => 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))) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_list__size__estimation_H,axiom,
% 191.21/191.71 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 191.21/191.71 => 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))) ) ) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_map__upds__fold__map__upd,axiom,
% 191.21/191.71 ! [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)) ).
% 191.21/191.71
% 191.21/191.71 fof(fact_elem__le__sum,axiom,
% 191.21/191.71 ! [V_ns_2,V_n_2] :
% 191.21/191.71 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 191.21/191.72 => 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))) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_list__size__conv__listsum,axiom,
% 191.21/191.72 ! [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)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_listrel__subset,axiom,
% 191.21/191.72 ! [V_A_2,V_r_2,T_b] :
% 191.21/191.72 ( 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))))
% 191.21/191.72 => 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))))) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_lists__accI,axiom,
% 191.21/191.72 ! [V_r_2,V_xs_2,T_b] :
% 191.21/191.72 ( 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))))
% 191.21/191.72 => 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)))) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_lists_ONil,axiom,
% 191.21/191.72 ! [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))) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_equiv__listrel,axiom,
% 191.21/191.72 ! [V_r_2,V_A_2,T_b] :
% 191.21/191.72 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 191.21/191.72 => 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)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_listrel__refl__on,axiom,
% 191.21/191.72 ! [V_r_2,V_A_2,T_b] :
% 191.21/191.72 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 191.21/191.72 => 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)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_lists__UNIV,axiom,
% 191.21/191.72 ! [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)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_append__in__lists__conv,axiom,
% 191.21/191.72 ! [V_A_2,V_ys_2,V_xs_2,T_b] :
% 191.21/191.72 ( 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)))
% 191.21/191.72 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 191.21/191.72 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_lists__mono,axiom,
% 191.21/191.72 ! [V_B_2,V_A_2,T_b] :
% 191.21/191.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 191.21/191.72 => 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))) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_Cons__in__lists__iff,axiom,
% 191.21/191.72 ! [V_A_2,V_xs_2,V_x_2,T_b] :
% 191.21/191.72 ( 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)))
% 191.21/191.72 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 191.21/191.72 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_in__lists__conv__set,axiom,
% 191.21/191.72 ! [V_A_2,V_xs_2,T_b] :
% 191.21/191.72 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 191.21/191.72 <=> ! [B_x] :
% 191.21/191.72 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.72 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_lists__eq__set,axiom,
% 191.21/191.72 ! [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)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_lists__empty,axiom,
% 191.21/191.72 ! [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))) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_lists__accD,axiom,
% 191.21/191.72 ! [V_r_2,V_xs_2,T_b] :
% 191.21/191.72 ( 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))))
% 191.21/191.72 => 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)))) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_lexord__append__rightI,axiom,
% 191.21/191.72 ! [V_r_2,V_x_2,T_b,V_y_2] :
% 191.21/191.72 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_b),B_z)
% 191.21/191.72 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_lexord__Nil__left,axiom,
% 191.21/191.72 ! [V_r_2,V_y_2,T_b] :
% 191.21/191.72 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 191.21/191.72 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_last__list__update,axiom,
% 191.21/191.72 ! [V_x,V_k,T_a,V_xs] :
% 191.21/191.72 ( V_xs != c_List_Olist_ONil(T_a)
% 191.21/191.72 => ( ( 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))
% 191.21/191.72 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x )
% 191.21/191.72 & ( 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))
% 191.21/191.72 => 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) ) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_listsum__mono,axiom,
% 191.21/191.72 ! [V_g_2,V_f_2,V_xs_2,T_b,T_c] :
% 191.21/191.72 ( ( class_Groups_Omonoid__add(T_c)
% 191.21/191.72 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 191.21/191.72 => ( ! [B_x] :
% 191.21/191.72 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 191.21/191.72 => 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)))) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_last__append,axiom,
% 191.21/191.72 ! [V_xs,T_a,V_ys] :
% 191.21/191.72 ( ( V_ys = c_List_Olist_ONil(T_a)
% 191.21/191.72 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) )
% 191.21/191.72 & ( V_ys != c_List_Olist_ONil(T_a)
% 191.21/191.72 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_last__appendR,axiom,
% 191.21/191.72 ! [V_xs,T_a,V_ys] :
% 191.21/191.72 ( V_ys != c_List_Olist_ONil(T_a)
% 191.21/191.72 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_last__appendL,axiom,
% 191.21/191.72 ! [V_xs,T_a,V_ys] :
% 191.21/191.72 ( V_ys = c_List_Olist_ONil(T_a)
% 191.21/191.72 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_last_Osimps,axiom,
% 191.21/191.72 ! [V_x,T_a,V_xs] :
% 191.21/191.72 ( ( V_xs = c_List_Olist_ONil(T_a)
% 191.21/191.72 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x )
% 191.21/191.72 & ( V_xs != c_List_Olist_ONil(T_a)
% 191.21/191.72 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_last__ConsR,axiom,
% 191.21/191.72 ! [V_x,T_a,V_xs] :
% 191.21/191.72 ( V_xs != c_List_Olist_ONil(T_a)
% 191.21/191.72 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_last__ConsL,axiom,
% 191.21/191.72 ! [V_x,T_a,V_xs] :
% 191.21/191.72 ( V_xs = c_List_Olist_ONil(T_a)
% 191.21/191.72 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_last__map,axiom,
% 191.21/191.72 ! [V_f_2,T_c,T_b,V_xs_2] :
% 191.21/191.72 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 191.21/191.72 => 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)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_last__in__set,axiom,
% 191.21/191.72 ! [T_b,V_as_2] :
% 191.21/191.72 ( V_as_2 != c_List_Olist_ONil(T_b)
% 191.21/191.72 => hBOOL(hAPP(hAPP(c_member(T_b),c_List_Olast(T_b,V_as_2)),hAPP(c_List_Oset(T_b),V_as_2))) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_last__snoc,axiom,
% 191.21/191.72 ! [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 ).
% 191.21/191.72
% 191.21/191.72 fof(fact_last__drop,axiom,
% 191.21/191.72 ! [V_xs,T_a,V_n] :
% 191.21/191.72 ( 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)))
% 191.21/191.72 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_last__conv__nth,axiom,
% 191.21/191.72 ! [T_a,V_xs] :
% 191.21/191.72 ( V_xs != c_List_Olist_ONil(T_a)
% 191.21/191.72 => 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))) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_lexord__linear,axiom,
% 191.21/191.72 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 191.21/191.72 ( ! [B_a,B_b] :
% 191.21/191.72 ( 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))
% 191.21/191.72 | B_a = B_b
% 191.21/191.72 | 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)) )
% 191.21/191.72 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 191.21/191.72 | V_x_2 = V_y_2
% 191.21/191.72 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_lexord__irreflexive,axiom,
% 191.21/191.72 ! [V_y_2,V_r_2,T_b] :
% 191.21/191.72 ( ! [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))
% 191.21/191.72 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_lists_Osimps,axiom,
% 191.21/191.72 ! [V_A_2,V_a_2,T_b] :
% 191.21/191.72 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2)))
% 191.21/191.72 <=> ( V_a_2 = c_List_Olist_ONil(T_b)
% 191.21/191.72 | ? [B_a,B_l] :
% 191.21/191.72 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l)
% 191.21/191.72 & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 191.21/191.72 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2))) ) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_list__size__pointwise,axiom,
% 191.21/191.72 ! [V_g_2,V_f_2,V_xs_2,T_b] :
% 191.21/191.72 ( ! [B_x] :
% 191.21/191.72 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 191.21/191.72 => 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))) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_butlast__take,axiom,
% 191.21/191.72 ! [V_xs,T_a,V_n] :
% 191.21/191.72 ( 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)))
% 191.21/191.72 => 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) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_nth__take__lemma,axiom,
% 191.21/191.72 ! [V_ys,V_xs,T_a,V_k] :
% 191.21/191.72 ( 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)))
% 191.21/191.72 => ( 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)))
% 191.21/191.72 => ( ! [B_i] :
% 191.21/191.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k))
% 191.21/191.72 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) )
% 191.21/191.72 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_map__butlast,axiom,
% 191.21/191.72 ! [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)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_distinct__butlast,axiom,
% 191.21/191.72 ! [T_a,V_xs] :
% 191.21/191.72 ( V_xs != c_List_Olist_ONil(T_a)
% 191.21/191.72 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 191.21/191.72 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_butlast_Osimps_I1_J,axiom,
% 191.21/191.72 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_in__set__butlastD,axiom,
% 191.21/191.72 ! [V_xs_2,V_x_2,T_b] :
% 191.21/191.72 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 191.21/191.72 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_butlast_Osimps_I2_J,axiom,
% 191.21/191.72 ! [V_x,T_a,V_xs] :
% 191.21/191.72 ( ( V_xs = c_List_Olist_ONil(T_a)
% 191.21/191.72 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) )
% 191.21/191.72 & ( V_xs != c_List_Olist_ONil(T_a)
% 191.21/191.72 => 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)) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_butlast__append,axiom,
% 191.21/191.72 ! [V_xs,T_a,V_ys] :
% 191.21/191.72 ( ( V_ys = c_List_Olist_ONil(T_a)
% 191.21/191.72 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) )
% 191.21/191.72 & ( V_ys != c_List_Olist_ONil(T_a)
% 191.21/191.72 => 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)) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_butlast__drop,axiom,
% 191.21/191.72 ! [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)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_drop__butlast,axiom,
% 191.21/191.72 ! [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)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_in__set__butlast__appendI,axiom,
% 191.21/191.72 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 191.21/191.72 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 191.21/191.72 | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_ys_2)))) )
% 191.21/191.72 => 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))))) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_butlast__snoc,axiom,
% 191.21/191.72 ! [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 ).
% 191.21/191.72
% 191.21/191.72 fof(fact_take__butlast,axiom,
% 191.21/191.72 ! [V_xs,T_a,V_n] :
% 191.21/191.72 ( 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)))
% 191.21/191.72 => 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) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_length__butlast,axiom,
% 191.21/191.72 ! [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)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_butlast__conv__take,axiom,
% 191.21/191.72 ! [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) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_butlast__list__update,axiom,
% 191.21/191.72 ! [V_x,V_xs,T_a,V_k] :
% 191.21/191.72 ( ( 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))
% 191.21/191.72 => 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) )
% 191.21/191.72 & ( 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))
% 191.21/191.72 => 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) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_append__butlast__last__id,axiom,
% 191.21/191.72 ! [T_a,V_xs] :
% 191.21/191.72 ( V_xs != c_List_Olist_ONil(T_a)
% 191.21/191.72 => 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 ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_snoc__eq__iff__butlast,axiom,
% 191.21/191.72 ! [V_ys_2,V_x_2,V_xs_2,T_b] :
% 191.21/191.72 ( 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
% 191.21/191.72 <=> ( V_ys_2 != c_List_Olist_ONil(T_b)
% 191.21/191.72 & c_List_Obutlast(T_b,V_ys_2) = V_xs_2
% 191.21/191.72 & c_List_Olast(T_b,V_ys_2) = V_x_2 ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_transpose__aux__max,axiom,
% 191.21/191.72 ! [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)))) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_partition__set,axiom,
% 191.21/191.72 ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] :
% 191.21/191.72 ( c_List_Opartition(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2)
% 191.21/191.72 => 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) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_filter__is__subset,axiom,
% 191.21/191.72 ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_length__filter__le,axiom,
% 191.21/191.72 ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_set__filter,axiom,
% 191.21/191.72 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)))),V_Pa_2)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_filter__append,axiom,
% 191.21/191.72 ! [V_ys_2,V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_ys_2)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_sum__length__filter__compl,axiom,
% 191.21/191.72 ! [V_xs_2,V_Pa_2,T_b] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2)),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_filter_Osimps_I2_J,axiom,
% 191.21/191.72 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 191.21/191.72 ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 191.21/191.72 => hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) )
% 191.21/191.72 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 191.21/191.72 => hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_filter__id__conv,axiom,
% 191.21/191.72 ! [V_xs_2,V_Pa_2,T_b] :
% 191.21/191.72 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = V_xs_2
% 191.21/191.72 <=> ! [B_x] :
% 191.21/191.72 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.72 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_filter__insort__triv,axiom,
% 191.21/191.72 ! [V_xs_2,V_f_2,T_b,V_x_2,V_Pa_2,T_c] :
% 191.21/191.72 ( class_Orderings_Olinorder(T_c)
% 191.21/191.72 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 191.21/191.72 => hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_distinct__filter,axiom,
% 191.21/191.72 ! [V_Pa_2,V_xs_2,T_b] :
% 191.21/191.72 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 191.21/191.72 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_filter__remove1,axiom,
% 191.21/191.72 ! [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)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_remove1__filter__not,axiom,
% 191.21/191.72 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 191.21/191.72 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 191.21/191.72 => c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_filter__filter,axiom,
% 191.21/191.72 ! [V_xs_2,V_Q_2,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_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_Pa_2)),V_xs_2) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_partition__filter1,axiom,
% 191.21/191.72 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_Product__Type_Ofst(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_Pa_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_filter__empty__conv,axiom,
% 191.21/191.72 ! [V_xs_2,V_Pa_2,T_b] :
% 191.21/191.72 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 191.21/191.72 <=> ! [B_x] :
% 191.21/191.72 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.72 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_filter_Osimps_I1_J,axiom,
% 191.21/191.72 ! [V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_partition__filter__conv,axiom,
% 191.21/191.72 ! [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)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_partition__filter2,axiom,
% 191.21/191.72 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_Product__Type_Osnd(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_Pa_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_Pa_2)),V_xs_2) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_filter__map,axiom,
% 191.21/191.72 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2)),V_xs_2)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_length__filter__map,axiom,
% 191.21/191.72 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2)),V_xs_2)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_length__filter__less,axiom,
% 191.21/191.72 ! [V_Pa_2,V_xs_2,V_x_2,T_b] :
% 191.21/191.72 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.72 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 191.21/191.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_set__minus__filter__out,axiom,
% 191.21/191.72 ! [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)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_partition__P,axiom,
% 191.21/191.72 ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] :
% 191.21/191.72 ( c_List_Opartition(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2)
% 191.21/191.72 => ( ! [B_x] :
% 191.21/191.72 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_yes_2)))
% 191.21/191.72 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 191.21/191.72 & ! [B_x] :
% 191.21/191.72 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_no_2)))
% 191.21/191.72 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_partition_Osimps_I1_J,axiom,
% 191.21/191.72 ! [V_Pa_2,T_b] : c_List_Opartition(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_filter__in__sublist,axiom,
% 191.21/191.72 ! [V_s_2,V_xs_2,T_b] :
% 191.21/191.72 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 191.21/191.72 => 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) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_partition_Osimps_I2_J,axiom,
% 191.21/191.72 ! [V_xs_2,V_x_2,V_Pa_2,T_b] : c_List_Opartition(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),hAPP(c_If(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(V_Pa_2,V_x_2)))),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_List_Olist_OCons(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_List_Olist(T_b))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(c_List_Olist_OCons(T_b),V_x_2)))),c_List_Opartition(T_b,V_Pa_2,V_xs_2)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_length__filter__conv__card,axiom,
% 191.21/191.72 ! [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))))) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_map__filter__def,axiom,
% 191.21/191.72 ! [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)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_transpose__max__length,axiom,
% 191.21/191.72 ! [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)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_map__of__filter__in,axiom,
% 191.21/191.72 ! [V_Pa_2,V_z_2,V_k_2,V_xs_2,T_b,T_c] :
% 191.21/191.72 ( 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)
% 191.21/191.72 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_k_2),V_z_2))
% 191.21/191.72 => hAPP(c_Map_Omap__of(T_c,T_b,hAPP(c_List_Ofilter(tc_prod(T_c,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_Pa_2)),V_xs_2)),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_z_2) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_transpose__map__map,axiom,
% 191.21/191.72 ! [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)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_map__filter__simps_I1_J,axiom,
% 191.21/191.72 ! [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)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_map__filter__simps_I2_J,axiom,
% 191.21/191.72 ! [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) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_transpose_Osimps_I1_J,axiom,
% 191.21/191.72 ! [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)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_transpose__empty,axiom,
% 191.21/191.72 ! [V_xs_2,T_b] :
% 191.21/191.72 ( c_List_Otranspose(T_b,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_b))
% 191.21/191.72 <=> ! [B_x] :
% 191.21/191.72 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 191.21/191.72 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_transpose_Osimps_I2_J,axiom,
% 191.21/191.72 ! [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) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_sublist__shift__lemma__Suc,axiom,
% 191.21/191.72 ! [V_is_2,V_xs_2,V_Pa_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_Pa_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(T_b,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(T_b,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),V_is_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_Pa_2),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),V_is_2)))) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_select__weigth__drop__zero,axiom,
% 191.21/191.72 ! [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) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_pick__drop__zero,axiom,
% 191.21/191.72 ! [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) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_nth__transpose,axiom,
% 191.21/191.72 ! [V_xs_2,T_b,V_i_2] :
% 191.21/191.72 ( 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))))
% 191.21/191.72 => 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)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_length__transpose,axiom,
% 191.21/191.72 ! [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)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_map__filter__map__filter,axiom,
% 191.21/191.72 ! [V_xs_2,V_Pa_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2)) = c_List_Omap__filter(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,tc_Option_Ooption(T_b),tc_Option_Ooption(T_b)),hAPP(hAPP(c_COMBS(T_c,tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_Option_Ooption(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(T_b),tc_fun(tc_Option_Ooption(T_b),tc_Option_Ooption(T_b))),T_c),c_If(tc_Option_Ooption(T_b))),V_Pa_2)),hAPP(hAPP(c_COMBB(T_b,tc_Option_Ooption(T_b),T_c),c_Option_Ooption_OSome(T_b)),V_f_2))),c_Option_Ooption_ONone(T_b)),V_xs_2) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_insort__key__remove1,axiom,
% 191.21/191.72 ! [V_f_2,V_xs_2,V_a_2,T_b,T_c] :
% 191.21/191.72 ( class_Orderings_Olinorder(T_c)
% 191.21/191.72 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.72 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 191.21/191.72 => ( 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
% 191.21/191.72 => 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 ) ) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_sublist__def,axiom,
% 191.21/191.72 ! [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))))) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_sorted_ONil,axiom,
% 191.21/191.72 ! [T_a] :
% 191.21/191.72 ( class_Orderings_Olinorder(T_a)
% 191.21/191.72 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_sorted__single,axiom,
% 191.21/191.72 ! [V_x,T_a] :
% 191.21/191.72 ( class_Orderings_Olinorder(T_a)
% 191.21/191.72 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_sorted__same,axiom,
% 191.21/191.72 ! [V_xs_2,V_g_2,T_b] :
% 191.21/191.72 ( class_Orderings_Olinorder(T_b)
% 191.21/191.72 => 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)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_sorted__map__same,axiom,
% 191.21/191.72 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 191.21/191.72 ( class_Orderings_Olinorder(T_b)
% 191.21/191.72 => 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))) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_sorted__filter,axiom,
% 191.21/191.72 ! [V_Pa_2,V_xs_2,V_f_2,T_c,T_b] :
% 191.21/191.72 ( class_Orderings_Olinorder(T_b)
% 191.21/191.72 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 191.21/191.72 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2))) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_length__upt,axiom,
% 191.21/191.72 ! [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) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_last__upt,axiom,
% 191.21/191.72 ! [V_j,V_i] :
% 191.21/191.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 191.21/191.72 => 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)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_sorted__butlast,axiom,
% 191.21/191.72 ! [V_xs,T_a] :
% 191.21/191.72 ( class_Orderings_Olinorder(T_a)
% 191.21/191.72 => ( V_xs != c_List_Olist_ONil(T_a)
% 191.21/191.72 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 191.21/191.72 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_take__upt,axiom,
% 191.21/191.72 ! [V_n,V_m,V_i] :
% 191.21/191.72 ( 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))
% 191.21/191.72 => 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)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_upt__conv__Nil,axiom,
% 191.21/191.72 ! [V_i,V_j] :
% 191.21/191.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 191.21/191.72 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_upt__eq__Nil__conv,axiom,
% 191.21/191.72 ! [V_j_2,V_i_2] :
% 191.21/191.72 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat)
% 191.21/191.72 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 191.21/191.72 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_sorted__many__eq,axiom,
% 191.21/191.72 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 191.21/191.72 ( class_Orderings_Olinorder(T_b)
% 191.21/191.72 => ( 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)))
% 191.21/191.72 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 191.21/191.72 & c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)) ) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_sorted__many,axiom,
% 191.21/191.72 ! [V_zs,V_y,V_x,T_a] :
% 191.21/191.72 ( class_Orderings_Olinorder(T_a)
% 191.21/191.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 191.21/191.72 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))
% 191.21/191.72 => 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))) ) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_upt__add__eq__append,axiom,
% 191.21/191.72 ! [V_k,V_j,V_i] :
% 191.21/191.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 191.21/191.72 => 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))) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_upt__Suc__append,axiom,
% 191.21/191.72 ! [V_j,V_i] :
% 191.21/191.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 191.21/191.72 => 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))) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_upt__Suc,axiom,
% 191.21/191.72 ! [V_j,V_i] :
% 191.21/191.72 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 191.21/191.72 => 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))) )
% 191.21/191.72 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 191.21/191.72 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_sorted__Cons,axiom,
% 191.21/191.72 ! [V_xs_2,V_x_2,T_b] :
% 191.21/191.72 ( class_Orderings_Olinorder(T_b)
% 191.21/191.72 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 191.21/191.72 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 191.21/191.72 & ! [B_x] :
% 191.21/191.72 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_sorted__append,axiom,
% 191.21/191.72 ! [V_ys_2,V_xs_2,T_b] :
% 191.21/191.72 ( class_Orderings_Olinorder(T_b)
% 191.21/191.72 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 191.21/191.72 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 191.21/191.72 & c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 191.21/191.72 & ! [B_x] :
% 191.21/191.72 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.72 => ! [B_xa] :
% 191.21/191.72 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2)))
% 191.21/191.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) ) ) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_drop__upt,axiom,
% 191.21/191.72 ! [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) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_sorted__drop,axiom,
% 191.21/191.72 ! [V_n,V_xs,T_a] :
% 191.21/191.72 ( class_Orderings_Olinorder(T_a)
% 191.21/191.72 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 191.21/191.72 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_hd__upt,axiom,
% 191.21/191.72 ! [V_j,V_i] :
% 191.21/191.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 191.21/191.72 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_sorted__insort__insert,axiom,
% 191.21/191.72 ! [V_x_2,V_xs_2,T_b] :
% 191.21/191.72 ( class_Orderings_Olinorder(T_b)
% 191.21/191.72 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 191.21/191.72 => 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)) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_upt__rec,axiom,
% 191.21/191.72 ! [V_j,V_i] :
% 191.21/191.72 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 191.21/191.72 => 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)) )
% 191.21/191.72 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 191.21/191.72 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_upt__conv__Cons,axiom,
% 191.21/191.72 ! [V_j,V_i] :
% 191.21/191.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 191.21/191.72 => 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)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_atLeastLessThan__upt,axiom,
% 191.21/191.72 ! [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)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_set__upt,axiom,
% 191.21/191.72 ! [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) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_sorted__distinct__set__unique,axiom,
% 191.21/191.72 ! [V_ys_2,V_xs_2,T_b] :
% 191.21/191.72 ( class_Orderings_Olinorder(T_b)
% 191.21/191.72 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 191.21/191.72 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 191.21/191.72 => ( c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 191.21/191.72 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 191.21/191.72 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 191.21/191.72 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_sorted__insort,axiom,
% 191.21/191.72 ! [V_xs_2,V_x_2,T_b] :
% 191.21/191.72 ( class_Orderings_Olinorder(T_b)
% 191.21/191.72 => ( 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))
% 191.21/191.72 <=> c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_distinct__upt,axiom,
% 191.21/191.72 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_sorted__remove1,axiom,
% 191.21/191.72 ! [V_a,V_xs,T_a] :
% 191.21/191.72 ( class_Orderings_Olinorder(T_a)
% 191.21/191.72 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 191.21/191.72 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_sorted__upt,axiom,
% 191.21/191.72 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_sorted__upto,axiom,
% 191.21/191.72 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_sorted__list__of__set__range,axiom,
% 191.21/191.72 ! [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) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_upt__0,axiom,
% 191.21/191.72 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_sorted_Oequations_I1_J,axiom,
% 191.21/191.72 ! [T_a] :
% 191.21/191.72 ( class_Orderings_Olinorder(T_a)
% 191.21/191.72 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_sorted__take,axiom,
% 191.21/191.72 ! [V_n,V_xs,T_a] :
% 191.21/191.72 ( class_Orderings_Olinorder(T_a)
% 191.21/191.72 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 191.21/191.72 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_sorted__tl,axiom,
% 191.21/191.72 ! [V_xs,T_a] :
% 191.21/191.72 ( class_Orderings_Olinorder(T_a)
% 191.21/191.72 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 191.21/191.72 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_upt__rec__number__of,axiom,
% 191.21/191.72 ! [V_n,V_m] :
% 191.21/191.72 ( ( 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)))
% 191.21/191.72 => 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))) )
% 191.21/191.72 & ( ~ 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)))
% 191.21/191.72 => 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) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_sorted__insort__key,axiom,
% 191.21/191.72 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 191.21/191.72 ( class_Orderings_Olinorder(T_b)
% 191.21/191.72 => ( 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)))
% 191.21/191.72 <=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_sorted__map__remove1,axiom,
% 191.21/191.72 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 191.21/191.72 ( class_Orderings_Olinorder(T_b)
% 191.21/191.72 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 191.21/191.72 => 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))) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_map__Suc__upt,axiom,
% 191.21/191.72 ! [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)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_sorted__insort__insert__key,axiom,
% 191.21/191.72 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 191.21/191.72 ( class_Orderings_Olinorder(T_b)
% 191.21/191.72 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 191.21/191.72 => 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))) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_upt__eq__Cons__conv,axiom,
% 191.21/191.72 ! [V_xs_2,V_x_2,V_j_2,V_i_2] :
% 191.21/191.72 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2)
% 191.21/191.72 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2))
% 191.21/191.72 & V_i_2 = V_x_2
% 191.21/191.72 & 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 ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_filter__insort,axiom,
% 191.21/191.72 ! [V_x_2,V_Pa_2,V_xs_2,V_f_2,T_c,T_b] :
% 191.21/191.72 ( class_Orderings_Olinorder(T_b)
% 191.21/191.72 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 191.21/191.72 => ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 191.21/191.72 => hAPP(c_List_Ofilter(T_c,V_Pa_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2)) ) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_map__nth,axiom,
% 191.21/191.72 ! [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 ).
% 191.21/191.72
% 191.21/191.72 fof(fact_atLeastAtMost__upt,axiom,
% 191.21/191.72 ! [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))) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_atLeast__upt,axiom,
% 191.21/191.72 ! [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)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
% 191.21/191.72 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 191.21/191.72 ( class_Groups_Ocomm__monoid__add(T_b)
% 191.21/191.72 => 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))) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
% 191.21/191.72 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 191.21/191.72 ( class_Groups_Ocomm__monoid__add(T_b)
% 191.21/191.72 => 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))) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_nth__upt,axiom,
% 191.21/191.72 ! [V_j,V_k,V_i] :
% 191.21/191.72 ( 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))
% 191.21/191.72 => 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) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_greaterThanAtMost__upt,axiom,
% 191.21/191.72 ! [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))) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_sorted_Oequations_I2_J,axiom,
% 191.21/191.72 ! [V_a1_2,V_a2_2,T_b] :
% 191.21/191.72 ( class_Orderings_Olinorder(T_b)
% 191.21/191.72 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2))
% 191.21/191.72 <=> ( ! [B_x] :
% 191.21/191.72 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2)))
% 191.21/191.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x)) )
% 191.21/191.72 & c_List_Olinorder__class_Osorted(T_b,V_a1_2) ) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_greaterThanLessThan__upt,axiom,
% 191.21/191.72 ! [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)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_nth__map__upt,axiom,
% 191.21/191.72 ! [V_f_2,T_b,V_m_2,V_n_2,V_i_2] :
% 191.21/191.72 ( 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)))
% 191.21/191.72 => 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)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_sorted__list__of__set,axiom,
% 191.21/191.72 ! [V_A_2,T_b] :
% 191.21/191.72 ( class_Orderings_Olinorder(T_b)
% 191.21/191.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 191.21/191.72 => ( hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) = V_A_2
% 191.21/191.72 & c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))
% 191.21/191.72 & hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))) ) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_atMost__upto,axiom,
% 191.21/191.72 ! [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))) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_insort__remove1,axiom,
% 191.21/191.72 ! [V_xs_2,V_a_2,T_b] :
% 191.21/191.72 ( class_Orderings_Olinorder(T_b)
% 191.21/191.72 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.72 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 191.21/191.72 => 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 ) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_sorted__nth__mono,axiom,
% 191.21/191.72 ! [V_j,V_i,V_xs,T_a] :
% 191.21/191.72 ( class_Orderings_Olinorder(T_a)
% 191.21/191.72 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 191.21/191.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 191.21/191.72 => ( 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)))
% 191.21/191.72 => 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))) ) ) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_sorted__equals__nth__mono,axiom,
% 191.21/191.72 ! [V_xs_2,T_b] :
% 191.21/191.72 ( class_Orderings_Olinorder(T_b)
% 191.21/191.72 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 191.21/191.72 <=> ! [B_j] :
% 191.21/191.72 ( 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)))
% 191.21/191.72 => ! [B_i] :
% 191.21/191.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 191.21/191.72 => 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))) ) ) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_map__sorted__distinct__set__unique,axiom,
% 191.21/191.72 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 191.21/191.72 ( class_Orderings_Olinorder(T_c)
% 191.21/191.72 => ( 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)))
% 191.21/191.72 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 191.21/191.72 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)))
% 191.21/191.72 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2))
% 191.21/191.72 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)))
% 191.21/191.72 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 191.21/191.72 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_sublist__shift__lemma,axiom,
% 191.21/191.72 ! [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))))) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_transpose__rectangle,axiom,
% 191.21/191.72 ! [V_n_2,T_b,V_xs_2] :
% 191.21/191.72 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 191.21/191.72 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 191.21/191.72 => ( ! [B_i] :
% 191.21/191.72 ( 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)))
% 191.21/191.72 => 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 )
% 191.21/191.72 => 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)) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_transpose_Opsimps_I2_J,axiom,
% 191.21/191.72 ! [V_xss_2,T_b] :
% 191.21/191.72 ( 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)))
% 191.21/191.72 => 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) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_transpose_Opsimps_I1_J,axiom,
% 191.21/191.72 ! [T_b] :
% 191.21/191.72 ( 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))))
% 191.21/191.72 => c_List_Otranspose(T_b,c_List_Olist_ONil(tc_List_Olist(T_b))) = c_List_Olist_ONil(tc_List_Olist(T_b)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_transpose__column,axiom,
% 191.21/191.72 ! [V_i_2,V_xs_2,T_b] :
% 191.21/191.72 ( 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)))
% 191.21/191.72 => ( 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)))
% 191.21/191.72 => 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) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_transpose__aux__filter__head,axiom,
% 191.21/191.72 ! [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)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_inj__on__rev,axiom,
% 191.21/191.72 ! [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) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_filter__concat,axiom,
% 191.21/191.72 ! [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)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_length__concat,axiom,
% 191.21/191.72 ! [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)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_rev__eq__Cons__iff,axiom,
% 191.21/191.72 ! [V_ys_2,V_y_2,V_xs_2,T_b] :
% 191.21/191.72 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
% 191.21/191.72 <=> 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))) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_rev_Osimps_I2_J,axiom,
% 191.21/191.72 ! [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))) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_concat_Osimps_I2_J,axiom,
% 191.21/191.72 ! [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)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_rev__singleton__conv,axiom,
% 191.21/191.72 ! [V_x_2,V_xs_2,T_b] :
% 191.21/191.72 ( 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))
% 191.21/191.72 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_singleton__rev__conv,axiom,
% 191.21/191.72 ! [V_xs_2,V_x_2,T_b] :
% 191.21/191.72 ( 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)
% 191.21/191.72 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_concat__eq__Nil__conv,axiom,
% 191.21/191.72 ! [V_xss_2,T_b] :
% 191.21/191.72 ( c_List_Oconcat(T_b,V_xss_2) = c_List_Olist_ONil(T_b)
% 191.21/191.72 <=> ! [B_x] :
% 191.21/191.72 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 191.21/191.72 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_Nil__eq__concat__conv,axiom,
% 191.21/191.72 ! [V_xss_2,T_b] :
% 191.21/191.72 ( c_List_Olist_ONil(T_b) = c_List_Oconcat(T_b,V_xss_2)
% 191.21/191.72 <=> ! [B_x] :
% 191.21/191.72 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 191.21/191.72 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_rev_Osimps_I1_J,axiom,
% 191.21/191.72 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_concat_Osimps_I1_J,axiom,
% 191.21/191.72 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_Nil__is__rev__conv,axiom,
% 191.21/191.72 ! [V_xs_2,T_b] :
% 191.21/191.72 ( c_List_Olist_ONil(T_b) = hAPP(c_List_Orev(T_b),V_xs_2)
% 191.21/191.72 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_rev__is__Nil__conv,axiom,
% 191.21/191.72 ! [V_xs_2,T_b] :
% 191.21/191.72 ( hAPP(c_List_Orev(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 191.21/191.72 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_rev__concat,axiom,
% 191.21/191.72 ! [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))) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_rev__map,axiom,
% 191.21/191.72 ! [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)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_map__concat,axiom,
% 191.21/191.72 ! [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)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_concat__conv__foldl,axiom,
% 191.21/191.72 ! [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) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_rev__foldl__cons,axiom,
% 191.21/191.72 ! [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) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_foldl__conv__concat,axiom,
% 191.21/191.72 ! [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)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_distinct__rev,axiom,
% 191.21/191.72 ! [V_xs_2,T_b] :
% 191.21/191.72 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2)))
% 191.21/191.72 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_rev__append,axiom,
% 191.21/191.72 ! [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)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_concat__append,axiom,
% 191.21/191.72 ! [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)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_set__concat,axiom,
% 191.21/191.72 ! [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)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_length__rev,axiom,
% 191.21/191.72 ! [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) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_listsum__rev,axiom,
% 191.21/191.72 ! [V_xs,T_a] :
% 191.21/191.72 ( class_Groups_Ocomm__monoid__add(T_a)
% 191.21/191.72 => 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) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_rev__is__rev__conv,axiom,
% 191.21/191.72 ! [V_ys_2,V_xs_2,T_b] :
% 191.21/191.72 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Orev(T_b),V_ys_2)
% 191.21/191.72 <=> V_xs_2 = V_ys_2 ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_rev__swap,axiom,
% 191.21/191.72 ! [V_ys_2,V_xs_2,T_b] :
% 191.21/191.72 ( hAPP(c_List_Orev(T_b),V_xs_2) = V_ys_2
% 191.21/191.72 <=> V_xs_2 = hAPP(c_List_Orev(T_b),V_ys_2) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_rev__rev__ident,axiom,
% 191.21/191.72 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ).
% 191.21/191.72
% 191.21/191.72 fof(fact_foldr__foldl,axiom,
% 191.21/191.72 ! [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)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_foldl__foldr,axiom,
% 191.21/191.72 ! [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) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_set__rev,axiom,
% 191.21/191.72 ! [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) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_zip__rev,axiom,
% 191.21/191.72 ! [V_ys,T_b,V_xs,T_a] :
% 191.21/191.72 ( 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)
% 191.21/191.72 => 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)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_rev__filter,axiom,
% 191.21/191.72 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Orev(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(c_List_Orev(T_b),V_xs_2)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_last__rev,axiom,
% 191.21/191.72 ! [T_a,V_xs] :
% 191.21/191.72 ( V_xs != c_List_Olist_ONil(T_a)
% 191.21/191.72 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_hd__rev,axiom,
% 191.21/191.72 ! [T_a,V_xs] :
% 191.21/191.72 ( V_xs != c_List_Olist_ONil(T_a)
% 191.21/191.72 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_sorted__transpose,axiom,
% 191.21/191.72 ! [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)))) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_rev__take,axiom,
% 191.21/191.72 ! [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)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_rev__drop,axiom,
% 191.21/191.72 ! [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)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_rotate__rev,axiom,
% 191.21/191.72 ! [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)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_transpose_Osimps_I3_J,axiom,
% 191.21/191.72 ! [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))))) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_rev__nth,axiom,
% 191.21/191.72 ! [V_xs,T_a,V_n] :
% 191.21/191.72 ( 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)))
% 191.21/191.72 => 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))) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_concat__injective,axiom,
% 191.21/191.72 ! [V_ys_2,V_xs_2,T_b] :
% 191.21/191.72 ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 191.21/191.72 => ( 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)
% 191.21/191.72 => ( ! [B_x] :
% 191.21/191.72 ( 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))))
% 191.21/191.72 => 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)) )
% 191.21/191.72 => V_xs_2 = V_ys_2 ) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_concat__eq__concat__iff,axiom,
% 191.21/191.72 ! [V_ys_2,V_xs_2,T_b] :
% 191.21/191.72 ( ! [B_x] :
% 191.21/191.72 ( 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))))
% 191.21/191.72 => 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)) )
% 191.21/191.72 => ( 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)
% 191.21/191.72 => ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 191.21/191.72 <=> V_xs_2 = V_ys_2 ) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_rev__update,axiom,
% 191.21/191.72 ! [V_y,V_xs,T_a,V_k] :
% 191.21/191.72 ( 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)))
% 191.21/191.72 => 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) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_concat__map__singleton,axiom,
% 191.21/191.72 ! [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) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_sorted__rev__nth__mono,axiom,
% 191.21/191.72 ! [V_j,V_i,V_xs,T_a] :
% 191.21/191.72 ( class_Orderings_Olinorder(T_a)
% 191.21/191.72 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs))
% 191.21/191.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 191.21/191.72 => ( 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)))
% 191.21/191.72 => 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))) ) ) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_foldr__max__sorted,axiom,
% 191.21/191.72 ! [V_y_2,V_xs_2,T_b] :
% 191.21/191.72 ( class_Orderings_Olinorder(T_b)
% 191.21/191.72 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),V_xs_2))
% 191.21/191.72 => ( ( V_xs_2 = c_List_Olist_ONil(T_b)
% 191.21/191.72 => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = V_y_2 )
% 191.21/191.72 & ( V_xs_2 != c_List_Olist_ONil(T_b)
% 191.21/191.72 => 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) ) ) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_transpose_Opsimps_I3_J,axiom,
% 191.21/191.72 ! [V_xss_2,V_xs_2,V_x_2,T_b] :
% 191.21/191.72 ( 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)))
% 191.21/191.72 => 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))))) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_length__transpose__sorted,axiom,
% 191.21/191.72 ! [V_xs_2,T_b] :
% 191.21/191.72 ( 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)))
% 191.21/191.72 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 191.21/191.72 => 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) )
% 191.21/191.72 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_b))
% 191.21/191.72 => 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))) ) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_transpose__column__length,axiom,
% 191.21/191.72 ! [V_i_2,V_xs_2,T_b] :
% 191.21/191.72 ( 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)))
% 191.21/191.72 => ( 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)))
% 191.21/191.72 => 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)) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_transpose__aux__filter__tail,axiom,
% 191.21/191.72 ! [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)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_nth__nth__transpose__sorted,axiom,
% 191.21/191.72 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 191.21/191.72 ( 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)))
% 191.21/191.72 => ( 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))))
% 191.21/191.72 => ( 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))))
% 191.21/191.72 => 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) ) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_transpose__transpose,axiom,
% 191.21/191.72 ! [V_xs_2,T_b] :
% 191.21/191.72 ( 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)))
% 191.21/191.72 => 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) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_transfer__nat__int__list__functions_I2_J,axiom,
% 191.21/191.72 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_takeWhile__map,axiom,
% 191.21/191.72 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OtakeWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2),V_xs_2)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_return__list__def,axiom,
% 191.21/191.72 ! [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) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_zip__takeWhile__snd,axiom,
% 191.21/191.72 ! [V_ys_2,V_Pa_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),c_List_OtakeWhile(T_c,V_Pa_2,V_ys_2)) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_c,tc_HOL_Obool,tc_prod(T_b,T_c),V_Pa_2),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_zip__takeWhile__fst,axiom,
% 191.21/191.72 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),V_ys_2) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,tc_prod(T_b,T_c),V_Pa_2),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_set__takeWhileD,axiom,
% 191.21/191.72 ! [V_xs_2,V_Pa_2,V_x_2,T_b] :
% 191.21/191.72 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))))
% 191.21/191.72 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.72 & hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_takeWhile__eq__all__conv,axiom,
% 191.21/191.72 ! [V_xs_2,V_Pa_2,T_b] :
% 191.21/191.72 ( c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = V_xs_2
% 191.21/191.72 <=> ! [B_x] :
% 191.21/191.72 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.72 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_length__takeWhile__le,axiom,
% 191.21/191.72 ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_takeWhile__eq__take,axiom,
% 191.21/191.72 ! [V_xs_2,V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),V_xs_2) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_distinct__takeWhile,axiom,
% 191.21/191.72 ! [V_Pa_2,V_xs_2,T_b] :
% 191.21/191.72 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 191.21/191.72 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_takeWhile_Osimps_I1_J,axiom,
% 191.21/191.72 ! [V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_sorted__takeWhile,axiom,
% 191.21/191.72 ! [V_Pa_2,V_xs_2,T_b] :
% 191.21/191.72 ( class_Orderings_Olinorder(T_b)
% 191.21/191.72 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 191.21/191.72 => c_List_Olinorder__class_Osorted(T_b,c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_takeWhile_Osimps_I2_J,axiom,
% 191.21/191.72 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 191.21/191.72 ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 191.21/191.72 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)) )
% 191.21/191.72 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 191.21/191.72 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_b) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_takeWhile__tail,axiom,
% 191.21/191.72 ! [V_l_2,V_xs_2,T_b,V_x_2,V_Pa_2] :
% 191.21/191.72 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 191.21/191.72 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2))) = c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_takeWhile__append1,axiom,
% 191.21/191.72 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] :
% 191.21/191.72 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 191.21/191.72 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 191.21/191.72 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_nth__length__takeWhile,axiom,
% 191.21/191.72 ! [V_xs_2,V_Pa_2,T_b] :
% 191.21/191.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 191.21/191.72 => ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))))) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_takeWhile__nth,axiom,
% 191.21/191.72 ! [V_xs_2,V_Pa_2,T_b,V_j_2] :
% 191.21/191.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))))
% 191.21/191.72 => hAPP(hAPP(c_List_Onth(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_map__upds__def,axiom,
% 191.21/191.72 ! [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)))) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_takeWhile__not__last,axiom,
% 191.21/191.72 ! [T_b,V_xs_2] :
% 191.21/191.72 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 191.21/191.72 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 191.21/191.72 => 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) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_filter__equals__takeWhile__sorted__rev,axiom,
% 191.21/191.72 ! [V_t_2,V_xs_2,V_f_2,T_c,T_b] :
% 191.21/191.72 ( class_Orderings_Olinorder(T_b)
% 191.21/191.72 => ( 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)))
% 191.21/191.72 => 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) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_transfer__nat__int__list__return__embed,axiom,
% 191.21/191.72 ! [V_l] :
% 191.21/191.72 ( c_List_Onat__list(V_l)
% 191.21/191.72 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_length__remdups__concat,axiom,
% 191.21/191.72 ! [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))) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_distinct__remdups,axiom,
% 191.21/191.72 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ).
% 191.21/191.72
% 191.21/191.72 fof(fact_length__remdups__leq,axiom,
% 191.21/191.72 ! [V_xs,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ).
% 191.21/191.72
% 191.21/191.72 %----Arity declarations (201)
% 191.21/191.72 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom,
% 191.21/191.72 class_Lattices_Obounded__lattice(tc_HOL_Obool) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_fun__Lattices_Obounded__lattice,axiom,
% 191.21/191.72 ! [T_2,T_1] :
% 191.21/191.72 ( class_Lattices_Obounded__lattice(T_1)
% 191.21/191.72 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
% 191.21/191.72 ! [T_2,T_1] :
% 191.21/191.72 ( class_Complete__Lattice_Ocomplete__lattice(T_1)
% 191.21/191.72 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_fun__Lattices_Obounded__lattice__top,axiom,
% 191.21/191.72 ! [T_2,T_1] :
% 191.21/191.72 ( class_Lattices_Obounded__lattice(T_1)
% 191.21/191.72 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
% 191.21/191.72 ! [T_2,T_1] :
% 191.21/191.72 ( class_Lattices_Obounded__lattice(T_1)
% 191.21/191.72 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_fun__Lattices_Osemilattice__sup,axiom,
% 191.21/191.72 ! [T_2,T_1] :
% 191.21/191.72 ( class_Lattices_Olattice(T_1)
% 191.21/191.72 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_fun__Lattices_Osemilattice__inf,axiom,
% 191.21/191.72 ! [T_2,T_1] :
% 191.21/191.72 ( class_Lattices_Olattice(T_1)
% 191.21/191.72 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_fun__Lattices_Odistrib__lattice,axiom,
% 191.21/191.72 ! [T_2,T_1] :
% 191.21/191.72 ( class_Lattices_Odistrib__lattice(T_1)
% 191.21/191.72 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_fun__Lattices_Oboolean__algebra,axiom,
% 191.21/191.72 ! [T_2,T_1] :
% 191.21/191.72 ( class_Lattices_Oboolean__algebra(T_1)
% 191.21/191.72 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_fun__Orderings_Opreorder,axiom,
% 191.21/191.72 ! [T_2,T_1] :
% 191.21/191.72 ( class_Orderings_Opreorder(T_1)
% 191.21/191.72 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_fun__Finite__Set_Ofinite,axiom,
% 191.21/191.72 ! [T_1,T_2] :
% 191.21/191.72 ( ( class_Finite__Set_Ofinite(T_2)
% 191.21/191.72 & class_Finite__Set_Ofinite(T_1) )
% 191.21/191.72 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_fun__Lattices_Olattice,axiom,
% 191.21/191.72 ! [T_2,T_1] :
% 191.21/191.72 ( class_Lattices_Olattice(T_1)
% 191.21/191.72 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_fun__Orderings_Oorder,axiom,
% 191.21/191.72 ! [T_2,T_1] :
% 191.21/191.72 ( class_Orderings_Oorder(T_1)
% 191.21/191.72 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_fun__Orderings_Otop,axiom,
% 191.21/191.72 ! [T_2,T_1] :
% 191.21/191.72 ( class_Orderings_Otop(T_1)
% 191.21/191.72 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_fun__Orderings_Oord,axiom,
% 191.21/191.72 ! [T_2,T_1] :
% 191.21/191.72 ( class_Orderings_Oord(T_1)
% 191.21/191.72 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_fun__Orderings_Obot,axiom,
% 191.21/191.72 ! [T_2,T_1] :
% 191.21/191.72 ( class_Orderings_Obot(T_1)
% 191.21/191.72 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_fun__Groups_Ouminus,axiom,
% 191.21/191.72 ! [T_2,T_1] :
% 191.21/191.72 ( class_Groups_Ouminus(T_1)
% 191.21/191.72 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_fun__Groups_Ominus,axiom,
% 191.21/191.72 ! [T_2,T_1] :
% 191.21/191.72 ( class_Groups_Ominus(T_1)
% 191.21/191.72 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 191.21/191.72 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 191.21/191.72 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 191.21/191.72 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 191.21/191.72 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 191.21/191.72 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom,
% 191.21/191.72 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 191.21/191.72 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 191.21/191.72 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 191.21/191.72 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 191.21/191.72 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 191.21/191.72 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 191.21/191.72 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 191.21/191.72 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 191.21/191.72 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 191.21/191.72 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 191.21/191.72 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 191.21/191.72 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 191.21/191.72 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 191.21/191.72 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 191.21/191.72 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 191.21/191.72 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 191.21/191.72 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom,
% 191.21/191.72 class_Lattices_Osemilattice__sup(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom,
% 191.21/191.72 class_Lattices_Osemilattice__inf(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom,
% 191.21/191.72 class_Lattices_Odistrib__lattice(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 191.21/191.72 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 191.21/191.72 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 191.21/191.72 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 191.21/191.72 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
% 191.21/191.72 class_Rings_Oordered__ring__abs(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 191.21/191.72 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 191.21/191.72 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 191.21/191.72 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 191.21/191.72 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 191.21/191.72 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom,
% 191.21/191.72 class_Groups_Osemigroup__add(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
% 191.21/191.72 class_Divides_Osemiring__div(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 191.21/191.72 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom,
% 191.21/191.72 class_Nat_Osemiring__char__0(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 191.21/191.72 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 191.21/191.72 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 191.21/191.72 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 191.21/191.72 class_Orderings_Opreorder(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 191.21/191.72 class_Orderings_Olinorder(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 191.21/191.72 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 191.21/191.72 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 191.21/191.72 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Smallcheck_Osmall,axiom,
% 191.21/191.72 class_Smallcheck_Osmall(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
% 191.21/191.72 class_Rings_Osemiring__1(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 191.21/191.72 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Lattices_Olattice,axiom,
% 191.21/191.72 class_Lattices_Olattice(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 191.21/191.72 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Divides_Oring__div,axiom,
% 191.21/191.72 class_Divides_Oring__div(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 191.21/191.72 class_Rings_Omult__zero(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
% 191.21/191.72 class_Rings_Ocomm__ring(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 191.21/191.72 class_Orderings_Oorder(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 191.21/191.72 class_Int_Oring__char__0(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Int_Onumber__ring,axiom,
% 191.21/191.72 class_Int_Onumber__ring(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 191.21/191.72 class_Rings_Osemiring(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 191.21/191.72 class_Orderings_Oord(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Groups_Ouminus,axiom,
% 191.21/191.72 class_Groups_Ouminus(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Groups_Osgn__if,axiom,
% 191.21/191.72 class_Groups_Osgn__if(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Groups_Oabs__if,axiom,
% 191.21/191.72 class_Groups_Oabs__if(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 191.21/191.72 class_Rings_Oring__1(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Groups_Ominus,axiom,
% 191.21/191.72 class_Groups_Ominus(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Power_Opower,axiom,
% 191.21/191.72 class_Power_Opower(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 191.21/191.72 class_Groups_Ozero(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Rings_Oring,axiom,
% 191.21/191.72 class_Rings_Oring(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 191.21/191.72 class_Rings_Oidom(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Int_Onumber,axiom,
% 191.21/191.72 class_Int_Onumber(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Groups_Oone,axiom,
% 191.21/191.72 class_Groups_Oone(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Int__Oint__Rings_Odvd,axiom,
% 191.21/191.72 class_Rings_Odvd(tc_Int_Oint) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 191.21/191.72 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 191.21/191.72 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 191.21/191.72 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 191.21/191.72 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom,
% 191.21/191.72 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 191.21/191.72 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 191.21/191.72 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 191.21/191.72 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 191.21/191.72 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 191.21/191.72 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 191.21/191.72 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 191.21/191.72 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 191.21/191.72 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 191.21/191.72 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom,
% 191.21/191.72 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom,
% 191.21/191.72 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom,
% 191.21/191.72 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 191.21/191.72 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 191.21/191.72 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 191.21/191.72 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 191.21/191.72 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 191.21/191.72 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 191.21/191.72 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 191.21/191.72 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom,
% 191.21/191.72 class_Groups_Osemigroup__add(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
% 191.21/191.72 class_Divides_Osemiring__div(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 191.21/191.72 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Orderings_Owellorder,axiom,
% 191.21/191.72 class_Orderings_Owellorder(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom,
% 191.21/191.72 class_Nat_Osemiring__char__0(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 191.21/191.72 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 191.21/191.72 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 191.21/191.72 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 191.21/191.72 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 191.21/191.72 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
% 191.21/191.72 class_Rings_Osemiring__1(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 191.21/191.72 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Lattices_Olattice,axiom,
% 191.21/191.72 class_Lattices_Olattice(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 191.21/191.72 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 191.21/191.72 class_Orderings_Oorder(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 191.21/191.72 class_Rings_Osemiring(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 191.21/191.72 class_Orderings_Oord(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Orderings_Obot,axiom,
% 191.21/191.72 class_Orderings_Obot(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Groups_Ominus,axiom,
% 191.21/191.72 class_Groups_Ominus(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Power_Opower,axiom,
% 191.21/191.72 class_Power_Opower(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 191.21/191.72 class_Groups_Ozero(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Int_Onumber,axiom,
% 191.21/191.72 class_Int_Onumber(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 191.21/191.72 class_Groups_Oone(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Nat__Onat__Rings_Odvd,axiom,
% 191.21/191.72 class_Rings_Odvd(tc_Nat_Onat) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom,
% 191.21/191.72 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom,
% 191.21/191.72 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom,
% 191.21/191.72 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom,
% 191.21/191.72 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom,
% 191.21/191.72 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom,
% 191.21/191.72 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
% 191.21/191.72 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 191.21/191.72 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
% 191.21/191.72 class_Finite__Set_Ofinite(tc_HOL_Obool) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_HOL__Obool__Lattices_Olattice,axiom,
% 191.21/191.72 class_Lattices_Olattice(tc_HOL_Obool) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 191.21/191.72 class_Orderings_Oorder(tc_HOL_Obool) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_HOL__Obool__Orderings_Otop,axiom,
% 191.21/191.72 class_Orderings_Otop(tc_HOL_Obool) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 191.21/191.72 class_Orderings_Oord(tc_HOL_Obool) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_HOL__Obool__Orderings_Obot,axiom,
% 191.21/191.72 class_Orderings_Obot(tc_HOL_Obool) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_HOL__Obool__Groups_Ouminus,axiom,
% 191.21/191.72 class_Groups_Ouminus(tc_HOL_Obool) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_HOL__Obool__Groups_Ominus,axiom,
% 191.21/191.72 class_Groups_Ominus(tc_HOL_Obool) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_sum__Finite__Set_Ofinite,axiom,
% 191.21/191.72 ! [T_1,T_2] :
% 191.21/191.72 ( ( class_Finite__Set_Ofinite(T_2)
% 191.21/191.72 & class_Finite__Set_Ofinite(T_1) )
% 191.21/191.72 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
% 191.21/191.72 ! [T_1] :
% 191.21/191.72 ( class_Finite__Set_Ofinite(T_1)
% 191.21/191.72 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_prod__Finite__Set_Ofinite,axiom,
% 191.21/191.72 ! [T_1,T_2] :
% 191.21/191.72 ( ( class_Finite__Set_Ofinite(T_2)
% 191.21/191.72 & class_Finite__Set_Ofinite(T_1) )
% 191.21/191.72 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_prod__Smallcheck_Osmall,axiom,
% 191.21/191.72 ! [T_1,T_2] :
% 191.21/191.72 ( ( class_Smallcheck_Osmall(T_2)
% 191.21/191.72 & class_Smallcheck_Osmall(T_1) )
% 191.21/191.72 => class_Smallcheck_Osmall(tc_prod(T_2,T_1)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
% 191.21/191.72 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Product____Type__Ounit__Smallcheck_Osmall,axiom,
% 191.21/191.72 class_Smallcheck_Osmall(tc_Product__Type_Ounit) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 191.21/191.72 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 191.21/191.72 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom,
% 191.21/191.72 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom,
% 191.21/191.72 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom,
% 191.21/191.72 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom,
% 191.21/191.72 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom,
% 191.21/191.72 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom,
% 191.21/191.72 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom,
% 191.21/191.72 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom,
% 191.21/191.72 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom,
% 191.21/191.72 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom,
% 191.21/191.72 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom,
% 191.21/191.72 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom,
% 191.21/191.72 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom,
% 191.21/191.72 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom,
% 191.21/191.72 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom,
% 191.21/191.72 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom,
% 191.21/191.72 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom,
% 191.21/191.72 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom,
% 191.21/191.72 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom,
% 191.21/191.72 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom,
% 191.21/191.72 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom,
% 191.21/191.72 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom,
% 191.21/191.72 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom,
% 191.21/191.72 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom,
% 191.21/191.72 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom,
% 191.21/191.72 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom,
% 191.21/191.72 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom,
% 191.21/191.72 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom,
% 191.21/191.72 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom,
% 191.21/191.72 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom,
% 191.21/191.72 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom,
% 191.21/191.72 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom,
% 191.21/191.72 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom,
% 191.21/191.72 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom,
% 191.21/191.72 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom,
% 191.21/191.72 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom,
% 191.21/191.72 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom,
% 191.21/191.72 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom,
% 191.21/191.72 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 fof(arity_Code____Numeral__Ocode____numeral__Rings_Odvd,axiom,
% 191.21/191.72 class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral) ).
% 191.21/191.72
% 191.21/191.72 %----Helper facts (20)
% 191.21/191.72 fof(help_c__COMBI__1,axiom,
% 191.21/191.72 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ).
% 191.21/191.72
% 191.21/191.72 fof(help_c__COMBK__1,axiom,
% 191.21/191.72 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ).
% 191.21/191.72
% 191.21/191.72 fof(help_c__COMBB__1,axiom,
% 191.21/191.72 ! [V_R_2,V_Q_2,V_Pa_2,T_d,T_b,T_c] : hAPP(hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_Pa_2),V_Q_2),V_R_2) = hAPP(V_Pa_2,hAPP(V_Q_2,V_R_2)) ).
% 191.21/191.72
% 191.21/191.72 fof(help_c__COMBC__1,axiom,
% 191.21/191.72 ! [V_R_2,V_Q_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_Pa_2),V_Q_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),V_Q_2) ).
% 191.21/191.72
% 191.21/191.72 fof(help_c__COMBS__1,axiom,
% 191.21/191.72 ! [V_R_2,V_Q_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBS(T_c,T_d,T_b),V_Pa_2),V_Q_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),hAPP(V_Q_2,V_R_2)) ).
% 191.21/191.72
% 191.21/191.72 fof(help_c__fequal__1,axiom,
% 191.21/191.72 ! [V_y_2,V_x_2] :
% 191.21/191.72 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
% 191.21/191.72 | V_x_2 = V_y_2 ) ).
% 191.21/191.72
% 191.21/191.72 fof(help_c__fequal__2,axiom,
% 191.21/191.72 ! [V_y_2,V_x_2] :
% 191.21/191.72 ( V_x_2 != V_y_2
% 191.21/191.72 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(help_c__fFalse__1,axiom,
% 191.21/191.72 ~ hBOOL(c_fFalse) ).
% 191.21/191.72
% 191.21/191.72 fof(help_c__fTrue__1,axiom,
% 191.21/191.72 hBOOL(c_fTrue) ).
% 191.21/191.72
% 191.21/191.72 fof(help_c__fNot__1,axiom,
% 191.21/191.72 ! [V_Pa_2] :
% 191.21/191.72 ( ~ hBOOL(hAPP(c_fNot,V_Pa_2))
% 191.21/191.72 | ~ hBOOL(V_Pa_2) ) ).
% 191.21/191.72
% 191.21/191.72 fof(help_c__fNot__2,axiom,
% 191.21/191.72 ! [V_Pa_2] :
% 191.21/191.72 ( ~ ~ hBOOL(V_Pa_2)
% 191.21/191.72 | hBOOL(hAPP(c_fNot,V_Pa_2)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(help_c__fconj__1,axiom,
% 191.21/191.72 ! [V_Q_2,V_Pa_2] :
% 191.21/191.72 ( ~ hBOOL(V_Pa_2)
% 191.21/191.72 | ~ hBOOL(V_Q_2)
% 191.21/191.72 | hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Q_2)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(help_c__fconj__2,axiom,
% 191.21/191.72 ! [V_Q_2,V_Pa_2] :
% 191.21/191.72 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Q_2))
% 191.21/191.72 | hBOOL(V_Pa_2) ) ).
% 191.21/191.72
% 191.21/191.72 fof(help_c__fconj__3,axiom,
% 191.21/191.72 ! [V_Q_2,V_Pa_2] :
% 191.21/191.72 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Q_2))
% 191.21/191.72 | hBOOL(V_Q_2) ) ).
% 191.21/191.72
% 191.21/191.72 fof(help_c__fdisj__1,axiom,
% 191.21/191.72 ! [V_Q_2,V_Pa_2] :
% 191.21/191.72 ( ~ hBOOL(V_Pa_2)
% 191.21/191.72 | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Q_2)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(help_c__fdisj__2,axiom,
% 191.21/191.72 ! [V_Pa_2,V_Q_2] :
% 191.21/191.72 ( ~ hBOOL(V_Q_2)
% 191.21/191.72 | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Q_2)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(help_c__fdisj__3,axiom,
% 191.21/191.72 ! [V_Q_2,V_Pa_2] :
% 191.21/191.72 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Q_2))
% 191.21/191.72 | hBOOL(V_Pa_2)
% 191.21/191.72 | hBOOL(V_Q_2) ) ).
% 191.21/191.72
% 191.21/191.72 fof(help_c__fimplies__1,axiom,
% 191.21/191.72 ! [V_Q_2,V_Pa_2] :
% 191.21/191.72 ( hBOOL(V_Pa_2)
% 191.21/191.72 | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Q_2)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(help_c__fimplies__2,axiom,
% 191.21/191.72 ! [V_Pa_2,V_Q_2] :
% 191.21/191.72 ( ~ hBOOL(V_Q_2)
% 191.21/191.72 | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Q_2)) ) ).
% 191.21/191.72
% 191.21/191.72 fof(help_c__fimplies__3,axiom,
% 191.21/191.72 ! [V_Q_2,V_Pa_2] :
% 191.21/191.72 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Q_2))
% 191.21/191.72 | ~ hBOOL(V_Pa_2)
% 191.21/191.72 | hBOOL(V_Q_2) ) ).
% 191.21/191.72
% 191.21/191.72 %----Conjectures (3)
% 191.21/191.72 fof(conj_0,hypothesis,
% 191.21/191.72 ! [B_n] :
% 191.21/191.72 ( ! [B_x] :
% 191.21/191.72 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G))
% 191.21/191.72 => c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,B_x) )
% 191.21/191.72 => ! [B_Z,B_s] :
% 191.21/191.72 ( ( v_P(B_Z,B_s)
% 191.21/191.72 & hBOOL(hAPP(v_b,B_s)) )
% 191.21/191.72 => ! [B_s_H] :
% 191.21/191.72 ( c_Natural_Oevaln(v_c,B_s,B_n,B_s_H)
% 191.21/191.72 => v_P(B_Z,B_s_H) ) ) ) ).
% 191.21/191.72
% 191.21/191.72 fof(conj_1,hypothesis,
% 191.21/191.72 c_Natural_Oevaln(v_d,v_s,v_n,v_s_H) ).
% 191.21/191.72
% 191.21/191.72 fof(conj_2,conjecture,
% 191.21/191.72 ( v_d = c_Com_Ocom_OWhile(v_b,v_c)
% 191.21/191.72 => ( ! [B_x] :
% 191.21/191.72 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G))
% 191.21/191.72 => c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,B_x) )
% 191.21/191.72 => ! [B_Z] :
% 191.21/191.72 ( v_P(B_Z,v_s)
% 191.21/191.72 => ( v_P(B_Z,v_s_H)
% 191.21/191.72 & ~ hBOOL(hAPP(v_b,v_s_H)) ) ) ) ) ).
% 191.21/191.72
% 191.21/191.72 %------------------------------------------------------------------------------
% 191.21/191.72 %-------------------------------------------
% 191.21/191.72 % Proof found
% 191.21/191.72 % SZS status Theorem for theBenchmark
% 191.21/191.72 % SZS output start Proof
% 191.21/191.73 %ClaNum:10036(EqnAxiom:2803)
% 191.21/191.73 %VarNum:68131(SingletonVarNum:20215)
% 191.21/191.73 %MaxLitNum:8
% 191.21/191.73 %MaxfuncDepth:13
% 191.21/191.73 %SharedTerms:1061
% 191.21/191.73 %goalClause: 2999 3002 4564 5463
% 191.21/191.73 %singleGoalClaCount:2
% 191.21/191.73 [2807]P1(a177)
% 191.21/191.73 [2808]P2(a847)
% 191.21/191.73 [2809]P2(a1)
% 191.21/191.73 [2810]P2(a101)
% 191.21/191.73 [2811]P3(a847)
% 191.21/191.73 [2812]P3(a1)
% 191.21/191.73 [2813]P3(a101)
% 191.21/191.73 [2814]P4(a847)
% 191.21/191.73 [2815]P4(a1)
% 191.21/191.73 [2816]P4(a101)
% 191.21/191.73 [2817]P5(a847)
% 191.21/191.73 [2818]P5(a1)
% 191.21/191.73 [2819]P5(a101)
% 191.21/191.73 [2820]P66(a847)
% 191.21/191.73 [2821]P66(a1)
% 191.21/191.73 [2822]P66(a101)
% 191.21/191.73 [2823]P67(a847)
% 191.21/191.73 [2824]P67(a1)
% 191.21/191.73 [2825]P67(a101)
% 191.21/191.73 [2826]P68(a1)
% 191.21/191.73 [2827]P73(a847)
% 191.21/191.73 [2828]P73(a1)
% 191.21/191.73 [2829]P73(a101)
% 191.21/191.73 [2830]P137(a847)
% 191.21/191.73 [2831]P137(a1)
% 191.21/191.73 [2832]P85(a847)
% 191.21/191.73 [2833]P85(a1)
% 191.21/191.73 [2834]P85(a101)
% 191.21/191.73 [2835]P74(a847)
% 191.21/191.73 [2836]P74(a1)
% 191.21/191.73 [2837]P74(a101)
% 191.21/191.73 [2838]P80(a847)
% 191.21/191.73 [2839]P80(a1)
% 191.21/191.73 [2840]P80(a101)
% 191.21/191.73 [2841]P110(a1)
% 191.21/191.73 [2842]P81(a847)
% 191.21/191.73 [2843]P81(a1)
% 191.21/191.73 [2844]P81(a101)
% 191.21/191.73 [2845]P117(a847)
% 191.21/191.73 [2846]P117(a1)
% 191.21/191.73 [2847]P117(a101)
% 191.21/191.73 [2848]P86(a847)
% 191.21/191.73 [2849]P86(a1)
% 191.21/191.73 [2850]P86(a101)
% 191.21/191.73 [2851]P99(a847)
% 191.21/191.73 [2852]P99(a841)
% 191.21/191.73 [2853]P99(a1)
% 191.21/191.73 [2854]P99(a101)
% 191.21/191.73 [2855]P103(a847)
% 191.21/191.73 [2856]P103(a841)
% 191.21/191.73 [2857]P103(a1)
% 191.21/191.73 [2858]P103(a101)
% 191.21/191.73 [2859]P100(a847)
% 191.21/191.73 [2860]P100(a1)
% 191.21/191.73 [2861]P100(a101)
% 191.21/191.73 [2862]P102(a847)
% 191.21/191.73 [2863]P102(a841)
% 191.21/191.73 [2864]P102(a1)
% 191.21/191.73 [2865]P102(a101)
% 191.21/191.73 [2866]P111(a1)
% 191.21/191.73 [2867]P120(a1)
% 191.21/191.73 [2868]P121(a1)
% 191.21/191.73 [2869]P64(a847)
% 191.21/191.73 [2870]P64(a1)
% 191.21/191.73 [2871]P64(a101)
% 191.21/191.73 [2872]P69(a1)
% 191.21/191.73 [2873]P70(a847)
% 191.21/191.73 [2874]P70(a1)
% 191.21/191.73 [2875]P70(a101)
% 191.21/191.73 [2876]P75(a847)
% 191.21/191.73 [2877]P75(a1)
% 191.21/191.73 [2878]P75(a101)
% 191.21/191.73 [2879]P76(a847)
% 191.21/191.73 [2880]P76(a1)
% 191.21/191.73 [2881]P76(a101)
% 191.21/191.73 [2882]P87(a1)
% 191.21/191.73 [2883]P133(a1)
% 191.21/191.73 [2884]P104(a1)
% 191.21/191.73 [2885]P77(a1)
% 191.21/191.73 [2886]P6(a1)
% 191.21/191.73 [2887]P122(a847)
% 191.21/191.73 [2888]P122(a1)
% 191.21/191.73 [2889]P122(a101)
% 191.21/191.73 [2890]P134(a1)
% 191.21/191.73 [2891]P127(a847)
% 191.21/191.73 [2892]P127(a1)
% 191.21/191.73 [2893]P127(a101)
% 191.21/191.73 [2894]P138(a847)
% 191.21/191.73 [2895]P138(a1)
% 191.21/191.73 [2896]P138(a101)
% 191.21/191.73 [2897]P109(a847)
% 191.21/191.73 [2898]P109(a1)
% 191.21/191.73 [2899]P109(a101)
% 191.21/191.73 [2900]P135(a847)
% 191.21/191.73 [2901]P135(a1)
% 191.21/191.73 [2902]P135(a101)
% 191.21/191.73 [2903]P118(a1)
% 191.21/191.73 [2904]P119(a1)
% 191.21/191.73 [2905]P123(a847)
% 191.21/191.73 [2906]P123(a1)
% 191.21/191.73 [2907]P123(a101)
% 191.21/191.73 [2908]P115(a847)
% 191.21/191.73 [2909]P115(a1)
% 191.21/191.73 [2910]P115(a101)
% 191.21/191.73 [2911]P82(a1)
% 191.21/191.73 [2912]P124(a1)
% 191.21/191.73 [2913]P78(a847)
% 191.21/191.73 [2914]P78(a1)
% 191.21/191.73 [2915]P78(a101)
% 191.21/191.73 [2916]P128(a847)
% 191.21/191.73 [2917]P128(a1)
% 191.21/191.73 [2918]P128(a101)
% 191.21/191.73 [2919]P129(a1)
% 191.21/191.73 [2920]P131(a847)
% 191.21/191.73 [2921]P131(a1)
% 191.21/191.73 [2922]P131(a101)
% 191.21/191.73 [2923]P130(a847)
% 191.21/191.73 [2924]P130(a1)
% 191.21/191.73 [2925]P130(a101)
% 191.21/191.73 [2926]P125(a847)
% 191.21/191.73 [2927]P125(a1)
% 191.21/191.73 [2928]P125(a101)
% 191.21/191.73 [2929]P126(a1)
% 191.21/191.73 [2930]P90(a841)
% 191.21/191.73 [2931]P7(a847)
% 191.21/191.73 [2932]P7(a1)
% 191.21/191.73 [2933]P7(a101)
% 191.21/191.73 [2934]P8(a1)
% 191.21/191.73 [2935]P84(a841)
% 191.21/191.73 [2936]P84(a1)
% 191.21/191.73 [2937]P71(a847)
% 191.21/191.73 [2938]P71(a841)
% 191.21/191.73 [2939]P71(a1)
% 191.21/191.73 [2940]P71(a101)
% 191.21/191.73 [2941]P88(a1)
% 191.21/191.73 [2942]P79(a1)
% 191.21/191.73 [2943]P89(a847)
% 191.21/191.73 [2944]P89(a1)
% 191.21/191.73 [2945]P89(a101)
% 191.21/191.73 [2946]P132(a1)
% 191.21/191.73 [2947]P65(a1)
% 191.21/191.73 [2948]P105(a847)
% 191.21/191.73 [2949]P105(a1)
% 191.21/191.73 [2950]P105(a101)
% 191.21/191.73 [2951]P136(a847)
% 191.21/191.73 [2952]P136(a1)
% 191.21/191.73 [2953]P136(a101)
% 191.21/191.73 [2954]P112(a847)
% 191.21/191.73 [2955]P112(a1)
% 191.21/191.73 [2956]P112(a101)
% 191.21/191.73 [2957]P108(a1)
% 191.21/191.73 [2958]P92(a847)
% 191.21/191.73 [2959]P92(a841)
% 191.21/191.73 [2960]P92(a1)
% 191.21/191.73 [2961]P93(a847)
% 191.21/191.73 [2962]P93(a841)
% 191.21/191.73 [2963]P93(a1)
% 191.21/191.73 [2964]P9(a841)
% 191.21/191.73 [2965]P106(a841)
% 191.21/191.73 [2966]P94(a841)
% 191.21/191.73 [2967]P59(a841)
% 191.21/191.73 [2968]P59(a850)
% 191.21/191.73 [2969]P101(a847)
% 191.21/191.73 [2970]P101(a841)
% 191.21/191.73 [2971]P95(a841)
% 191.21/191.73 [2972]P97(a847)
% 191.21/191.73 [2973]P97(a841)
% 191.21/191.73 [2974]P97(a1)
% 191.21/191.73 [2975]P98(a847)
% 191.21/191.73 [2976]P98(a841)
% 191.21/191.73 [2977]P98(a1)
% 191.21/191.73 [2978]P72(a847)
% 191.21/191.73 [2979]P72(a1)
% 191.21/191.73 [2980]P72(a101)
% 191.21/191.73 [2981]P107(a847)
% 191.21/191.73 [2982]P139(a1)
% 191.21/191.73 [2983]P139(a850)
% 191.21/191.73 [2984]P83(a847)
% 191.21/191.73 [2985]P83(a1)
% 191.21/191.73 [2986]P83(a101)
% 191.21/191.73 [2987]P96(a841)
% 191.21/191.73 [3000]P36(a847,a237)
% 191.21/191.73 [3001]P36(a847,a323)
% 191.21/191.73 [3002]P142(a329,a860)
% 191.21/191.73 [3391]P39(a859,a860,a861,a862)
% 191.21/191.73 [4358]~E(a99,a85)
% 191.21/191.73 [4359]~P1(a178)
% 191.21/191.73 [2804]E(f2(a1),a85)
% 191.21/191.73 [2805]E(f3(a101),a4)
% 191.21/191.73 [2806]E(f102(a101),a5)
% 191.21/191.73 [2988]E(f34(a25),f2(a847))
% 191.21/191.73 [2989]E(f86(a177),f2(a847))
% 191.21/191.73 [2990]E(f86(a178),f2(a847))
% 191.21/191.73 [2991]E(f179(a847),f103(a847))
% 191.21/191.73 [2992]E(f180(a847),f2(a847))
% 191.21/191.73 [2993]E(f236(a847),f104(a847))
% 191.21/191.73 [2994]E(f105(a1),f39(a1))
% 191.21/191.73 [2995]P10(f2(a1))
% 191.21/191.73 [2996]P10(f80(a1))
% 191.21/191.73 [2999]E(f35(a853,a858),a859)
% 191.21/191.73 [3040]P1(f773(a26,a25))
% 191.21/191.73 [3049]P36(f854(a847,a847),a40)
% 191.21/191.73 [3078]E(f166(a843,a842,a29),a30)
% 191.21/191.73 [3390]E(f325(a847,a847,a237,a237),a40)
% 191.21/191.73 [4360]~E(f80(a1),f2(a1))
% 191.21/191.73 [2997]E(f113(f2(a847)),f2(a847))
% 191.21/191.73 [2998]E(f6(f2(a101)),f2(a847))
% 191.21/191.73 [3004]E(f773(f81(a1),a85),a85)
% 191.21/191.73 [3008]E(f773(a5,f2(a847)),f2(a101))
% 191.21/191.73 [3009]E(f773(a114,f2(a847)),f80(a847))
% 191.21/191.73 [3010]E(f773(a107,f80(a1)),f80(a847))
% 191.21/191.73 [3011]E(f773(a5,f80(a847)),f80(a101))
% 191.21/191.73 [3013]E(f773(f106(a1),a85),f2(a1))
% 191.21/191.73 [3014]E(f773(f106(a101),a85),f2(a101))
% 191.21/191.73 [3015]E(f773(a107,f2(a1)),f2(a847))
% 191.21/191.73 [3016]E(f773(f181(a842),a25),f2(a847))
% 191.21/191.73 [3017]E(f773(f181(a841),a177),f2(a847))
% 191.21/191.73 [3018]E(f773(f181(a841),a178),f2(a847))
% 191.21/191.73 [3019]E(f773(f106(a847),a85),f2(a847))
% 191.21/191.73 [3025]E(f773(f81(a1),f80(a1)),a99)
% 191.21/191.73 [3033]E(f773(f181(a101),f2(a101)),f2(a847))
% 191.21/191.73 [3034]E(f773(f102(a1),f2(a847)),f2(a1))
% 191.21/191.73 [3035]E(f773(f102(a1),f80(a847)),f80(a1))
% 191.21/191.73 [3036]E(f773(f81(a1),f2(a1)),f2(a1))
% 191.21/191.73 [3045]E(f773(a107,f80(a1)),f773(a114,f2(a847)))
% 191.21/191.73 [3047]E(f324(f854(a847,a847),a40),a41)
% 191.21/191.73 [3048]E(f326(f854(a847,a847),a40),a70)
% 191.21/191.73 [3069]E(f773(f257(a847),f2(a847)),f180(f855(a847,a841)))
% 191.21/191.73 [3070]E(f773(f258(a847),f2(a847)),f239(f855(a847,a841)))
% 191.21/191.73 [3080]P38(f180(f855(a1,a841)))
% 191.21/191.73 [3115]E(f773(f773(f3(a101),f2(a101)),f80(a101)),f2(a101))
% 191.21/191.73 [3187]P1(f773(f773(f233(a1),a99),f2(a1)))
% 191.21/191.73 [3212]P1(f773(f773(f233(a1),f2(a1)),f80(a1)))
% 191.21/191.73 [3214]P1(f773(f773(f232(a1),f2(a1)),f80(a1)))
% 191.21/191.73 [3381]P1(f773(f63(a843),f169(a843,a842,a30)))
% 191.21/191.73 [3424]E(f773(f773(f281(a847,a847,a847),a323),f300(a847,a323)),a237)
% 191.21/191.73 [3461]P40(a1,a847,a107,f773(f232(a1),f2(a1)))
% 191.21/191.73 [3464]E(f773(f773(f46(a847,f855(a847,a841)),f239(f855(a847,a841))),f257(a847)),f239(f855(a847,a841)))
% 191.21/191.73 [3465]E(f773(f773(f46(a847,f855(a847,a841)),f239(f855(a847,a841))),f293(a847)),f239(f855(a847,a841)))
% 191.21/191.73 [3466]E(f773(f773(f46(a847,f855(a847,a841)),f239(f855(a847,a841))),f258(a847)),f239(f855(a847,a841)))
% 191.21/191.73 [3467]E(f773(f773(f47(a847,f855(a847,a841)),f239(f855(a847,a841))),f296(a847)),f180(f855(a847,a841)))
% 191.21/191.73 [3483]P29(a847,a1,f102(a1),f239(f855(a847,a841)))
% 191.21/191.73 [3496]P40(a847,a1,f102(a1),f773(f18(a841,a847),a177))
% 191.21/191.73 [3627]E(f773(f75(a847,a101,a1,a5),a107),f106(a101))
% 191.21/191.73 [3845]P55(a101,a847,a22,a5,f239(f855(a847,a841)))
% 191.21/191.73 [3853]P55(a1,f855(f854(a847,a847),a841),a109,a91,a100)
% 191.21/191.73 [4122]E(f252(a1,a1,a1,a1,f39(a1),f81(a1)),a58)
% 191.21/191.73 [4391]~E(f773(f106(a1),a99),f773(f106(a1),a85))
% 191.21/191.73 [4392]~P1(f773(a186,f2(a1)))
% 191.21/191.73 [4393]~P1(f773(a186,f80(a1)))
% 191.21/191.73 [4449]~P1(f773(f773(f233(a1),a85),f2(a1)))
% 191.21/191.73 [3063]E(f773(f773(f3(a1),a99),a99),a85)
% 191.21/191.73 [3077]E(f773(f102(a1),f773(a114,f2(a847))),f80(a1))
% 191.21/191.73 [3139]E(f773(f42(a850),f239(f855(a850,a841))),f80(a847))
% 191.21/191.73 [3161]P1(f773(a186,f773(f106(a1),a99)))
% 191.21/191.73 [3162]P1(f773(f773(f233(a1),a99),a85))
% 191.21/191.73 [3164]P1(f773(f773(f232(a1),a99),a85))
% 191.21/191.73 [3223]E(f773(f773(f302(a847),f2(a847)),f180(f855(a847,a841))),f773(f293(a847),f2(a847)))
% 191.21/191.73 [3279]P1(f773(f773(f232(a1),f2(a1)),f773(f106(a1),a85)))
% 191.21/191.73 [3290]E(f773(f303(a847,a847,a114),f239(f855(a847,a841))),f773(f296(a847),f2(a847)))
% 191.21/191.73 [3328]P12(f854(a847,a847),f239(f855(f854(a847,a847),a841)),a111)
% 191.21/191.73 [3634]E(f773(f75(a847,a1,a101,f102(a1)),a22),a23)
% 191.21/191.73 [3694]P36(a847,f773(f256(f854(a847,a847)),f773(f251(a847,a847,a841),f233(a847))))
% 191.21/191.73 [4440]~P1(f773(a186,f773(f106(a1),a85)))
% 191.21/191.73 [4441]~P1(f773(f773(f233(a1),a99),a99))
% 191.21/191.73 [4442]~P1(f773(f773(f233(a1),a85),a99))
% 191.21/191.73 [4443]~P1(f773(f773(f233(a1),a85),a85))
% 191.21/191.73 [4444]~P1(f773(f773(f232(a1),a85),a99))
% 191.21/191.73 [4459]~P1(f773(f63(a847),f239(f855(a847,a841))))
% 191.21/191.73 [4460]~P1(f773(f63(a1),f239(f855(a1,a841))))
% 191.21/191.73 [4287]E(f773(f251(a1,a1,a841),f773(f773(f10(f855(a1,a841),f855(a1,a841),a1),f773(f20(a1,a841,a841),f773(f773(f10(a841,f855(a841,a841),a1),a331),f773(f233(a1),f2(a1))))),f773(f773(f9(a1,a1,f855(a1,a841)),f773(f773(f10(f855(a1,f855(a1,a841)),f855(a1,f855(a1,a841)),a1),f9(a1,a1,a841)),f773(f773(f10(f855(a1,a1),f855(a1,f855(a1,a841)),a1),f773(f10(a1,f855(a1,a841),a1),a330)),a212))),f80(a1)))),a208)
% 191.21/191.73 [3363]E(f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99),f773(f81(a1),a99))
% 191.21/191.73 [3406]E(f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99),f773(f773(f3(a1),a85),a99))
% 191.21/191.73 [3559]E(f773(f773(f61(f854(a847,a847)),f239(f855(f854(a847,a847),a841))),a111),a100)
% 191.21/191.73 [3589]E(f773(f106(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f80(a1))
% 191.21/191.73 [3590]E(f773(f106(a101),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f80(a101))
% 191.21/191.73 [3591]E(f773(f106(a847),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f80(a847))
% 191.21/191.73 [3594]E(f773(f106(a847),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(a114,f2(a847)))
% 191.21/191.73 [3983]E(f773(f773(f103(f855(f854(f854(a847,a847),f854(a847,a847)),a841)),a40),f300(f854(a847,a847),f180(f855(f854(f854(a847,a847),f854(a847,a847)),a841)))),a72)
% 191.21/191.73 [4054]E(f773(a91,f773(f277(f854(a847,a847),f854(a847,a847),a111),f773(f773(f302(f854(a847,a847)),f773(f773(f241(a847,a847),f2(a847)),f2(a847))),f180(f855(f854(a847,a847),a841))))),f2(a1))
% 191.21/191.73 [4055]E(f773(a91,f773(f277(f854(a847,a847),f854(a847,a847),a111),f773(f773(f302(f854(a847,a847)),f773(f773(f241(a847,a847),f80(a847)),f2(a847))),f180(f855(f854(a847,a847),a841))))),f80(a1))
% 191.21/191.73 [4069]E(f773(f256(f854(a847,a847)),f773(f251(a847,a847,a841),f773(f773(f10(a847,f855(a847,a841),a847),f773(f9(a847,a847,a841),a330)),a114))),a323)
% 191.21/191.73 [4038]E(f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))),f773(a114,f773(a114,f2(a847))))
% 191.21/191.73 [4041]E(f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))),f773(f773(f82(a847),f80(a847)),f80(a847)))
% 191.21/191.73 [4042]E(f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))),f773(f42(a841),f239(f855(a841,a841))))
% 191.21/191.73 [4107]P10(f773(f106(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))
% 191.21/191.73 [4181]P30(f855(f854(a847,a847),a841),f773(f773(f241(f855(f854(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841)),a841),f855(f854(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841)),a841)),a41),a71))
% 191.21/191.73 [4182]P30(f855(f854(a847,a847),a841),f773(f773(f241(f855(f854(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841)),a841),f855(f854(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841)),a841)),a70),a73))
% 191.21/191.73 [4219]E(f773(f773(f103(f855(f854(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841)),a841)),f326(f854(a847,a847),a72)),f773(f773(f302(f854(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841))),f773(f773(f241(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841)),f180(f855(f854(a847,a847),a841))),f180(f855(f854(a847,a847),a841)))),f180(f855(f854(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841)),a841)))),a73)
% 191.21/191.73 [4220]E(f773(f773(f103(f855(f854(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841)),a841)),f324(f854(a847,a847),a72)),f773(f773(f302(f854(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841))),f773(f773(f241(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841)),f180(f855(f854(a847,a847),a841))),f180(f855(f854(a847,a847),a841)))),f180(f855(f854(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841)),a841)))),a71)
% 191.21/191.73 [4109]E(f773(a107,f773(f106(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),f773(a114,f773(a114,f2(a847))))
% 191.21/191.73 [4158]E(f773(f102(a1),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),f773(f106(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))
% 191.21/191.73 [4191]P1(f773(f773(f232(a1),f2(a1)),f773(f106(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))))
% 191.21/191.73 [4192]E(f773(f106(a847),f773(f773(f3(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))),a99)),f773(a114,f773(a114,f773(a114,f2(a847)))))
% 191.21/191.73 [4232]P10(f773(f106(a1),f773(f773(f3(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))),a99)))
% 191.21/191.73 [4259]E(f773(f102(a1),f773(f106(a847),f773(f773(f3(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))),a99))),f773(f106(a1),f773(f773(f3(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))),a99)))
% 191.21/191.73 [4273]P1(f773(f773(f232(a1),f2(a1)),f773(f106(a1),f773(f773(f3(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))),a99))))
% 191.21/191.73 [3003]P11(x30031,a330)
% 191.21/191.73 [3392]P29(a847,a847,a114,x33921)
% 191.21/191.73 [3020]P36(a1,f108(x30201))
% 191.21/191.73 [3021]P36(a1,f110(x30211))
% 191.21/191.73 [3024]P37(x30241,f183(x30241))
% 191.21/191.73 [3066]P36(f855(x30661,a841),f299(x30661))
% 191.21/191.73 [3106]E(f52(a1,x31061,x31061),f2(a1))
% 191.21/191.73 [3158]P19(x31581,f855(x31581,a841),f302(x31581))
% 191.21/191.73 [4362]~E(f773(a27,x43621),a25)
% 191.21/191.73 [4364]~E(f773(a114,x43641),x43641)
% 191.21/191.73 [4376]~E(f773(a114,x43761),f2(a847))
% 191.21/191.73 [3005]E(f773(f181(a847),x30051),x30051)
% 191.21/191.73 [3006]E(f773(f106(a1),x30061),x30061)
% 191.21/191.73 [3022]E(f773(a91,f333(x30221)),x30221)
% 191.21/191.73 [3023]E(f238(x30231,f2(a101)),f2(a101))
% 191.21/191.73 [3037]E(f116(x30371,f115(x30371)),f115(x30371))
% 191.21/191.73 [3041]E(f34(f773(a27,x30411)),f2(a847))
% 191.21/191.73 [3042]E(f773(f141(x30421),f115(x30421)),f115(x30421))
% 191.21/191.73 [3043]E(f773(f157(x30431),f115(x30431)),f115(x30431))
% 191.21/191.73 [3044]E(f773(f142(x30441),f115(x30441)),f115(x30441))
% 191.21/191.73 [3050]E(f773(f106(a1),x30501),f773(f105(a1),x30501))
% 191.21/191.73 [3052]E(f773(a5,f773(a22,x30521)),x30521)
% 191.21/191.73 [3053]E(f773(a22,f773(a5,x30531)),x30531)
% 191.21/191.73 [3054]E(f773(a91,f773(a109,x30541)),x30541)
% 191.21/191.73 [3055]P10(f773(f102(a1),x30551))
% 191.21/191.73 [3059]E(f773(f181(f851(x30591)),f183(x30591)),f2(a847))
% 191.21/191.73 [3060]E(f773(f181(f848(x30601)),f115(x30601)),f2(a847))
% 191.21/191.73 [3065]E(f773(f181(a842),f773(a27,x30651)),f2(a847))
% 191.21/191.73 [3075]E(f226(x30751,f183(x30751)),f180(f855(x30751,a841)))
% 191.21/191.73 [3083]E(f773(f773(f82(a847),x30831),f2(a847)),x30831)
% 191.21/191.73 [3084]E(f773(f773(f82(a1),x30841),f2(a1)),x30841)
% 191.21/191.73 [3085]E(f773(f773(f83(a847),x30851),f80(a847)),x30851)
% 191.21/191.73 [3086]E(f773(f773(f83(a1),x30861),f80(a1)),x30861)
% 191.21/191.73 [3087]E(f773(f773(f3(a847),x30871),f2(a847)),x30871)
% 191.21/191.73 [3088]E(f773(f773(f179(a847),x30881),f2(a847)),x30881)
% 191.21/191.73 [3089]E(f773(f773(f83(a847),x30891),f2(a847)),f2(a847))
% 191.21/191.73 [3090]E(f773(f773(f43(a1),x30901),f2(a1)),f2(a1))
% 191.21/191.73 [3091]E(f773(f773(f236(a847),x30911),f2(a847)),f2(a847))
% 191.21/191.73 [3097]E(f773(f158(x30971),f115(x30971)),f180(f855(x30971,a841)))
% 191.21/191.73 [3101]P1(f773(f127(x31011),f115(x31011)))
% 191.21/191.73 [3107]E(f773(f143(x31071,x31071),f7(x31071)),f39(f848(x31071)))
% 191.21/191.73 [3108]E(f773(f143(x31081,x31081),f39(x31081)),f39(f848(x31081)))
% 191.21/191.73 [3109]E(f773(f196(x31091,x31091),f7(x31091)),f39(f851(x31091)))
% 191.21/191.73 [3110]E(f773(f196(x31101,x31101),f39(x31101)),f39(f851(x31101)))
% 191.21/191.73 [3111]E(f52(a1,x31111,f2(a1)),x31111)
% 191.21/191.73 [3112]E(f773(f232(a847),f773(a114,x31121)),f773(f233(a847),x31121))
% 191.21/191.73 [3113]E(f773(f257(a847),f773(a114,x31131)),f773(f293(a847),x31131))
% 191.21/191.73 [3114]E(f773(f258(a847),f773(a114,x31141)),f773(f296(a847),x31141))
% 191.21/191.73 [3116]E(f52(a1,f2(a1),x31161),f2(a1))
% 191.21/191.73 [3123]E(f773(f773(f82(a847),x31231),f80(a847)),f773(a114,x31231))
% 191.21/191.73 [3133]E(f773(f294(a847,x31331),f2(a847)),f180(f855(a847,a841)))
% 191.21/191.73 [3144]E(f295(a847,f2(a847),x31441),f773(f293(a847),x31441))
% 191.21/191.73 [3190]E(f773(f773(f3(a847),f773(a114,x31901)),f80(a847)),x31901)
% 191.21/191.73 [3203]E(f54(f2(a1),x32031),f773(f773(f241(a1,a1),f2(a1)),f2(a1)))
% 191.21/191.73 [3253]P1(f773(f773(f233(a847),x32531),f773(a114,x32531)))
% 191.21/191.73 [3267]P1(f773(f773(f233(a847),f2(a847)),f773(a114,x32671)))
% 191.21/191.73 [3546]E(f773(f773(f3(a101),f773(a5,f773(a114,f773(a22,x35461)))),f80(a101)),x35461)
% 191.21/191.73 [3616]P1(f773(f773(f232(a1),f773(f81(a1),f773(f102(a1),x36161))),f2(a1)))
% 191.21/191.73 [3769]P1(f773(f773(f233(a1),f773(f81(a1),f773(f102(a1),f773(a114,x37691)))),f2(a1)))
% 191.21/191.73 [4399]~E(f239(f855(x43991,a841)),f180(f855(x43991,a841)))
% 191.21/191.73 [4452]~P1(f773(f773(f233(a847),x44521),f2(a847)))
% 191.21/191.73 [4468]~P1(f773(f773(f233(a1),f773(f102(a1),x44681)),f2(a1)))
% 191.21/191.73 [3064]E(f164(x30641,f115(f848(x30641))),f115(f848(x30641)))
% 191.21/191.73 [3067]E(f773(f773(f83(a1),a85),x30671),a85)
% 191.21/191.73 [3068]E(f773(f773(f82(a1),a85),x30681),x30681)
% 191.21/191.73 [3071]E(f773(a107,f773(f102(a1),x30711)),x30711)
% 191.21/191.73 [3072]E(f773(f773(f82(a1),x30721),a85),x30721)
% 191.21/191.73 [3073]E(f773(f773(f3(a1),x30731),a85),x30731)
% 191.21/191.73 [3076]E(f773(f773(f3(a847),x30761),x30761),f2(a847))
% 191.21/191.73 [3081]E(f773(f81(a1),f773(f81(a1),x30811)),x30811)
% 191.21/191.73 [3082]E(f773(f42(a847),f773(f257(a847),x30821)),x30821)
% 191.21/191.73 [3092]E(f773(f773(f82(a847),f2(a847)),x30921),x30921)
% 191.21/191.73 [3093]E(f773(f773(f82(a1),f2(a1)),x30931),x30931)
% 191.21/191.73 [3094]E(f773(f773(f83(a847),f80(a847)),x30941),x30941)
% 191.21/191.73 [3095]E(f773(f773(f83(a1),f80(a1)),x30951),x30951)
% 191.21/191.73 [3096]E(f773(f773(f179(a847),f2(a847)),x30961),x30961)
% 191.21/191.73 [3102]E(f773(f773(f83(a847),f2(a847)),x31021),f2(a847))
% 191.21/191.73 [3103]E(f773(f773(f43(a1),f2(a1)),x31031),f2(a1))
% 191.21/191.73 [3104]E(f773(f773(f3(a847),f2(a847)),x31041),f2(a847))
% 191.21/191.73 [3105]E(f773(f773(f236(a847),f2(a847)),x31051),f2(a847))
% 191.21/191.73 [3121]E(f773(f294(a847,f2(a847)),x31211),f773(f257(a847),x31211))
% 191.21/191.73 [3122]E(f773(f773(f83(a1),a99),x31221),f773(f81(a1),x31221))
% 191.21/191.73 [3125]E(f773(a107,f773(f106(a1),x31251)),f773(f106(a847),x31251))
% 191.21/191.73 [3126]E(f773(a22,f773(f106(a101),x31261)),f773(f106(a847),x31261))
% 191.21/191.73 [3127]E(f773(f42(a847),f773(f293(a847),x31271)),f773(a114,x31271))
% 191.21/191.73 [3137]E(f773(f773(f82(a847),f80(a847)),x31371),f773(a114,x31371))
% 191.21/191.73 [3140]E(f773(f105(a1),f773(f102(a1),x31401)),f773(f102(a1),x31401))
% 191.21/191.73 [3141]E(f773(f77(a1),f773(f102(a1),x31411)),f773(f102(a1),x31411))
% 191.21/191.73 [3146]E(f773(f42(x31461),f180(f855(x31461,a841))),f2(a847))
% 191.21/191.73 [3148]E(f773(f773(f43(a847),x31481),f773(a114,f2(a847))),x31481)
% 191.21/191.73 [3159]E(f52(a847,x31591,f773(a114,f2(a847))),f2(a847))
% 191.21/191.73 [3160]E(f52(a1,x31601,f773(f106(a1),a99)),f2(a1))
% 191.21/191.73 [3174]E(f773(f773(f43(a1),x31741),f773(f106(a1),a99)),f773(f81(a1),x31741))
% 191.21/191.73 [3178]E(f130(a847,f773(f294(a847,x31781),f2(a847))),f115(a847))
% 191.21/191.73 [3179]E(f773(f773(f3(a1),x31791),f80(a1)),f773(f773(f82(a1),x31791),a99))
% 191.21/191.73 [3180]E(f773(f773(f82(a1),x31801),f80(a1)),f773(f773(f3(a1),x31801),a99))
% 191.21/191.73 [3183]P1(f773(f773(f187(a25),x31831),x31831))
% 191.21/191.73 [3184]P1(f773(f773(f232(a847),x31841),x31841))
% 191.21/191.73 [3185]P1(f773(f773(f232(a1),x31851),x31851))
% 191.21/191.73 [3186]P1(f773(f773(f279(a847),x31861),x31861))
% 191.21/191.73 [3191]E(f773(f81(a1),f773(f106(a1),x31911)),f773(f106(a1),f773(f81(a1),x31911)))
% 191.21/191.73 [3192]P1(f773(f63(a847),f773(f257(a847),x31921)))
% 191.21/191.73 [3193]P1(f773(f63(a847),f773(f293(a847),x31931)))
% 191.21/191.73 [3201]E(f149(x32011,f239(f855(x32011,a841))),f239(f855(f848(x32011),a841)))
% 191.21/191.73 [3206]P1(f773(f773(f232(a847),f2(a847)),x32061))
% 191.21/191.73 [3217]E(f773(f773(f82(a847),f113(x32171)),f773(a114,f2(a847))),f113(f773(a114,x32171)))
% 191.21/191.73 [3218]E(f773(f256(x32181),f773(f18(a841,x32181),a177)),f239(f855(x32181,a841)))
% 191.21/191.73 [3219]E(f773(f256(x32191),f773(f18(a841,x32191),a178)),f180(f855(x32191,a841)))
% 191.21/191.73 [3222]E(f773(f773(f302(a847),x32221),f773(f257(a847),x32221)),f773(f257(a847),f773(a114,x32221)))
% 191.21/191.73 [3233]E(f773(f773(f82(a1),f80(a1)),f773(f102(a1),x32331)),f773(f102(a1),f773(a114,x32331)))
% 191.21/191.73 [3256]E(f180(f855(f854(x32561,x32561),a841)),f260(x32561,f180(f855(x32561,a841))))
% 191.21/191.73 [3257]E(f773(f301(x32571),f239(f855(x32571,a841))),f239(f855(f855(x32571,a841),a841)))
% 191.21/191.73 [3258]E(f773(f81(f855(x32581,a841)),f239(f855(x32581,a841))),f180(f855(x32581,a841)))
% 191.21/191.73 [3259]E(f773(f81(f855(x32591,a841)),f180(f855(x32591,a841))),f239(f855(x32591,a841)))
% 191.21/191.73 [3261]P1(f773(f63(x32611),f180(f855(x32611,a841))))
% 191.21/191.73 [3263]E(f773(f294(a847,x32631),f773(a114,x32631)),f773(f773(f302(a847),x32631),f180(f855(a847,a841))))
% 191.21/191.73 [3264]E(f87(f854(a847,a847),f55(x32641,f2(a847))),f773(f773(f241(a847,a847),f2(a847)),x32641))
% 191.21/191.73 [3278]E(f773(f773(f302(a847),f773(a114,x32781)),f773(f293(a847),x32781)),f773(f293(a847),f773(a114,x32781)))
% 191.21/191.73 [3281]P36(x32811,f180(f855(f854(x32811,x32811),a841)))
% 191.21/191.73 [3284]P1(f773(f773(f232(a1),f2(a1)),f773(f102(a1),x32841)))
% 191.21/191.73 [3292]E(f773(f773(f82(a847),f773(f181(a847),x32921)),f773(a114,f2(a847))),f773(f181(a847),f773(a114,x32921)))
% 191.21/191.73 [3399]P38(f773(f303(a847,a1,f102(a1)),x33991))
% 191.21/191.73 [3439]P47(x34391,f180(f855(x34391,a841)),f180(f855(f854(x34391,x34391),a841)))
% 191.21/191.73 [3458]E(f773(f773(f241(a1,a1),f773(f106(a1),a99)),f773(f773(f3(a1),x34581),f80(a1))),f57(f773(f106(a1),a99),x34581))
% 191.21/191.73 [3508]P58(x35081,f773(f18(f855(x35081,a841),x35081),f773(f18(a841,x35081),a178)))
% 191.21/191.73 [3517]E(f282(a847,f279(a847),x35171,x35171),f773(f773(f302(a847),x35171),f180(f855(a847,a841))))
% 191.21/191.73 [3708]P1(f773(f773(f334(f855(f854(a847,a847),a841)),f333(x37081)),a100))
% 191.21/191.73 [3733]P1(f773(f773(f334(f855(f854(a847,a847),a841)),f773(a109,x37331)),a100))
% 191.21/191.73 [3863]P29(x38631,f855(x38631,a841),f773(f773(f9(x38631,f855(x38631,a841),f855(x38631,a841)),f302(x38631)),f180(f855(x38631,a841))),f239(f855(x38631,a841)))
% 191.21/191.73 [4395]~E(f773(f773(f82(a1),x43951),x43951),a99)
% 191.21/191.73 [4439]~E(f773(a5,f773(a114,f773(a22,x44391))),f2(a101))
% 191.21/191.73 [4445]~P1(f773(a186,f773(f102(a1),x44451)))
% 191.21/191.73 [4448]~P1(f773(f773(f233(a847),x44481),x44481))
% 191.21/191.73 [4461]~P1(f773(f773(f232(a847),f773(a114,x44611)),x44611))
% 191.21/191.73 [3208]E(f773(a107,f773(f81(a1),f773(f102(a1),x32081))),f2(a847))
% 191.21/191.73 [3211]E(f773(f773(f82(a1),f773(f81(a1),x32111)),x32111),f2(a1))
% 191.21/191.73 [3216]E(f773(f42(a1),f773(f294(a1,f2(a1)),x32161)),f773(a107,x32161))
% 191.21/191.73 [3226]E(f773(f773(f242(a847),f773(a114,f2(a847))),x32261),f773(a114,f2(a847)))
% 191.21/191.73 [3325]E(f773(f276(x33251),f180(f855(f854(x33251,x33251),a841))),f180(f855(x33251,a841)))
% 191.21/191.73 [3333]E(f45(f855(x33331,a841),f239(f855(f855(x33331,a841),a841))),f180(f855(x33331,a841)))
% 191.21/191.73 [3334]E(f45(f855(x33341,a841),f180(f855(f855(x33341,a841),a841))),f239(f855(x33341,a841)))
% 191.21/191.73 [3335]E(f44(f855(x33351,a841),f239(f855(f855(x33351,a841),a841))),f239(f855(x33351,a841)))
% 191.21/191.73 [3336]E(f44(f855(x33361,a841),f180(f855(f855(x33361,a841),a841))),f180(f855(x33361,a841)))
% 191.21/191.73 [3341]P1(f773(f773(f279(a847),f773(a114,f2(a847))),x33411))
% 191.21/191.73 [3379]E(f773(f773(f302(f848(x33791)),f115(x33791)),f180(f855(f848(x33791),a841))),f150(x33791,f115(f855(x33791,a841))))
% 191.21/191.73 [3380]E(f773(f773(f302(f848(x33801)),f115(x33801)),f180(f855(f848(x33801),a841))),f149(x33801,f180(f855(x33801,a841))))
% 191.21/191.73 [3423]E(f773(f773(f82(a847),f6(x34231)),f773(a114,f2(a847))),f6(f773(a5,f773(a114,f773(a22,x34231)))))
% 191.21/191.73 [3450]E(f773(f42(a1),f773(f303(a847,a1,f102(a1)),x34501)),f773(f42(a847),x34501))
% 191.21/191.73 [3453]P1(f773(f773(f232(a847),x34531),f773(f773(f83(a847),x34531),x34531)))
% 191.21/191.73 [3489]E(f773(f303(a1,a847,a107),f295(a1,f2(a1),f773(f102(a1),x34891))),f773(f293(a847),x34891))
% 191.21/191.73 [3503]E(f773(f773(f43(a847),f773(a114,f2(a847))),f773(f106(a847),x35031)),f773(a107,f773(f773(f43(a1),f80(a1)),f773(f106(a1),x35031))))
% 191.21/191.73 [3505]E(f773(f158(a847),f130(a847,f773(f294(a847,f2(a847)),f773(a114,x35051)))),f773(f293(a847),x35051))
% 191.21/191.73 [3506]E(f773(f773(f82(a847),f773(f181(a101),x35061)),f773(a114,f2(a847))),f773(f181(a101),f773(a5,f773(a114,f773(a22,x35061)))))
% 191.21/191.73 [3522]E(f773(f303(a1,a847,a107),f773(f303(a847,a1,f102(a1)),x35221)),x35221)
% 191.21/191.73 [3551]E(f773(f773(f302(a847),f2(a847)),f773(f303(a847,a847,a114),f773(f257(a847),x35511))),f773(f257(a847),f773(a114,x35511)))
% 191.21/191.73 [3558]P53(x35581,x35581,f300(x35581,f180(f855(f854(x35581,x35581),a841))))
% 191.21/191.73 [3564]P1(f773(a186,f773(f81(a1),f773(f102(a1),f773(a114,x35641)))))
% 191.21/191.73 [3575]E(f773(f773(f3(f855(a847,a841)),f773(f258(a847),x35751)),f773(f773(f302(a847),x35751),f180(f855(a847,a841)))),f773(f258(a847),f773(a114,x35751)))
% 191.21/191.73 [3592]E(f773(f773(f82(a1),f773(f773(f3(a1),a85),x35921)),f773(f773(f3(a1),a85),x35921)),f773(f773(f3(a1),a85),f773(f773(f82(a1),x35921),x35921)))
% 191.21/191.73 [3606]E(f773(f773(f302(f855(x36061,a841)),f180(f855(x36061,a841))),f180(f855(f855(x36061,a841),a841))),f773(f301(x36061),f180(f855(x36061,a841))))
% 191.21/191.73 [3635]E(f773(f773(f3(f855(a847,a841)),f773(f296(a847),x36351)),f773(f773(f302(a847),f773(a114,x36351)),f180(f855(a847,a841)))),f773(f296(a847),f773(a114,x36351)))
% 191.21/191.73 [3644]E(f773(f773(f302(f851(x36441)),f183(x36441)),f773(f303(x36441,f851(x36441),f227(x36441)),f239(f855(x36441,a841)))),f239(f855(f851(x36441),a841)))
% 191.21/191.73 [3745]E(f773(f106(a847),f773(f773(f82(a1),x37451),x37451)),f773(f773(f88(a847,a847),f773(f106(a847),x37451)),f773(f773(f20(a847,a847,a847),f82(a847)),f7(a847))))
% 191.21/191.73 [4133]P19(x41331,f855(x41331,a841),f773(f773(f10(f855(x41331,a841),f855(f855(x41331,a841),f855(x41331,a841)),x41331),f773(f9(f855(x41331,a841),f855(x41331,a841),f855(x41331,a841)),f3(f855(x41331,a841)))),f773(f773(f9(x41331,f855(x41331,a841),f855(x41331,a841)),f302(x41331)),f180(f855(x41331,a841)))))
% 191.21/191.73 [4218]E(f773(f256(f854(a1,a1)),f773(f251(a1,a1,a841),f773(f773(f10(f855(a1,a841),f855(a1,a841),a1),f773(f20(a1,a841,a841),f773(f773(f10(a841,f855(a841,a841),a1),a331),f773(f232(a1),x42181)))),f233(a1)))),f110(x42181))
% 191.21/191.73 [4250]E(f773(f256(f854(a1,a1)),f773(f251(a1,a1,a841),f773(f773(f20(a1,f855(a1,a841),f855(a1,a841)),f773(f773(f10(f855(a841,a841),f855(f855(a1,a841),f855(a1,a841)),a1),f10(a841,a841,a1)),f773(f773(f10(a841,f855(a841,a841),a1),a331),f773(f232(a1),x42501)))),f233(a1)))),f108(x42501))
% 191.21/191.73 [4302]E(f773(f256(f854(f855(x43021,a841),f855(x43021,a841))),f773(f251(f855(x43021,a841),f855(x43021,a841),a841),f773(f773(f9(f855(x43021,a841),f855(f855(x43021,a841),a841),f855(f855(x43021,a841),a841)),f773(f773(f10(f855(f855(x43021,a841),f855(a841,a841)),f855(f855(f855(x43021,a841),a841),f855(f855(x43021,a841),a841)),f855(x43021,a841)),f20(f855(x43021,a841),a841,a841)),f773(f773(f10(f855(f855(x43021,a841),a841),f855(f855(x43021,a841),f855(a841,a841)),f855(x43021,a841)),f773(f10(a841,f855(a841,a841),f855(x43021,a841)),a331)),f233(f855(x43021,a841))))),f63(x43021)))),f299(x43021))
% 191.21/191.73 [4465]~P1(f773(f63(f848(x44651)),f239(f855(f848(x44651),a841))))
% 191.21/191.73 [4478]~P1(f773(f773(f232(a1),f2(a1)),f773(f81(a1),f773(f102(a1),f773(a114,x44781)))))
% 191.21/191.73 [3357]E(f773(f773(f3(a1),f773(f773(f82(a1),x33571),a99)),a99),x33571)
% 191.21/191.73 [3373]E(f773(f158(a847),f130(a847,f773(f294(a847,f2(a847)),x33731))),f773(f257(a847),x33731))
% 191.21/191.73 [3612]E(f773(f773(f82(a1),f773(f773(f82(a1),f80(a1)),x36121)),x36121),f773(f773(f3(a1),f773(f773(f82(a1),x36121),x36121)),a99))
% 191.21/191.73 [3662]E(f773(f278(x36621,x36621),f300(x36621,f180(f855(f854(x36621,x36621),a841)))),f300(x36621,f180(f855(f854(x36621,x36621),a841))))
% 191.21/191.73 [3711]P1(f773(f773(f232(a847),x37111),f773(f773(f83(a847),x37111),f773(f773(f83(a847),x37111),x37111))))
% 191.21/191.73 [3987]P1(f773(f63(a847),f773(f256(a847),f773(f773(f9(a847,a847,a841),f233(a847)),x39871))))
% 191.21/191.73 [3988]P1(f773(f63(a847),f773(f256(a847),f773(f773(f9(a847,a847,a841),f232(a847)),x39881))))
% 191.21/191.73 [4269]E(f773(f256(f854(x42691,x42691)),f773(f773(f10(f855(x42691,a841),a841,f854(x42691,x42691)),f89(x42691)),f773(f773(f9(f854(x42691,x42691),f855(x42691,f854(x42691,x42691)),f855(x42691,a841)),f773(f773(f10(f855(f854(x42691,x42691),a841),f855(f855(x42691,f854(x42691,x42691)),f855(x42691,a841)),f854(x42691,x42691)),f10(f854(x42691,x42691),a841,x42691)),a330)),f773(f773(f20(x42691,x42691,f854(x42691,x42691)),f241(x42691,x42691)),f7(x42691))))),f300(x42691,f180(f855(f854(x42691,x42691),a841))))
% 191.21/191.73 [4467]~E(f773(f773(f3(a1),f773(f773(f82(a1),x44671),x44671)),a99),a85)
% 191.21/191.73 [4469]~E(f773(f773(f82(a1),f773(f773(f82(a1),f80(a1)),x44691)),x44691),f2(a1))
% 191.21/191.73 [3757]E(f773(f773(f82(a1),f773(f773(f3(a1),a99),x37571)),f773(f773(f3(a1),a99),x37571)),f773(f773(f3(a1),a99),f773(f773(f3(a1),f773(f773(f82(a1),x37571),x37571)),a99)))
% 191.21/191.73 [3871]E(f773(f773(f3(a1),f773(f773(f82(a1),f773(f773(f3(a1),a99),x38711)),f773(f773(f3(a1),a99),x38711))),a99),f773(f773(f3(a1),a99),f773(f773(f82(a1),x38711),x38711)))
% 191.21/191.73 [3907]E(f773(f773(f3(a1),f773(f773(f82(a1),f773(f773(f82(a1),x39071),a99)),f773(f773(f82(a1),x39071),a99))),a99),f773(f773(f82(a1),f773(f773(f82(a1),x39071),x39071)),a99))
% 191.21/191.73 [3946]E(f773(f773(f3(a1),f773(f773(f82(a1),f773(f773(f3(a1),a99),x39461)),f773(f773(f3(a1),a99),x39461))),a99),f773(f773(f3(a1),a85),f773(f773(f3(a1),f773(f773(f82(a1),x39461),x39461)),a99)))
% 191.21/191.73 [4050]E(f773(a91,f773(f277(f854(a847,a847),f854(a847,a847),a111),f773(f773(f302(f854(a847,a847)),f773(f773(f241(a847,a847),x40501),f2(a847))),f180(f855(f854(a847,a847),a841))))),f773(f102(a1),x40501))
% 191.21/191.73 [4060]E(f773(a91,f773(f277(f854(a847,a847),f854(a847,a847),a111),f773(f773(f302(f854(a847,a847)),f773(f773(f241(a847,a847),f337(x40601)),f490(x40601))),f180(f855(f854(a847,a847),a841))))),x40601)
% 191.21/191.73 [4090]E(f773(f256(a1),f773(f773(f20(a1,a841,a841),f773(f773(f10(a841,f855(a841,a841),a1),a331),f773(f232(a1),f2(a1)))),x40901)),f773(f303(a847,a1,f102(a1)),f773(f256(a847),f773(f773(f10(a1,a841,a847),x40901),f102(a1)))))
% 191.21/191.73 [4141]P38(f773(f256(a1),f773(f773(f20(a1,a841,a841),f773(f773(f10(a841,f855(a841,a841),a1),a331),f773(f232(a1),f2(a1)))),x41411)))
% 191.21/191.73 [4161]P1(f773(f773(f334(f854(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841))),f773(f773(f241(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841)),x41611),f180(f855(f854(a847,a847),a841)))),a73))
% 191.21/191.73 [4167]E(f773(f303(a1,a847,a107),f773(f256(a1),f773(f773(f20(a1,a841,a841),f773(f773(f10(a841,f855(a841,a841),a1),a331),f773(f232(a1),f2(a1)))),f773(f773(f10(a847,a841,a1),x41671),a107)))),f773(f256(a847),x41671))
% 191.21/191.73 [4316]E(f306(a847,f773(f773(f46(f854(a847,a847),f855(a847,a841)),f773(a109,x43161)),f773(f251(a847,a847,f855(a847,a841)),f773(f773(f9(a847,f855(a847,a841),f855(a847,f855(a847,a841))),f773(f773(f10(f855(a847,f855(f855(a847,a841),f855(a847,a841))),f855(f855(a847,a841),f855(a847,f855(a847,a841))),a847),f9(a847,f855(a847,a841),f855(a847,a841))),f773(f773(f10(f855(a847,a847),f855(a847,f855(f855(a847,a841),f855(a847,a841))),a847),f773(f10(a847,f855(f855(a847,a841),f855(a847,a841)),a847),f302(a847))),f3(a847)))),f180(f855(a847,a841)))))),f773(a107,x43161))
% 191.21/191.73 [3800]E(f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),x38001),x38001)),a99)),a99),f773(f773(f82(a1),x38001),x38001))
% 191.21/191.73 [3846]E(f773(f773(f3(a1),f773(f773(f3(a1),f773(f773(f82(a1),x38461),x38461)),a99)),a99),f773(f773(f82(a1),f773(f773(f3(a1),x38461),a99)),f773(f773(f3(a1),x38461),a99)))
% 191.21/191.73 [4067]E(f773(f773(f3(a1),f773(f773(f82(a1),f773(f773(f82(a1),f773(f81(a1),x40671)),a99)),f773(f773(f82(a1),f773(f81(a1),x40671)),a99))),a99),f773(f81(a1),f773(f773(f3(a1),f773(f773(f82(a1),x40671),x40671)),a99)))
% 191.21/191.73 [4110]E(f773(f773(f82(a847),x41101),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),f773(a114,f773(a114,x41101)))
% 191.21/191.73 [4111]E(f773(f773(f83(a847),x41111),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),f773(f773(f82(a847),x41111),x41111))
% 191.21/191.73 [4112]E(f773(f773(f43(a847),f773(f773(f82(a847),x41121),x41121)),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),x41121)
% 191.21/191.73 [4194]E(f52(a847,f773(a114,f773(a114,x41941)),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),f52(a847,x41941,f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))))
% 191.21/191.73 [4333]E(f773(a91,f773(f773(f46(f854(a847,a847),f855(f854(a847,a847),a841)),f773(a109,x43331)),f773(f251(a847,a847,f855(f854(a847,a847),a841)),f773(f773(f10(f855(a847,f855(f854(a847,a847),a841)),f855(a847,f855(f854(a847,a847),a841)),a847),f773(f10(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841),a847),f277(f854(a847,a847),f854(a847,a847),a111))),f773(f773(f9(a847,f855(f854(a847,a847),a841),f855(a847,f855(f854(a847,a847),a841))),f773(f773(f10(f855(a847,f855(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841))),f855(f855(f854(a847,a847),a841),f855(a847,f855(f854(a847,a847),a841))),a847),f9(a847,f855(f854(a847,a847),a841),f855(f854(a847,a847),a841))),f773(f773(f10(f855(a847,f854(a847,a847)),f855(a847,f855(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841))),a847),f773(f10(f854(a847,a847),f855(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841)),a847),f302(f854(a847,a847)))),f773(f9(a847,a847,f854(a847,a847)),f241(a847,a847))))),f180(f855(f854(a847,a847),a841))))))),f773(f81(a1),x43331))
% 191.21/191.73 [4189]E(f773(f773(f82(a847),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),x41891),f773(a114,f773(a114,x41891)))
% 191.21/191.73 [4190]E(f773(f773(f83(a847),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),x41901),f773(f773(f82(a847),x41901),x41901))
% 191.21/191.73 [4223]E(f773(f773(f43(a847),f773(a114,f773(a114,x42231))),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),f773(a114,f773(f773(f43(a847),x42231),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))))
% 191.21/191.73 [4274]E(f773(f773(f82(a847),f773(f106(a847),f773(f773(f3(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))),a99))),x42741),f773(a114,f773(a114,f773(a114,x42741))))
% 191.21/191.73 [4354]E(f773(f251(a1,a1,f854(a1,a1)),f773(f773(f20(a1,f855(a1,f854(a1,a1)),f855(a1,f854(a1,a1))),f773(f773(f10(f855(a1,f855(f854(a1,a1),f854(a1,a1))),f855(f855(a1,f854(a1,a1)),f855(a1,f854(a1,a1))),a1),f20(a1,f854(a1,a1),f854(a1,a1))),f773(f773(f10(f855(a1,f854(a1,a1)),f855(a1,f855(f854(a1,a1),f854(a1,a1))),a1),f773(f20(a1,f854(a1,a1),f855(f854(a1,a1),f854(a1,a1))),f773(f773(f10(a841,f855(f854(a1,a1),f855(f854(a1,a1),f854(a1,a1))),a1),f98(f854(a1,a1))),f773(f773(f10(a1,a841,a1),f773(f232(a1),f2(a1))),f773(f773(f9(a1,a1,a1),f3(a1)),x43541))))),f773(f773(f9(a1,f855(a1,a1),f855(a1,f854(a1,a1))),f773(f773(f10(f855(a1,f854(a1,a1)),f855(f855(a1,a1),f855(a1,f854(a1,a1))),a1),f10(a1,f854(a1,a1),a1)),f773(f773(f10(a1,f855(a1,f854(a1,a1)),a1),f241(a1,a1)),f773(f773(f9(a1,a1,a1),f773(f773(f10(a1,f855(a1,a1),a1),f82(a1)),f773(f83(a1),f773(f106(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))))),f80(a1))))),f773(f773(f9(a1,a1,a1),f3(a1)),x43541))))),f773(f773(f10(a1,f855(a1,f854(a1,a1)),a1),f241(a1,a1)),f773(f83(a1),f773(f106(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))))),f50(x43541))
% 191.21/191.73 [3402]P39(a25,x34021,x34022,x34021)
% 191.21/191.73 [3058]P18(a1,f163(x30581,x30582))
% 191.21/191.73 [3154]P47(x31541,x31542,f260(x31541,x31542))
% 191.21/191.73 [3155]P53(x31551,x31551,f260(x31551,x31552))
% 191.21/191.73 [3426]P29(x34261,x34261,f7(x34261),x34262)
% 191.21/191.73 [3427]P29(x34271,x34271,f39(x34271),x34272)
% 191.21/191.73 [3434]P34(x34341,x34342,f115(x34341),f115(x34341))
% 191.21/191.73 [3435]P29(x34351,f851(x34351),f227(x34351),x34352)
% 191.21/191.73 [3444]P29(f848(x34441),f848(x34441),f142(x34441),x34442)
% 191.21/191.73 [4368]~E(f35(x43681,x43682),a25)
% 191.21/191.73 [4369]~E(f36(x43691,x43692),a25)
% 191.21/191.73 [4370]~E(f28(x43701,x43702),a25)
% 191.21/191.73 [3026]E(f773(f7(x30261),x30262),x30262)
% 191.21/191.73 [3027]E(f773(f256(x30271),x30272),x30272)
% 191.21/191.73 [3029]E(f773(f39(x30291),x30292),x30292)
% 191.21/191.73 [3038]E(f773(f184(x30381),x30382),f117(x30381))
% 191.21/191.73 [3046]E(f34(f28(x30461,x30462)),f2(a847))
% 191.21/191.73 [3056]E(f87(x30561,f773(a330,x30562)),x30562)
% 191.21/191.73 [3057]E(f92(x30571,f773(a330,x30572)),x30572)
% 191.21/191.73 [3074]E(f773(f181(a842),f28(x30741,x30742)),f2(a847))
% 191.21/191.73 [3079]E(f773(f126(x30791,x30792),f115(x30791)),f115(x30791))
% 191.21/191.73 [3098]E(f300(x30981,f300(x30981,x30982)),f300(x30981,x30982))
% 191.21/191.73 [3119]E(f773(f773(f125(x31191),x31192),f115(x31191)),x31192)
% 191.21/191.73 [3128]E(f773(f773(f159(x31281),x31282),f115(x31281)),f115(x31281))
% 191.21/191.73 [3129]E(f773(f773(f128(x31291),x31292),f115(x31291)),f115(x31291))
% 191.21/191.73 [3131]E(f228(x31311,x31312,f183(x31311)),f2(a847))
% 191.21/191.73 [3132]E(f144(x31321,x31322,f115(x31321)),f2(a847))
% 191.21/191.73 [3134]E(f151(x31341,x31342,f115(x31341)),f115(x31341))
% 191.21/191.73 [3135]E(f162(x31351,x31352,f115(x31351)),f115(x31351))
% 191.21/191.73 [3136]E(f160(x31361,f115(x31361),x31362),f115(x31361))
% 191.21/191.73 [3142]E(f773(f259(x31421,x31421),f260(x31421,x31422)),x31422)
% 191.21/191.73 [3143]E(f773(f261(x31431,x31431),f260(x31431,x31432)),x31432)
% 191.21/191.73 [3152]P1(f773(a26,f28(x31521,x31522)))
% 191.21/191.73 [3153]E(f773(f278(x31531,x31531),f260(x31531,x31532)),f260(x31531,x31532))
% 191.21/191.73 [3166]E(f300(f848(x31661),f146(x31661,x31662)),f147(x31661,f300(x31661,x31662)))
% 191.21/191.73 [3168]P1(f773(f127(a1),f163(x31681,x31682)))
% 191.21/191.73 [3176]E(f773(f259(x31761,x31761),f300(x31761,x31762)),f239(f855(x31761,a841)))
% 191.21/191.73 [3177]E(f773(f261(x31771,x31771),f300(x31771,x31772)),f239(f855(x31771,a841)))
% 191.21/191.73 [3181]P1(f773(f127(x31811),f152(x31811,x31812)))
% 191.21/191.73 [3189]E(f773(f158(a1),f163(x31891,x31892)),f295(a1,x31891,x31892))
% 191.21/191.73 [3204]P54(x32041,f180(f855(x32041,a841)),x32042)
% 191.21/191.73 [3209]E(f773(f250(a1,a1),f53(x32091,x32092)),f52(a1,x32091,x32092))
% 191.21/191.73 [3210]E(f773(f294(a847,x32101),f773(a114,x32102)),f295(a847,x32101,x32102))
% 191.21/191.73 [3237]E(f295(a847,f773(a114,x32371),x32372),f297(a847,x32371,x32372))
% 191.21/191.73 [3240]P47(x32401,f239(f855(x32401,a841)),f300(x32401,x32402))
% 191.21/191.73 [3303]E(f773(f773(f3(a847),x33031),f773(a114,x33032)),f773(f42(a847),f298(a847,x33032,x33031)))
% 191.21/191.73 [3358]E(f156(x33581,x33582,f115(x33581)),f773(f773(f241(f848(x33581),f848(x33581)),f115(x33581)),f115(x33581)))
% 191.21/191.73 [3377]E(f773(f251(x33771,x33772,f854(x33771,x33772)),f241(x33771,x33772)),f39(f854(x33771,x33772)))
% 191.21/191.73 [3382]P1(f773(f773(f334(f848(x33821)),f115(x33821)),f149(x33821,x33822)))
% 191.21/191.73 [3383]E(f773(f181(f848(x33831)),f116(x33831,x33832)),f773(f773(f3(a847),f773(f181(f848(x33831)),x33832)),f80(a847)))
% 191.21/191.73 [3393]P1(f773(f63(a847),f295(a847,x33931,x33932)))
% 191.21/191.73 [3394]P1(f773(f63(a847),f297(a847,x33941,x33942)))
% 191.21/191.73 [3395]P1(f773(f63(a847),f298(a847,x33951,x33952)))
% 191.21/191.73 [3396]P1(f773(f63(a1),f295(a1,x33961,x33962)))
% 191.21/191.73 [3397]P1(f773(f63(a1),f297(a1,x33971,x33972)))
% 191.21/191.73 [3398]P1(f773(f63(a1),f298(a1,x33981,x33982)))
% 191.21/191.73 [3502]E(f773(f303(a847,a847,a114),f295(a847,x35021,x35022)),f295(a847,f773(a114,x35021),f773(a114,x35022)))
% 191.21/191.73 [3519]E(f773(f773(f281(x35191,x35191,x35191),f300(x35191,x35192)),f300(x35191,x35192)),f300(x35191,x35192))
% 191.21/191.73 [3549]E(f773(f773(f241(a1,a1),f773(f773(f43(a1),x35491),x35492)),f52(a1,x35491,x35492)),f53(x35491,x35492))
% 191.21/191.73 [3550]E(f773(f773(f241(a101,a101),f773(f773(f43(a101),x35501),x35502)),f52(a101,x35501,x35502)),f24(x35501,x35502))
% 191.21/191.73 [3579]E(f773(f773(f241(a847,a847),f773(f773(f43(a847),x35791),x35792)),f52(a847,x35791,x35792)),f87(f854(a847,a847),f55(x35791,x35792)))
% 191.21/191.73 [3631]P1(f773(f773(f233(a847),f773(f773(f3(a847),x36311),x36312)),f773(a114,x36311)))
% 191.21/191.73 [3732]E(f773(f773(f82(a1),f773(f773(f83(a1),x37321),f773(f773(f43(a1),x37322),x37321))),f52(a1,x37322,x37321)),x37322)
% 191.21/191.73 [3736]E(f773(f773(f46(a847,f855(f854(f848(x37361),f848(x37361)),a841)),f239(f855(a847,a841))),f133(x37361,x37362)),f135(x37361,x37362))
% 191.21/191.73 [3961]P1(f773(f773(f334(f854(f848(x39611),f848(x39611))),f773(f773(f241(f848(x39611),f848(x39611)),f115(x39611)),f115(x39611))),f147(x39611,x39612)))
% 191.21/191.73 [4124]E(f252(x41241,x41241,x41242,x41242,f7(x41241),f7(x41242)),f39(f854(x41241,x41242)))
% 191.21/191.73 [4126]E(f252(x41261,x41261,x41262,x41262,f39(x41261),f39(x41262)),f39(f854(x41261,x41262)))
% 191.21/191.73 [4378]~E(f773(f227(x43781),x43782),f183(x43781))
% 191.21/191.73 [4396]~P37(x43961,f773(f227(x43961),x43962))
% 191.21/191.73 [3117]E(f773(f231(x31171),f773(f227(x31171),x31172)),x31172)
% 191.21/191.73 [3118]E(f773(f142(x31181),f773(f142(x31181),x31182)),x31182)
% 191.21/191.73 [3120]E(f773(f773(f128(x31201),f2(a847)),x31202),x31202)
% 191.21/191.73 [3130]E(f773(f773(f159(x31301),f2(a847)),x31302),f115(x31301))
% 191.21/191.73 [3138]E(f773(f773(f125(x31381),f115(x31381)),x31382),x31382)
% 191.21/191.73 [3145]E(f773(f181(f851(x31451)),f773(f227(x31451),x31452)),f2(a847))
% 191.21/191.73 [3147]E(f44(f855(x31471,a841),f773(f301(x31471),x31472)),x31472)
% 191.21/191.73 [3149]E(f773(f158(x31491),f773(f141(x31491),x31492)),f773(f158(x31491),x31492))
% 191.21/191.73 [3150]E(f773(f158(x31501),f773(f142(x31501),x31502)),f773(f158(x31501),x31502))
% 191.21/191.73 [3157]E(f773(f773(f3(a101),x31571),x31572),f773(f773(a4,x31571),x31572))
% 191.21/191.73 [3170]E(f773(f773(f82(a847),x31701),x31702),f773(f773(f82(a847),x31702),x31701))
% 191.21/191.73 [3171]E(f773(f773(f82(a1),x31711),x31712),f773(f773(f82(a1),x31712),x31711))
% 191.21/191.73 [3172]E(f773(f773(f83(a847),x31721),x31722),f773(f773(f83(a847),x31722),x31721))
% 191.21/191.73 [3173]E(f773(f773(f83(a1),x31731),x31732),f773(f773(f83(a1),x31732),x31731))
% 191.21/191.73 [3196]E(f773(f773(f173(x31961,x31961),f2(a847)),x31962),f39(x31961))
% 191.21/191.73 [3197]E(f773(f181(f848(x31971)),f773(f141(x31971),x31972)),f773(f181(f848(x31971)),x31972))
% 191.21/191.73 [3198]E(f773(f181(f848(x31981)),f773(f142(x31981),x31982)),f773(f181(f848(x31981)),x31982))
% 191.21/191.73 [3199]E(f160(x31991,x31992,f180(f855(a847,a841))),f115(x31991))
% 191.21/191.73 [3200]E(f773(f773(f143(x32001,x32001),f7(x32001)),x32002),x32002)
% 191.21/191.73 [3202]E(f773(f240(a1,a1),f53(x32021,x32022)),f773(f773(f43(a1),x32021),x32022))
% 191.21/191.73 [3220]E(f34(f35(x32201,x32202)),f773(f773(f82(a847),f34(x32202)),f773(a114,f2(a847))))
% 191.21/191.73 [3221]E(f773(f276(x32211),f773(f278(x32211,x32211),x32212)),f773(f276(x32211),x32212))
% 191.21/191.73 [3225]P1(f773(f63(x32251),f773(f158(x32251),x32252)))
% 191.21/191.73 [3232]E(f773(f773(f82(a1),x32321),f773(f81(a1),x32322)),f773(f773(f3(a1),x32321),x32322))
% 191.21/191.73 [3239]P28(x32391,x32392,f180(f855(f846(x32391),a841)))
% 191.21/191.73 [3243]E(f773(f303(x32431,x32431,f7(x32431)),x32432),x32432)
% 191.21/191.73 [3244]E(f773(f303(x32441,x32441,f39(x32441)),x32442),x32442)
% 191.21/191.73 [3245]E(f773(f305(x32451,x32451,f7(x32451)),x32452),x32452)
% 191.21/191.73 [3246]E(f773(f305(x32461,x32461,f39(x32461)),x32462),x32462)
% 191.21/191.73 [3247]P1(f773(f239(f855(x32471,a841)),x32472))
% 191.21/191.73 [3249]E(f773(f42(a847),f773(f294(a847,x32491),x32492)),f773(f773(f3(a847),x32492),x32491))
% 191.21/191.73 [3250]E(f773(f294(a847,f773(a114,x32501)),x32502),f298(a847,x32501,x32502))
% 191.21/191.73 [3262]E(f773(f773(f302(x32621),x32622),f180(f855(x32621,a841))),f773(f256(x32621),f773(a330,x32622)))
% 191.21/191.73 [3268]E(f773(f773(f302(x32681),x32682),f180(f855(x32681,a841))),f226(x32681,f773(f227(x32681),x32682)))
% 191.21/191.73 [3270]E(f300(x32701,f773(f278(x32701,x32701),x32702)),f773(f278(x32701,x32701),f300(x32701,x32702)))
% 191.21/191.73 [3274]E(f773(f773(f82(a847),f773(a114,x32741)),x32742),f773(f773(f82(a847),x32741),f773(a114,x32742)))
% 191.21/191.73 [3275]E(f773(f773(f3(a847),f773(a114,x32751)),f773(a114,x32752)),f773(f773(f3(a847),x32751),x32752))
% 191.21/191.73 [3280]E(f773(f42(a847),f297(a847,x32801,x32802)),f773(f773(f3(a847),x32802),x32801))
% 191.21/191.73 [3289]P36(x32891,f773(f773(f280(a847,x32891),a237),x32892))
% 191.21/191.73 [3291]P18(a847,f130(a847,f773(f294(a847,x32911),x32912)))
% 191.21/191.73 [3293]P1(f773(f63(a847),f773(f294(a847,x32931),x32932)))
% 191.21/191.73 [3294]P1(f773(f63(a1),f773(f294(a1,x32941),x32942)))
% 191.21/191.73 [3296]E(f773(f278(f848(x32961),f848(x32961)),f146(x32961,x32962)),f146(x32961,f773(f278(x32961,x32961),x32962)))
% 191.21/191.73 [3297]E(f773(f181(a842),f35(x32971,x32972)),f773(f773(f82(a847),f773(f181(a842),x32972)),f773(a114,f2(a847))))
% 191.21/191.73 [3299]E(f773(f294(a1,x32991),f773(f773(f82(a1),x32992),f80(a1))),f295(a1,x32991,x32992))
% 191.21/191.73 [3302]E(f773(f773(f43(a1),f773(f81(a1),x33021)),f773(f81(a1),x33022)),f773(f773(f43(a1),x33021),x33022))
% 191.21/191.73 [3310]E(f171(x33101,x33102,f773(f18(f851(x33102),x33101),f183(x33102))),f180(f855(x33102,a841)))
% 191.21/191.73 [3311]E(f169(x33111,x33112,f773(f18(f851(x33112),x33111),f183(x33112))),f180(f855(x33111,a841)))
% 191.21/191.73 [3312]E(f773(f773(f173(f854(x33121,x33121),a841),f80(a847)),x33122),x33122)
% 191.21/191.73 [3314]E(f773(f773(f3(f855(x33141,a841)),x33142),f180(f855(x33141,a841))),x33142)
% 191.21/191.73 [3315]E(f773(f773(f103(f855(x33151,a841)),x33152),f180(f855(x33151,a841))),x33152)
% 191.21/191.73 [3316]E(f773(f773(f104(f855(x33161,a841)),x33162),f239(f855(x33161,a841))),x33162)
% 191.21/191.73 [3317]E(f773(f240(a847,a847),f87(f854(a847,a847),f55(x33171,x33172))),f773(f773(f43(a847),x33171),x33172))
% 191.21/191.73 [3323]E(f307(x33231,f773(a23,x33232),f773(f81(a1),f773(a23,x33232))),f773(f773(f310(a1),x33231),x33232))
% 191.21/191.73 [3324]E(f295(a1,f773(f773(f82(a1),x33241),f80(a1)),x33242),f297(a1,x33241,x33242))
% 191.21/191.73 [3329]E(f773(f250(a847,a847),f87(f854(a847,a847),f55(x33291,x33292))),f52(a847,x33291,x33292))
% 191.21/191.73 [3337]E(f308(x33371,f773(a23,x33372),f773(f81(a1),f773(a23,x33372))),f309(a1,x33371,x33372))
% 191.21/191.73 [3340]P1(f773(f773(f334(x33401),x33402),f239(f855(x33401,a841))))
% 191.21/191.73 [3344]E(f773(f773(f3(a847),f773(a114,x33441)),x33442),f773(f42(a847),f295(a847,x33442,x33441)))
% 191.21/191.73 [3369]E(f773(f773(f3(f855(x33691,a841)),x33692),f239(f855(x33691,a841))),f180(f855(x33691,a841)))
% 191.21/191.73 [3370]E(f773(f773(f103(f855(x33701,a841)),x33702),f239(f855(x33701,a841))),f239(f855(x33701,a841)))
% 191.21/191.73 [3371]E(f773(f773(f104(f855(x33711,a841)),x33712),f180(f855(x33711,a841))),f180(f855(x33711,a841)))
% 191.21/191.73 [3385]E(f52(a1,f773(f102(a1),x33851),f773(f102(a1),x33852)),f773(f102(a1),f52(a847,x33851,x33852)))
% 191.21/191.73 [3386]E(f52(a1,f773(f81(a1),x33861),f773(f81(a1),x33862)),f773(f81(a1),f52(a1,x33861,x33862)))
% 191.21/191.73 [3400]E(f773(f181(f848(x34001)),f773(f157(x34001),x34002)),f773(f773(f3(a847),f773(f181(f848(x34001)),x34002)),f80(a847)))
% 191.21/191.73 [3428]E(f773(f773(f43(a1),f52(a1,x34281,x34282)),x34282),f2(a1))
% 191.21/191.73 [3437]E(f773(a5,f52(a847,f773(a22,x34371),f773(a22,x34372))),f52(a101,x34371,x34372))
% 191.21/191.73 [3469]E(f773(a5,f773(f773(f82(a847),f773(a22,x34691)),f773(a22,x34692))),f773(f773(f82(a101),x34691),x34692))
% 191.21/191.73 [3470]E(f773(a5,f773(f773(f83(a847),f773(a22,x34701)),f773(a22,x34702))),f773(f773(f83(a101),x34701),x34702))
% 191.21/191.73 [3471]E(f773(a5,f773(f773(f43(a847),f773(a22,x34711)),f773(a22,x34712))),f773(f773(f43(a101),x34711),x34712))
% 191.21/191.73 [3472]E(f773(a5,f773(f773(f3(a847),f773(a22,x34721)),f773(a22,x34722))),f773(f773(f3(a101),x34721),x34722))
% 191.21/191.73 [3481]E(f773(f303(a847,a847,a114),f773(f294(a847,x34811),x34812)),f773(f294(a847,f773(a114,x34811)),f773(a114,x34812)))
% 191.21/191.73 [3507]P1(f773(f55(x35071,x35072),f87(f854(a847,a847),f55(x35071,x35072))))
% 191.21/191.73 [3524]E(f773(f773(f82(a847),f773(f773(f82(a847),f34(x35241)),f34(x35242))),f773(a114,f2(a847))),f34(f36(x35241,x35242)))
% 191.21/191.73 [3525]E(f52(a847,f773(a114,f52(a847,x35251,x35252)),x35252),f52(a847,f773(a114,x35251),x35252))
% 191.21/191.73 [3539]E(f773(f773(f47(f855(x35391,a841),f855(x35391,a841)),x35392),f7(f855(x35391,a841))),f45(f855(x35391,a841),x35392))
% 191.21/191.73 [3540]E(f773(f773(f46(f855(x35401,a841),f855(x35401,a841)),x35402),f7(f855(x35401,a841))),f44(f855(x35401,a841),x35402))
% 191.21/191.73 [3543]P1(f773(f773(f334(f855(x35431,a841)),x35432),f773(f301(x35431),x35432)))
% 191.21/191.73 [3548]E(f52(a1,f773(f81(a1),f52(a1,x35481,x35482)),x35482),f52(a1,f773(f81(a1),x35481),x35482))
% 191.21/191.73 [3560]P1(f773(f773(f232(f855(x35601,a841)),x35602),f239(f855(x35601,a841))))
% 191.21/191.73 [3562]E(f773(f773(f281(x35621,x35621,x35621),f300(x35621,x35622)),f300(x35621,f300(x35621,x35622))),f300(x35621,x35622))
% 191.21/191.73 [3563]E(f773(f773(f103(f855(x35631,a841)),f773(f261(x35631,x35631),x35632)),f773(f259(x35631,x35631),x35632)),f773(f276(x35631),x35632))
% 191.21/191.73 [3585]E(f314(x35851,x35852,f239(f855(x35851,a841)),f239(f855(x35852,a841))),f239(f855(f856(x35851,x35852),a841)))
% 191.21/191.73 [3636]P1(f773(f773(f232(a847),f52(a847,x36361,x36362)),x36361))
% 191.21/191.73 [3660]P1(f773(f773(f232(a1),f773(f81(a1),f773(f102(a1),x36601))),f773(f102(a1),x36602)))
% 191.21/191.73 [3685]P1(f773(f773(f334(f855(x36851,a841)),f180(f855(x36851,a841))),f773(f301(x36851),x36852)))
% 191.21/191.73 [3690]E(f300(x36901,f773(f773(f281(x36901,x36901,x36901),x36902),f300(x36901,x36902))),f300(x36901,x36902))
% 191.21/191.73 [3693]E(f773(f773(f281(x36931,x36931,x36931),f300(x36931,x36932)),x36932),f773(f773(f281(x36931,x36931,x36931),x36932),f300(x36931,x36932)))
% 191.21/191.73 [3695]E(f773(a107,f773(f773(f82(a1),f773(f773(f3(a1),x36951),x36952)),f80(a1))),f773(f42(a1),f295(a1,x36952,x36951)))
% 191.21/191.73 [3712]E(f773(f259(x37121,x37121),f773(f773(f281(x37121,x37121,x37121),x37122),f300(x37121,x37122))),f773(f259(x37121,x37121),x37122))
% 191.21/191.73 [3713]E(f773(f261(x37131,x37131),f773(f773(f281(x37131,x37131,x37131),x37132),f300(x37131,x37132))),f773(f261(x37131,x37131),x37132))
% 191.21/191.73 [3728]E(f773(f773(f82(a847),f773(f773(f82(a847),f773(f181(a842),x37281)),f773(f181(a842),x37282))),f773(a114,f2(a847))),f773(f181(a842),f36(x37281,x37282)))
% 191.21/191.73 [3740]P29(a847,a847,f773(f773(f9(a847,a847,a847),f82(a847)),x37401),x37402)
% 191.21/191.73 [3742]P18(a847,f773(f142(a847),f773(f773(f143(f848(x37421),a847),f181(f848(x37421))),f164(x37421,x37422))))
% 191.21/191.73 [3789]P1(f773(f773(f233(a1),f773(f81(a1),f773(f102(a1),f773(a114,x37891)))),f773(f102(a1),x37892)))
% 191.21/191.73 [3829]E(f773(f132(f848(x38291),x38291,f773(f9(x38291,f848(x38291),f848(x38291)),f140(x38291)),f115(x38291)),x38292),f773(f142(x38291),x38292))
% 191.21/191.73 [3878]P1(f773(f773(f232(f855(f854(f848(x38781),f848(x38781)),a841)),f147(x38781,x38782)),f300(f848(x38781),f146(x38781,x38782))))
% 191.21/191.73 [3911]P1(f773(f55(x39111,x39112),f773(f773(f241(a847,a847),f773(f773(f43(a847),x39111),x39112)),f52(a847,x39111,x39112))))
% 191.21/191.73 [3922]P1(f773(f773(f232(f855(f854(f848(x39221),f848(x39221)),a841)),f146(x39221,f300(x39221,x39222))),f300(f848(x39221),f146(x39221,x39222))))
% 191.21/191.73 [4153]E(f773(f773(f253(f854(a101,a101),a101,f854(a101,a101),f854(x41531,f854(a101,a101))),f264(f773(f155(a101),f773(f773(f143(f854(a101,x41531),a101),f240(a101,x41531)),x41532)))),f773(f773(f10(x41531,f855(f854(a101,a101),f854(x41531,f854(a101,a101))),a101),f241(x41531,f854(a101,a101))),f265(x41531,x41532))),f263(x41531,x41532))
% 191.21/191.73 [4332]E(f773(f251(f855(f854(x43321,x43321),a841),f855(f854(x43321,x43321),a841),f855(f855(x43322,x43321),f854(f855(f854(x43322,x43322),a841),f855(f854(x43322,x43322),a841)))),f773(f773(f9(f855(f854(x43321,x43321),a841),f855(f855(f854(x43321,x43321),a841),f855(f855(x43322,x43321),f855(f854(x43322,x43322),a841))),f855(f855(f854(x43321,x43321),a841),f855(f855(x43322,x43321),f854(f855(f854(x43322,x43322),a841),f855(f854(x43322,x43322),a841))))),f773(f773(f10(f855(f855(f855(x43322,x43321),f855(f854(x43322,x43322),a841)),f855(f855(x43322,x43321),f854(f855(f854(x43322,x43322),a841),f855(f854(x43322,x43322),a841)))),f855(f855(f855(f854(x43321,x43321),a841),f855(f855(x43322,x43321),f855(f854(x43322,x43322),a841))),f855(f855(f854(x43321,x43321),a841),f855(f855(x43322,x43321),f854(f855(f854(x43322,x43322),a841),f855(f854(x43322,x43322),a841))))),f855(f854(x43321,x43321),a841)),f10(f855(f855(x43322,x43321),f855(f854(x43322,x43322),a841)),f855(f855(x43322,x43321),f854(f855(f854(x43322,x43322),a841),f855(f854(x43322,x43322),a841))),f855(f854(x43321,x43321),a841))),f773(f773(f10(f855(f855(x43322,x43321),f855(f855(f854(x43322,x43322),a841),f854(f855(f854(x43322,x43322),a841),f855(f854(x43322,x43322),a841)))),f855(f855(f855(x43322,x43321),f855(f854(x43322,x43322),a841)),f855(f855(x43322,x43321),f854(f855(f854(x43322,x43322),a841),f855(f854(x43322,x43322),a841)))),f855(f854(x43321,x43321),a841)),f20(f855(x43322,x43321),f855(f854(x43322,x43322),a841),f854(f855(f854(x43322,x43322),a841),f855(f854(x43322,x43322),a841)))),f773(f773(f10(f855(f855(x43322,x43321),f855(f854(x43322,x43322),a841)),f855(f855(x43322,x43321),f855(f855(f854(x43322,x43322),a841),f854(f855(f854(x43322,x43322),a841),f855(f854(x43322,x43322),a841)))),f855(f854(x43321,x43321),a841)),f773(f10(f855(f854(x43322,x43322),a841),f855(f855(f854(x43322,x43322),a841),f854(f855(f854(x43322,x43322),a841),f855(f854(x43322,x43322),a841))),f855(x43322,x43321)),f241(f855(f854(x43322,x43322),a841),f855(f854(x43322,x43322),a841)))),f280(x43321,x43322))))),f280(x43321,x43322))),f76(x43321,x43322))
% 191.21/191.73 [4446]~E(f773(f301(x44461),x44462),f180(f855(f855(x44461,a841),a841)))
% 191.21/191.73 [4464]~P1(f773(f773(f334(x44641),x44642),f180(f855(x44641,a841))))
% 191.21/191.73 [4473]~P1(f773(f773(f233(f855(x44731,a841)),x44732),f180(f855(x44731,a841))))
% 191.21/191.73 [3252]E(f773(f773(f3(a847),x32521),f773(f773(f82(a847),x32521),x32522)),f2(a847))
% 191.21/191.73 [3254]E(f773(f773(f103(f855(x32541,a841)),x32542),x32542),x32542)
% 191.21/191.73 [3255]E(f773(f773(f104(f855(x32551,a841)),x32552),x32552),x32552)
% 191.21/191.73 [3282]E(f773(f773(f3(f855(x32821,a841)),x32822),x32822),f180(f855(x32821,a841)))
% 191.21/191.73 [3285]E(f773(f133(x32851,x32852),f2(a847)),f180(f855(f854(f848(x32851),f848(x32851)),a841)))
% 191.21/191.73 [3286]E(f773(f773(f82(a847),x32861),f773(a114,x32862)),f773(a114,f773(f773(f82(a847),x32861),x32862)))
% 191.21/191.73 [3298]E(f188(f773(f102(a1),x32981),f773(f102(a1),x32982)),f773(f102(a1),f773(f773(f3(a847),x32981),x32982)))
% 191.21/191.73 [3301]E(f773(f773(f43(a1),f773(f81(a1),x33011)),x33012),f773(f773(f43(a1),x33011),f773(f81(a1),x33012)))
% 191.21/191.73 [3305]E(f773(f42(a1),f773(f294(a1,x33051),x33052)),f773(a107,f773(f773(f3(a1),x33052),x33051)))
% 191.21/191.73 [3308]E(f773(f773(f82(a847),f773(a114,x33081)),x33082),f773(a114,f773(f773(f82(a847),x33081),x33082)))
% 191.21/191.73 [3313]E(f773(f81(f855(x33131,a841)),f773(f81(f855(x33131,a841)),x33132)),x33132)
% 191.21/191.73 [3326]E(f164(x33261,f773(f773(f140(f848(x33261)),f115(x33261)),x33262)),f164(x33261,x33262))
% 191.21/191.73 [3330]E(f773(f773(f82(a847),x33301),f773(f773(f83(a847),x33301),x33302)),f773(f773(f83(a847),x33301),f773(a114,x33302)))
% 191.21/191.73 [3338]E(f773(f773(a4,f773(a5,x33381)),f773(a5,x33382)),f773(a5,f773(f773(f3(a847),x33381),x33382)))
% 191.21/191.73 [3349]E(f773(f773(f83(a1),f773(f81(a1),x33491)),x33492),f773(f81(a1),f773(f773(f83(a1),x33491),x33492)))
% 191.21/191.73 [3351]E(f773(f773(f242(a1),f773(f102(a1),x33511)),x33512),f773(f102(a1),f773(f773(f242(a847),x33511),x33512)))
% 191.21/191.73 [3352]E(f773(f773(f82(a101),f773(a5,x33521)),f773(a5,x33522)),f773(a5,f773(f773(f82(a847),x33521),x33522)))
% 191.21/191.73 [3353]E(f773(f773(f83(a101),f773(a5,x33531)),f773(a5,x33532)),f773(a5,f773(f773(f83(a847),x33531),x33532)))
% 191.21/191.73 [3354]E(f773(f773(f236(a847),f773(a114,x33541)),f773(a114,x33542)),f773(a114,f773(f773(f236(a847),x33541),x33542)))
% 191.21/191.73 [3355]E(f773(f773(f179(a847),f773(a114,x33551)),f773(a114,x33552)),f773(a114,f773(f773(f179(a847),x33551),x33552)))
% 191.21/191.73 [3361]E(f773(f158(a847),f130(a847,f773(f294(a847,x33611),x33612))),f773(f294(a847,x33611),x33612))
% 191.21/191.73 [3362]E(f306(x33621,f773(f773(f302(x33621),x33622),f180(f855(x33621,a841)))),x33622)
% 191.21/191.73 [3367]E(f773(f259(x33671,x33672),f180(f855(f854(x33671,x33672),a841))),f180(f855(x33672,a841)))
% 191.21/191.73 [3368]E(f773(f261(x33681,x33682),f180(f855(f854(x33681,x33682),a841))),f180(f855(x33681,a841)))
% 191.21/191.73 [3372]E(f773(a107,f773(f773(f3(a1),x33721),x33722)),f773(f42(a1),f297(a1,x33722,x33721)))
% 191.21/191.73 [3376]E(f773(f773(f82(a847),x33761),f773(f773(f83(a847),x33762),x33761)),f773(f773(f83(a847),f773(a114,x33762)),x33761))
% 191.21/191.73 [3378]E(f773(f773(f61(x33781),f180(f855(x33781,a841))),x33782),f180(f855(f855(x33781,a841),a841)))
% 191.21/191.73 [3387]E(f773(f181(f848(a847)),f130(a847,f773(f294(a847,x33871),x33872))),f773(f773(f3(a847),x33872),x33871))
% 191.21/191.73 [3407]E(f773(f773(f103(f855(x34071,a841)),f180(f855(x34071,a841))),x34072),x34072)
% 191.21/191.73 [3408]E(f773(f773(f104(f855(x34081,a841)),f239(f855(x34081,a841))),x34082),x34082)
% 191.21/191.73 [3411]E(f773(f773(f82(a1),f773(f81(a1),x34111)),f773(f81(a1),x34112)),f773(f81(a1),f773(f773(f82(a1),x34111),x34112)))
% 191.21/191.73 [3414]E(f773(f773(f82(a1),f773(f102(a1),x34141)),f773(f102(a1),x34142)),f773(f102(a1),f773(f773(f82(a847),x34141),x34142)))
% 191.21/191.73 [3415]E(f773(f773(f82(a1),f773(f106(a1),x34151)),f773(f106(a1),x34152)),f773(f106(a1),f773(f773(f82(a1),x34151),x34152)))
% 191.21/191.73 [3417]E(f773(f773(f83(a1),f773(f102(a1),x34171)),f773(f102(a1),x34172)),f773(f102(a1),f773(f773(f83(a847),x34171),x34172)))
% 191.21/191.73 [3418]E(f773(f773(f83(a1),f773(f106(a1),x34181)),f773(f106(a1),x34182)),f773(f106(a1),f773(f773(f83(a1),x34181),x34182)))
% 191.21/191.73 [3419]E(f773(f773(f43(a1),f773(f102(a1),x34191)),f773(f102(a1),x34192)),f773(f102(a1),f773(f773(f43(a847),x34191),x34192)))
% 191.21/191.73 [3438]E(f773(f773(f8(x34381,a847),f773(f18(a847,x34381),f80(a847))),x34382),f773(f42(x34381),x34382))
% 191.21/191.73 [3445]E(f773(f81(a1),f52(a1,f773(f81(a1),x34451),x34452)),f52(a1,x34451,f773(f81(a1),x34452)))
% 191.21/191.73 [3447]E(f773(f158(a1),f163(x34471,f773(f773(f3(a1),x34472),f80(a1)))),f773(f294(a1,x34471),x34472))
% 191.21/191.73 [3451]P1(f773(f773(f232(a847),x34511),f773(f773(f82(a847),x34512),x34511)))
% 191.21/191.73 [3452]P1(f773(f773(f232(a847),x34521),f773(f773(f82(a847),x34521),x34522)))
% 191.21/191.73 [3455]E(f773(f773(f3(f855(x34551,a841)),f180(f855(x34551,a841))),x34552),f180(f855(x34551,a841)))
% 191.21/191.73 [3456]E(f773(f773(f103(f855(x34561,a841)),f239(f855(x34561,a841))),x34562),f239(f855(x34561,a841)))
% 191.21/191.73 [3457]E(f773(f773(f104(f855(x34571,a841)),f180(f855(x34571,a841))),x34572),f180(f855(x34571,a841)))
% 191.21/191.73 [3462]E(f773(f773(f241(a1,a1),x34621),f773(f81(a1),x34622)),f773(a58,f773(f773(f241(a1,a1),x34621),x34622)))
% 191.21/191.73 [3463]E(f773(f294(a1,f773(f773(f82(a1),x34631),f80(a1))),x34632),f298(a1,x34631,x34632))
% 191.21/191.73 [3473]E(f773(f773(f83(a847),x34731),f773(f773(f43(a847),x34732),x34731)),f773(f773(f3(a847),x34732),f52(a847,x34732,x34731)))
% 191.21/191.73 [3474]E(f773(f773(f83(a1),x34741),f773(f773(f43(a1),x34742),x34741)),f773(f773(f3(a1),x34742),f52(a1,x34742,x34741)))
% 191.21/191.73 [3478]E(f773(f158(a1),f163(f773(f773(f82(a1),x34781),f80(a1)),x34782)),f297(a1,x34781,x34782))
% 191.21/191.73 [3482]P1(f773(f773(f232(f855(x34821,a841)),x34822),x34822))
% 191.21/191.73 [3487]E(f773(f773(f103(f855(x34871,a841)),x34872),f773(f81(f855(x34871,a841)),x34872)),f239(f855(x34871,a841)))
% 191.21/191.73 [3488]E(f773(f773(f104(f855(x34881,a841)),x34882),f773(f81(f855(x34881,a841)),x34882)),f180(f855(x34881,a841)))
% 191.21/191.73 [3494]E(f773(f773(f3(a847),f773(f773(f3(a847),x34941),f80(a847))),x34942),f773(f773(f3(a847),x34941),f773(a114,x34942)))
% 191.21/191.73 [3499]E(f773(f773(f3(f855(x34991,a841)),f239(f855(x34991,a841))),x34992),f773(f81(f855(x34991,a841)),x34992))
% 191.21/191.73 [3500]E(f773(f773(f3(a1),f773(f106(a1),x35001)),f773(f106(a1),x35002)),f773(f106(a1),f773(f773(f82(a1),x35001),f773(f81(a1),x35002))))
% 191.21/191.73 [3512]E(f773(f158(a847),f130(a847,f773(f294(a847,x35121),f773(a114,x35122)))),f295(a847,x35121,x35122))
% 191.21/191.73 [3541]E(f773(f773(f173(f854(x35411,x35411),a841),f2(a847)),x35412),f300(x35411,f180(f855(f854(x35411,x35411),a841))))
% 191.21/191.73 [3545]P1(f773(f127(a847),f130(a847,f773(f294(a847,x35451),x35452))))
% 191.21/191.73 [3561]E(f773(f303(a1,a847,a107),f295(a1,f773(f102(a1),x35611),f773(f102(a1),x35612))),f295(a847,x35611,x35612))
% 191.21/191.73 [3571]E(f175(a847,f2(a847),f7(a847),f773(f773(f3(a847),x35711),x35712)),f773(f773(f3(a847),x35711),f773(a114,x35712)))
% 191.21/191.73 [3572]E(f773(a107,f773(f773(f3(a1),x35721),f773(f773(f82(a1),x35722),f80(a1)))),f773(f42(a1),f298(a1,x35722,x35721)))
% 191.21/191.73 [3607]E(f773(f773(f143(a847,a847),a114),f130(a847,f773(f294(a847,x36071),x36072))),f130(a847,f773(f294(a847,f773(a114,x36071)),f773(a114,x36072))))
% 191.21/191.73 [3614]E(f773(f158(a1),f163(f773(f773(f82(a1),x36141),f80(a1)),f773(f773(f3(a1),x36142),f80(a1)))),f298(a1,x36141,x36142))
% 191.21/191.73 [3628]P1(f773(f773(f232(f855(x36281,a841)),f180(f855(x36281,a841))),x36282))
% 191.21/191.73 [3632]E(f87(x36321,f773(f773(f9(x36321,x36321,a841),a330),x36322)),x36322)
% 191.21/191.73 [3633]E(f92(x36331,f773(f773(f9(x36331,x36331,a841),a330),x36332)),x36332)
% 191.21/191.73 [3637]E(f773(f158(a847),f130(a847,f773(f294(a847,f773(a114,x36371)),f773(a114,x36372)))),f297(a847,x36371,x36372))
% 191.21/191.73 [3663]E(f773(f773(f248(x36631,x36632),f239(f855(x36631,a841))),f773(f18(f855(x36632,a841),x36631),f239(f855(x36632,a841)))),f239(f855(f854(x36631,x36632),a841)))
% 191.21/191.73 [3699]E(f773(f256(x36991),f773(f773(f10(a841,a841,x36991),a328),x36992)),f773(f81(f855(x36991,a841)),f773(f256(x36991),x36992)))
% 191.21/191.73 [3702]E(f773(f256(x37021),f773(f773(f9(x37021,x37021,a841),a330),x37022)),f773(f773(f302(x37021),x37022),f180(f855(x37021,a841))))
% 191.21/191.73 [3709]E(f773(f773(f82(a1),f773(f773(f82(a1),x37091),x37091)),f773(f773(f82(a1),x37092),x37092)),f773(f773(f82(a1),f773(f773(f82(a1),x37091),x37092)),f773(f773(f82(a1),x37091),x37092)))
% 191.21/191.73 [3710]E(f773(f773(f3(a1),f773(f773(f82(a1),x37101),x37101)),f773(f773(f82(a1),x37102),x37102)),f773(f773(f82(a1),f773(f773(f3(a1),x37101),x37102)),f773(f773(f3(a1),x37101),x37102)))
% 191.21/191.73 [3725]P1(f773(f773(f232(a847),f773(f42(x37251),f773(f158(x37251),x37252))),f773(f181(f848(x37251)),x37252)))
% 191.21/191.73 [3726]P1(f773(f773(f232(a847),f773(f181(f848(x37261)),f152(x37261,x37262))),f773(f181(f848(x37261)),x37262)))
% 191.21/191.73 [3737]E(f773(f256(x37371),f773(f773(f9(x37371,f855(x37371,a841),a841),f334(x37371)),x37372)),x37372)
% 191.21/191.73 [3753]E(f773(f773(f159(x37531),f773(f773(f3(a847),f773(f181(f848(x37531)),x37532)),f80(a847))),x37532),f116(x37531,x37532))
% 191.21/191.73 [3776]E(f175(a847,f2(a847),f773(f773(f10(a847,a847,a847),a114),f773(f236(a847),x37761)),x37762),f773(f773(f236(a847),f773(a114,x37761)),x37762))
% 191.21/191.73 [3780]E(f44(f855(x37801,a841),f773(f303(f855(f854(x37801,x37801),a841),f855(x37801,a841),f276(x37801)),x37802)),f773(f276(x37801),f44(f855(f854(x37801,x37801),a841),x37802)))
% 191.21/191.73 [3781]E(f175(a847,f773(a114,x37811),f773(f773(f10(a847,a847,a847),a114),f773(f179(a847),x37811)),x37812),f773(f773(f179(a847),f773(a114,x37811)),x37812))
% 191.21/191.73 [3783]E(f773(f773(f241(a1,a1),f773(f773(f43(a1),f773(f77(a1),x37831)),f773(f77(a1),x37832))),f52(a1,f773(f77(a1),x37831),f773(f77(a1),x37832))),f60(x37831,x37832))
% 191.21/191.73 [3803]P1(f773(f773(f232(f855(f855(x38031,a841),a841)),x38032),f773(f301(x38031),f44(f855(x38031,a841),x38032))))
% 191.21/191.73 [3834]E(f773(f773(f46(x38341,f855(x38341,a841)),x38342),f773(f773(f9(x38341,f855(x38341,a841),f855(x38341,a841)),f302(x38341)),f180(f855(x38341,a841)))),x38342)
% 191.21/191.73 [3835]E(f773(f773(f281(x38351,x38351,x38351),f773(f278(x38351,x38351),x38352)),f300(x38351,f773(f278(x38351,x38351),x38352))),f773(f278(x38351,x38351),f773(f773(f281(x38351,x38351,x38351),x38352),f300(x38351,x38352))))
% 191.21/191.73 [3903]E(f773(f158(x39031),f773(f132(f848(x39031),f848(x39031),f125(x39031),f115(x39031)),x39032)),f773(f773(f46(f848(x39031),f855(x39031,a841)),f773(f158(f848(x39031)),x39032)),f158(x39031)))
% 191.21/191.73 [3934]E(f773(f773(f103(f855(f854(x39341,x39341),a841)),f300(x39341,f180(f855(f854(x39341,x39341),a841)))),f773(f773(f281(x39341,x39341,x39341),f300(x39341,x39342)),x39342)),f300(x39341,x39342))
% 191.21/191.73 [3972]E(f773(f773(f167(x39721,x39721),x39722),x39722),f773(f773(f143(x39721,f854(x39721,x39721)),f773(f773(f20(x39721,x39721,f854(x39721,x39721)),f241(x39721,x39721)),f7(x39721))),x39722))
% 191.21/191.73 [4086]E(f773(f132(a847,f848(x40861),f773(f9(f848(x40861),a847,a847),f773(f773(f10(a847,f855(a847,a847),f848(x40861)),f179(a847)),f181(f848(x40861)))),f2(a847)),f773(f142(f848(x40861)),x40862)),f773(f181(f848(f848(x40861))),f164(x40861,x40862)))
% 191.21/191.73 [4166]E(f773(f773(f280(f854(a847,f848(x41661)),f848(x41661)),f325(a847,f848(x41661),a237,f135(x41661,x41662))),f773(f773(f20(f848(x41661),f848(x41661),f854(a847,f848(x41661))),f773(f773(f10(a847,f855(f848(x41661),f854(a847,f848(x41661))),f848(x41661)),f241(a847,f848(x41661))),f181(f848(x41661)))),f7(f848(x41661)))),f136(x41661,x41662))
% 191.21/191.73 [4289]E(f773(f256(x42891),f773(f773(f10(f855(f855(x42891,a841),a841),a841,x42891),f90(f855(x42891,a841))),f773(f773(f10(f855(f855(x42891,a841),a841),f855(f855(x42891,a841),a841),x42891),f773(f20(f855(x42891,a841),a841,a841),f773(f773(f10(a841,f855(a841,a841),f855(x42891,a841)),a335),f773(f773(f9(f855(x42891,a841),f855(f855(x42891,a841),a841),a841),f334(f855(x42891,a841))),x42892)))),f334(x42891)))),f45(f855(x42891,a841),x42892))
% 191.21/191.73 [4474]~P1(f773(f773(f233(a1),f773(f102(a1),x44741)),f773(f81(a1),f773(f102(a1),x44742))))
% 191.21/191.73 [3374]E(f773(f773(f3(a847),f773(f773(f82(a847),x33741),x33742)),x33742),x33741)
% 191.21/191.73 [3375]E(f773(f773(f3(a847),f773(f773(f82(a847),x33751),x33752)),x33751),x33752)
% 191.21/191.73 [3446]E(f773(f773(f82(a847),f773(f773(f3(a847),x34461),x34462)),x34462),f773(f773(f179(a847),x34461),x34462))
% 191.21/191.73 [3547]E(f773(f773(f83(a847),f773(f773(f43(a847),x35471),x35472)),x35472),f773(f773(f3(a847),x35471),f52(a847,x35471,x35472)))
% 191.21/191.73 [3576]E(f773(f158(a847),f130(a847,f773(f294(a847,f773(a114,x35761)),x35762))),f298(a847,x35761,x35762))
% 191.21/191.73 [3584]E(f773(f102(a1),f211(f773(a107,f773(f77(a1),x35841)),f773(a107,f773(f77(a1),x35842)))),f773(f773(a212,x35841),x35842))
% 191.21/191.73 [3586]E(f773(f773(f103(f855(x35861,a841)),f773(f81(f855(x35861,a841)),x35862)),x35862),f239(f855(x35861,a841)))
% 191.21/191.73 [3587]E(f773(f773(f104(f855(x35871,a841)),f773(f81(f855(x35871,a841)),x35872)),x35872),f180(f855(x35871,a841)))
% 191.21/191.73 [3603]P1(f773(f773(f232(a847),f773(f773(f43(a847),x36031),x36032)),x36031))
% 191.21/191.73 [3604]P1(f773(f773(f232(a847),f773(f773(f3(a847),x36041),x36042)),x36041))
% 191.21/191.73 [3629]P1(f773(f773(f233(a847),x36291),f773(a114,f773(f773(f82(a847),x36292),x36291))))
% 191.21/191.73 [3630]P1(f773(f773(f233(a847),x36301),f773(a114,f773(f773(f82(a847),x36301),x36302))))
% 191.21/191.73 [3649]E(f773(f773(f83(a847),f773(a107,f773(f77(a1),x36491))),f773(a107,f773(f77(a1),x36492))),f773(a107,f773(f77(a1),f773(f773(f83(a1),x36491),x36492))))
% 191.21/191.73 [3659]P1(f773(f773(f232(a1),f2(a1)),f773(f773(f242(a1),f773(f77(a1),x36591)),x36592)))
% 191.21/191.73 [3731]E(f773(f277(f848(x37311),f848(x37311),f147(x37311,x37312)),f773(f773(f302(f848(x37311)),f115(x37311)),f180(f855(f848(x37311),a841)))),f773(f773(f302(f848(x37311)),f115(x37311)),f180(f855(f848(x37311),a841))))
% 191.21/191.73 [3749]E(f773(f773(f103(f855(f854(x37491,x37491),a841)),f300(x37491,x37492)),f300(x37491,f180(f855(f854(x37491,x37491),a841)))),f300(x37491,x37492))
% 191.21/191.73 [3765]E(f773(f773(f43(a1),f773(f106(a1),f773(f773(f82(a1),x37651),x37651))),f773(f106(a1),f773(f773(f82(a1),x37652),x37652))),f773(f773(f43(a1),f773(f106(a1),x37651)),f773(f106(a1),x37652)))
% 191.21/191.73 [3824]E(f773(f773(f242(a1),x38241),f773(f106(a847),f773(f773(f82(a1),x38242),x38242))),f773(f773(f88(a1,a1),f773(f773(f242(a1),x38241),f773(f106(a847),x38242))),f773(f773(f20(a1,a1,a1),f83(a1)),f7(a1))))
% 191.21/191.73 [3830]E(f773(f256(f855(x38301,a841)),f773(f773(f9(f855(x38301,a841),f855(x38301,a841),a841),f232(f855(x38301,a841))),x38302)),f773(f301(x38301),x38302))
% 191.21/191.73 [3877]E(f773(f303(a1,a1,f773(f773(f9(a1,a1,a1),f82(a1)),x38771)),f773(f294(a1,f2(a1)),f773(f773(f3(a1),x38772),x38771))),f773(f294(a1,x38771),x38772))
% 191.21/191.73 [3880]P48(x38801,f773(f773(f3(f855(f854(x38801,x38801),a841)),x38802),f300(x38801,f180(f855(f854(x38801,x38801),a841)))))
% 191.21/191.73 [3900]E(f773(f181(f848(x39001)),f773(f132(f848(x39001),f848(x39001),f125(x39001),f115(x39001)),x39002)),f773(f155(a847),f773(f773(f143(f848(x39001),a847),f181(f848(x39001))),x39002)))
% 191.21/191.73 [3905]P47(x39051,f239(f855(x39051,a841)),f773(f773(f103(f855(f854(x39051,x39051),a841)),x39052),f300(x39051,f180(f855(f854(x39051,x39051),a841)))))
% 191.21/191.73 [3951]E(f175(a847,f2(a847),f773(f773(f10(a847,a847,a847),a114),f773(f773(f9(a847,a847,a847),f236(a847)),x39511)),x39512),f773(f773(f236(a847),x39512),f773(a114,x39511)))
% 191.21/191.73 [3954]E(f175(a847,f773(a114,x39541),f773(f773(f10(a847,a847,a847),a114),f773(f773(f9(a847,a847,a847),f179(a847)),x39541)),x39542),f773(f773(f179(a847),x39542),f773(a114,x39541)))
% 191.21/191.73 [3957]E(f773(f303(x39571,f848(x39571),f773(f773(f9(x39571,f848(x39571),f848(x39571)),f140(x39571)),f115(x39571))),x39572),f161(x39571,x39572,f773(f773(f302(f848(x39571)),f115(x39571)),f180(f855(f848(x39571),a841)))))
% 191.21/191.73 [3958]E(f773(f773(f103(f855(f854(x39581,x39581),a841)),f773(f773(f281(x39581,x39581,x39581),x39582),f300(x39581,x39582))),f300(x39581,f180(f855(f854(x39581,x39581),a841)))),f300(x39581,x39582))
% 191.21/191.73 [3966]P1(f773(f773(f232(f855(f854(x39661,x39661),a841)),f260(x39661,x39662)),f773(f773(f248(x39661,x39661),x39662),f773(f18(f855(x39661,a841),x39661),x39662))))
% 191.21/191.73 [3970]E(f773(f303(a1,a847,a107),f773(f773(f103(f855(a1,a841)),f773(f303(a847,a1,f102(a1)),x39701)),f773(f303(a847,a1,f102(a1)),x39702))),f773(f773(f103(f855(a847,a841)),x39701),x39702))
% 191.21/191.73 [3971]E(f773(f303(a1,a847,a107),f773(f773(f104(f855(a1,a841)),f773(f303(a847,a1,f102(a1)),x39711)),f773(f303(a847,a1,f102(a1)),x39712))),f773(f773(f104(f855(a847,a841)),x39711),x39712))
% 191.21/191.73 [3975]E(f773(f256(x39751),f773(f773(f10(a841,a841,x39751),a328),f773(f773(f9(x39751,f855(x39751,a841),a841),f334(x39751)),x39752))),f773(f81(f855(x39751,a841)),x39752))
% 191.21/191.73 [4002]E(f773(f132(f848(x40021),f848(x40021),f125(x40021),f115(x40021)),f773(f773(f143(f848(x40021),f848(x40021)),f142(x40021)),f773(f142(f848(x40021)),x40022))),f773(f142(x40021),f773(f132(f848(x40021),f848(x40021),f125(x40021),f115(x40021)),x40022)))
% 191.21/191.73 [4029]E(f773(f773(f46(a847,f855(f854(x40291,x40291),a841)),f239(f855(a847,a841))),f773(f773(f9(a847,f855(f854(x40291,x40291),a841),f855(f854(x40291,x40291),a841)),f173(f854(x40291,x40291),a841)),x40292)),f300(x40291,x40292))
% 191.21/191.73 [4051]E(f87(x40511,f773(f773(f10(f855(x40511,a841),a841,x40511),f773(a330,x40512)),f773(f773(f9(x40511,f855(x40511,a841),f855(x40511,a841)),f302(x40511)),f180(f855(x40511,a841))))),f306(x40511,x40512))
% 191.21/191.73 [4059]E(f773(f181(f848(x40591)),f152(x40591,f773(f132(f848(x40591),f848(x40591),f125(x40591),f115(x40591)),x40592))),f773(f42(x40591),f773(f773(f46(f848(x40591),f855(x40591,a841)),f773(f158(f848(x40591)),x40592)),f158(x40591))))
% 191.21/191.73 [4074]E(f773(f773(f103(f855(f854(x40741,x40741),a841)),x40742),f773(f773(f281(x40741,x40741,x40741),f773(f773(f281(x40741,x40741,x40741),x40742),f300(x40741,x40742))),x40742)),f773(f773(f281(x40741,x40741,x40741),x40742),f300(x40741,x40742)))
% 191.21/191.73 [4095]P1(f773(f773(f232(f855(f854(x40951,x40951),a841)),f773(f773(f281(x40951,x40951,x40951),x40952),f300(x40951,x40952))),f773(f773(f248(x40951,x40951),f773(f276(x40951),x40952)),f773(f18(f855(x40951,a841),x40951),f773(f276(x40951),x40952)))))
% 191.21/191.73 [4142]E(f773(f256(f848(x41421)),f773(f773(f9(f848(x41421),f855(x41421,a841),a841),f773(f773(f10(f855(x41421,a841),f855(f855(x41421,a841),a841),f848(x41421)),f232(f855(x41421,a841))),f158(x41421))),x41422)),f149(x41421,x41422))
% 191.21/191.73 [4154]E(f773(f145(f848(x41541),x41541,f115(x41541),f773(f773(f10(f848(x41541),f855(f848(x41541),f848(x41541)),x41541),f773(f9(f848(x41541),f848(x41541),f848(x41541)),f125(x41541))),f773(f773(f9(x41541,f848(x41541),f848(x41541)),f140(x41541)),f115(x41541)))),x41542),f773(f141(x41541),x41542))
% 191.21/191.73 [4193]P29(f855(x41931,x41932),f855(f854(x41931,x41932),a841),f773(f773(f10(f855(f854(x41931,x41932),a841),f855(f854(x41931,x41932),a841),f855(x41931,x41932)),f256(f854(x41931,x41932))),f773(f773(f10(f855(x41931,f855(x41932,a841)),f855(f854(x41931,x41932),a841),f855(x41931,x41932)),f251(x41931,x41932,a841)),f773(f10(x41932,f855(x41932,a841),x41931),f773(f9(x41932,x41932,a841),a330)))),f239(f855(f855(x41931,x41932),a841)))
% 191.21/191.73 [4198]E(f52(a1,f773(f106(a1),f773(f773(f82(a1),x41981),x41981)),f773(f106(a1),f773(f773(f82(a1),x41982),x41982))),f773(f773(f83(a1),f773(f106(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),f52(a1,f773(f106(a1),x41981),f773(f106(a1),x41982))))
% 191.21/191.73 [4239]E(f773(f773(f46(x42391,f855(f854(x42391,x42391),a841)),x42392),f773(f773(f9(x42391,f855(f854(x42391,x42391),a841),f855(f854(x42391,x42391),a841)),f773(f773(f10(f854(x42391,x42391),f855(f855(f854(x42391,x42391),a841),f855(f854(x42391,x42391),a841)),x42391),f302(f854(x42391,x42391))),f773(f773(f20(x42391,x42391,f854(x42391,x42391)),f241(x42391,x42391)),f7(x42391)))),f180(f855(f854(x42391,x42391),a841)))),f260(x42391,x42392))
% 191.21/191.73 [4247]E(f198(x42471,f773(f773(f241(a1,a1),f773(f81(a1),f773(f773(f75(f854(a1,a1),a1,x42471,f240(a1,a1)),f207(x42471)),x42472))),f773(f773(f75(f854(a1,a1),a1,x42471,f250(a1,a1)),f207(x42471)),x42472))),f221(x42471,x42472))
% 191.21/191.73 [4327]E(f773(f256(f855(x43271,a841)),f773(f773(f10(f855(f855(x43271,a841),a841),a841,f855(x43271,a841)),f89(f855(x43271,a841))),f773(f773(f9(f855(x43271,a841),f855(f855(x43271,a841),a841),f855(f855(x43271,a841),a841)),f773(f773(f10(f855(f855(x43271,a841),f855(a841,a841)),f855(f855(f855(x43271,a841),a841),f855(f855(x43271,a841),a841)),f855(x43271,a841)),f20(f855(x43271,a841),a841,a841)),f773(f773(f10(f855(f855(x43271,a841),a841),f855(f855(x43271,a841),f855(a841,a841)),f855(x43271,a841)),f773(f10(a841,f855(a841,a841),f855(x43271,a841)),a331)),f773(f773(f9(f855(x43271,a841),f855(f855(x43271,a841),f855(x43271,a841)),f855(f855(x43271,a841),a841)),f773(f773(f10(f855(f855(x43271,a841),a841),f855(f855(f855(x43271,a841),f855(x43271,a841)),f855(f855(x43271,a841),a841)),f855(x43271,a841)),f10(f855(x43271,a841),a841,f855(x43271,a841))),a330)),f81(f855(x43271,a841)))))),f773(f773(f10(f855(f855(x43271,a841),a841),a841,f855(x43271,a841)),f773(f334(f855(x43271,a841)),x43272)),f301(x43271))))),f773(f301(x43271),f773(f81(f855(x43271,a841)),x43272)))
% 191.21/191.73 [4471]~E(f773(f773(f82(a1),x44711),x44711),f773(f773(f3(a1),f773(f773(f82(a1),x44712),x44712)),a99))
% 191.21/191.73 [4476]~P1(f773(f773(f233(a847),f773(f773(f82(a847),x44761),x44762)),x44762))
% 191.21/191.73 [4477]~P1(f773(f773(f233(a847),f773(f773(f82(a847),x44771),x44772)),x44771))
% 191.21/191.73 [3664]E(f773(f773(f3(a847),x36641),f773(f773(f83(a847),f773(f773(f43(a847),x36641),x36642)),x36642)),f52(a847,x36641,x36642))
% 191.21/191.73 [3665]E(f773(f773(f3(a1),x36651),f773(f773(f83(a1),f773(f773(f43(a1),x36651),x36652)),x36652)),f52(a1,x36651,x36652))
% 191.21/191.73 [3700]E(f773(f773(f143(a847,x37001),f773(f153(x37001),x37002)),f130(a847,f773(f294(a847,f2(a847)),f773(f181(f848(x37001)),x37002)))),x37002)
% 191.21/191.73 [3761]E(f773(f277(x37611,x37611,f300(x37611,f180(f855(f854(x37611,x37611),a841)))),x37612),x37612)
% 191.21/191.73 [3881]E(f300(x38811,f773(f773(f3(f855(f854(x38811,x38811),a841)),x38812),f300(x38811,f180(f855(f854(x38811,x38811),a841))))),f300(x38811,x38812))
% 191.21/191.73 [3882]E(f300(x38821,f773(f773(f103(f855(f854(x38821,x38821),a841)),x38822),f300(x38821,f180(f855(f854(x38821,x38821),a841))))),f300(x38821,x38822))
% 191.21/191.73 [3938]E(f773(f773(f3(a1),f773(f773(f3(a1),f773(f773(f82(a1),x39381),x39381)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),x39382),x39382)),a99)),f773(f773(f82(a1),f773(f773(f3(a1),x39381),x39382)),f773(f773(f3(a1),x39381),x39382)))
% 191.21/191.73 [3980]E(f773(f773(f3(a1),f773(f773(f82(a1),f773(f773(f82(a1),x39801),x39802)),f773(f773(f82(a1),x39801),x39802))),a99),f773(f773(f82(a1),f773(f773(f82(a1),x39801),x39801)),f773(f773(f3(a1),f773(f773(f82(a1),x39802),x39802)),a99)))
% 191.21/191.73 [4006]E(f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),x40061),x40061)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),x40062),x40062)),a99)),f773(f773(f82(a1),f773(f773(f82(a1),x40061),f773(f773(f3(a1),x40062),a99))),f773(f773(f82(a1),x40061),f773(f773(f3(a1),x40062),a99))))
% 191.21/191.73 [4017]E(f773(f773(f3(a1),f773(f773(f82(a1),f773(f773(f82(a1),x40171),x40172)),f773(f773(f82(a1),x40171),x40172))),a99),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),x40171),x40171)),a99)),f773(f773(f82(a1),x40172),x40172)))
% 191.21/191.73 [4018]E(f773(f773(f3(a1),f773(f773(f82(a1),f773(f773(f3(a1),x40181),x40182)),f773(f773(f3(a1),x40181),x40182))),a99),f773(f773(f3(a1),f773(f773(f3(a1),f773(f773(f82(a1),x40181),x40181)),a99)),f773(f773(f82(a1),x40182),x40182)))
% 191.21/191.73 [4071]E(f773(f102(a1),f773(f773(f43(a847),f773(f773(f83(a847),f773(a107,f773(f77(a1),x40711))),f773(a107,f773(f77(a1),x40712)))),f211(f773(a107,f773(f77(a1),x40711)),f773(a107,f773(f77(a1),x40712))))),f213(x40711,x40712))
% 191.21/191.73 [4116]E(f773(f773(f253(f854(a101,a101),a101,f854(a101,a101),f854(x41161,f854(a101,a101))),f264(f773(a5,f773(f181(f848(x41161)),x41162)))),f773(f773(f10(x41161,f855(f854(a101,a101),f854(x41161,f854(a101,a101))),a101),f241(x41161,f854(a101,a101))),f773(f773(f10(a847,x41161,a101),f773(f153(x41161),x41162)),a22))),f270(x41161,x41162))
% 191.21/191.73 [4199]E(f773(f132(a847,f848(x41991),f773(f9(f848(x41991),a847,a847),f773(f773(f10(a847,f855(a847,a847),f848(x41991)),f179(a847)),f181(f848(x41991)))),f2(a847)),f773(f142(f848(x41991)),f164(x41991,x41992))),f773(f181(f848(f848(x41991))),f773(f126(f848(x41991),f773(f773(f10(a841,a841,f848(x41991)),a328),f773(f773(f9(f848(x41991),f848(x41991),a841),a330),f115(x41991)))),x41992)))
% 191.21/191.73 [4205]E(f773(f773(f46(a847,f855(x42051,a841)),f239(f855(a847,a841))),f773(f773(f9(a847,f855(a847,f855(x42051,a841)),f855(x42051,a841)),f773(f773(f10(f855(a847,a841),f855(f855(a847,f855(x42051,a841)),f855(x42051,a841)),a847),f46(a847,f855(x42051,a841))),f294(a847,f2(a847)))),x42052)),f773(f773(f46(a847,f855(x42051,a841)),f239(f855(a847,a841))),x42052))
% 191.21/191.73 [4224]P1(f773(f63(a847),f773(f256(a847),f773(f773(f20(a847,a841,a841),f773(f773(f10(a841,f855(a841,a841),a847),a331),x42241)),f773(f773(f9(a847,a847,a841),f233(a847)),x42242)))))
% 191.21/191.73 [4337]E(f773(f256(f854(f848(x43371),f848(x43371))),f773(f251(f848(x43371),f848(x43371),a841),f773(f773(f20(f848(x43371),f855(f848(x43371),a841),f855(f848(x43371),a841)),f773(f773(f10(f855(f848(x43371),f855(a841,a841)),f855(f855(f848(x43371),a841),f855(f848(x43371),a841)),f848(x43371)),f20(f848(x43371),a841,a841)),f773(f773(f10(f855(f848(x43371),a841),f855(f848(x43371),f855(a841,a841)),f848(x43371)),f773(f10(a841,f855(a841,a841),f848(x43371)),a332)),f773(f773(f9(f848(x43371),f855(f848(x43371),a847),f855(f848(x43371),a841)),f773(f773(f10(f855(a847,a841),f855(f855(f848(x43371),a847),f855(f848(x43371),a841)),f848(x43371)),f10(a847,a841,f848(x43371))),f773(f773(f10(a847,f855(a847,a841),f848(x43371)),f233(a847)),f181(f848(x43371))))),f181(f848(x43371)))))),f773(f773(f20(f848(x43371),f855(f848(x43371),a841),f855(f848(x43371),a841)),f773(f773(f10(f855(f848(x43371),f855(a841,a841)),f855(f855(f848(x43371),a841),f855(f848(x43371),a841)),f848(x43371)),f20(f848(x43371),a841,a841)),f773(f773(f10(f855(f848(x43371),a841),f855(f848(x43371),f855(a841,a841)),f848(x43371)),f773(f10(a841,f855(a841,a841),f848(x43371)),a331)),f773(f773(f9(f848(x43371),f855(f848(x43371),a847),f855(f848(x43371),a841)),f773(f773(f10(f855(a847,a841),f855(f855(f848(x43371),a847),f855(f848(x43371),a841)),f848(x43371)),f10(a847,a841,f848(x43371))),f773(f773(f10(a847,f855(a847,a841),f848(x43371)),a330),f181(f848(x43371))))),f181(f848(x43371)))))),f773(f773(f9(f848(x43371),f855(f854(f848(x43371),f848(x43371)),a841),f855(f848(x43371),a841)),f773(f773(f10(f855(f848(x43371),f855(f855(f854(f848(x43371),f848(x43371)),a841),a841)),f855(f855(f854(f848(x43371),f848(x43371)),a841),f855(f848(x43371),a841)),f848(x43371)),f9(f848(x43371),f855(f854(f848(x43371),f848(x43371)),a841),a841)),f773(f773(f10(f855(f848(x43371),f854(f848(x43371),f848(x43371))),f855(f848(x43371),f855(f855(f854(f848(x43371),f848(x43371)),a841),a841)),f848(x43371)),f773(f10(f854(f848(x43371),f848(x43371)),f855(f855(f854(f848(x43371),f848(x43371)),a841),a841),f848(x43371)),f334(f854(f848(x43371),f848(x43371))))),f241(f848(x43371),f848(x43371))))),f135(x43371,x43372)))))),f136(x43371,x43372))
% 191.21/191.73 [4009]E(f773(f773(f82(a1),f773(f773(f82(a1),f773(f773(f83(a1),x40091),x40092)),f773(f773(f83(a1),x40091),x40092))),x40092),f773(f773(f83(a1),f773(f773(f3(a1),f773(f773(f82(a1),x40091),x40091)),a99)),x40092))
% 191.21/191.73 [4114]E(f773(a107,f773(a91,f773(f277(f854(a847,a847),f854(a847,a847),a111),f773(f773(f302(f854(a847,a847)),f773(f773(f241(a847,a847),x41141),x41142)),f180(f855(f854(a847,a847),a841)))))),f773(f773(f3(a847),x41141),x41142))
% 191.21/191.73 [4120]E(f773(f773(f281(x41201,x41201,x41201),f773(f773(f103(f855(f854(x41201,x41201),a841)),x41202),f300(x41201,f180(f855(f854(x41201,x41201),a841))))),f300(x41201,f773(f773(f103(f855(f854(x41201,x41201),a841)),x41202),f300(x41201,f180(f855(f854(x41201,x41201),a841)))))),f300(x41201,x41202))
% 191.21/191.73 [4159]E(f265(x41591,f773(f126(f854(a101,x41591),f773(f251(a101,x41591,a841),f773(f773(f10(a841,f855(x41591,a841),a101),f18(a841,x41591)),f773(f233(a101),f2(a101))))),x41592)),f265(x41591,x41592))
% 191.21/191.73 [4160]E(f263(x41601,f773(f126(f854(a101,x41601),f773(f251(a101,x41601,a841),f773(f773(f10(a841,f855(x41601,a841),a101),f18(a841,x41601)),f773(f233(a101),f2(a101))))),x41602)),f263(x41601,x41602))
% 191.21/191.73 [4162]E(f773(f81(a1),f773(a91,f773(f277(f854(a847,a847),f854(a847,a847),a111),f773(f773(f302(f854(a847,a847)),f773(f773(f241(a847,a847),x41621),x41622)),f180(f855(f854(a847,a847),a841)))))),f773(a91,f773(f277(f854(a847,a847),f854(a847,a847),a111),f773(f773(f302(f854(a847,a847)),f773(f773(f241(a847,a847),x41622),x41621)),f180(f855(f854(a847,a847),a841))))))
% 191.21/191.73 [4236]E(f773(f773(f88(a1,a847),f773(f106(a1),f773(f773(f82(a1),x42361),a99))),f773(f773(f20(a1,a847,a847),f773(f773(f9(a1,a847,f855(a847,a847)),f773(f773(f10(a841,f855(a847,f855(a847,a847)),a1),f98(a847)),a186)),f2(a847))),f773(f773(f10(a847,a847,a1),a114),f773(f773(f10(a847,a847,a1),f773(f236(a847),x42362)),a107)))),f773(f773(f236(a847),f773(a114,x42362)),f773(f106(a847),x42361)))
% 191.21/191.73 [4237]E(f773(f773(f88(a1,a847),f773(f106(a1),f773(f773(f82(a1),x42371),a99))),f773(f773(f20(a1,a847,a847),f773(f773(f9(a1,a847,f855(a847,a847)),f773(f773(f10(a841,f855(a847,f855(a847,a847)),a1),f98(a847)),a186)),f773(a114,x42372))),f773(f773(f10(a847,a847,a1),a114),f773(f773(f10(a847,a847,a1),f773(f179(a847),x42372)),a107)))),f773(f773(f179(a847),f773(a114,x42372)),f773(f106(a847),x42371)))
% 191.21/191.73 [4257]E(f773(f132(f848(x42571),f848(x42571),f125(x42571),f115(x42571)),f773(f773(f143(f848(x42571),f848(x42571)),f145(f848(x42571),x42571,f115(x42571),f773(f773(f10(f848(x42571),f855(f848(x42571),f848(x42571)),x42571),f18(f848(x42571),f848(x42571))),f773(f773(f9(x42571,f848(x42571),f848(x42571)),f140(x42571)),f115(x42571))))),x42572)),f773(f773(f143(f848(x42571),x42571),f131(x42571)),f773(f126(f848(x42571),f773(f773(f10(a841,a841,f848(x42571)),a328),f773(f773(f9(f848(x42571),f848(x42571),a841),a330),f115(x42571)))),x42572)))
% 191.21/191.73 [4317]E(f773(f251(a1,a1,a841),f773(f773(f9(a1,f855(a1,a841),f855(a1,a841)),f773(f773(f10(f855(a1,f855(a841,a841)),f855(f855(a1,a841),f855(a1,a841)),a1),f20(a1,a841,a841)),f773(f773(f10(f855(a1,a841),f855(a1,f855(a841,a841)),a1),f773(f10(a841,f855(a841,a841),a1),a331)),f773(f773(f10(f855(a1,a1),f855(a1,a841),a1),f773(f10(a1,a841,a1),f773(a330,x43171))),f773(f773(f10(a1,f855(a1,a1),a1),f82(a1)),f773(f83(a1),x43172)))))),f773(f773(f20(a1,a841,a841),f773(f773(f10(a841,f855(a841,a841),a1),a331),f773(f773(f10(a841,a841,a1),f773(a335,f773(f773(f233(a1),f2(a1)),x43172))),f773(f773(f20(a1,a841,a841),f773(f773(f10(a841,f855(a841,a841),a1),a331),f773(f232(a1),f2(a1)))),f773(f773(f9(a1,a1,a841),f233(a1)),x43172))))),f773(f773(f10(a841,a841,a1),f773(a335,f773(a328,f773(f773(f233(a1),f2(a1)),x43172)))),f773(f773(f20(a1,a841,a841),f773(f773(f10(a841,f855(a841,a841),a1),a331),f773(f233(a1),x43172))),f773(f773(f9(a1,a1,a841),f232(a1)),f2(a1))))))),f56(x43171,x43172))
% 191.21/191.73 [4319]E(f773(f256(x43191),f773(f773(f10(f855(a847,a841),a841,x43191),f89(a847)),f773(f773(f9(x43191,f855(a847,a841),f855(a847,a841)),f773(f773(f10(f855(a847,f855(a841,a841)),f855(f855(a847,a841),f855(a847,a841)),x43191),f20(a847,a841,a841)),f773(f773(f10(f855(a847,a841),f855(a847,f855(a841,a841)),x43191),f773(f10(a841,f855(a841,a841),a847),a331)),f773(f773(f9(x43191,f855(a847,x43191),f855(a847,a841)),f773(f773(f10(f855(x43191,a841),f855(f855(a847,x43191),f855(a847,a841)),x43191),f10(x43191,a841,a847)),a330)),f773(f153(x43191),x43192))))),f773(f773(f9(a847,a847,a841),f233(a847)),f773(f181(f848(x43191)),x43192))))),f773(f158(x43191),x43192))
% 191.21/191.73 [4132]E(f773(f773(f3(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),x41321),a99)),x41322)),f773(f773(f3(a1),f773(f773(f82(a1),x41321),a99)),x41322))),a99),f773(f773(f3(a1),f773(f773(f82(a1),x41321),x41321)),f773(f773(f3(a1),f773(f773(f82(a1),x41322),x41322)),a99)))
% 191.21/191.73 [4252]E(f773(f132(f848(f848(x42521)),f848(f848(x42521)),f125(f848(x42521)),f115(f848(x42521))),f773(f773(f143(f848(x42521),f848(f848(x42521))),f145(f848(f848(x42521)),x42521,f115(f848(x42521)),f773(f18(f855(f848(x42521),f848(f848(x42521))),x42521),f773(f773(f9(f848(x42521),f848(f848(x42521)),f848(f848(x42521))),f140(f848(x42521))),f115(f848(x42521)))))),x42522)),f773(f773(f143(f848(x42521),f848(x42521)),f157(x42521)),f773(f126(f848(x42521),f773(f773(f10(a841,a841,f848(x42521)),a328),f773(f773(f9(f848(x42521),f848(x42521),a841),a330),f115(x42521)))),x42522)))
% 191.21/191.73 [4262]E(f773(f773(f88(a1,a847),f773(f106(a1),f773(f773(f82(a1),x42621),a99))),f773(f773(f20(a1,a847,a847),f773(f773(f9(a1,a847,f855(a847,a847)),f773(f773(f10(a841,f855(a847,f855(a847,a847)),a1),f98(a847)),a186)),f2(a847))),f773(f773(f10(a847,a847,a1),a114),f773(f773(f9(a1,a847,a847),f773(f773(f10(a847,f855(a847,a847),a1),f236(a847)),a107)),x42622)))),f773(f773(f236(a847),f773(f106(a847),x42621)),f773(a114,x42622)))
% 191.21/191.73 [4263]E(f773(f773(f88(a1,a847),f773(f106(a1),f773(f773(f82(a1),x42631),a99))),f773(f773(f20(a1,a847,a847),f773(f773(f9(a1,a847,f855(a847,a847)),f773(f773(f10(a841,f855(a847,f855(a847,a847)),a1),f98(a847)),a186)),f773(a114,x42632))),f773(f773(f10(a847,a847,a1),a114),f773(f773(f9(a1,a847,a847),f773(f773(f10(a847,f855(a847,a847),a1),f179(a847)),a107)),x42632)))),f773(f773(f179(a847),f773(f106(a847),x42631)),f773(a114,x42632)))
% 191.21/191.73 [4251]E(f773(f251(x42511,x42511,a841),f773(f773(f20(x42511,a841,f855(x42511,a841)),f773(f773(f10(f855(x42511,f855(a841,a841)),f855(a841,f855(x42511,a841)),x42511),f9(x42511,a841,a841)),f773(f773(f10(f855(x42511,a841),f855(x42511,f855(a841,a841)),x42511),f773(f10(a841,f855(a841,a841),x42511),a331)),a330))),x42512)),f260(x42511,x42512))
% 191.21/191.73 [4295]E(f773(f773(f43(a847),x42951),f773(f773(f82(a847),f773(f106(a847),f773(f773(f3(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))),a99))),x42952)),f773(f773(f43(a847),x42951),f773(a114,f773(a114,f773(a114,x42952)))))
% 191.21/191.73 [4296]E(f52(a847,x42961,f773(f773(f82(a847),f773(f106(a847),f773(f773(f3(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))),a99))),x42962)),f52(a847,x42961,f773(a114,f773(a114,f773(a114,x42962)))))
% 191.21/191.73 [4297]E(f52(a847,f773(f773(f82(a847),f773(f106(a847),f773(f773(f3(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))),a99))),x42971),x42972),f52(a847,f773(a114,f773(a114,f773(a114,x42971))),x42972))
% 191.21/191.73 [4310]E(f122(f773(x43101,f773(f773(f83(a101),f773(f106(a101),f773(f773(f3(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))),a99))),x43102))),f773(f195(x43101),x43102))
% 191.21/191.73 [4311]E(f773(f773(f43(a847),f773(f773(f82(a847),f773(f106(a847),f773(f773(f3(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))),a99))),x43111)),x43112),f773(f773(f43(a847),f773(a114,f773(a114,f773(a114,x43111)))),x43112))
% 191.21/191.73 [3485]P29(x34851,f856(x34852,x34851),f313(x34851,x34852),x34853)
% 191.21/191.73 [3486]P29(x34861,f856(x34861,x34862),f304(x34861,x34862),x34863)
% 191.21/191.73 [4379]~E(f35(x43791,x43792),f773(a27,x43793))
% 191.21/191.73 [4380]~E(f36(x43801,x43802),f773(a27,x43803))
% 191.21/191.73 [4381]~E(f28(x43811,x43812),f773(a27,x43813))
% 191.21/191.73 [4382]~E(f773(a27,x43821),f35(x43822,x43823))
% 191.21/191.73 [4383]~E(f773(a27,x43831),f36(x43832,x43833))
% 191.21/191.73 [4384]~E(f773(a27,x43841),f28(x43842,x43843))
% 191.21/191.73 [4403]~E(f33(x44031,x44032,x44033),a25)
% 191.21/191.73 [4404]~E(f32(x44041,x44042,x44043),a25)
% 191.21/191.73 [4405]~E(f31(x44051,x44052,x44053),a25)
% 191.21/191.73 [3099]E(f773(f185(x30991,x30992),x30993),f120(x30991,x30992))
% 191.21/191.73 [3100]E(f773(f194(x31001,x31002),x31003),f123(x31001,x31002))
% 191.21/191.73 [3194]E(f773(f773(f143(x31941,x31942),x31943),f115(x31941)),f115(x31942))
% 191.21/191.73 [3195]E(f773(f773(f196(x31951,x31952),x31953),f183(x31951)),f183(x31952))
% 191.21/191.73 [3215]E(f34(f31(x32151,x32152,x32153)),f2(a847))
% 191.21/191.73 [3234]E(f773(f174(x32341,x32342,x32343),f2(a847)),x32342)
% 191.21/191.73 [3235]E(f773(f181(a842),f31(x32351,x32352,x32353)),f2(a847))
% 191.21/191.73 [3236]E(f773(f773(f167(x32361,x32362),x32363),f115(x32362)),f115(f854(x32361,x32362)))
% 191.21/191.73 [3273]E(f87(x32731,f64(x32731,x32732,x32733)),f773(f65(x32731,x32732),x32733))
% 191.21/191.73 [3342]E(f773(f240(f848(x33421),f848(x33421)),f156(x33421,x33422,x33423)),f773(f126(x33421,x33422),x33423))
% 191.21/191.73 [3420]E(f175(x34201,x34202,x34203,f2(a847)),x34202)
% 191.21/191.73 [3421]E(f19(x34211,x34212,x34213,f2(a101)),x34212)
% 191.21/191.73 [3422]E(f21(x34221,x34222,x34223,f2(a101)),x34222)
% 191.21/191.73 [3429]E(f154(x34291,x34292,x34293,f115(x34291)),f115(x34292))
% 191.21/191.73 [3436]E(f773(f773(f153(x34361),f773(f773(f140(x34361),x34362),x34363)),f2(a847)),x34362)
% 191.21/191.73 [3484]P29(x34841,x34842,x34843,f180(f855(x34841,a841)))
% 191.21/191.73 [3580]E(f262(x35801,x35802,x35803),f773(f241(f855(a101,f855(a841,f851(f849(x35801)))),f854(a101,a101)),f48(x35801)))
% 191.21/191.73 [3639]E(f773(f75(x36391,x36392,x36391,x36393),f39(x36391)),x36393)
% 191.21/191.73 [3815]P1(f773(f773(f334(f854(x38151,x38151)),f773(f773(f241(x38151,x38151),x38152),x38152)),f300(x38151,x38153)))
% 191.21/191.73 [4480]~P1(f773(f773(f334(f854(f848(x44801),f848(x44801))),f773(f773(f241(f848(x44801),f848(x44801)),x44802),f115(x44801))),f135(x44801,x44803)))
% 191.21/191.73 [4481]~P1(f773(f773(f334(f854(f848(x44811),f848(x44811))),f773(f773(f241(f848(x44811),f848(x44811)),x44812),f115(x44811))),f137(x44811,x44813)))
% 191.21/191.73 [4482]~P1(f773(f773(f334(f854(f848(x44821),f848(x44821))),f773(f773(f241(f848(x44821),f848(x44821)),x44822),f115(x44821))),f146(x44821,x44823)))
% 191.21/191.73 [4483]~P1(f773(f773(f334(f854(f848(x44831),f848(x44831))),f773(f773(f241(f848(x44831),f848(x44831)),f115(x44831)),x44832)),f135(x44831,x44833)))
% 191.21/191.73 [4484]~P1(f773(f773(f334(f854(f848(x44841),f848(x44841))),f773(f773(f241(f848(x44841),f848(x44841)),f115(x44841)),x44842)),f146(x44841,x44843)))
% 191.21/191.73 [3169]E(f773(f773(f197(x31691),x31692),x31693),f198(x31691,f210(x31692,x31693)))
% 191.21/191.73 [3224]E(f773(f278(x32241,x32242),f773(f278(x32242,x32241),x32243)),x32243)
% 191.21/191.73 [3241]E(f312(x32411,x32412,f773(f304(x32411,x32412),x32413)),x32413)
% 191.21/191.73 [3242]E(f315(x32421,x32422,f773(f313(x32422,x32421),x32423)),x32423)
% 191.21/191.73 [3248]E(f773(f773(f167(x32481,x32482),f115(x32481)),x32483),f115(f854(x32481,x32482)))
% 191.21/191.73 [3251]E(f160(x32511,x32512,f773(f257(a847),x32513)),f773(f773(f159(x32511),x32513),x32512))
% 191.21/191.73 [3265]E(f773(f181(f856(x32651,x32652)),f773(f304(x32651,x32652),x32653)),f2(a847))
% 191.21/191.73 [3266]E(f773(f181(f856(x32661,x32662)),f773(f313(x32662,x32661),x32663)),f2(a847))
% 191.21/191.73 [3271]E(f773(f259(x32711,x32712),f773(f278(x32712,x32711),x32713)),f773(f261(x32712,x32711),x32713))
% 191.21/191.73 [3272]E(f773(f261(x32721,x32722),f773(f278(x32722,x32721),x32723)),f773(f259(x32722,x32721),x32723))
% 191.21/191.73 [3287]E(f773(f126(x32871,x32872),f773(f142(x32871),x32873)),f773(f142(x32871),f773(f126(x32871,x32872),x32873)))
% 191.21/191.73 [3300]E(f773(f773(f128(x33001),x33002),f773(f157(x33001),x33003)),f773(f773(f128(x33001),f773(a114,x33002)),x33003))
% 191.21/191.73 [3318]E(f34(f32(x33181,x33182,x33183)),f773(f773(f82(a847),f34(x33183)),f773(a114,f2(a847))))
% 191.21/191.73 [3319]E(f773(f303(x33191,x33192,x33193),f180(f855(x33191,a841))),f180(f855(x33192,a841)))
% 191.21/191.73 [3320]E(f773(f277(x33201,x33202,x33203),f180(f855(x33201,a841))),f180(f855(x33202,a841)))
% 191.21/191.73 [3321]E(f773(f305(x33211,x33212,x33213),f239(f855(x33212,a841))),f239(f855(x33211,a841)))
% 191.21/191.73 [3322]E(f773(f305(x33221,x33222,x33223),f180(f855(x33222,a841))),f180(f855(x33221,a841)))
% 191.21/191.73 [3359]E(f228(x33591,x33592,f773(f227(x33591),x33593)),f773(f773(f82(a847),f773(x33592,x33593)),f773(a114,f2(a847))))
% 191.21/191.73 [3440]E(f773(f181(a842),f32(x34401,x34402,x34403)),f773(f773(f82(a847),f773(f181(a842),x34403)),f773(a114,f2(a847))))
% 191.21/191.73 [3441]E(f773(f303(f854(x34411,x34412),x34412,f250(x34411,x34412)),x34413),f773(f259(x34411,x34412),x34413))
% 191.21/191.73 [3442]E(f773(f303(f854(x34421,x34422),x34421,f240(x34421,x34422)),x34423),f773(f261(x34421,x34422),x34423))
% 191.21/191.73 [3511]E(f773(f773(f241(x35111,x35112),f773(f240(x35111,x35112),x35113)),f773(f250(x35111,x35112),x35113)),x35113)
% 191.21/191.73 [3518]E(f773(f773(f251(x35181,x35182,x35181),f18(x35181,x35182)),x35183),f773(f240(x35181,x35182),x35183))
% 191.21/191.73 [3537]E(f170(x35371,x35372,x35373,f773(f18(f851(x35372),x35371),f183(x35372))),x35373)
% 191.21/191.73 [3538]E(f170(x35381,x35382,f773(f18(f851(x35382),x35381),f183(x35382)),x35383),x35383)
% 191.21/191.73 [3593]E(f34(f33(x35931,x35932,x35933)),f773(f773(f82(a847),f773(f773(f82(a847),f34(x35932)),f34(x35933))),f773(a114,f2(a847))))
% 191.21/191.73 [3643]E(f773(f75(x36431,x36431,x36432,f39(x36431)),x36433),x36433)
% 191.21/191.73 [3729]P1(f773(f63(x37291),f169(x37291,x37292,f166(x37291,x37292,x37293))))
% 191.21/191.73 [3752]P1(f773(f773(f187(f28(x37521,x37522)),x37523),f773(f773(f773(a189,x37523),x37521),f773(x37522,x37523))))
% 191.21/191.73 [3754]E(f773(f181(a842),f33(x37541,x37542,x37543)),f773(f773(f82(a847),f773(f773(f82(a847),f773(f181(a842),x37542)),f773(f181(a842),x37543))),f773(a114,f2(a847))))
% 191.21/191.73 [3825]P1(f773(f773(f232(f855(x38251,a841)),f773(f158(x38251),f773(f126(x38251,x38252),x38253))),f773(f158(x38251),x38253)))
% 191.21/191.73 [3868]P1(f773(f773(f232(f855(x38681,a841)),f773(f158(x38681),f773(f773(f159(x38681),x38682),x38683))),f773(f158(x38681),x38683)))
% 191.21/191.73 [3869]P1(f773(f773(f232(f855(x38691,a841)),f773(f158(x38691),f773(f773(f128(x38691),x38692),x38693))),f773(f158(x38691),x38693)))
% 191.21/191.73 [3873]P1(f773(f773(f232(f855(x38731,a841)),f773(f158(x38731),f151(x38731,x38732,x38733))),f773(f158(x38731),x38733)))
% 191.21/191.73 [3874]P1(f773(f773(f232(f855(x38741,a841)),f773(f158(x38741),f160(x38741,x38742,x38743))),f773(f158(x38741),x38742)))
% 191.21/191.73 [3898]P29(f854(x38981,x38982),f854(x38982,x38981),f773(f251(x38981,x38982,f854(x38982,x38981)),f773(f9(x38982,x38981,f854(x38982,x38981)),f241(x38982,x38981))),x38983)
% 191.21/191.73 [3910]E(f773(f773(f773(f173(f848(x39101),f848(x39101)),f52(a847,x39102,f773(f181(f848(x39101)),x39103))),f141(x39101)),x39103),f773(f773(f773(f173(f848(x39101),f848(x39101)),x39102),f141(x39101)),x39103))
% 191.21/191.73 [3955]P1(f773(f773(f334(f854(f848(x39551),f848(x39551))),f773(f773(f241(f848(x39551),f848(x39551)),x39552),x39552)),f147(x39551,f300(x39551,x39553))))
% 191.21/191.73 [4099]E(f87(f854(x40991,x40992),f773(f773(f20(f854(x40991,x40992),x40992,a841),f773(f773(f10(x40991,f855(x40992,a841),f854(x40991,x40992)),x40993),f240(x40991,x40992))),f250(x40991,x40992))),f87(f854(x40991,x40992),f773(f251(x40991,x40992,a841),x40993)))
% 191.21/191.73 [4100]E(f92(f854(x41001,x41002),f773(f773(f20(f854(x41001,x41002),x41002,a841),f773(f773(f10(x41001,f855(x41002,a841),f854(x41001,x41002)),x41003),f240(x41001,x41002))),f250(x41001,x41002))),f92(f854(x41001,x41002),f773(f251(x41001,x41002,a841),x41003)))
% 191.21/191.73 [4139]E(f773(f773(f280(f854(a847,x41391),x41391),f325(a847,x41391,a237,x41392)),f773(f773(f20(x41391,x41391,f854(a847,x41391)),f773(f773(f10(a847,f855(x41391,f854(a847,x41391)),x41391),f241(a847,x41391)),x41393)),f7(x41391))),f327(x41391,x41393,x41392))
% 191.21/191.73 [4201]E(f773(f252(x42011,x42011,x42012,x42012,f7(x42011),f7(x42012)),x42013),x42013)
% 191.21/191.73 [4336]E(f773(f773(f88(a1,x43361),f213(f773(f773(f75(f854(a1,a1),a1,x43361,f250(a1,a1)),f207(x43361)),x43362),f773(f773(f75(f854(a1,a1),a1,x43361,f250(a1,a1)),f207(x43361)),x43363))),f773(f773(f20(a1,a1,x43361),f773(f773(f10(a1,f855(a1,x43361),a1),f197(x43361)),f773(f773(f20(a1,a1,a1),f773(f773(f10(a1,f855(a1,a1),a1),f82(a1)),f773(f773(f10(a1,a1,a1),f773(f83(a1),f773(f773(f75(f854(a1,a1),a1,x43361,f240(a1,a1)),f207(x43361)),x43362))),f773(f773(f9(a1,a1,a1),f43(a1)),f773(f773(f75(f854(a1,a1),a1,x43361,f250(a1,a1)),f207(x43361)),x43362))))),f773(f773(f10(a1,a1,a1),f773(f83(a1),f773(f773(f75(f854(a1,a1),a1,x43361,f240(a1,a1)),f207(x43361)),x43363))),f773(f773(f9(a1,a1,a1),f43(a1)),f773(f773(f75(f854(a1,a1),a1,x43361,f250(a1,a1)),f207(x43361)),x43363)))))),f7(a1))),f224(x43361,x43362,x43363))
% 191.21/191.73 [4398]~E(f773(f773(f140(x43981),x43982),x43983),x43983)
% 191.21/191.73 [4407]~E(f773(f773(f140(x44071),x44072),x44073),f115(x44071))
% 191.21/191.73 [4433]~E(f773(f773(f302(x44331),x44332),x44333),f180(f855(x44331,a841)))
% 191.21/191.73 [4462]~E(f773(f303(x44621,f855(x44621,a841),x44622),x44623),f773(f301(x44621),x44623))
% 191.21/191.73 [3228]E(f773(f773(f148(x32281,f115(x32281)),x32282),x32283),f115(x32281))
% 191.21/191.73 [3229]E(f773(f131(x32291),f773(f773(f140(x32291),x32292),x32293)),x32292)
% 191.21/191.73 [3230]E(f773(f157(x32301),f773(f773(f140(x32301),x32302),x32303)),x32303)
% 191.21/191.73 [3276]E(f773(f773(f128(x32761),f80(a847)),f773(f773(f140(x32761),x32762),x32763)),x32763)
% 191.21/191.73 [3307]E(f116(x33071,f773(f773(f128(x33071),x33072),x33073)),f773(f773(f128(x33071),x33072),f116(x33071,x33073)))
% 191.21/191.73 [3309]E(f773(f773(f148(x33091,x33092),x33093),f773(f773(f153(x33091),x33092),x33093)),x33092)
% 191.21/191.73 [3332]E(f773(f773(f302(x33321),x33322),f773(f773(f302(x33321),x33322),x33323)),f773(f773(f302(x33321),x33322),x33323))
% 191.21/191.73 [3345]E(f773(f773(f302(x33451),x33452),f773(f158(x33451),x33453)),f773(f158(x33451),f773(f773(f140(x33451),x33452),x33453)))
% 191.21/191.73 [3347]E(f773(f773(f128(x33471),x33472),f773(f157(x33471),x33473)),f773(f157(x33471),f773(f773(f128(x33471),x33472),x33473)))
% 191.21/191.73 [3356]E(f773(f773(f159(x33561),f80(a847)),f773(f773(f140(x33561),x33562),x33563)),f773(f773(f140(x33561),x33562),f115(x33561)))
% 191.21/191.73 [3389]E(f773(f166(x33891,x33892,f115(f854(x33891,x33892))),x33893),f183(x33892))
% 191.21/191.73 [3405]E(f773(f65(x34051,x34052),f773(f773(f302(x34051),x34053),f180(f855(x34051,a841)))),x34053)
% 191.21/191.73 [3448]E(f773(f773(f82(a847),x34481),f773(f773(f82(a847),x34482),x34483)),f773(f773(f82(a847),x34482),f773(f773(f82(a847),x34481),x34483)))
% 191.21/191.73 [3449]E(f773(f773(f82(a1),x34491),f773(f773(f82(a1),x34492),x34493)),f773(f773(f82(a1),x34492),f773(f773(f82(a1),x34491),x34493)))
% 191.21/191.73 [3454]E(f773(f773(f248(x34541,x34542),f180(f855(x34541,a841))),x34543),f180(f855(f854(x34541,x34542),a841)))
% 191.21/191.73 [3476]E(f773(f773(f103(f855(x34761,a841)),x34762),x34763),f773(f773(f103(f855(x34761,a841)),x34763),x34762))
% 191.21/191.73 [3477]E(f773(f773(f104(f855(x34771,a841)),x34772),x34773),f773(f773(f104(f855(x34771,a841)),x34773),x34772))
% 191.21/191.73 [3479]E(f773(f773(f125(x34791),x34792),f773(f773(f140(x34791),x34793),f115(x34791))),f773(f141(x34791),f773(f773(f140(x34791),x34793),x34792)))
% 191.21/191.73 [3480]E(f773(f773(f125(x34801),f773(f142(x34801),x34802)),f773(f142(x34801),x34803)),f773(f142(x34801),f773(f773(f125(x34801),x34803),x34802)))
% 191.21/191.73 [3490]E(f773(f157(x34901),f773(f773(f159(x34901),f773(a114,x34902)),x34903)),f773(f773(f159(x34901),x34902),f773(f157(x34901),x34903)))
% 191.21/191.73 [3497]P1(f773(f773(f334(x34971),x34972),f773(f773(f302(x34971),x34972),x34973)))
% 191.21/191.73 [3501]E(f773(f773(f47(x35011,f855(x35012,a841)),f180(f855(x35011,a841))),x35013),f239(f855(x35012,a841)))
% 191.21/191.73 [3504]E(f773(f277(x35041,x35041,f260(x35041,x35042)),x35043),f773(f773(f104(f855(x35041,a841)),x35042),x35043))
% 191.21/191.73 [3516]E(f773(f181(f848(x35161)),f773(f773(f140(x35161),x35162),x35163)),f773(f773(f82(a847),f773(f181(f848(x35161)),x35163)),f773(a114,f2(a847))))
% 191.21/191.73 [3520]E(f134(x35201,f773(f773(f125(x35201),x35202),f773(f773(f140(x35201),x35203),f115(x35201)))),x35203)
% 191.21/191.73 [3521]E(f116(x35211,f773(f773(f125(x35211),x35212),f773(f773(f140(x35211),x35213),f115(x35211)))),x35212)
% 191.21/191.73 [3526]E(f773(f773(f125(x35261),f773(f773(f159(x35261),x35262),x35263)),f773(f773(f128(x35261),x35262),x35263)),x35263)
% 191.21/191.73 [3535]E(f773(f773(f3(a847),f773(f773(f82(a847),x35351),x35352)),f773(f773(f82(a847),x35353),x35352)),f773(f773(f3(a847),x35351),x35353))
% 191.21/191.73 [3536]E(f773(f773(f3(a847),f773(f773(f82(a847),x35361),x35362)),f773(f773(f82(a847),x35361),x35363)),f773(f773(f3(a847),x35362),x35363))
% 191.21/191.73 [3542]E(f773(f773(f125(x35421),f773(f142(x35421),x35422)),f773(f773(f140(x35421),x35423),f115(x35421))),f773(f142(x35421),f773(f773(f140(x35421),x35423),x35422)))
% 191.21/191.73 [3544]E(f773(f773(f82(a847),f773(f181(f848(x35441)),x35442)),f773(f181(f848(x35441)),x35443)),f773(f181(f848(x35441)),f773(f773(f125(x35441),x35442),x35443)))
% 191.21/191.73 [3554]E(f773(f773(f103(f855(x35541,a841)),f773(f158(x35541),x35542)),f773(f158(x35541),x35543)),f773(f158(x35541),f773(f773(f125(x35541),x35542),x35543)))
% 191.21/191.73 [3555]E(f52(a847,f773(f773(f83(a847),x35551),x35552),f773(f773(f83(a847),x35551),x35553)),f773(f773(f83(a847),x35551),f52(a847,x35552,x35553)))
% 191.21/191.73 [3568]E(f773(f773(f159(x35681),f773(f773(f3(a847),x35682),f80(a847))),f773(f157(x35681),x35683)),f773(f157(x35681),f773(f773(f159(x35681),x35682),x35683)))
% 191.21/191.73 [3573]E(f773(f773(f104(f855(x35731,a841)),x35732),f773(f81(f855(x35731,a841)),x35733)),f773(f773(f3(f855(x35731,a841)),x35732),x35733))
% 191.21/191.73 [3574]E(f773(f773(f3(f855(x35741,a841)),x35742),f773(f81(f855(x35741,a841)),x35743)),f773(f773(f104(f855(x35741,a841)),x35742),x35743))
% 191.21/191.73 [3596]E(f773(f773(f248(x35961,x35962),x35963),f773(f18(f855(x35962,a841),x35961),f180(f855(x35962,a841)))),f180(f855(f854(x35961,x35962),a841)))
% 191.21/191.73 [3598]E(f773(f773(f82(a847),f773(f773(f83(a847),x35981),x35982)),f773(f773(f83(a847),x35981),x35983)),f773(f773(f83(a847),x35981),f773(f773(f82(a847),x35982),x35983)))
% 191.21/191.73 [3599]E(f773(f773(f3(a847),f773(f773(f83(a847),x35991),x35992)),f773(f773(f83(a847),x35991),x35993)),f773(f773(f83(a847),x35991),f773(f773(f3(a847),x35992),x35993)))
% 191.21/191.73 [3600]E(f773(f773(f82(a1),f773(f773(f83(a1),x36001),x36002)),f773(f773(f83(a1),x36001),x36003)),f773(f773(f83(a1),x36001),f773(f773(f82(a1),x36002),x36003)))
% 191.21/191.73 [3601]E(f773(f773(f3(a1),f773(f773(f83(a1),x36011),x36012)),f773(f773(f83(a1),x36011),x36013)),f773(f773(f83(a1),x36011),f773(f773(f3(a1),x36012),x36013)))
% 191.21/191.73 [3602]E(f773(f773(f83(a1),f773(f773(f242(a1),x36021),x36022)),f773(f773(f242(a1),x36021),x36023)),f773(f773(f242(a1),x36021),f773(f773(f82(a847),x36022),x36023)))
% 191.21/191.73 [3615]E(f773(f773(f46(x36151,f855(x36152,a841)),x36153),f773(f18(f855(x36152,a841),x36151),f180(f855(x36152,a841)))),f180(f855(x36152,a841)))
% 191.21/191.73 [3617]E(f52(a847,f773(f773(f83(a847),x36171),x36172),f773(f773(f83(a847),x36173),x36172)),f773(f773(f83(a847),f52(a847,x36171,x36173)),x36172))
% 191.21/191.73 [3622]E(f52(a1,f773(f773(f83(a1),x36221),f52(a1,x36222,x36223)),x36223),f52(a1,f773(f773(f83(a1),x36221),x36222),x36223))
% 191.21/191.73 [3623]E(f52(a1,f773(f773(f3(a1),x36231),f52(a1,x36232,x36233)),x36233),f52(a1,f773(f773(f3(a1),x36231),x36232),x36233))
% 191.21/191.73 [3624]P1(f773(f773(f232(f855(x36241,a841)),x36242),f773(f773(f302(x36241),x36243),x36242)))
% 191.21/191.73 [3648]E(f773(f303(f854(x36481,x36482),x36481,f240(x36481,x36482)),f773(f158(f854(x36481,x36482)),x36483)),f169(x36481,x36482,f166(x36481,x36482,x36483)))
% 191.21/191.73 [3705]E(f773(f773(f47(f855(x37051,a841),f855(x37051,a841)),x37052),f773(f103(f855(x37051,a841)),x37053)),f773(f773(f103(f855(x37051,a841)),x37053),f45(f855(x37051,a841),x37052)))
% 191.21/191.73 [3706]E(f773(f773(f46(f855(x37061,a841),f855(x37061,a841)),x37062),f773(f104(f855(x37061,a841)),x37063)),f773(f773(f104(f855(x37061,a841)),x37063),f44(f855(x37061,a841),x37062)))
% 191.21/191.73 [3716]E(f773(f158(x37161),f773(f773(f773(f173(f848(x37161),f848(x37161)),x37162),f141(x37161)),x37163)),f773(f158(x37161),x37163))
% 191.21/191.73 [3720]E(f773(f773(f159(x37201),f773(f181(f848(x37201)),f162(x37201,x37202,x37203))),x37203),f162(x37201,x37202,x37203))
% 191.21/191.73 [3721]E(f169(x37211,x37212,f773(f773(f10(x37212,f851(x37212),x37211),f227(x37212)),x37213)),f239(f855(x37211,a841)))
% 191.21/191.73 [3724]E(f773(f181(f848(x37241)),f773(f773(f773(f173(f848(x37241),f848(x37241)),x37242),f141(x37241)),x37243)),f773(f181(f848(x37241)),x37243))
% 191.21/191.73 [3727]E(f773(f773(f251(x37271,x37272,x37272),f773(f18(f855(x37272,x37272),x37271),f7(x37272))),x37273),f773(f250(x37271,x37272),x37273))
% 191.21/191.73 [3734]E(f52(a1,f773(f773(f3(a1),f52(a1,x37341,x37342)),x37343),x37342),f52(a1,f773(f773(f3(a1),x37341),x37343),x37342))
% 191.21/191.73 [3735]E(f52(a1,f773(f773(f242(a1),f52(a1,x37351,x37352)),x37353),x37352),f52(a1,f773(f773(f242(a1),x37351),x37353),x37352))
% 191.21/191.73 [3738]E(f773(f773(f46(f855(f854(x37381,x37382),a841),f855(x37382,a841)),x37383),f259(x37381,x37382)),f773(f259(x37381,x37382),f44(f855(f854(x37381,x37382),a841),x37383)))
% 191.21/191.73 [3739]E(f773(f773(f46(f855(f854(x37391,x37392),a841),f855(x37391,a841)),x37393),f261(x37391,x37392)),f773(f261(x37391,x37392),f44(f855(f854(x37391,x37392),a841),x37393)))
% 191.21/191.73 [3767]E(f773(f75(x37671,x37671,x37671,x37672),f773(f773(f173(x37671,x37671),x37673),x37672)),f773(f773(f173(x37671,x37671),f773(a114,x37673)),x37672))
% 191.21/191.73 [3777]E(f229(f851(x37771),x37772,f183(x37771),f773(f773(f10(x37771,f851(x37771),x37772),f227(x37771)),x37773)),f773(f196(x37772,x37771),x37773))
% 191.21/191.73 [3784]E(f773(f773(f128(x37841),f773(f773(f3(a847),f773(f181(f848(x37841)),x37842)),x37843)),f773(f142(x37841),x37842)),f773(f142(x37841),f773(f773(f159(x37841),x37843),x37842)))
% 191.21/191.73 [3785]E(f773(f773(f159(x37851),f773(f773(f3(a847),f773(f181(f848(x37851)),x37852)),x37853)),f773(f142(x37851),x37852)),f773(f142(x37851),f773(f773(f128(x37851),x37853),x37852)))
% 191.21/191.73 [3788]E(f773(f773(f82(a847),f773(f155(a847),f773(f773(f143(x37881,a847),x37882),x37883))),f773(f181(f848(x37881)),x37883)),f144(x37881,x37882,x37883))
% 191.21/191.73 [3804]E(f773(f141(x38041),f773(f773(f773(f173(f848(x38041),f848(x38041)),x38042),f141(x38041)),x38043)),f773(f773(f773(f173(f848(x38041),f848(x38041)),f773(a114,x38042)),f141(x38041)),x38043))
% 191.21/191.73 [3816]P1(f773(f773(f232(a847),f773(f181(f848(x38161)),f773(f126(x38161,x38162),x38163))),f773(f181(f848(x38161)),x38163)))
% 191.21/191.73 [3833]E(f773(f773(f103(f855(f855(x38331,a841),a841)),f773(f301(x38331),x38332)),f773(f303(f855(x38331,a841),f855(x38331,a841),f773(f302(x38331),x38333)),f773(f301(x38331),x38332))),f773(f301(x38331),f773(f773(f302(x38331),x38333),x38332)))
% 191.21/191.73 [3849]P28(x38491,x38492,f773(f773(f302(f846(x38491)),f773(f773(f773(f93(x38491),x38493),a25),x38493)),f180(f855(f846(x38491),a841))))
% 191.21/191.73 [3865]P1(f773(f773(f232(a847),f773(f181(f848(x38651)),f162(x38651,x38652,x38653))),f773(f181(f848(x38651)),x38653)))
% 191.21/191.73 [3872]E(f773(f261(x38721,x38722),f773(f256(f854(x38721,x38722)),f773(f251(x38721,x38722,a841),x38723))),f773(f256(x38721),f773(f773(f10(f855(x38722,a841),a841,x38721),f89(x38722)),x38723)))
% 191.21/191.73 [3885]E(f773(f303(a847,a847,f773(f773(f9(a847,a847,a847),f82(a847)),x38851)),f295(a847,x38852,x38853)),f295(a847,f773(f773(f82(a847),x38852),x38851),f773(f773(f82(a847),x38853),x38851)))
% 191.21/191.73 [3901]E(f773(f303(a847,a847,f773(f773(f9(a847,a847,a847),f82(a847)),x39011)),f773(f294(a847,x39012),x39013)),f773(f294(a847,f773(f773(f82(a847),x39012),x39011)),f773(f773(f82(a847),x39013),x39011)))
% 191.21/191.73 [3919]E(f773(f773(f167(x39191,x39192),f773(f773(f143(f854(x39191,x39192),x39191),f240(x39191,x39192)),x39193)),f773(f773(f143(f854(x39191,x39192),x39192),f250(x39191,x39192)),x39193)),x39193)
% 191.21/191.73 [3924]E(f773(f773(f82(a847),f773(f773(f83(a847),x39241),f52(a847,f773(f773(f43(a847),x39242),x39241),x39243))),f52(a847,x39242,x39241)),f52(a847,x39242,f773(f773(f83(a847),x39241),x39243)))
% 191.21/191.73 [3935]P1(f773(f63(f851(x39351)),f773(f303(x39352,f851(x39351),f166(x39352,x39351,x39353)),f239(f855(x39352,a841)))))
% 191.21/191.73 [3939]E(f773(f773(f125(x39391),x39392),f773(f132(f848(x39391),f848(x39391),f125(x39391),f115(x39391)),x39393)),f773(f132(f848(x39391),f848(x39391),f125(x39391),x39392),x39393))
% 191.21/191.73 [3959]P1(f773(f773(f334(f854(x39591,x39591)),f773(f773(f241(x39591,x39591),x39592),x39592)),f773(f773(f173(f854(x39591,x39591),a841),f2(a847)),x39593)))
% 191.21/191.73 [3965]E(f773(f256(x39651),f773(f773(f10(f855(x39652,a841),a841,x39651),f89(x39652)),f773(f9(x39652,x39651,a841),x39653))),f773(f259(x39652,x39651),f773(f256(f854(x39652,x39651)),f773(f251(x39652,x39651,a841),x39653))))
% 191.21/191.73 [3984]E(f773(f773(f103(f855(x39841,a841)),f773(f773(f46(a847,f855(x39841,a841)),f295(a847,f80(a847),x39842)),x39843)),f773(x39843,f2(a847))),f773(f773(f46(a847,f855(x39841,a841)),f773(f293(a847),x39842)),x39843))
% 191.21/191.73 [3999]E(f773(f132(f848(x39991),f848(x39991),f125(x39991),f115(x39991)),f773(f773(f143(f848(x39991),f848(x39991)),f126(x39991,x39992)),x39993)),f773(f126(x39991,x39992),f773(f132(f848(x39991),f848(x39991),f125(x39991),f115(x39991)),x39993)))
% 191.21/191.73 [4004]E(f773(f250(f848(x40041),f848(x40041)),f156(x40041,x40042,x40043)),f773(f126(x40041,f773(f75(a841,a841,x40041,a328),x40042)),x40043))
% 191.21/191.73 [4053]E(f773(f773(f82(a1),f773(f773(f82(a1),f773(f773(f83(a1),x40531),f773(f773(f43(a1),x40532),x40531))),f52(a1,x40532,x40531))),x40533),f773(f773(f82(a1),x40532),x40533))
% 191.21/191.73 [4087]E(f773(f773(f82(a1),f773(f773(f82(a1),f773(f773(f83(a1),f773(f773(f43(a1),x40871),x40872)),x40872)),f52(a1,x40871,x40872))),x40873),f773(f773(f82(a1),x40871),x40873))
% 191.21/191.73 [4117]E(f87(f854(x41171,x41172),f773(f251(x41171,x41172,a841),f773(f773(f10(f855(x41172,f854(x41171,x41172)),f855(x41172,a841),x41171),f773(f10(f854(x41171,x41172),a841,x41172),x41173)),f241(x41171,x41172)))),f87(f854(x41171,x41172),x41173))
% 191.21/191.73 [4118]E(f92(f854(x41181,x41182),f773(f251(x41181,x41182,a841),f773(f773(f10(f855(x41182,f854(x41181,x41182)),f855(x41182,a841),x41181),f773(f10(f854(x41181,x41182),a841,x41182),x41183)),f241(x41181,x41182)))),f92(f854(x41181,x41182),x41183))
% 191.21/191.73 [4150]P1(f773(f773(f232(f855(x41501,a841)),f44(f855(x41501,a841),f773(f773(f104(f855(f855(x41501,a841),a841)),x41502),x41503))),f773(f773(f104(f855(x41501,a841)),f44(f855(x41501,a841),x41502)),f44(f855(x41501,a841),x41503))))
% 191.21/191.73 [4151]E(f773(f142(x41511),f773(f773(f773(f173(f848(x41511),f848(x41511)),f773(f773(f3(a847),f773(f181(f848(x41511)),x41512)),f52(a847,x41513,f773(f181(f848(x41511)),x41512)))),f141(x41511)),x41512)),f773(f773(f773(f173(f848(x41511),f848(x41511)),x41513),f141(x41511)),f773(f142(x41511),x41512)))
% 191.21/191.73 [4163]E(f773(f256(x41631),f773(f773(f10(a841,a841,x41631),a328),f773(f773(f9(x41631,f851(x41632),a841),f773(f773(f10(f851(x41632),f855(f851(x41632),a841),x41631),a330),x41633)),f183(x41632)))),f169(x41631,x41632,x41633))
% 191.21/191.73 [4226]E(f773(f256(x42261),f773(f773(f10(f855(x42262,a841),a841,x42261),f89(x42262)),f773(f773(f10(f851(x42261),f855(x42262,a841),x42261),f773(f9(x42262,f851(x42261),a841),f773(f773(f10(f851(x42261),f855(f851(x42261),a841),x42262),a330),x42263))),f227(x42261)))),f171(x42262,x42261,x42263))
% 191.21/191.73 [4475]~P1(f773(f64(x44751,x44752,f180(f855(x44751,a841))),x44753))
% 191.21/191.73 [3491]E(f773(f181(f848(x34911)),f773(f773(f159(x34911),x34912),x34913)),f773(f773(f236(a847),f773(f181(f848(x34911)),x34913)),x34912))
% 191.21/191.73 [3492]E(f773(f181(f848(x34921)),f773(f773(f128(x34921),x34922),x34923)),f773(f773(f3(a847),f773(f181(f848(x34921)),x34923)),x34922))
% 191.21/191.73 [3528]E(f773(f773(f43(a847),f773(f773(f43(a847),x35281),x35282)),x35283),f773(f773(f43(a847),x35281),f773(f773(f83(a847),x35282),x35283)))
% 191.21/191.73 [3529]E(f773(f773(f82(a847),f773(f773(f82(a847),x35291),x35292)),x35293),f773(f773(f82(a847),x35291),f773(f773(f82(a847),x35292),x35293)))
% 191.21/191.73 [3530]E(f773(f773(f82(a1),f773(f773(f82(a1),x35301),x35302)),x35303),f773(f773(f82(a1),x35301),f773(f773(f82(a1),x35302),x35303)))
% 191.21/191.73 [3531]E(f773(f773(f83(a847),f773(f773(f83(a847),x35311),x35312)),x35313),f773(f773(f83(a847),x35311),f773(f773(f83(a847),x35312),x35313)))
% 191.21/191.73 [3532]E(f773(f773(f83(a1),f773(f773(f83(a1),x35321),x35322)),x35323),f773(f773(f83(a1),x35321),f773(f773(f83(a1),x35322),x35323)))
% 191.21/191.73 [3533]E(f773(f773(f3(a847),f773(f773(f3(a847),x35331),x35332)),x35333),f773(f773(f3(a847),x35331),f773(f773(f82(a847),x35332),x35333)))
% 191.21/191.73 [3534]E(f773(f773(f242(a1),f773(f773(f242(a1),x35341),x35342)),x35343),f773(f773(f242(a1),x35341),f773(f773(f83(a847),x35342),x35343)))
% 191.21/191.73 [3552]E(f150(x35521,f773(f773(f140(f855(x35521,a841)),x35522),x35523)),f161(x35521,x35522,f150(x35521,x35523)))
% 191.21/191.73 [3597]E(f773(f773(f3(a847),f773(f773(f3(a847),x35971),x35972)),x35973),f773(f773(f3(a847),f773(f773(f3(a847),x35971),x35973)),x35972))
% 191.21/191.73 [3605]E(f773(f773(f104(f855(x36051,a841)),x36052),f773(f773(f3(f855(x36051,a841)),x36053),x36052)),f180(f855(x36051,a841)))
% 191.21/191.73 [3650]E(f45(f855(x36501,a841),f773(f773(f302(f855(x36501,a841)),x36502),x36503)),f773(f773(f104(f855(x36501,a841)),x36502),f45(f855(x36501,a841),x36503)))
% 191.21/191.73 [3651]E(f44(f855(x36511,a841),f773(f773(f302(f855(x36511,a841)),x36512),x36513)),f773(f773(f103(f855(x36511,a841)),x36512),f44(f855(x36511,a841),x36513)))
% 191.21/191.73 [3653]E(f773(f773(f82(a847),f773(f773(f83(a847),x36531),x36532)),f773(f773(f83(a847),x36533),x36532)),f773(f773(f83(a847),f773(f773(f82(a847),x36531),x36533)),x36532))
% 191.21/191.73 [3654]E(f773(f773(f3(a847),f773(f773(f83(a847),x36541),x36542)),f773(f773(f83(a847),x36543),x36542)),f773(f773(f83(a847),f773(f773(f3(a847),x36541),x36543)),x36542))
% 191.21/191.73 [3655]E(f773(f773(f82(a1),f773(f773(f83(a1),x36551),x36552)),f773(f773(f83(a1),x36553),x36552)),f773(f773(f83(a1),f773(f773(f82(a1),x36551),x36553)),x36552))
% 191.21/191.73 [3657]E(f773(f773(f3(a1),f773(f773(f83(a1),x36571),x36572)),f773(f773(f83(a1),x36573),x36572)),f773(f773(f83(a1),f773(f773(f3(a1),x36571),x36573)),x36572))
% 191.21/191.73 [3658]E(f773(f773(f236(a847),f773(f773(f3(a847),x36581),x36582)),f773(f773(f3(a847),x36583),x36582)),f773(f773(f3(a847),f773(f773(f236(a847),x36581),x36583)),x36582))
% 191.21/191.73 [3682]E(f773(f773(f103(f855(x36821,a841)),x36822),f773(f773(f3(f855(x36821,a841)),x36823),x36822)),f773(f773(f103(f855(x36821,a841)),x36822),x36823))
% 191.21/191.73 [3683]E(f773(f773(f103(f855(x36831,a841)),x36832),f773(f773(f103(f855(x36831,a841)),x36832),x36833)),f773(f773(f103(f855(x36831,a841)),x36832),x36833))
% 191.21/191.73 [3684]E(f773(f773(f104(f855(x36841,a841)),x36842),f773(f773(f104(f855(x36841,a841)),x36842),x36843)),f773(f773(f104(f855(x36841,a841)),x36842),x36843))
% 191.21/191.73 [3696]E(f773(f773(f281(x36961,x36962,x36962),x36963),f300(x36962,f180(f855(f854(x36962,x36962),a841)))),x36963)
% 191.21/191.73 [3701]E(f773(f773(f103(f855(x37011,a841)),f773(f773(f302(x37011),x37012),f180(f855(x37011,a841)))),x37013),f773(f773(f302(x37011),x37012),x37013))
% 191.21/191.73 [3719]E(f773(f773(f3(a847),f773(f773(f3(a847),f773(a114,x37191)),x37192)),f773(a114,x37193)),f773(f773(f3(a847),f773(f773(f3(a847),x37191),x37192)),x37193))
% 191.21/191.73 [3747]E(f773(f773(f104(f855(f855(x37471,a841),a841)),f773(f301(x37471),x37472)),f773(f301(x37471),x37473)),f773(f301(x37471),f773(f773(f104(f855(x37471,a841)),x37472),x37473)))
% 191.21/191.73 [3750]E(f773(f773(f103(f855(x37501,a841)),f773(f81(f855(x37501,a841)),x37502)),x37503),f773(f81(f855(x37501,a841)),f773(f773(f3(f855(x37501,a841)),x37502),x37503)))
% 191.21/191.73 [3763]E(f773(f773(f302(x37631),x37632),f773(f773(f3(f855(x37631,a841)),x37633),f773(f773(f302(x37631),x37632),f180(f855(x37631,a841))))),f773(f773(f302(x37631),x37632),x37633))
% 191.21/191.73 [3774]P1(f773(f773(f232(f855(x37741,a841)),x37742),f773(f773(f103(f855(x37741,a841)),x37743),x37742)))
% 191.21/191.73 [3775]P1(f773(f773(f232(f855(x37751,a841)),x37752),f773(f773(f103(f855(x37751,a841)),x37752),x37753)))
% 191.21/191.73 [3778]E(f773(f773(f104(f855(x37781,a841)),f773(f81(f855(x37781,a841)),x37782)),f773(f81(f855(x37781,a841)),x37783)),f773(f81(f855(x37781,a841)),f773(f773(f103(f855(x37781,a841)),x37782),x37783)))
% 191.21/191.73 [3779]E(f773(f773(f103(f855(x37791,a841)),f773(f81(f855(x37791,a841)),x37792)),f773(f81(f855(x37791,a841)),x37793)),f773(f81(f855(x37791,a841)),f773(f773(f104(f855(x37791,a841)),x37792),x37793)))
% 191.21/191.73 [3792]P1(f773(f773(f232(f855(x37921,a841)),f773(f158(x37921),x37922)),f773(f158(x37921),f773(f773(f140(x37921),x37923),x37922))))
% 191.21/191.73 [3801]E(f773(f773(f103(f855(x38011,a841)),f773(f773(f3(f855(x38011,a841)),x38012),x38013)),f773(f773(f104(f855(x38011,a841)),x38012),x38013)),x38012)
% 191.21/191.73 [3851]E(f773(f773(f8(x38511,a1),f773(f773(f10(a847,a1,x38511),f102(a1)),x38512)),x38513),f773(f102(a1),f773(f773(f8(x38511,a847),x38512),x38513)))
% 191.21/191.73 [3852]E(f773(f773(f11(x38521,a1),f773(f773(f10(a847,a1,x38521),f102(a1)),x38522)),x38523),f773(f102(a1),f773(f773(f11(x38521,a847),x38522),x38523)))
% 191.21/191.73 [3908]E(f773(f81(f855(f854(x39081,x39082),a841)),f773(f773(f248(x39081,x39082),x39083),f773(f18(f855(x39082,a841),x39081),f239(f855(x39082,a841))))),f773(f773(f248(x39081,x39082),f773(f81(f855(x39081,a841)),x39083)),f773(f18(f855(x39082,a841),x39081),f239(f855(x39082,a841)))))
% 191.21/191.73 [3909]E(f773(f81(f855(f854(x39091,x39092),a841)),f773(f773(f248(x39091,x39092),f239(f855(x39091,a841))),f773(f18(f855(x39092,a841),x39091),x39093))),f773(f773(f248(x39091,x39092),f239(f855(x39091,a841))),f773(f18(f855(x39092,a841),x39091),f773(f81(f855(x39092,a841)),x39093))))
% 191.21/191.73 [3960]E(f773(f773(f46(f855(x39601,a841),f855(x39601,a841)),x39602),f773(f773(f9(f855(x39601,a841),f855(x39601,a841),f855(x39601,a841)),f104(f855(x39601,a841))),x39603)),f773(f773(f104(f855(x39601,a841)),f44(f855(x39601,a841),x39602)),x39603))
% 191.21/191.73 [3967]E(f773(f132(f848(x39671),f848(x39671),f125(x39671),f115(x39671)),f773(f773(f140(f848(x39671)),x39672),x39673)),f773(f773(f125(x39671),x39672),f773(f132(f848(x39671),f848(x39671),f125(x39671),f115(x39671)),x39673)))
% 191.21/191.73 [3990]E(f773(f773(f302(f855(x39901,a841)),f773(f277(x39901,x39901,x39902),f773(f773(f302(x39901),x39903),f180(f855(x39901,a841))))),f180(f855(f855(x39901,a841),a841))),f773(f773(f61(x39901),f773(f773(f302(x39901),x39903),f180(f855(x39901,a841)))),x39902))
% 191.21/191.73 [4000]E(f773(f773(f82(a847),f773(f773(f83(a847),x40001),f773(f773(f43(a847),x40002),x40003))),f773(f773(f43(a847),f773(f773(f83(a847),x40001),f52(a847,x40002,x40003))),x40003)),f773(f773(f43(a847),f773(f773(f83(a847),x40001),x40002)),x40003))
% 191.21/191.73 [4001]E(f773(f773(f82(a1),f773(f773(f83(a1),x40011),f773(f773(f43(a1),x40012),x40013))),f773(f773(f43(a1),f773(f773(f83(a1),x40011),f52(a1,x40012,x40013))),x40013)),f773(f773(f43(a1),f773(f773(f83(a1),x40011),x40012)),x40013))
% 191.21/191.73 [4085]E(f773(f773(f125(x40851),f773(f132(f848(x40851),f848(x40851),f125(x40851),f115(x40851)),x40852)),f773(f132(f848(x40851),f848(x40851),f125(x40851),f115(x40851)),x40853)),f773(f132(f848(x40851),f848(x40851),f125(x40851),f115(x40851)),f773(f773(f125(f848(x40851)),x40852),x40853)))
% 191.21/191.73 [4088]E(f773(f773(f241(f848(x40881),f848(x40881)),f773(f126(x40881,x40882),x40883)),f773(f126(x40881,f773(f75(a841,a841,x40881,a328),x40882)),x40883)),f156(x40881,x40882,x40883))
% 191.21/191.73 [4091]E(f773(f773(f82(a847),f773(f773(f82(a847),f773(f773(f43(a847),x40911),x40912)),f773(f773(f43(a847),x40913),x40912))),f773(f773(f43(a847),f773(f773(f82(a847),f52(a847,x40911,x40912)),f52(a847,x40913,x40912))),x40912)),f773(f773(f43(a847),f773(f773(f82(a847),x40911),x40913)),x40912))
% 191.21/191.73 [4092]E(f773(f773(f82(a1),f773(f773(f82(a1),f773(f773(f43(a1),x40921),x40922)),f773(f773(f43(a1),x40923),x40922))),f773(f773(f43(a1),f773(f773(f82(a1),f52(a1,x40921,x40922)),f52(a1,x40923,x40922))),x40922)),f773(f773(f43(a1),f773(f773(f82(a1),x40921),x40923)),x40922))
% 191.21/191.73 [4165]E(f773(f256(x41651),f773(f773(f20(x41651,a841,a841),f773(f773(f10(a841,f855(a841,a841),x41651),a332),f773(f773(f9(x41651,x41651,a841),a330),x41652))),f773(f773(f9(x41651,f855(x41651,a841),a841),f334(x41651)),x41653))),f773(f773(f302(x41651),x41652),x41653))
% 191.21/191.73 [4187]E(f773(f256(x41871),f773(f773(f20(x41871,a841,a841),f773(f773(f10(a841,f855(a841,a841),x41871),a332),f773(f773(f9(x41871,f855(x41871,a841),a841),f334(x41871)),x41872))),f773(f773(f9(x41871,f855(x41871,a841),a841),f334(x41871)),x41873))),f773(f773(f103(f855(x41871,a841)),x41872),x41873))
% 191.21/191.73 [4188]E(f773(f256(x41881),f773(f773(f20(x41881,a841,a841),f773(f773(f10(a841,f855(a841,a841),x41881),a331),f773(f773(f9(x41881,f855(x41881,a841),a841),f334(x41881)),x41882))),f773(f773(f9(x41881,f855(x41881,a841),a841),f334(x41881)),x41883))),f773(f773(f104(f855(x41881,a841)),x41882),x41883))
% 191.21/191.73 [4275]E(f773(f773(f46(x42751,f855(f855(x42751,a841),a841)),x42752),f773(f773(f9(x42751,f855(f855(x42751,a841),a841),f855(f855(x42751,a841),a841)),f773(f773(f10(f855(x42751,a841),f855(f855(f855(x42751,a841),a841),f855(f855(x42751,a841),a841)),x42751),f302(f855(x42751,a841))),f773(f773(f10(f855(x42751,a841),f855(x42751,a841),x42751),f277(x42751,x42751,x42753)),f773(f773(f9(x42751,f855(x42751,a841),f855(x42751,a841)),f302(x42751)),f180(f855(x42751,a841)))))),f180(f855(f855(x42751,a841),a841)))),f773(f773(f61(x42751),x42752),x42753))
% 191.21/191.73 [4277]E(f773(f773(f197(x42771),f773(f773(f83(a1),f773(f773(f75(f854(a1,a1),a1,x42771,f240(a1,a1)),f207(x42771)),x42772)),f773(f773(f75(f854(a1,a1),a1,x42771,f240(a1,a1)),f207(x42771)),x42773))),f773(f773(f83(a1),f773(f773(f75(f854(a1,a1),a1,x42771,f250(a1,a1)),f207(x42771)),x42772)),f773(f773(f75(f854(a1,a1),a1,x42771,f250(a1,a1)),f207(x42771)),x42773))),f222(x42771,x42772,x42773))
% 191.21/191.73 [3671]E(f52(a847,f773(f773(f82(a847),f773(f773(f83(a847),x36711),x36712)),x36713),x36712),f52(a847,x36713,x36712))
% 191.21/191.73 [3718]E(f130(a847,f773(f294(a847,f773(f773(f82(a847),x37181),x37182)),x37183)),f773(f773(f128(a847),x37182),f130(a847,f773(f294(a847,x37181),x37183))))
% 191.21/191.73 [3762]E(f773(f773(f82(a1),f773(f102(a1),x37621)),f773(f773(f82(a1),f773(f102(a1),x37622)),x37623)),f773(f773(f82(a1),f773(f102(a1),f773(f773(f82(a847),x37621),x37622))),x37623))
% 191.21/191.73 [3770]E(f773(f773(f3(f855(x37701,a841)),f773(f773(f3(f855(x37701,a841)),x37702),x37703)),x37703),f773(f773(f3(f855(x37701,a841)),x37702),x37703))
% 191.21/191.73 [3771]E(f773(f773(f103(f855(x37711,a841)),f773(f773(f3(f855(x37711,a841)),x37712),x37713)),x37713),f773(f773(f103(f855(x37711,a841)),x37712),x37713))
% 191.21/191.73 [3793]E(f773(f773(f281(x37931,x37931,x37932),f300(x37931,f180(f855(f854(x37931,x37931),a841)))),x37933),x37933)
% 191.21/191.73 [3798]E(f773(f773(f103(f855(x37981,a841)),f773(f276(x37981),x37982)),f773(f276(x37981),x37983)),f773(f276(x37981),f773(f773(f103(f855(f854(x37981,x37981),a841)),x37982),x37983)))
% 191.21/191.73 [3807]E(f263(x38071,f773(f773(f140(f854(a101,x38071)),f773(f773(f241(a101,x38071),f2(a101)),x38072)),x38073)),f263(x38071,x38073))
% 191.21/191.73 [3810]E(f773(f773(f104(f855(x38101,a841)),f45(f855(x38101,a841),x38102)),f45(f855(x38101,a841),x38103)),f45(f855(x38101,a841),f773(f773(f103(f855(f855(x38101,a841),a841)),x38102),x38103)))
% 191.21/191.73 [3811]E(f773(f773(f103(f855(x38111,a841)),f44(f855(x38111,a841),x38112)),f44(f855(x38111,a841),x38113)),f44(f855(x38111,a841),f773(f773(f103(f855(f855(x38111,a841),a841)),x38112),x38113)))
% 191.21/191.73 [3844]E(f773(f773(f281(x38441,x38441,x38441),f773(f773(f173(f854(x38441,x38441),a841),x38442),x38443)),x38443),f773(f773(f173(f854(x38441,x38441),a841),f773(a114,x38442)),x38443))
% 191.21/191.73 [3894]P1(f773(f773(f232(f855(x38941,a841)),f773(f773(f3(f855(x38941,a841)),x38942),x38943)),x38942))
% 191.21/191.73 [3895]P1(f773(f773(f232(f855(x38951,a841)),f773(f773(f104(f855(x38951,a841)),x38952),x38953)),x38953))
% 191.21/191.73 [3896]P1(f773(f773(f232(f855(x38961,a841)),f773(f773(f104(f855(x38961,a841)),x38962),x38963)),x38962))
% 191.21/191.73 [3921]E(f300(x39211,f773(f773(f103(f855(f854(x39211,x39211),a841)),f300(x39211,x39212)),f300(x39211,x39213))),f300(x39211,f773(f773(f103(f855(f854(x39211,x39211),a841)),x39212),x39213)))
% 191.21/191.73 [3925]E(f44(f855(x39251,a841),f773(f773(f302(f855(x39251,a841)),x39252),f773(f773(f302(f855(x39251,a841)),x39253),f180(f855(f855(x39251,a841),a841))))),f773(f773(f103(f855(x39251,a841)),x39252),x39253))
% 191.21/191.73 [3926]E(f45(f855(x39261,a841),f773(f773(f302(f855(x39261,a841)),x39262),f773(f773(f302(f855(x39261,a841)),x39263),f180(f855(f855(x39261,a841),a841))))),f773(f773(f104(f855(x39261,a841)),x39262),x39263))
% 191.21/191.73 [3932]E(f773(f773(f281(x39321,x39321,x39321),f773(f773(f173(f854(x39321,x39321),a841),x39322),x39323)),x39323),f773(f773(f281(x39321,x39321,x39321),x39323),f773(f773(f173(f854(x39321,x39321),a841),x39322),x39323)))
% 191.21/191.73 [4005]E(f773(f773(f103(f855(x40051,a841)),f773(f256(x40051),f773(f773(f9(x40051,x40051,a841),a330),x40052))),x40053),f773(f773(f302(x40051),x40052),x40053))
% 191.21/191.73 [4007]E(f773(a107,f773(f773(f8(x40071,a1),f773(f773(f10(a847,a1,x40071),f102(a1)),x40072)),x40073)),f773(f773(f8(x40071,a847),x40072),x40073))
% 191.21/191.73 [4008]E(f773(a107,f773(f773(f11(x40081,a1),f773(f773(f10(a847,a1,x40081),f102(a1)),x40082)),x40083)),f773(f773(f11(x40081,a847),x40082),x40083))
% 191.21/191.73 [4082]E(f773(f145(f848(x40821),x40821,f773(f157(x40821),x40822),f773(f18(f855(f848(x40821),f848(x40821)),x40821),f773(f773(f9(f848(x40821),f848(x40821),f848(x40821)),f125(x40821)),x40822))),x40823),f773(f157(x40821),f773(f773(f125(x40821),x40823),x40822)))
% 191.21/191.73 [4113]P1(f773(f773(f232(f855(f855(x41131,a841),a841)),f773(f773(f103(f855(f855(x41131,a841),a841)),f773(f301(x41131),x41132)),f773(f301(x41131),x41133))),f773(f301(x41131),f773(f773(f103(f855(x41131,a841)),x41132),x41133))))
% 191.21/191.73 [4206]E(f773(f256(x42061),f773(f773(f20(x42061,a841,a841),f773(f773(f10(a841,f855(a841,a841),x42061),a331),f773(f773(f9(x42061,f855(x42061,a841),a841),f334(x42061)),x42062))),f773(f773(f10(a841,a841,x42061),a328),f773(f773(f9(x42061,f855(x42061,a841),a841),f334(x42061)),x42063)))),f773(f773(f3(f855(x42061,a841)),x42062),x42063))
% 191.21/191.73 [4227]E(f773(f42(a847),f773(f256(a847),f773(f773(f20(a847,a841,a841),f773(f773(f10(a841,f855(a841,a841),a847),a331),f773(f773(f9(a847,a847,a841),f233(a847)),f773(f181(f848(x42271)),x42272)))),f773(f773(f10(x42271,a841,a847),x42273),f773(f153(x42271),x42272))))),f773(f181(f848(x42271)),f773(f126(x42271,x42273),x42272)))
% 191.21/191.73 [4229]E(f773(f181(f848(x42291)),f160(x42291,x42292,x42293)),f773(f42(a847),f773(f256(a847),f773(f773(f20(a847,a841,a841),f773(f773(f10(a841,f855(a841,a841),a847),a331),f773(f773(f9(a847,a847,a841),f233(a847)),f773(f181(f848(x42291)),x42292)))),f773(f773(f9(a847,f855(a847,a841),a841),f334(a847)),x42293)))))
% 191.21/191.73 [4322]E(f773(f773(f104(f855(f854(f848(x43221),f848(x43221)),a841)),f773(f303(f854(f854(x43221,f848(x43221)),f854(x43221,f848(x43221))),f854(f848(x43221),f848(x43221)),f252(f854(x43221,f848(x43221)),f848(x43221),f854(x43221,f848(x43221)),f848(x43221),f773(f251(x43221,f848(x43221),f848(x43221)),f140(x43221)),f773(f251(x43221,f848(x43221),f848(x43221)),f140(x43221)))),f325(x43221,f848(x43221),x43222,f773(f133(x43221,x43222),x43223)))),f773(f256(f854(f848(x43221),f848(x43221))),f773(f251(f848(x43221),f848(x43221),a841),f773(f773(f9(f848(x43221),f855(f848(x43221),a841),f855(f848(x43221),a841)),f773(f773(f10(f855(a841,a841),f855(f855(f848(x43221),a841),f855(f848(x43221),a841)),f848(x43221)),f10(a841,a841,f848(x43221))),f773(f773(f10(a841,f855(a841,a841),f848(x43221)),a331),f773(f773(f9(f848(x43221),a847,a841),f773(f773(f10(a847,f855(a847,a841),f848(x43221)),a330),f181(f848(x43221)))),f773(a114,x43223))))),f773(f773(f9(f848(x43221),a847,a841),f773(f773(f10(a847,f855(a847,a841),f848(x43221)),a330),f181(f848(x43221)))),f773(a114,x43223)))))),f773(f133(x43221,x43222),f773(a114,x43223)))
% 191.21/191.73 [3812]E(f52(a847,f773(a114,f773(f773(f82(a847),f773(f773(f83(a847),x38121),x38122)),x38123)),x38122),f52(a847,f773(a114,x38123),x38122))
% 191.21/191.73 [4072]E(f773(f256(x40721),f773(f773(f20(x40721,a841,a841),f773(f773(f10(a841,f855(a841,a841),x40721),a331),x40722)),x40723)),f773(f773(f104(f855(x40721,a841)),f773(f256(x40721),x40722)),f773(f256(x40721),x40723)))
% 191.21/191.73 [4073]E(f773(f256(x40731),f773(f773(f20(x40731,a841,a841),f773(f773(f10(a841,f855(a841,a841),x40731),a332),x40732)),x40733)),f773(f773(f103(f855(x40731,a841)),f773(f256(x40731),x40732)),f773(f256(x40731),x40733)))
% 191.21/191.73 [4075]E(f773(f773(f125(x40751),f773(f773(f128(x40751),f52(a847,x40752,f773(f181(f848(x40751)),x40753))),x40753)),f773(f773(f159(x40751),f52(a847,x40752,f773(f181(f848(x40751)),x40753))),x40753)),f773(f773(f773(f173(f848(x40751),f848(x40751)),x40752),f141(x40751)),x40753))
% 191.21/191.73 [4080]E(f773(f256(x40801),f773(f773(f20(x40801,a841,a841),f773(f773(f10(a841,f855(a841,a841),x40801),a335),x40802)),x40803)),f773(f773(f103(f855(x40801,a841)),f773(f81(f855(x40801,a841)),f773(f256(x40801),x40802))),f773(f256(x40801),x40803)))
% 191.21/191.73 [4094]E(f773(f773(f82(a847),f773(f181(f848(x40941)),f773(f126(x40941,x40942),x40943))),f773(f181(f848(x40941)),f773(f126(x40941,f773(f773(f10(a841,a841,x40941),a328),x40942)),x40943))),f773(f181(f848(x40941)),x40943))
% 191.21/191.73 [4121]P1(f773(f773(f232(f855(x41211,a841)),f773(f773(f103(f855(x41211,a841)),f45(f855(x41211,a841),x41212)),f45(f855(x41211,a841),x41213))),f45(f855(x41211,a841),f773(f773(f104(f855(f855(x41211,a841),a841)),x41212),x41213))))
% 191.21/191.73 [4137]E(f773(f158(x41371),f773(f126(x41371,f773(f773(f10(a841,a841,x41371),a328),f773(f773(f9(x41371,x41371,a841),a330),x41372))),x41373)),f773(f773(f3(f855(x41371,a841)),f773(f158(x41371),x41373)),f773(f773(f302(x41371),x41372),f180(f855(x41371,a841)))))
% 191.21/191.73 [4146]P1(f773(f773(f232(f855(f854(x41461,x41461),a841)),f773(f773(f103(f855(f854(x41461,x41461),a841)),f300(x41461,x41462)),f300(x41461,x41463))),f300(x41461,f773(f773(f103(f855(f854(x41461,x41461),a841)),x41462),x41463))))
% 191.21/191.73 [4170]E(f773(f773(f83(a847),f773(a114,f773(a114,f2(a847)))),f773(f773(f8(a847,a847),f773(f773(f10(a847,a847,a847),f773(f82(a847),x41701)),f773(f773(f9(a847,a847,a847),f83(a847)),x41702))),f773(f257(a847),x41703))),f773(f773(f83(a847),x41703),f773(f773(f82(a847),x41701),f773(f773(f82(a847),x41701),f773(f773(f83(a847),f773(f773(f3(a847),x41703),f80(a847))),x41702)))))
% 191.21/191.73 [4180]E(f773(f256(x41801),f773(f773(f20(x41801,a841,a841),f773(f773(f10(a841,f855(a841,a841),x41801),a331),f773(f773(f9(x41801,f855(x41801,a841),a841),f334(x41801)),f773(f158(x41801),x41802)))),x41803)),f773(f158(x41801),f773(f126(x41801,x41803),x41802)))
% 191.21/191.73 [4321]E(f773(f256(x43211),f773(f773(f10(f855(a847,a841),a841,x43211),f89(a847)),f773(f773(f9(x43211,f855(a847,a841),f855(a847,a841)),f773(f773(f10(f855(a847,f855(a841,a841)),f855(f855(a847,a841),f855(a847,a841)),x43211),f20(a847,a841,a841)),f773(f773(f10(f855(a847,a841),f855(a847,f855(a841,a841)),x43211),f773(f10(a841,f855(a841,a841),a847),a331)),f773(f773(f9(x43211,f855(a847,x43211),f855(a847,a841)),f773(f773(f10(f855(x43211,a841),f855(f855(a847,x43211),f855(a847,a841)),x43211),f10(x43211,a841,a847)),a330)),f773(f153(x43211),x43212))))),f773(f773(f20(a847,a841,a841),f773(f773(f10(a841,f855(a841,a841),a847),a331),f773(f773(f9(a847,a847,a841),f233(a847)),f773(f181(f848(x43211)),x43212)))),f773(f773(f9(a847,f855(a847,a841),a841),f334(a847)),x43213))))),f773(f158(x43211),f160(x43211,x43212,x43213)))
% 191.21/191.73 [4217]E(f773(f256(x42171),f773(f773(f20(x42171,a841,a841),f773(f773(f10(a841,f855(a841,a841),x42171),a335),f773(f773(f10(a841,a841,x42171),a328),f773(f773(f9(x42171,x42171,a841),a330),x42172)))),x42173)),f773(f773(f302(x42171),x42172),f773(f256(x42171),x42173)))
% 191.21/191.73 [4248]E(f773(f773(f143(f854(x42481,a847),x42481),f240(x42481,a847)),f773(f126(f854(x42481,a847),f773(f773(f9(f854(x42481,a847),f855(a847,a841),a841),f773(f773(f10(a847,f855(f855(a847,a841),a841),f854(x42481,a847)),f334(a847)),f250(x42481,a847))),x42482)),f773(f773(f167(x42481,a847),x42483),f130(a847,f773(f294(a847,f2(a847)),f773(f181(f848(x42481)),x42483)))))),f160(x42481,x42483,x42482))
% 191.21/191.73 [4276]E(f773(f773(f83(a1),f773(f106(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),f773(f773(f8(a847,a1),f773(f773(f10(a1,a1,a847),f773(f82(a1),x42761)),f773(f773(f9(a847,a1,a1),f773(f773(f10(a1,f855(a1,a1),a847),f83(a1)),f102(a1))),x42762))),f773(f257(a847),x42763))),f773(f773(f83(a1),f773(f102(a1),x42763)),f773(f773(f82(a1),x42761),f773(f773(f82(a1),x42761),f773(f773(f83(a1),f773(f102(a1),f773(f773(f3(a847),x42763),f80(a847)))),x42762)))))
% 191.21/191.73 [4315]E(f773(f256(f854(x43151,x43152)),f773(f251(x43151,x43152,a841),f773(f773(f9(x43151,f855(f854(x43152,x43151),a841),f855(x43152,a841)),f773(f773(f10(f855(x43152,f855(f855(f854(x43152,x43151),a841),a841)),f855(f855(f854(x43152,x43151),a841),f855(x43152,a841)),x43151),f9(x43152,f855(f854(x43152,x43151),a841),a841)),f773(f773(f10(f855(x43152,f854(x43152,x43151)),f855(x43152,f855(f855(f854(x43152,x43151),a841),a841)),x43151),f773(f10(f854(x43152,x43151),f855(f855(f854(x43152,x43151),a841),a841),x43152),f334(f854(x43152,x43151)))),f773(f9(x43152,x43151,f854(x43152,x43151)),f241(x43152,x43151))))),x43153))),f773(f278(x43152,x43151),x43153))
% 191.21/191.73 [4350]E(f773(f256(f848(x43501)),f773(f773(f10(f855(x43501,a841),a841,f848(x43501)),f89(x43501)),f773(f773(f10(f855(x43501,f855(f848(x43501),a841)),f855(x43501,a841),f848(x43501)),f773(f10(f855(f848(x43501),a841),a841,x43501),f89(f848(x43501)))),f773(f773(f9(f848(x43501),f855(x43501,f855(f848(x43501),a841)),f855(x43501,f855(f848(x43501),a841))),f773(f773(f10(f855(x43501,f855(f855(f848(x43501),a841),f855(f848(x43501),a841))),f855(f855(x43501,f855(f848(x43501),a841)),f855(x43501,f855(f848(x43501),a841))),f848(x43501)),f20(x43501,f855(f848(x43501),a841),f855(f848(x43501),a841))),f773(f773(f10(f855(x43501,f855(f848(x43501),f855(a841,a841))),f855(x43501,f855(f855(f848(x43501),a841),f855(f848(x43501),a841))),f848(x43501)),f773(f10(f855(f848(x43501),f855(a841,a841)),f855(f855(f848(x43501),a841),f855(f848(x43501),a841)),x43501),f20(f848(x43501),a841,a841))),f773(f773(f10(f855(x43501,f855(f848(x43501),a841)),f855(x43501,f855(f848(x43501),f855(a841,a841))),f848(x43501)),f773(f10(f855(f848(x43501),a841),f855(f848(x43501),f855(a841,a841)),x43501),f773(f10(a841,f855(a841,a841),f848(x43501)),a331))),f773(f773(f9(f848(x43501),f855(x43501,f855(f848(x43501),f848(x43501))),f855(x43501,f855(f848(x43501),a841))),f773(f773(f10(f855(f855(f848(x43501),f848(x43501)),f855(f848(x43501),a841)),f855(f855(x43501,f855(f848(x43501),f848(x43501))),f855(x43501,f855(f848(x43501),a841))),f848(x43501)),f10(f855(f848(x43501),f848(x43501)),f855(f848(x43501),a841),x43501)),f773(f773(f10(f855(f848(x43501),a841),f855(f855(f848(x43501),f848(x43501)),f855(f848(x43501),a841)),f848(x43501)),f10(f848(x43501),a841,f848(x43501))),a330))),f140(x43501)))))),f773(f773(f9(x43501,f855(f848(x43501),a841),f855(f848(x43501),a841)),f773(f773(f10(f855(a841,a841),f855(f855(f848(x43501),a841),f855(f848(x43501),a841)),x43501),f10(a841,a841,f848(x43501))),f773(f773(f10(a841,f855(a841,a841),x43501),a331),f773(f773(f9(x43501,f855(x43501,a841),a841),f334(x43501)),x43502)))),f773(f773(f9(f848(x43501),f855(f848(x43501),a841),a841),f334(f848(x43501))),x43503)))))),f161(x43501,x43502,x43503))
% 191.21/191.73 [4335]E(f773(f773(f88(a1,f854(a1,a1)),f773(f773(f3(a1),x43351),x43352)),f773(f773(f9(a1,f854(a1,a1),f854(a1,a1)),f773(f773(f20(a1,f854(a1,a1),f855(f854(a1,a1),f854(a1,a1))),f773(f773(f10(a841,f855(f854(a1,a1),f855(f854(a1,a1),f854(a1,a1))),a1),f98(f854(a1,a1))),f773(f232(a1),f2(a1)))),f773(f241(a1,a1),f773(f773(f82(a1),f773(f773(f83(a1),f773(f106(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),x43353)),f80(a1))))),f773(f773(f241(a1,a1),f773(f773(f83(a1),f773(f106(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),x43353)),x43351))),f773(f50(x43352),f773(f773(f241(a1,a1),x43353),x43351)))
% 191.21/191.73 [4386]~E(f36(x43861,x43862),f35(x43863,x43864))
% 191.21/191.73 [4389]~E(f28(x43891,x43892),f35(x43893,x43894))
% 191.21/191.73 [4390]~E(f28(x43901,x43902),f36(x43903,x43904))
% 191.21/191.73 [4408]~E(f773(a27,x44081),f33(x44082,x44083,x44084))
% 191.21/191.73 [4409]~E(f773(a27,x44091),f32(x44092,x44093,x44094))
% 191.21/191.73 [4410]~E(f773(a27,x44101),f31(x44102,x44103,x44104))
% 191.21/191.73 [4411]~E(f33(x44111,x44112,x44113),f773(a27,x44114))
% 191.21/191.73 [4412]~E(f32(x44121,x44122,x44123),f773(a27,x44124))
% 191.21/191.73 [4413]~E(f31(x44131,x44132,x44133),f773(a27,x44134))
% 191.21/191.73 [3366]E(f773(f773(f773(f74(x33661,x33662),x33663),x33664),f773(x33663,x33664)),x33663)
% 191.21/191.73 [3430]E(f773(f773(f243(x34301,x34302,x34303),x34304),f2(a847)),x34302)
% 191.21/191.73 [3468]E(f175(x34681,x34682,x34683,f773(a114,x34684)),f773(x34683,x34684))
% 191.21/191.73 [3509]E(f151(x35091,x35092,f151(x35091,x35093,x35094)),f151(x35091,x35093,f151(x35091,x35092,x35094)))
% 191.21/191.73 [3626]P39(f28(x36261,x36262),x36263,x36264,f773(f773(f773(a189,x36263),x36261),f773(x36262,x36263)))
% 191.21/191.73 [3638]E(f773(f229(x36381,x36382,x36383,x36384),f183(x36382)),x36383)
% 191.21/191.73 [3640]E(f773(f145(x36401,x36402,x36403,x36404),f115(x36402)),x36403)
% 191.21/191.73 [3641]E(f773(f132(x36411,x36412,x36413,x36414),f115(x36412)),x36414)
% 191.21/191.73 [3678]E(f773(f181(f852(x36781,x36782)),f215(x36781,x36782,x36783,x36784)),f2(a847))
% 191.21/191.73 [3703]E(f773(f251(x37031,x37032,x37033),f249(x37031,x37032,x37033,x37034)),x37034)
% 191.21/191.73 [3759]E(f773(f229(f851(x37591),x37592,f183(x37591),f773(f18(f851(x37591),x37592),f183(x37591))),f773(x37593,x37594)),f183(x37591))
% 191.21/191.73 [3802]E(f773(f773(f103(f855(x38021,a841)),f169(x38021,x38022,x38023)),f169(x38021,x38022,x38024)),f169(x38021,x38022,f170(x38021,x38022,x38024,x38023)))
% 191.21/191.73 [3831]E(f773(f773(f253(x38311,x38312,x38313,f854(x38312,x38313)),x38314),f241(x38312,x38313)),x38314)
% 191.21/191.73 [3840]E(f230(x38401,x38402,x38403,x38404,f183(x38402)),x38403)
% 191.21/191.73 [4128]P41(x41281,x41282,x41283,x41284,f180(f855(x41281,a841)),x41284)
% 191.21/191.73 [4437]~E(f773(f313(x44371,x44372),x44373),f773(f304(x44372,x44371),x44374))
% 191.21/191.73 [3175]E(f773(f773(f18(x31751,x31752),x31753),x31754),x31753)
% 191.21/191.73 [3288]E(f773(f773(f196(x32881,x32882),x32883),f773(f227(x32881),x32884)),f773(f227(x32882),f773(x32883,x32884)))
% 191.21/191.73 [3460]E(f151(x34601,x34602,f773(f126(x34601,x34603),x34604)),f773(f126(x34601,x34603),f151(x34601,x34602,x34604)))
% 191.21/191.73 [3493]E(f773(f773(f66(x34931,x34932,x34933),x34934),f180(f855(x34931,a841))),x34934)
% 191.21/191.73 [3515]E(f773(f773(f153(x35151),f773(f773(f140(x35151),x35152),x35153)),f773(a114,x35154)),f773(f773(f153(x35151),x35153),x35154))
% 191.21/191.73 [3553]P31(x35531,f2(a847),f773(f773(f773(f93(x35531),x35532),f773(a27,x35533)),x35534))
% 191.21/191.73 [3578]E(f773(f773(x35781,x35782),f773(f174(x35783,x35784,x35781),x35782)),f773(f174(x35783,x35784,x35781),f773(a114,x35782)))
% 191.21/191.73 [3618]E(f249(x36181,x36182,x36183,f773(f251(x36181,x36182,x36183),x36184)),x36184)
% 191.21/191.73 [3676]E(f773(f773(f148(x36761,f773(f773(f140(x36761),x36762),x36763)),f2(a847)),x36764),f773(f773(f140(x36761),x36764),x36763))
% 191.21/191.73 [3686]E(f773(f773(f46(f855(x36861,a841),f855(x36862,a841)),x36863),f303(x36861,x36862,x36864)),f773(f303(x36861,x36862,x36864),f44(f855(x36861,a841),x36863)))
% 191.21/191.73 [3687]E(f773(f773(f46(f855(x36871,a841),f855(x36872,a841)),x36873),f305(x36872,x36871,x36874)),f773(f305(x36872,x36871,x36874),f44(f855(x36871,a841),x36873)))
% 191.21/191.73 [3787]E(f169(x37871,x37872,f172(x37871,x37872,x37873,x37874)),f773(f773(f104(f855(x37871,a841)),f169(x37871,x37872,x37873)),x37874))
% 191.21/191.73 [3806]E(f773(f132(x38061,x38062,f773(f9(x38062,x38061,x38061),x38063),x38064),f773(f142(x38062),f115(x38062))),x38064)
% 191.21/191.73 [3850]E(f78(x38501,x38502,x38503,x38504,f180(f855(x38501,a841))),x38503)
% 191.21/191.73 [3897]E(f773(f773(f773(f773(f74(x38971,f851(x38972)),f773(f18(f851(x38972),x38971),f183(x38972))),x38973),f183(x38972)),x38974),f183(x38972))
% 191.21/191.73 [4046]E(f319(x40461,x40462,x40463,f773(f773(f10(f856(x40461,x40463),x40462,x40461),x40464),f304(x40461,x40463)),f773(f773(f10(f856(x40461,x40463),x40462,x40463),x40464),f313(x40463,x40461))),x40464)
% 191.21/191.73 [4056]E(f773(f251(x40561,x40562,x40563),f773(f773(f10(f855(x40562,f854(x40561,x40562)),f855(x40562,x40563),x40561),f773(f10(f854(x40561,x40562),x40563,x40562),x40564)),f241(x40561,x40562))),x40564)
% 191.21/191.73 [3364]E(f773(f250(x33641,x33642),f773(f773(f241(x33641,x33642),x33643),x33644)),x33644)
% 191.21/191.73 [3365]E(f773(f240(x33651,x33652),f773(f773(f241(x33651,x33652),x33653),x33654)),x33653)
% 191.21/191.73 [3403]E(f773(f181(f848(x34031)),f773(f773(f143(x34032,x34031),x34033),x34034)),f773(f181(f848(x34032)),x34034))
% 191.21/191.73 [3404]E(f773(f181(f848(x34041)),f773(f773(f148(x34041,x34042),x34043),x34044)),f773(f181(f848(x34041)),x34042))
% 191.21/191.73 [3425]E(f773(f773(f128(x34251),f773(a114,x34252)),f773(f773(f140(x34251),x34253),x34254)),f773(f773(f128(x34251),x34252),x34254))
% 191.21/191.73 [3495]E(f773(f773(f302(x34951),x34952),f773(f773(f302(x34951),x34953),x34954)),f773(f773(f302(x34951),x34953),f773(f773(f302(x34951),x34952),x34954)))
% 191.21/191.73 [3498]E(f773(f773(f143(x34981,x34982),x34983),f116(x34981,x34984)),f116(x34982,f773(f773(f143(x34981,x34982),x34983),x34984)))
% 191.21/191.73 [3513]E(f773(f142(x35131),f773(f773(f143(x35132,x35131),x35133),x35134)),f773(f773(f143(x35132,x35131),x35133),f773(f142(x35132),x35134)))
% 191.21/191.73 [3514]E(f773(f773(f143(x35141,x35142),x35143),f773(f157(x35141),x35144)),f773(f157(x35142),f773(f773(f143(x35141,x35142),x35143),x35144)))
% 191.21/191.73 [3523]E(f773(f773(f159(x35231),f773(a114,x35232)),f773(f773(f140(x35231),x35233),x35234)),f773(f773(f140(x35231),x35233),f773(f773(f159(x35231),x35232),x35234)))
% 191.21/191.73 [3527]E(f773(f158(x35271),f773(f773(f143(x35272,x35271),x35273),x35274)),f773(f303(x35272,x35271,x35273),f773(f158(x35272),x35274)))
% 191.21/191.73 [3577]E(f19(x35771,x35772,x35773,f773(a5,f773(a114,f773(a22,x35774)))),f773(x35773,x35774))
% 191.21/191.73 [3581]E(f773(f773(f125(x35811),f773(f126(x35811,x35812),x35813)),f773(f126(x35811,x35812),x35814)),f773(f126(x35811,x35812),f773(f773(f125(x35811),x35813),x35814)))
% 191.21/191.73 [3608]E(f773(f278(x36081,x36081),f773(f773(f280(x36082,x36081),x36083),x36084)),f773(f773(f280(x36082,x36081),f773(f278(x36082,x36082),x36083)),x36084))
% 191.21/191.73 [3619]E(f773(f773(f281(x36191,x36192,x36193),x36194),f180(f855(f854(x36192,x36193),a841))),f180(f855(f854(x36191,x36193),a841)))
% 191.21/191.73 [3620]E(f773(f773(f159(x36201),f773(f773(f3(a847),x36202),x36203)),f773(f773(f128(x36201),x36203),x36204)),f773(f773(f128(x36201),x36203),f773(f773(f159(x36201),x36202),x36204)))
% 191.21/191.73 [3642]E(f773(f773(f773(f273(x36421),x36422),x36423),x36424),f773(f241(f855(a101,f855(a841,f851(f849(x36421)))),f854(a101,a101)),f773(f49(x36421),x36422)))
% 191.21/191.73 [3668]E(f45(f855(x36681,a841),f773(f303(x36682,f855(x36681,a841),x36683),x36684)),f773(f773(f47(x36682,f855(x36681,a841)),x36684),x36683))
% 191.21/191.73 [3669]E(f44(f855(x36691,a841),f773(f303(x36692,f855(x36691,a841),x36693),x36694)),f773(f773(f46(x36692,f855(x36691,a841)),x36694),x36693))
% 191.21/191.73 [3670]E(f773(f181(f848(f854(x36701,x36702))),f773(f773(f167(x36701,x36702),x36703),x36704)),f773(f773(f236(a847),f773(f181(f848(x36701)),x36703)),f773(f181(f848(x36702)),x36704)))
% 191.21/191.73 [3672]E(f773(f305(x36721,x36722,x36723),f773(f81(f855(x36722,a841)),x36724)),f773(f81(f855(x36721,a841)),f773(f305(x36721,x36722,x36723),x36724)))
% 191.21/191.73 [3704]E(f773(f172(x37041,x37042,x37043,f180(f855(x37041,a841))),x37044),f183(x37042))
% 191.21/191.73 [3723]E(f773(f305(x37231,x37232,x37233),f773(f256(x37232),x37234)),f773(f256(x37231),f773(f773(f10(x37232,a841,x37231),x37234),x37233)))
% 191.21/191.73 [3741]E(f773(f773(f153(x37411),f773(f773(f125(x37411),x37412),f773(f773(f140(x37411),x37413),x37414))),f773(f181(f848(x37411)),x37412)),x37413)
% 191.21/191.73 [3746]E(f773(f172(x37461,x37462,f773(f18(f851(x37462),x37461),f183(x37462)),x37463),x37464),f183(x37462))
% 191.21/191.73 [3768]E(f773(f303(x37681,x37682,x37683),f773(f305(x37681,x37682,x37683),x37684)),f773(f773(f104(f855(x37682,a841)),x37684),f773(f303(x37681,x37682,x37683),f239(f855(x37681,a841)))))
% 191.21/191.73 [3786]P1(f773(f773(f334(x37861),f773(x37862,x37863)),f773(f303(x37864,x37861,x37862),f239(f855(x37864,a841)))))
% 191.21/191.73 [3794]E(f21(x37941,x37942,x37943,f773(a5,f773(a114,f773(a22,x37944)))),f773(f773(x37943,x37944),f21(x37941,x37942,x37943,x37944)))
% 191.21/191.73 [3809]E(f144(x38091,x38092,f773(f773(f140(x38091),x38093),x38094)),f773(f773(f82(a847),f773(f773(f82(a847),f773(x38092,x38093)),f144(x38091,x38092,x38094))),f773(a114,f2(a847))))
% 191.21/191.73 [3822]E(f175(f848(x38221),f773(f773(f140(x38221),x38222),x38223),f773(f773(f9(a847,f848(x38221),f848(x38221)),f128(x38221)),x38223),x38224),f773(f773(f128(x38221),x38224),f773(f773(f140(x38221),x38222),x38223)))
% 191.21/191.73 [3823]P29(x38231,f854(x38232,x38231),f336(x38233,x38234,x38232,x38231),f773(f773(f46(x38232,f855(x38231,a841)),x38234),x38233))
% 191.21/191.73 [3832]E(f773(f773(f3(f855(x38321,a841)),f773(f773(f3(f855(x38321,a841)),x38322),x38323)),f773(f773(f302(x38321),x38324),f180(f855(x38321,a841)))),f773(f773(f3(f855(x38321,a841)),x38322),f773(f773(f302(x38321),x38324),x38323)))
% 191.21/191.73 [3843]E(f773(f773(f173(f855(x38431,x38432),f855(x38431,x38432)),x38433),f75(x38432,x38432,x38431,x38434)),f75(x38432,x38432,x38431,f773(f773(f173(x38432,x38432),x38433),x38434)))
% 191.21/191.73 [3920]E(f773(f773(f773(f173(f848(x39201),f848(x39201)),x39202),f141(x39201)),f773(f773(f773(f173(f848(x39201),f848(x39201)),x39203),f141(x39201)),x39204)),f773(f773(f773(f173(f848(x39201),f848(x39201)),f773(f773(f82(a847),x39202),x39203)),f141(x39201)),x39204))
% 191.21/191.73 [3969]E(f773(f773(f103(f855(f856(x39691,x39692),a841)),f773(f303(x39691,f856(x39691,x39692),f304(x39691,x39692)),x39693)),f773(f303(x39692,f856(x39691,x39692),f313(x39692,x39691)),x39694)),f314(x39691,x39692,x39693,x39694))
% 191.21/191.73 [4010]P1(f773(f773(f232(f855(x40101,a841)),f773(f158(x40101),f773(f773(f148(x40101,x40102),x40103),x40104))),f773(f773(f302(x40101),x40104),f773(f158(x40101),x40102))))
% 191.21/191.73 [4044]E(f773(f773(f46(f855(x40441,a841),f855(f854(x40441,x40442),a841)),x40443),f773(f773(f9(f855(x40441,a841),f855(x40441,f855(x40442,a841)),f855(f854(x40441,x40442),a841)),f248(x40441,x40442)),x40444)),f773(f773(f248(x40441,x40442),f44(f855(x40441,a841),x40443)),x40444))
% 191.21/191.73 [4081]E(f204(x40811,x40812,x40813,f773(f75(x40812,f855(a101,f855(a101,f855(f854(a101,a101),f855(a101,f849(x40812))))),x40811,f203(x40812)),x40814)),f205(x40811,x40812,x40814,x40813))
% 191.21/191.73 [4097]E(f200(x40971,x40972,x40973,f773(f75(x40972,f855(a101,f855(a101,f855(f854(a101,a101),f855(a101,f849(f851(x40972)))))),x40971,f199(x40972)),x40974)),f201(x40971,x40972,x40974,x40973))
% 191.21/191.73 [4102]P1(f773(f68(x41021,x41022,x41023,x41024,f180(f855(x41021,a841))),x41024))
% 191.21/191.73 [4149]E(f773(f773(f46(x41491,f855(x41492,a841)),x41493),f773(f773(f9(x41491,f855(x41492,a841),f855(x41492,a841)),f773(f773(f10(x41492,f855(f855(x41492,a841),f855(x41492,a841)),x41491),f302(x41492)),x41494)),f180(f855(x41492,a841)))),f773(f303(x41491,x41492,x41494),x41493))
% 191.21/191.73 [4155]P1(f773(f773(f232(f855(x41551,a841)),f773(f259(x41552,x41551),f773(f773(f104(f855(f854(x41552,x41551),a841)),x41553),x41554))),f773(f773(f104(f855(x41551,a841)),f773(f259(x41552,x41551),x41553)),f773(f259(x41552,x41551),x41554))))
% 191.21/191.73 [4156]P1(f773(f773(f232(f855(x41561,a841)),f773(f261(x41561,x41562),f773(f773(f104(f855(f854(x41561,x41562),a841)),x41563),x41564))),f773(f773(f104(f855(x41561,a841)),f773(f261(x41561,x41562),x41563)),f773(f261(x41561,x41562),x41564))))
% 191.21/191.73 [4215]P1(f773(f773(f232(f855(f854(x42151,x42152),a841)),f773(f303(x42152,f854(x42151,x42152),f336(x42153,x42154,x42151,x42152)),f773(f773(f46(x42151,f855(x42152,a841)),x42154),x42153))),f773(f773(f248(x42151,x42152),x42154),x42153)))
% 191.21/191.73 [4216]E(f271(x42161,x42162,x42163,f773(f75(x42162,f855(a101,f855(a101,f855(f854(a101,a101),f854(f855(a101,f855(a841,f851(f849(x42162)))),f854(a101,a101))))),x42161,f273(x42162)),x42164)),f274(x42161,x42162,x42164,x42163))
% 191.21/191.73 [4254]E(f87(f854(x42541,x42542),f773(f251(x42541,x42542,a841),f773(f773(f9(x42541,f855(x42542,a841),f855(x42542,a841)),f773(f773(f10(f855(a841,a841),f855(f855(x42542,a841),f855(x42542,a841)),x42541),f10(a841,a841,x42542)),f773(f773(f10(a841,f855(a841,a841),x42541),a331),f773(a330,x42543)))),f773(a330,x42544)))),f773(f773(f241(x42541,x42542),x42543),x42544))
% 191.21/191.73 [4255]E(f92(f854(x42551,x42552),f773(f251(x42551,x42552,a841),f773(f773(f9(x42551,f855(x42552,a841),f855(x42552,a841)),f773(f773(f10(f855(a841,a841),f855(f855(x42552,a841),f855(x42552,a841)),x42551),f10(a841,a841,x42552)),f773(f773(f10(a841,f855(a841,a841),x42551),a331),f773(a330,x42553)))),f773(a330,x42554)))),f773(f773(f241(x42551,x42552),x42553),x42554))
% 191.21/191.73 [4325]E(f773(f773(f251(f848(x43251),f848(x43251),f854(f848(x43251),f848(x43251))),f773(f773(f20(f848(x43251),f855(f848(x43251),f854(f848(x43251),f848(x43251))),f855(f848(x43251),f854(f848(x43251),f848(x43251)))),f773(f773(f10(f855(f848(x43251),f855(f854(f848(x43251),f848(x43251)),f854(f848(x43251),f848(x43251)))),f855(f855(f848(x43251),f854(f848(x43251),f848(x43251))),f855(f848(x43251),f854(f848(x43251),f848(x43251)))),f848(x43251)),f20(f848(x43251),f854(f848(x43251),f848(x43251)),f854(f848(x43251),f848(x43251)))),f773(f773(f10(f855(f848(x43251),f854(f848(x43251),f848(x43251))),f855(f848(x43251),f855(f854(f848(x43251),f848(x43251)),f854(f848(x43251),f848(x43251)))),f848(x43251)),f773(f10(f854(f848(x43251),f848(x43251)),f855(f854(f848(x43251),f848(x43251)),f854(f848(x43251),f848(x43251))),f848(x43251)),f773(f98(f854(f848(x43251),f848(x43251))),f773(x43252,x43253)))),f773(f773(f10(f848(x43251),f855(f848(x43251),f854(f848(x43251),f848(x43251))),f848(x43251)),f241(f848(x43251),f848(x43251))),f773(f140(x43251),x43253))))),f773(f773(f9(f848(x43251),f855(f848(x43251),f848(x43251)),f855(f848(x43251),f854(f848(x43251),f848(x43251)))),f773(f773(f10(f855(f848(x43251),f854(f848(x43251),f848(x43251))),f855(f855(f848(x43251),f848(x43251)),f855(f848(x43251),f854(f848(x43251),f848(x43251)))),f848(x43251)),f10(f848(x43251),f854(f848(x43251),f848(x43251)),f848(x43251))),f241(f848(x43251),f848(x43251)))),f773(f140(x43251),x43253)))),f156(x43251,x43252,x43254)),f156(x43251,x43252,f773(f773(f140(x43251),x43253),x43254)))
% 191.21/191.73 [4331]E(f773(f132(f855(x43311,f851(x43312)),f854(x43311,x43312),f773(f9(f854(x43311,x43312),f855(x43311,f851(x43312)),f855(x43311,f851(x43312))),f773(f251(x43311,x43312,f855(f855(x43311,f851(x43312)),f855(x43311,f851(x43312)))),f773(f773(f9(x43311,f855(x43312,f851(x43312)),f855(x43312,f855(f855(x43311,f851(x43312)),f855(x43311,f851(x43312))))),f773(f773(f10(f855(f851(x43312),f855(f855(x43311,f851(x43312)),f855(x43311,f851(x43312)))),f855(f855(x43312,f851(x43312)),f855(x43312,f855(f855(x43311,f851(x43312)),f855(x43311,f851(x43312))))),x43311),f10(f851(x43312),f855(f855(x43311,f851(x43312)),f855(x43311,f851(x43312))),x43312)),f773(f773(f10(f855(f855(x43311,f851(x43312)),f855(f851(x43312),f855(x43311,f851(x43312)))),f855(f851(x43312),f855(f855(x43311,f851(x43312)),f855(x43311,f851(x43312)))),x43311),f9(f855(x43311,f851(x43312)),f851(x43312),f855(x43311,f851(x43312)))),f773(f9(f855(x43311,f851(x43312)),x43311,f855(f851(x43312),f855(x43311,f851(x43312)))),f74(x43311,f851(x43312)))))),f227(x43312)))),x43313),f773(f142(f854(x43311,x43312)),x43314)),f170(x43311,x43312,x43313,f166(x43311,x43312,x43314)))
% 191.21/191.73 [3443]E(f773(f181(f846(x34431)),f773(f773(f773(f93(x34431),x34432),x34433),x34434)),f2(a847))
% 191.21/191.73 [3556]E(f773(f773(f159(x35561),x35562),f773(f773(f159(x35561),x35563),x35564)),f773(f773(f159(x35561),f773(f773(f236(a847),x35562),x35563)),x35564))
% 191.21/191.73 [3557]E(f773(f773(f128(x35571),x35572),f773(f773(f128(x35571),x35573),x35574)),f773(f773(f128(x35571),f773(f773(f82(a847),x35572),x35573)),x35574))
% 191.21/191.73 [3569]E(f773(f773(f125(x35691),f773(f773(f140(x35691),x35692),x35693)),x35694),f773(f773(f140(x35691),x35692),f773(f773(f125(x35691),x35693),x35694)))
% 191.21/191.73 [3570]E(f773(f773(f125(x35701),f773(f773(f125(x35701),x35702),x35703)),x35704),f773(f773(f125(x35701),x35702),f773(f773(f125(x35701),x35703),x35704)))
% 191.21/191.73 [3652]E(f773(f773(f153(x36521),f773(f773(f140(x36521),x36522),x36523)),x36524),f175(x36521,x36522,f773(f153(x36521),x36523),x36524))
% 191.21/191.73 [3661]E(f773(f773(f173(x36611,x36611),x36612),f773(f773(f173(x36611,x36611),x36613),x36614)),f773(f773(f173(x36611,x36611),f773(f773(f83(a847),x36613),x36612)),x36614))
% 191.21/191.73 [3689]E(f773(f773(f103(f855(x36891,a841)),x36892),f773(f773(f302(x36891),x36893),x36894)),f773(f773(f302(x36891),x36893),f773(f773(f103(f855(x36891,a841)),x36892),x36894)))
% 191.21/191.73 [3707]E(f773(f773(f773(f173(x37071,x37071),x37072),x37073),f773(x37073,x37074)),f773(x37073,f773(f773(f773(f173(x37071,x37071),x37072),x37073),x37074)))
% 191.21/191.73 [3714]E(f773(f773(f281(x37141,x37142,x37143),f180(f855(f854(x37141,x37142),a841))),x37144),f180(f855(f854(x37141,x37143),a841)))
% 191.21/191.73 [3730]E(f773(f773(f103(f855(x37301,a841)),f773(f773(f302(x37301),x37302),x37303)),x37304),f773(f773(f302(x37301),x37302),f773(f773(f103(f855(x37301,a841)),x37303),x37304)))
% 191.21/191.73 [3748]E(f773(f42(f854(x37481,x37482)),f773(f773(f248(x37481,x37482),x37483),f773(f18(f855(x37482,a841),x37481),x37484))),f773(f773(f83(a847),f773(f42(x37481),x37483)),f773(f42(x37482),x37484)))
% 191.21/191.73 [3756]E(f773(f773(f104(f855(x37561,a841)),f773(f773(f302(x37561),x37562),x37563)),f773(f773(f302(x37561),x37562),x37564)),f773(f773(f302(x37561),x37562),f773(f773(f104(f855(x37561,a841)),x37563),x37564)))
% 191.21/191.73 [3766]E(f170(x37661,x37662,f166(x37661,x37662,x37663),f166(x37661,x37662,x37664)),f166(x37661,x37662,f773(f773(f125(f854(x37661,x37662)),x37664),x37663)))
% 191.21/191.73 [3772]E(f773(f773(f103(f855(x37721,a841)),x37722),f773(f773(f103(f855(x37721,a841)),x37723),x37724)),f773(f773(f103(f855(x37721,a841)),x37723),f773(f773(f103(f855(x37721,a841)),x37722),x37724)))
% 191.21/191.73 [3773]E(f773(f773(f104(f855(x37731,a841)),x37732),f773(f773(f104(f855(x37731,a841)),x37733),x37734)),f773(f773(f104(f855(x37731,a841)),x37733),f773(f773(f104(f855(x37731,a841)),x37732),x37734)))
% 191.21/191.73 [3782]E(f66(x37821,x37822,f773(f773(f10(x37822,f855(x37822,x37822),x37821),x37823),x37824)),f773(f67(x37822,x37821,x37823),x37824))
% 191.21/191.73 [3791]E(f164(x37911,f773(f773(f143(f848(x37912),f848(x37911)),f773(f143(x37912,x37911),x37913)),x37914)),f773(f773(f143(f848(x37912),f848(x37911)),f773(f143(x37912,x37911),x37913)),f164(x37912,x37914)))
% 191.21/191.73 [3808]E(f172(x38081,x38082,x38083,f773(f81(f855(x38081,a841)),f773(f773(f302(x38081),x38084),f180(f855(x38081,a841))))),f773(f773(f773(f74(x38081,f851(x38082)),x38083),x38084),f183(x38082)))
% 191.21/191.73 [3864]E(f773(f75(x38641,x38641,x38641,f773(f773(f173(x38641,x38641),x38642),x38643)),f773(f773(f173(x38641,x38641),x38644),x38643)),f773(f773(f173(x38641,x38641),f773(f773(f82(a847),x38642),x38644)),x38643))
% 191.21/191.73 [3879]E(f773(f773(f773(f74(x38791,f851(x38792)),f166(x38791,x38792,x38793)),f773(f240(x38791,x38792),x38794)),f773(f227(x38792),f773(f250(x38791,x38792),x38794))),f166(x38791,x38792,f773(f773(f140(f854(x38791,x38792)),x38794),x38793)))
% 191.21/191.73 [3886]E(f170(x38861,x38862,x38863,f166(x38861,x38862,f773(f142(f854(x38861,x38862)),f773(f773(f167(x38861,x38862),x38864),f115(x38862))))),x38863)
% 191.21/191.73 [3889]E(f773(f773(f104(f855(x38891,a841)),f773(f773(f3(f855(x38891,a841)),x38892),x38893)),f773(f773(f3(f855(x38891,a841)),x38892),x38894)),f773(f773(f3(f855(x38891,a841)),x38892),f773(f773(f103(f855(x38891,a841)),x38893),x38894)))
% 191.21/191.73 [3890]E(f773(f773(f103(f855(x38901,a841)),f773(f773(f3(f855(x38901,a841)),x38902),x38903)),f773(f773(f3(f855(x38901,a841)),x38902),x38904)),f773(f773(f3(f855(x38901,a841)),x38902),f773(f773(f104(f855(x38901,a841)),x38903),x38904)))
% 191.21/191.73 [3891]E(f773(f773(f104(f855(x38911,a841)),f773(f773(f103(f855(x38911,a841)),x38912),x38913)),f773(f773(f103(f855(x38911,a841)),x38912),x38914)),f773(f773(f103(f855(x38911,a841)),x38912),f773(f773(f104(f855(x38911,a841)),x38913),x38914)))
% 191.21/191.73 [3892]E(f773(f773(f3(f855(x38921,a841)),f773(f773(f104(f855(x38921,a841)),x38922),x38923)),f773(f773(f104(f855(x38921,a841)),x38922),x38924)),f773(f773(f104(f855(x38921,a841)),x38922),f773(f773(f3(f855(x38921,a841)),x38923),x38924)))
% 191.21/191.73 [3893]E(f773(f773(f103(f855(x38931,a841)),f773(f773(f104(f855(x38931,a841)),x38932),x38933)),f773(f773(f104(f855(x38931,a841)),x38932),x38934)),f773(f773(f104(f855(x38931,a841)),x38932),f773(f773(f103(f855(x38931,a841)),x38933),x38934)))
% 191.21/191.73 [3899]E(f773(f42(f854(x38991,x38992)),f773(f773(f248(x38991,x38992),f773(f773(f302(x38991),x38993),f180(f855(x38991,a841)))),f773(f18(f855(x38992,a841),x38991),x38994))),f773(f42(x38992),x38994))
% 191.21/191.73 [3936]E(f773(f773(f47(x39361,f855(x39362,a841)),x39363),f773(f773(f10(f855(x39362,a841),f855(x39362,a841),x39361),f81(f855(x39362,a841))),x39364)),f773(f81(f855(x39362,a841)),f773(f773(f46(x39361,f855(x39362,a841)),x39363),x39364)))
% 191.21/191.73 [3937]E(f773(f773(f46(x39371,f855(x39372,a841)),x39373),f773(f773(f10(f855(x39372,a841),f855(x39372,a841),x39371),f81(f855(x39372,a841))),x39374)),f773(f81(f855(x39372,a841)),f773(f773(f47(x39371,f855(x39372,a841)),x39373),x39374)))
% 191.21/191.73 [3953]E(f773(f773(f281(x39531,x39531,x39531),f773(f773(f173(f854(x39531,x39531),a841),x39532),x39533)),f773(f773(f173(f854(x39531,x39531),a841),x39534),x39533)),f773(f773(f173(f854(x39531,x39531),a841),f773(f773(f82(a847),x39532),x39534)),x39533))
% 191.21/191.73 [3985]E(f773(f773(f47(x39851,f855(f855(x39852,a841),a841)),x39853),f773(f773(f10(f855(x39852,a841),f855(f855(x39852,a841),a841),x39851),f301(x39852)),x39854)),f773(f301(x39852),f773(f773(f47(x39851,f855(x39852,a841)),x39853),x39854)))
% 191.21/191.73 [4015]E(f773(f773(f46(f855(x40151,a841),f855(x40152,a841)),x40153),f773(f773(f9(f855(x40151,a841),f855(x40151,f855(x40152,a841)),f855(x40152,a841)),f46(x40151,f855(x40152,a841))),x40154)),f773(f773(f46(x40151,f855(x40152,a841)),f44(f855(x40151,a841),x40153)),x40154))
% 191.21/191.73 [4016]E(f773(f773(f47(f855(x40161,a841),f855(x40162,a841)),x40163),f773(f773(f9(f855(x40161,a841),f855(x40161,f855(x40162,a841)),f855(x40162,a841)),f47(x40161,f855(x40162,a841))),x40164)),f773(f773(f47(x40161,f855(x40162,a841)),f44(f855(x40161,a841),x40163)),x40164))
% 191.21/191.73 [4021]E(f773(f773(f143(x40211,x40212),x40213),f773(f132(f848(x40211),f848(x40211),f125(x40211),f115(x40211)),x40214)),f773(f132(f848(x40212),f848(x40212),f125(x40212),f115(x40212)),f773(f773(f143(f848(x40211),f848(x40212)),f773(f143(x40211,x40212),x40213)),x40214)))
% 191.21/191.73 [4023]E(f175(f848(x40231),f115(x40231),f773(f773(f10(f848(x40231),f848(x40231),a847),f773(f140(x40231),x40232)),f773(f773(f9(a847,f848(x40231),f848(x40231)),f159(x40231)),x40233)),x40234),f773(f773(f159(x40231),x40234),f773(f773(f140(x40231),x40232),x40233)))
% 191.21/191.73 [4066]P1(f773(f773(f232(f855(x40661,a841)),f773(f303(x40662,x40661,x40663),f773(f305(x40662,x40661,x40663),x40664))),x40664))
% 191.21/191.73 [4068]E(f773(f303(f854(x40681,x40682),f854(x40682,x40681),f773(f251(x40681,x40682,f854(x40682,x40681)),f773(f9(x40682,x40681,f854(x40682,x40681)),f241(x40682,x40681)))),f773(f773(f248(x40681,x40682),x40683),f773(f18(f855(x40682,a841),x40681),x40684))),f773(f773(f248(x40682,x40681),x40684),f773(f18(f855(x40681,a841),x40682),x40683)))
% 191.21/191.73 [4077]E(f773(f773(f46(x40771,f855(x40772,a841)),x40773),f773(f773(f10(f855(x40771,a841),f855(x40772,a841),x40771),f277(x40771,x40772,x40774)),f773(f773(f9(x40771,f855(x40771,a841),f855(x40771,a841)),f302(x40771)),f180(f855(x40771,a841))))),f773(f277(x40771,x40772,x40774),x40773))
% 191.21/191.73 [4078]E(f773(f773(f46(x40781,f855(x40782,a841)),x40783),f773(f773(f10(f855(x40781,a841),f855(x40782,a841),x40781),f305(x40782,x40781,x40784)),f773(f773(f9(x40781,f855(x40781,a841),f855(x40781,a841)),f302(x40781)),f180(f855(x40781,a841))))),f773(f305(x40782,x40781,x40784),x40783))
% 191.21/191.73 [4169]E(f773(f773(f104(f855(x41691,a841)),f773(f773(f104(f855(x41691,a841)),f773(f773(f103(f855(x41691,a841)),x41692),x41693)),f773(f773(f103(f855(x41691,a841)),x41693),x41694))),f773(f773(f103(f855(x41691,a841)),x41694),x41692)),f773(f773(f103(f855(x41691,a841)),f773(f773(f103(f855(x41691,a841)),f773(f773(f104(f855(x41691,a841)),x41692),x41693)),f773(f773(f104(f855(x41691,a841)),x41693),x41694))),f773(f773(f104(f855(x41691,a841)),x41694),x41692)))
% 191.21/191.73 [4228]E(f773(f132(f848(x42281),f848(x42281),f125(x42281),f115(x42281)),f773(f773(f143(x42282,f848(x42281)),f773(f773(f9(x42282,f848(x42281),f848(x42281)),f773(f773(f10(x42281,f855(f848(x42281),f848(x42281)),x42282),f140(x42281)),x42283)),f115(x42281))),x42284)),f773(f773(f143(x42282,x42281),x42283),x42284))
% 191.21/191.73 [4238]E(f773(f773(f88(a1,x42381),f773(f106(a1),f773(f773(f82(a1),x42382),a99))),f773(f773(f20(a1,x42381,x42381),f773(f773(f9(a1,x42381,f855(x42381,x42381)),f773(f773(f10(a841,f855(x42381,f855(x42381,x42381)),a1),f98(x42381)),a186)),x42383)),f773(f773(f10(a847,x42381,a1),x42384),a107))),f175(x42381,x42383,x42384,f773(f106(a847),x42382)))
% 191.21/191.73 [4479]~P1(f773(f773(f180(f855(x44791,f855(x44792,a841))),x44793),x44794))
% 191.21/191.73 [3717]E(f773(f773(f153(x37171),f773(f773(f125(x37171),x37172),x37173)),f773(f773(f82(a847),f773(f181(f848(x37171)),x37172)),x37174)),f773(f773(f153(x37171),x37173),x37174))
% 191.21/191.73 [3722]E(f773(f773(f128(x37221),x37222),f773(f773(f159(x37221),f773(f773(f82(a847),x37223),x37222)),x37224)),f773(f773(f159(x37221),x37223),f773(f773(f128(x37221),x37222),x37224)))
% 191.21/191.73 [3820]E(f773(f773(f103(f855(x38201,a841)),f773(f259(x38202,x38201),x38203)),f773(f259(x38202,x38201),x38204)),f773(f259(x38202,x38201),f773(f773(f103(f855(f854(x38202,x38201),a841)),x38203),x38204)))
% 191.21/191.73 [3821]E(f773(f773(f103(f855(x38211,a841)),f773(f261(x38211,x38212),x38213)),f773(f261(x38211,x38212),x38214)),f773(f261(x38211,x38212),f773(f773(f103(f855(f854(x38211,x38212),a841)),x38213),x38214)))
% 191.21/191.73 [3826]E(f773(f773(f3(f855(x38261,a841)),f773(f773(f104(f855(x38261,a841)),x38262),x38263)),x38264),f773(f773(f104(f855(x38261,a841)),x38262),f773(f773(f3(f855(x38261,a841)),x38263),x38264)))
% 191.21/191.73 [3827]E(f773(f773(f103(f855(x38271,a841)),f773(f773(f103(f855(x38271,a841)),x38272),x38273)),x38274),f773(f773(f103(f855(x38271,a841)),x38272),f773(f773(f103(f855(x38271,a841)),x38273),x38274)))
% 191.21/191.73 [3828]E(f773(f773(f104(f855(x38281,a841)),f773(f773(f104(f855(x38281,a841)),x38282),x38283)),x38284),f773(f773(f104(f855(x38281,a841)),x38282),f773(f773(f104(f855(x38281,a841)),x38283),x38284)))
% 191.21/191.73 [3866]E(f773(f773(f103(f855(f854(x38661,x38662),a841)),f773(f278(x38662,x38661),x38663)),f773(f278(x38662,x38661),x38664)),f773(f278(x38662,x38661),f773(f773(f103(f855(f854(x38662,x38661),a841)),x38663),x38664)))
% 191.21/191.73 [3867]E(f773(f773(f104(f855(f854(x38671,x38672),a841)),f773(f278(x38672,x38671),x38673)),f773(f278(x38672,x38671),x38674)),f773(f278(x38672,x38671),f773(f773(f104(f855(f854(x38672,x38671),a841)),x38673),x38674)))
% 191.21/191.73 [3902]E(f170(x39021,x39022,x39023,f166(x39021,x39022,f773(f142(f854(x39021,x39022)),f773(f773(f167(x39021,x39022),f115(x39021)),x39024)))),x39023)
% 191.21/191.73 [3940]E(f773(f773(f103(f855(x39401,a841)),f773(f773(f3(f855(x39401,a841)),x39402),x39403)),f773(f773(f3(f855(x39401,a841)),x39404),x39403)),f773(f773(f3(f855(x39401,a841)),f773(f773(f103(f855(x39401,a841)),x39402),x39404)),x39403))
% 191.21/191.73 [3941]E(f773(f773(f104(f855(x39411,a841)),f773(f773(f103(f855(x39411,a841)),x39412),x39413)),f773(f773(f103(f855(x39411,a841)),x39414),x39413)),f773(f773(f103(f855(x39411,a841)),f773(f773(f104(f855(x39411,a841)),x39412),x39414)),x39413))
% 191.21/191.73 [3942]E(f773(f773(f3(f855(x39421,a841)),f773(f773(f104(f855(x39421,a841)),x39422),x39423)),f773(f773(f104(f855(x39421,a841)),x39424),x39423)),f773(f773(f104(f855(x39421,a841)),f773(f773(f3(f855(x39421,a841)),x39422),x39424)),x39423))
% 191.21/191.73 [3943]E(f773(f773(f103(f855(x39431,a841)),f773(f773(f104(f855(x39431,a841)),x39432),x39433)),f773(f773(f104(f855(x39431,a841)),x39434),x39433)),f773(f773(f104(f855(x39431,a841)),f773(f773(f103(f855(x39431,a841)),x39432),x39434)),x39433))
% 191.21/191.73 [3944]E(f773(f773(f3(f855(x39441,a841)),f773(f773(f104(f855(x39441,a841)),x39442),x39443)),f773(f773(f104(f855(x39441,a841)),x39444),x39443)),f773(f773(f3(f855(x39441,a841)),f773(f773(f104(f855(x39441,a841)),x39442),x39443)),x39444))
% 191.21/191.73 [3956]E(f773(f773(f3(f855(x39561,a841)),f773(f773(f3(f855(x39561,a841)),x39562),f773(f773(f302(x39561),x39563),f180(f855(x39561,a841))))),x39564),f773(f773(f3(f855(x39561,a841)),x39562),f773(f773(f302(x39561),x39563),x39564)))
% 191.21/191.73 [4012]E(f773(f773(f103(f855(x40121,a841)),f773(f773(f302(x40121),x40122),f773(f773(f302(x40121),x40123),f180(f855(x40121,a841))))),f773(f276(x40121),x40124)),f773(f276(x40121),f773(f773(f302(f854(x40121,x40121)),f773(f773(f241(x40121,x40121),x40122),x40123)),x40124)))
% 191.21/191.73 [4039]E(f773(f773(f46(a847,f855(x40391,a841)),f773(f293(a847),x40392)),f773(f773(f10(a847,f855(x40391,a841),a847),x40393),f773(f773(f9(a847,a847,a847),f82(a847)),x40394))),f773(f773(f46(a847,f855(x40391,a841)),f295(a847,x40394,f773(f773(f82(a847),x40392),x40394))),x40393))
% 191.21/191.73 [4040]E(f161(x40401,f773(f277(x40401,x40401,x40402),f773(f773(f302(x40401),x40403),f180(f855(x40401,a841)))),f773(f277(f848(x40401),f848(x40401),f147(x40401,x40402)),f773(f773(f302(f848(x40401)),x40404),f180(f855(f848(x40401),a841))))),f773(f277(f848(x40401),f848(x40401),f147(x40401,x40402)),f773(f773(f302(f848(x40401)),f773(f773(f140(x40401),x40403),x40404)),f180(f855(f848(x40401),a841)))))
% 191.21/191.73 [4103]E(f166(x41031,x41032,f773(f773(f143(x41031,f854(x41031,x41032)),f773(f773(f20(x41031,x41032,f854(x41031,x41032)),f241(x41031,x41032)),x41033)),x41034)),f172(x41031,x41032,f773(f75(x41032,f851(x41032),x41031,f227(x41032)),x41033),f773(f158(x41031),x41034)))
% 191.21/191.73 [4106]E(f773(f256(x41061),f773(f773(f9(x41061,f855(x41062,a841),a841),f773(f773(f10(x41062,f855(f855(x41062,a841),a841),x41061),f334(x41062)),x41063)),x41064)),f773(f305(x41061,x41062,x41063),x41064))
% 191.21/191.73 [4200]E(f773(f256(x42001),f773(f773(f9(x42001,f855(f854(x42002,x42001),a841),a841),f773(f773(f10(f854(x42002,x42001),f855(f855(f854(x42002,x42001),a841),a841),x42001),f334(f854(x42002,x42001))),f773(f241(x42002,x42001),x42003))),x42004)),f773(f277(x42002,x42001,x42004),f773(f773(f302(x42002),x42003),f180(f855(x42002,a841)))))
% 191.21/191.73 [4214]E(f773(f773(f143(f854(x42141,a847),x42141),f240(x42141,a847)),f773(f126(f854(x42141,a847),f773(f773(f10(a847,a841,f854(x42141,a847)),x42142),f773(f773(f10(a847,a847,f854(x42141,a847)),a114),f250(x42141,a847)))),f773(f773(f167(x42141,a847),x42143),x42144))),f773(f773(f143(f854(x42141,a847),x42141),f240(x42141,a847)),f773(f126(f854(x42141,a847),f773(f773(f10(a847,a841,f854(x42141,a847)),x42142),f250(x42141,a847))),f773(f773(f167(x42141,a847),x42143),f773(f773(f143(a847,a847),a114),x42144)))))
% 191.21/191.73 [4221]P1(f773(f773(f232(f855(f855(x42211,a841),a841)),f773(f773(f46(x42212,f855(f855(x42211,a841),a841)),x42213),f773(f773(f10(f855(x42211,a841),f855(f855(x42211,a841),a841),x42212),f301(x42211)),x42214))),f773(f301(x42211),f773(f773(f46(x42212,f855(x42211,a841)),x42213),x42214))))
% 191.21/191.73 [4261]E(f773(f773(f88(a1,x42611),f773(f106(a1),f773(f773(f82(a1),x42612),a99))),f773(f773(f20(a1,x42611,x42611),f773(f773(f9(a1,x42611,f855(x42611,x42611)),f773(f773(f10(a841,f855(x42611,f855(x42611,x42611)),a1),f98(x42611)),a186)),x42613)),f773(f773(f20(a1,x42611,x42611),f773(f773(f10(a847,f855(x42611,x42611),a1),x42614),a107)),f773(f773(f10(a847,x42611,a1),f174(x42611,x42613,x42614)),a107)))),f773(f174(x42611,x42613,x42614),f773(f106(a847),x42612)))
% 191.21/191.73 [4264]E(f773(f773(f143(x42641,x42642),f773(f75(f851(x42642),x42642,x42641,f231(x42642)),x42643)),f773(f126(x42641,f773(f773(f10(a841,a841,x42641),a328),f773(f773(f9(x42641,f851(x42642),a841),f773(f773(f10(f851(x42642),f855(f851(x42642),a841),x42641),a330),x42643)),f183(x42642)))),x42644)),f154(x42641,x42642,x42643,x42644))
% 191.21/191.73 [4285]E(f773(f256(f854(x42851,x42852)),f773(f251(x42851,x42852,a841),f773(f773(f9(x42851,f855(x42852,a841),f855(x42852,a841)),f773(f773(f10(f855(a841,a841),f855(f855(x42852,a841),f855(x42852,a841)),x42851),f10(a841,a841,x42852)),f773(f773(f10(a841,f855(a841,a841),x42851),a331),f773(f773(f9(x42851,f855(x42851,a841),a841),f334(x42851)),x42853)))),f773(f773(f9(x42852,f855(x42852,a841),a841),f334(x42852)),x42854)))),f223(x42851,x42852,x42853,x42854))
% 191.21/191.73 [4318]E(f773(f773(f46(x43181,f855(f854(x43181,x43182),a841)),x43183),f773(f773(f20(x43181,f855(x43182,f855(f854(x43181,x43182),a841)),f855(f854(x43181,x43182),a841)),f773(f773(f10(f855(x43182,a841),f855(f855(x43182,f855(f854(x43181,x43182),a841)),f855(f854(x43181,x43182),a841)),x43181),f46(x43182,f855(f854(x43181,x43182),a841))),x43184)),f773(f773(f9(x43181,f855(f854(x43181,x43182),a841),f855(x43182,f855(f854(x43181,x43182),a841))),f773(f773(f10(f855(x43182,f855(f855(f854(x43181,x43182),a841),f855(f854(x43181,x43182),a841))),f855(f855(f854(x43181,x43182),a841),f855(x43182,f855(f854(x43181,x43182),a841))),x43181),f9(x43182,f855(f854(x43181,x43182),a841),f855(f854(x43181,x43182),a841))),f773(f773(f10(f855(x43182,f854(x43181,x43182)),f855(x43182,f855(f855(f854(x43181,x43182),a841),f855(f854(x43181,x43182),a841))),x43181),f773(f10(f854(x43181,x43182),f855(f855(f854(x43181,x43182),a841),f855(f854(x43181,x43182),a841)),x43182),f302(f854(x43181,x43182)))),f241(x43181,x43182)))),f180(f855(f854(x43181,x43182),a841))))),f773(f773(f248(x43181,x43182),x43183),x43184))
% 191.21/191.73 [3875]E(f773(f773(f125(x38751),f773(f773(f159(x38751),x38752),x38753)),f773(f773(f159(x38751),f773(f773(f3(a847),x38752),f773(f181(f848(x38751)),x38753))),x38754)),f773(f773(f159(x38751),x38752),f773(f773(f125(x38751),x38753),x38754)))
% 191.21/191.73 [3876]E(f773(f773(f125(x38761),f773(f773(f128(x38761),x38762),x38763)),f773(f773(f128(x38761),f773(f773(f3(a847),x38762),f773(f181(f848(x38761)),x38763))),x38764)),f773(f773(f128(x38761),x38762),f773(f773(f125(x38761),x38763),x38764)))
% 191.21/191.73 [3929]E(f773(f773(f82(a847),f773(f773(f83(a847),x39291),x39292)),f773(f773(f82(a847),f773(f773(f83(a847),x39293),x39292)),x39294)),f773(f773(f82(a847),f773(f773(f83(a847),f773(f773(f82(a847),x39291),x39293)),x39292)),x39294))
% 191.21/191.73 [4134]P1(f773(f773(f232(f855(x41341,a841)),f773(f773(f3(f855(x41341,a841)),f773(f259(x41342,x41341),x41343)),f773(f259(x41342,x41341),x41344))),f773(f259(x41342,x41341),f773(f773(f3(f855(f854(x41342,x41341),a841)),x41343),x41344))))
% 191.21/191.73 [4135]P1(f773(f773(f232(f855(x41351,a841)),f773(f773(f3(f855(x41351,a841)),f773(f261(x41351,x41352),x41353)),f773(f261(x41351,x41352),x41354))),f773(f261(x41351,x41352),f773(f773(f3(f855(f854(x41351,x41352),a841)),x41353),x41354))))
% 191.21/191.73 [4240]E(f773(f773(f82(a1),f773(a91,f773(f277(f854(a847,a847),f854(a847,a847),a111),f773(f773(f302(f854(a847,a847)),f773(f773(f241(a847,a847),x42401),x42402)),f180(f855(f854(a847,a847),a841)))))),f773(a91,f773(f277(f854(a847,a847),f854(a847,a847),a111),f773(f773(f302(f854(a847,a847)),f773(f773(f241(a847,a847),x42403),x42404)),f180(f855(f854(a847,a847),a841)))))),f773(a91,f773(f277(f854(a847,a847),f854(a847,a847),a111),f773(f773(f302(f854(a847,a847)),f773(f773(f241(a847,a847),f773(f773(f82(a847),x42401),x42403)),f773(f773(f82(a847),x42402),x42404))),f180(f855(f854(a847,a847),a841))))))
% 191.21/191.73 [4280]E(f773(f773(f83(a1),f773(a91,f773(f277(f854(a847,a847),f854(a847,a847),a111),f773(f773(f302(f854(a847,a847)),f773(f773(f241(a847,a847),x42801),x42802)),f180(f855(f854(a847,a847),a841)))))),f773(a91,f773(f277(f854(a847,a847),f854(a847,a847),a111),f773(f773(f302(f854(a847,a847)),f773(f773(f241(a847,a847),x42803),x42804)),f180(f855(f854(a847,a847),a841)))))),f773(a91,f773(f277(f854(a847,a847),f854(a847,a847),a111),f773(f773(f302(f854(a847,a847)),f773(f773(f241(a847,a847),f773(f773(f82(a847),f773(f773(f83(a847),x42801),x42803)),f773(f773(f83(a847),x42802),x42804))),f773(f773(f82(a847),f773(f773(f83(a847),x42801),x42804)),f773(f773(f83(a847),x42802),x42803)))),f180(f855(f854(a847,a847),a841))))))
% 191.21/191.73 [4300]E(f773(f256(x43001),f773(f773(f10(f855(x43002,a841),a841,x43001),f90(x43002)),f773(f773(f10(f855(x43002,a841),f855(x43002,a841),x43001),f773(f20(x43002,a841,a841),f773(f773(f10(a841,f855(a841,a841),x43002),a335),f773(f773(f9(x43002,f855(x43002,a841),a841),f334(x43002)),x43003)))),f773(f773(f9(x43001,f855(x43002,f855(x43001,a841)),f855(x43002,a841)),f773(f773(f10(f855(f855(x43001,a841),a841),f855(f855(x43002,f855(x43001,a841)),f855(x43002,a841)),x43001),f10(f855(x43001,a841),a841,x43002)),f334(x43001))),x43004)))),f773(f773(f47(x43002,f855(x43001,a841)),x43003),x43004))
% 191.21/191.73 [4334]E(f773(f773(f281(x43341,x43341,x43341),f773(f773(f302(f854(x43341,x43341)),f773(f773(f241(x43341,x43341),x43342),x43343)),x43344)),f300(x43341,f773(f773(f302(f854(x43341,x43341)),f773(f773(f241(x43341,x43341),x43342),x43343)),x43344))),f773(f773(f103(f855(f854(x43341,x43341),a841)),f773(f773(f281(x43341,x43341,x43341),x43344),f300(x43341,x43344))),f773(f256(f854(x43341,x43341)),f773(f251(x43341,x43341,a841),f773(f773(f9(x43341,f855(x43341,a841),f855(x43341,a841)),f773(f773(f10(f855(a841,a841),f855(f855(x43341,a841),f855(x43341,a841)),x43341),f10(a841,a841,x43341)),f773(f773(f10(a841,f855(a841,a841),x43341),a331),f773(f773(f9(x43341,f855(f854(x43341,x43341),a841),a841),f773(f773(f10(f854(x43341,x43341),f855(f855(f854(x43341,x43341),a841),a841),x43341),f334(f854(x43341,x43341))),f773(f773(f9(x43341,x43341,f854(x43341,x43341)),f241(x43341,x43341)),x43342))),f300(x43341,x43344))))),f773(f773(f9(x43341,f855(f854(x43341,x43341),a841),a841),f773(f773(f10(f854(x43341,x43341),f855(f855(f854(x43341,x43341),a841),a841),x43341),f334(f854(x43341,x43341))),f773(f241(x43341,x43341),x43343))),f300(x43341,x43344)))))))
% 191.21/191.73 [4136]E(f773(f126(x41361,f773(f773(f20(x41361,a841,a841),f773(f773(f10(a841,f855(a841,a841),x41361),a331),x41362)),x41363)),x41364),f773(f126(x41361,x41363),f773(f126(x41361,x41362),x41364)))
% 191.21/191.73 [4234]E(f773(f773(f125(x42341),f773(f773(f773(f98(f848(x42341)),f773(f773(f334(a847),f2(a847)),x42342)),f773(f773(f140(x42341),x42343),f115(x42341))),f115(x42341))),f160(x42341,x42344,f773(f256(a847),f773(f773(f9(a847,f855(a847,a841),a841),f773(f773(f10(a847,f855(f855(a847,a841),a841),a847),f334(a847)),a114)),x42342)))),f160(x42341,f773(f773(f140(x42341),x42343),x42344),x42342))
% 191.21/191.73 [4329]E(f773(f256(f854(x43291,x43292)),f773(f773(f10(f855(a847,a841),a841,f854(x43291,x43292)),f89(a847)),f773(f773(f9(f854(x43291,x43292),f855(a847,a841),f855(a847,a841)),f773(f773(f10(f855(a847,f855(a841,a841)),f855(f855(a847,a841),f855(a847,a841)),f854(x43291,x43292)),f20(a847,a841,a841)),f773(f773(f10(f855(a847,a841),f855(a847,f855(a841,a841)),f854(x43291,x43292)),f773(f10(a841,f855(a841,a841),a847),a331)),f773(f773(f9(f854(x43291,x43292),f855(a847,f854(x43291,x43292)),f855(a847,a841)),f773(f773(f10(f855(f854(x43291,x43292),a841),f855(f855(a847,f854(x43291,x43292)),f855(a847,a841)),f854(x43291,x43292)),f10(f854(x43291,x43292),a841,a847)),a330)),f773(f773(f20(a847,x43292,f854(x43291,x43292)),f773(f773(f10(x43291,f855(x43292,f854(x43291,x43292)),a847),f241(x43291,x43292)),f773(f153(x43291),x43293))),f773(f153(x43292),x43294)))))),f773(f773(f9(a847,a847,a841),f233(a847)),f773(f773(f236(a847),f773(f181(f848(x43291)),x43293)),f773(f181(f848(x43292)),x43294)))))),f773(f158(f854(x43291,x43292)),f773(f773(f167(x43291,x43292),x43293),x43294)))
% 191.21/191.73 [4253]E(f773(f256(f854(x42531,x42532)),f773(f251(x42531,x42532,a841),f773(f773(f9(x42531,f855(x42532,a841),f855(x42532,a841)),f773(f773(f10(f855(a841,a841),f855(f855(x42532,a841),f855(x42532,a841)),x42531),f10(a841,a841,x42532)),f773(f773(f10(a841,f855(a841,a841),x42531),a331),x42533))),x42534))),f773(f773(f248(x42531,x42532),f773(f256(x42531),x42533)),f773(f18(f855(x42532,a841),x42531),f773(f256(x42532),x42534))))
% 191.21/191.73 [4256]E(f773(f256(f854(x42561,x42562)),f773(f251(x42561,x42562,a841),f773(f773(f20(x42561,f855(x42562,a841),f855(x42562,a841)),f773(f773(f10(f855(a841,a841),f855(f855(x42562,a841),f855(x42562,a841)),x42561),f10(a841,a841,x42562)),f773(f773(f10(a841,f855(a841,a841),x42561),a331),x42563))),x42564))),f773(f773(f248(x42561,x42562),f773(f256(x42561),x42563)),f773(f773(f10(f855(x42562,a841),f855(x42562,a841),x42561),f256(x42562)),x42564)))
% 191.21/191.73 [4271]E(f773(f256(x42711),f773(f773(f10(f855(x42712,a841),a841,x42711),f90(x42712)),f773(f773(f10(f855(x42712,a841),f855(x42712,a841),x42711),f773(f20(x42712,a841,a841),f773(f773(f10(a841,f855(a841,a841),x42712),a335),f773(f773(f9(x42712,f855(x42712,a841),a841),f334(x42712)),x42713)))),x42714))),f773(f773(f47(x42712,f855(x42711,a841)),x42713),f773(f773(f10(f855(x42711,a841),f855(x42711,a841),x42712),f256(x42711)),f773(f9(x42711,x42712,a841),x42714))))
% 191.21/191.73 [4313]E(f773(f773(f143(f854(x43131,a847),x43131),f240(x43131,a847)),f773(f126(f854(x43131,a847),f773(f773(f9(f854(x43131,a847),f855(a847,a841),a841),f773(f773(f10(a847,f855(f855(a847,a841),a841),f854(x43131,a847)),f334(a847)),f250(x43131,a847))),x43132)),f773(f773(f167(x43131,a847),x43133),f130(a847,f773(f294(a847,x43134),f773(f773(f82(a847),x43134),f773(f181(f848(x43131)),x43133))))))),f773(f773(f143(f854(x43131,a847),x43131),f240(x43131,a847)),f773(f126(f854(x43131,a847),f773(f773(f9(f854(x43131,a847),f855(a847,a841),a841),f773(f773(f10(a847,f855(f855(a847,a841),a841),f854(x43131,a847)),f334(a847)),f773(f773(f9(f854(x43131,a847),a847,a847),f773(f773(f10(a847,f855(a847,a847),f854(x43131,a847)),f82(a847)),f250(x43131,a847))),x43134))),x43132)),f773(f773(f167(x43131,a847),x43133),f130(a847,f773(f294(a847,f2(a847)),f773(f181(f848(x43131)),x43133)))))))
% 191.21/191.73 [4314]E(f773(a114,f773(f773(f179(a847),f773(f181(f848(x43141)),x43142)),f773(f132(a847,f848(x43143),f773(f9(f848(x43143),a847,a847),f773(f773(f10(a847,f855(a847,a847),f848(x43143)),f179(a847)),f773(f773(f9(f848(x43143),a847,a847),f773(f773(f10(a847,f855(a847,a847),f848(x43143)),f3(a847)),f181(f848(x43143)))),f773(a114,f2(a847))))),f2(a847)),f773(f142(f848(x43143)),f773(f126(f848(x43143),f773(f773(f10(a841,a841,f848(x43143)),a328),f773(f773(f9(f848(x43143),f848(x43143),a841),a330),f115(x43143)))),x43144))))),f773(f773(f179(a847),f773(a114,f773(f181(f848(x43141)),x43142))),f773(f132(a847,f848(x43143),f773(f9(f848(x43143),a847,a847),f773(f773(f10(a847,f855(a847,a847),f848(x43143)),f179(a847)),f181(f848(x43143)))),f2(a847)),f773(f142(f848(x43143)),x43144))))
% 191.21/191.73 [4270]E(f773(f773(f125(x42701),f160(x42701,x42702,x42703)),f160(x42701,x42704,f773(f256(a847),f773(f773(f9(a847,f855(a847,a841),a841),f773(f773(f10(a847,f855(f855(a847,a841),a841),a847),f334(a847)),f773(f773(f9(a847,a847,a847),f82(a847)),f773(f181(f848(x42701)),x42702)))),x42703)))),f160(x42701,f773(f773(f125(x42701),x42702),x42704),x42703))
% 191.21/191.73 [4320]E(f773(f773(f140(f848(x43201)),f773(f773(f140(x43201),x43202),f773(f132(f848(x43201),f848(x43201),f125(x43201),f115(x43201)),f773(f773(f143(f848(x43201),f848(x43201)),f145(f848(x43201),x43201,f115(x43201),f773(f773(f10(f848(x43201),f855(f848(x43201),f848(x43201)),x43201),f18(f848(x43201),f848(x43201))),f773(f773(f9(x43201,f848(x43201),f848(x43201)),f140(x43201)),f115(x43201))))),x43203)))),f164(x43201,f773(f773(f140(f848(x43201)),x43204),f773(f132(f848(f848(x43201)),f848(f848(x43201)),f125(f848(x43201)),f115(f848(x43201))),f773(f773(f143(f848(x43201),f848(f848(x43201))),f145(f848(f848(x43201)),x43201,f115(f848(x43201)),f773(f18(f855(f848(x43201),f848(f848(x43201))),x43201),f773(f773(f9(f848(x43201),f848(f848(x43201)),f848(f848(x43201))),f140(f848(x43201))),f115(f848(x43201)))))),x43203))))),f164(x43201,f773(f773(f140(f848(x43201)),f773(f773(f140(x43201),x43202),x43204)),x43203)))
% 191.21/191.73 [4330]E(f773(f256(f854(x43301,x43301)),f773(f251(x43301,x43301,a841),f773(f773(f9(x43301,f855(f854(x43302,x43302),a841),f855(x43301,a841)),f773(f773(f10(f855(x43301,f855(f855(f854(x43302,x43302),a841),a841)),f855(f855(f854(x43302,x43302),a841),f855(x43301,a841)),x43301),f9(x43301,f855(f854(x43302,x43302),a841),a841)),f773(f773(f10(f855(x43301,f854(x43302,x43302)),f855(x43301,f855(f855(f854(x43302,x43302),a841),a841)),x43301),f773(f10(f854(x43302,x43302),f855(f855(f854(x43302,x43302),a841),a841),x43301),f334(f854(x43302,x43302)))),f773(f773(f9(x43301,f855(x43301,x43302),f855(x43301,f854(x43302,x43302))),f773(f773(f10(f855(x43302,f854(x43302,x43302)),f855(f855(x43301,x43302),f855(x43301,f854(x43302,x43302))),x43301),f10(x43302,f854(x43302,x43302),x43301)),f773(f773(f10(x43302,f855(x43302,f854(x43302,x43302)),x43301),f241(x43302,x43302)),x43303))),x43303)))),x43304))),f773(f773(f280(x43302,x43301),x43304),x43303))
% 191.21/191.73 [4414]~E(f35(x44141,x44142),f33(x44143,x44144,x44145))
% 191.21/191.73 [4415]~E(f35(x44151,x44152),f32(x44153,x44154,x44155))
% 191.21/191.73 [4416]~E(f35(x44161,x44162),f31(x44163,x44164,x44165))
% 191.21/191.73 [4417]~E(f36(x44171,x44172),f33(x44173,x44174,x44175))
% 191.21/191.73 [4418]~E(f36(x44181,x44182),f32(x44183,x44184,x44185))
% 191.21/191.73 [4419]~E(f36(x44191,x44192),f31(x44193,x44194,x44195))
% 191.21/191.73 [4420]~E(f28(x44201,x44202),f33(x44203,x44204,x44205))
% 191.21/191.73 [4421]~E(f28(x44211,x44212),f32(x44213,x44214,x44215))
% 191.21/191.73 [4422]~E(f28(x44221,x44222),f31(x44223,x44224,x44225))
% 191.21/191.73 [4423]~E(f33(x44231,x44232,x44233),f35(x44234,x44235))
% 191.21/191.73 [4424]~E(f33(x44241,x44242,x44243),f36(x44244,x44245))
% 191.21/191.73 [4425]~E(f33(x44251,x44252,x44253),f28(x44254,x44255))
% 191.21/191.73 [4426]~E(f32(x44261,x44262,x44263),f35(x44264,x44265))
% 191.21/191.73 [4427]~E(f32(x44271,x44272,x44273),f36(x44274,x44275))
% 191.21/191.73 [4428]~E(f32(x44281,x44282,x44283),f28(x44284,x44285))
% 191.21/191.73 [4429]~E(f31(x44291,x44292,x44293),f35(x44294,x44295))
% 191.21/191.73 [4430]~E(f31(x44301,x44302,x44303),f36(x44304,x44305))
% 191.21/191.73 [4431]~E(f31(x44311,x44312,x44313),f28(x44314,x44315))
% 191.21/191.73 [3818]E(f773(f170(x38181,x38182,x38183,x38184),x38185),f773(f229(f851(x38182),x38182,f773(x38183,x38185),f227(x38182)),f773(x38184,x38185)))
% 191.21/191.73 [3904]E(f170(x39041,x39042,f170(x39041,x39042,x39043,x39044),x39045),f170(x39041,x39042,x39043,f170(x39041,x39042,x39044,x39045)))
% 191.21/191.73 [3647]E(f773(f773(f251(x36471,x36472,x36473),x36474),x36475),f773(f773(x36474,f773(f240(x36471,x36472),x36475)),f773(f250(x36471,x36472),x36475)))
% 191.21/191.73 [3673]E(f773(f229(x36731,x36732,x36733,x36734),f773(f227(x36732),x36735)),f773(x36734,x36735))
% 191.21/191.73 [3681]E(f773(f773(f773(f67(x36811,x36812,x36813),x36814),x36815),f180(f855(x36812,a841))),x36815)
% 191.21/191.73 [3697]E(f773(f316(x36971,x36972,x36973,x36974),f773(f304(x36971,x36973),x36975)),f773(x36974,x36975))
% 191.21/191.73 [3698]E(f773(f317(x36981,x36982,x36983,x36984),f773(f313(x36981,x36983),x36985)),f773(x36984,x36985))
% 191.21/191.73 [3847]E(f230(x38471,x38472,x38473,x38474,f773(f227(x38472),x38475)),f773(x38474,x38475))
% 191.21/191.73 [3883]E(f318(x38831,x38832,x38833,x38834,f773(f304(x38831,x38832),x38835)),f773(f773(f82(a847),f773(x38833,x38835)),f773(a114,f2(a847))))
% 191.21/191.73 [3884]E(f318(x38841,x38842,x38843,x38844,f773(f313(x38842,x38841),x38845)),f773(f773(f82(a847),f773(x38844,x38845)),f773(a114,f2(a847))))
% 191.21/191.73 [3962]E(f773(f75(f851(x39621),f851(x39622),f851(x39623),f773(f196(x39621,x39622),x39624)),f773(f196(x39623,x39621),x39625)),f773(f196(x39623,x39622),f773(f75(x39621,x39622,x39623,x39624),x39625)))
% 191.21/191.73 [3964]E(f773(f75(f848(x39641),f848(x39642),f848(x39643),f773(f143(x39641,x39642),x39644)),f773(f143(x39643,x39641),x39645)),f773(f143(x39643,x39642),f773(f75(x39641,x39642,x39643,x39644),x39645)))
% 191.21/191.73 [4043]E(f87(x40431,f68(x40432,x40431,x40433,x40434,x40435)),f773(f773(f66(x40432,x40431,x40433),x40434),x40435))
% 191.21/191.73 [4079]E(f773(f773(f82(a847),f773(f773(f82(a847),f773(x40791,f773(f240(x40792,x40793),x40794))),f773(x40795,f773(f250(x40792,x40793),x40794)))),f773(a114,f2(a847))),f255(x40792,x40793,x40791,x40795,x40794))
% 191.21/191.73 [4266]E(f154(x42661,x42662,f773(f773(f9(x42661,f851(x42662),f851(x42662)),f773(f773(f20(x42661,f851(x42662),f855(f851(x42662),f851(x42662))),f773(f773(f10(a841,f855(f851(x42662),f855(f851(x42662),f851(x42662))),x42661),f98(f851(x42662))),x42663)),f773(f773(f10(x42662,f851(x42662),x42661),f227(x42662)),x42664))),f183(x42662)),x42665),f773(f773(f143(x42661,x42662),x42664),f773(f126(x42661,x42663),x42665)))
% 191.21/191.73 [4472]~E(f773(f773(f773(f74(x44721,f851(x44722)),x44723),x44724),f773(f227(x44722),x44725)),f773(f18(f851(x44722),x44721),f183(x44722)))
% 191.21/191.73 [3582]E(f773(f773(f159(x35821),x35822),f773(f773(f143(x35823,x35821),x35824),x35825)),f773(f773(f143(x35823,x35821),x35824),f773(f773(f159(x35823),x35822),x35825)))
% 191.21/191.73 [3583]E(f773(f773(f128(x35831),x35832),f773(f773(f143(x35833,x35831),x35834),x35835)),f773(f773(f143(x35833,x35831),x35834),f773(f773(f128(x35833),x35832),x35835)))
% 191.21/191.73 [3613]E(f773(f773(f143(x36131,x36132),x36133),f773(f773(f140(x36131),x36134),x36135)),f773(f773(f140(x36132),f773(x36133,x36134)),f773(f773(f143(x36131,x36132),x36133),x36135)))
% 191.21/191.73 [3677]E(f773(f303(x36771,x36772,x36773),f773(f773(f302(x36771),x36774),x36775)),f773(f773(f302(x36772),f773(x36773,x36774)),f773(f303(x36771,x36772,x36773),x36775)))
% 191.21/191.73 [3743]E(f773(f773(f167(x37431,x37432),f773(f773(f159(x37431),x37433),x37434)),f773(f773(f159(x37432),x37433),x37435)),f773(f773(f159(f854(x37431,x37432)),x37433),f773(f773(f167(x37431,x37432),x37434),x37435)))
% 191.21/191.73 [3744]E(f773(f773(f167(x37441,x37442),f773(f773(f128(x37441),x37443),x37444)),f773(f773(f128(x37442),x37443),x37445)),f773(f773(f128(f854(x37441,x37442)),x37443),f773(f773(f167(x37441,x37442),x37444),x37445)))
% 191.21/191.73 [3755]E(f773(f773(f148(x37551,f773(f773(f140(x37551),x37552),x37553)),f773(a114,x37554)),x37555),f773(f773(f140(x37551),x37552),f773(f773(f148(x37551,x37553),x37554),x37555)))
% 191.21/191.73 [3758]E(f773(f229(f851(x37581),x37582,f183(x37581),x37583),f773(f773(f18(f851(x37582),x37584),f183(x37582)),x37585)),f183(x37581))
% 191.21/191.73 [3760]E(f773(f773(f125(x37601),f773(f773(f143(x37602,x37601),x37603),x37604)),f773(f773(f143(x37602,x37601),x37603),x37605)),f773(f773(f143(x37602,x37601),x37603),f773(f773(f125(x37602),x37604),x37605)))
% 191.21/191.73 [3764]E(f773(f773(x37641,x37642),f773(f773(f243(x37643,x37644,x37641),x37642),x37645)),f773(f773(f243(x37643,x37644,x37641),x37642),f773(a114,x37645)))
% 191.21/191.73 [3805]E(f773(f773(f281(x38051,x38052,x38053),f773(f278(x38052,x38051),x38054)),f773(f278(x38053,x38052),x38055)),f773(f278(x38053,x38051),f773(f773(f281(x38053,x38052,x38051),x38055),x38054)))
% 191.21/191.73 [3836]E(f773(f773(f773(f173(f848(x38361),f848(x38361)),x38362),f141(x38361)),f773(f773(f143(x38363,x38361),x38364),x38365)),f773(f773(f143(x38363,x38361),x38364),f773(f773(f773(f173(f848(x38363),f848(x38363)),x38362),f141(x38363)),x38365)))
% 191.21/191.73 [3837]E(f773(f773(f253(x38371,x38372,x38371,x38373),f773(f241(x38372,x38371),x38374)),x38375),f773(x38375,x38374))
% 191.21/191.73 [3861]E(f144(x38611,x38612,f773(f773(f143(x38613,x38611),x38614),x38615)),f144(x38613,f773(f75(x38611,a847,x38613,x38612),x38614),x38615))
% 191.21/191.73 [3927]E(f773(f773(f75(f851(x39271),f851(x39272),x39273,f773(f196(x39271,x39272),x39274)),f773(f18(f851(x39271),x39273),f183(x39271))),x39275),f183(x39272))
% 191.21/191.73 [3928]E(f162(f854(x39281,x39282),f773(f75(x39282,a841,f854(x39281,x39282),x39283),f250(x39281,x39282)),f773(f773(f167(x39281,x39282),x39284),x39285)),f773(f773(f167(x39281,x39282),x39284),f162(x39282,x39283,x39285)))
% 191.21/191.73 [3933]E(f773(f303(x39331,x39332,f773(f773(f10(x39333,x39332,x39331),x39334),x39335)),f239(f855(x39331,a841))),f773(f303(x39333,x39332,x39334),f773(f303(x39331,x39333,x39335),f239(f855(x39331,a841)))))
% 191.21/191.73 [3947]E(f162(f854(x39471,x39472),f773(f75(x39471,a841,f854(x39471,x39472),x39473),f240(x39471,x39472)),f773(f773(f167(x39471,x39472),x39474),x39475)),f773(f773(f167(x39471,x39472),f162(x39471,x39473,x39474)),x39475))
% 191.21/191.73 [3968]E(f773(f773(f103(f855(x39681,a841)),f773(f305(x39681,x39682,x39683),f773(f773(f302(x39682),x39684),f180(f855(x39682,a841))))),f773(f305(x39681,x39682,x39683),x39685)),f773(f305(x39681,x39682,x39683),f773(f773(f302(x39682),x39684),x39685)))
% 191.21/191.73 [4028]E(f773(f773(f143(x40281,x40282),x40283),f162(x40281,f773(f75(x40282,a841,x40281,x40284),x40283),x40285)),f162(x40282,x40284,f773(f773(f143(x40281,x40282),x40283),x40285)))
% 191.21/191.73 [4035]E(f773(f132(x40351,x40352,f773(f9(x40352,x40351,x40351),f773(f9(x40351,x40352,x40351),x40353)),x40354),f773(f142(x40352),f773(f142(x40352),x40355))),f773(f132(x40351,x40352,x40353,x40354),x40355))
% 191.21/191.73 [4036]E(f773(f773(f773(f74(x40361,f851(x40362)),f172(x40361,x40362,x40363,x40364)),x40365),f773(x40363,x40365)),f172(x40361,x40362,x40363,f773(f773(f302(x40361),x40365),x40364)))
% 191.21/191.73 [4045]E(f773(f319(x40451,x40452,x40453,f773(f18(x40452,x40451),x40454),f773(f18(x40452,x40453),x40454)),x40455),x40454)
% 191.21/191.73 [4104]E(f773(f229(f848(x41041),x41041,f154(x41042,x41041,x41043,x41044),f773(f773(f9(x41041,f848(x41041),f848(x41041)),f140(x41041)),f154(x41042,x41041,x41043,x41044))),f773(x41043,x41045)),f154(x41042,x41041,x41043,f773(f773(f140(x41042),x41045),x41044)))
% 191.21/191.73 [4144]P1(f773(f773(f232(f855(x41441,a841)),f773(f303(x41442,x41441,x41443),f773(f773(f104(f855(x41442,a841)),x41444),x41445))),f773(f773(f104(f855(x41441,a841)),f773(f303(x41442,x41441,x41443),x41444)),f773(f303(x41442,x41441,x41443),x41445))))
% 191.21/191.73 [4145]P1(f773(f773(f232(f855(x41451,a841)),f773(f277(x41452,x41451,x41453),f773(f773(f104(f855(x41452,a841)),x41454),x41455))),f773(f773(f104(f855(x41451,a841)),f773(f277(x41452,x41451,x41453),x41454)),f773(f277(x41452,x41451,x41453),x41455))))
% 191.21/191.73 [4241]E(f773(f250(x42411,x42412),f773(f252(x42413,x42411,x42412,x42412,x42414,f39(x42412)),x42415)),f773(f250(x42413,x42412),x42415))
% 191.21/191.73 [4242]E(f773(f240(x42421,x42422),f773(f252(x42421,x42421,x42423,x42422,f39(x42421),x42424),x42425)),f773(f240(x42421,x42423),x42425))
% 191.21/191.73 [4324]P28(x43241,x43242,f773(f773(f302(f846(x43241)),f773(f773(f773(f93(x43241),f773(f773(f9(x43241,f855(a844,a844),f855(a844,a841)),f773(f773(f10(f855(a844,a841),f855(f855(a844,a844),f855(a844,a841)),x43241),f10(a844,a841,a844)),x43243)),f773(f773(f20(a844,a847,a844),f773(f773(f9(a844,a845,f855(a847,a844)),a189),x43244)),x43245))),f28(x43244,x43245)),x43243)),f180(f855(f846(x43241),a841))))
% 191.21/191.73 [4328]P28(x43281,x43282,f773(f773(f302(f846(x43281)),f773(f773(f773(f93(x43281),f773(f773(f9(x43281,f855(a844,a841),f855(a844,a841)),f773(f773(f10(f855(a844,f855(a841,a841)),f855(f855(a844,a841),f855(a844,a841)),x43281),f20(a844,a841,a841)),f773(f773(f10(f855(a844,a841),f855(a844,f855(a841,a841)),x43281),f773(f10(a841,f855(a841,a841),a844),a331)),x43283))),f773(f773(f10(a841,a841,a844),a328),x43284))),f35(x43284,x43285)),x43283)),f180(f855(f846(x43281),a841))))
% 191.21/191.73 [3431]E(f773(f773(f773(f773(f199(x34311),x34312),x34313),x34314),x34315),f185(x34311,x34312))
% 191.21/191.73 [3432]E(f773(f773(f773(f773(f203(x34321),x34322),x34323),x34324),x34325),f194(x34321,x34322))
% 191.21/191.73 [3475]E(f95(x34751,x34752,f773(f773(f773(f93(x34751),x34753),x34754),x34755)),f2(a847))
% 191.21/191.73 [3565]E(f773(f773(f773(f773(f74(x35651,x35652),x35653),x35654),x35655),x35654),x35655)
% 191.21/191.73 [3795]E(f773(f773(f46(x37951,f855(x37952,a841)),f773(f773(f302(x37951),x37953),x37954)),x37955),f773(f773(f103(f855(x37952,a841)),f773(x37955,x37953)),f773(f773(f46(x37951,f855(x37952,a841)),x37954),x37955)))
% 191.21/191.73 [3796]E(f773(f773(f47(x37961,f855(x37962,a841)),f773(f773(f302(x37961),x37963),x37964)),x37965),f773(f773(f104(f855(x37962,a841)),f773(x37965,x37963)),f773(f773(f47(x37961,f855(x37962,a841)),x37964),x37965)))
% 191.21/191.73 [3854]E(f773(f773(f103(f855(x38541,a841)),f773(f303(x38542,x38541,x38543),x38544)),f773(f303(x38542,x38541,x38543),x38545)),f773(f303(x38542,x38541,x38543),f773(f773(f103(f855(x38542,a841)),x38544),x38545)))
% 191.21/191.73 [3855]E(f773(f773(f103(f855(x38551,a841)),f773(f277(x38552,x38551,x38553),x38554)),f773(f277(x38552,x38551,x38553),x38555)),f773(f277(x38552,x38551,x38553),f773(f773(f103(f855(x38552,a841)),x38554),x38555)))
% 191.21/191.73 [3856]E(f773(f773(f3(f855(x38561,a841)),f773(f305(x38561,x38562,x38563),x38564)),f773(f305(x38561,x38562,x38563),x38565)),f773(f305(x38561,x38562,x38563),f773(f773(f3(f855(x38562,a841)),x38564),x38565)))
% 191.21/191.73 [3857]E(f773(f773(f103(f855(x38571,a841)),f773(f305(x38571,x38572,x38573),x38574)),f773(f305(x38571,x38572,x38573),x38575)),f773(f305(x38571,x38572,x38573),f773(f773(f103(f855(x38572,a841)),x38574),x38575)))
% 191.21/191.73 [3858]E(f773(f773(f104(f855(x38581,a841)),f773(f305(x38581,x38582,x38583),x38584)),f773(f305(x38581,x38582,x38583),x38585)),f773(f305(x38581,x38582,x38583),f773(f773(f104(f855(x38582,a841)),x38584),x38585)))
% 191.21/191.73 [3860]E(f172(x38601,x38602,f172(x38601,x38602,x38603,x38604),x38605),f172(x38601,x38602,x38603,f773(f773(f104(f855(x38601,a841)),x38604),x38605)))
% 191.21/191.73 [3862]E(f118(x38621,x38622,f773(x38623,x38624),f773(f773(f9(x38621,a101,f849(x38622)),x38625),x38624)),f773(f192(x38621,x38622,x38623,x38625),x38624))
% 191.21/191.73 [3923]E(f773(f773(f148(x39231,f773(f773(f125(x39231),x39232),f773(f773(f140(x39231),x39233),x39234))),f773(f181(f848(x39231)),x39232)),x39235),f773(f773(f125(x39231),x39232),f773(f773(f140(x39231),x39235),x39234)))
% 191.21/191.73 [3931]E(f773(f773(f47(x39311,f855(x39312,a841)),x39313),f773(f773(f10(f855(x39312,a841),f855(x39312,a841),x39311),f773(f302(x39312),x39314)),x39315)),f773(f773(f302(x39312),x39314),f773(f773(f47(x39311,f855(x39312,a841)),x39313),x39315)))
% 191.21/191.73 [4003]E(f172(x40031,x40032,f773(f773(f773(f74(x40031,f851(x40032)),x40033),x40034),f773(f227(x40032),x40035)),f773(f81(f855(x40031,a841)),f773(f773(f302(x40031),x40034),f180(f855(x40031,a841))))),f172(x40031,x40032,x40033,f773(f81(f855(x40031,a841)),f773(f773(f302(x40031),x40034),f180(f855(x40031,a841))))))
% 191.21/191.73 [4089]E(f773(f773(f143(x40891,x40892),x40893),f773(f126(x40891,f773(f75(x40892,a841,x40891,x40894),x40893)),x40895)),f773(f126(x40892,x40894),f773(f773(f143(x40891,x40892),x40893),x40895)))
% 191.21/191.73 [4096]E(f773(f181(f848(x40961)),f773(f126(x40961,x40962),f773(f773(f143(x40963,x40961),x40964),x40965))),f773(f181(f848(x40963)),f773(f126(x40963,f773(f75(x40961,a841,x40963,x40962),x40964)),x40965)))
% 191.21/191.73 [4233]E(f773(f773(f103(f855(x42331,a841)),f773(f773(f3(f855(x42331,a841)),f169(x42331,x42332,x42333)),f773(f256(x42331),f773(f773(f9(x42331,f855(x42331,a841),a841),f334(x42331)),f773(f773(f3(f855(x42331,a841)),x42334),f169(x42331,x42332,x42335)))))),f773(f256(x42331),f773(f773(f9(x42331,f855(x42331,a841),a841),f334(x42331)),f773(f773(f104(f855(x42331,a841)),x42334),f169(x42331,x42332,x42335))))),f169(x42331,x42332,f78(x42331,f851(x42332),x42333,x42335,x42334)))
% 191.21/191.73 [4305]E(f773(f145(f848(f854(x43051,x43052)),x43052,f115(f854(x43051,x43052)),f773(f773(f9(x43052,f855(f848(x43052),f848(f854(x43051,x43052))),f855(f848(x43052),f848(f854(x43051,x43052)))),f773(f773(f10(f855(f848(f854(x43051,x43052)),f848(f854(x43051,x43052))),f855(f855(f848(x43052),f848(f854(x43051,x43052))),f855(f848(x43052),f848(f854(x43051,x43052)))),x43052),f10(f848(f854(x43051,x43052)),f848(f854(x43051,x43052)),f848(x43052))),f773(f773(f10(f854(x43051,x43052),f855(f848(f854(x43051,x43052)),f848(f854(x43051,x43052))),x43052),f140(f854(x43051,x43052))),f773(f241(x43051,x43052),x43053)))),f773(f167(x43051,x43052),x43054))),x43055),f773(f773(f167(x43051,x43052),f773(f773(f140(x43051),x43053),x43054)),x43055))
% 191.21/191.73 [3790]E(f773(f773(f148(x37901,f773(f773(f148(x37901,x37902),x37903),x37904)),x37903),x37905),f773(f773(f148(x37901,x37902),x37903),x37905))
% 191.21/191.73 [3838]E(f773(f259(x38381,x38382),f773(f773(f302(f854(x38381,x38382)),f773(f773(f241(x38381,x38382),x38383),x38384)),x38385)),f773(f773(f302(x38382),x38384),f773(f259(x38381,x38382),x38385)))
% 191.21/191.73 [3839]E(f773(f261(x38391,x38392),f773(f773(f302(f854(x38391,x38392)),f773(f773(f241(x38391,x38392),x38393),x38394)),x38395)),f773(f773(f302(x38391),x38393),f773(f261(x38391,x38392),x38395)))
% 191.21/191.73 [3887]E(f121(x38871,x38872,f773(x38873,x38874),f773(f773(f9(x38871,a101,f849(f851(x38872))),x38875),x38874)),f773(f190(x38871,x38872,x38873,x38875),x38874))
% 191.21/191.73 [3916]E(f773(f773(f3(f855(f854(x39161,x39162),a841)),f773(f773(f248(x39161,x39162),x39163),x39164)),f773(f773(f248(x39161,x39162),x39165),x39164)),f773(f773(f248(x39161,x39162),f773(f773(f3(f855(x39161,a841)),x39163),x39165)),x39164))
% 191.21/191.73 [3917]E(f773(f773(f103(f855(f854(x39171,x39172),a841)),f773(f773(f248(x39171,x39172),x39173),x39174)),f773(f773(f248(x39171,x39172),x39175),x39174)),f773(f773(f248(x39171,x39172),f773(f773(f103(f855(x39171,a841)),x39173),x39175)),x39174))
% 191.21/191.73 [3918]E(f773(f773(f104(f855(f854(x39181,x39182),a841)),f773(f773(f248(x39181,x39182),x39183),x39184)),f773(f773(f248(x39181,x39182),x39185),x39184)),f773(f773(f248(x39181,x39182),f773(f773(f104(f855(x39181,a841)),x39183),x39185)),x39184))
% 191.21/191.73 [3981]E(f773(f773(f103(f855(x39811,a841)),f773(f773(f46(x39812,f855(x39811,a841)),x39813),x39814)),f773(f773(f46(x39812,f855(x39811,a841)),x39815),x39814)),f773(f773(f46(x39812,f855(x39811,a841)),f773(f773(f103(f855(x39812,a841)),x39813),x39815)),x39814))
% 191.21/191.73 [3982]E(f773(f773(f104(f855(x39821,a841)),f773(f773(f47(x39822,f855(x39821,a841)),x39823),x39824)),f773(f773(f47(x39822,f855(x39821,a841)),x39825),x39824)),f773(f773(f47(x39822,f855(x39821,a841)),f773(f773(f103(f855(x39822,a841)),x39823),x39825)),x39824))
% 191.21/191.73 [3996]E(f773(f773(f46(x39961,f855(x39962,a841)),x39963),f773(f773(f10(f855(x39962,a841),f855(x39962,a841),x39961),f773(f3(f855(x39962,a841)),x39964)),x39965)),f773(f773(f3(f855(x39962,a841)),x39964),f773(f773(f47(x39961,f855(x39962,a841)),x39963),x39965)))
% 191.21/191.73 [3997]E(f773(f773(f46(x39971,f855(x39972,a841)),x39973),f773(f773(f10(f855(x39972,a841),f855(x39972,a841),x39971),f773(f104(f855(x39972,a841)),x39974)),x39975)),f773(f773(f104(f855(x39972,a841)),x39974),f773(f773(f46(x39971,f855(x39972,a841)),x39973),x39975)))
% 191.21/191.73 [3998]E(f773(f773(f47(x39981,f855(x39982,a841)),x39983),f773(f773(f10(f855(x39982,a841),f855(x39982,a841),x39981),f773(f103(f855(x39982,a841)),x39984)),x39985)),f773(f773(f103(f855(x39982,a841)),x39984),f773(f773(f47(x39981,f855(x39982,a841)),x39983),x39985)))
% 191.21/191.73 [4057]E(f175(f848(x40571),f773(f773(f140(x40571),x40572),x40573),f773(f773(f10(f848(x40571),f848(x40571),a847),f773(f140(x40571),x40574)),f773(f773(f9(a847,x40571,f848(x40571)),f148(x40571,x40573)),x40572)),x40575),f773(f773(f148(x40571,f773(f773(f140(x40571),x40574),x40573)),x40575),x40572))
% 191.21/191.73 [4061]E(f773(f773(f46(x40611,f855(f854(x40612,x40613),a841)),x40614),f773(f773(f10(f855(f854(x40613,x40612),a841),f855(f854(x40612,x40613),a841),x40611),f278(x40613,x40612)),x40615)),f773(f278(x40613,x40612),f773(f773(f46(x40611,f855(f854(x40613,x40612),a841)),x40614),x40615)))
% 191.21/191.73 [4062]E(f773(f773(f47(x40621,f855(f854(x40622,x40623),a841)),x40624),f773(f773(f10(f855(f854(x40623,x40622),a841),f855(f854(x40622,x40623),a841),x40621),f278(x40623,x40622)),x40625)),f773(f278(x40623,x40622),f773(f773(f47(x40621,f855(f854(x40623,x40622),a841)),x40624),x40625)))
% 191.21/191.73 [4115]E(f169(x41151,x41152,f773(f773(f20(x41151,f851(x41153),f851(x41152)),f773(f773(f10(f855(x41153,x41152),f855(f851(x41153),f851(x41152)),x41151),f196(x41153,x41152)),x41154)),x41155)),f169(x41151,x41153,x41155))
% 191.21/191.73 [4168]P1(f773(f773(f232(f855(x41681,a841)),f773(f773(f3(f855(x41681,a841)),f773(f303(x41682,x41681,x41683),x41684)),f773(f303(x41682,x41681,x41683),x41685))),f773(f303(x41682,x41681,x41683),f773(f773(f3(f855(x41682,a841)),x41684),x41685))))
% 191.21/191.73 [4309]E(f773(f145(f848(f854(x43091,x43092)),x43091,f115(f854(x43091,x43092)),f773(f773(f9(x43091,f855(f848(x43091),f848(f854(x43091,x43092))),f855(f848(x43091),f848(f854(x43091,x43092)))),f773(f773(f10(f855(f848(f854(x43091,x43092)),f848(f854(x43091,x43092))),f855(f855(f848(x43091),f848(f854(x43091,x43092))),f855(f848(x43091),f848(f854(x43091,x43092)))),x43091),f10(f848(f854(x43091,x43092)),f848(f854(x43091,x43092)),f848(x43091))),f773(f773(f10(f854(x43091,x43092),f855(f848(f854(x43091,x43092)),f848(f854(x43091,x43092))),x43091),f140(f854(x43091,x43092))),f773(f773(f9(x43091,x43092,f854(x43091,x43092)),f241(x43091,x43092)),x43093)))),f773(f773(f9(f848(x43091),f848(x43092),f848(f854(x43091,x43092))),f167(x43091,x43092)),x43094))),x43095),f773(f773(f167(x43091,x43092),x43095),f773(f773(f140(x43092),x43093),x43094)))
% 191.21/191.73 [4326]E(f773(f132(f855(x43261,f851(x43262)),f854(x43261,x43262),f773(f773(f10(f855(x43261,f855(x43262,f855(x43261,f851(x43262)))),f855(f854(x43261,x43262),f855(x43261,f851(x43262))),f855(x43261,f851(x43262))),f251(x43261,x43262,f855(x43261,f851(x43262)))),f773(f773(f9(f855(x43261,f851(x43262)),f855(x43262,f851(x43262)),f855(x43261,f855(x43262,f855(x43261,f851(x43262))))),f773(f773(f10(f855(x43261,f855(f855(x43262,f851(x43262)),f855(x43262,f855(x43261,f851(x43262))))),f855(f855(x43262,f851(x43262)),f855(x43261,f855(x43262,f855(x43261,f851(x43262))))),f855(x43261,f851(x43262))),f9(x43261,f855(x43262,f851(x43262)),f855(x43262,f855(x43261,f851(x43262))))),f773(f773(f10(f855(x43261,f855(f851(x43262),f855(x43261,f851(x43262)))),f855(x43261,f855(f855(x43262,f851(x43262)),f855(x43262,f855(x43261,f851(x43262))))),f855(x43261,f851(x43262))),f773(f10(f855(f851(x43262),f855(x43261,f851(x43262))),f855(f855(x43262,f851(x43262)),f855(x43262,f855(x43261,f851(x43262)))),x43261),f10(f851(x43262),f855(x43261,f851(x43262)),x43262))),f74(x43261,f851(x43262))))),f227(x43262))),x43263),f773(f773(f167(x43261,x43262),x43264),x43265)),f170(x43261,x43262,x43263,f166(x43261,x43262,f773(f142(f854(x43261,x43262)),f773(f773(f167(x43261,x43262),x43264),x43265)))))
% 191.21/191.73 [4022]E(f773(f773(f103(f855(x40221,a841)),f773(f277(x40222,x40221,x40223),x40224)),f773(f277(x40222,x40221,x40225),x40224)),f773(f277(x40222,x40221,f773(f773(f103(f855(f854(x40222,x40221),a841)),x40223),x40225)),x40224))
% 191.21/191.73 [4064]E(f773(f773(f125(f854(x40641,x40642)),f773(f773(f167(x40641,x40642),x40643),f773(f773(f159(x40642),f773(f181(f848(x40641)),x40643)),x40644))),f773(f773(f167(x40641,x40642),x40645),f773(f773(f128(x40642),f773(f181(f848(x40641)),x40643)),x40644))),f773(f773(f167(x40641,x40642),f773(f773(f125(x40641),x40643),x40645)),x40644))
% 191.21/191.73 [4093]E(f169(x40931,x40932,f170(x40931,x40932,x40933,f166(x40931,x40932,f773(f142(f854(x40931,x40932)),f773(f773(f167(x40931,x40932),x40934),x40935))))),f773(f773(f103(f855(x40931,a841)),f773(f158(x40931),f773(f773(f159(x40931),f773(f181(f848(x40932)),x40935)),x40934))),f169(x40931,x40932,x40933)))
% 191.21/191.73 [4171]E(f773(f773(f248(x41711,x41712),x41713),f773(f773(f20(x41711,f855(x41712,a841),f855(x41712,a841)),f773(f773(f10(f855(x41712,a841),f855(f855(x41712,a841),f855(x41712,a841)),x41711),f3(f855(x41712,a841))),x41714)),x41715)),f773(f773(f3(f855(f854(x41711,x41712),a841)),f773(f773(f248(x41711,x41712),x41713),x41714)),f773(f773(f248(x41711,x41712),x41713),x41715)))
% 191.21/191.73 [4172]E(f773(f773(f248(x41721,x41722),x41723),f773(f773(f20(x41721,f855(x41722,a841),f855(x41722,a841)),f773(f773(f10(f855(x41722,a841),f855(f855(x41722,a841),f855(x41722,a841)),x41721),f103(f855(x41722,a841))),x41724)),x41725)),f773(f773(f103(f855(f854(x41721,x41722),a841)),f773(f773(f248(x41721,x41722),x41723),x41724)),f773(f773(f248(x41721,x41722),x41723),x41725)))
% 191.21/191.73 [4173]E(f773(f773(f248(x41731,x41732),x41733),f773(f773(f20(x41731,f855(x41732,a841),f855(x41732,a841)),f773(f773(f10(f855(x41732,a841),f855(f855(x41732,a841),f855(x41732,a841)),x41731),f104(f855(x41732,a841))),x41734)),x41735)),f773(f773(f104(f855(f854(x41731,x41732),a841)),f773(f773(f248(x41731,x41732),x41733),x41734)),f773(f773(f248(x41731,x41732),x41733),x41735)))
% 191.21/191.73 [4177]E(f773(f773(f46(x41771,f855(x41772,a841)),x41773),f773(f773(f9(x41771,f855(x41772,a841),f855(x41772,a841)),f773(f773(f10(f855(x41772,a841),f855(f855(x41772,a841),f855(x41772,a841)),x41771),f3(f855(x41772,a841))),x41774)),x41775)),f773(f773(f3(f855(x41772,a841)),f773(f773(f46(x41771,f855(x41772,a841)),x41773),x41774)),x41775))
% 191.21/191.73 [4178]E(f773(f773(f46(x41781,f855(x41782,a841)),x41783),f773(f773(f9(x41781,f855(x41782,a841),f855(x41782,a841)),f773(f773(f10(f855(x41782,a841),f855(f855(x41782,a841),f855(x41782,a841)),x41781),f104(f855(x41782,a841))),x41784)),x41785)),f773(f773(f104(f855(x41782,a841)),f773(f773(f46(x41781,f855(x41782,a841)),x41783),x41784)),x41785))
% 191.21/191.73 [4179]E(f773(f773(f47(x41791,f855(x41792,a841)),x41793),f773(f773(f9(x41791,f855(x41792,a841),f855(x41792,a841)),f773(f773(f10(f855(x41792,a841),f855(f855(x41792,a841),f855(x41792,a841)),x41791),f103(f855(x41792,a841))),x41794)),x41795)),f773(f773(f103(f855(x41792,a841)),f773(f773(f47(x41791,f855(x41792,a841)),x41793),x41794)),x41795))
% 191.21/191.73 [4183]E(f773(f773(f46(x41831,f855(x41832,a841)),x41833),f773(f773(f20(x41831,f855(x41832,a841),f855(x41832,a841)),f773(f773(f10(f855(x41832,a841),f855(f855(x41832,a841),f855(x41832,a841)),x41831),f103(f855(x41832,a841))),x41834)),x41835)),f773(f773(f103(f855(x41832,a841)),f773(f773(f46(x41831,f855(x41832,a841)),x41833),x41834)),f773(f773(f46(x41831,f855(x41832,a841)),x41833),x41835)))
% 191.21/191.73 [4184]E(f773(f773(f47(x41841,f855(x41842,a841)),x41843),f773(f773(f20(x41841,f855(x41842,a841),f855(x41842,a841)),f773(f773(f10(f855(x41842,a841),f855(f855(x41842,a841),f855(x41842,a841)),x41841),f104(f855(x41842,a841))),x41844)),x41845)),f773(f773(f104(f855(x41842,a841)),f773(f773(f47(x41841,f855(x41842,a841)),x41843),x41844)),f773(f773(f47(x41841,f855(x41842,a841)),x41843),x41845)))
% 191.21/191.73 [4196]E(f773(f773(f46(x41961,f855(x41962,a841)),x41963),f773(f773(f20(x41961,f855(x41962,a841),f855(x41962,a841)),f773(f773(f10(f855(x41962,a841),f855(f855(x41962,a841),f855(x41962,a841)),x41961),f103(f855(x41962,a841))),x41964)),x41965)),f773(f773(f103(f855(x41962,a841)),f44(f855(x41962,a841),f773(f303(x41961,f855(x41962,a841),x41964),x41963))),f44(f855(x41962,a841),f773(f303(x41961,f855(x41962,a841),x41965),x41963))))
% 191.21/191.73 [4197]E(f773(f773(f47(x41971,f855(x41972,a841)),x41973),f773(f773(f20(x41971,f855(x41972,a841),f855(x41972,a841)),f773(f773(f10(f855(x41972,a841),f855(f855(x41972,a841),f855(x41972,a841)),x41971),f104(f855(x41972,a841))),x41974)),x41975)),f773(f773(f104(f855(x41972,a841)),f45(f855(x41972,a841),f773(f303(x41971,f855(x41972,a841),x41974),x41973))),f45(f855(x41972,a841),f773(f303(x41971,f855(x41972,a841),x41975),x41973))))
% 191.21/191.73 [4105]E(f773(f773(f125(f854(x41051,x41052)),f773(f773(f167(x41051,x41052),f773(f773(f159(x41051),f773(f181(f848(x41052)),x41053)),x41054)),x41053)),f773(f773(f167(x41051,x41052),f773(f773(f128(x41051),f773(f181(f848(x41052)),x41053)),x41054)),x41055)),f773(f773(f167(x41051,x41052),x41054),f773(f773(f125(x41052),x41053),x41055)))
% 191.21/191.73 [4222]E(f87(x42221,f773(f773(f20(x42221,a841,a841),f773(f773(f10(a841,f855(a841,a841),x42221),a331),f773(f773(f9(x42221,f855(x42221,a841),a841),f334(x42221)),x42222))),f773(f773(f9(x42221,x42223,a841),f773(f773(f10(x42223,f855(x42223,a841),x42221),a330),x42224)),x42225))),f773(f79(x42221,x42223,x42222,x42224),x42225))
% 191.21/191.73 [4272]E(f773(f773(f88(a1,x42721),f773(f106(a1),f773(f773(f82(a1),x42722),a99))),f773(f773(f20(a1,x42721,x42721),f773(f773(f9(a1,x42721,f855(x42721,x42721)),f773(f773(f10(a841,f855(x42721,f855(x42721,x42721)),a1),f98(x42721)),a186)),f175(x42721,x42723,x42724,x42725))),f773(f773(f10(a847,x42721,a1),x42724),f773(f773(f9(a1,a847,a847),f773(f773(f10(a847,f855(a847,a847),a1),f82(a847)),a107)),x42725)))),f175(x42721,x42723,x42724,f773(f773(f82(a847),f773(f106(a847),x42722)),x42725)))
% 191.21/191.73 [4306]E(f166(x43061,x43062,f773(f773(f143(f854(x43061,x43063),f854(x43061,x43062)),f773(f251(x43061,x43063,f854(x43061,x43062)),f773(f773(f9(x43061,f855(x43063,x43062),f855(x43063,f854(x43061,x43062))),f773(f773(f10(f855(x43062,f854(x43061,x43062)),f855(f855(x43063,x43062),f855(x43063,f854(x43061,x43062))),x43061),f10(x43062,f854(x43061,x43062),x43063)),f241(x43061,x43062))),x43064))),x43065)),f773(f75(f851(x43063),f851(x43062),x43061,f773(f196(x43063,x43062),x43064)),f166(x43061,x43063,x43065)))
% 191.21/191.73 [4265]E(f169(x42651,x42652,f773(f773(f20(x42651,f851(x42652),f851(x42652)),f773(f773(f20(x42651,f851(x42652),f855(f851(x42652),f851(x42652))),f773(f773(f10(a841,f855(f851(x42652),f855(f851(x42652),f851(x42652))),x42651),f98(f851(x42652))),x42653)),x42654)),x42655)),f773(f773(f103(f855(x42651,a841)),f773(f773(f104(f855(x42651,a841)),f169(x42651,x42652,x42654)),f773(f256(x42651),x42653))),f773(f773(f104(f855(x42651,a841)),f169(x42651,x42652,x42655)),f773(f256(x42651),f773(f773(f10(a841,a841,x42651),a328),x42653)))))
% 191.21/191.73 [4304]E(f773(f773(f88(a1,x43041),f773(f106(a1),f773(f773(f82(a1),x43042),a99))),f773(f773(f20(a1,x43041,x43041),f773(f773(f9(a1,x43041,f855(x43041,x43041)),f773(f773(f10(a841,f855(x43041,f855(x43041,x43041)),a1),f98(x43041)),a186)),f773(f174(x43041,x43043,x43044),x43045))),f773(f773(f20(a1,x43041,x43041),f773(f773(f10(a847,f855(x43041,x43041),a1),x43044),f773(f773(f9(a1,a847,a847),f773(f773(f10(a847,f855(a847,a847),a1),f82(a847)),a107)),x43045))),f773(f773(f10(a847,x43041,a1),f174(x43041,x43043,x43044)),f773(f773(f9(a1,a847,a847),f773(f773(f10(a847,f855(a847,a847),a1),f82(a847)),a107)),x43045))))),f773(f174(x43041,x43043,x43044),f773(f773(f82(a847),f773(f106(a847),x43042)),x43045)))
% 191.21/191.73 [4353]E(f773(f256(f854(x43531,x43532)),f773(f251(x43531,x43532,a841),f773(f773(f10(f855(x43532,f855(x43533,a841)),f855(x43532,a841),x43531),f773(f10(f855(x43533,a841),a841,x43532),f89(x43533))),f773(f773(f9(x43531,f855(x43532,f855(x43533,a841)),f855(x43532,f855(x43533,a841))),f773(f773(f10(f855(f855(x43533,a841),f855(x43533,a841)),f855(f855(x43532,f855(x43533,a841)),f855(x43532,f855(x43533,a841))),x43531),f10(f855(x43533,a841),f855(x43533,a841),x43532)),f773(f773(f10(f855(x43533,f855(a841,a841)),f855(f855(x43533,a841),f855(x43533,a841)),x43531),f20(x43533,a841,a841)),f773(f773(f10(f855(x43533,a841),f855(x43533,f855(a841,a841)),x43531),f773(f10(a841,f855(a841,a841),x43533),a331)),f773(f773(f9(x43531,f855(f854(x43531,x43533),a841),f855(x43533,a841)),f773(f773(f10(f855(x43533,f855(f855(f854(x43531,x43533),a841),a841)),f855(f855(f854(x43531,x43533),a841),f855(x43533,a841)),x43531),f9(x43533,f855(f854(x43531,x43533),a841),a841)),f773(f773(f10(f855(x43533,f854(x43531,x43533)),f855(x43533,f855(f855(f854(x43531,x43533),a841),a841)),x43531),f773(f10(f854(x43531,x43533),f855(f855(f854(x43531,x43533),a841),a841),x43533),f334(f854(x43531,x43533)))),f241(x43531,x43533)))),x43534))))),f773(f773(f9(x43532,f855(f854(x43533,x43532),a841),f855(x43533,a841)),f773(f773(f10(f855(x43533,f855(f855(f854(x43533,x43532),a841),a841)),f855(f855(f854(x43533,x43532),a841),f855(x43533,a841)),x43532),f9(x43533,f855(f854(x43533,x43532),a841),a841)),f773(f773(f10(f855(x43533,f854(x43533,x43532)),f855(x43533,f855(f855(f854(x43533,x43532),a841),a841)),x43532),f773(f10(f854(x43533,x43532),f855(f855(f854(x43533,x43532),a841),a841),x43533),f334(f854(x43533,x43532)))),f773(f9(x43533,x43532,f854(x43533,x43532)),f241(x43533,x43532))))),x43535))))),f773(f773(f281(x43531,x43533,x43532),x43534),x43535))
% 191.21/191.73 [4454]~E(f32(x44541,x44542,x44543),f33(x44544,x44545,x44546))
% 191.21/191.73 [4457]~E(f31(x44571,x44572,x44573),f33(x44574,x44575,x44576))
% 191.21/191.73 [4458]~E(f31(x44581,x44582,x44583),f32(x44584,x44585,x44586))
% 191.21/191.73 [3948]E(f218(x39481,x39482,x39483,x39484,f215(x39481,x39482,x39485,x39486)),f773(f773(x39484,x39485),x39486))
% 191.21/191.73 [3949]E(f219(x39491,x39492,x39493,x39494,f215(x39491,x39492,x39495,x39496)),f773(f773(x39494,x39495),x39496))
% 191.21/191.73 [4212]E(f773(f75(f854(x42121,x42122),x42122,f854(x42123,x42124),f250(x42121,x42122)),f252(x42123,x42121,x42124,x42122,x42125,x42126)),f773(f75(x42124,x42122,f854(x42123,x42124),x42126),f250(x42123,x42124)))
% 191.21/191.73 [4213]E(f773(f75(f854(x42131,x42132),x42131,f854(x42133,x42134),f240(x42131,x42132)),f252(x42133,x42131,x42134,x42132,x42135,x42136)),f773(f75(x42133,x42131,f854(x42133,x42134),x42135),f240(x42133,x42134)))
% 191.21/191.73 [3814]E(f773(f773(f75(x38141,x38142,x38143,x38144),x38145),x38146),f773(x38144,f773(x38145,x38146)))
% 191.21/191.73 [4011]E(f220(x40111,x40112,x40113,x40114,f215(x40111,x40112,x40115,x40116)),f773(f773(f82(a847),f773(f773(f82(a847),f773(x40113,x40115)),f773(x40114,x40116))),f773(a114,f2(a847))))
% 191.21/191.73 [4033]E(f773(f319(x40331,x40332,x40333,x40334,x40335),f773(f304(x40331,x40333),x40336)),f773(x40334,x40336))
% 191.21/191.73 [4034]E(f773(f319(x40341,x40342,x40343,x40344,x40345),f773(f313(x40343,x40341),x40346)),f773(x40345,x40346))
% 191.21/191.73 [4129]E(f320(x41291,x41292,x41293,x41294,x41295,f773(f304(x41291,x41293),x41296)),f773(x41294,x41296))
% 191.21/191.73 [4130]E(f320(x41301,x41302,x41303,x41304,x41305,f773(f313(x41303,x41301),x41306)),f773(x41305,x41306))
% 191.21/191.73 [3611]E(f773(f773(f251(x36111,x36112,x36113),x36114),f773(f773(f241(x36111,x36112),x36115),x36116)),f773(f773(x36114,x36115),x36116))
% 191.21/191.73 [3674]E(f773(f773(f773(f10(x36741,x36742,x36743),x36744),x36745),x36746),f773(x36744,f773(x36745,x36746)))
% 191.21/191.73 [3675]E(f773(f773(f773(f9(x36751,x36752,x36753),x36754),x36755),x36756),f773(f773(x36754,x36756),x36755))
% 191.21/191.73 [3691]E(f773(f773(f773(f20(x36911,x36912,x36913),x36914),x36915),x36916),f773(f773(x36914,x36916),f773(x36915,x36916)))
% 191.21/191.73 [3715]E(f773(f145(x37151,x37152,x37153,x37154),f773(f773(f140(x37152),x37155),x37156)),f773(f773(x37154,x37155),x37156))
% 191.21/191.73 [3817]E(f773(f773(f140(f854(x38171,x38172)),f773(f773(f241(x38171,x38172),x38173),x38174)),f773(f773(f167(x38171,x38172),x38175),x38176)),f773(f773(f167(x38171,x38172),f773(f773(f140(x38171),x38173),x38175)),f773(f773(f140(x38172),x38174),x38176)))
% 191.21/191.73 [3819]E(f773(f773(f143(x38191,x38192),x38193),f773(f773(f148(x38191,x38194),x38195),x38196)),f773(f773(f148(x38192,f773(f773(f143(x38191,x38192),x38193),x38194)),x38195),f773(x38193,x38196)))
% 191.21/191.73 [3842]E(f773(f773(f249(x38421,x38422,x38423,x38424),x38425),x38426),f773(x38424,f773(f773(f241(x38421,x38422),x38425),x38426)))
% 191.21/191.73 [3859]E(f773(f132(x38591,x38592,x38593,x38594),f773(f773(f140(x38592),x38595),x38596)),f773(f132(x38591,x38592,x38593,f773(f773(x38593,x38594),x38595)),x38596))
% 191.21/191.73 [3888]E(f254(x38881,x38882,x38883,x38884,f773(f773(f241(x38881,x38882),x38885),x38886)),f773(f773(x38884,x38885),x38886))
% 191.21/191.73 [3974]E(f773(f773(f46(x39741,f855(x39742,a841)),x39743),f773(f75(x39744,f855(x39742,a841),x39741,x39745),x39746)),f773(f773(f46(x39744,f855(x39742,a841)),f773(f303(x39741,x39744,x39746),x39743)),x39745))
% 191.21/191.73 [4025]E(f773(f773(f143(x40251,x40252),x40253),f773(f773(f143(x40254,x40251),x40255),x40256)),f773(f773(f143(x40254,x40252),f773(f75(x40251,x40252,x40254,x40253),x40255)),x40256))
% 191.21/191.73 [4027]E(f773(f773(f196(x40271,x40272),x40273),f773(f773(f196(x40274,x40271),x40275),x40276)),f773(f773(f196(x40274,x40272),f773(f75(x40271,x40272,x40274,x40273),x40275)),x40276))
% 191.21/191.73 [4031]E(f773(f303(x40311,x40312,f773(f75(x40313,x40312,x40311,x40314),x40315)),x40316),f773(f303(x40313,x40312,x40314),f773(f303(x40311,x40313,x40315),x40316)))
% 191.21/191.73 [4032]E(f773(f305(x40321,x40322,f773(f75(x40323,x40322,x40321,x40324),x40325)),x40326),f773(f305(x40321,x40323,x40325),f773(f305(x40323,x40322,x40324),x40326)))
% 191.21/191.73 [4063]E(f170(x40631,x40632,x40633,f773(f773(f773(f74(x40631,f851(x40632)),x40634),x40635),f773(f227(x40632),x40636))),f773(f773(f773(f74(x40631,f851(x40632)),f170(x40631,x40632,x40633,x40634)),x40635),f773(f227(x40632),x40636)))
% 191.21/191.73 [4065]E(f773(f132(x40651,x40652,x40653,f773(f132(x40651,x40652,x40653,x40654),x40655)),x40656),f773(f132(x40651,x40652,x40653,x40654),f773(f773(f125(x40652),x40655),x40656)))
% 191.21/191.73 [4202]E(f773(f252(x42021,x42021,x42022,x42023,f39(x42021),x42024),f773(f773(f241(x42021,x42022),x42025),x42026)),f773(f773(f241(x42021,x42023),x42025),f773(x42024,x42026)))
% 191.21/191.73 [4203]E(f773(f252(x42031,x42032,x42033,x42033,x42034,f39(x42033)),f773(f773(f241(x42031,x42033),x42035),x42036)),f773(f773(f241(x42032,x42033),f773(x42034,x42035)),x42036))
% 191.21/191.73 [4288]E(f773(f773(f143(f854(x42881,x42882),f854(x42881,x42883)),f773(f251(x42881,x42882,f854(x42881,x42883)),f773(f773(f9(x42881,f855(x42882,x42883),f855(x42882,f854(x42881,x42883))),f773(f773(f10(f855(x42883,f854(x42881,x42883)),f855(f855(x42882,x42883),f855(x42882,f854(x42881,x42883))),x42881),f10(x42883,f854(x42881,x42883),x42882)),f241(x42881,x42883))),x42884))),f773(f773(f167(x42881,x42882),x42885),x42886)),f773(f773(f167(x42881,x42883),x42885),f773(f773(f143(x42882,x42883),x42884),x42886)))
% 191.21/191.73 [3679]E(f96(x36791,x36792,x36793,f773(f773(f773(f93(x36791),x36794),x36795),x36796)),f773(f773(f773(x36793,x36794),x36795),x36796))
% 191.21/191.73 [3680]E(f97(x36801,x36802,x36803,f773(f773(f773(f93(x36801),x36804),x36805),x36806)),f773(f773(f773(x36803,x36804),x36805),x36806))
% 191.21/191.73 [3870]E(f773(f773(f75(x38701,x38702,x38703,f773(f18(x38702,x38701),x38704)),x38705),x38706),x38704)
% 191.21/191.73 [3906]E(f773(f303(x39061,x39062,x39063),f773(f303(x39064,x39061,x39065),x39066)),f773(f303(x39064,x39062,f773(f773(f10(x39061,x39062,x39064),x39063),x39065)),x39066))
% 191.21/191.73 [3912]E(f773(f773(f46(x39121,f855(x39122,a841)),f773(f303(x39123,x39121,x39124),x39125)),x39126),f773(f773(f46(x39123,f855(x39122,a841)),x39125),f773(f773(f10(x39121,f855(x39122,a841),x39123),x39126),x39124)))
% 191.21/191.73 [3913]E(f773(f773(f47(x39131,f855(x39132,a841)),f773(f303(x39133,x39131,x39134),x39135)),x39136),f773(f773(f47(x39133,f855(x39132,a841)),x39135),f773(f773(f10(x39131,f855(x39132,a841),x39133),x39136),x39134)))
% 191.21/191.73 [3914]E(f773(f773(f46(x39141,f855(x39142,a841)),x39143),f773(f773(f10(x39144,f855(x39142,a841),x39141),x39145),x39146)),f773(f773(f46(x39144,f855(x39142,a841)),f773(f303(x39141,x39144,x39146),x39143)),x39145))
% 191.21/191.73 [3915]E(f773(f773(f47(x39151,f855(x39152,a841)),x39153),f773(f773(f10(x39154,f855(x39152,a841),x39151),x39155),x39156)),f773(f773(f47(x39154,f855(x39152,a841)),f773(f303(x39151,x39154,x39156),x39153)),x39155))
% 191.21/191.73 [3976]E(f773(f773(f46(x39761,f855(x39762,a841)),x39763),f773(f773(f10(f855(x39764,a841),f855(x39762,a841),x39761),f303(x39764,x39762,x39765)),x39766)),f773(f303(x39764,x39762,x39765),f773(f773(f46(x39761,f855(x39764,a841)),x39763),x39766)))
% 191.21/191.73 [3977]E(f773(f773(f46(x39771,f855(x39772,a841)),x39773),f773(f773(f10(f855(x39774,a841),f855(x39772,a841),x39771),f277(x39774,x39772,x39775)),x39776)),f773(f277(x39774,x39772,x39775),f773(f773(f46(x39771,f855(x39774,a841)),x39773),x39776)))
% 191.21/191.73 [3978]E(f773(f773(f46(x39781,f855(x39782,a841)),x39783),f773(f773(f10(f855(x39784,a841),f855(x39782,a841),x39781),f305(x39782,x39784,x39785)),x39786)),f773(f305(x39782,x39784,x39785),f773(f773(f46(x39781,f855(x39784,a841)),x39783),x39786)))
% 191.21/191.73 [3979]E(f773(f773(f47(x39791,f855(x39792,a841)),x39793),f773(f773(f10(f855(x39794,a841),f855(x39792,a841),x39791),f305(x39792,x39794,x39795)),x39796)),f773(f305(x39792,x39794,x39795),f773(f773(f47(x39791,f855(x39794,a841)),x39793),x39796)))
% 191.21/191.73 [4070]E(f773(f132(x40701,x40702,f773(f9(x40702,x40701,x40701),x40703),x40704),f773(f142(x40702),f773(f773(f140(x40702),x40705),x40706))),f773(f773(x40703,x40705),f773(f132(x40701,x40702,f773(f9(x40702,x40701,x40701),x40703),x40704),f773(f142(x40702),x40706))))
% 191.21/191.73 [4131]E(f773(f773(f20(f854(x41311,x41312),x41312,x41313),f773(f773(f10(x41314,f855(x41312,x41313),f854(x41311,x41312)),x41315),f773(f773(f10(x41311,x41314,f854(x41311,x41312)),x41316),f240(x41311,x41312)))),f250(x41311,x41312)),f773(f251(x41311,x41312,x41313),f773(f773(f10(x41314,f855(x41312,x41313),x41311),x41315),x41316)))
% 191.21/191.73 [4138]E(f773(f132(x41381,x41382,f773(f9(x41382,x41381,x41381),x41383),f773(f132(x41381,x41382,f773(f9(x41382,x41381,x41381),x41383),x41384),f773(f142(x41382),x41385))),f773(f142(x41382),x41386)),f773(f132(x41381,x41382,f773(f9(x41382,x41381,x41381),x41383),x41384),f773(f142(x41382),f773(f773(f125(x41382),x41386),x41385))))
% 191.21/191.73 [4140]E(f773(f773(f143(f854(x41401,x41402),f854(x41403,x41402)),f773(f251(x41401,x41402,f854(x41403,x41402)),f773(f773(f10(x41403,f855(x41402,f854(x41403,x41402)),x41401),f241(x41403,x41402)),x41404))),f773(f773(f167(x41401,x41402),x41405),x41406)),f773(f773(f167(x41403,x41402),f773(f773(f143(x41401,x41403),x41404),x41405)),x41406))
% 191.21/191.73 [4186]P1(f773(f773(f232(f855(x41861,a841)),f773(f277(x41862,x41861,x41863),f773(f773(f47(x41864,f855(x41862,a841)),x41865),x41866))),f773(f773(f47(x41864,f855(x41861,a841)),x41865),f773(f773(f10(f855(x41862,a841),f855(x41861,a841),x41864),f277(x41862,x41861,x41863)),x41866))))
% 191.21/191.73 [3989]E(f773(f773(f167(x39891,x39892),f773(f773(f148(x39891,x39893),x39894),f773(f240(x39891,x39892),x39895))),f773(f773(f148(x39892,x39896),x39894),f773(f250(x39891,x39892),x39895))),f773(f773(f148(f854(x39891,x39892),f773(f773(f167(x39891,x39892),x39893),x39896)),x39894),x39895))
% 191.21/191.73 [4052]E(f773(f773(f103(f855(f854(x40521,x40522),a841)),f773(f773(f281(x40521,x40523,x40522),x40524),x40525)),f773(f773(f281(x40521,x40523,x40522),x40524),x40526)),f773(f773(f281(x40521,x40523,x40522),x40524),f773(f773(f103(f855(f854(x40523,x40522),a841)),x40525),x40526)))
% 191.21/191.73 [4152]E(f773(f773(f302(f854(x41521,x41522)),f773(f773(f241(x41521,x41522),x41523),x41524)),f773(f773(f103(f855(f854(x41521,x41522),a841)),f773(f773(f248(x41521,x41522),x41525),f773(f18(f855(x41522,a841),x41521),f773(f773(f302(x41522),x41524),x41526)))),f773(f773(f248(x41521,x41522),f773(f773(f302(x41521),x41523),x41525)),f773(f18(f855(x41522,a841),x41521),x41526)))),f773(f773(f248(x41521,x41522),f773(f773(f302(x41521),x41523),x41525)),f773(f18(f855(x41522,a841),x41521),f773(f773(f302(x41522),x41524),x41526))))
% 191.21/191.73 [4225]E(f773(f773(f104(f855(x42251,a841)),f773(f305(x42251,x42252,f773(f75(f854(x42252,x42253),x42252,x42251,f240(x42252,x42253)),x42254)),x42255)),f773(f305(x42251,x42253,f773(f75(f854(x42252,x42253),x42253,x42251,f250(x42252,x42253)),x42254)),x42256)),f773(f305(x42251,f854(x42252,x42253),x42254),f773(f773(f248(x42252,x42253),x42255),f773(f18(f855(x42253,a841),x42252),x42256))))
% 191.21/191.73 [3973]E(f773(f773(f773(f74(x39731,x39732),f773(f773(f773(f74(x39731,x39732),x39733),x39734),x39735)),x39734),x39736),f773(f773(f773(f74(x39731,x39732),x39733),x39734),x39736))
% 191.21/191.73 [4076]E(f773(f773(f103(f855(f854(x40761,x40762),a841)),f773(f773(f281(x40761,x40763,x40762),x40764),x40765)),f773(f773(f281(x40761,x40763,x40762),x40766),x40765)),f773(f773(f281(x40761,x40763,x40762),f773(f773(f103(f855(f854(x40761,x40763),a841)),x40764),x40766)),x40765))
% 191.21/191.73 [4210]E(f773(f773(f46(x42101,f855(x42102,a841)),x42103),f773(f773(f9(x42101,f855(x42104,f855(x42102,a841)),f855(x42102,a841)),f773(f773(f10(f855(x42104,a841),f855(f855(x42104,f855(x42102,a841)),f855(x42102,a841)),x42101),f46(x42104,f855(x42102,a841))),x42105)),x42106)),f773(f773(f46(x42104,f855(x42102,a841)),f773(f773(f46(x42101,f855(x42104,a841)),x42103),x42105)),x42106))
% 191.21/191.73 [4211]E(f773(f773(f47(x42111,f855(x42112,a841)),x42113),f773(f773(f9(x42111,f855(x42114,f855(x42112,a841)),f855(x42112,a841)),f773(f773(f10(f855(x42114,a841),f855(f855(x42114,f855(x42112,a841)),f855(x42112,a841)),x42111),f47(x42114,f855(x42112,a841))),x42115)),x42116)),f773(f773(f47(x42114,f855(x42112,a841)),f773(f773(f46(x42111,f855(x42114,a841)),x42113),x42115)),x42116))
% 191.21/191.73 [4260]E(f773(f251(x42601,x42602,f854(x42603,x42604)),f773(f773(f9(x42601,f855(x42602,x42604),f855(x42602,f854(x42603,x42604))),f773(f773(f10(f855(x42604,f854(x42603,x42604)),f855(f855(x42602,x42604),f855(x42602,f854(x42603,x42604))),x42601),f10(x42604,f854(x42603,x42604),x42602)),f773(f773(f10(x42603,f855(x42604,f854(x42603,x42604)),x42601),f241(x42603,x42604)),x42605))),x42606)),f252(x42601,x42603,x42602,x42604,x42605,x42606))
% 191.21/191.73 [4185]E(f773(f773(f773(f74(x41851,f851(x41852)),f172(x41851,x41852,x41853,f773(f773(f3(f855(x41851,a841)),x41854),f773(f773(f302(x41851),x41855),f180(f855(x41851,a841)))))),x41855),x41856),f773(f773(f773(f74(x41851,f851(x41852)),f172(x41851,x41852,x41853,x41854)),x41855),x41856))
% 191.21/191.73 [4283]E(f773(f303(x42831,x42832,f773(f773(f20(x42831,x42832,x42832),f773(f773(f20(x42831,x42832,f855(x42832,x42832)),f773(f773(f10(a841,f855(x42832,f855(x42832,x42832)),x42831),f98(x42832)),x42833)),x42834)),x42835)),x42836),f773(f773(f103(f855(x42832,a841)),f773(f303(x42831,x42832,x42834),f773(f773(f104(f855(x42831,a841)),x42836),f773(f256(x42831),x42833)))),f773(f303(x42831,x42832,x42835),f773(f773(f104(f855(x42831,a841)),x42836),f773(f256(x42831),f773(f773(f10(a841,a841,x42831),a328),x42833))))))
% 191.21/191.73 [4294]E(f773(f303(x42941,f854(x42942,x42943),f773(f773(f20(x42941,x42943,f854(x42942,x42943)),f773(f773(f10(x42942,f855(x42943,f854(x42942,x42943)),x42941),f241(x42942,x42943)),x42944)),x42945)),x42946),f773(f773(f248(x42942,x42943),f773(f303(x42941,x42942,x42944),x42946)),f773(f773(f10(f855(x42941,a841),f855(x42943,a841),x42942),f303(x42941,x42943,x42945)),f773(f773(f9(x42942,f855(x42941,a841),f855(x42941,a841)),f773(f773(f10(f855(x42941,a841),f855(f855(x42941,a841),f855(x42941,a841)),x42942),f104(f855(x42941,a841))),f773(f773(f10(f855(x42942,a841),f855(x42941,a841),x42942),f305(x42941,x42942,x42944)),f773(f773(f9(x42942,f855(x42942,a841),f855(x42942,a841)),f302(x42942)),f180(f855(x42942,a841)))))),x42946))))
% 191.21/191.73 [4243]E(f773(f250(x42431,x42432),f773(f252(x42433,x42431,x42434,x42432,x42435,x42436),x42437)),f773(x42436,f773(f250(x42433,x42434),x42437)))
% 191.21/191.73 [4244]E(f773(f240(x42441,x42442),f773(f252(x42443,x42441,x42444,x42442,x42445,x42446),x42447)),f773(x42445,f773(f240(x42443,x42444),x42447)))
% 191.21/191.73 [3950]E(f773(f773(f167(x39501,x39502),f773(f773(f148(x39501,x39503),x39504),x39505)),f773(f773(f148(x39502,x39506),x39504),x39507)),f773(f773(f148(f854(x39501,x39502),f773(f773(f167(x39501,x39502),x39503),x39506)),x39504),f773(f773(f241(x39501,x39502),x39505),x39507)))
% 191.21/191.73 [4020]E(f773(f773(f773(f253(x40201,x40202,x40203,x40204),x40205),x40206),x40207),f773(f773(f251(x40202,x40203,x40204),x40206),f773(x40205,x40207)))
% 191.21/191.73 [4030]E(f773(f773(f773(f253(x40301,x40302,x40303,x40304),x40305),x40306),x40307),f773(f773(x40306,f773(f240(x40302,x40303),f773(x40305,x40307))),f773(f250(x40302,x40303),f773(x40305,x40307))))
% 191.21/191.73 [4083]E(f773(f75(x40831,x40832,x40833,x40834),f773(f75(x40835,x40831,x40833,x40836),x40837)),f773(f75(x40835,x40832,x40833,f773(f75(x40831,x40832,x40835,x40834),x40836)),x40837))
% 191.21/191.73 [4147]E(f773(f75(f851(x41471),f851(x41472),x41473,f773(f196(x41471,x41472),x41474)),f773(f773(f773(f74(x41473,f851(x41471)),x41475),x41476),f773(f227(x41471),x41477))),f773(f773(f773(f74(x41473,f851(x41472)),f773(f75(f851(x41471),f851(x41472),x41473,f773(f196(x41471,x41472),x41474)),x41475)),x41476),f773(f227(x41472),f773(x41474,x41477))))
% 191.21/191.73 [4267]E(f773(f252(x42671,x42672,x42673,x42673,x42674,f39(x42673)),f773(f252(x42671,x42671,x42675,x42673,f39(x42671),x42676),x42677)),f773(f773(f241(x42672,x42673),f773(x42674,f773(f240(x42671,x42675),x42677))),f773(x42676,f773(f250(x42671,x42675),x42677))))
% 191.21/191.73 [4268]E(f773(f252(x42681,x42681,x42682,x42683,f39(x42681),x42684),f773(f252(x42685,x42681,x42682,x42682,x42686,f39(x42682)),x42687)),f773(f773(f241(x42681,x42683),f773(x42686,f773(f240(x42685,x42682),x42687))),f773(x42684,f773(f250(x42685,x42682),x42687))))
% 191.21/191.73 [4281]E(f773(f252(x42811,x42812,x42813,x42813,x42814,f39(x42813)),f773(f252(x42815,x42811,x42813,x42813,x42816,f39(x42813)),x42817)),f773(f252(x42815,x42812,x42813,x42813,f773(f75(x42811,x42812,x42815,x42814),x42816),f39(x42813)),x42817))
% 191.21/191.73 [4282]E(f773(f252(x42821,x42821,x42822,x42823,f39(x42821),x42824),f773(f252(x42821,x42821,x42825,x42822,f39(x42821),x42826),x42827)),f773(f252(x42821,x42821,x42825,x42823,f39(x42821),f773(f75(x42822,x42823,x42825,x42824),x42826)),x42827))
% 191.21/191.73 [4291]E(f773(f252(x42911,x42912,x42913,x42913,x42914,f39(x42913)),f773(f252(x42911,x42911,x42915,x42913,f39(x42911),x42916),x42917)),f773(f252(x42912,x42912,x42915,x42913,f39(x42912),x42916),f773(f252(x42911,x42912,x42915,x42915,x42914,f39(x42915)),x42917)))
% 191.21/191.73 [3986]E(f773(f773(f281(x39861,x39862,x39863),f773(f773(f281(x39861,x39864,x39862),x39865),x39866)),x39867),f773(f773(f281(x39861,x39864,x39863),x39865),f773(f773(f281(x39864,x39862,x39863),x39866),x39867)))
% 191.21/191.73 [4058]E(f773(f773(f251(x40581,x40582,x40583),f773(f75(x40584,f855(x40582,x40583),x40581,x40585),x40586)),x40587),f773(f773(x40585,f773(x40586,f773(f240(x40581,x40582),x40587))),f773(f250(x40581,x40582),x40587)))
% 191.21/191.73 [4108]E(f773(f75(x41081,x41082,x41083,x41084),f773(f773(f773(f74(x41083,x41081),x41085),x41086),x41087)),f773(f773(f773(f74(x41083,x41082),f773(f75(x41081,x41082,x41083,x41084),x41085)),x41086),f773(x41084,x41087)))
% 191.21/191.73 [4143]E(f773(f132(x41431,x41432,f773(f9(x41432,x41431,x41431),x41433),x41434),f773(f142(x41432),f773(f773(f143(x41435,x41432),x41436),x41437))),f773(f132(x41431,x41435,f773(f9(x41435,x41431,x41431),f773(f75(x41432,f855(x41431,x41431),x41435,x41433),x41436)),x41434),f773(f142(x41435),x41437)))
% 191.21/191.73 [4148]E(f319(x41481,f851(x41482),x41483,f773(f75(f851(x41484),f851(x41482),x41481,f773(f196(x41484,x41482),x41485)),x41486),f773(f75(f851(x41484),f851(x41482),x41483,f773(f196(x41484,x41482),x41485)),x41487)),f773(f75(f851(x41484),f851(x41482),f856(x41481,x41483),f773(f196(x41484,x41482),x41485)),f319(x41481,f851(x41484),x41483,x41486,x41487)))
% 191.21/191.73 [4084]E(f773(f773(f46(x40841,f855(f854(x40842,x40843),a841)),x40844),f773(f773(f10(f855(f854(x40845,x40843),a841),f855(f854(x40842,x40843),a841),x40841),f773(f281(x40842,x40845,x40843),x40846)),x40847)),f773(f773(f281(x40842,x40845,x40843),x40846),f773(f773(f46(x40841,f855(f854(x40845,x40843),a841)),x40844),x40847)))
% 191.21/191.73 [4119]E(f170(x41191,x41192,f773(f773(f773(f74(x41191,f851(x41192)),x41193),x41194),f773(f227(x41192),x41195)),f166(x41191,x41192,f773(f142(f854(x41191,x41192)),f773(f773(f167(x41191,x41192),x41196),x41197)))),f170(x41191,x41192,x41193,f166(x41191,x41192,f773(f142(f854(x41191,x41192)),f773(f773(f167(x41191,x41192),f773(f773(f140(x41191),x41194),x41196)),f773(f773(f140(x41192),x41195),x41197))))))
% 191.21/191.73 [4230]E(f773(f773(f46(x42301,f855(f854(x42302,x42303),a841)),x42304),f773(f773(f9(x42301,f855(f854(x42305,x42303),a841),f855(f854(x42302,x42303),a841)),f773(f773(f10(f855(f854(x42302,x42305),a841),f855(f855(f854(x42305,x42303),a841),f855(f854(x42302,x42303),a841)),x42301),f281(x42302,x42305,x42303)),x42306)),x42307)),f773(f773(f281(x42302,x42305,x42303),f773(f773(f46(x42301,f855(f854(x42302,x42305),a841)),x42304),x42306)),x42307))
% 191.21/191.73 [4231]E(f773(f132(x42311,x42312,f773(f773(f9(x42311,f855(x42312,x42313),f855(x42312,x42311)),f773(f773(f10(f855(x42313,x42311),f855(f855(x42312,x42313),f855(x42312,x42311)),x42311),f10(x42313,x42311,x42312)),x42314)),x42315),x42316),x42317),f773(f132(x42311,x42313,x42314,x42316),f773(f773(f143(x42312,x42313),x42315),x42317)))
% 191.21/191.73 [4292]E(f773(f773(f47(x42921,f855(x42922,a841)),x42923),f773(f773(f10(f855(x42924,f855(x42922,a841)),f855(x42922,a841),x42921),f773(f47(x42924,f855(x42922,a841)),x42925)),f773(f773(f9(x42921,f855(x42924,f855(x42922,a841)),f855(x42924,f855(x42922,a841))),f773(f773(f10(f855(f855(x42922,a841),f855(x42922,a841)),f855(f855(x42924,f855(x42922,a841)),f855(x42924,f855(x42922,a841))),x42921),f10(f855(x42922,a841),f855(x42922,a841),x42924)),f773(f773(f10(f855(x42922,a841),f855(f855(x42922,a841),f855(x42922,a841)),x42921),f103(f855(x42922,a841))),x42926))),x42927))),f773(f773(f103(f855(x42922,a841)),f773(f773(f47(x42921,f855(x42922,a841)),x42923),x42926)),f773(f773(f47(x42924,f855(x42922,a841)),x42925),x42927)))
% 191.21/191.73 [4293]E(f773(f773(f46(x42931,f855(x42932,a841)),x42933),f773(f773(f10(f855(x42934,f855(x42932,a841)),f855(x42932,a841),x42931),f773(f46(x42934,f855(x42932,a841)),x42935)),f773(f773(f9(x42931,f855(x42934,f855(x42932,a841)),f855(x42934,f855(x42932,a841))),f773(f773(f10(f855(f855(x42932,a841),f855(x42932,a841)),f855(f855(x42934,f855(x42932,a841)),f855(x42934,f855(x42932,a841))),x42931),f10(f855(x42932,a841),f855(x42932,a841),x42934)),f773(f773(f10(f855(x42932,a841),f855(f855(x42932,a841),f855(x42932,a841)),x42931),f104(f855(x42932,a841))),x42936))),x42937))),f773(f773(f104(f855(x42932,a841)),f773(f773(f46(x42931,f855(x42932,a841)),x42933),x42936)),f773(f773(f46(x42934,f855(x42932,a841)),x42935),x42937)))
% 191.21/191.73 [4286]E(f192(x42861,x42862,f773(f773(f773(x42863,x42864),x42865),x42866),f773(f773(f9(x42861,f854(a101,a101),f855(a101,f849(x42862))),f773(f773(f9(x42861,a101,f855(f854(a101,a101),f855(a101,f849(x42862)))),f773(f773(f9(x42861,a101,f855(a101,f855(f854(a101,a101),f855(a101,f849(x42862))))),x42867),x42864)),x42865)),x42866)),f773(f773(f773(f204(x42861,x42862,x42863,x42867),x42864),x42865),x42866))
% 191.21/191.73 [4299]E(f193(x42991,x42992,f773(f773(f773(x42993,x42994),x42995),x42996),f773(f773(f9(x42991,f854(a101,a101),f855(a101,f849(x42992))),f773(f773(f9(x42991,a101,f855(f854(a101,a101),f855(a101,f849(x42992)))),f773(f773(f9(x42991,a101,f855(a101,f855(f854(a101,a101),f855(a101,f849(x42992))))),x42997),x42994)),x42995)),x42996)),f206(x42991,x42992,x42993,x42997,x42994,x42995,x42996))
% 191.21/191.73 [4290]E(f190(x42901,x42902,f773(f773(f773(x42903,x42904),x42905),x42906),f773(f773(f9(x42901,f854(a101,a101),f855(a101,f849(f851(x42902)))),f773(f773(f9(x42901,a101,f855(f854(a101,a101),f855(a101,f849(f851(x42902))))),f773(f773(f9(x42901,a101,f855(a101,f855(f854(a101,a101),f855(a101,f849(f851(x42902)))))),x42907),x42904)),x42905)),x42906)),f773(f773(f773(f200(x42901,x42902,x42903,x42907),x42904),x42905),x42906))
% 191.21/191.73 [4301]E(f191(x43011,x43012,f773(f773(f773(x43013,x43014),x43015),x43016),f773(f773(f9(x43011,f854(a101,a101),f855(a101,f849(f851(x43012)))),f773(f773(f9(x43011,a101,f855(f854(a101,a101),f855(a101,f849(f851(x43012))))),f773(f773(f9(x43011,a101,f855(a101,f855(f854(a101,a101),f855(a101,f849(f851(x43012)))))),x43017),x43014)),x43015)),x43016)),f202(x43011,x43012,x43013,x43017,x43014,x43015,x43016))
% 191.21/191.73 [4204]E(f773(f252(x42041,x42042,x42043,x42044,x42045,x42046),f773(f773(f241(x42041,x42043),x42047),x42048)),f773(f773(f241(x42042,x42044),f773(x42045,x42047)),f773(x42046,x42048)))
% 191.21/191.73 [4303]E(f773(f773(f143(f854(x43031,x43032),f854(x43033,x43034)),f773(f251(x43031,x43032,f854(x43033,x43034)),f773(f773(f9(x43031,f855(x43032,x43034),f855(x43032,f854(x43033,x43034))),f773(f773(f10(f855(x43034,f854(x43033,x43034)),f855(f855(x43032,x43034),f855(x43032,f854(x43033,x43034))),x43031),f10(x43034,f854(x43033,x43034),x43032)),f773(f773(f10(x43033,f855(x43034,f854(x43033,x43034)),x43031),f241(x43033,x43034)),x43035))),x43036))),f773(f773(f167(x43031,x43032),x43037),x43038)),f773(f773(f167(x43033,x43034),f773(f773(f143(x43031,x43033),x43035),x43037)),f773(f773(f143(x43032,x43034),x43036),x43038)))
% 191.21/191.73 [4307]E(f773(f773(f143(f854(x43071,x43072),x43073),f773(f251(x43071,x43072,x43073),f773(f773(f10(f855(x43072,f854(x43071,x43074)),f855(x43072,x43073),x43071),f773(f10(f854(x43071,x43074),x43073,x43072),x43075)),f773(f773(f9(x43071,f855(x43072,x43074),f855(x43072,f854(x43071,x43074))),f773(f773(f10(f855(x43074,f854(x43071,x43074)),f855(f855(x43072,x43074),f855(x43072,f854(x43071,x43074))),x43071),f10(x43074,f854(x43071,x43074),x43072)),f241(x43071,x43074))),x43076)))),f773(f773(f167(x43071,x43072),x43077),x43078)),f773(f773(f143(f854(x43071,x43074),x43073),x43075),f773(f773(f167(x43071,x43074),x43077),f773(f773(f143(x43072,x43074),x43076),x43078))))
% 191.21/191.73 [4235]E(f773(f773(f143(f854(x42351,x42352),x42353),f773(f251(x42351,x42352,x42353),f773(f773(f10(f855(x42352,f854(x42354,x42352)),f855(x42352,x42353),x42351),f773(f10(f854(x42354,x42352),x42353,x42352),x42355)),f773(f773(f10(x42354,f855(x42352,f854(x42354,x42352)),x42351),f241(x42354,x42352)),x42356)))),f773(f773(f167(x42351,x42352),x42357),x42358)),f773(f773(f143(f854(x42354,x42352),x42353),x42355),f773(f773(f167(x42354,x42352),f773(f773(f143(x42351,x42354),x42356),x42357)),x42358)))
% 191.21/191.73 [4195]E(f773(f773(f251(x41951,x41952,x41953),f773(f773(f10(f855(x41952,f854(x41954,x41955)),f855(x41952,x41953),x41951),f773(f10(f854(x41954,x41955),x41953,x41952),f773(f251(x41954,x41955,x41953),x41956))),x41957)),x41958),f773(f773(f251(x41954,x41955,x41953),x41956),f773(f773(f251(x41951,x41952,f854(x41954,x41955)),x41957),x41958)))
% 191.21/191.73 [4308]E(f773(f773(f46(f854(x43081,x43082),f855(f854(x43083,x43084),a841)),f773(f773(f248(x43081,x43082),x43085),f773(f18(f855(x43082,a841),x43081),x43086))),f773(f251(x43081,x43082,f855(f854(x43083,x43084),a841)),f773(f773(f9(x43081,f855(x43082,f855(x43083,f855(x43084,a841))),f855(x43082,f855(f854(x43083,x43084),a841))),f773(f773(f10(f855(f855(x43083,f855(x43084,a841)),f855(f854(x43083,x43084),a841)),f855(f855(x43082,f855(x43083,f855(x43084,a841))),f855(x43082,f855(f854(x43083,x43084),a841))),x43081),f10(f855(x43083,f855(x43084,a841)),f855(f854(x43083,x43084),a841),x43082)),f773(f773(f10(f855(x43083,a841),f855(f855(x43083,f855(x43084,a841)),f855(f854(x43083,x43084),a841)),x43081),f248(x43083,x43084)),x43087))),f773(f773(f10(f855(x43084,a841),f855(x43083,f855(x43084,a841)),x43082),f18(f855(x43084,a841),x43083)),x43088)))),f773(f773(f248(x43083,x43084),f773(f773(f46(x43081,f855(x43083,a841)),x43085),x43087)),f773(f18(f855(x43084,a841),x43083),f773(f773(f46(x43082,f855(x43084,a841)),x43086),x43088))))
% 191.21/191.73 [4338]E(f37(x43381,x43382,x43383,x43384,x43385,x43386,x43387,x43388,x43389,a25),x43382)
% 191.21/191.73 [4339]E(f38(x43391,x43392,x43393,x43394,x43395,x43396,x43397,x43398,x43399,a25),x43392)
% 191.21/191.73 [4249]E(f773(f773(f253(x42491,x42492,x42493,x42494),f773(f773(f253(x42491,x42495,x42496,f854(x42492,x42493)),x42497),x42498)),x42499),f773(f773(f253(x42491,x42495,x42496,x42494),x42497),f773(f773(f9(x42495,f855(x42492,f855(x42493,x42494)),f855(x42496,x42494)),f773(f773(f10(f855(x42496,f854(x42492,x42493)),f855(f855(x42492,f855(x42493,x42494)),f855(x42496,x42494)),x42495),f253(x42496,x42492,x42493,x42494)),x42498)),x42499)))
% 191.21/191.73 [4340]E(f37(x43401,x43402,x43403,x43404,x43405,x43406,x43407,x43408,x43409,f773(a27,x434010)),f773(x43408,x434010))
% 191.21/191.73 [4341]E(f38(x43411,x43412,x43413,x43414,x43415,x43416,x43417,x43418,x43419,f773(a27,x434110)),f773(x43418,x434110))
% 191.21/191.73 [4279]E(f773(f75(f854(x42791,x42792),f854(x42793,x42794),f854(x42795,x42796),f252(x42791,x42793,x42792,x42794,x42797,x42798)),f252(x42795,x42791,x42796,x42792,x42799,x427910)),f252(x42795,x42793,x42796,x42794,f773(f75(x42791,x42793,x42795,x42797),x42799),f773(f75(x42792,x42794,x42796,x42798),x427910)))
% 191.21/191.73 [4342]E(f37(x43421,x43422,x43423,x43424,x43425,x43426,x43427,x43428,x43429,f35(x434210,x434211)),f773(f773(x43427,x434210),x434211))
% 191.21/191.73 [4343]E(f37(x43431,x43432,x43433,x43434,x43435,x43436,x43437,x43438,x43439,f36(x434310,x434311)),f773(f773(x43435,x434310),x434311))
% 191.21/191.73 [4344]E(f37(x43441,x43442,x43443,x43444,x43445,x43446,x43447,x43448,x43449,f28(x434410,x434411)),f773(f773(x43443,x434410),x434411))
% 191.21/191.73 [4345]E(f38(x43451,x43452,x43453,x43454,x43455,x43456,x43457,x43458,x43459,f28(x434510,x434511)),f773(f773(x43453,x434510),x434511))
% 191.21/191.73 [4351]E(f773(f773(f773(x43511,x43512),x43513),f38(x43514,x43515,x43516,x43517,x43518,x43519,x43511,x435110,x435111,x43513)),f38(x43514,x43515,x43516,x43517,x43518,x43519,x43511,x435110,x435111,f35(x43512,x43513)))
% 191.21/191.73 [4355]E(f773(f773(f773(f773(x43551,x43552),x43553),f38(x43554,x43555,x43556,x43557,x43551,x43558,x43559,x435510,x435511,x43552)),f38(x43554,x43555,x43556,x43557,x43551,x43558,x43559,x435510,x435511,x43553)),f38(x43554,x43555,x43556,x43557,x43551,x43558,x43559,x435510,x435511,f36(x43552,x43553)))
% 191.21/191.73 [4284]E(f773(f252(x42841,x42842,x42843,x42844,x42845,x42846),f773(f252(x42847,x42841,x42848,x42843,x42849,x428410),x428411)),f773(f252(x42847,x42842,x42848,x42844,f773(f75(x42841,x42842,x42847,x42845),x42849),f773(f75(x42843,x42844,x42848,x42846),x428410)),x428411))
% 191.21/191.73 [4352]E(f773(f773(f773(f773(x43521,x43522),x43523),x43524),f38(x43525,x43526,x43527,x43521,x43528,x43529,x435210,x435211,x435212,x43524)),f38(x43525,x43526,x43527,x43521,x43528,x43529,x435210,x435211,x435212,f32(x43522,x43523,x43524)))
% 191.21/191.73 [4356]E(f773(f773(f773(f773(f773(x43561,x43562),x43563),x43564),f38(x43565,x43566,x43567,x43568,x43569,x43561,x435610,x435611,x435612,x43563)),f38(x43565,x43566,x43567,x43568,x43569,x43561,x435610,x435611,x435612,x43564)),f38(x43565,x43566,x43567,x43568,x43569,x43561,x435610,x435611,x435612,f33(x43562,x43563,x43564)))
% 191.21/191.73 [4346]E(f37(x43461,x43462,x43463,x43464,x43465,x43466,x43467,x43468,x43469,f33(x434610,x434611,x434612)),f773(f773(f773(x43466,x434610),x434611),x434612))
% 191.21/191.73 [4347]E(f37(x43471,x43472,x43473,x43474,x43475,x43476,x43477,x43478,x43479,f32(x434710,x434711,x434712)),f773(f773(f773(x43474,x434710),x434711),x434712))
% 191.21/191.73 [4348]E(f37(x43481,x43482,x43483,x43484,x43485,x43486,x43487,x43488,x43489,f31(x434810,x434811,x434812)),f773(f773(f773(x43489,x434810),x434811),x434812))
% 191.21/191.73 [4349]E(f38(x43491,x43492,x43493,x43494,x43495,x43496,x43497,x43498,x43499,f31(x434910,x434911,x434912)),f773(f773(f773(x43499,x434910),x434911),x434912))
% 191.21/191.73 [4564]~P142(a329,a862)+P1(f773(a853,a862))
% 191.21/191.73 [6357]P13(a5000)+P1(f773(f773(f334(f854(a843,a842)),a695),f773(f158(f854(a843,a842)),a29)))
% 191.21/191.73 [8400]P13(a5000)+~P1(f773(f773(f251(a843,a842,a841),f773(f18(f855(a842,a841),a843),a26)),a695))
% 191.21/191.73 [4485]~P59(x44851)+P59(f851(x44851))
% 191.21/191.73 [4488]~P138(x44881)+~E(f80(x44881),f2(x44881))
% 191.21/191.73 [4490]~E(x44901,f2(a101))+E(f773(a23,x44901),f2(a1))
% 191.21/191.73 [4491]~E(x44911,f2(a1))+E(f84(a1,x44911),f2(a1))
% 191.21/191.73 [4497]~P2(x44971)+P33(x44971,f2(x44971))
% 191.21/191.73 [4499]~P100(x44991)+P18(x44991,f115(x44991))
% 191.21/191.73 [4508]P1(x45081)+P1(f773(a328,x45081))
% 191.21/191.73 [4549]~P2(x45491)+~P33(x45491,f80(x45491))
% 191.21/191.73 [4594]~P1(x45941)+~P1(f773(a328,x45941))
% 191.21/191.73 [4618]E(f773(a107,x46181),f2(a847))+~P1(f773(a186,x46181))
% 191.21/191.73 [4678]~P91(x46781)+P19(x46781,x46781,f83(x46781))
% 191.21/191.73 [4679]~P100(x46791)+P19(x46791,x46791,f236(x46791))
% 191.21/191.73 [4680]~P100(x46801)+P19(x46801,x46801,f179(x46801))
% 191.21/191.73 [4681]~P92(x46811)+P19(x46811,x46811,f103(x46811))
% 191.21/191.73 [4682]~P98(x46821)+P19(x46821,x46821,f104(x46821))
% 191.21/191.73 [4683]~P64(x46831)+P20(x46831,x46831,f83(x46831))
% 191.21/191.73 [4495]E(x44951,f2(a847))+E(f773(a114,f554(x44951)),x44951)
% 191.21/191.73 [4496]~E(x44961,f2(a847))+E(f773(f102(a1),x44961),f2(a1))
% 191.21/191.73 [4502]~P88(x45021)+E(f773(f106(x45021),a85),f2(x45021))
% 191.21/191.73 [4504]~E(f600(x45041),f2(a847))+E(f773(f155(a847),x45041),f2(a847))
% 191.21/191.73 [4505]~P102(x45051)+E(f234(x45051,f232(x45051)),f236(x45051))
% 191.21/191.73 [4506]~P102(x45061)+E(f235(x45061,f232(x45061)),f179(x45061))
% 191.21/191.73 [4507]~P82(x45071)+E(f84(x45071,f2(x45071)),f2(x45071))
% 191.21/191.73 [4514]~P2(x45141)+E(f773(f102(x45141),f2(a847)),f2(x45141))
% 191.21/191.73 [4515]~P2(x45151)+E(f773(f102(x45151),f80(a847)),f80(x45151))
% 191.21/191.73 [4516]~P133(x45161)+E(f773(f105(x45161),f2(a1)),f2(x45161))
% 191.21/191.73 [4517]~P133(x45171)+E(f773(f105(x45171),f80(a1)),f80(x45171))
% 191.21/191.73 [4518]E(x45181,f2(a847))+~E(f773(f102(a1),x45181),f2(a1))
% 191.21/191.73 [4543]~P69(x45431)+E(f773(f81(x45431),f2(x45431)),f2(x45431))
% 191.21/191.73 [4544]~P90(x45441)+E(f773(f81(x45441),f239(x45441)),f180(x45441))
% 191.21/191.73 [4545]~P90(x45451)+E(f773(f81(x45451),f180(x45451)),f239(x45451))
% 191.21/191.73 [4546]~P79(x45461)+E(f773(f77(x45461),f2(x45461)),f2(x45461))
% 191.21/191.73 [4547]~P110(x45471)+E(f773(f77(x45471),f80(x45471)),f80(x45471))
% 191.21/191.73 [4548]~P67(x45481)+E(f773(f155(x45481),f115(x45481)),f2(x45481))
% 191.21/191.73 [4570]~P35(x45701)+P38(f773(f158(a1),x45701))
% 191.21/191.73 [4599]~P88(x45991)+E(f773(f81(x45991),f80(x45991)),f773(f106(x45991),a99))
% 191.21/191.73 [4617]~P88(x46171)+P33(x46171,f773(f106(x46171),a85))
% 191.21/191.73 [4642]P35(x46421)+~P38(f773(f158(a1),x46421))
% 191.21/191.73 [4684]E(f773(f102(a1),f773(a107,x46841)),x46841)+P1(f773(a186,x46841))
% 191.21/191.73 [4750]~P105(x47501)+E(f243(x47501,f80(x47501),f83(x47501)),f242(x47501))
% 191.21/191.73 [4778]~P88(x47781)+~P33(x47781,f773(f106(x47781),a99))
% 191.21/191.73 [4788]E(f773(a30,x47881),f183(a842))+P1(f773(a26,f773(a27,x47881)))
% 191.21/191.73 [4918]E(f773(f77(a1),x49181),x49181)+P1(f773(f773(f233(a1),x49181),f2(a1)))
% 191.21/191.73 [4938]~E(f773(a107,x49381),f2(a847))+P1(f773(f773(f232(a1),x49381),f2(a1)))
% 191.21/191.73 [4973]~E(f773(f77(a1),x49731),f80(a1))+P1(f773(f773(f279(a1),x49731),f80(a1)))
% 191.21/191.73 [5003]~P1(f773(a186,x50031))+P1(f773(f773(f233(a1),x50031),f2(a1)))
% 191.21/191.73 [5043]~P2(x50431)+P1(f773(f773(f334(x50431),f2(x50431)),f176(x50431)))
% 191.21/191.73 [5044]~P133(x50441)+P1(f773(f773(f334(x50441),f2(x50441)),f112(x50441)))
% 191.21/191.73 [5045]~P2(x50451)+P1(f773(f773(f334(x50451),f80(x50451)),f176(x50451)))
% 191.21/191.73 [5046]~P133(x50461)+P1(f773(f773(f334(x50461),f80(x50461)),f112(x50461)))
% 191.21/191.73 [5047]~P117(x50471)+P1(f773(f773(f233(x50471),f2(x50471)),f80(x50471)))
% 191.21/191.73 [5048]~P117(x50481)+P1(f773(f773(f232(x50481),f2(x50481)),f80(x50481)))
% 191.21/191.73 [5051]E(f773(f227(a842),f449(x50511)),f773(a30,x50511))+~P1(f773(a26,f773(a27,x50511)))
% 191.21/191.73 [5052]E(f773(f227(a842),f471(x50521)),f773(a30,x50521))+~P1(f773(a26,f773(a27,x50521)))
% 191.21/191.73 [5102]E(x51021,f2(a847))+~P1(f773(f773(f232(a847),x51021),f2(a847)))
% 191.21/191.73 [5103]E(x51031,f80(a847))+~P1(f773(f773(f279(a847),x51031),f80(a847)))
% 191.21/191.73 [5145]E(f773(a107,x51451),f2(a847))+~P1(f773(f773(f232(a1),x51451),f2(a1)))
% 191.21/191.73 [5173]E(f773(f77(a1),x51731),f80(a1))+~P1(f773(f773(f279(a1),x51731),f80(a1)))
% 191.21/191.73 [5200]P1(f773(a186,x52001))+~P1(f773(f773(f233(a1),x52001),f2(a1)))
% 191.21/191.73 [5205]~P100(x52051)+P20(x52051,f848(x52051),f138(x52051,x52051,f7(x52051)))
% 191.21/191.73 [5223]P38(x52231)+~P1(f773(f773(f232(a1),f2(a1)),f338(x52231)))
% 191.21/191.73 [5229]E(f773(f77(a1),x52291),f773(f81(a1),x52291))+~P1(f773(f773(f233(a1),x52291),f2(a1)))
% 191.21/191.73 [5398]~P117(x53981)+~P1(f773(f773(f233(x53981),f80(x53981)),f2(x53981)))
% 191.21/191.73 [5399]~P117(x53991)+~P1(f773(f773(f232(x53991),f80(x53991)),f2(x53991)))
% 191.21/191.73 [5411]~E(x54111,f2(a1))+P1(f773(f773(f233(a1),f773(f77(a1),x54111)),f80(a1)))
% 191.21/191.73 [5412]~E(x54121,f2(a847))+P1(f773(f773(f232(a1),f773(f102(a1),x54121)),f2(a1)))
% 191.21/191.73 [5526]~P67(x55261)+E(f132(x55261,x55261,f82(x55261),f2(x55261)),f155(x55261))
% 191.21/191.73 [5701]~P86(x57011)+P29(a847,x57011,f102(x57011),f239(f855(a847,a841)))
% 191.21/191.73 [5898]E(x58981,f2(a847))+~P1(f773(f773(f232(a1),f773(f102(a1),x58981)),f2(a1)))
% 191.21/191.73 [5899]E(x58991,f2(a1))+~P1(f773(f773(f233(a1),f773(f77(a1),x58991)),f80(a1)))
% 191.21/191.73 [6730]~P1(f773(f773(f233(a1),x67301),f2(a1)))+P1(f773(f773(f233(a1),f773(f773(f82(a1),x67301),x67301)),f2(a1)))
% 191.21/191.73 [7305]P1(f773(f773(f233(a1),x73051),f2(a1)))+~P1(f773(f773(f233(a1),f773(f773(f82(a1),x73051),x73051)),f2(a1)))
% 191.21/191.73 [7870]E(x78701,f773(a5,f2(a847)))+P1(f773(f773(f233(a847),f773(f773(f3(a847),f773(a22,x78701)),f773(a114,f2(a847)))),f773(a22,x78701)))
% 191.21/191.73 [8612]~P1(f773(f773(f233(a1),x86121),f2(a1)))+P1(f773(f773(f233(a1),f773(f773(f3(a1),f773(f773(f82(a1),x86121),x86121)),a99)),f2(a1)))
% 191.21/191.73 [8696]~P1(f773(f773(f233(a1),x86961),f2(a1)))+P1(f773(f773(f233(a1),f773(f773(f82(a1),f773(f773(f82(a1),f80(a1)),x86961)),x86961)),f2(a1)))
% 191.21/191.73 [8980]P1(f773(f773(f233(a1),x89801),f2(a1)))+~P1(f773(f773(f233(a1),f773(f773(f3(a1),f773(f773(f82(a1),x89801),x89801)),a99)),f2(a1)))
% 191.21/191.73 [9044]P1(f773(f773(f233(a1),x90441),f2(a1)))+~P1(f773(f773(f233(a1),f773(f773(f82(a1),f773(f773(f82(a1),f80(a1)),x90441)),x90441)),f2(a1)))
% 191.21/191.73 [4587]~E(a85,x45871)+E(f773(f773(f82(a1),x45871),x45871),a85)
% 191.21/191.73 [4588]~E(x45881,a85)+E(f773(f773(f82(a1),x45881),x45881),a85)
% 191.21/191.73 [4603]E(x46031,f2(a1))+E(f773(f773(f43(a1),x46031),x46031),f80(a1))
% 191.21/191.73 [4728]E(x47281,a85)+~E(f773(f773(f82(a1),x47281),x47281),a85)
% 191.21/191.73 [4729]E(a85,x47291)+~E(f773(f773(f82(a1),x47291),x47291),a85)
% 191.21/191.73 [4740]~P9(x47401)+E(f45(x47401,f239(f855(x47401,a841))),f180(x47401))
% 191.21/191.73 [4741]~P9(x47411)+E(f45(x47411,f180(f855(x47411,a841))),f239(x47411))
% 191.21/191.73 [4742]~P9(x47421)+E(f44(x47421,f239(f855(x47421,a841))),f239(x47421))
% 191.21/191.73 [4743]~P9(x47431)+E(f44(x47431,f180(f855(x47431,a841))),f180(x47431))
% 191.21/191.73 [4744]~P100(x47441)+E(f130(x47441,f180(f855(x47441,a841))),f115(x47441))
% 191.21/191.73 [4878]E(x48781,f2(a847))+P1(f773(f773(f233(a847),f2(a847)),x48781))
% 191.21/191.73 [4898]~P10(x48981)+P1(f773(f773(f232(a1),f2(a1)),x48981))
% 191.21/191.73 [4929]~E(f773(f106(a847),x49291),f2(a847))+P1(f773(f773(f232(a1),x49291),a85))
% 191.21/191.73 [4934]P38(x49341)+P1(f773(f773(f334(a1),f338(x49341)),x49341))
% 191.21/191.73 [4935]E(x49351,f773(a5,f2(a847)))+P1(f773(f773(f232(a101),f80(a101)),x49351))
% 191.21/191.73 [4978]P1(f773(a186,x49781))+P1(f773(f773(f232(a1),f2(a1)),x49781))
% 191.21/191.73 [5025]E(f773(f102(a1),f773(a107,x50251)),f2(a1))+P1(f773(f773(f232(a1),f2(a1)),x50251))
% 191.21/191.73 [5090]E(f773(f102(a1),f773(f106(a847),x50901)),f773(f106(a1),x50901))+P1(f773(a186,f773(f106(a1),x50901)))
% 191.21/191.73 [5110]E(f773(f106(a847),x51101),f2(a847))+~P1(f773(a186,f773(f106(a1),x51101)))
% 191.21/191.73 [5111]E(f773(f106(a847),x51111),f2(a847))+~P1(f773(f773(f232(a1),x51111),a85))
% 191.21/191.73 [5142]P10(x51421)+~P1(f773(f773(f232(a1),f2(a1)),x51421))
% 191.21/191.73 [5208]E(f773(a114,f579(x52081)),x52081)+~P1(f773(f773(f233(a847),f2(a847)),x52081))
% 191.21/191.73 [5209]E(f773(a114,f617(x52091)),x52091)+~P1(f773(f773(f233(a847),f2(a847)),x52091))
% 191.21/191.73 [5217]E(f773(a114,f773(f106(a847),x52171)),f80(a847))+~P1(f773(a186,f773(f106(a1),x52171)))
% 191.21/191.73 [5225]E(f773(f102(a1),f625(x52251)),x52251)+~P1(f773(f773(f233(a1),f2(a1)),x52251))
% 191.21/191.73 [5232]~E(x52321,f773(a5,f2(a847)))+~P1(f773(f773(f232(a101),f80(a101)),x52321))
% 191.21/191.73 [5239]E(f773(f102(a1),f773(f106(a847),x52391)),f2(a1))+~P1(f773(a186,f773(f106(a1),x52391)))
% 191.21/191.73 [5263]E(f773(f155(a847),x52631),f2(a847))+P1(f773(f773(f334(a847),f600(x52631)),f773(f158(a847),x52631)))
% 191.21/191.73 [5283]E(f773(f102(a1),f773(a107,x52831)),x52831)+~P1(f773(f773(f232(a1),f2(a1)),x52831))
% 191.21/191.73 [5292]~P1(f773(a186,x52921))+~P1(f773(f773(f232(a1),f2(a1)),x52921))
% 191.21/191.73 [5391]E(f773(f773(f82(a847),f80(a847)),f773(f106(a847),x53911)),f80(a847))+~P1(f773(f773(f233(a1),x53911),a85))
% 191.21/191.73 [5448]E(x54481,f2(a847))+~P1(f773(f773(f233(a847),x54481),f773(a114,f2(a847))))
% 191.21/191.73 [5469]E(x54691,f773(a114,f2(a847)))+~P1(f773(f773(f279(a847),x54691),f773(a114,f2(a847))))
% 191.21/191.73 [5487]E(f773(f773(f82(a847),f773(f106(a847),x54871)),f80(a847)),f80(a847))+~P1(f773(f773(f233(a1),x54871),a85))
% 191.21/191.73 [5488]E(f773(f773(f3(a847),f773(f106(a847),x54881)),f80(a847)),f2(a847))+~P1(f773(f773(f232(a1),x54881),a85))
% 191.21/191.73 [5498]~P38(x54981)+E(f773(f42(a847),f773(f303(a1,a847,a107),x54981)),f773(f42(a1),x54981))
% 191.21/191.73 [5527]~P100(x55271)+E(f234(x55271,f773(f9(x55271,x55271,a841),f232(x55271))),f179(x55271))
% 191.21/191.73 [5528]~P100(x55281)+E(f235(x55281,f773(f9(x55281,x55281,a841),f232(x55281))),f236(x55281))
% 191.21/191.73 [5537]E(f52(a847,f773(a114,f2(a847)),f773(f106(a847),x55371)),f773(a114,f2(a847)))+~P1(f773(a186,f773(f106(a1),x55371)))
% 191.21/191.73 [5545]P1(f773(f773(f233(a1),f2(a1)),x55451))+~P1(f773(f773(f232(a1),f80(a1)),x55451))
% 191.21/191.73 [5546]~P1(f773(f773(f233(a1),f2(a1)),x55461))+P1(f773(f773(f232(a1),f80(a1)),x55461))
% 191.21/191.73 [5556]E(f773(a114,f773(f773(f3(a847),x55561),f80(a847))),x55561)+~P1(f773(f773(f233(a847),f2(a847)),x55561))
% 191.21/191.73 [5614]P1(f773(f773(f233(a847),f2(a847)),f625(x56141)))+~P1(f773(f773(f233(a1),f2(a1)),x56141))
% 191.21/191.73 [5671]E(f52(a1,f773(f106(a1),a99),x56711),f773(f773(f3(a1),x56711),f80(a1)))+~P1(f773(f773(f233(a1),f2(a1)),x56711))
% 191.21/191.73 [5716]~P1(f773(f773(f233(a1),a85),x57161))+P1(f773(f773(f233(a847),f2(a847)),f773(f106(a847),x57161)))
% 191.21/191.73 [5770]P1(f773(f773(f233(a847),f2(a847)),f773(a107,x57701)))+~P1(f773(f773(f233(a1),f2(a1)),x57701))
% 191.21/191.73 [5817]~P1(f773(f773(f233(a847),f2(a847)),x58171))+P1(f773(f773(f233(a1),f2(a1)),f773(f102(a1),x58171)))
% 191.21/191.73 [5852]~P1(f773(f773(f233(a847),f2(a847)),f773(a107,x58521)))+P1(f773(f773(f233(a1),f2(a1)),x58521))
% 191.21/191.73 [5867]~P38(x58671)+E(f773(f303(a847,a1,f102(a1)),f773(f303(a1,a847,a107),x58671)),x58671)
% 191.21/191.73 [5878]P1(f773(f773(f233(a1),a85),x58781))+~P1(f773(f773(f233(a847),f2(a847)),f773(f106(a847),x58781)))
% 191.21/191.73 [5940]P1(f773(f773(f233(a847),f2(a847)),x59401))+~P1(f773(f773(f233(a1),f2(a1)),f773(f102(a1),x59401)))
% 191.21/191.73 [6056]E(f773(f303(a847,a1,f102(a1)),f773(f257(a847),f773(a107,x60561))),f773(f294(a1,f2(a1)),x60561))+~P1(f773(f773(f232(a1),f2(a1)),x60561))
% 191.21/191.73 [6072]~P117(x60721)+P1(f773(f773(f233(x60721),f2(x60721)),f773(f773(f82(x60721),f80(x60721)),f80(x60721))))
% 191.21/191.73 [6123]P1(f773(f773(f233(a847),f773(a114,f2(a847))),f773(a107,x61231)))+~P1(f773(f773(f233(a1),f80(a1)),x61231))
% 191.21/191.73 [6220]E(x62201,f2(a1))+P1(f773(f56(f2(a1),x62201),f773(f773(f241(a1,a1),f2(a1)),f2(a1))))
% 191.21/191.73 [6400]~P1(f773(f773(f233(a847),f773(a114,f2(a847))),f773(a107,x64001)))+P1(f773(f773(f233(a1),f80(a1)),x64001))
% 191.21/191.73 [6852]~P107(x68521)+P36(x68521,f773(f256(f854(x68521,x68521)),f773(f251(x68521,x68521,a841),f233(x68521))))
% 191.21/191.73 [5108]~P35(x51081)+E(f129(f773(f773(f143(a1,a847),a107),x51081)),x51081)
% 191.21/191.73 [5438]E(f773(f106(a847),f773(f773(f3(a1),x54381),a99)),f773(a114,f773(f106(a847),x54381)))+P1(f773(a186,f773(f106(a1),x54381)))
% 191.21/191.73 [5463]P31(a840,a861,x54631)+~P1(f773(f773(f334(f846(a840)),x54631),a857))
% 191.21/191.73 [5562]E(f773(f81(a1),f773(f102(a1),f773(a114,f683(x55621)))),x55621)+~P1(f773(f773(f233(a1),x55621),f2(a1)))
% 191.21/191.73 [5572]E(f773(f773(f82(a847),f80(a847)),f773(f106(a847),x55721)),f773(f106(a847),f773(f773(f3(a1),x55721),a99)))+P1(f773(f773(f233(a1),x55721),a85))
% 191.21/191.73 [5616]E(f773(f773(f43(a1),f773(f106(a1),a99)),x56161),f773(f106(a1),a99))+~P1(f773(f773(f233(a1),f2(a1)),x56161))
% 191.21/191.73 [5712]E(f773(f773(f82(a847),f773(f106(a847),x57121)),f80(a847)),f773(f106(a847),f773(f773(f3(a1),x57121),a99)))+P1(f773(f773(f233(a1),x57121),a85))
% 191.21/191.73 [5713]E(f773(f773(f3(a847),f773(f106(a847),x57131)),f80(a847)),f773(f106(a847),f773(f773(f82(a1),x57131),a99)))+P1(f773(f773(f232(a1),x57131),a85))
% 191.21/191.73 [5756]E(f773(a107,f773(f773(f82(a1),f80(a1)),x57561)),f773(a114,f773(a107,x57561)))+~P1(f773(f773(f232(a1),f2(a1)),x57561))
% 191.21/191.73 [5794]E(f773(a114,f773(f773(f3(a847),x57941),f773(a114,f2(a847)))),x57941)+~P1(f773(f773(f233(a847),f2(a847)),x57941))
% 191.21/191.73 [6001]E(f52(a847,f773(a114,f2(a847)),f773(f106(a847),x60011)),f773(a107,f52(a1,f80(a1),f773(f106(a1),x60011))))+P1(f773(a186,f773(f106(a1),x60011)))
% 191.21/191.73 [6047]~P1(f773(f773(f233(a1),a99),x60471))+P1(f773(f773(f233(a1),a99),f773(f773(f82(a1),x60471),x60471)))
% 191.21/191.73 [6048]~P1(f773(f773(f233(a1),a85),x60481))+P1(f773(f773(f233(a1),a85),f773(f773(f82(a1),x60481),x60481)))
% 191.21/191.73 [6049]~P1(f773(f773(f233(a1),a99),x60491))+P1(f773(f773(f232(a1),a99),f773(f773(f82(a1),x60491),x60491)))
% 191.21/191.73 [6050]~P1(f773(f773(f232(a1),a85),x60501))+P1(f773(f773(f232(a1),a85),f773(f773(f82(a1),x60501),x60501)))
% 191.21/191.73 [6234]~P1(f773(f63(x62341),f239(f855(x62341,a841))))+P1(f773(f63(f851(x62341)),f239(f855(f851(x62341),a841))))
% 191.21/191.73 [6325]~P1(f773(f773(f232(a1),f2(a1)),x63251))+P1(f773(f773(f233(a1),f2(a1)),f773(f773(f82(a1),f80(a1)),x63251)))
% 191.21/191.73 [6331]E(f773(f240(a1,a1),f54(f80(a1),f773(f106(a1),x63311))),f773(f773(f43(a1),f80(a1)),f773(f106(a1),x63311)))+~P1(f773(f773(f232(a1),f2(a1)),f773(f106(a1),x63311)))
% 191.21/191.73 [6356]E(f773(f250(a1,a1),f54(f80(a1),f773(f106(a1),x63561))),f52(a1,f80(a1),f773(f106(a1),x63561)))+~P1(f773(f773(f232(a1),f2(a1)),f773(f106(a1),x63561)))
% 191.21/191.73 [6369]P1(f773(f63(x63691),f239(f855(x63691,a841))))+~P1(f773(f63(f851(x63691)),f239(f855(f851(x63691),a841))))
% 191.21/191.73 [6401]P1(f773(f773(f233(a1),a99),x64011))+~P1(f773(f773(f233(a1),a99),f773(f773(f82(a1),x64011),x64011)))
% 191.21/191.73 [6402]P1(f773(f773(f233(a1),a99),x64021))+~P1(f773(f773(f232(a1),a99),f773(f773(f82(a1),x64021),x64021)))
% 191.21/191.73 [6403]P1(f773(f773(f233(a1),a85),x64031))+~P1(f773(f773(f233(a1),a85),f773(f773(f82(a1),x64031),x64031)))
% 191.21/191.73 [6404]P1(f773(f773(f232(a1),a85),x64041))+~P1(f773(f773(f232(a1),a85),f773(f773(f82(a1),x64041),x64041)))
% 191.21/191.73 [6736]~P1(f773(f63(x67361),f239(f855(x67361,a841))))+P1(f773(f773(f233(a847),f2(a847)),f773(f42(x67361),f239(f855(x67361,a841)))))
% 191.21/191.73 [7350]P1(f773(f63(a847),x73501))+~P1(f773(f63(a1),f773(f303(a847,a1,f102(a1)),x73501)))
% 191.21/191.73 [5366]~E(a99,x53661)+E(f773(f773(f3(a1),f773(f773(f82(a1),x53661),x53661)),a99),a99)
% 191.21/191.73 [5367]~E(x53671,a99)+E(f773(f773(f3(a1),f773(f773(f82(a1),x53671),x53671)),a99),a99)
% 191.21/191.73 [5872]E(x58721,a99)+~E(f773(f773(f3(a1),f773(f773(f82(a1),x58721),x58721)),a99),a99)
% 191.21/191.73 [5873]E(a99,x58731)+~E(f773(f773(f3(a1),f773(f773(f82(a1),x58731),x58731)),a99),a99)
% 191.21/191.73 [6294]~E(f773(f106(a847),x62941),f2(a847))+P1(f773(a186,f773(f106(a1),f773(f773(f82(a1),x62941),a99))))
% 191.21/191.73 [6660]~P1(f773(a186,f773(f106(a1),x66601)))+P1(f773(a186,f773(f106(a1),f773(f773(f82(a1),x66601),x66601))))
% 191.21/191.73 [6661]~P1(f773(f773(f232(a1),x66611),a99))+P1(f773(f773(f233(a1),f773(f773(f82(a1),x66611),x66611)),a99))
% 191.21/191.73 [6662]~P1(f773(f773(f233(a1),x66621),a85))+P1(f773(f773(f233(a1),f773(f773(f82(a1),x66621),x66621)),a85))
% 191.21/191.73 [6663]~P1(f773(f773(f232(a1),x66631),a99))+P1(f773(f773(f232(a1),f773(f773(f82(a1),x66631),x66631)),a99))
% 191.21/191.73 [6664]~P1(f773(f773(f232(a1),x66641),a85))+P1(f773(f773(f232(a1),f773(f773(f82(a1),x66641),x66641)),a85))
% 191.21/191.73 [6994]E(f773(f106(a847),x69941),f2(a847))+~P1(f773(a186,f773(f106(a1),f773(f773(f82(a1),x69941),a99))))
% 191.21/191.73 [7253]~P1(f773(f773(f232(a1),f2(a1)),f773(f106(a1),x72531)))+P1(f773(f773(f232(a1),f2(a1)),f773(f106(a1),f773(f773(f82(a1),x72531),x72531))))
% 191.21/191.73 [7254]P1(f773(a186,f773(f106(a1),x72541)))+~P1(f773(a186,f773(f106(a1),f773(f773(f82(a1),x72541),x72541))))
% 191.21/191.73 [7255]P1(f773(f773(f233(a1),x72551),a85))+~P1(f773(f773(f233(a1),f773(f773(f82(a1),x72551),x72551)),a85))
% 191.21/191.73 [7256]P1(f773(f773(f232(a1),x72561),a99))+~P1(f773(f773(f233(a1),f773(f773(f82(a1),x72561),x72561)),a99))
% 191.21/191.73 [7257]P1(f773(f773(f232(a1),x72571),a99))+~P1(f773(f773(f232(a1),f773(f773(f82(a1),x72571),x72571)),a99))
% 191.21/191.73 [7258]P1(f773(f773(f232(a1),x72581),a85))+~P1(f773(f773(f232(a1),f773(f773(f82(a1),x72581),x72581)),a85))
% 191.21/191.73 [7637]E(f773(a109,f571(x76371)),x76371)+~P1(f773(f773(f334(f855(f854(a847,a847),a841)),x76371),a100))
% 191.21/191.73 [6207]~P88(x62071)+E(f773(f106(x62071),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f80(x62071))
% 191.21/191.73 [6714]~P1(f773(a186,f773(f106(a1),x67141)))+E(f773(f106(a847),f773(f773(f3(a1),f773(f773(f82(a1),x67141),x67141)),a99)),f2(a847))
% 191.21/191.73 [7816]~P1(f773(f773(f233(a1),f773(f106(a1),x78161)),f2(a1)))+E(f773(f240(a1,a1),f773(a58,f57(f773(f81(a1),f80(a1)),f773(f81(a1),f773(f106(a1),x78161))))),f773(f773(f43(a1),f80(a1)),f773(f106(a1),x78161)))
% 191.21/191.73 [7829]~P1(f773(f773(f233(a1),f773(f106(a1),x78291)),f2(a1)))+E(f773(f250(a1,a1),f773(a58,f57(f773(f81(a1),f80(a1)),f773(f81(a1),f773(f106(a1),x78291))))),f52(a1,f80(a1),f773(f106(a1),x78291)))
% 191.21/191.73 [7876]~P1(f773(f773(f233(a1),a99),x78761))+P1(f773(f773(f233(a1),a99),f773(f773(f3(a1),f773(f773(f82(a1),x78761),x78761)),a99)))
% 191.21/191.73 [7877]~P1(f773(f773(f232(a1),a85),x78771))+P1(f773(f773(f233(a1),a85),f773(f773(f3(a1),f773(f773(f82(a1),x78771),x78771)),a99)))
% 191.21/191.73 [7878]~P1(f773(f773(f232(a1),a99),x78781))+P1(f773(f773(f232(a1),a99),f773(f773(f3(a1),f773(f773(f82(a1),x78781),x78781)),a99)))
% 191.21/191.73 [7879]~P1(f773(f773(f232(a1),a85),x78791))+P1(f773(f773(f232(a1),a85),f773(f773(f3(a1),f773(f773(f82(a1),x78791),x78791)),a99)))
% 191.21/191.73 [8176]~P88(x81761)+~P33(x81761,f773(f106(x81761),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))
% 191.21/191.73 [8356]P1(f773(f773(f233(a1),a99),x83561))+~P1(f773(f773(f233(a1),a99),f773(f773(f3(a1),f773(f773(f82(a1),x83561),x83561)),a99)))
% 191.21/191.73 [8357]P1(f773(f773(f232(a1),a99),x83571))+~P1(f773(f773(f232(a1),a99),f773(f773(f3(a1),f773(f773(f82(a1),x83571),x83571)),a99)))
% 191.21/191.73 [8358]P1(f773(f773(f232(a1),a85),x83581))+~P1(f773(f773(f233(a1),a85),f773(f773(f3(a1),f773(f773(f82(a1),x83581),x83581)),a99)))
% 191.21/191.73 [8359]P1(f773(f773(f232(a1),a85),x83591))+~P1(f773(f773(f232(a1),a85),f773(f773(f3(a1),f773(f773(f82(a1),x83591),x83591)),a99)))
% 191.21/191.73 [8655]E(f773(f106(a847),f773(f773(f3(a1),f773(f773(f82(a1),x86551),x86551)),a99)),f773(f773(f88(a847,a847),f773(f106(a847),x86551)),f773(f773(f10(a847,a847,a847),a114),f773(f773(f20(a847,a847,a847),f82(a847)),f7(a847)))))+P1(f773(a186,f773(f106(a1),x86551)))
% 191.21/191.73 [9428]E(x94281,f180(f855(f854(a847,a847),a841)))+P1(f773(f773(f334(f854(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841))),f773(f773(f241(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841)),x94281),f180(f855(f854(a847,a847),a841)))),a70))
% 191.21/191.73 [8589]~P1(f773(a186,f773(f106(a1),x85891)))+P1(f773(a186,f773(f106(a1),f773(f773(f3(a1),f773(f773(f82(a1),x85891),x85891)),a99))))
% 191.21/191.73 [8590]~P1(f773(f773(f233(a1),x85901),a99))+P1(f773(f773(f233(a1),f773(f773(f3(a1),f773(f773(f82(a1),x85901),x85901)),a99)),a99))
% 191.21/191.73 [8591]~P1(f773(f773(f233(a1),x85911),a85))+P1(f773(f773(f233(a1),f773(f773(f3(a1),f773(f773(f82(a1),x85911),x85911)),a99)),a85))
% 191.21/191.73 [8592]~P1(f773(f773(f232(a1),x85921),a99))+P1(f773(f773(f232(a1),f773(f773(f3(a1),f773(f773(f82(a1),x85921),x85921)),a99)),a99))
% 191.21/191.73 [8593]~P1(f773(f773(f233(a1),x85931),a85))+P1(f773(f773(f232(a1),f773(f773(f3(a1),f773(f773(f82(a1),x85931),x85931)),a99)),a85))
% 191.21/191.73 [8689]~P1(f773(f773(f232(a1),f2(a1)),f773(f106(a1),x86891)))+P1(f773(f773(f232(a1),f2(a1)),f773(f106(a1),f773(f773(f3(a1),f773(f773(f82(a1),x86891),x86891)),a99))))
% 191.21/191.73 [8819]~P88(x88191)+E(f773(f773(f82(x88191),f80(x88191)),f80(x88191)),f773(f106(x88191),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))
% 191.21/191.73 [8966]P1(f773(a186,f773(f106(a1),x89661)))+~P1(f773(a186,f773(f106(a1),f773(f773(f3(a1),f773(f773(f82(a1),x89661),x89661)),a99))))
% 191.21/191.73 [8967]P1(f773(f773(f233(a1),x89671),a99))+~P1(f773(f773(f233(a1),f773(f773(f3(a1),f773(f773(f82(a1),x89671),x89671)),a99)),a99))
% 191.21/191.73 [8968]P1(f773(f773(f233(a1),x89681),a85))+~P1(f773(f773(f233(a1),f773(f773(f3(a1),f773(f773(f82(a1),x89681),x89681)),a99)),a85))
% 191.21/191.73 [8969]P1(f773(f773(f233(a1),x89691),a85))+~P1(f773(f773(f232(a1),f773(f773(f3(a1),f773(f773(f82(a1),x89691),x89691)),a99)),a85))
% 191.21/191.73 [8970]P1(f773(f773(f232(a1),x89701),a99))+~P1(f773(f773(f232(a1),f773(f773(f3(a1),f773(f773(f82(a1),x89701),x89701)),a99)),a99))
% 191.21/191.73 [9476]~P1(f773(f63(f854(a847,a847)),x94761))+P1(f773(f773(f334(f854(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841))),f773(f773(f241(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841)),f180(f855(f854(a847,a847),a841))),x94761)),a71))
% 191.21/191.73 [9262]~P2(x92621)+E(f773(f773(f242(x92621),f2(x92621)),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),f2(x92621))
% 191.21/191.73 [9263]~P2(x92631)+E(f773(f773(f242(x92631),f80(x92631)),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),f80(x92631))
% 191.21/191.73 [9673]~P1(f773(f773(f233(a847),f80(a847)),x96731))+P1(f773(f773(f233(a847),f2(a847)),f773(f773(f43(a847),x96731),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))))
% 191.21/191.73 [9679]~P1(f773(f773(f233(a847),f2(a847)),x96791))+P1(f773(f773(f233(a847),f2(a847)),f773(f773(f43(a847),f773(f773(f82(a847),x96791),f80(a847))),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))))
% 191.21/191.73 [9718]~E(f52(a847,x97181,f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),f80(a847))+P1(f773(f773(f233(a847),f2(a847)),f52(a847,x97181,f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))))
% 191.21/191.73 [9753]E(f52(a847,x97531,f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),f80(a847))+~P1(f773(f773(f233(a847),f2(a847)),f52(a847,x97531,f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))))
% 191.21/191.73 [4522]~P36(x45221,x45222)+P56(x45221,x45222)
% 191.21/191.73 [4523]~P42(x45231,x45232)+P56(x45231,x45232)
% 191.21/191.73 [4486]~E(x44861,x44862)+E(f266(x44861,x44862),f80(a101))
% 191.21/191.73 [4489]E(f211(x44891,x44892),x44891)+~E(x44892,f2(a847))
% 191.21/191.73 [4494]P37(x44941,x44942)+~E(x44942,f183(x44941))
% 191.21/191.73 [4500]~P37(x45002,x45001)+E(x45001,f183(x45002))
% 191.21/191.73 [4527]~P99(x45272)+P99(f855(x45271,x45272))
% 191.21/191.73 [4528]~P103(x45282)+P103(f855(x45281,x45282))
% 191.21/191.73 [4529]~P102(x45292)+P102(f855(x45291,x45292))
% 191.21/191.73 [4530]~P90(x45302)+P90(f855(x45301,x45302))
% 191.21/191.73 [4531]~P84(x45312)+P84(f855(x45311,x45312))
% 191.21/191.73 [4532]~P71(x45322)+P71(f855(x45321,x45322))
% 191.21/191.73 [4533]~P93(x45332)+P92(f855(x45331,x45332))
% 191.21/191.73 [4534]~P93(x45342)+P93(f855(x45341,x45342))
% 191.21/191.73 [4535]~P9(x45352)+P9(f855(x45351,x45352))
% 191.21/191.73 [4536]~P106(x45362)+P106(f855(x45361,x45362))
% 191.21/191.73 [4537]~P96(x45372)+P94(f855(x45371,x45372))
% 191.21/191.73 [4538]~P101(x45382)+P101(f855(x45381,x45382))
% 191.21/191.73 [4539]~P96(x45392)+P95(f855(x45391,x45392))
% 191.21/191.73 [4540]~P97(x45402)+P97(f855(x45401,x45402))
% 191.21/191.73 [4541]~P93(x45412)+P98(f855(x45411,x45412))
% 191.21/191.73 [4542]~P96(x45422)+P96(f855(x45421,x45422))
% 191.21/191.73 [4555]E(x45551,x45552)+~E(f773(a114,x45551),f773(a114,x45552))
% 191.21/191.73 [4556]E(x45561,x45562)+~E(f773(a27,x45561),f773(a27,x45562))
% 191.21/191.73 [4557]E(x45571,x45572)+~E(f773(a5,x45571),f773(a5,x45572))
% 191.21/191.73 [4559]E(x45591,x45592)+~E(f773(a22,x45591),f773(a22,x45592))
% 191.21/191.73 [4560]E(x45601,x45602)+~E(f773(a109,x45601),f773(a109,x45602))
% 191.21/191.73 [4658]~P7(x46581)+E(f52(x46581,x46582,x46582),f2(x46581))
% 191.21/191.73 [4691]~P36(x46911,x46912)+P36(f848(x46911),f136(x46911,x46912))
% 191.21/191.73 [4692]~P36(x46921,x46922)+P36(f848(x46921),f135(x46921,x46922))
% 191.21/191.73 [4783]~P36(x47831,x47832)+P36(f855(x47831,a841),f326(x47831,x47832))
% 191.21/191.73 [4784]~P36(x47841,x47842)+P36(f855(x47841,a841),f324(x47841,x47842))
% 191.21/191.73 [4903]~P10(x49031)+P38(f295(a1,x49031,x49032))
% 191.21/191.73 [5006]~P36(x50061,x50062)+P58(x50061,f69(x50061,x50061,x50062))
% 191.21/191.73 [5492]~P77(x54921)+P29(x54921,x54921,f81(x54921),x54922)
% 191.21/191.73 [4510]~E(x45102,f115(x45101))+E(f773(f141(x45101),x45102),f115(x45101))
% 191.21/191.73 [4511]~E(x45112,f115(x45111))+E(f773(f142(x45111),x45112),f115(x45111))
% 191.21/191.73 [4565]E(x45651,f773(a107,x45652))+~E(f773(f102(a1),x45651),x45652)
% 191.21/191.73 [4568]E(x45681,f115(x45682))+~E(f773(f141(x45682),x45681),f115(x45682))
% 191.21/191.73 [4569]E(x45691,f115(x45692))+~E(f773(f142(x45692),x45691),f115(x45692))
% 191.21/191.73 [4584]~P88(x45841)+E(f773(f106(x45841),x45842),f773(f105(x45841),x45842))
% 191.21/191.73 [4591]~E(x45912,f183(x45911))+E(f226(x45911,x45912),f180(f855(x45911,a841)))
% 191.21/191.73 [4593]~P59(x45931)+P1(f773(f63(x45931),x45932))
% 191.21/191.73 [4600]E(x46001,f183(x46002))+E(f773(f227(x46002),f491(x46002,x46001)),x46001)
% 191.21/191.73 [4601]E(x46011,f183(x46012))+E(f773(f227(x46012),f492(x46012,x46011)),x46011)
% 191.21/191.73 [4602]E(x46021,f183(x46022))+E(f773(f227(x46022),f503(x46022,x46021)),x46021)
% 191.21/191.73 [4604]~E(f721(x46042,x46041),f115(x46041))+E(f164(x46041,x46042),f115(f848(x46041)))
% 191.21/191.73 [4613]~E(x46132,f115(x46131))+E(f773(f158(x46131),x46132),f180(f855(x46131,a841)))
% 191.21/191.73 [4614]~E(x46142,f115(x46141))+E(f180(f855(x46141,a841)),f773(f158(x46141),x46142))
% 191.21/191.73 [4616]E(x46161,x46162)+~E(f773(f102(a1),x46161),f773(f102(a1),x46162))
% 191.21/191.73 [4619]E(f209(x46191,x46192),f2(a847))+P1(f773(f63(x46191),x46192))
% 191.21/191.73 [4637]~P110(x46371)+E(f84(x46371,f84(x46371,x46372)),f84(x46371,x46372))
% 191.21/191.73 [4649]~P85(x46491)+E(f773(f773(f242(x46491),x46492),f80(a847)),x46492)
% 191.21/191.73 [4650]~P75(x46501)+E(f773(f773(f242(x46501),x46502),f80(a847)),x46502)
% 191.21/191.73 [4652]E(x46521,x46522)+E(f266(x46521,x46522),f773(f773(f82(a101),x46522),f80(a101)))
% 191.21/191.73 [4655]E(f773(f42(x46551),x46552),f2(a847))+P1(f773(f63(x46551),x46552))
% 191.21/191.73 [4661]~P66(x46611)+E(f773(f773(f82(x46611),x46612),f2(x46611)),x46612)
% 191.21/191.73 [4662]~P67(x46621)+E(f773(f773(f82(x46621),x46622),f2(x46621)),x46622)
% 191.21/191.73 [4663]~P85(x46631)+E(f773(f773(f82(x46631),x46632),f2(x46631)),x46632)
% 191.21/191.73 [4664]~P85(x46641)+E(f773(f773(f83(x46641),x46642),f80(x46641)),x46642)
% 191.21/191.73 [4665]~P70(x46651)+E(f773(f773(f83(x46651),x46652),f80(x46651)),x46652)
% 191.21/191.73 [4666]~P75(x46661)+E(f773(f773(f83(x46661),x46662),f80(x46661)),x46662)
% 191.21/191.73 [4667]~P7(x46671)+E(f773(f773(f43(x46671),x46672),f80(x46671)),x46672)
% 191.21/191.73 [4668]~P69(x46681)+E(f773(f773(f3(x46681),x46682),f2(x46681)),x46682)
% 191.21/191.73 [4669]~P113(x46691)+E(f773(f773(f283(x46691),x46692),f80(x46691)),x46692)
% 191.21/191.73 [4670]~P95(x46701)+E(f773(f773(f103(x46701),x46702),f180(x46701)),x46702)
% 191.21/191.73 [4671]~P94(x46711)+E(f773(f773(f104(x46711),x46712),f239(x46711)),x46712)
% 191.21/191.73 [4672]~P85(x46721)+E(f773(f773(f242(x46721),x46722),f2(a847)),f80(x46721))
% 191.21/191.73 [4673]~P105(x46731)+E(f773(f773(f242(x46731),x46732),f2(a847)),f80(x46731))
% 191.21/191.73 [4674]~E(x46742,f180(f855(x46741,a841)))+E(f773(f42(x46741),x46742),f2(a847))
% 191.21/191.73 [4685]~P7(x46851)+E(f52(x46851,x46852,f2(x46851)),x46852)
% 191.21/191.73 [4693]~P85(x46931)+E(f773(f773(f83(x46931),x46932),f2(x46931)),f2(x46931))
% 191.21/191.73 [4694]~P122(x46941)+E(f773(f773(f83(x46941),x46942),f2(x46941)),f2(x46941))
% 191.21/191.73 [4695]~P7(x46951)+E(f773(f773(f43(x46951),x46952),f2(x46951)),f2(x46951))
% 191.21/191.73 [4696]~P114(x46961)+E(f773(f773(f283(x46961),x46962),f2(x46961)),f2(x46961))
% 191.21/191.73 [4697]~P94(x46971)+E(f773(f773(f103(x46971),x46972),f239(x46971)),f239(x46971))
% 191.21/191.73 [4698]~P95(x46981)+E(f773(f773(f104(x46981),x46982),f180(x46981)),f180(x46981))
% 191.21/191.73 [4699]E(x46991,f183(x46992))+~E(f226(x46992,x46991),f180(f855(x46992,a841)))
% 191.21/191.73 [4700]~P7(x47001)+E(f52(x47001,x47002,f80(x47001)),f2(x47001))
% 191.21/191.73 [4701]~P7(x47011)+E(f52(x47011,f2(x47011),x47012),f2(x47011))
% 191.21/191.73 [4752]P36(x47521,x47522)+~E(f601(x47522,x47521),f180(f855(x47521,a841)))
% 191.21/191.73 [4753]E(x47531,f115(x47532))+~E(f773(f158(x47532),x47531),f180(f855(x47532,a841)))
% 191.21/191.73 [4754]E(x47541,f115(x47542))+~E(f180(f855(x47542,a841)),f773(f158(x47542),x47541))
% 191.21/191.73 [4757]~E(x47571,x47572)+P1(f773(f773(a330,x47571),x47572))
% 191.21/191.73 [4767]P1(x47671)+P1(f773(f773(a335,x47671),x47672))
% 191.21/191.73 [4768]E(x47681,f115(x47682))+E(f773(f773(f153(x47682),x47681),f2(a847)),f773(f131(x47682),x47681))
% 191.21/191.73 [4774]~P1(x47742)+P1(f773(f773(a335,x47741),x47742))
% 191.21/191.73 [4775]~P1(x47752)+P1(f773(f773(a332,x47751),x47752))
% 191.21/191.73 [4776]~P1(x47761)+P1(f773(f773(a332,x47761),x47762))
% 191.21/191.73 [4786]~E(f722(x47862,x47861),f726(x47862,x47861))+P1(f773(f127(x47861),x47862))
% 191.21/191.73 [4794]E(f773(f256(x47941),x47942),f180(f855(x47941,a841)))+P1(f773(x47942,f557(x47942)))
% 191.21/191.73 [4795]E(f180(f855(x47951,a841)),f773(f256(x47951),x47952))+P1(f773(x47952,f558(x47952)))
% 191.21/191.73 [4859]~P110(x48591)+E(f773(f773(f83(x48591),x48592),f84(x48591,x48592)),f773(f77(x48591),x48592))
% 191.21/191.73 [4871]~E(x48711,f2(a1))+E(f53(x48711,x48712),f773(f773(f241(a1,a1),f2(a1)),f2(a1)))
% 191.21/191.73 [4902]~P56(x49021,x49022)+P56(x49021,f773(f278(x49021,x49021),x49022))
% 191.21/191.73 [4919]~E(f773(a30,x49191),f773(f227(a842),x49192))+P1(f773(a26,f773(a27,x49191)))
% 191.21/191.73 [4923]E(x49231,x49232)+~P1(f773(f773(a330,x49231),x49232))
% 191.21/191.73 [4927]~P1(f773(a26,x49272))+P1(f773(a26,f35(x49271,x49272)))
% 191.21/191.73 [4936]P1(x49361)+~P1(f773(f773(a331,x49362),x49361))
% 191.21/191.73 [4937]P1(x49371)+~P1(f773(f773(a331,x49371),x49372))
% 191.21/191.73 [4941]~P106(x49411)+P1(f773(f773(f232(x49411),x49412),f239(x49411)))
% 191.21/191.73 [4942]~P85(x49421)+P1(f773(f773(f279(x49421),x49422),f2(x49421)))
% 191.21/191.73 [4946]E(x49461,x49462)+~E(f773(x49461,f373(x49462,x49461)),f773(x49462,f373(x49462,x49461)))
% 191.21/191.73 [4980]E(x49801,f2(a847))+E(f211(x49801,f52(a847,x49802,x49801)),f211(x49802,x49801))
% 191.21/191.73 [4985]~P100(x49851)+P18(x49851,f773(f773(f140(x49851),x49852),f115(x49851)))
% 191.21/191.73 [4987]E(x49871,f2(a1))+P1(f773(f56(x49872,x49871),f53(x49872,x49871)))
% 191.21/191.73 [5004]~E(x50041,x50042)+P1(f773(f773(f233(a847),x50041),f773(a114,x50042)))
% 191.21/191.73 [5014]~E(x50141,f2(a847))+P1(f773(f773(f233(a847),x50141),f773(a114,x50142)))
% 191.21/191.73 [5024]P1(f773(x50241,x50242))+P1(f773(f773(f232(a1),f2(a1)),f774(x50241)))
% 191.21/191.73 [5061]P1(f773(a26,x50611))+~P1(f773(a26,f35(x50612,x50611)))
% 191.21/191.73 [5063]P1(f773(a26,x50631))+~P1(f773(a26,f36(x50632,x50631)))
% 191.21/191.73 [5065]P1(f773(a26,x50651))+~P1(f773(a26,f36(x50651,x50652)))
% 191.21/191.73 [5093]P56(x50931,x50932)+~P56(x50931,f773(f278(x50931,x50931),x50932))
% 191.21/191.73 [5095]~E(f52(a847,x50952,x50951),f2(a847))+E(f773(f773(f83(a847),x50951),f786(x50951,x50952)),x50952)
% 191.21/191.73 [5096]~E(f52(a1,x50962,x50961),f2(a1))+E(f773(f773(f83(a1),x50961),f787(x50961,x50962)),x50962)
% 191.21/191.73 [5123]~P1(f773(x51231,x51232))+P1(f773(f773(f232(a1),f2(a1)),f759(x51231)))
% 191.21/191.73 [5134]E(f773(f773(f3(a847),f773(a107,x51341)),f773(a107,x51342)),f773(a107,x51341))+~P1(f773(a186,x51342))
% 191.21/191.73 [5162]E(f267(x51621,x51622),f80(a101))+~P1(f773(f773(f232(a101),x51621),f80(a101)))
% 191.21/191.73 [5251]E(f773(f773(f153(x52511),x52512),f722(x52512,x52511)),f773(f773(f153(x52511),x52512),f726(x52512,x52511)))+P1(f773(f127(x52511),x52512))
% 191.21/191.73 [5293]~P1(f773(x52931,f92(x52932,x52931)))+P1(f773(x52931,f602(x52932,x52931)))
% 191.21/191.73 [5356]P58(x53561,x53562)+~P1(f773(f321(x53561,x53562),f580(x53562,x53561)))
% 191.21/191.73 [5499]~E(f773(a114,f52(a847,x54991,x54992)),x54992)+E(f52(a847,f773(a114,x54991),x54992),f2(a847))
% 191.21/191.73 [5552]P36(x55521,x55522)+P1(f773(f773(f334(x55521),f681(x55522,x55521)),f682(x55522,x55521)))
% 191.21/191.73 [5558]~P2(x55581)+P1(f773(f773(f334(x55581),f773(f102(x55581),x55582)),f176(x55581)))
% 191.21/191.73 [5559]~P133(x55591)+P1(f773(f773(f334(x55591),f773(f102(x55591),x55592)),f112(x55591)))
% 191.21/191.73 [5560]~P133(x55601)+P1(f773(f773(f334(x55601),f773(f105(x55601),x55602)),f112(x55601)))
% 191.21/191.73 [5561]~P88(x55611)+P1(f773(f773(f334(x55611),f773(f106(x55611),x55612)),f112(x55611)))
% 191.21/191.73 [5715]E(f773(a114,f52(a847,x57151,x57152)),x57152)+E(f52(a847,f773(a114,x57151),x57152),f773(a114,f52(a847,x57151,x57152)))
% 191.21/191.73 [6136]P36(x61361,x61362)+~P1(f773(f773(f334(x61361),f582(x61362,x61361)),f322(x61361,x61362)))
% 191.21/191.73 [6170]~P117(x61701)+~P1(f773(f773(f233(x61701),f773(f102(x61701),x61702)),f2(x61701)))
% 191.21/191.73 [6171]~P79(x61711)+~P1(f773(f773(f233(x61711),f773(f77(x61711),x61712)),f2(x61711)))
% 191.21/191.73 [6263]P1(f773(f773(f233(a1),x62631),f52(a1,x62632,x62631)))+~P1(f773(f773(f233(a1),x62631),f2(a1)))
% 191.21/191.73 [6371]E(f773(f773(f302(a847),f773(a114,x63711)),f295(a847,x63712,x63711)),f295(a847,x63712,f773(a114,x63711)))+~P1(f773(f773(f232(a847),x63712),f773(a114,x63711)))
% 191.21/191.73 [6598]E(f773(f141(x65981),x65982),x65982)+~P1(f773(f773(f232(a847),f773(f181(f848(x65981)),x65982)),f80(a847)))
% 191.21/191.73 [6621]~P79(x66211)+P1(f773(f773(f232(x66211),f773(f81(x66211),f773(f77(x66211),x66212))),f2(x66211)))
% 191.21/191.73 [6657]~P36(x66571,x66572)+P36(x66571,f773(f773(f281(x66571,x66571,x66571),x66572),f300(x66571,x66572)))
% 191.21/191.73 [6889]~P1(f773(f773(f233(a1),x68892),f2(a1)))+P1(f773(f773(f232(a1),f52(a1,x68891,x68892)),f2(a1)))
% 191.21/191.73 [7300]~P2(x73001)+E(f182(x73001,f773(f773(f9(x73001,x73001,x73001),f82(x73001)),f80(x73001)),x73002,f2(x73001)),f773(f102(x73001),x73002))
% 191.21/191.73 [7333]~P118(x73331)+~P1(f773(f773(f233(x73331),f773(f773(f83(x73331),x73332),x73332)),f2(x73331)))
% 191.21/191.73 [9848]~P110(x98481)+~P1(f773(f773(f233(x98481),f773(f773(f242(x98481),x98482),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))),f2(x98481)))
% 191.21/191.73 [4566]~E(x45662,f115(x45661))+E(f773(f181(f848(x45661)),x45662),f2(a847))
% 191.21/191.73 [4605]~E(x46051,f2(a847))+E(f773(f773(f82(a847),x46051),x46052),x46052)
% 191.21/191.73 [4606]~E(x46062,f2(a847))+E(f773(f773(f83(a847),x46061),x46062),f2(a847))
% 191.21/191.73 [4608]~E(x46081,f2(a847))+E(f773(f773(f83(a847),x46081),x46082),f2(a847))
% 191.21/191.73 [4609]~E(x46092,f2(a1))+E(f773(f773(f43(a1),x46091),x46092),f2(a1))
% 191.21/191.73 [4610]~E(x46102,f2(a847))+E(f773(f773(f242(a847),x46101),x46102),f80(a847))
% 191.21/191.73 [4620]E(x46201,f115(x46202))+~E(f773(f181(f848(x46202)),x46201),f2(a847))
% 191.21/191.73 [4622]~P91(x46221)+E(f773(f773(f83(x46221),x46222),x46222),x46222)
% 191.21/191.73 [4624]~P100(x46241)+E(f773(f773(f236(x46241),x46242),x46242),x46242)
% 191.21/191.73 [4626]~P100(x46261)+E(f773(f773(f179(x46261),x46262),x46262),x46262)
% 191.21/191.73 [4628]~P92(x46281)+E(f773(f773(f103(x46281),x46282),x46282),x46282)
% 191.21/191.73 [4629]~P93(x46291)+E(f773(f773(f103(x46291),x46292),x46292),x46292)
% 191.21/191.73 [4630]~P93(x46301)+E(f773(f773(f104(x46301),x46302),x46302),x46302)
% 191.21/191.73 [4632]~P98(x46321)+E(f773(f773(f104(x46321),x46322),x46322),x46322)
% 191.21/191.73 [4648]~P69(x46481)+E(f773(f773(f3(x46481),x46482),x46482),f2(x46481))
% 191.21/191.73 [4659]~P69(x46591)+E(f773(f81(x46591),f773(f81(x46591),x46592)),x46592)
% 191.21/191.73 [4660]~P90(x46601)+E(f773(f81(x46601),f773(f81(x46601),x46602)),x46602)
% 191.21/191.73 [4677]~E(x46772,f2(a847))+E(f773(f773(f242(a847),x46771),x46772),f773(a114,f2(a847)))
% 191.21/191.73 [4709]~P66(x47091)+E(f773(f773(f82(x47091),f2(x47091)),x47092),x47092)
% 191.21/191.73 [4710]~P67(x47101)+E(f773(f773(f82(x47101),f2(x47101)),x47102),x47102)
% 191.21/191.73 [4711]~P85(x47111)+E(f773(f773(f82(x47111),f2(x47111)),x47112),x47112)
% 191.21/191.73 [4712]~P85(x47121)+E(f773(f773(f83(x47121),f80(x47121)),x47122),x47122)
% 191.21/191.73 [4713]~P70(x47131)+E(f773(f773(f83(x47131),f80(x47131)),x47132),x47132)
% 191.21/191.73 [4714]~P75(x47141)+E(f773(f773(f83(x47141),f80(x47141)),x47142),x47142)
% 191.21/191.73 [4715]~P95(x47151)+E(f773(f773(f103(x47151),f180(x47151)),x47152),x47152)
% 191.21/191.73 [4716]~P94(x47161)+E(f773(f773(f104(x47161),f239(x47161)),x47162),x47162)
% 191.21/191.73 [4733]~P85(x47331)+E(f773(f773(f83(x47331),f2(x47331)),x47332),f2(x47331))
% 191.21/191.73 [4734]~P122(x47341)+E(f773(f773(f83(x47341),f2(x47341)),x47342),f2(x47341))
% 191.21/191.73 [4735]~P7(x47351)+E(f773(f773(f43(x47351),f2(x47351)),x47352),f2(x47351))
% 191.21/191.73 [4736]~P75(x47361)+E(f773(f773(f242(x47361),f80(x47361)),x47362),f80(x47361))
% 191.21/191.73 [4737]~P113(x47371)+E(f773(f773(f283(x47371),f2(x47371)),x47372),f2(x47371))
% 191.21/191.73 [4738]~P94(x47381)+E(f773(f773(f103(x47381),f239(x47381)),x47382),f239(x47381))
% 191.21/191.73 [4739]~P95(x47391)+E(f773(f773(f104(x47391),f180(x47391)),x47392),f180(x47391))
% 191.21/191.73 [4747]E(x47471,f115(x47472))+E(f134(x47472,f773(f142(x47472),x47471)),f773(f131(x47472),x47471))
% 191.21/191.73 [4748]E(x47481,f115(x47482))+E(f773(f131(x47482),f773(f142(x47482),x47481)),f134(x47482,x47481))
% 191.21/191.73 [4749]E(x47491,f2(a847))+~E(f773(f773(f82(a847),x47492),x47491),x47492)
% 191.21/191.73 [4755]~P133(x47551)+E(f773(f105(x47551),f773(f102(a1),x47552)),f773(f102(x47551),x47552))
% 191.21/191.73 [4756]~P88(x47561)+E(f773(f105(x47561),f773(f106(a1),x47562)),f773(f106(x47561),x47562))
% 191.21/191.73 [4763]E(x47631,f2(a847))+~E(f773(f773(f82(a847),x47632),x47631),f2(a847))
% 191.21/191.73 [4764]E(x47641,f2(a847))+~E(f773(f773(f82(a847),x47641),x47642),f2(a847))
% 191.21/191.73 [4765]E(x47651,f80(a847))+~E(f773(f773(f83(a847),x47652),x47651),f80(a847))
% 191.21/191.73 [4766]E(x47661,f80(a847))+~E(f773(f773(f83(a847),x47661),x47662),f80(a847))
% 191.21/191.73 [4779]~P110(x47791)+E(f773(f77(x47791),f773(f102(x47791),x47792)),f773(f102(x47791),x47792))
% 191.21/191.73 [4780]~P79(x47801)+E(f773(f77(x47801),f773(f81(x47801),x47802)),f773(f77(x47801),x47802))
% 191.21/191.73 [4781]~P79(x47811)+E(f773(f77(x47811),f773(f77(x47811),x47812)),f773(f77(x47811),x47812))
% 191.21/191.73 [4782]~P66(x47821)+E(f773(f155(x47821),f773(f142(x47821),x47822)),f773(f155(x47821),x47822))
% 191.21/191.73 [4787]~E(x47871,f773(a114,f2(a847)))+E(f773(f773(f242(a847),x47871),x47872),f773(a114,f2(a847)))
% 191.21/191.73 [4797]~P69(x47971)+E(f773(f773(f3(x47971),f2(x47971)),x47972),f773(f81(x47971),x47972))
% 191.21/191.73 [4798]~E(x47982,f2(a847))+E(f130(a847,f773(f294(a847,x47981),x47982)),f115(a847))
% 191.21/191.73 [4807]~P88(x48071)+E(f773(f773(f82(x48071),x48072),f773(f106(x48071),a85)),x48072)
% 191.21/191.73 [4808]E(x48081,f2(a1))+E(f54(f773(f77(a1),x48082),f773(f77(a1),x48081)),f60(x48082,x48081))
% 191.21/191.73 [4820]~E(x48201,x48202)+P1(f773(f773(f232(a847),x48201),x48202))
% 191.21/191.73 [4824]~E(x48241,x48242)+P1(f773(f773(f279(a847),x48241),x48242))
% 191.21/191.73 [4831]~E(x48311,f2(a101))+E(f773(f773(f82(a847),f773(a22,x48311)),x48312),x48312)
% 191.21/191.73 [4832]~E(f773(f106(a1),x48322),f773(f102(a1),x48321))+E(x48321,f773(a107,f773(f106(a1),x48322)))
% 191.21/191.73 [4841]~P10(x48411)+P10(f773(f773(f242(a1),x48411),x48412))
% 191.21/191.73 [4842]~P69(x48421)+E(f773(f773(f82(x48421),x48422),f773(f81(x48421),x48422)),f2(x48421))
% 191.21/191.73 [4843]~P90(x48431)+E(f773(f773(f103(x48431),x48432),f773(f81(x48431),x48432)),f239(x48431))
% 191.21/191.73 [4844]~P90(x48441)+E(f773(f773(f104(x48441),x48442),f773(f81(x48441),x48442)),f180(x48441))
% 191.21/191.73 [4868]E(x48681,f2(a847))+~E(f773(f81(a1),f773(f102(a1),x48682)),f773(f102(a1),x48681))
% 191.21/191.73 [4869]E(x48691,f2(a847))+~E(f773(f81(a1),f773(f102(a1),x48691)),f773(f102(a1),x48692))
% 191.21/191.73 [4879]E(f188(x48791,x48792),f2(a1))+P1(f773(f773(f232(a1),x48792),x48791))
% 191.21/191.73 [4880]E(f238(x48801,x48802),f2(a101))+P1(f773(f773(f233(a101),x48801),x48802))
% 191.21/191.73 [4881]E(f163(x48811,x48812),f115(a1))+P1(f773(f773(f232(a1),x48811),x48812))
% 191.21/191.73 [4894]E(x48941,f773(a114,f2(a847)))+~E(f773(f773(f83(a847),x48942),x48941),f773(a114,f2(a847)))
% 191.21/191.73 [4895]E(x48951,f773(a114,f2(a847)))+~E(f773(f773(f83(a847),x48951),x48952),f773(a114,f2(a847)))
% 191.21/191.73 [4896]~P103(x48961)+P1(f773(f773(f232(x48961),x48962),x48962))
% 191.21/191.73 [4897]~P85(x48971)+P1(f773(f773(f279(x48971),x48972),x48972))
% 191.21/191.73 [4900]~P88(x49001)+E(f773(f773(f83(x49001),x49002),f773(f106(x49001),a99)),f773(f81(x49001),x49002))
% 191.21/191.73 [4916]~P133(x49161)+E(f773(f81(x49161),f773(f105(x49161),x49162)),f773(f105(x49161),f773(f81(a1),x49162)))
% 191.21/191.73 [4917]~P88(x49171)+E(f773(f81(x49171),f773(f106(x49171),x49172)),f773(f106(x49171),f773(f81(a1),x49172)))
% 191.21/191.73 [4951]~E(x49511,f773(a114,x49512))+P1(f773(f773(f233(a847),f2(a847)),x49511))
% 191.21/191.73 [4968]~P100(x49681)+E(f773(f81(f855(x49681,a841)),f773(f257(x49681),x49682)),f773(f258(x49681),x49682))
% 191.21/191.73 [4969]~P100(x49691)+E(f773(f81(f855(x49691,a841)),f773(f296(x49691),x49692)),f773(f293(x49691),x49692))
% 191.21/191.73 [4970]~P100(x49701)+E(f773(f81(f855(x49701,a841)),f773(f293(x49701),x49702)),f773(f296(x49701),x49702))
% 191.21/191.73 [4971]~P100(x49711)+E(f773(f81(f855(x49711,a841)),f773(f258(x49711),x49712)),f773(f257(x49711),x49712))
% 191.21/191.73 [4979]~E(f773(f102(a1),x49792),x49791)+P1(f773(f773(f232(a1),f2(a1)),x49791))
% 191.21/191.73 [4986]~E(x49862,f2(a1))+E(f60(x49861,x49862),f773(f773(f241(a1,a1),f2(a1)),f773(f77(a1),x49861)))
% 191.21/191.73 [4988]~P101(x49881)+P1(f773(f773(f232(x49881),f180(x49881)),x49882))
% 191.21/191.73 [4989]~P85(x49891)+P1(f773(f773(f279(x49891),f80(x49891)),x49892))
% 191.21/191.73 [5019]E(x50191,x50192)+~E(f773(f773(f82(a1),x50191),x50191),f773(f773(f82(a1),x50192),x50192))
% 191.21/191.73 [5023]~P1(f773(x50231,x50232))+P1(f773(x50231,f773(a107,f759(x50231))))
% 191.21/191.73 [5049]~P110(x50491)+E(f773(f773(f83(x50491),f84(x50491,x50492)),f773(f77(x50491),x50492)),x50492)
% 191.21/191.73 [5050]E(x50501,x50502)+~P1(f773(f773(f187(a25),x50501),x50502))
% 191.21/191.73 [5059]~E(x50592,f2(a847))+E(f87(f854(a847,a847),f55(x50591,x50592)),f773(f773(f241(a847,a847),f2(a847)),x50591))
% 191.21/191.73 [5070]~E(x50701,x50702)+~P1(f773(f773(f233(a847),x50701),x50702))
% 191.21/191.73 [5071]~E(x50711,x50712)+~P1(f773(f773(f233(a1),x50711),x50712))
% 191.21/191.73 [5074]~P2(x50741)+E(f773(f773(f82(x50741),f80(x50741)),f773(f102(x50741),x50742)),f773(f102(x50741),f773(a114,x50742)))
% 191.21/191.73 [5078]~E(x50781,f2(a847))+~P1(f773(f773(f233(a847),x50782),x50781))
% 191.21/191.73 [5091]E(f773(f42(x50911),f773(f158(x50911),x50912)),f773(f181(f848(x50911)),x50912))+~P1(f773(f127(x50911),x50912))
% 191.21/191.73 [5100]~P1(f773(x51001,f727(x51001)))+P1(f773(x51001,f773(f102(a1),x51002)))
% 191.21/191.73 [5112]E(f238(x51121,x51122),x51122)+~P1(f773(f773(f233(a101),x51121),x51122))
% 191.21/191.73 [5114]E(f267(x51141,x51142),f80(a101))+~P1(f773(f773(f233(a101),x51142),x51141))
% 191.21/191.73 [5115]E(f163(x51151,x51152),f115(a1))+~P1(f773(f773(f233(a1),x51152),x51151))
% 191.21/191.73 [5118]~P99(x51181)+E(f295(x51181,x51182,x51182),f773(f773(f302(x51181),x51182),f180(f855(x51181,a841))))
% 191.21/191.73 [5137]~E(f773(f773(f3(a847),x51371),x51372),f2(a847))+P1(f773(f773(f232(a847),x51371),x51372))
% 191.21/191.73 [5163]~P103(x51631)+~P1(f773(f773(f233(x51631),x51632),x51632))
% 191.21/191.73 [5166]~E(f52(a1,x51661,x51662),f2(a1))+E(f52(a1,x51661,f773(f81(a1),x51662)),f2(a1))
% 191.21/191.73 [5168]~E(f52(a1,x51681,x51682),f2(a1))+E(f52(a1,f773(f81(a1),x51681),x51682),f2(a1))
% 191.21/191.73 [5175]E(f773(f294(a847,x51751),f773(a114,x51752)),f180(f855(a847,a841)))+P1(f773(f773(f232(a847),x51751),x51752))
% 191.21/191.73 [5192]E(f130(a847,f773(f294(a847,x51921),x51922)),f115(a847))+P1(f773(f773(f233(a847),x51921),x51922))
% 191.21/191.73 [5197]~E(f773(f42(x51971),f773(f158(x51971),x51972)),f773(f181(f848(x51971)),x51972))+P1(f773(f127(x51971),x51972))
% 191.21/191.73 [5201]~P1(f773(f127(x52011),x52012))+P1(f773(f127(x52011),f773(f141(x52011),x52012)))
% 191.21/191.73 [5202]~P1(f773(f127(x52021),x52022))+P1(f773(f127(x52021),f773(f157(x52021),x52022)))
% 191.21/191.73 [5203]~P1(f773(f127(x52031),x52032))+P1(f773(f127(x52031),f773(f142(x52031),x52032)))
% 191.21/191.73 [5211]P1(f773(x52111,x52112))+~P1(f773(x52111,f773(a107,f774(x52111))))
% 191.21/191.73 [5212]P1(f773(f773(f232(a847),x52122),x52121))+P1(f773(f773(f232(a847),x52121),x52122))
% 191.21/191.73 [5213]P1(f773(f773(f232(a1),x52132),x52131))+P1(f773(f773(f232(a1),x52131),x52132))
% 191.21/191.73 [5215]~P79(x52151)+P1(f773(f773(f232(x52151),x52152),f773(f77(x52151),x52152)))
% 191.21/191.73 [5218]P1(f773(x52181,f728(x52181)))+~P1(f773(x52181,f773(f102(a1),x52182)))
% 191.21/191.73 [5242]E(f773(f773(f43(a847),x52421),x52422),f2(a847))+~P1(f773(f773(f233(a847),x52421),x52422))
% 191.21/191.73 [5244]E(f773(f773(f3(a847),x52441),x52442),f2(a847))+~P1(f773(f773(f232(a847),x52441),x52442))
% 191.21/191.73 [5261]E(f52(a847,x52611,x52612),x52611)+~P1(f773(f773(f233(a847),x52611),x52612))
% 191.21/191.73 [5268]E(f52(a1,x52681,f773(f81(a1),x52682)),f284(x52681,x52682))+P1(f773(f773(f232(a1),f2(a1)),x52682))
% 191.21/191.73 [5281]E(f773(f773(f3(a1),x52811),x52812),f188(x52811,x52812))+~P1(f773(f773(f232(a1),x52812),x52811))
% 191.21/191.73 [5299]P1(f773(f773(f232(a1),f2(a1)),f727(x52991)))+P1(f773(x52991,f773(f102(a1),x52992)))
% 191.21/191.73 [5312]~P117(x53121)+P1(f773(f773(f232(x53121),f2(x53121)),f773(f102(x53121),x53122)))
% 191.21/191.73 [5313]~P79(x53131)+P1(f773(f773(f232(x53131),f2(x53131)),f773(f77(x53131),x53132)))
% 191.21/191.73 [5341]E(f773(f773(f82(a847),x53411),f680(x53412,x53411)),x53412)+~P1(f773(f773(f232(a847),x53411),x53412))
% 191.21/191.73 [5342]E(f773(f773(f82(a847),x53421),f603(x53422,x53421)),x53422)+~P1(f773(f773(f233(a847),x53421),x53422))
% 191.21/191.73 [5354]~E(f773(f106(a1),x53541),f773(f102(a1),x53542))+P1(f773(f773(f232(a1),f2(a1)),f773(f106(a1),x53541)))
% 191.21/191.73 [5357]E(f295(a1,x53571,x53572),f180(f855(a1,a841)))+~P1(f773(f773(f233(a1),x53572),x53571))
% 191.21/191.73 [5360]~P110(x53601)+E(f773(f773(f83(x53601),f773(f77(x53601),x53602)),f773(f77(x53601),x53602)),f773(f773(f83(x53601),x53602),x53602))
% 191.21/191.73 [5365]E(f130(a847,f773(f294(a847,x53651),f773(a114,x53652))),f115(a847))+P1(f773(f773(f232(a847),x53651),x53652))
% 191.21/191.73 [5369]E(f773(f773(f43(a1),x53691),x53692),f285(x53691,x53692))+~P1(f773(f773(f232(a1),f2(a1)),x53692))
% 191.21/191.73 [5389]P1(f773(f127(x53891),x53892))+~P1(f773(f127(x53891),f773(f141(x53891),x53892)))
% 191.21/191.73 [5390]P1(f773(f127(x53901),x53902))+~P1(f773(f127(x53901),f773(f142(x53901),x53902)))
% 191.21/191.73 [5413]P1(f773(f63(a847),x54131))+P1(f773(f773(f334(a847),f375(x54131,x54132)),x54131))
% 191.21/191.73 [5414]P1(f773(f63(a847),x54141))+P1(f773(f773(f334(a847),f400(x54141,x54142)),x54141))
% 191.21/191.73 [5415]P1(f773(f773(f233(a847),x54152),f773(a114,x54151)))+P1(f773(f773(f233(a847),x54151),x54152))
% 191.21/191.73 [5416]E(f52(a1,x54161,x54162),f284(x54161,x54162))+~P1(f773(f773(f232(a1),f2(a1)),x54162))
% 191.21/191.73 [5419]E(f130(a847,f773(f294(a847,x54191),x54192)),f115(a847))+~P1(f773(f773(f232(a847),x54192),x54191))
% 191.21/191.73 [5420]~P77(x54201)+E(f773(f303(x54201,x54201,f81(x54201)),f773(f257(x54201),x54202)),f773(f296(x54201),f773(f81(x54201),x54202)))
% 191.21/191.73 [5421]~P77(x54211)+E(f773(f303(x54211,x54211,f81(x54211)),f773(f296(x54211),x54212)),f773(f257(x54211),f773(f81(x54211),x54212)))
% 191.21/191.73 [5422]~P77(x54221)+E(f773(f303(x54221,x54221,f81(x54221)),f773(f293(x54221),x54222)),f773(f258(x54221),f773(f81(x54221),x54222)))
% 191.21/191.73 [5423]~P77(x54231)+E(f773(f303(x54231,x54231,f81(x54231)),f773(f258(x54231),x54232)),f773(f293(x54231),f773(f81(x54231),x54232)))
% 191.21/191.73 [5434]E(x54341,f180(f855(x54342,a841)))+P1(f773(f773(f334(x54342),f402(x54341,x54342)),x54341))
% 191.21/191.73 [5435]E(x54351,f180(f855(x54352,a841)))+P1(f773(f773(f334(x54352),f403(x54351,x54352)),x54351))
% 191.21/191.73 [5446]~P1(f773(f773(f233(a847),x54461),x54462))+P1(f773(f773(f232(a847),x54461),x54462))
% 191.21/191.73 [5447]~P1(f773(f773(f233(a1),x54471),x54472))+P1(f773(f773(f232(a1),x54471),x54472))
% 191.21/191.73 [5459]E(f54(x54591,x54592),f773(f773(f241(a1,a1),f2(a1)),x54591))+~P1(f773(f773(f233(a1),x54591),x54592))
% 191.21/191.73 [5460]E(f210(f773(f81(a1),x54601),f773(f81(a1),x54602)),f210(x54601,x54602))+~P1(f773(f773(f233(a1),x54602),f2(a1)))
% 191.21/191.73 [5473]E(x54731,x54732)+~E(f773(a5,f773(a114,f773(a22,x54731))),f773(a5,f773(a114,f773(a22,x54732))))
% 191.21/191.73 [5478]E(f54(x54781,x54782),f773(f773(f241(a1,a1),f2(a1)),x54781))+~P1(f773(f773(f232(a1),x54782),f2(a1)))
% 191.21/191.73 [5505]E(f52(a847,f773(f106(a847),x55051),f773(f106(a847),x55052)),f2(a847))+~P1(f773(a186,f773(f106(a1),x55051)))
% 191.21/191.73 [5519]P1(f773(f773(f232(a1),f2(a1)),f728(x55191)))+~P1(f773(x55191,f773(f102(a1),x55192)))
% 191.21/191.73 [5550]P38(f295(a1,x55501,x55502))+~P1(f773(f773(f232(a1),f2(a1)),x55501))
% 191.21/191.73 [5554]~P1(f773(f63(x55541),x55542))+P1(f773(f63(f855(x55541,a841)),f773(f301(x55541),x55542)))
% 191.21/191.73 [5567]E(f773(f773(f82(a1),x55671),f773(f102(a1),f788(x55672,x55671))),x55672)+~P1(f773(f773(f232(a1),x55671),x55672))
% 191.21/191.73 [5575]P1(f773(f773(f232(a847),x55751),x55752))+P1(f773(f773(f232(a847),f773(a114,x55752)),x55751))
% 191.21/191.73 [5620]E(f773(f773(f43(a847),f773(f106(a847),x56201)),f773(f106(a847),x56202)),f2(a847))+~P1(f773(a186,f773(f106(a1),x56201)))
% 191.21/191.73 [5621]E(f773(f773(f83(a847),f773(f106(a847),x56211)),f773(f106(a847),x56212)),f2(a847))+~P1(f773(f773(f233(a1),x56211),a85))
% 191.21/191.73 [5623]P1(f773(f773(f233(a847),x56231),f773(a114,x56232)))+~P1(f773(f773(f233(a847),x56231),x56232))
% 191.21/191.73 [5625]P1(f773(f773(f233(a847),x56251),f773(a114,x56252)))+~P1(f773(f773(f232(a847),x56251),x56252))
% 191.21/191.73 [5627]P1(f773(f773(f232(a847),x56271),f773(a114,x56272)))+~P1(f773(f773(f232(a847),x56271),x56272))
% 191.21/191.73 [5628]~E(x56281,x56282)+P1(f773(f773(f233(a1),x56281),f773(f773(f82(a1),x56282),f80(a1))))
% 191.21/191.73 [5631]E(f52(a1,x56311,x56312),f2(a1))+E(f773(f773(f3(a1),x56312),f52(a1,x56311,x56312)),f52(a1,f773(f81(a1),x56311),x56312))
% 191.21/191.73 [5639]E(x56391,f115(x56392))+P1(f773(f773(f334(x56392),f134(x56392,x56391)),f773(f158(x56392),x56391)))
% 191.21/191.73 [5651]E(f87(f854(a847,a847),f55(x56511,x56512)),f773(f773(f241(a847,a847),f2(a847)),x56511))+~P1(f773(f773(f233(a847),x56511),x56512))
% 191.21/191.73 [5691]E(f773(f773(f82(a847),f773(f106(a847),x56911)),f773(f106(a847),x56912)),f773(f106(a847),x56912))+~P1(f773(f773(f233(a1),x56911),a85))
% 191.21/191.73 [5692]E(f773(f773(f3(a847),f773(f106(a847),x56921)),f773(f106(a847),x56922)),f773(f106(a847),x56921))+~P1(f773(f773(f233(a1),x56922),a85))
% 191.21/191.73 [5697]E(f773(a114,f773(f773(f82(a847),x56971),f581(x56972,x56971))),x56972)+~P1(f773(f773(f233(a847),x56971),x56972))
% 191.21/191.73 [5698]E(f773(a114,f773(f773(f82(a847),x56981),f604(x56982,x56981))),x56982)+~P1(f773(f773(f233(a847),x56981),x56982))
% 191.21/191.73 [5705]~P1(f773(f773(f279(a1),x57051),x57052))+P1(f773(f773(f279(a1),x57051),f773(f81(a1),x57052)))
% 191.21/191.73 [5706]P1(f773(f773(f233(a847),f2(a847)),f603(x57061,x57062)))+~P1(f773(f773(f233(a847),x57062),x57061))
% 191.21/191.73 [5725]P1(f773(x57251,x57252))+~P1(f773(x57251,f773(a91,f605(x57252,x57251))))
% 191.21/191.73 [5733]~P1(f773(f773(f233(a847),x57331),f773(a114,x57332)))+P1(f773(f773(f232(a847),x57331),x57332))
% 191.21/191.73 [5782]E(f773(f773(f302(a847),x57821),f773(f294(a847,x57822),x57821)),f773(f294(a847,x57822),f773(a114,x57821)))+~P1(f773(f773(f232(a847),x57822),x57821))
% 191.21/191.73 [5787]E(x57871,f115(x57872))+E(f773(f773(f125(x57872),f116(x57872,x57871)),f773(f773(f140(x57872),f134(x57872,x57871)),f115(x57872))),x57871)
% 191.21/191.74 [5798]P1(f773(f63(x57981),x57982))+~P1(f773(f773(f233(a847),f2(a847)),f773(f42(x57981),x57982)))
% 191.21/191.74 [5802]~E(x58021,f180(f855(x58022,a841)))+~P1(f773(f773(f233(a847),f2(a847)),f773(f42(x58022),x58021)))
% 191.21/191.74 [5812]~P1(f773(f773(f233(a847),x58121),x58122))+P1(f773(f773(f232(a847),f773(a114,x58121)),x58122))
% 191.21/191.74 [5820]E(x58201,f115(x58202))+P1(f773(f773(f334(x58202),f773(f131(x58202),x58201)),f773(f158(x58202),x58201)))
% 191.21/191.74 [5826]~P117(x58261)+P1(f773(f773(f233(x58261),x58262),f773(f773(f82(x58261),x58262),f80(x58261))))
% 191.21/191.74 [5828]~P79(x58281)+P1(f773(f773(f232(x58281),f773(f81(x58281),x58282)),f773(f77(x58281),x58282)))
% 191.21/191.74 [5840]P1(f773(f773(f279(a1),x58401),x58402))+~P1(f773(f773(f279(a1),x58401),f773(f81(a1),x58402)))
% 191.21/191.74 [5841]~E(x58411,x58412)+E(f282(a847,f279(a847),x58411,x58412),f773(f773(f302(a847),x58411),f180(f855(a847,a841))))
% 191.21/191.74 [5859]P1(f773(f63(a847),x58591))+~P1(f773(f773(f233(a847),f400(x58591,x58592)),x58592))
% 191.21/191.74 [5860]P1(f773(f63(a847),x58601))+~P1(f773(f773(f232(a847),f375(x58601,x58602)),x58602))
% 191.21/191.74 [5864]~P1(f773(f63(f854(x58641,x58641)),x58642))+P1(f773(f63(x58641),f773(f276(x58641),x58642)))
% 191.21/191.74 [5915]E(f282(a847,f279(a847),x59151,x59152),f180(f855(a847,a841)))+P1(f773(f773(f279(a847),x59151),x59152))
% 191.21/191.74 [5921]~P1(f773(f773(f233(a847),x59212),f773(a114,x59211)))+~P1(f773(f773(f233(a847),x59211),x59212))
% 191.21/191.74 [5922]~P99(x59221)+E(f773(f773(f104(f855(x59221,a841)),f773(f293(x59221),x59222)),f773(f258(x59221),x59222)),f773(f773(f302(x59221),x59222),f180(f855(x59221,a841))))
% 191.21/191.74 [5935]P1(f773(f63(x59351),x59352))+~P1(f773(f63(f855(x59351,a841)),f773(f301(x59351),x59352)))
% 191.21/191.74 [5959]P1(f773(f773(f233(a847),f773(a114,x59591)),f773(a114,x59592)))+~P1(f773(f773(f233(a847),x59591),x59592))
% 191.21/191.74 [5960]P1(f773(f773(f233(a847),f773(a22,x59601)),f773(a22,x59602)))+~P1(f773(f773(f233(a101),x59601),x59602))
% 191.21/191.74 [5961]P1(f773(f773(f233(a101),f773(a5,x59611)),f773(a5,x59612)))+~P1(f773(f773(f233(a847),x59611),x59612))
% 191.21/191.74 [5962]P1(f773(f773(f232(a847),f773(a114,x59621)),f773(a114,x59622)))+~P1(f773(f773(f232(a847),x59621),x59622))
% 191.21/191.74 [5963]P1(f773(f773(f232(a847),f773(a22,x59631)),f773(a22,x59632)))+~P1(f773(f773(f232(a101),x59631),x59632))
% 191.21/191.74 [5964]P1(f773(f773(f232(a101),f773(a5,x59641)),f773(a5,x59642)))+~P1(f773(f773(f232(a847),x59641),x59642))
% 191.21/191.74 [5967]E(x59671,x59672)+~E(f773(f303(a847,a1,f102(a1)),x59671),f773(f303(a847,a1,f102(a1)),x59672))
% 191.21/191.74 [5983]P1(f773(f773(f233(a847),x59831),x59832))+~P1(f773(f773(f233(a847),f773(a114,x59831)),x59832))
% 191.21/191.74 [5986]P1(f773(f773(f233(a847),x59861),x59862))+~P1(f773(f773(f232(a847),f773(a114,x59861)),x59862))
% 191.21/191.74 [5987]P1(f773(f773(f232(a847),x59871),x59872))+~P1(f773(f773(f232(a847),f773(a114,x59871)),x59872))
% 191.21/191.74 [6004]E(f52(a1,x60041,x60042),f2(a1))+E(f773(f773(f3(a1),f52(a1,x60041,x60042)),x60042),f52(a1,x60041,f773(f81(a1),x60042)))
% 191.21/191.74 [6075]E(f773(f42(f855(x60751,a841)),f773(f301(x60751),x60752)),f773(f773(f242(a847),f773(a114,f773(a114,f2(a847)))),f773(f42(x60751),x60752)))+~P1(f773(f63(x60751),x60752))
% 191.21/191.74 [6078]E(x60781,f115(x60782))+E(f773(f773(f153(x60782),x60781),f773(f773(f3(a847),f773(f181(f848(x60782)),x60781)),f80(a847))),f134(x60782,x60781))
% 191.21/191.74 [6102]E(x61021,f115(x61022))+E(f773(f773(f125(x61022),f773(f157(x61022),x61021)),f773(f773(f140(x61022),f773(f131(x61022),x61021)),f115(x61022))),f773(f141(x61022),x61021))
% 191.21/191.74 [6133]~P1(f773(f63(x61331),f44(f855(x61331,a841),x61332)))+P1(f773(f63(f855(x61331,a841)),x61332))
% 191.21/191.74 [6154]P1(f773(f773(f232(a847),f773(f106(a847),x61541)),f773(f106(a847),x61542)))+~P1(f773(f773(f232(a1),x61541),a85))
% 191.21/191.74 [6174]~P1(f773(f773(f233(a1),x61741),x61742))+P1(f773(f773(f233(a1),x61741),f773(f773(f82(a1),x61742),f80(a1))))
% 191.21/191.74 [6175]~P1(f773(f773(f232(a1),x61751),x61752))+P1(f773(f773(f233(a1),x61751),f773(f773(f82(a1),x61752),f80(a1))))
% 191.21/191.74 [6176]~P1(f773(f773(f233(a1),x61761),x61762))+P1(f773(f773(f232(a1),x61761),f773(f773(f3(a1),x61762),f80(a1))))
% 191.21/191.74 [6179]~P1(f773(f773(f233(a847),x61791),x61792))+P1(f773(f773(f233(a1),f773(f102(a1),x61791)),f773(f102(a1),x61792)))
% 191.21/191.74 [6180]~P1(f773(f773(f233(a1),x61801),x61802))+P1(f773(f773(f233(a1),f773(f106(a1),x61801)),f773(f106(a1),x61802)))
% 191.21/191.74 [6181]~P1(f773(f773(f232(a1),x61811),x61812))+P1(f773(f773(f232(a847),f773(f106(a847),x61811)),f773(f106(a847),x61812)))
% 191.21/191.74 [6183]~P1(f773(f773(f232(a847),x61831),x61832))+P1(f773(f773(f232(a1),f773(f102(a1),x61831)),f773(f102(a1),x61832)))
% 191.21/191.74 [6184]~P1(f773(f773(f232(a1),x61841),x61842))+P1(f773(f773(f232(a1),f773(f106(a1),x61841)),f773(f106(a1),x61842)))
% 191.21/191.74 [6186]~P1(f773(f773(f279(a847),x61861),x61862))+P1(f773(f773(f279(a1),f773(f102(a1),x61861)),f773(f102(a1),x61862)))
% 191.21/191.74 [6202]~P1(f773(f773(f232(a847),x62021),x62022))+~P1(f773(f773(f232(a847),f773(a114,x62022)),x62021))
% 191.21/191.74 [6250]~P1(f773(f773(f233(a847),f773(a114,x62501)),f773(a114,x62502)))+P1(f773(f773(f233(a847),x62501),x62502))
% 191.21/191.74 [6251]~P1(f773(f773(f233(a101),f773(a5,x62511)),f773(a5,x62512)))+P1(f773(f773(f233(a847),x62511),x62512))
% 191.21/191.74 [6252]~P1(f773(f773(f233(a847),f773(a107,x62521)),f773(a107,x62522)))+P1(f773(f773(f233(a1),x62521),x62522))
% 191.21/191.74 [6253]~P1(f773(f773(f233(a847),f773(a22,x62531)),f773(a22,x62532)))+P1(f773(f773(f233(a101),x62531),x62532))
% 191.21/191.74 [6254]~P1(f773(f773(f232(a847),f773(a114,x62541)),f773(a114,x62542)))+P1(f773(f773(f232(a847),x62541),x62542))
% 191.21/191.74 [6255]~P1(f773(f773(f232(a101),f773(a5,x62551)),f773(a5,x62552)))+P1(f773(f773(f232(a847),x62551),x62552))
% 191.21/191.74 [6256]~P1(f773(f773(f232(a847),f773(a22,x62561)),f773(a22,x62562)))+P1(f773(f773(f232(a101),x62561),x62562))
% 191.21/191.74 [6300]~P1(f773(f773(f233(a847),f773(a107,x63002)),f773(a107,x63001)))+P1(f773(f773(f233(a1),f2(a1)),x63001))
% 191.21/191.74 [6311]~E(f52(a1,f773(f106(a1),x63112),f773(f106(a1),x63111)),f2(a1))+P1(f773(f773(f279(a1),f773(f106(a1),x63111)),f773(f106(a1),x63112)))
% 191.21/191.74 [6330]P1(f773(f773(f232(a1),f2(a1)),f52(a1,x63301,x63302)))+~P1(f773(f773(f233(a1),f2(a1)),x63302))
% 191.21/191.74 [6499]P36(x64991,x64992)+~E(f773(f773(f281(x64991,x64991,x64991),x64992),x64992),f180(f855(f854(x64991,x64991),a841)))
% 191.21/191.74 [6515]~P36(x65151,x65152)+P36(x65151,f773(f773(f281(x65151,x65151,x65151),x65152),x65152))
% 191.21/191.74 [6527]P1(f773(f773(f233(a1),x65271),x65272))+~P1(f773(f773(f232(a1),x65271),f773(f773(f3(a1),x65272),f80(a1))))
% 191.21/191.74 [6528]P1(f773(f773(f232(a1),x65281),x65282))+~P1(f773(f773(f233(a1),x65281),f773(f773(f82(a1),x65282),f80(a1))))
% 191.21/191.74 [6531]P1(f773(f773(f233(a847),x65311),x65312))+~P1(f773(f773(f233(a1),f773(f102(a1),x65311)),f773(f102(a1),x65312)))
% 191.21/191.74 [6532]P1(f773(f773(f233(a1),x65321),x65322))+~P1(f773(f773(f233(a847),f773(f106(a847),x65321)),f773(f106(a847),x65322)))
% 191.21/191.74 [6533]P1(f773(f773(f233(a1),x65331),x65332))+~P1(f773(f773(f233(a1),f773(f106(a1),x65331)),f773(f106(a1),x65332)))
% 191.21/191.74 [6535]P1(f773(f773(f232(a847),x65351),x65352))+~P1(f773(f773(f232(a1),f773(f102(a1),x65351)),f773(f102(a1),x65352)))
% 191.21/191.74 [6536]P1(f773(f773(f232(a1),x65361),x65362))+~P1(f773(f773(f232(a1),f773(f106(a1),x65361)),f773(f106(a1),x65362)))
% 191.21/191.74 [6538]P1(f773(f773(f279(a847),x65381),x65382))+~P1(f773(f773(f279(a1),f773(f102(a1),x65381)),f773(f102(a1),x65382)))
% 191.21/191.74 [6594]E(f52(a1,f773(f106(a1),x65941),f773(f106(a1),x65942)),f2(a1))+~P1(f773(f773(f279(a1),f773(f106(a1),x65942)),f773(f106(a1),x65941)))
% 191.21/191.74 [6609]~E(f282(a847,f279(a847),x66091,x66092),f180(f855(a847,a841)))+~P1(f773(f773(f279(a847),x66091),x66092))
% 191.21/191.74 [6637]~E(f768(x66372,x66371),f115(x66371))+E(f773(f132(f848(x66371),f848(x66371),f125(x66371),f115(x66371)),x66372),f115(x66371))
% 191.21/191.74 [6638]~E(f769(x66382,x66381),f115(x66381))+E(f773(f132(f848(x66381),f848(x66381),f125(x66381),f115(x66381)),x66382),f115(x66381))
% 191.21/191.74 [6645]~P9(x66451)+E(f773(f132(x66451,x66451,f104(x66451),f239(x66451)),x66452),f45(x66451,f773(f158(x66451),x66452)))
% 191.21/191.74 [6646]~P9(x66461)+E(f773(f132(x66461,x66461,f103(x66461),f180(x66461)),x66462),f44(x66461,f773(f158(x66461),x66462)))
% 191.21/191.74 [6658]E(x66581,f2(a101))+E(f773(f773(f82(a847),f773(a22,f773(f773(f3(a101),x66581),f80(a101)))),f773(a114,x66582)),f773(f773(f82(a847),f773(a22,x66581)),x66582))
% 191.21/191.74 [6710]P1(f773(f773(f233(a1),f773(f773(f3(a1),x67101),x67102)),f2(a1)))+~P1(f773(f773(f233(a1),x67101),x67102))
% 191.21/191.74 [6738]~P100(x67381)+E(f773(f773(f103(f855(x67381,a841)),f773(f773(f302(x67381),x67382),f180(f855(x67381,a841)))),f773(f296(x67381),x67382)),f773(f258(x67381),x67382))
% 191.21/191.74 [6820]~P58(x68201,x68202)+P36(x68201,f773(f256(f854(x68201,x68201)),f773(f251(x68201,x68201,a841),x68202)))
% 191.21/191.74 [6821]~P58(x68211,x68212)+P56(x68211,f773(f256(f854(x68211,x68211)),f773(f251(x68211,x68211,a841),x68212)))
% 191.21/191.74 [6822]E(x68221,f180(f855(x68222,a841)))+~P1(f773(f773(f232(f855(x68222,a841)),x68221),f180(f855(x68222,a841))))
% 191.21/191.74 [6907]~P1(f773(f773(f233(a847),f2(a847)),x69072))+P1(f773(f773(f233(a847),f52(a847,x69071,x69072)),x69072))
% 191.21/191.74 [6909]~P1(f773(f773(f233(a1),f2(a1)),x69092))+P1(f773(f773(f233(a1),f52(a1,x69091,x69092)),x69092))
% 191.21/191.74 [6910]~P1(f773(f773(f233(a847),f2(a847)),x69102))+P1(f773(f773(f232(a847),f52(a847,x69101,x69102)),x69102))
% 191.21/191.74 [6911]~P1(f773(f773(f232(a1),f2(a1)),x69111))+P1(f773(f773(f232(a1),f52(a1,x69111,x69112)),x69111))
% 191.21/191.74 [6983]~P99(x69831)+E(f773(f773(f3(f855(x69831,a841)),f773(f773(f302(x69831),x69832),f180(f855(x69831,a841)))),f773(f257(x69831),x69832)),f773(f773(f302(x69831),x69832),f180(f855(x69831,a841))))
% 191.21/191.74 [7061]~P49(x70611,x70612)+P47(x70611,f239(f855(x70611,a841)),f773(f256(f854(x70611,x70611)),f773(f251(x70611,x70611,a841),x70612)))
% 191.21/191.74 [7062]P1(f773(x70621,x70622))+P1(f773(f773(f334(f855(f854(a847,a847),a841)),f605(x70622,x70621)),a100))
% 191.21/191.74 [7105]E(f773(f773(f125(a847),f130(a847,f773(f294(a847,x71051),x71052))),f773(f773(f140(a847),x71052),f115(a847))),f130(a847,f773(f294(a847,x71051),f773(a114,x71052))))+~P1(f773(f773(f232(a847),x71051),x71052))
% 191.21/191.74 [7262]E(x72621,f2(a847))+~E(f773(f132(a847,a847,f82(a847),x72621),x72622),f2(a847))
% 191.21/191.74 [7291]~P1(f773(f773(f233(a1),f773(f773(f3(a1),x72911),x72912)),f2(a1)))+P1(f773(f773(f233(a1),x72911),x72912))
% 191.21/191.74 [7321]P36(x73211,x73212)+~P36(x73211,f773(f773(f281(x73211,x73211,x73211),x73212),x73212))
% 191.21/191.74 [7353]~P1(f773(f773(f232(a847),f773(a114,x73531)),x73532))+P1(f175(a841,a178,f773(f232(a847),x73531),x73532))
% 191.21/191.74 [7513]P29(a847,a847,f773(f773(f9(a847,a847,a847),f3(a847)),x75131),x75132)+P1(f773(f773(f334(a847),f607(x75131,x75132)),x75132))
% 191.21/191.74 [7572]E(f773(f773(f773(f67(a847,x75721,f82(a847)),f773(f18(a847,x75721),f80(a847))),f2(a847)),x75722),f773(f42(x75721),x75722))+~P1(f773(f63(x75721),x75722))
% 191.21/191.74 [7615]P29(a847,a847,f773(f773(f9(a847,a847,a847),f3(a847)),x76151),x76152)+~P1(f773(f773(f232(a847),x76151),f607(x76151,x76152)))
% 191.21/191.74 [7672]P36(x76721,x76722)+P1(f773(f773(f232(f855(x76721,a841)),f601(x76722,x76721)),f773(f277(x76721,x76721,x76722),f601(x76722,x76721))))
% 191.21/191.74 [7676]P58(x76761,x76762)+~P36(x76761,f773(f256(f854(x76761,x76761)),f773(f251(x76761,x76761,a841),x76762)))
% 191.21/191.74 [7748]P1(f773(f773(f232(a847),f773(a114,x77481)),x77482))+~P1(f175(a841,a178,f773(f232(a847),x77481),x77482))
% 191.21/191.74 [7804]P1(f773(f773(f334(f854(a847,a847)),f773(f773(f241(a847,a847),x78041),x78042)),f300(a847,a323)))+~P1(f773(f773(f232(a847),x78041),x78042))
% 191.21/191.74 [7898]P49(x78981,x78982)+~P47(x78981,f239(f855(x78981,a841)),f773(f256(f854(x78981,x78981)),f773(f251(x78981,x78981,a841),x78982)))
% 191.21/191.74 [8154]~P36(x81541,f773(f278(x81541,x81541),x81542))+P36(x81541,f773(f278(x81541,x81541),f773(f773(f281(x81541,x81541,x81541),x81542),f300(x81541,x81542))))
% 191.21/191.74 [8271]P1(f773(f63(f854(x82711,x82711)),f773(f773(f281(x82711,x82711,x82711),x82712),f300(x82711,x82712))))+~P1(f773(f63(f854(x82711,x82711)),x82712))
% 191.21/191.74 [8301]E(x83011,f2(a1))+P1(f773(f56(x83012,x83011),f773(f773(f241(a1,a1),f773(f773(f43(a1),x83012),x83011)),f52(a1,x83012,x83011))))
% 191.21/191.74 [8315]~P1(f773(f773(f334(f854(a847,a847)),f773(f773(f241(a847,a847),x83151),x83152)),f300(a847,a323)))+P1(f773(f773(f232(a847),x83151),x83152))
% 191.21/191.74 [8336]~P67(x83361)+E(f773(f132(x83361,x83361,f773(f9(x83361,x83361,x83361),f82(x83361)),f2(x83361)),f773(f142(x83361),x83362)),f773(f132(x83361,x83361,f82(x83361),f2(x83361)),x83362))
% 191.21/191.74 [8611]P1(f773(f773(f334(f854(a847,a847)),f773(f773(f241(a847,a847),x86111),x86112)),f773(f773(f281(a847,a847,a847),a323),f300(a847,a323))))+~P1(f773(f773(f233(a847),x86111),x86112))
% 191.21/191.74 [8653]~P1(f773(f63(f854(x86531,x86531)),f773(f773(f281(x86531,x86531,x86531),x86532),f300(x86531,x86532))))+P1(f773(f63(f854(x86531,x86531)),x86532))
% 191.21/191.74 [8873]P56(x88731,x88732)+P1(f773(f773(f334(f854(x88731,x88731)),f773(f773(f241(x88731,x88731),f634(x88732,x88731)),f634(x88732,x88731))),f773(f773(f281(x88731,x88731,x88731),x88732),f300(x88731,x88732))))
% 191.21/191.74 [8874]P56(x88741,x88742)+P1(f773(f773(f334(f854(x88741,x88741)),f773(f773(f241(x88741,x88741),f641(x88742,x88741)),f641(x88742,x88741))),f773(f773(f281(x88741,x88741,x88741),x88742),f300(x88741,x88742))))
% 191.21/191.74 [8983]~P1(f773(f773(f334(f854(a847,a847)),f773(f773(f241(a847,a847),x89831),x89832)),f773(f773(f281(a847,a847,a847),a323),f300(a847,a323))))+P1(f773(f773(f233(a847),x89831),x89832))
% 191.21/191.74 [4964]~P88(x49641)+E(f773(f773(f82(x49641),f773(f106(x49641),a85)),x49642),x49642)
% 191.21/191.74 [4994]~P69(x49941)+E(f773(f773(f82(x49941),f773(f81(x49941),x49942)),x49942),f2(x49941))
% 191.21/191.74 [4995]~P6(x49951)+E(f773(f773(f82(x49951),f773(f81(x49951),x49952)),x49952),f2(x49951))
% 191.21/191.74 [4996]~P90(x49961)+E(f773(f773(f103(x49961),f773(f81(x49961),x49962)),x49962),f239(x49961))
% 191.21/191.74 [4997]~P90(x49971)+E(f773(f773(f104(x49971),f773(f81(x49971),x49972)),x49972),f180(x49971))
% 191.21/191.74 [5027]~P88(x50271)+E(f773(f773(f83(x50271),f773(f106(x50271),a99)),x50272),f773(f81(x50271),x50272))
% 191.21/191.74 [5186]~P104(x51861)+E(f773(f773(f83(x51861),f773(f81(x51861),f80(x51861))),x51862),f773(f81(x51861),x51862))
% 191.21/191.74 [5228]E(f773(f77(a1),x52281),f80(a1))+~E(f773(f77(a1),f773(f773(f83(a1),x52281),x52282)),f80(a1))
% 191.21/191.74 [5315]~P88(x53151)+E(f773(f773(f82(x53151),f80(x53151)),f773(f106(x53151),x53152)),f773(f106(x53151),f773(f773(f3(a1),x53152),a99)))
% 191.21/191.74 [5370]~P93(x53701)+E(f15(x53701,f773(f773(f302(x53701),x53702),f180(f855(x53701,a841)))),x53702)
% 191.21/191.74 [5371]~P100(x53711)+E(f16(x53711,f773(f773(f302(x53711),x53712),f180(f855(x53711,a841)))),x53712)
% 191.21/191.74 [5372]~P100(x53721)+E(f17(x53721,f773(f773(f302(x53721),x53722),f180(f855(x53721,a841)))),x53722)
% 191.21/191.74 [5373]~P93(x53731)+E(f12(x53731,f773(f773(f302(x53731),x53732),f180(f855(x53731,a841)))),x53732)
% 191.21/191.74 [5374]~P9(x53741)+E(f45(x53741,f773(f773(f302(x53741),x53742),f180(f855(x53741,a841)))),x53742)
% 191.21/191.74 [5375]~P9(x53751)+E(f44(x53751,f773(f773(f302(x53751),x53752),f180(f855(x53751,a841)))),x53752)
% 191.21/191.74 [5397]E(f773(f773(f82(a847),x53971),f773(f773(f3(a847),x53972),x53971)),x53972)+P1(f773(f773(f233(a847),x53972),x53971))
% 191.21/191.74 [5429]E(x54291,f115(x54292))+P1(f773(f773(f233(a847),f2(a847)),f773(f181(f848(x54292)),x54291)))
% 191.21/191.74 [5547]~P100(x55471)+E(f13(x55471,f179(x55471),f773(f773(f302(x55471),x55472),f180(f855(x55471,a841)))),x55472)
% 191.21/191.74 [5548]~P100(x55481)+E(f14(x55481,f236(x55481),f773(f773(f302(x55481),x55482),f180(f855(x55481,a841)))),x55482)
% 191.21/191.74 [5609]E(f773(f773(f82(a847),x56091),f773(f773(f3(a847),x56092),x56091)),x56092)+~P1(f773(f773(f232(a847),x56091),x56092))
% 191.21/191.74 [5610]E(f773(f773(f83(a1),x56101),f773(f773(f43(a1),x56102),x56101)),x56102)+~P1(f773(f773(f279(a1),x56101),x56102))
% 191.21/191.74 [5611]E(f773(f773(f3(a847),x56111),f773(f773(f3(a847),x56111),x56112)),x56112)+~P1(f773(f773(f232(a847),x56112),x56111))
% 191.21/191.74 [5630]E(f52(a847,f773(f773(f3(a847),x56301),x56302),x56302),f52(a847,x56301,x56302))+P1(f773(f773(f233(a847),x56301),x56302))
% 191.21/191.74 [5640]E(f773(f81(a1),f773(f773(f43(a1),x56401),f773(f81(a1),x56402))),f285(x56401,x56402))+P1(f773(f773(f232(a1),f2(a1)),x56402))
% 191.21/191.74 [5642]~E(x56422,f2(a847))+P1(f773(f773(f233(a847),f2(a847)),f773(f773(f242(a847),x56421),x56422)))
% 191.21/191.74 [5702]~P88(x57021)+E(f773(f773(f82(x57021),f773(f81(x57021),f80(x57021))),f773(f106(x57021),x57022)),f773(f106(x57021),f773(f773(f82(a1),x57022),a99)))
% 191.21/191.74 [5703]E(f773(f773(f242(a847),f773(f106(a847),x57031)),x57032),f773(f773(f242(a847),f2(a847)),x57032))+~P1(f773(a186,f773(f106(a1),x57031)))
% 191.21/191.74 [5804]E(f773(f131(a847),f130(a847,f773(f294(a847,x58041),x58042))),x58041)+~P1(f773(f773(f233(a847),x58041),x58042))
% 191.21/191.74 [5821]E(f773(f773(f83(a847),f773(f106(a847),x58211)),f773(f106(a847),x58212)),f773(f106(a847),f773(f773(f83(a1),x58211),x58212)))+P1(f773(f773(f233(a1),x58211),a85))
% 191.21/191.74 [5827]~P118(x58271)+P1(f773(f773(f232(x58271),f2(x58271)),f773(f773(f83(x58271),x58272),x58272)))
% 191.21/191.74 [5839]E(f773(f773(f3(a847),f773(a114,x58391)),x58392),f773(a114,f773(f773(f3(a847),x58391),x58392)))+~P1(f773(f773(f232(a847),x58392),x58391))
% 191.21/191.74 [5842]E(f52(a847,f773(f773(f3(a847),x58421),x58422),x58422),f52(a847,x58421,x58422))+~P1(f773(f773(f232(a847),x58422),x58421))
% 191.21/191.74 [5894]E(f773(f773(f242(a847),f773(a107,x58941)),x58942),f773(a107,f773(f773(f242(a1),x58941),x58942)))+~P1(f773(f773(f232(a1),f2(a1)),x58941))
% 191.21/191.74 [5910]P1(f773(f127(x59101),x59102))+P1(f773(f773(f233(a847),f722(x59102,x59101)),f773(f181(f848(x59101)),x59102)))
% 191.21/191.74 [5911]P1(f773(f127(x59111),x59112))+P1(f773(f773(f233(a847),f726(x59112,x59111)),f773(f181(f848(x59111)),x59112)))
% 191.21/191.74 [5926]~P1(f773(f773(f279(a1),x59261),x59262))+P1(f773(f773(f279(a1),f773(f81(a1),x59261)),x59262))
% 191.21/191.74 [5929]~E(x59291,f115(x59292))+~P1(f773(f773(f233(a847),f2(a847)),f773(f181(f848(x59292)),x59291)))
% 191.21/191.74 [5942]E(f134(a847,f130(a847,f773(f294(a847,x59421),x59422))),f773(f773(f3(a847),x59422),f80(a847)))+~P1(f773(f773(f233(a847),x59421),x59422))
% 191.21/191.74 [5945]E(f773(f773(f82(a1),x59451),f773(f102(a1),f773(a114,f628(x59452,x59451)))),x59452)+~P1(f773(f773(f233(a1),x59451),x59452))
% 191.21/191.74 [5951]E(x59511,f2(a847))+E(f773(f773(f83(a847),x59512),f773(f773(f242(a847),x59512),f773(f773(f3(a847),x59511),f80(a847)))),f773(f773(f242(a847),x59512),x59511))
% 191.21/191.74 [5977]E(f773(f773(f83(a847),f773(a107,x59771)),f773(a107,x59772)),f773(a107,f773(f773(f83(a1),x59771),x59772)))+~P1(f773(f773(f232(a1),f2(a1)),x59771))
% 191.21/191.74 [5978]E(f773(f773(f43(a847),f773(a107,x59781)),f773(a107,x59782)),f773(a107,f773(f773(f43(a1),x59781),x59782)))+~P1(f773(f773(f232(a1),f2(a1)),x59781))
% 191.21/191.74 [5992]~P85(x59921)+E(f773(f773(f82(x59921),x59922),x59922),f773(f773(f83(x59921),f773(f773(f82(x59921),f80(x59921)),f80(x59921))),x59922))
% 191.21/191.74 [6011]E(f773(f773(f43(a1),f773(f77(a1),x60111)),f773(f77(a1),x60112)),f773(f77(a1),f773(f773(f43(a1),x60111),x60112)))+~P1(f773(f773(f279(a1),x60112),x60111))
% 191.21/191.74 [6012]E(f773(f773(f3(a1),f773(f102(a1),x60121)),f773(f102(a1),x60122)),f773(f102(a1),f773(f773(f3(a847),x60121),x60122)))+~P1(f773(f773(f232(a847),x60122),x60121))
% 191.21/191.74 [6014]E(f773(f773(f241(a1,a1),f773(f106(a1),a99)),f773(f773(f82(a1),x60141),x60142)),f57(x60141,x60142))+~P1(f773(f773(f232(a1),x60142),f2(a1)))
% 191.21/191.74 [6053]E(f164(x60531,x60532),f115(f848(x60531)))+P1(f773(f773(f334(f848(x60531)),f721(x60532,x60531)),f773(f158(f848(x60531)),x60532)))
% 191.21/191.74 [6117]~P1(f773(f773(f279(a847),x61171),x61172))+P1(f773(f773(f279(a847),x61171),f773(f773(f82(a847),x61172),x61171)))
% 191.21/191.74 [6139]E(f773(f773(f140(a1),x61391),f163(f773(f773(f82(a1),x61391),f80(a1)),x61392)),f163(x61391,x61392))+~P1(f773(f773(f232(a1),x61391),x61392))
% 191.21/191.74 [6177]~P1(f773(f773(f233(a847),x61772),x61771))+P1(f773(f773(f233(a847),f2(a847)),f773(f773(f3(a847),x61771),x61772)))
% 191.21/191.74 [6209]~P1(f773(f773(f233(a847),x62091),f773(a107,x62092)))+P1(f773(f773(f233(a1),f773(f102(a1),x62091)),x62092))
% 191.21/191.74 [6210]P1(f773(f773(f279(a1),x62101),x62102))+~P1(f773(f773(f279(a1),f773(f81(a1),x62101)),x62102))
% 191.21/191.74 [6240]~P100(x62401)+E(f773(f773(f103(f855(x62401,a841)),f773(f257(x62401),x62402)),f773(f773(f302(x62401),x62402),f180(f855(x62401,a841)))),f773(f293(x62401),x62402))
% 191.21/191.74 [6243]~P1(f773(f773(f233(a847),f2(a847)),x62431))+P1(f773(f773(f233(a847),f2(a847)),f773(f773(f242(a847),x62431),x62432)))
% 191.21/191.74 [6244]~P1(f773(f773(f232(a1),f2(a1)),x62441))+P1(f773(f773(f232(a1),f2(a1)),f773(f773(f242(a1),x62441),x62442)))
% 191.21/191.74 [6272]~E(f773(x62721,f2(a847)),f2(a847))+E(f773(f773(f8(a847,a847),x62721),f295(a847,f773(a114,f2(a847)),x62722)),f773(f773(f8(a847,a847),x62721),f295(a847,f2(a847),x62722)))
% 191.21/191.74 [6338]~P88(x63381)+E(f773(f773(f83(x63381),f773(f773(f82(x63381),f80(x63381)),f80(x63381))),f773(f106(x63381),x63382)),f773(f106(x63381),f773(f773(f82(a1),x63382),x63382)))
% 191.21/191.74 [6360]E(f773(f773(f302(a1),x63601),f295(a1,f773(f773(f82(a1),x63601),f80(a1)),x63602)),f295(a1,x63601,x63602))+P1(f773(f773(f233(a1),x63602),x63601))
% 191.21/191.74 [6361]P1(f773(f773(f233(a847),x63611),f773(a107,x63612)))+~P1(f773(f773(f233(a1),f773(f102(a1),x63611)),x63612))
% 191.21/191.74 [6463]P1(f773(f773(f279(a847),x64631),x64632))+~P1(f773(f773(f279(a847),x64631),f773(f773(f82(a847),x64632),x64631)))
% 191.21/191.74 [6469]E(f773(a107,f773(f773(f43(a1),f773(f106(a1),x64691)),f773(f106(a1),x64692))),f773(f773(f43(a847),f773(f106(a847),x64691)),f773(f106(a847),x64692)))+P1(f773(a186,f773(f106(a1),x64691)))
% 191.21/191.74 [6529]P1(f773(f773(f233(a847),x65291),x65292))+~P1(f773(f773(f233(a847),f2(a847)),f773(f773(f3(a847),x65292),x65291)))
% 191.21/191.74 [6572]P1(f773(f773(f233(a847),f2(a847)),x65721))+~P1(f773(f773(f233(a847),f2(a847)),f773(f773(f83(a847),x65722),x65721)))
% 191.21/191.74 [6573]P1(f773(f773(f233(a847),f2(a847)),x65731))+~P1(f773(f773(f233(a847),f2(a847)),f773(f773(f83(a847),x65731),x65732)))
% 191.21/191.74 [6590]~P1(f773(f773(f232(a1),x65901),f2(a1)))+E(f773(f773(f83(a847),f773(a107,f773(f81(a1),x65901))),f773(a107,f773(f81(a1),x65902))),f773(a107,f773(f773(f83(a1),x65901),x65902)))
% 191.21/191.74 [6656]~E(x66562,f180(f855(x66561,a841)))+P1(f773(f773(f232(f855(x66561,a841)),x66562),f773(f81(f855(x66561,a841)),x66562)))
% 191.21/191.74 [6719]~P88(x67191)+E(f773(f773(f82(x67191),f773(f773(f82(x67191),f2(x67191)),f773(f106(x67191),x67192))),f773(f106(x67191),x67192)),f773(f106(x67191),f773(f773(f82(a1),x67192),x67192)))
% 191.21/191.74 [6728]~P1(f773(f773(f279(a1),f773(f102(a1),x67281)),x67282))+P1(f773(f773(f279(a847),x67281),f773(a107,f773(f77(a1),x67282))))
% 191.21/191.74 [6780]~P1(f773(f773(f233(a1),x67801),x67802))+P1(f773(f773(f232(a1),f773(f773(f82(a1),x67801),f80(a1))),x67802))
% 191.21/191.74 [6819]P1(f773(f773(f279(a1),f773(f102(a1),x68191)),x68192))+~P1(f773(f773(f279(a847),x68191),f773(a107,f773(f77(a1),x68192))))
% 191.21/191.74 [6853]E(x68531,f2(a847))+~P1(f773(f773(f232(a1),f773(f102(a1),x68532)),f773(f81(a1),f773(f102(a1),x68531))))
% 191.21/191.74 [6854]E(x68541,f2(a847))+~P1(f773(f773(f232(a1),f773(f102(a1),x68541)),f773(f81(a1),f773(f102(a1),x68542))))
% 191.21/191.74 [6959]E(f773(f773(f241(a1,a1),f773(f106(a1),a99)),f773(f773(f82(a1),x69591),x69592)),f57(x69591,x69592))+~P1(f773(f773(f232(a1),f2(a1)),f773(f773(f82(a1),x69591),x69592)))
% 191.21/191.74 [6996]~P30(x69961,x69962)+P36(x69961,f773(f240(f855(f854(x69961,x69961),a841),f855(f854(x69961,x69961),a841)),x69962))
% 191.21/191.74 [7017]~P1(f773(f773(f232(a847),f773(a114,f2(a847))),x70171))+P1(f773(f773(f232(a847),f773(a114,f2(a847))),f773(f773(f242(a847),x70171),x70172)))
% 191.21/191.74 [7187]~P1(f773(f773(f233(a1),x71871),x71872))+P1(f773(f773(f233(a1),f773(f773(f82(a1),x71871),x71871)),f773(f773(f82(a1),x71872),x71872)))
% 191.21/191.74 [7199]~P1(f773(f773(f232(a1),x71991),x71992))+P1(f773(f773(f232(a1),f773(f773(f82(a1),x71991),x71991)),f773(f773(f82(a1),x71992),x71992)))
% 191.21/191.74 [7266]~P1(f773(f773(f233(a847),f2(a847)),x72661))+P1(f773(f773(f233(a847),f773(f773(f3(a847),x72661),f773(a114,x72662))),x72661))
% 191.21/191.74 [7303]P1(f773(f773(f232(a847),f773(a114,f2(a847))),x73031))+~P1(f773(f773(f232(a847),f773(a114,f2(a847))),f773(f773(f83(a847),x73032),x73031)))
% 191.21/191.74 [7304]P1(f773(f773(f232(a847),f773(a114,f2(a847))),x73041))+~P1(f773(f773(f232(a847),f773(a114,f2(a847))),f773(f773(f83(a847),x73041),x73042)))
% 191.21/191.74 [7308]P1(f773(f773(f232(a847),f773(f773(f153(a847),x73081),x73082)),f773(f155(a847),x73081)))+~P1(f773(f773(f233(a847),x73082),f773(f181(f848(a847)),x73081)))
% 191.21/191.74 [7352]P1(f773(f773(f233(a1),x73521),x73522))+~P1(f773(f773(f232(a1),f773(f773(f82(a1),x73521),f80(a1))),x73522))
% 191.21/191.74 [7398]P1(f773(f63(x73981),f239(f855(x73981,a841))))+~P1(f773(f63(f855(x73982,x73981)),f239(f855(f855(x73982,x73981),a841))))
% 191.21/191.74 [7399]P1(f773(f63(x73991),f239(f855(x73991,a841))))+~P1(f773(f63(f856(x73992,x73991)),f239(f855(f856(x73992,x73991),a841))))
% 191.21/191.74 [7400]P1(f773(f63(x74001),f239(f855(x74001,a841))))+~P1(f773(f63(f856(x74001,x74002)),f239(f855(f856(x74001,x74002),a841))))
% 191.21/191.74 [7439]E(x74391,f180(f855(x74392,a841)))+~P1(f773(f773(f232(f855(x74392,a841)),x74391),f773(f81(f855(x74392,a841)),x74391)))
% 191.21/191.74 [7582]E(f773(f132(f848(x75821),f848(x75821),f125(x75821),f115(x75821)),x75822),f115(x75821))+P1(f773(f773(f334(f848(x75821)),f768(x75822,x75821)),f773(f158(f848(x75821)),x75822)))
% 191.21/191.74 [7583]E(f773(f132(f848(x75831),f848(x75831),f125(x75831),f115(x75831)),x75832),f115(x75831))+P1(f773(f773(f334(f848(x75831)),f769(x75832,x75831)),f773(f158(f848(x75831)),x75832)))
% 191.21/191.74 [7824]P1(f773(f773(f233(a1),x78241),x78242))+~P1(f773(f773(f233(a1),f773(f773(f82(a1),x78241),x78241)),f773(f773(f82(a1),x78242),x78242)))
% 191.21/191.74 [7827]P1(f773(f773(f232(a1),x78271),x78272))+~P1(f773(f773(f232(a1),f773(f773(f82(a1),x78271),x78271)),f773(f773(f82(a1),x78272),x78272)))
% 191.21/191.74 [7919]~P85(x79191)+E(f773(f773(f83(x79191),f773(f773(f82(x79191),f80(x79191)),f80(x79191))),f773(f773(f8(a847,x79191),f102(x79191)),f295(a847,f80(a847),x79192))),f773(f773(f83(x79191),f773(f102(x79191),x79192)),f773(f773(f82(x79191),f773(f102(x79191),x79192)),f80(x79191))))
% 191.21/191.74 [7975]P1(f773(f773(f334(a847),x79751),x79752))+~P1(f773(f773(f334(a1),f773(f102(a1),x79751)),f773(f303(a847,a1,f102(a1)),x79752)))
% 191.21/191.74 [8125]~P1(f773(f63(x81251),x81252))+E(f773(f303(a847,x81251,f583(x81252,x81251)),f773(f256(a847),f773(f773(f9(a847,a847,a841),f233(a847)),f584(x81252,x81251)))),x81252)
% 191.21/191.74 [8409]P48(x84091,x84092)+P1(f773(f773(f334(f854(x84091,x84091)),f773(f773(f241(x84091,x84091),f473(x84092,x84091)),f473(x84092,x84091))),x84092))
% 191.21/191.74 [8545]~P88(x85451)+E(f773(f773(f3(x85451),f80(x85451)),f773(f106(x85451),x85452)),f773(f106(x85451),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f81(a1),x85452))))
% 191.21/191.74 [8649]~P1(f773(f773(f233(f855(a847,a841)),x86491),x86492))+P1(f773(f773(f233(f855(a1,a841)),f773(f303(a847,a1,f102(a1)),x86491)),f773(f303(a847,a1,f102(a1)),x86492)))
% 191.21/191.74 [8676]~P1(f773(f773(f233(a1),x86761),x86762))+P1(f773(f773(f233(a1),f773(f773(f3(a1),f773(f773(f82(a1),x86761),x86761)),a99)),f773(f773(f82(a1),x86762),x86762)))
% 191.21/191.74 [8678]~P1(f773(f773(f233(a1),x86781),x86782))+P1(f773(f773(f232(a1),f773(f773(f3(a1),f773(f773(f82(a1),x86781),x86781)),a99)),f773(f773(f82(a1),x86782),x86782)))
% 191.21/191.74 [8745]~P1(f773(f773(f334(a847),x87451),f773(f158(a847),x87452)))+P1(f773(f773(f232(a847),x87451),f773(f132(a847,a847,f82(a847),f2(a847)),x87452)))
% 191.21/191.74 [8817]P44(x88171,x88172)+~P1(f773(f773(f334(f854(x88171,x88171)),f773(f773(f241(x88171,x88171),f427(x88172,x88171)),f427(x88172,x88171))),x88172))
% 191.21/191.74 [8950]~P1(f773(f773(f233(f855(a1,a841)),f773(f303(a847,a1,f102(a1)),x89501)),f773(f303(a847,a1,f102(a1)),x89502)))+P1(f773(f773(f233(f855(a847,a841)),x89501),x89502))
% 191.21/191.74 [8951]~P1(f773(f773(f232(f855(a1,a841)),f773(f303(a847,a1,f102(a1)),x89511)),f773(f303(a847,a1,f102(a1)),x89512)))+P1(f773(f773(f232(f855(a847,a841)),x89511),x89512))
% 191.21/191.74 [9033]P1(f773(f773(f233(a1),x90331),x90332))+~P1(f773(f773(f233(a1),f773(f773(f3(a1),f773(f773(f82(a1),x90331),x90331)),a99)),f773(f773(f82(a1),x90332),x90332)))
% 191.21/191.74 [9035]P1(f773(f773(f233(a1),x90351),x90352))+~P1(f773(f773(f232(a1),f773(f773(f3(a1),f773(f773(f82(a1),x90351),x90351)),a99)),f773(f773(f82(a1),x90352),x90352)))
% 191.21/191.74 [9888]~P1(f773(f63(x98881),x98882))+E(f773(f181(f848(x98881)),f92(f848(x98881),f773(f773(f20(f848(x98881),a841,a841),f773(f773(f10(a841,f855(a841,a841),f848(x98881)),a331),f773(f773(f9(f848(x98881),f855(x98881,a841),a841),f773(f773(f10(f855(x98881,a841),f855(f855(x98881,a841),a841),f848(x98881)),a330),f158(x98881))),x98882))),f127(x98881)))),f209(x98881,x98882))
% 191.21/191.74 [5941]E(f773(f773(f82(a847),f773(f773(f3(a847),x59411),x59412)),x59412),x59411)+~P1(f773(f773(f232(a847),x59412),x59411))
% 191.21/191.74 [6007]E(f773(f773(f43(a847),f773(f773(f83(a847),x60071),x60072)),x60072),x60071)+~P1(f773(f773(f233(a847),f2(a847)),x60072))
% 191.21/191.74 [6008]E(f773(f773(f43(a847),f773(f773(f83(a847),x60081),x60082)),x60081),x60082)+~P1(f773(f773(f233(a847),f2(a847)),x60081))
% 191.21/191.74 [6013]~P66(x60131)+E(f773(f773(f8(a847,x60131),f773(f153(x60131),x60132)),f773(f294(a847,f2(a847)),f773(f181(f848(x60131)),x60132))),f773(f155(x60131),x60132))
% 191.21/191.74 [6131]E(f52(a847,f773(a114,f773(f773(f83(a847),x61311),x61312)),x61311),f80(a847))+~P1(f773(f773(f233(a847),f80(a847)),x61311))
% 191.21/191.74 [6137]E(f773(a114,f773(f773(f82(a847),f773(f106(a847),x61371)),x61372)),f773(f773(f82(a847),f80(a847)),x61372))+~P1(f773(a186,f773(f106(a1),x61371)))
% 191.21/191.74 [6163]E(f773(a107,f773(f773(f242(a1),f773(f106(a1),x61631)),x61632)),f773(f773(f242(a847),f773(f106(a847),x61631)),x61632))+P1(f773(a186,f773(f106(a1),x61631)))
% 191.21/191.74 [6416]E(f773(f773(f3(a847),x64161),f773(f106(a847),f773(f773(f82(a1),x64162),a99))),f773(f773(f3(a847),f773(a114,x64161)),f773(f106(a847),x64162)))+~P1(f773(f773(f233(a1),a85),x64162))
% 191.21/191.74 [6498]E(x64981,f2(a847))+E(f773(a114,f773(f773(f82(a847),f773(f773(f3(a847),x64981),f80(a847))),x64982)),f773(f773(f82(a847),x64981),x64982))
% 191.21/191.74 [6543]E(x65431,f2(a1))+P1(f773(f773(f233(a1),f2(a1)),f773(f773(f242(a1),f773(f77(a1),x65431)),x65432)))
% 191.21/191.74 [6558]~E(x65582,f2(a847))+P1(f773(f773(f233(a1),f2(a1)),f773(f773(f242(a1),f773(f77(a1),x65581)),x65582)))
% 191.21/191.74 [6595]E(x65951,f2(a847))+E(f773(f773(f82(a847),x65952),f773(f773(f83(a847),f773(f773(f3(a847),x65951),f80(a847))),x65952)),f773(f773(f83(a847),x65951),x65952))
% 191.21/191.74 [6650]~P1(f773(f773(f232(a1),x66501),x66502))+P1(f773(f773(f233(a1),f773(f773(f82(a1),x66501),a99)),x66502))
% 191.21/191.74 [6784]E(f773(f773(f140(a847),x67841),f130(a847,f773(f294(a847,f773(a114,x67841)),x67842))),f130(a847,f773(f294(a847,x67841),x67842)))+~P1(f773(f773(f233(a847),x67841),x67842))
% 191.21/191.74 [6953]~P1(f773(f773(f279(a1),x69531),f773(f102(a1),x69532)))+P1(f773(f773(f279(a847),f773(a107,f773(f77(a1),x69531))),x69532))
% 191.21/191.74 [6987]E(x69871,x69872)+~E(f773(f773(f3(a1),f773(f773(f82(a1),x69871),x69871)),a99),f773(f773(f3(a1),f773(f773(f82(a1),x69872),x69872)),a99))
% 191.21/191.74 [6990]E(x69901,f115(x69902))+E(f263(x69902,f773(f773(f143(x69902,f854(a101,x69902)),f773(f241(a101,x69902),f80(a101))),x69901)),f270(x69902,x69901))
% 191.21/191.74 [7229]P1(f773(f773(f232(a1),x72291),x72292))+~P1(f773(f773(f233(a1),f773(f773(f82(a1),x72291),a99)),x72292))
% 191.21/191.74 [7371]P1(f773(f773(f279(a1),x73711),f773(f102(a1),x73712)))+~P1(f773(f773(f279(a847),f773(a107,f773(f77(a1),x73711))),x73712))
% 191.21/191.74 [7721]~P1(f773(f773(f233(a847),x77211),x77212))+P1(f773(f773(f334(f854(a847,a847)),f773(f773(f241(a847,a847),x77211),x77212)),a237))
% 191.21/191.74 [7949]~P1(f773(f773(f233(a101),f2(a101)),x79491))+P1(f773(f773(f233(a101),f773(f240(a101,f854(a101,a101)),f773(f264(x79491),x79492))),x79491))
% 191.21/191.74 [8250]~P79(x82501)+P1(f773(f773(f232(x82501),f773(f77(x82501),f773(f155(x82501),x82502))),f773(f155(x82501),f773(f773(f143(x82501,x82501),f77(x82501)),x82502))))
% 191.21/191.74 [8273]P1(f773(f773(f233(a847),x82731),x82732))+~P1(f773(f773(f334(f854(a847,a847)),f773(f773(f241(a847,a847),x82731),x82732)),a237))
% 191.21/191.74 [8433]E(f773(f773(f241(x84331,x84331),f653(x84332,x84331)),f653(x84332,x84331)),x84332)+~P1(f773(f773(f334(f854(x84331,x84331)),x84332),f300(x84331,f180(f855(f854(x84331,x84331),a841)))))
% 191.21/191.74 [8478]E(f773(f294(a847,x84781),f773(f773(f82(a847),x84781),f773(f42(a847),x84782))),x84782)+~P1(f773(f773(f232(f855(a847,a841)),x84782),f773(f294(a847,x84781),f773(f773(f82(a847),x84781),f773(f42(a847),x84782)))))
% 191.21/191.74 [8778]E(f773(f773(f43(a1),f773(f106(a1),f773(f773(f3(a1),f773(f773(f82(a1),x87781),x87781)),a99))),f773(f106(a1),f773(f773(f82(a1),x87782),x87782))),f773(f773(f43(a1),f773(f106(a1),x87781)),f773(f106(a1),x87782)))+~P1(f773(f773(f232(a1),f2(a1)),f773(f106(a1),x87782)))
% 191.21/191.74 [8883]E(f162(f848(x88831),f773(f773(f10(a841,a841,f848(x88831)),a328),f773(f773(f9(f848(x88831),f848(x88831),a841),a330),f115(x88831))),x88832),f164(x88831,f164(x88831,x88832)))+~P18(a847,f773(f142(a847),f773(f773(f143(f848(x88831),a847),f181(f848(x88831))),x88832)))
% 191.21/191.74 [8886]E(f773(f773(f43(a1),f773(f106(a1),f773(f773(f3(a1),f773(f773(f82(a1),x88861),x88861)),a99))),f773(f106(a1),f773(f773(f82(a1),x88862),x88862))),f773(f773(f43(a1),f773(f773(f82(a1),f773(f106(a1),x88861)),f80(a1))),f773(f106(a1),x88862)))+P1(f773(f773(f232(a1),f2(a1)),f773(f106(a1),x88862)))
% 191.21/191.74 [9658]P1(f773(a186,x96582))+E(f773(f773(f88(a1,a847),f773(f773(f3(a1),x96581),x96582)),f773(f773(f20(a1,a847,a847),f773(f773(f9(a1,a847,f855(a847,a847)),f773(f773(f10(a841,f855(a847,f855(a847,a847)),a1),f98(a847)),a186)),f2(a847))),a107)),f773(f773(f3(a847),f773(a107,x96581)),f773(a107,x96582)))
% 191.21/191.74 [9662]E(f773(f773(f88(a1,a847),f773(f106(a1),f773(f773(f82(a1),x96621),f773(f81(a1),x96622)))),f773(f773(f20(a1,a847,a847),f773(f773(f9(a1,a847,f855(a847,a847)),f773(f773(f10(a841,f855(a847,f855(a847,a847)),a1),f98(a847)),a186)),f2(a847))),a107)),f773(f773(f3(a847),f773(f106(a847),x96621)),f773(f106(a847),x96622)))+P1(f773(f773(f233(a1),x96622),a85))
% 191.21/191.74 [9663]~P30(x96631,x96632)+P1(f773(f773(f232(f855(f854(x96631,x96631),a841)),f773(f773(f281(x96631,x96631,x96631),f773(f240(f855(f854(x96631,x96631),a841),f855(f854(x96631,x96631),a841)),x96632)),f773(f250(f855(f854(x96631,x96631),a841),f855(f854(x96631,x96631),a841)),x96632))),f773(f240(f855(f854(x96631,x96631),a841),f855(f854(x96631,x96631),a841)),x96632)))
% 191.21/191.74 [9719]~E(f773(f42(a847),f773(f256(a847),f773(f773(f20(a847,a841,a841),f773(f773(f10(a841,f855(a841,a841),a847),a331),f773(f773(f9(a847,f855(a847,a841),a841),f334(a847)),x97191))),f773(f773(f9(a847,a847,a841),f233(a847)),f773(a114,x97192))))),f2(a847))+~P1(f773(f773(f334(a847),f2(a847)),x97191))
% 191.21/191.74 [9732]E(f291(a847,f773(f773(f20(a847,f855(a847,a841),f855(a847,a841)),f773(f773(f10(f855(a847,f855(a841,a841)),f855(f855(a847,a841),f855(a847,a841)),a847),f20(a847,a841,a841)),f773(f773(f10(f855(a847,a841),f855(a847,f855(a841,a841)),a847),f773(f10(a841,f855(a841,a841),a847),a331)),f279(a847)))),f773(f773(f10(f855(a847,a841),f855(a847,a841),a847),f773(f10(a841,a841,a847),a328)),f773(f9(a847,a847,a841),f279(a847)))),x97321,x97322),f180(f855(a847,a841)))+~P1(f773(f773(f279(a847),x97322),x97321))
% 191.21/191.74 [9740]E(f292(a847,f279(a847),f773(f773(f20(a847,f855(a847,a841),f855(a847,a841)),f773(f773(f10(f855(a847,f855(a841,a841)),f855(f855(a847,a841),f855(a847,a841)),a847),f20(a847,a841,a841)),f773(f773(f10(f855(a847,a841),f855(a847,f855(a841,a841)),a847),f773(f10(a841,f855(a841,a841),a847),a331)),f279(a847)))),f773(f773(f10(f855(a847,a841),f855(a847,a841),a847),f773(f10(a841,a841,a847),a328)),f773(f9(a847,a847,a841),f279(a847)))),x97401,x97402),f180(f855(a847,a841)))+P1(f773(f773(f279(a847),x97401),x97402))
% 191.21/191.74 [9741]E(f289(a847,f279(a847),f773(f773(f20(a847,f855(a847,a841),f855(a847,a841)),f773(f773(f10(f855(a847,f855(a841,a841)),f855(f855(a847,a841),f855(a847,a841)),a847),f20(a847,a841,a841)),f773(f773(f10(f855(a847,a841),f855(a847,f855(a841,a841)),a847),f773(f10(a841,f855(a841,a841),a847),a331)),f279(a847)))),f773(f773(f10(f855(a847,a841),f855(a847,a841),a847),f773(f10(a841,a841,a847),a328)),f773(f9(a847,a847,a841),f279(a847)))),x97411,x97412),f180(f855(a847,a841)))+P1(f773(f773(f279(a847),x97411),x97412))
% 191.21/191.74 [9745]E(f292(a847,f279(a847),f773(f773(f20(a847,f855(a847,a841),f855(a847,a841)),f773(f773(f10(f855(a847,f855(a841,a841)),f855(f855(a847,a841),f855(a847,a841)),a847),f20(a847,a841,a841)),f773(f773(f10(f855(a847,a841),f855(a847,f855(a841,a841)),a847),f773(f10(a841,f855(a841,a841),a847),a331)),f279(a847)))),f773(f773(f10(f855(a847,a841),f855(a847,a841),a847),f773(f10(a841,a841,a847),a328)),f773(f9(a847,a847,a841),f279(a847)))),x97451,x97452),f180(f855(a847,a841)))+~P1(f773(f773(f279(a847),x97452),x97451))
% 191.21/191.74 [9747]E(f289(a847,f279(a847),f773(f773(f20(a847,f855(a847,a841),f855(a847,a841)),f773(f773(f10(f855(a847,f855(a841,a841)),f855(f855(a847,a841),f855(a847,a841)),a847),f20(a847,a841,a841)),f773(f773(f10(f855(a847,a841),f855(a847,f855(a841,a841)),a847),f773(f10(a841,f855(a841,a841),a847),a331)),f279(a847)))),f773(f773(f10(f855(a847,a841),f855(a847,a841),a847),f773(f10(a841,a841,a847),a328)),f773(f9(a847,a847,a841),f279(a847)))),x97471,x97472),f180(f855(a847,a841)))+~P1(f773(f773(f279(a847),x97472),x97471))
% 191.21/191.74 [9790]E(f52(a1,f773(f106(a1),f773(f773(f3(a1),f773(f773(f82(a1),x97901),x97901)),a99)),f773(f106(a1),f773(f773(f82(a1),x97902),x97902))),f773(f773(f82(a1),f773(f773(f83(a1),f773(f106(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),f52(a1,f773(f106(a1),x97901),f773(f106(a1),x97902)))),f80(a1)))+~P1(f773(f773(f232(a1),f2(a1)),f773(f106(a1),x97902)))
% 191.21/191.74 [9799]E(f52(a1,f773(f106(a1),f773(f773(f3(a1),f773(f773(f82(a1),x97991),x97991)),a99)),f773(f106(a1),f773(f773(f82(a1),x97992),x97992))),f773(f773(f3(a1),f773(f773(f83(a1),f773(f106(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),f52(a1,f773(f773(f82(a1),f773(f106(a1),x97991)),f80(a1)),f773(f106(a1),x97992)))),f80(a1)))+P1(f773(f773(f232(a1),f2(a1)),f773(f106(a1),x97992)))
% 191.21/191.74 [9857]~P9(x98571)+E(f44(x98571,f773(f256(x98571),f773(f773(f10(f855(x98571,a841),a841,x98571),f90(x98571)),f773(f773(f10(f855(x98571,a841),f855(x98571,a841),x98571),f773(f20(x98571,a841,a841),f773(f773(f10(a841,f855(a841,a841),x98571),a335),f773(f773(f9(x98571,f855(x98571,a841),a841),f334(x98571)),x98572)))),f232(x98571))))),f45(x98571,x98572))
% 191.21/191.74 [9881]~P36(x98811,x98812)+P58(x98811,f773(f773(f9(x98811,f855(f854(x98811,x98811),a841),f855(x98811,a841)),f773(f773(f10(f855(x98811,f855(f855(f854(x98811,x98811),a841),a841)),f855(f855(f854(x98811,x98811),a841),f855(x98811,a841)),x98811),f9(x98811,f855(f854(x98811,x98811),a841),a841)),f773(f773(f10(f855(x98811,f854(x98811,x98811)),f855(x98811,f855(f855(f854(x98811,x98811),a841),a841)),x98811),f773(f10(f854(x98811,x98811),f855(f855(f854(x98811,x98811),a841),a841),x98811),f334(f854(x98811,x98811)))),f241(x98811,x98811)))),x98812))
% 191.21/191.74 [9882]~P12(x98821,f239(f855(x98821,a841)),x98822)+P11(x98821,f773(f773(f9(x98821,f855(f854(x98821,x98821),a841),f855(x98821,a841)),f773(f773(f10(f855(x98821,f855(f855(f854(x98821,x98821),a841),a841)),f855(f855(f854(x98821,x98821),a841),f855(x98821,a841)),x98821),f9(x98821,f855(f854(x98821,x98821),a841),a841)),f773(f773(f10(f855(x98821,f854(x98821,x98821)),f855(x98821,f855(f855(f854(x98821,x98821),a841),a841)),x98821),f773(f10(f854(x98821,x98821),f855(f855(f854(x98821,x98821),a841),a841),x98821),f334(f854(x98821,x98821)))),f241(x98821,x98821)))),x98822))
% 191.21/191.74 [9919]P36(x99191,x99192)+~P58(x99191,f773(f773(f9(x99191,f855(f854(x99191,x99191),a841),f855(x99191,a841)),f773(f773(f10(f855(x99191,f855(f855(f854(x99191,x99191),a841),a841)),f855(f855(f854(x99191,x99191),a841),f855(x99191,a841)),x99191),f9(x99191,f855(f854(x99191,x99191),a841),a841)),f773(f773(f10(f855(x99191,f854(x99191,x99191)),f855(x99191,f855(f855(f854(x99191,x99191),a841),a841)),x99191),f773(f10(f854(x99191,x99191),f855(f855(f854(x99191,x99191),a841),a841),x99191),f334(f854(x99191,x99191)))),f241(x99191,x99191)))),x99192))
% 191.21/191.74 [9920]P12(x99201,f239(f855(x99201,a841)),x99202)+~P11(x99201,f773(f773(f9(x99201,f855(f854(x99201,x99201),a841),f855(x99201,a841)),f773(f773(f10(f855(x99201,f855(f855(f854(x99201,x99201),a841),a841)),f855(f855(f854(x99201,x99201),a841),f855(x99201,a841)),x99201),f9(x99201,f855(f854(x99201,x99201),a841),a841)),f773(f773(f10(f855(x99201,f854(x99201,x99201)),f855(x99201,f855(f855(f854(x99201,x99201),a841),a841)),x99201),f773(f10(f854(x99201,x99201),f855(f855(f854(x99201,x99201),a841),a841),x99201),f334(f854(x99201,x99201)))),f241(x99201,x99201)))),x99202))
% 191.21/191.74 [7175]E(f773(f773(f82(a847),f773(f106(a847),f773(f773(f3(a1),x71751),a99))),x71752),f773(a114,f773(f773(f82(a847),f773(f106(a847),x71751)),x71752)))+P1(f773(a186,f773(f106(a1),x71751)))
% 191.21/191.74 [7640]~P88(x76401)+E(f773(f773(f82(x76401),f773(f773(f82(x76401),f80(x76401)),f773(f106(x76401),x76402))),f773(f106(x76401),x76402)),f773(f106(x76401),f773(f773(f3(a1),f773(f773(f82(a1),x76402),x76402)),a99)))
% 191.21/191.74 [8275]~P1(f773(f773(f232(a1),x82751),x82752))+P1(f773(f773(f233(a1),f773(f773(f82(a1),x82751),x82751)),f773(f773(f3(a1),f773(f773(f82(a1),x82752),x82752)),a99)))
% 191.21/191.74 [8277]~P1(f773(f773(f232(a1),x82771),x82772))+P1(f773(f773(f232(a1),f773(f773(f82(a1),x82771),x82771)),f773(f773(f3(a1),f773(f773(f82(a1),x82772),x82772)),a99)))
% 191.21/191.74 [8680]P1(f773(f773(f232(a1),x86801),x86802))+~P1(f773(f773(f233(a1),f773(f773(f82(a1),x86801),x86801)),f773(f773(f3(a1),f773(f773(f82(a1),x86802),x86802)),a99)))
% 191.21/191.74 [8682]P1(f773(f773(f232(a1),x86821),x86822))+~P1(f773(f773(f232(a1),f773(f773(f82(a1),x86821),x86821)),f773(f773(f3(a1),f773(f773(f82(a1),x86822),x86822)),a99)))
% 191.21/191.74 [8941]~P1(f773(f773(f233(a1),x89411),x89412))+P1(f773(f773(f233(a1),f773(f773(f3(a1),f773(f773(f82(a1),x89411),x89411)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),x89412),x89412)),a99)))
% 191.21/191.74 [8943]~P1(f773(f773(f232(a1),x89431),x89432))+P1(f773(f773(f232(a1),f773(f773(f3(a1),f773(f773(f82(a1),x89431),x89431)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),x89432),x89432)),a99)))
% 191.21/191.74 [9177]P1(f773(f773(f233(a1),x91771),x91772))+~P1(f773(f773(f233(a1),f773(f773(f3(a1),f773(f773(f82(a1),x91771),x91771)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),x91772),x91772)),a99)))
% 191.21/191.74 [9179]P1(f773(f773(f232(a1),x91791),x91792))+~P1(f773(f773(f232(a1),f773(f773(f3(a1),f773(f773(f82(a1),x91791),x91791)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),x91792),x91792)),a99)))
% 191.21/191.74 [9210]~P1(f773(f63(x92101),x92102))+P1(f773(f63(f855(x92101,a841)),f773(f256(f855(x92101,a841)),f773(f773(f9(f855(x92101,a841),f855(x92101,a841),a841),f232(f855(x92101,a841))),x92102))))
% 191.21/191.74 [9257]~E(f773(f277(f854(a847,a847),f854(a847,a847),a111),f773(f773(f302(f854(a847,a847)),x92571),f180(f855(f854(a847,a847),a841)))),f773(f277(f854(a847,a847),f854(a847,a847),a111),f773(f773(f302(f854(a847,a847)),x92572),f180(f855(f854(a847,a847),a841)))))+P1(f773(f773(f334(f854(f854(a847,a847),f854(a847,a847))),f773(f773(f241(f854(a847,a847),f854(a847,a847)),x92571),x92572)),a111))
% 191.21/191.74 [9343]E(f773(f277(f854(a847,a847),f854(a847,a847),a111),f773(f773(f302(f854(a847,a847)),x93431),f180(f855(f854(a847,a847),a841)))),f773(f277(f854(a847,a847),f854(a847,a847),a111),f773(f773(f302(f854(a847,a847)),x93432),f180(f855(f854(a847,a847),a841)))))+~P1(f773(f773(f334(f854(f854(a847,a847),f854(a847,a847))),f773(f773(f241(f854(a847,a847),f854(a847,a847)),x93431),x93432)),a111))
% 191.21/191.74 [9377]P1(f773(f773(f232(a1),f2(a1)),f698(x93771,x93772)))+E(f773(f256(a1),f773(f773(f20(a1,a841,a841),f773(f773(f10(a841,f855(a841,a841),a1),a331),f773(f232(a1),f2(a1)))),x93771)),f773(f256(a1),f773(f773(f20(a1,a841,a841),f773(f773(f10(a841,f855(a841,a841),a1),a331),f773(f232(a1),f2(a1)))),x93772)))
% 191.21/191.74 [9867]~P9(x98671)+E(f45(x98671,f773(f256(x98671),f773(f773(f10(f855(x98671,a841),a841,x98671),f90(x98671)),f773(f773(f10(f855(x98671,a841),f855(x98671,a841),x98671),f773(f20(x98671,a841,a841),f773(f773(f10(a841,f855(a841,a841),x98671),a335),f773(f773(f9(x98671,f855(x98671,a841),a841),f334(x98671)),x98672)))),f773(f9(x98671,x98671,a841),f232(x98671)))))),f44(x98671,x98672))
% 191.21/191.74 [9887]P1(f773(f773(f334(a847),f2(a847)),x98871))+E(f773(f42(a847),f773(f256(a847),f773(f773(f20(a847,a841,a841),f773(f773(f10(a841,f855(a841,a841),a847),a331),f773(f773(f9(a847,f855(a847,a841),a841),f773(f773(f10(a847,f855(f855(a847,a841),a841),a847),f334(a847)),a114)),x98871))),f773(f773(f9(a847,a847,a841),f233(a847)),x98872)))),f773(f42(a847),f773(f256(a847),f773(f773(f20(a847,a841,a841),f773(f773(f10(a841,f855(a841,a841),a847),a331),f773(f773(f9(a847,f855(a847,a841),a841),f334(a847)),x98871))),f773(f773(f9(a847,a847,a841),f233(a847)),f773(a114,x98872))))))
% 191.21/191.74 [9934]P1(f773(f773(f279(a847),x99341),x99342))+~P1(f773(f773(f334(a847),x99342),f287(a847,f773(f773(f20(a847,f855(a847,a841),f855(a847,a841)),f773(f773(f10(f855(a847,f855(a841,a841)),f855(f855(a847,a841),f855(a847,a841)),a847),f20(a847,a841,a841)),f773(f773(f10(f855(a847,a841),f855(a847,f855(a841,a841)),a847),f773(f10(a841,f855(a841,a841),a847),a331)),f279(a847)))),f773(f773(f10(f855(a847,a841),f855(a847,a841),a847),f773(f10(a841,a841,a847),a328)),f773(f9(a847,a847,a841),f279(a847)))),x99341)))
% 191.21/191.74 [9935]P1(f773(f773(f279(a847),x99351),x99352))+~P1(f773(f773(f334(a847),x99351),f290(a847,f773(f773(f20(a847,f855(a847,a841),f855(a847,a841)),f773(f773(f10(f855(a847,f855(a841,a841)),f855(f855(a847,a841),f855(a847,a841)),a847),f20(a847,a841,a841)),f773(f773(f10(f855(a847,a841),f855(a847,f855(a841,a841)),a847),f773(f10(a841,f855(a841,a841),a847),a331)),f279(a847)))),f773(f773(f10(f855(a847,a841),f855(a847,a841),a847),f773(f10(a841,a841,a847),a328)),f773(f9(a847,a847,a841),f279(a847)))),x99352)))
% 191.21/191.74 [9936]~P1(f773(f773(f279(a847),x99361),x99362))+~P1(f773(f773(f334(a847),x99362),f290(a847,f773(f773(f20(a847,f855(a847,a841),f855(a847,a841)),f773(f773(f10(f855(a847,f855(a841,a841)),f855(f855(a847,a841),f855(a847,a841)),a847),f20(a847,a841,a841)),f773(f773(f10(f855(a847,a841),f855(a847,f855(a841,a841)),a847),f773(f10(a841,f855(a841,a841),a847),a331)),f279(a847)))),f773(f773(f10(f855(a847,a841),f855(a847,a841),a847),f773(f10(a841,a841,a847),a328)),f773(f9(a847,a847,a841),f279(a847)))),x99361)))
% 191.21/191.74 [9937]~P1(f773(f773(f279(a847),x99371),x99372))+~P1(f773(f773(f334(a847),x99371),f287(a847,f773(f773(f20(a847,f855(a847,a841),f855(a847,a841)),f773(f773(f10(f855(a847,f855(a841,a841)),f855(f855(a847,a841),f855(a847,a841)),a847),f20(a847,a841,a841)),f773(f773(f10(f855(a847,a841),f855(a847,f855(a841,a841)),a847),f773(f10(a841,f855(a841,a841),a847),a331)),f279(a847)))),f773(f773(f10(f855(a847,a841),f855(a847,a841),a847),f773(f10(a841,a841,a847),a328)),f773(f9(a847,a847,a841),f279(a847)))),x99372)))
% 191.21/191.74 [7507]~P88(x75071)+E(f773(f773(f83(x75071),x75072),f773(f106(x75071),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))),x75072)
% 191.21/191.74 [7774]~P88(x77741)+E(f773(f773(f82(x77741),f773(f106(x77741),x77742)),f80(x77741)),f773(f106(x77741),f773(f773(f82(a1),x77742),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))
% 191.21/191.74 [7918]P1(f773(f773(f232(a1),f2(a1)),f773(f106(a1),x79182)))+E(f773(f773(f242(a1),x79181),f773(f106(a847),f773(f773(f3(a1),f773(f773(f82(a1),x79182),x79182)),a99))),f80(a1))
% 191.21/191.74 [9234]~P1(f773(f773(f232(a1),f2(a1)),f773(f106(a1),x92342)))+E(f773(f773(f242(a1),x92341),f773(f106(a847),f773(f773(f3(a1),f773(f773(f82(a1),x92342),x92342)),a99))),f773(f773(f88(a1,a1),f773(f773(f242(a1),x92341),f773(f106(a847),x92342))),f773(f773(f20(a1,a1,a1),f773(f773(f10(a1,f855(a1,a1),a1),f83(a1)),f773(f83(a1),x92341))),f7(a1))))
% 191.21/191.74 [9709]~P1(f773(f773(f233(a847),f773(f106(a847),x97091)),f773(a114,x97092)))+P1(f773(f773(f88(a1,a841),f773(f106(a1),f773(f773(f82(a1),x97091),a99))),f773(f773(f20(a1,a841,a841),f773(f773(f10(a841,f855(a841,a841),a1),a335),f773(f773(f10(a841,a841,a1),a328),a186))),f773(f773(f9(a1,a847,a841),f773(f773(f10(a847,f855(a847,a841),a1),f233(a847)),a107)),x97092))))
% 191.21/191.74 [9710]~P1(f773(f773(f232(a847),f773(f106(a847),x97101)),f773(a114,x97102)))+P1(f773(f773(f88(a1,a841),f773(f106(a1),f773(f773(f82(a1),x97101),a99))),f773(f773(f20(a1,a841,a841),f773(f773(f10(a841,f855(a841,a841),a1),a335),f773(f773(f10(a841,a841,a1),a328),a186))),f773(f773(f9(a1,a847,a841),f773(f773(f10(a847,f855(a847,a841),a1),f232(a847)),a107)),x97102))))
% 191.21/191.74 [9774]P1(f773(f773(f233(a847),f773(f106(a847),x97741)),f773(a114,x97742)))+~P1(f773(f773(f88(a1,a841),f773(f106(a1),f773(f773(f82(a1),x97741),a99))),f773(f773(f20(a1,a841,a841),f773(f773(f10(a841,f855(a841,a841),a1),a335),f773(f773(f10(a841,a841,a1),a328),a186))),f773(f773(f9(a1,a847,a841),f773(f773(f10(a847,f855(a847,a841),a1),f233(a847)),a107)),x97742))))
% 191.21/191.74 [9775]P1(f773(f773(f232(a847),f773(f106(a847),x97751)),f773(a114,x97752)))+~P1(f773(f773(f88(a1,a841),f773(f106(a1),f773(f773(f82(a1),x97751),a99))),f773(f773(f20(a1,a841,a841),f773(f773(f10(a841,f855(a841,a841),a1),a335),f773(f773(f10(a841,a841,a1),a328),a186))),f773(f773(f9(a1,a847,a841),f773(f773(f10(a847,f855(a847,a841),a1),f232(a847)),a107)),x97752))))
% 191.21/191.74 [9805]~P1(f773(f773(f233(a847),f773(a114,x98052)),f773(f106(a847),x98051)))+P1(f773(f773(f88(a1,a841),f773(f106(a1),f773(f773(f82(a1),x98051),a99))),f773(f773(f20(a1,a841,a841),f773(f773(f10(a841,f855(a841,a841),a1),a331),f773(f773(f10(a841,a841,a1),a328),a186))),f773(f773(f20(a1,a841,a841),f773(f773(f10(a841,f855(a841,a841),a1),a335),f773(f773(f10(a841,a841,a1),a328),a186))),f773(f773(f10(a847,a841,a1),f773(f233(a847),x98052)),a107)))))
% 191.21/191.74 [9806]~P1(f773(f773(f232(a847),f773(a114,x98062)),f773(f106(a847),x98061)))+P1(f773(f773(f88(a1,a841),f773(f106(a1),f773(f773(f82(a1),x98061),a99))),f773(f773(f20(a1,a841,a841),f773(f773(f10(a841,f855(a841,a841),a1),a331),f773(f773(f10(a841,a841,a1),a328),a186))),f773(f773(f20(a1,a841,a841),f773(f773(f10(a841,f855(a841,a841),a1),a335),f773(f773(f10(a841,a841,a1),a328),a186))),f773(f773(f10(a847,a841,a1),f773(f232(a847),x98062)),a107)))))
% 191.21/191.74 [9855]P1(f773(f773(f233(a847),f773(a114,x98551)),f773(f106(a847),x98552)))+~P1(f773(f773(f88(a1,a841),f773(f106(a1),f773(f773(f82(a1),x98552),a99))),f773(f773(f20(a1,a841,a841),f773(f773(f10(a841,f855(a841,a841),a1),a331),f773(f773(f10(a841,a841,a1),a328),a186))),f773(f773(f20(a1,a841,a841),f773(f773(f10(a841,f855(a841,a841),a1),a335),f773(f773(f10(a841,a841,a1),a328),a186))),f773(f773(f10(a847,a841,a1),f773(f233(a847),x98551)),a107)))))
% 191.21/191.74 [9856]P1(f773(f773(f232(a847),f773(a114,x98561)),f773(f106(a847),x98562)))+~P1(f773(f773(f88(a1,a841),f773(f106(a1),f773(f773(f82(a1),x98562),a99))),f773(f773(f20(a1,a841,a841),f773(f773(f10(a841,f855(a841,a841),a1),a331),f773(f773(f10(a841,a841,a1),a328),a186))),f773(f773(f20(a1,a841,a841),f773(f773(f10(a841,f855(a841,a841),a1),a335),f773(f773(f10(a841,a841,a1),a328),a186))),f773(f773(f10(a847,a841,a1),f773(f232(a847),x98561)),a107)))))
% 191.21/191.74 [9927]~P1(f773(f773(f334(a847),f2(a847)),x99271))+E(f773(a114,f773(f42(a847),f773(f256(a847),f773(f773(f20(a847,a841,a841),f773(f773(f10(a841,f855(a841,a841),a847),a331),f773(f773(f9(a847,f855(a847,a841),a841),f773(f773(f10(a847,f855(f855(a847,a841),a841),a847),f334(a847)),a114)),x99271))),f773(f773(f9(a847,a847,a841),f233(a847)),x99272))))),f773(f42(a847),f773(f256(a847),f773(f773(f20(a847,a841,a841),f773(f773(f10(a841,f855(a841,a841),a847),a331),f773(f773(f9(a847,f855(a847,a841),a841),f334(a847)),x99271))),f773(f773(f9(a847,a847,a841),f233(a847)),f773(a114,x99272))))))
% 191.21/191.74 [8459]~P88(x84591)+E(f773(f773(f83(x84591),f773(f106(x84591),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))),x84592),x84592)
% 191.21/191.74 [8519]~P88(x85191)+E(f773(f773(f82(x85191),f80(x85191)),f773(f106(x85191),x85192)),f773(f106(x85191),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),x85192)))
% 191.21/191.74 [8565]~P88(x85651)+E(f773(f773(f3(x85651),f773(f106(x85651),x85652)),f80(x85651)),f773(f106(x85651),f773(f773(f82(a1),x85652),f773(f81(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))))
% 191.21/191.74 [8698]~P1(f773(f773(f233(a847),f773(f106(a847),a85)),x86982))+E(f773(f773(f3(a847),x86981),f773(f773(f3(a847),x86982),f773(f106(a847),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),f773(f773(f3(a847),f773(a114,x86981)),x86982))
% 191.21/191.74 [9273]~P85(x92731)+E(f773(f773(f83(x92731),x92732),x92732),f773(f773(f242(x92731),x92732),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))))
% 191.21/191.74 [9274]~P75(x92741)+E(f773(f773(f242(x92741),x92742),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),f773(f773(f83(x92741),x92742),x92742))
% 191.21/191.74 [9276]~P88(x92761)+E(f773(f773(f83(x92761),x92762),f773(f106(x92761),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),f773(f773(f82(x92761),x92762),x92762))
% 191.21/191.74 [9509]~P133(x95091)+E(f773(f773(f242(x95091),f773(f81(x95091),x95092)),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),f773(f773(f242(x95091),x95092),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))))
% 191.21/191.74 [9510]~P110(x95101)+E(f773(f773(f242(x95101),f773(f77(x95101),x95102)),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),f773(f773(f242(x95101),x95102),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))))
% 191.21/191.74 [9506]~P88(x95061)+E(f773(f773(f83(x95061),f773(f106(x95061),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),x95062),f773(f773(f82(x95061),x95062),x95062))
% 191.21/191.74 [9620]~P110(x96201)+E(f773(f77(x96201),f773(f773(f242(x96201),x96202),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))),f773(f773(f242(x96201),x96202),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))))
% 191.21/191.74 [9670]~P110(x96701)+P1(f773(f773(f232(x96701),f2(x96701)),f773(f773(f242(x96701),x96702),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))))
% 191.21/191.74 [9846]~E(f773(a114,x98462),f773(f106(a847),x98461))+P1(f773(f773(f88(a1,a841),f773(f106(a1),f773(f773(f82(a1),x98461),a99))),f773(f773(f20(a1,a841,a841),f773(f773(f10(a841,f855(a841,a841),a1),a331),f773(f773(f10(a841,a841,a1),a328),a186))),f773(f773(f20(a1,a841,a841),f773(f773(f10(a841,f855(a841,a841),a1),a335),f773(f773(f10(a841,a841,a1),a328),a186))),f773(f773(f9(a1,a847,a841),f773(f773(f10(a847,f855(a847,a841),a1),a330),a107)),x98462)))))
% 191.21/191.74 [9847]~E(f773(f106(a847),x98471),f773(a114,x98472))+P1(f773(f773(f88(a1,a841),f773(f106(a1),f773(f773(f82(a1),x98471),a99))),f773(f773(f20(a1,a841,a841),f773(f773(f10(a841,f855(a841,a841),a1),a331),f773(f773(f10(a841,a841,a1),a328),a186))),f773(f773(f20(a1,a841,a841),f773(f773(f10(a841,f855(a841,a841),a1),a335),f773(f773(f10(a841,a841,a1),a328),a186))),f773(f773(f9(a1,a847,a841),f773(f773(f10(a847,f855(a847,a841),a1),a330),a107)),x98472)))))
% 191.21/191.74 [9890]E(f773(a114,x98901),f773(f106(a847),x98902))+~P1(f773(f773(f88(a1,a841),f773(f106(a1),f773(f773(f82(a1),x98902),a99))),f773(f773(f20(a1,a841,a841),f773(f773(f10(a841,f855(a841,a841),a1),a331),f773(f773(f10(a841,a841,a1),a328),a186))),f773(f773(f20(a1,a841,a841),f773(f773(f10(a841,f855(a841,a841),a1),a335),f773(f773(f10(a841,a841,a1),a328),a186))),f773(f773(f9(a1,a847,a841),f773(f773(f10(a847,f855(a847,a841),a1),a330),a107)),x98901)))))
% 191.21/191.74 [9891]E(f773(f106(a847),x98911),f773(a114,x98912))+~P1(f773(f773(f88(a1,a841),f773(f106(a1),f773(f773(f82(a1),x98911),a99))),f773(f773(f20(a1,a841,a841),f773(f773(f10(a841,f855(a841,a841),a1),a331),f773(f773(f10(a841,a841,a1),a328),a186))),f773(f773(f20(a1,a841,a841),f773(f773(f10(a841,f855(a841,a841),a1),a335),f773(f773(f10(a841,a841,a1),a328),a186))),f773(f773(f9(a1,a847,a841),f773(f773(f10(a847,f855(a847,a841),a1),a330),a107)),x98912)))))
% 191.21/191.74 [9668]~P88(x96681)+E(f773(f773(f242(x96681),f773(f106(x96681),a99)),f773(f773(f83(a847),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),x96682)),f80(x96681))
% 191.21/191.74 [9669]~P133(x96691)+E(f773(f773(f242(x96691),f773(f81(x96691),f80(x96691))),f773(f773(f83(a847),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),x96692)),f80(x96691))
% 191.21/191.74 [9672]~P75(x96721)+E(f773(f773(f242(x96721),x96722),f773(f106(a847),f773(f773(f3(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))),a99))),f773(f773(f83(x96721),f773(f773(f83(x96721),x96722),x96722)),x96722))
% 191.21/191.74 [9870]~P1(f773(f773(f232(a1),f2(a1)),x98702))+E(f52(a1,f773(f773(f82(a1),f80(a1)),f773(f773(f83(a1),f773(f106(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),x98701)),f773(f773(f83(a1),f773(f106(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),x98702)),f773(f773(f82(a1),f80(a1)),f773(f773(f83(a1),f773(f106(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),f52(a1,x98701,x98702))))
% 191.21/191.74 [9893]~P1(f773(f773(f232(a1),f2(a1)),x98932))+E(f773(f773(f43(a1),f773(f773(f82(a1),f80(a1)),f773(f773(f83(a1),f773(f106(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),x98931))),f773(f773(f83(a1),f773(f106(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),x98932)),f773(f773(f43(a1),x98931),x98932))
% 191.21/191.74 [9895]~P1(f773(f773(f232(a1),x98952),f2(a1)))+E(f773(f773(f43(a1),f773(f773(f82(a1),f80(a1)),f773(f773(f83(a1),f773(f106(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),x98951))),f773(f773(f83(a1),f773(f106(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),x98952)),f773(f773(f43(a1),f773(f773(f82(a1),x98951),f80(a1))),x98952))
% 191.21/191.74 [9896]~P1(f773(f773(f232(a1),x98962),f2(a1)))+E(f52(a1,f773(f773(f82(a1),f80(a1)),f773(f773(f83(a1),f773(f106(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),x98961)),f773(f773(f83(a1),f773(f106(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),x98962)),f773(f773(f3(a1),f773(f773(f83(a1),f773(f106(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),f52(a1,f773(f773(f82(a1),x98961),f80(a1)),x98962))),f80(a1)))
% 191.21/191.74 [9765]~P88(x97651)+E(f773(f773(f242(x97651),f773(f106(x97651),a99)),f773(a114,f773(f773(f83(a847),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),x97652))),f773(f106(x97651),a99))
% 191.21/191.74 [9767]~P133(x97671)+E(f773(f773(f242(x97671),f773(f81(x97671),f80(x97671))),f773(a114,f773(f773(f83(a847),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),x97672))),f773(f81(x97671),f80(x97671)))
% 191.21/191.74 [5993]E(x59931,x59932)+~P39(a25,x59931,x59933,x59932)
% 191.21/191.74 [5005]~P36(x50051,x50053)+P36(x50051,f327(x50051,x50052,x50053))
% 191.21/191.74 [5169]P31(x51691,x51692,x51693)+~P31(x51691,f773(a114,x51692),x51693)
% 191.21/191.74 [5252]~P12(x52521,x52522,x52523)+P12(f848(x52521),f149(x52521,x52522),f147(x52521,x52523))
% 191.21/191.74 [5253]~P47(x52531,x52532,x52533)+P47(f848(x52531),f149(x52531,x52532),f147(x52531,x52533))
% 191.21/191.74 [5362]P54(x53621,x53622,x53623)+~E(f626(x53623,x53622,x53621),f627(x53623,x53622,x53621))
% 191.21/191.74 [5363]P53(x53631,x53632,x53633)+~E(f639(x53633,x53632,x53631),f640(x53633,x53632,x53631))
% 191.21/191.74 [6315]P32(x63151,x63152,x63153)+~P31(x63151,f669(x63153,x63152,x63151),f781(x63153,x63152,x63151))
% 191.21/191.74 [4562]~E(x45621,f183(x45622))+~E(x45621,f773(f227(x45622),x45623))
% 191.21/191.74 [4611]~E(f773(f142(x46112),x46111),x46113)+E(x46111,f773(f142(x46112),x46113))
% 191.21/191.74 [4612]~E(x46122,f773(f142(x46121),x46123))+E(f773(f142(x46121),x46122),x46123)
% 191.21/191.74 [4656]E(x46561,x46562)+~E(f773(f227(x46563),x46561),f773(f227(x46563),x46562))
% 191.21/191.74 [4657]E(x46571,x46572)+~E(f773(f142(x46573),x46571),f773(f142(x46573),x46572))
% 191.21/191.74 [4855]~P11(x48553,x48551)+P1(f773(f773(x48551,x48552),x48552))
% 191.21/191.74 [4856]~P49(x48563,x48561)+P1(f773(f773(x48561,x48562),x48562))
% 191.21/191.74 [4858]~P58(x48581,x48582)+P1(f773(f321(x48581,x48582),x48583))
% 191.21/191.74 [4920]~P36(x49201,x49202)+P36(f848(x49201),f773(f133(x49201,x49202),x49203))
% 191.21/191.74 [4924]~P1(f773(x49242,x49243))+~E(f773(f256(x49241),x49242),f180(f855(x49241,a841)))
% 191.21/191.74 [4925]~P1(f773(x49252,x49253))+~E(f180(f855(x49251,a841)),f773(f256(x49251),x49252))
% 191.21/191.74 [4961]~P1(f773(x49611,x49613))+P1(f773(x49611,f92(x49612,x49611)))
% 191.21/191.74 [5085]~E(x50852,x50853)+P1(f773(f773(f334(x50851),x50852),f773(a330,x50853)))
% 191.21/191.74 [5138]E(f773(f142(x51381),x51382),f773(f773(f140(x51381),x51383),f115(x51381)))+~E(x51382,f773(f773(f140(x51381),x51383),f115(x51381)))
% 191.21/191.74 [5139]~E(x51393,f773(f773(f140(x51391),x51392),f115(x51391)))+E(f773(f773(f140(x51391),x51392),f115(x51391)),f773(f142(x51391),x51393))
% 191.21/191.74 [5164]~E(x51643,f773(f18(f851(x51642),x51641),f183(x51642)))+E(f169(x51641,x51642,x51643),f180(f855(x51641,a841)))
% 191.21/191.74 [5185]E(f773(f42(x51851),f374(x51852,x51853,x51851)),x51852)+~E(f773(f42(x51851),x51853),f773(a114,x51852))
% 191.21/191.74 [5191]~P36(x51911,x51913)+P1(f773(f773(f334(x51911),x51912),f322(x51911,x51913)))
% 191.21/191.74 [5194]~E(f773(f142(x51942),x51941),f773(f773(f140(x51942),x51943),f115(x51942)))+E(x51941,f773(f773(f140(x51942),x51943),f115(x51942)))
% 191.21/191.74 [5195]~E(f773(f773(f140(x51952),x51953),f115(x51952)),f773(f142(x51952),x51951))+E(x51951,f773(f773(f140(x51952),x51953),f115(x51952)))
% 191.21/191.74 [5210]E(x52101,f773(f18(f851(x52102),x52103),f183(x52102)))+~E(f169(x52103,x52102,x52101),f180(f855(x52103,a841)))
% 191.21/191.74 [5216]E(f87(f854(a847,a847),f55(x52161,x52162)),x52163)+~P1(f773(f55(x52161,x52162),x52163))
% 191.21/191.74 [5224]~E(x52243,f773(f227(x52241),x52242))+P1(f773(f773(f334(x52241),x52242),f226(x52241,x52243)))
% 191.21/191.74 [5314]~E(x53142,f115(x53141))+P1(f773(f773(f334(f848(x53141)),x53142),f149(x53141,x53143)))
% 191.21/191.74 [5322]~P47(x53221,x53222,x53223)+P47(x53221,x53222,f773(f278(x53221,x53221),x53223))
% 191.21/191.74 [5323]~P54(x53231,x53232,x53233)+P54(x53231,x53232,f773(f278(x53231,x53231),x53233))
% 191.21/191.74 [5343]~P7(x53431)+E(f52(x53431,f52(x53431,x53432,x53433),x53433),f52(x53431,x53432,x53433))
% 191.21/191.74 [5440]E(x54401,x54402)+~P1(f773(f773(f334(x54403),x54401),f773(a330,x54402)))
% 191.21/191.74 [5483]~P2(x54831)+E(f182(x54831,x54832,f2(a847),x54833),x54833)
% 191.21/191.74 [5503]P47(x55031,x55032,x55033)+~P47(x55031,x55032,f773(f278(x55031,x55031),x55033))
% 191.21/191.74 [5504]P54(x55041,x55042,x55043)+~P54(x55041,x55042,f773(f278(x55041,x55041),x55043))
% 191.21/191.74 [5525]E(x55251,f773(f227(x55252),x55253))+~P1(f773(f773(f334(x55252),x55253),f226(x55252,x55251)))
% 191.21/191.74 [5607]~P1(f773(a26,x56073))+P1(f773(a26,f32(x56071,x56072,x56073)))
% 191.21/191.74 [5619]E(f773(f126(x56191,x56192),x56193),f115(x56191))+P1(f773(x56192,f746(x56193,x56192,x56191)))
% 191.21/191.74 [5775]~P1(f773(f127(x57751),x57753))+P1(f773(f127(x57751),f151(x57751,x57752,x57753)))
% 191.21/191.74 [5776]~P1(f773(f127(x57761),x57762))+P1(f773(f127(x57761),f160(x57761,x57762,x57763)))
% 191.21/191.74 [5777]~P1(f773(f127(x57771),x57773))+P1(f773(f127(x57771),f162(x57771,x57772,x57773)))
% 191.21/191.74 [5778]~P140(x57781,x57783,x57782)+P1(f773(x57781,f52(a1,x57782,x57783)))
% 191.21/191.74 [5877]P1(f773(a26,f31(x58771,x58772,x58773)))+~P1(f773(a26,f773(a27,x58772)))
% 191.21/191.74 [5889]~P99(x58891)+E(f773(f773(f104(f855(x58891,a841)),f773(f257(x58891),x58892)),f295(x58891,x58892,x58893)),f180(f855(x58891,a841)))
% 191.21/191.74 [5890]~P99(x58901)+E(f773(f773(f104(f855(x58901,a841)),f773(f293(x58901),x58902)),f297(x58901,x58902,x58903)),f180(f855(x58901,a841)))
% 191.21/191.74 [5891]~P99(x58911)+E(f773(f773(f104(f855(x58911,a841)),f773(f293(x58911),x58912)),f298(x58911,x58912,x58913)),f180(f855(x58911,a841)))
% 191.21/191.74 [6042]P1(f773(a26,x60421))+~P1(f773(a26,f32(x60422,x60423,x60421)))
% 191.21/191.74 [6044]P1(f773(a26,x60441))+~P1(f773(a26,f33(x60442,x60443,x60441)))
% 191.21/191.74 [6046]P1(f773(a26,x60461))+~P1(f773(a26,f33(x60462,x60461,x60463)))
% 191.21/191.74 [6126]E(f773(f126(x61261,x61262),x61263),x61263)+~P1(f773(x61262,f758(x61263,x61262,x61261)))
% 191.21/191.74 [6128]E(f773(f773(f302(x61281),f414(x61282,x61283,x61281)),f374(x61282,x61283,x61281)),x61283)+~E(f773(f42(x61281),x61283),f773(a114,x61282))
% 191.21/191.74 [6143]P140(x61431,x61432,x61433)+~P1(f773(x61431,f52(a1,x61433,x61432)))
% 191.21/191.74 [6195]E(f162(x61951,x61952,x61953),x61953)+~P1(f773(x61952,f767(x61953,x61952,x61951)))
% 191.21/191.74 [6236]~P1(f773(a26,f31(x62362,x62361,x62363)))+P1(f773(a26,f773(a27,x62361)))
% 191.21/191.74 [6284]~P1(f773(x62842,f817(x62843,x62842,x62841)))+P1(f773(f245(x62841,x62842),x62843))
% 191.21/191.74 [6544]~P1(f773(f321(x65441,x65442),f818(x65443,x65442,x65441)))+P1(f773(f321(x65441,x65442),x65443))
% 191.21/191.74 [6545]~P1(f773(f321(x65451,x65452),f819(x65453,x65452,x65451)))+P1(f773(f321(x65451,x65452),x65453))
% 191.21/191.74 [7176]~P7(x71761)+E(f773(f773(f82(x71761),f773(f773(f83(x71761),x71762),f773(f773(f43(x71761),x71763),x71762))),f52(x71761,x71763,x71762)),x71763)
% 191.21/191.74 [7664]E(f773(f773(f241(x76641,x76641),f472(x76642,x76643,x76641)),f472(x76642,x76643,x76641)),x76643)+~P1(f773(f773(f334(f854(x76641,x76641)),x76643),f260(x76641,x76642)))
% 191.21/191.74 [7783]~P1(f773(f773(f334(x77831),f526(x77833,x77832,x77831)),f322(x77831,x77833)))+P1(f773(f773(f334(x77831),x77832),f322(x77831,x77833)))
% 191.21/191.74 [7784]~P1(f773(f773(f334(x77841),f619(x77843,x77842,x77841)),f322(x77841,x77843)))+P1(f773(f773(f334(x77841),x77842),f322(x77841,x77843)))
% 191.21/191.74 [7785]~P1(f773(f773(f334(x77851),f621(x77853,x77852,x77851)),f322(x77851,x77853)))+P1(f773(f773(f334(x77851),x77852),f322(x77851,x77853)))
% 191.21/191.74 [7971]~P7(x79711)+E(f773(f773(f82(x79711),f773(f773(f83(x79711),f773(f773(f43(x79711),x79712),x79713)),x79713)),f52(x79711,x79712,x79713)),x79712)
% 191.21/191.74 [8012]~E(f773(f42(x80121),x80122),f773(a114,x80123))+~P1(f773(f773(f334(x80121),f414(x80123,x80122,x80121)),f374(x80123,x80122,x80121)))
% 191.21/191.74 [8613]P1(f773(f773(f232(f855(f854(x86131,x86131),a841)),f300(x86131,x86132)),f300(x86131,x86133)))+~P1(f773(f773(f232(f855(f854(x86131,x86131),a841)),x86132),f300(x86131,x86133)))
% 191.21/191.74 [8851]E(x88511,f115(x88512))+~P1(f773(f773(f334(f854(f848(x88512),f848(x88512))),f773(f773(f241(f848(x88512),f848(x88512)),x88511),f115(x88512))),f147(x88512,x88513)))
% 191.21/191.74 [8877]E(x88771,f115(x88772))+~P1(f773(f773(f334(f854(f848(x88772),f848(x88772))),f773(f773(f241(f848(x88772),f848(x88772)),f115(x88772)),x88771)),f147(x88772,x88773)))
% 191.21/191.74 [9004]E(f773(f773(f140(x90041),f749(x90042,x90043,x90041)),f750(x90042,x90043,x90041)),x90043)+~P1(f773(f773(f334(f854(f848(x90041),f848(x90041))),f773(f773(f241(f848(x90041),f848(x90041)),f115(x90041)),x90043)),f137(x90041,x90042)))
% 191.21/191.74 [9203]~P118(x92031)+~P1(f773(f773(f233(x92031),f773(f773(f82(x92031),f773(f773(f83(x92031),x92032),x92032)),f773(f773(f83(x92031),x92033),x92033))),f2(x92031)))
% 191.21/191.74 [9252]P1(f773(f63(x92521),x92522))+~P1(f773(f773(f334(f854(f855(x92521,a841),f855(x92521,a841))),f773(f773(f241(f855(x92521,a841),f855(x92521,a841)),x92523),x92522)),f299(x92521)))
% 191.21/191.74 [9530]~P45(x95301,x95302,x95303)+P1(f773(f773(f233(a1),f773(f773(f75(f854(a1,a1),a1,x95301,f240(a1,a1)),f207(x95301)),f224(x95301,x95302,f221(x95301,x95303)))),f2(a1)))
% 191.21/191.74 [9531]~P46(x95311,x95312,x95313)+P1(f773(f773(f232(a1),f773(f773(f75(f854(a1,a1),a1,x95311,f240(a1,a1)),f207(x95311)),f224(x95311,x95312,f221(x95311,x95313)))),f2(a1)))
% 191.21/191.74 [9645]P45(x96451,x96452,x96453)+~P1(f773(f773(f233(a1),f773(f773(f75(f854(a1,a1),a1,x96451,f240(a1,a1)),f207(x96451)),f224(x96451,x96452,f221(x96451,x96453)))),f2(a1)))
% 191.21/191.74 [9646]P46(x96461,x96462,x96463)+~P1(f773(f773(f232(a1),f773(f773(f75(f854(a1,a1),a1,x96461,f240(a1,a1)),f207(x96461)),f224(x96461,x96462,f221(x96461,x96463)))),f2(a1)))
% 191.21/191.74 [9976]~P110(x99761)+~P1(f773(f773(f233(x99761),f773(f773(f82(x99761),f773(f773(f242(x99761),x99762),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))),f773(f773(f242(x99761),x99763),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))))),f2(x99761)))
% 191.21/191.74 [4640]~E(x46403,f115(x46401))+E(f773(f773(f125(x46401),x46402),x46403),x46402)
% 191.21/191.74 [4641]~E(x46412,f115(x46411))+E(f773(f773(f125(x46411),x46412),x46413),x46413)
% 191.21/191.74 [4647]~E(x46472,f2(a847))+E(f773(f773(f159(x46471),x46472),x46473),f115(x46471))
% 191.21/191.74 [4651]~E(x46513,f115(x46511))+E(f773(f773(f159(x46511),x46512),x46513),f115(x46511))
% 191.21/191.74 [4690]~E(x46901,x46903)+E(x46901,f773(f773(f125(x46902),f115(x46902)),x46903))
% 191.21/191.74 [4771]~P106(x47712)+E(f773(f239(f855(x47711,x47712)),x47713),f239(x47712))
% 191.21/191.74 [4773]~P101(x47732)+E(f773(f180(f855(x47731,x47732)),x47733),f180(x47732))
% 191.21/191.74 [4792]E(x47921,f115(x47922))+~E(f773(f773(f125(x47922),x47923),x47921),x47923)
% 191.21/191.74 [4793]E(x47931,f115(x47932))+~E(f773(f773(f125(x47932),x47931),x47933),x47933)
% 191.21/191.74 [4801]E(x48011,f115(x48012))+~E(f773(f773(f125(x48012),x48013),x48011),f115(x48012))
% 191.21/191.74 [4802]E(x48021,f115(x48022))+~E(f773(f773(f125(x48022),x48021),x48023),f115(x48022))
% 191.21/191.74 [4827]~E(x48272,f2(a847))+E(f773(f773(f83(a847),x48271),x48272),f773(f773(f83(a847),x48273),x48272))
% 191.21/191.74 [4829]~E(x48291,f2(a847))+E(f773(f773(f83(a847),x48291),x48292),f773(f773(f83(a847),x48291),x48293))
% 191.21/191.74 [4882]~P85(x48821)+E(f773(f773(f82(x48821),x48822),x48823),f773(f773(f82(x48821),x48823),x48822))
% 191.21/191.74 [4883]~P85(x48831)+E(f773(f773(f83(x48831),x48832),x48833),f773(f773(f83(x48831),x48833),x48832))
% 191.21/191.74 [4885]~P100(x48851)+E(f773(f773(f236(x48851),x48852),x48853),f773(f773(f236(x48851),x48853),x48852))
% 191.21/191.74 [4887]~P100(x48871)+E(f773(f773(f179(x48871),x48872),x48873),f773(f773(f179(x48871),x48873),x48872))
% 191.21/191.74 [4889]~P92(x48891)+E(f773(f773(f103(x48891),x48892),x48893),f773(f773(f103(x48891),x48893),x48892))
% 191.21/191.74 [4890]~P93(x48901)+E(f773(f773(f103(x48901),x48902),x48903),f773(f773(f103(x48901),x48903),x48902))
% 191.21/191.74 [4891]~P93(x48911)+E(f773(f773(f104(x48911),x48912),x48913),f773(f773(f104(x48911),x48913),x48912))
% 191.21/191.74 [4893]~P98(x48931)+E(f773(f773(f104(x48931),x48932),x48933),f773(f773(f104(x48931),x48933),x48932))
% 191.21/191.74 [4956]E(f52(a847,x49561,x49562),f2(a847))+~E(x49561,f773(f773(f83(a847),x49562),x49563))
% 191.21/191.74 [4957]E(f52(a1,x49571,x49572),f2(a1))+~E(x49571,f773(f773(f83(a1),x49572),x49573))
% 191.21/191.74 [5017]E(x50171,x50172)+~E(f773(f773(f82(a847),x50173),x50171),f773(f773(f82(a847),x50173),x50172))
% 191.21/191.74 [5018]E(x50181,x50182)+~E(f773(f773(f82(a847),x50181),x50183),f773(f773(f82(a847),x50182),x50183))
% 191.21/191.74 [5028]~P69(x50281)+E(f773(f773(f82(x50281),x50282),f773(f81(x50281),x50283)),f773(f773(f3(x50281),x50282),x50283))
% 191.21/191.74 [5029]~P104(x50291)+E(f773(f773(f82(x50291),x50292),f773(f81(x50291),x50293)),f773(f773(f3(x50291),x50292),x50293))
% 191.21/191.74 [5030]~P6(x50301)+E(f773(f773(f82(x50301),x50302),f773(f81(x50301),x50303)),f773(f773(f3(x50301),x50302),x50303))
% 191.21/191.74 [5031]~P90(x50311)+E(f773(f773(f104(x50311),x50312),f773(f81(x50311),x50313)),f773(f773(f3(x50311),x50312),x50313))
% 191.21/191.74 [5032]~P69(x50321)+E(f773(f773(f3(x50321),x50322),f773(f81(x50321),x50323)),f773(f773(f82(x50321),x50322),x50323))
% 191.21/191.74 [5079]~P1(f773(x50793,x50792))+P1(f773(f773(f334(x50791),x50792),x50793))
% 191.21/191.74 [5081]~P66(x50812)+E(f773(f773(f8(x50811,x50812),x50813),f180(f855(x50811,a841))),f2(x50812))
% 191.21/191.74 [5083]~P70(x50832)+E(f773(f773(f11(x50831,x50832),x50833),f180(f855(x50831,a841))),f80(x50832))
% 191.21/191.74 [5128]~E(x51282,f773(f773(f82(a847),x51281),x51283))+P1(f773(f773(f232(a847),x51281),x51282))
% 191.21/191.74 [5130]~E(x51302,f180(f855(x51301,a841)))+E(f773(f773(f61(x51301),x51302),x51303),f180(f855(f855(x51301,a841),a841)))
% 191.21/191.74 [5131]~E(x51312,f180(f855(x51311,a841)))+E(f180(f855(f855(x51311,a841),a841)),f773(f773(f61(x51311),x51312),x51313))
% 191.21/191.74 [5198]~E(f773(f259(x51982,x51983),x51981),f180(f855(x51983,a841)))+E(x51981,f180(f855(f854(x51982,x51983),a841)))
% 191.21/191.74 [5199]~E(f773(f261(x51992,x51993),x51991),f180(f855(x51992,a841)))+E(x51991,f180(f855(f854(x51992,x51993),a841)))
% 191.21/191.74 [5230]E(f773(f259(x52301,x52302),x52303),f180(f855(x52302,a841)))+~E(x52303,f180(f855(f854(x52301,x52302),a841)))
% 191.21/191.74 [5231]E(f773(f261(x52311,x52312),x52313),f180(f855(x52311,a841)))+~E(x52313,f180(f855(f854(x52311,x52312),a841)))
% 191.21/191.74 [5234]E(f269(x52341,x52342,x52343),f773(f773(f3(a101),x52342),x52343))+P1(f773(f773(f233(a101),x52342),x52343))
% 191.21/191.74 [5250]P1(f773(x52501,x52502))+~P1(f773(f773(f334(x52503),x52502),x52501))
% 191.21/191.74 [5286]E(x52861,x52862)+~E(f773(f81(f855(x52863,a841)),x52861),f773(f81(f855(x52863,a841)),x52862))
% 191.21/191.74 [5291]E(f307(x52911,x52912,x52913),f183(f848(a839)))+~P1(f773(f773(f233(a1),x52912),x52913))
% 191.21/191.74 [5296]~E(x52961,f180(f855(x52962,a841)))+~P1(f773(f773(f334(x52962),x52963),x52961))
% 191.21/191.74 [5324]~E(x53242,f773(f773(f82(a1),x53241),f773(f102(a1),x53243)))+P1(f773(f773(f232(a1),x53241),x53242))
% 191.21/191.74 [5340]E(f773(f773(f302(x53401),x53402),x53403),x53403)+~P1(f773(f773(f334(x53401),x53402),x53403))
% 191.21/191.74 [5352]E(x53521,f180(f855(x53522,a841)))+~E(f773(f773(f61(x53522),x53521),x53523),f180(f855(f855(x53522,a841),a841)))
% 191.21/191.74 [5353]E(x53531,f180(f855(x53532,a841)))+~E(f180(f855(f855(x53532,a841),a841)),f773(f773(f61(x53532),x53531),x53533))
% 191.21/191.74 [5359]~P121(x53591)+E(f773(f773(f83(x53591),f773(f81(x53591),x53592)),f773(f81(x53591),x53593)),f773(f773(f83(x53591),x53592),x53593))
% 191.21/191.74 [5361]~P60(x53611)+E(f773(f773(f283(x53611),f773(f81(x53611),x53612)),f773(f81(x53611),x53613)),f773(f773(f283(x53611),x53612),x53613))
% 191.21/191.74 [5393]~P1(f773(x53933,x53932))+P1(f773(f773(f334(x53931),x53932),f773(f256(x53931),x53933)))
% 191.21/191.74 [5433]E(f151(x54331,x54332,x54333),x54333)+P1(f773(f773(f334(x54331),x54332),f773(f158(x54331),x54333)))
% 191.21/191.74 [5511]~P1(f773(f127(x55111),x55113))+P1(f773(f127(x55111),f773(f126(x55111,x55112),x55113)))
% 191.21/191.74 [5553]~P7(x55531)+E(f773(f773(f43(x55531),f52(x55531,x55532,x55533)),x55533),f2(x55531))
% 191.21/191.74 [5571]E(f160(x55711,f773(f773(f140(x55711),x55712),f115(x55711)),x55713),f115(x55711))+P1(f773(f773(f334(a847),f2(a847)),x55713))
% 191.21/191.74 [5636]E(x56361,x56362)+~E(f773(f773(f83(a847),f773(a114,x56363)),x56361),f773(f773(f83(a847),f773(a114,x56363)),x56362))
% 191.21/191.74 [5637]~E(x56372,f773(f773(f82(a1),x56371),f773(f102(a1),f773(a114,x56373))))+P1(f773(f773(f233(a1),x56371),x56372))
% 191.21/191.74 [5755]~E(x57553,f115(x57551))+E(f773(f773(f773(f173(f848(x57551),f848(x57551)),x57552),f141(x57551)),x57553),f115(x57551))
% 191.21/191.74 [5759]P1(f773(x57591,x57592))+~P1(f773(f773(f334(x57593),x57592),f773(f256(x57593),x57591)))
% 191.21/191.74 [5793]E(x57931,x57932)+~E(f773(f773(f302(x57933),x57931),f180(f855(x57933,a841))),f773(f773(f302(x57933),x57932),f180(f855(x57933,a841))))
% 191.21/191.74 [5803]~P99(x58031)+E(f773(f773(f104(f855(x58031,a841)),f773(f257(x58031),x58032)),f773(f294(x58031,x58032),x58033)),f180(f855(x58031,a841)))
% 191.21/191.74 [5863]~P77(x58631)+E(f773(f303(x58631,x58631,f81(x58631)),f773(f294(x58631,x58632),x58633)),f297(x58631,f773(f81(x58631),x58633),f773(f81(x58631),x58632)))
% 191.21/191.74 [5871]E(f773(f181(f848(x58711)),f151(x58711,x58712,x58713)),f773(f181(f848(x58711)),x58713))+P1(f773(f773(f334(x58711),x58712),f773(f158(x58711),x58713)))
% 191.21/191.74 [5928]~P99(x59281)+E(f773(f773(f104(f855(x59281,a841)),f773(f294(x59281,x59282),x59283)),f773(f258(x59281),x59283)),f180(f855(x59281,a841)))
% 191.21/191.74 [5949]~P77(x59491)+E(f773(f303(x59491,x59491,f81(x59491)),f295(x59491,x59492,x59493)),f295(x59491,f773(f81(x59491),x59493),f773(f81(x59491),x59492)))
% 191.21/191.74 [5950]~P77(x59501)+E(f773(f303(x59501,x59501,f81(x59501)),f298(x59501,x59502,x59503)),f298(x59501,f773(f81(x59501),x59503),f773(f81(x59501),x59502)))
% 191.21/191.74 [6009]E(f160(x60091,f773(f773(f140(x60091),x60092),f115(x60091)),x60093),f773(f773(f140(x60091),x60092),f115(x60091)))+~P1(f773(f773(f334(a847),f2(a847)),x60093))
% 191.21/191.74 [6017]~P77(x60171)+E(f773(f303(x60171,x60171,f81(x60171)),f297(x60171,x60172,x60173)),f773(f294(x60171,f773(f81(x60171),x60173)),f773(f81(x60171),x60172)))
% 191.21/191.74 [6037]~P8(x60371)+E(f52(x60371,f773(f81(x60371),f52(x60371,x60372,x60373)),x60373),f52(x60371,f773(f81(x60371),x60372),x60373))
% 191.21/191.74 [6141]~P1(f773(f63(f854(x61412,x61411)),x61413))+P1(f773(f63(x61411),f773(f259(x61412,x61411),x61413)))
% 191.21/191.74 [6142]~P1(f773(f63(f854(x61421,x61422)),x61423))+P1(f773(f63(x61421),f773(f261(x61421,x61422),x61423)))
% 191.21/191.74 [6147]~P99(x61471)+E(f773(f773(f104(f855(x61471,a841)),f295(x61471,x61472,x61473)),f773(f296(x61471),x61473)),f180(f855(x61471,a841)))
% 191.21/191.74 [6148]~P99(x61481)+E(f773(f773(f104(f855(x61481,a841)),f297(x61481,x61482,x61483)),f773(f296(x61481),x61483)),f180(f855(x61481,a841)))
% 191.21/191.74 [6149]~P99(x61491)+E(f773(f773(f104(f855(x61491,a841)),f298(x61491,x61492,x61493)),f773(f258(x61491),x61493)),f180(f855(x61491,a841)))
% 191.21/191.74 [6218]E(f773(f773(f153(x62181),x62182),f729(x62182,x62183,x62181)),x62183)+~P1(f773(f773(f334(x62181),x62183),f773(f158(x62181),x62182)))
% 191.21/191.74 [6370]E(x63701,f115(x63702))+~E(f773(f773(f773(f173(f848(x63702),f848(x63702)),x63703),f141(x63702)),x63701),f115(x63702))
% 191.21/191.74 [6449]P39(x64491,x64492,f407(x64493,x64492,x64491),x64493)+~P1(f773(f773(f187(x64491),x64492),x64493))
% 191.21/191.74 [6450]P39(x64501,x64502,f521(x64503,x64502,x64501),x64503)+~P1(f773(f773(f187(x64501),x64502),x64503))
% 191.21/191.74 [6480]~P1(f773(f63(f854(x64802,x64801)),x64803))+P1(f773(f63(f854(x64801,x64802)),f773(f278(x64802,x64801),x64803)))
% 191.21/191.74 [6502]E(x65021,x65022)+~E(f282(a847,f279(a847),x65023,x65021),f773(f773(f302(a847),x65022),f180(f855(a847,a841))))
% 191.21/191.74 [6503]E(x65031,x65032)+~E(f282(a847,f279(a847),x65031,x65032),f773(f773(f302(a847),x65033),f180(f855(a847,a841))))
% 191.21/191.74 [6639]P54(x66391,x66392,x66393)+P1(f773(f773(f334(x66391),f627(x66393,x66392,x66391)),x66392))
% 191.21/191.74 [6640]P54(x66401,x66402,x66403)+P1(f773(f773(f334(x66401),f626(x66403,x66402,x66401)),x66402))
% 191.21/191.74 [6652]P1(f773(f321(x66521,x66522),x66523))+P1(f773(f773(x66522,f818(x66523,x66522,x66521)),x66523))
% 191.21/191.74 [6653]P1(f773(f321(x66531,x66532),x66533))+P1(f773(f773(x66532,f819(x66533,x66532,x66531)),x66533))
% 191.21/191.74 [6684]E(f773(f181(f848(x66841)),f151(x66841,x66842,x66843)),f773(f773(f3(a847),f773(f181(f848(x66841)),x66843)),f80(a847)))+~P1(f773(f773(f334(x66841),x66842),f773(f158(x66841),x66843)))
% 191.21/191.74 [6724]P1(f773(f245(x67241,x67242),x67243))+P1(f773(f773(f334(x67241),f817(x67243,x67242,x67241)),x67243))
% 191.21/191.74 [6737]~P1(f773(f63(f854(x67372,x67371)),f773(f278(x67371,x67372),x67373)))+P1(f773(f63(f854(x67371,x67372)),x67373))
% 191.21/191.74 [6798]~P1(f773(f773(f334(x67981),x67982),f773(f158(x67981),f116(x67981,x67983))))+P1(f773(f773(f334(x67981),x67982),f773(f158(x67981),x67983)))
% 191.21/191.74 [6805]P32(x68051,x68052,x68053)+P1(f773(f773(f334(f846(x68051)),f781(x68053,x68052,x68051)),x68053))
% 191.21/191.74 [6834]E(f773(f126(x68341,x68342),x68343),x68343)+P1(f773(f773(f334(x68341),f758(x68343,x68342,x68341)),f773(f158(x68341),x68343)))
% 191.21/191.74 [6851]E(f773(f126(x68511,x68512),x68513),f115(x68511))+P1(f773(f773(f334(x68511),f746(x68513,x68512,x68511)),f773(f158(x68511),x68513)))
% 191.21/191.74 [6879]E(f162(x68791,x68792,x68793),x68793)+P1(f773(f773(f334(x68791),f767(x68793,x68792,x68791)),f773(f158(x68791),x68793)))
% 191.21/191.74 [7000]P1(f773(f773(f334(x70001),x70002),f696(x70003,x70002,x70001)))+~P1(f773(f773(f334(x70001),x70002),f44(f855(x70001,a841),x70003)))
% 191.21/191.74 [7002]~P66(x70021)+E(f773(f773(f82(x70021),f773(f773(f8(a847,x70021),x70022),f773(f257(a847),x70023))),f773(x70022,x70023)),f773(f773(f8(a847,x70021),x70022),f773(f257(a847),f773(a114,x70023))))
% 191.21/191.74 [7106]~P1(f773(f773(f334(x71061),x71062),f685(x71062,x71063,x71061)))+P1(f773(f773(f334(x71061),x71062),f45(f855(x71061,a841),x71063)))
% 191.21/191.74 [7135]~P66(x71351)+E(f773(f773(f82(x71351),f773(f773(f8(a847,x71351),x71352),f773(f293(a847),x71353))),f773(x71352,f773(a114,x71353))),f773(f773(f8(a847,x71351),x71352),f773(f293(a847),f773(a114,x71353))))
% 191.21/191.74 [7289]P1(f773(f773(f334(f848(x72891)),x72892),f149(x72891,x72893)))+P1(f773(f773(f334(x72891),f745(x72893,x72892,x72891)),f773(f158(x72891),x72892)))
% 191.21/191.74 [7306]~P1(f773(f773(f334(f848(x73061)),x73062),f149(x73061,f322(x73061,x73063))))+P1(f773(f773(f334(f848(x73061)),x73062),f322(f848(x73061),f146(x73061,x73063))))
% 191.21/191.74 [7334]~P1(f773(f773(f334(f848(x73341)),x73342),f322(f848(x73341),f146(x73341,x73343))))+P1(f773(f773(f334(f848(x73341)),x73342),f149(x73341,f322(x73341,x73343))))
% 191.21/191.74 [7374]E(f773(f773(f773(f173(f848(x73741),f848(x73741)),x73742),f141(x73741)),x73743),x73743)+~P1(f773(f773(f232(a847),f773(f181(f848(x73741)),x73743)),f80(a847)))
% 191.21/191.74 [7428]~P29(x74281,x74282,x74283,f239(f855(x74281,a841)))+P29(f848(x74281),f848(x74282),f773(f143(x74281,x74282),x74283),f239(f855(f848(x74281),a841)))
% 191.21/191.74 [7585]E(x75851,f773(f773(f82(a847),f773(f773(f83(a847),f773(f240(a847,a847),x75852)),x75853)),f773(f250(a847,a847),x75852)))+~P1(f773(f55(x75851,x75853),x75852))
% 191.21/191.74 [7593]P29(x75931,x75932,x75933,f239(f855(x75931,a841)))+~P29(f848(x75931),f848(x75932),f773(f143(x75931,x75932),x75933),f239(f855(f848(x75931),a841)))
% 191.21/191.74 [7636]P1(f773(f773(f334(f855(x76361,a841)),f685(x76362,x76363,x76361)),x76363))+P1(f773(f773(f334(x76361),x76362),f45(f855(x76361,a841),x76363)))
% 191.21/191.74 [7725]P1(f773(f773(f334(f848(x77251)),x77252),f149(x77251,x77253)))+~P1(f773(f773(f334(x77251),f745(x77253,x77252,x77251)),x77253))
% 191.21/191.74 [7856]E(x78561,x78562)+~E(f773(f773(f9(x78563,f855(x78563,a841),a841),f334(x78563)),x78561),f773(f773(f9(x78563,f855(x78563,a841),a841),f334(x78563)),x78562))
% 191.21/191.74 [7862]~P1(f773(f773(f334(f854(x78621,x78621)),x78623),f260(x78621,x78622)))+P1(f773(f773(f334(x78621),f472(x78622,x78623,x78621)),x78622))
% 191.21/191.74 [7864]~P1(f773(f773(f334(x78641),x78643),f44(f855(x78641,a841),x78642)))+P1(f773(f773(f334(f855(x78641,a841)),f696(x78642,x78643,x78641)),x78642))
% 191.21/191.74 [8124]E(f773(f229(f851(f848(a839)),f848(a839),f307(x81241,x81242,f773(f773(f82(a1),x81243),f80(a1))),f227(f848(a839))),f773(x81241,x81243)),f307(x81241,x81242,x81243))+P1(f773(f773(f233(a1),x81242),x81243))
% 191.21/191.74 [8223]E(x82231,f115(x82232))+P1(f773(f773(f334(x82232),f773(f240(x82232,f854(a101,a101)),f773(f270(x82232,x82231),x82233))),f773(f158(x82232),x82231)))
% 191.21/191.74 [8321]~P5(x83211)+E(f773(f132(x83211,x83211,f773(f9(x83211,x83211,x83211),f82(x83211)),x83212),f773(f142(x83211),x83213)),f773(f132(x83211,x83211,f82(x83211),x83212),x83213))
% 191.21/191.74 [8782]~P100(x87821)+E(f773(f158(x87821),f139(x87821,x87821,f7(x87821),x87822,x87823)),f773(f773(f302(x87821),x87822),f773(f158(x87821),x87823)))
% 191.21/191.74 [8791]P1(f773(f773(f233(a847),f2(a847)),f638(x87911,x87912,x87913)))+~P1(f773(f773(f334(f854(x87913,x87913)),x87912),f773(f773(f281(x87913,x87913,x87913),x87911),f300(x87913,x87911))))
% 191.21/191.74 [9054]~P56(x90541,x90542)+~P1(f773(f773(f334(f854(x90541,x90541)),f773(f773(f241(x90541,x90541),x90543),x90543)),f773(f773(f281(x90541,x90541,x90541),x90542),f300(x90541,x90542))))
% 191.21/191.74 [9165]~E(f773(f773(f104(f855(f854(x91651,x91651),a841)),f773(f278(x91651,x91651),x91652)),f300(x91651,x91652)),f180(f855(f854(x91651,x91651),a841)))+~P1(f773(f773(f334(f854(x91651,x91651)),f773(f773(f241(x91651,x91651),x91653),x91653)),f773(f773(f281(x91651,x91651,x91651),x91652),f300(x91651,x91652))))
% 191.21/191.74 [9339]~P1(f773(f63(x93391),x93392))+P1(f773(f773(f232(a847),f773(f42(x93391),f773(f773(f3(f855(x93391,a841)),x93392),f773(f773(f302(x93391),x93393),f180(f855(x93391,a841)))))),f773(f42(x93391),x93392)))
% 191.21/191.74 [4940]~E(x49403,f115(x49401))+E(f134(x49401,f773(f773(f140(x49401),x49402),x49403)),x49402)
% 191.21/191.74 [4953]~E(x49533,f115(x49531))+E(f116(x49531,f773(f773(f140(x49531),x49532),x49533)),f115(x49531))
% 191.21/191.74 [4982]E(x49821,f115(x49822))+E(f134(x49822,f773(f773(f140(x49822),x49823),x49821)),f134(x49822,x49821))
% 191.21/191.74 [4984]E(x49841,f115(x49842))+E(f134(x49842,f773(f773(f125(x49842),x49843),x49841)),f134(x49842,x49841))
% 191.21/191.74 [4991]~E(x49913,f115(x49911))+E(f134(x49911,f773(f773(f125(x49911),x49912),x49913)),f134(x49911,x49912))
% 191.21/191.74 [4992]~E(x49923,f115(x49921))+E(f116(x49921,f773(f773(f125(x49921),x49922),x49923)),f116(x49921,x49922))
% 191.21/191.74 [5022]E(x50221,f115(x50222))+E(f773(f131(x50222),f773(f773(f125(x50222),x50221),x50223)),f773(f131(x50222),x50221))
% 191.21/191.74 [5053]~E(x50532,f115(x50531))+E(f773(f131(x50531),f773(f773(f125(x50531),x50532),x50533)),f773(f131(x50531),x50533))
% 191.21/191.74 [5104]~P100(x51041)+E(f773(f773(f236(x51041),x51042),f773(f773(f179(x51041),x51042),x51043)),x51042)
% 191.21/191.74 [5105]~P100(x51051)+E(f773(f773(f179(x51051),x51052),f773(f773(f236(x51051),x51052),x51053)),x51052)
% 191.21/191.74 [5106]~P93(x51061)+E(f773(f773(f103(x51061),x51062),f773(f773(f104(x51061),x51062),x51063)),x51062)
% 191.21/191.74 [5107]~P93(x51071)+E(f773(f773(f104(x51071),x51072),f773(f773(f103(x51071),x51072),x51073)),x51072)
% 191.21/191.74 [5126]~P7(x51261)+E(f52(x51261,f773(f773(f83(x51261),x51262),x51263),x51263),f2(x51261))
% 191.21/191.74 [5127]~P7(x51271)+E(f52(x51271,f773(f773(f83(x51271),x51272),x51273),x51272),f2(x51271))
% 191.21/191.74 [5193]~P6(x51931)+E(f773(f81(x51931),f773(f773(f3(x51931),x51932),x51933)),f773(f773(f3(x51931),x51933),x51932))
% 191.21/191.74 [5254]E(x52541,f115(x52542))+E(f116(x52542,f773(f773(f140(x52542),x52543),x52541)),f773(f773(f140(x52542),x52543),f116(x52542,x52541)))
% 191.21/191.74 [5255]E(x52551,f115(x52552))+E(f116(x52552,f773(f773(f125(x52552),x52553),x52551)),f773(f773(f125(x52552),x52553),f116(x52552,x52551)))
% 191.21/191.74 [5256]~P9(x52561)+E(f45(x52561,f773(f773(f302(x52561),x52562),x52563)),f773(f773(f104(x52561),x52562),f45(x52561,x52563)))
% 191.21/191.74 [5257]~P9(x52571)+E(f44(x52571,f773(f773(f302(x52571),x52572),x52573)),f773(f773(f103(x52571),x52572),f44(x52571,x52573)))
% 191.21/191.74 [5300]~P91(x53001)+E(f773(f773(f83(x53001),x53002),f773(f773(f83(x53001),x53002),x53003)),f773(f773(f83(x53001),x53002),x53003))
% 191.21/191.74 [5302]~P100(x53021)+E(f773(f773(f236(x53021),x53022),f773(f773(f236(x53021),x53022),x53023)),f773(f773(f236(x53021),x53022),x53023))
% 191.21/191.74 [5304]~P100(x53041)+E(f773(f773(f179(x53041),x53042),f773(f773(f179(x53041),x53042),x53043)),f773(f773(f179(x53041),x53042),x53043))
% 191.21/191.74 [5306]~P92(x53061)+E(f773(f773(f103(x53061),x53062),f773(f773(f103(x53061),x53062),x53063)),f773(f773(f103(x53061),x53062),x53063))
% 191.21/191.74 [5307]~P93(x53071)+E(f773(f773(f103(x53071),x53072),f773(f773(f103(x53071),x53072),x53073)),f773(f773(f103(x53071),x53072),x53073))
% 191.21/191.74 [5308]~P93(x53081)+E(f773(f773(f104(x53081),x53082),f773(f773(f104(x53081),x53082),x53083)),f773(f773(f104(x53081),x53082),x53083))
% 191.21/191.74 [5310]~P98(x53101)+E(f773(f773(f104(x53101),x53102),f773(f773(f104(x53101),x53102),x53103)),f773(f773(f104(x53101),x53102),x53103))
% 191.21/191.74 [5317]~P7(x53171)+E(f52(x53171,f773(f773(f82(x53171),x53172),x53173),x53173),f52(x53171,x53172,x53173))
% 191.21/191.74 [5318]~P7(x53181)+E(f52(x53181,f773(f773(f82(x53181),x53182),x53183),x53182),f52(x53181,x53183,x53182))
% 191.21/191.74 [5325]~P121(x53251)+E(f773(f773(f83(x53251),x53252),f773(f81(x53251),x53253)),f773(f81(x53251),f773(f773(f83(x53251),x53252),x53253)))
% 191.21/191.74 [5326]~P60(x53261)+E(f773(f773(f283(x53261),x53262),f773(f81(x53261),x53263)),f773(f81(x53261),f773(f773(f283(x53261),x53262),x53263)))
% 191.21/191.74 [5327]~P67(x53271)+E(f773(f773(f82(x53271),x53272),f773(f155(x53271),x53273)),f773(f155(x53271),f773(f773(f140(x53271),x53272),x53273)))
% 191.21/191.74 [5358]~P121(x53581)+E(f773(f773(f83(x53581),f773(f81(x53581),x53582)),x53583),f773(f773(f83(x53581),x53582),f773(f81(x53581),x53583)))
% 191.21/191.74 [5364]~P12(x53641,x53642,x53643)+E(f44(f855(x53641,a841),f773(f773(f61(x53641),x53642),x53643)),x53642)
% 191.21/191.74 [5425]~P105(x54251)+E(f773(f773(f83(x54251),x54252),f773(f773(f242(x54251),x54252),x54253)),f773(f773(f242(x54251),x54252),f773(a114,x54253)))
% 191.21/191.74 [5426]~P85(x54261)+E(f773(f773(f83(x54261),x54262),f773(f773(f242(x54261),x54262),x54263)),f773(f773(f242(x54261),x54262),f773(a114,x54263)))
% 191.21/191.74 [5436]~P69(x54361)+E(f773(f773(f82(x54361),f773(f81(x54361),x54362)),f773(f773(f82(x54361),x54362),x54363)),x54363)
% 191.21/191.74 [5455]~P2(x54551)+E(f773(f773(f242(x54551),f773(f102(x54551),x54552)),x54553),f773(f102(x54551),f773(f773(f242(a847),x54552),x54553)))
% 191.21/191.74 [5456]~P133(x54561)+E(f773(f773(f242(x54561),f773(f105(x54561),x54562)),x54563),f773(f105(x54561),f773(f773(f242(a1),x54562),x54563)))
% 191.21/191.74 [5461]~P79(x54611)+E(f773(f77(x54611),f773(f773(f3(x54611),x54612),x54613)),f773(f77(x54611),f773(f773(f3(x54611),x54613),x54612)))
% 191.21/191.74 [5464]~P110(x54641)+E(f773(f773(f83(x54641),f84(x54641,x54642)),f84(x54641,x54643)),f84(x54641,f773(f773(f83(x54641),x54642),x54643)))
% 191.21/191.74 [5468]E(x54681,f115(x54682))+E(f773(f773(f125(x54682),f773(f157(x54682),x54681)),x54683),f773(f157(x54682),f773(f773(f125(x54682),x54681),x54683)))
% 191.21/191.74 [5474]~E(x54742,f773(a114,f773(f773(f82(a847),x54741),x54743)))+P1(f773(f773(f233(a847),x54741),x54742))
% 191.21/191.74 [5475]~P121(x54751)+E(f773(f773(f83(x54751),f773(f81(x54751),x54752)),x54753),f773(f81(x54751),f773(f773(f83(x54751),x54752),x54753)))
% 191.21/191.74 [5476]~P113(x54761)+E(f773(f773(f283(x54761),f773(f81(x54761),x54762)),x54763),f773(f81(x54761),f773(f773(f283(x54761),x54762),x54763)))
% 191.21/191.74 [5477]~P110(x54771)+E(f773(f773(f242(x54771),f773(f77(x54771),x54772)),x54773),f773(f77(x54771),f773(f773(f242(x54771),x54772),x54773)))
% 191.21/191.74 [5570]E(f493(x55701,x55702,x55703),f497(x55701,x55702,x55703))+E(f773(f773(f104(f855(x55703,a841)),x55702),x55701),f180(f855(x55703,a841)))
% 191.21/191.74 [5584]~P66(x55842)+E(f773(f773(f8(x55841,x55842),f773(f18(x55842,x55841),f2(x55842))),x55843),f2(x55842))
% 191.21/191.74 [5585]~P70(x55852)+E(f773(f773(f11(x55851,x55852),f773(f18(x55852,x55851),f80(x55852))),x55853),f80(x55852))
% 191.21/191.74 [5587]~P2(x55871)+E(f773(f773(f82(x55871),f773(f102(x55871),x55872)),f773(f102(x55871),x55873)),f773(f102(x55871),f773(f773(f82(a847),x55872),x55873)))
% 191.21/191.74 [5588]~P2(x55881)+E(f773(f773(f83(x55881),f773(f102(x55881),x55882)),f773(f102(x55881),x55883)),f773(f102(x55881),f773(f773(f83(a847),x55882),x55883)))
% 191.21/191.74 [5589]~P133(x55891)+E(f773(f773(f82(x55891),f773(f105(x55891),x55892)),f773(f105(x55891),x55893)),f773(f105(x55891),f773(f773(f82(a1),x55892),x55893)))
% 191.21/191.74 [5590]~P133(x55901)+E(f773(f773(f83(x55901),f773(f105(x55901),x55902)),f773(f105(x55901),x55903)),f773(f105(x55901),f773(f773(f83(a1),x55902),x55903)))
% 191.21/191.74 [5591]~P133(x55911)+E(f773(f773(f3(x55911),f773(f105(x55911),x55912)),f773(f105(x55911),x55913)),f773(f105(x55911),f773(f773(f3(a1),x55912),x55913)))
% 191.21/191.74 [5594]~P88(x55941)+E(f773(f773(f3(x55941),f773(f106(x55941),x55942)),f773(f106(x55941),x55943)),f773(f106(x55941),f773(f773(f3(a1),x55942),x55943)))
% 191.21/191.74 [5595]~P88(x55951)+E(f773(f773(f82(x55951),f773(f106(x55951),x55952)),f773(f106(x55951),x55953)),f773(f106(x55951),f773(f773(f82(a1),x55952),x55953)))
% 191.21/191.74 [5596]~P88(x55961)+E(f773(f773(f83(x55961),f773(f106(x55961),x55962)),f773(f106(x55961),x55963)),f773(f106(x55961),f773(f773(f83(a1),x55962),x55963)))
% 191.21/191.74 [5643]~E(x56433,x56432)+P1(f773(f773(f232(f855(x56431,a841)),x56432),x56433))
% 191.21/191.74 [5649]~E(x56492,x56493)+P1(f773(f773(f232(f855(x56491,a841)),x56492),x56493))
% 191.21/191.74 [5654]~P69(x56541)+E(f773(f773(f82(x56541),f773(f81(x56541),x56542)),f773(f81(x56541),x56543)),f773(f81(x56541),f773(f773(f82(x56541),x56543),x56542)))
% 191.21/191.74 [5655]~P6(x56551)+E(f773(f773(f82(x56551),f773(f81(x56551),x56552)),f773(f81(x56551),x56553)),f773(f81(x56551),f773(f773(f82(x56551),x56552),x56553)))
% 191.21/191.74 [5656]~P68(x56561)+E(f773(f773(f179(x56561),f773(f81(x56561),x56562)),f773(f81(x56561),x56563)),f773(f81(x56561),f773(f773(f236(x56561),x56562),x56563)))
% 191.21/191.74 [5657]~P68(x56571)+E(f773(f773(f236(x56571),f773(f81(x56571),x56572)),f773(f81(x56571),x56573)),f773(f81(x56571),f773(f773(f179(x56571),x56572),x56573)))
% 191.21/191.74 [5658]~P90(x56581)+E(f773(f773(f104(x56581),f773(f81(x56581),x56582)),f773(f81(x56581),x56583)),f773(f81(x56581),f773(f773(f103(x56581),x56582),x56583)))
% 191.21/191.74 [5659]~P90(x56591)+E(f773(f773(f103(x56591),f773(f81(x56591),x56592)),f773(f81(x56591),x56593)),f773(f81(x56591),f773(f773(f104(x56591),x56592),x56593)))
% 191.21/191.74 [5660]~P110(x56601)+E(f773(f773(f83(x56601),f773(f77(x56601),x56602)),f773(f77(x56601),x56603)),f773(f77(x56601),f773(f773(f83(x56601),x56602),x56603)))
% 191.21/191.74 [5661]~P62(x56611)+E(f773(f773(f283(x56611),f773(f77(x56611),x56612)),f773(f77(x56611),x56613)),f773(f77(x56611),f773(f773(f283(x56611),x56612),x56613)))
% 191.21/191.74 [5662]~P67(x56621)+E(f773(f773(f82(x56621),f773(f155(x56621),x56622)),f773(f155(x56621),x56623)),f773(f155(x56621),f773(f773(f125(x56621),x56622),x56623)))
% 191.21/191.74 [5663]E(x56631,f180(f855(x56632,a841)))+~E(f773(f773(f103(f855(x56632,a841)),x56633),x56631),f180(f855(x56632,a841)))
% 191.21/191.74 [5664]E(x56641,f180(f855(x56642,a841)))+~E(f773(f773(f103(f855(x56642,a841)),x56641),x56643),f180(f855(x56642,a841)))
% 191.21/191.74 [5665]~P141(x56651,x56653,x56652)+P1(f773(x56651,f773(f773(f43(a1),x56652),x56653)))
% 191.21/191.74 [5727]~P1(f773(f63(x57271),x57273))+P1(f773(f63(x57271),f773(f773(f302(x57271),x57272),x57273)))
% 191.21/191.74 [5728]~P1(f773(f127(x57281),x57283))+P1(f773(f127(x57281),f773(f773(f159(x57281),x57282),x57283)))
% 191.21/191.74 [5729]~P1(f773(f127(x57291),x57293))+P1(f773(f127(x57291),f773(f773(f128(x57291),x57292),x57293)))
% 191.21/191.74 [5760]~P100(x57601)+P1(f773(f773(f232(x57601),x57602),f773(f773(f179(x57601),x57603),x57602)))
% 191.21/191.74 [5761]~P100(x57611)+P1(f773(f773(f232(x57611),x57612),f773(f773(f179(x57611),x57612),x57613)))
% 191.21/191.74 [5762]~P92(x57621)+P1(f773(f773(f232(x57621),x57622),f773(f773(f103(x57621),x57623),x57622)))
% 191.21/191.74 [5763]~P93(x57631)+P1(f773(f773(f232(x57631),x57632),f773(f773(f103(x57631),x57633),x57632)))
% 191.21/191.74 [5764]~P92(x57641)+P1(f773(f773(f232(x57641),x57642),f773(f773(f103(x57641),x57642),x57643)))
% 191.21/191.74 [5765]~P93(x57651)+P1(f773(f773(f232(x57651),x57652),f773(f773(f103(x57651),x57652),x57653)))
% 191.21/191.74 [5766]~P85(x57661)+P1(f773(f773(f279(x57661),x57662),f773(f773(f83(x57661),x57663),x57662)))
% 191.21/191.74 [5767]~P85(x57671)+P1(f773(f773(f279(x57671),x57672),f773(f773(f83(x57671),x57672),x57673)))
% 191.21/191.74 [5780]~E(x57801,f2(a847))+E(f773(f773(f43(a847),f773(f773(f83(a847),x57801),x57802)),f773(f773(f83(a847),x57801),x57803)),f2(a847))
% 191.21/191.74 [5844]P1(f773(x58441,x58442))+P1(f773(f773(f187(f35(x58441,x58443)),x58442),x58442))
% 191.21/191.74 [5856]~P88(x58561)+E(f773(f773(f3(x58561),f773(f106(x58561),x58562)),f773(f106(x58561),x58563)),f773(f106(x58561),f773(f773(f82(a1),x58562),f773(f81(a1),x58563))))
% 191.21/191.74 [5912]E(x59121,f2(a847))+E(f773(f773(f43(a847),f773(f773(f83(a847),x59121),x59122)),f773(f773(f83(a847),x59121),x59123)),f773(f773(f43(a847),x59122),x59123))
% 191.21/191.74 [5981]P141(x59811,x59812,x59813)+~P1(f773(x59811,f773(f773(f43(a1),x59813),x59812)))
% 191.21/191.74 [6058]E(x60581,f115(x60582))+E(f773(f773(f140(x60582),f773(f131(x60582),x60581)),f773(f773(f159(x60582),x60583),f773(f157(x60582),x60581))),f773(f773(f159(x60582),f773(a114,x60583)),x60581))
% 191.21/191.74 [6066]E(f773(f773(f3(f855(x60661,a841)),x60662),x60663),x60662)+~E(f773(f773(f104(f855(x60661,a841)),x60662),x60663),f180(f855(x60661,a841)))
% 191.21/191.74 [6110]~P1(f773(f773(f233(a847),x61101),x61103))+P1(f773(f773(f233(a847),x61101),f773(f773(f82(a847),x61102),x61103)))
% 191.21/191.74 [6112]~P1(f773(f773(f233(a847),x61121),x61122))+P1(f773(f773(f233(a847),x61121),f773(f773(f82(a847),x61122),x61123)))
% 191.21/191.74 [6114]~P1(f773(f773(f232(a847),x61141),x61143))+P1(f773(f773(f232(a847),x61141),f773(f773(f82(a847),x61142),x61143)))
% 191.21/191.74 [6116]~P1(f773(f773(f232(a847),x61161),x61162))+P1(f773(f773(f232(a847),x61161),f773(f773(f82(a847),x61162),x61163)))
% 191.21/191.74 [6155]P1(f773(f63(x61551),x61552))+~P1(f773(f63(x61551),f773(f773(f302(x61551),x61553),x61552)))
% 191.21/191.74 [6156]P1(f773(f127(x61561),x61562))+~P1(f773(f127(x61561),f773(f773(f140(x61561),x61563),x61562)))
% 191.21/191.74 [6157]P1(f773(f127(x61571),x61572))+~P1(f773(f127(x61571),f773(f773(f125(x61571),x61573),x61572)))
% 191.21/191.74 [6158]P1(f773(f127(x61581),x61582))+~P1(f773(f127(x61581),f773(f773(f125(x61581),x61582),x61583)))
% 191.21/191.74 [6203]~E(f52(a1,x62032,x62031),f52(a1,x62033,x62031))+P1(f773(f773(f279(a1),x62031),f773(f773(f3(a1),x62032),x62033)))
% 191.21/191.74 [6208]~P85(x62081)+E(f773(f773(f82(x62081),x62082),f773(f773(f83(x62081),x62083),x62082)),f773(f773(f83(x62081),f773(f773(f82(x62081),x62083),f80(x62081))),x62082))
% 191.21/191.74 [6257]~E(x62571,x62572)+~P1(f773(f773(f233(f855(x62573,a841)),x62571),x62572))
% 191.21/191.74 [6305]P1(f773(f773(f334(x63051),x63052),x63053))+P1(f773(f773(f334(x63051),x63052),f773(f81(f855(x63051,a841)),x63053)))
% 191.21/191.74 [6312]E(f134(x63121,f773(f773(f128(x63121),x63122),x63123)),f134(x63121,x63123))+~P1(f773(f773(f233(a847),x63122),f773(f181(f848(x63121)),x63123)))
% 191.21/191.74 [6313]E(f773(f773(f159(x63131),x63132),f116(x63131,x63133)),f773(f773(f159(x63131),x63132),x63133))+~P1(f773(f773(f233(a847),x63132),f773(f181(f848(x63131)),x63133)))
% 191.21/191.74 [6372]E(f773(f773(f773(f173(f848(x63721),f848(x63721)),x63722),f141(x63721)),x63723),x63723)+~E(f52(a847,x63722,f773(f181(f848(x63721)),x63723)),f2(a847))
% 191.21/191.74 [6381]~P12(x63811,x63813,x63812)+E(f773(f773(f281(x63811,x63811,x63811),f773(f278(x63811,x63811),x63812)),x63812),x63812)
% 191.21/191.74 [6424]~E(f773(f773(f103(f855(x64241,a841)),x64242),x64243),x64243)+P1(f773(f773(f232(f855(x64241,a841)),x64242),x64243))
% 191.21/191.74 [6429]~P53(x64291,x64291,x64293)+P53(x64291,x64291,f773(f773(f173(f854(x64291,x64291),a841),x64292),x64293))
% 191.21/191.74 [6431]~P1(f773(f773(f334(x64311),x64313),f773(f158(x64311),x64312)))+P1(f773(f773(f233(a847),f2(a847)),f773(f181(f848(x64311)),x64312)))
% 191.21/191.74 [6461]~P79(x64611)+E(f773(f77(x64611),f773(f773(f82(x64611),f773(f77(x64611),x64612)),f773(f77(x64611),x64613))),f773(f773(f82(x64611),f773(f77(x64611),x64612)),f773(f77(x64611),x64613)))
% 191.21/191.74 [6473]E(f773(f773(f43(a847),f773(f773(f83(a847),x64731),x64732)),f773(f773(f83(a847),x64731),x64733)),f773(f773(f43(a847),x64732),x64733))+~P1(f773(f773(f233(a847),f2(a847)),x64731))
% 191.21/191.74 [6500]E(f52(a1,x65001,x65002),f52(a1,x65003,x65002))+~P1(f773(f773(f279(a1),x65002),f773(f773(f3(a1),x65001),x65003)))
% 191.21/191.74 [6614]~P1(f773(f63(x66141),x66143))+E(f773(f773(f66(x66141,f855(x66141,a841),f302(x66141)),x66142),x66143),f773(f773(f103(f855(x66141,a841)),x66143),x66142))
% 191.21/191.74 [6677]E(f773(f773(f103(f855(x66771,a841)),x66772),x66773),x66772)+~P1(f773(f773(f232(f855(x66771,a841)),x66773),x66772))
% 191.21/191.74 [6679]E(f773(f773(f103(f855(x66791,a841)),x66792),x66793),x66793)+~P1(f773(f773(f232(f855(x66791,a841)),x66792),x66793))
% 191.21/191.74 [6680]E(f773(f773(f104(f855(x66801,a841)),x66802),x66803),x66803)+~P1(f773(f773(f232(f855(x66801,a841)),x66803),x66802))
% 191.21/191.74 [6681]E(f773(f773(f104(f855(x66811,a841)),x66812),x66813),x66812)+~P1(f773(f773(f232(f855(x66811,a841)),x66812),x66813))
% 191.21/191.74 [6734]~P1(f773(f127(x67341),x67342))+E(f773(f773(f3(f855(x67341,a841)),f773(f158(x67341),x67342)),f773(f773(f302(x67341),x67343),f180(f855(x67341,a841)))),f773(f158(x67341),f151(x67341,x67343,x67342)))
% 191.21/191.74 [6793]P36(x67931,x67932)+~P36(x67931,f773(f773(f173(f854(x67931,x67931),a841),x67933),x67932))
% 191.21/191.74 [6809]~E(x68091,f2(a847))+P1(f773(f773(f279(a847),f773(f773(f83(a847),x68091),x68092)),f773(f773(f83(a847),x68091),x68093)))
% 191.21/191.74 [6863]P1(f773(f56(x68631,x68632),f773(a58,x68633)))+~P1(f773(f56(f773(f81(a1),x68631),f773(f81(a1),x68632)),x68633))
% 191.21/191.74 [6868]E(f773(f773(f3(f855(x68681,a841)),f773(f773(f302(x68681),x68682),x68683)),f773(f773(f302(x68681),x68682),f180(f855(x68681,a841)))),x68683)+P1(f773(f773(f334(x68681),x68682),x68683))
% 191.21/191.74 [6887]E(f773(f773(f104(f855(x68871,a841)),f773(f158(x68871),x68872)),f773(f158(x68871),x68873)),f180(f855(x68871,a841)))+~P1(f773(f127(x68871),f773(f773(f125(x68871),x68872),x68873)))
% 191.21/191.74 [6904]~P1(f773(f773(f334(x69041),x69042),f773(f158(x69041),x69043)))+~P1(f773(f127(x69041),f773(f773(f140(x69041),x69042),x69043)))
% 191.21/191.74 [6981]E(f773(f773(f104(f855(x69811,a841)),x69812),x69813),f180(f855(x69811,a841)))+P1(f773(f773(f334(x69811),f493(x69813,x69812,x69811)),x69812))
% 191.21/191.74 [6982]E(f773(f773(f104(f855(x69821,a841)),x69822),x69823),f180(f855(x69821,a841)))+P1(f773(f773(f334(x69821),f497(x69823,x69822,x69821)),x69823))
% 191.21/191.74 [6986]E(f116(x69861,f773(f773(f159(x69861),x69862),x69863)),f773(f773(f159(x69861),f773(f773(f3(a847),x69862),f80(a847))),x69863))+~P1(f773(f773(f232(a847),x69862),f773(f181(f848(x69861)),x69863)))
% 191.21/191.74 [7068]P1(f773(f773(f233(a847),f2(a847)),x70681))+P1(f773(f773(f232(a847),f773(f773(f83(a847),x70682),x70681)),f773(f773(f83(a847),x70683),x70681)))
% 191.21/191.74 [7069]P1(f773(f773(f233(a847),f2(a847)),x70691))+P1(f773(f773(f232(a847),f773(f773(f83(a847),x70691),x70692)),f773(f773(f83(a847),x70691),x70693)))
% 191.21/191.74 [7072]~P1(f773(f773(f334(x70721),x70722),x70723))+~P1(f773(f773(f334(x70721),x70722),f773(f81(f855(x70721,a841)),x70723)))
% 191.21/191.74 [7078]~P1(f773(f773(f233(f855(x70781,a841)),x70782),x70783))+P1(f773(f773(f232(f855(x70781,a841)),x70782),x70783))
% 191.21/191.74 [7183]~P1(f773(f773(f233(a847),x71832),x71833))+P1(f773(f773(f233(a847),f773(f773(f82(a847),x71831),x71832)),f773(f773(f82(a847),x71831),x71833)))
% 191.21/191.74 [7184]~P1(f773(f773(f233(a847),x71841),x71843))+P1(f773(f773(f233(a847),f773(f773(f82(a847),x71841),x71842)),f773(f773(f82(a847),x71843),x71842)))
% 191.21/191.74 [7185]~P1(f773(f773(f233(a1),x71851),x71853))+P1(f773(f773(f233(a1),f773(f773(f82(a1),x71851),x71852)),f773(f773(f82(a1),x71853),x71852)))
% 191.21/191.74 [7188]~P1(f773(f773(f232(a847),x71882),x71883))+P1(f773(f773(f232(a847),f773(f773(f82(a847),x71881),x71882)),f773(f773(f82(a847),x71881),x71883)))
% 191.21/191.74 [7189]~P1(f773(f773(f232(a847),x71891),x71893))+P1(f773(f773(f232(a847),f773(f773(f82(a847),x71891),x71892)),f773(f773(f82(a847),x71893),x71892)))
% 191.21/191.74 [7191]~P1(f773(f773(f232(a847),x71912),x71913))+P1(f773(f773(f232(a847),f773(f773(f83(a847),x71911),x71912)),f773(f773(f83(a847),x71911),x71913)))
% 191.21/191.74 [7193]~P1(f773(f773(f232(a847),x71931),x71933))+P1(f773(f773(f232(a847),f773(f773(f83(a847),x71931),x71932)),f773(f773(f83(a847),x71933),x71932)))
% 191.21/191.74 [7194]~P1(f773(f773(f232(a847),x71941),x71943))+P1(f773(f773(f232(a847),f773(f773(f43(a847),x71941),x71942)),f773(f773(f43(a847),x71943),x71942)))
% 191.21/191.74 [7195]~P1(f773(f773(f232(a847),x71953),x71952))+P1(f773(f773(f232(a847),f773(f773(f3(a847),x71951),x71952)),f773(f773(f3(a847),x71951),x71953)))
% 191.21/191.74 [7196]~P1(f773(f773(f232(a847),x71961),x71963))+P1(f773(f773(f232(a847),f773(f773(f3(a847),x71961),x71962)),f773(f773(f3(a847),x71963),x71962)))
% 191.21/191.74 [7197]~P1(f773(f773(f232(a1),x71972),x71973))+P1(f773(f773(f232(a1),f773(f773(f82(a1),x71971),x71972)),f773(f773(f82(a1),x71971),x71973)))
% 191.21/191.74 [7200]~P1(f773(f773(f279(a847),x72002),x72003))+P1(f773(f773(f279(a847),f773(f773(f83(a847),x72001),x72002)),f773(f773(f83(a847),x72001),x72003)))
% 191.21/191.74 [7288]E(x72881,x72882)+~P1(f773(f773(f334(x72883),x72881),f773(f773(f302(x72883),x72882),f180(f855(x72883,a841)))))
% 191.21/191.74 [7290]~E(f773(f773(f104(f855(x72901,a841)),x72902),x72903),f180(f855(x72901,a841)))+P1(f773(f773(f232(f855(x72901,a841)),x72902),f773(f81(f855(x72901,a841)),x72903)))
% 191.21/191.74 [7297]P1(f773(f773(f334(f855(x72971,a841)),x72972),f773(f301(x72971),x72973)))+~P1(f773(f773(f232(f855(x72971,a841)),x72972),x72973))
% 191.21/191.74 [7354]E(f773(f773(f140(x73541),f773(f773(f153(x73541),x73542),x73543)),f773(f773(f128(x73541),f773(a114,x73543)),x73542)),f773(f773(f128(x73541),x73543),x73542))+~P1(f773(f773(f233(a847),x73543),f773(f181(f848(x73541)),x73542)))
% 191.21/191.74 [7384]P1(f773(f773(f334(f854(x73841,x73841)),x73842),f300(x73841,x73843)))+~P1(f773(f773(f334(f854(x73841,x73841)),x73842),x73843))
% 191.21/191.74 [7394]~P1(f773(f773(f334(f855(x73941,a841)),x73942),f773(f301(x73941),x73943)))+P1(f773(f773(f232(f855(x73941,a841)),x73942),x73943))
% 191.21/191.74 [7436]P1(f773(f773(f232(f855(x74361,a841)),x74362),f44(f855(x74361,a841),x74363)))+~P1(f773(f773(f334(f855(x74361,a841)),x74362),x74363))
% 191.21/191.74 [7464]~P133(x74641)+E(f773(f773(f83(x74641),f773(f773(f242(x74641),f773(f81(x74641),f80(x74641))),x74642)),f773(f773(f242(x74641),x74643),x74642)),f773(f773(f242(x74641),f773(f81(x74641),x74643)),x74642))
% 191.21/191.74 [7486]E(f773(f773(f153(x74861),x74862),f773(f773(f3(a847),f773(f181(f848(x74861)),x74862)),f773(a114,x74863))),f773(f773(f153(x74861),f773(f142(x74861),x74862)),x74863))+~P1(f773(f773(f233(a847),x74863),f773(f181(f848(x74861)),x74862)))
% 191.21/191.74 [7503]~E(f773(f773(f104(f855(x75031,a841)),f650(x75033,x75032,x75031)),x75033),f180(f855(x75031,a841)))+E(f773(f773(f104(f855(x75031,a841)),f44(f855(x75031,a841),x75032)),x75033),f180(f855(x75031,a841)))
% 191.21/191.74 [7567]~P1(f773(f773(f334(x75673),x75672),f773(f158(x75673),x75671)))+P1(f773(f773(f233(a847),f729(x75671,x75672,x75673)),f773(f181(f848(x75673)),x75671)))
% 191.21/191.74 [7575]P1(f773(f773(f334(x75751),f773(f773(f153(x75751),x75752),x75753)),f773(f158(x75751),x75752)))+~P1(f773(f773(f233(a847),x75753),f773(f181(f848(x75751)),x75752)))
% 191.21/191.74 [7684]P1(f773(f773(f232(f855(f848(x76841),a841)),f149(x76841,x76842)),f149(x76841,x76843)))+~P1(f773(f773(f232(f855(x76841,a841)),x76842),x76843))
% 191.21/191.74 [7713]E(f773(f773(f104(f855(x77131,a841)),f44(f855(x77131,a841),x77132)),x77133),f180(f855(x77131,a841)))+P1(f773(f773(f334(f855(x77131,a841)),f650(x77133,x77132,x77131)),x77132))
% 191.21/191.74 [7715]~P1(f773(f773(f334(f855(x77151,a841)),x77153),x77152))+P1(f773(f773(f232(f855(x77151,a841)),f45(f855(x77151,a841),x77152)),x77153))
% 191.21/191.74 [7717]E(f773(f773(f104(f855(x77171,a841)),x77172),x77173),f180(f855(x77171,a841)))+~P1(f773(f773(f232(f855(x77171,a841)),x77172),f773(f81(f855(x77171,a841)),x77173)))
% 191.21/191.74 [7770]E(f773(f773(f3(a847),f773(f773(f82(a847),f773(f155(a847),x77701)),x77702)),f773(f773(f153(a847),x77701),x77703)),f773(f155(a847),f773(f773(f148(a847,x77701),x77703),x77702)))+~P1(f773(f773(f233(a847),x77703),f773(f181(f848(a847)),x77701)))
% 191.21/191.74 [7820]P1(f773(f773(f233(a847),x78201),x78202))+~P1(f773(f773(f233(a847),f773(f773(f82(a847),x78203),x78201)),f773(f773(f82(a847),x78203),x78202)))
% 191.21/191.74 [7821]P1(f773(f773(f233(a847),x78211),x78212))+~P1(f773(f773(f233(a847),f773(f773(f83(a847),x78213),x78211)),f773(f773(f83(a847),x78213),x78212)))
% 191.21/191.74 [7822]P1(f773(f773(f233(a847),x78221),x78222))+~P1(f773(f773(f233(a847),f773(f773(f83(a847),x78221),x78223)),f773(f773(f83(a847),x78222),x78223)))
% 191.21/191.74 [7825]P1(f773(f773(f232(a847),x78251),x78252))+~P1(f773(f773(f232(a847),f773(f773(f82(a847),x78253),x78251)),f773(f773(f82(a847),x78253),x78252)))
% 191.21/191.74 [7854]P1(f773(f773(f233(a847),f2(a847)),x78541))+~P1(f773(f773(f233(a847),f773(f773(f83(a847),x78542),x78541)),f773(f773(f83(a847),x78543),x78541)))
% 191.21/191.74 [7855]P1(f773(f773(f233(a847),f2(a847)),x78551))+~P1(f773(f773(f233(a847),f773(f773(f83(a847),x78551),x78552)),f773(f773(f83(a847),x78551),x78553)))
% 191.21/191.74 [7928]E(f244(x79281,x79282,x79283),x79282)+~P1(f773(f773(f232(f855(x79281,a841)),x79283),f773(f773(f302(x79281),x79282),f180(f855(x79281,a841)))))
% 191.21/191.74 [8007]E(f773(f773(f125(x80071),f773(f773(f159(x80071),x80072),x80073)),f773(f773(f140(x80071),f773(f773(f153(x80071),x80073),x80072)),f115(x80071))),f773(f773(f159(x80071),f773(a114,x80072)),x80073))+~P1(f773(f773(f233(a847),x80072),f773(f181(f848(x80071)),x80073)))
% 191.21/191.74 [8076]P1(f773(f773(f232(f855(f855(x80761,a841),a841)),f245(x80761,x80762)),f245(x80761,x80763)))+~P1(f773(f773(f232(f855(x80761,a841)),x80762),x80763))
% 191.21/191.74 [8115]~P1(f773(f127(x81151),x81153))+P1(f773(f127(x81151),f773(f773(f773(f173(f848(x81151),f848(x81151)),x81152),f141(x81151)),x81153)))
% 191.21/191.74 [8120]~P1(f773(f773(f233(a847),x81202),x81203))+P1(f773(f773(f233(a847),f773(f773(f83(a847),f773(a114,x81201)),x81202)),f773(f773(f83(a847),f773(a114,x81201)),x81203)))
% 191.21/191.74 [8143]P1(f773(f773(f232(f855(f855(x81431,a841),a841)),f773(f301(x81431),x81432)),f773(f301(x81431),x81433)))+~P1(f773(f773(f232(f855(x81431,a841)),x81432),x81433))
% 191.21/191.74 [8300]~P1(f773(f773(f232(f855(x83001,a841)),x83003),x83002))+P1(f773(f773(f232(f855(x83001,a841)),f773(f81(f855(x83001,a841)),x83002)),f773(f81(f855(x83001,a841)),x83003)))
% 191.21/191.74 [8339]E(f773(f303(a847,a847,f773(f773(f9(a847,a847,a847),f3(a847)),x83391)),f773(f294(a847,x83392),x83393)),f773(f294(a847,f773(f773(f3(a847),x83392),x83391)),f773(f773(f3(a847),x83393),x83391)))+~P1(f773(f773(f233(a847),x83391),x83393))
% 191.21/191.74 [8365]~P67(x83651)+E(f773(f773(f82(x83651),x83652),f773(f132(x83651,x83651,f82(x83651),f2(x83651)),x83653)),f773(f132(x83651,x83651,f82(x83651),x83652),x83653))
% 191.21/191.74 [8446]~P79(x84461)+P1(f773(f773(f232(x84461),f773(f77(x84461),f773(f773(f82(x84461),x84462),x84463))),f773(f773(f82(x84461),f773(f77(x84461),x84462)),f773(f77(x84461),x84463))))
% 191.21/191.74 [8447]~P79(x84471)+P1(f773(f773(f232(x84471),f773(f77(x84471),f773(f773(f3(x84471),x84472),x84473))),f773(f773(f82(x84471),f773(f77(x84471),x84472)),f773(f77(x84471),x84473))))
% 191.21/191.74 [8457]E(f773(f773(f82(a1),f773(f773(f83(a1),x84571),f52(a1,f773(f773(f43(a1),x84572),x84571),x84573))),f52(a1,x84572,x84571)),f52(a1,x84572,f773(f773(f83(a1),x84571),x84573)))+~P1(f773(f773(f233(a1),f2(a1)),x84573))
% 191.21/191.74 [8466]E(f773(f773(f125(x84661),f773(f773(f159(x84661),x84662),x84663)),f773(f773(f140(x84661),f773(f131(x84661),f773(f773(f128(x84661),x84662),x84663))),f115(x84661))),f773(f773(f159(x84661),f773(a114,x84662)),x84663))+~P1(f773(f773(f233(a847),x84662),f773(f181(f848(x84661)),x84663)))
% 191.21/191.74 [8485]E(f773(f265(x84851,f773(f773(f143(x84851,f854(a101,x84851)),f773(f241(a101,x84851),f80(a101))),x84852)),f773(a5,x84853)),f773(f773(f153(x84851),x84852),x84853))+~P1(f773(f773(f233(a847),x84853),f773(f181(f848(x84851)),x84852)))
% 191.21/191.74 [8542]P1(f773(f773(f334(f854(x85421,x85421)),x85422),f773(f773(f281(x85421,x85421,x85421),x85423),f300(x85421,x85423))))+~P1(f773(f773(f334(f854(x85421,x85421)),x85422),x85423))
% 191.21/191.74 [8559]P1(f773(f773(f232(a847),x85591),x85592))+~P1(f773(f773(f232(a847),f773(f773(f83(a847),f773(a114,x85593)),x85591)),f773(f773(f83(a847),f773(a114,x85593)),x85592)))
% 191.21/191.74 [8570]P1(f773(f773(f232(f855(x85701,a841)),x85702),x85703))+~P1(f773(f773(f232(f855(x85701,a841)),f773(f81(f855(x85701,a841)),x85703)),f773(f81(f855(x85701,a841)),x85702)))
% 191.21/191.74 [8588]P1(f773(f127(x85881),x85882))+~P1(f773(f127(x85881),f773(f773(f773(f173(f848(x85881),f848(x85881)),x85883),f141(x85881)),x85882)))
% 191.21/191.74 [8654]E(f773(f277(x86541,x86541,f300(x86541,x86542)),x86543),x86543)+~P1(f773(f773(f232(f855(x86541,a841)),f773(f277(x86541,x86541,x86542),x86543)),x86543))
% 191.21/191.74 [8656]E(f773(f303(f854(x86561,x86562),x86562,f250(x86561,x86562)),f773(f158(f854(x86561,x86562)),x86563)),f171(x86561,x86562,f166(x86561,x86562,x86563)))+~P1(f773(f127(x86561),f773(f773(f143(f854(x86561,x86562),x86561),f240(x86561,x86562)),x86563)))
% 191.21/191.74 [8695]~P100(x86951)+P18(x86951,f773(f126(x86951,f773(f773(f9(x86951,x86951,a841),a330),f773(x86952,x86953))),x86953))
% 191.21/191.74 [8700]~P1(f773(f773(f232(a847),x87001),x87002))+P1(f773(f773(f232(a847),x87001),f773(f132(a847,a847,f82(a847),x87002),x87003)))
% 191.21/191.74 [8771]~P1(f773(f773(f334(f854(x87711,x87711)),x87712),f300(x87711,x87713)))+P1(f773(f773(f334(f854(x87711,x87711)),x87712),f773(f773(f173(f854(x87711,x87711),a841),f633(x87713,x87712,x87711)),x87713)))
% 191.21/191.74 [8840]~P67(x88401)+E(f773(f773(f82(x88401),x88402),f773(f132(x88401,x88401,f773(f9(x88401,x88401,x88401),f82(x88401)),f2(x88401)),f773(f142(x88401),x88403))),f773(f132(x88401,x88401,f82(x88401),x88402),x88403))
% 191.21/191.74 [9099]P53(x90991,x90992,x90993)+P1(f773(f773(f334(f854(x90991,x90992)),f773(f773(f241(x90991,x90992),f646(x90993,x90992,x90991)),f640(x90993,x90992,x90991))),x90993))
% 191.21/191.74 [9100]P53(x91001,x91002,x91003)+P1(f773(f773(f334(f854(x91001,x91002)),f773(f773(f241(x91001,x91002),f646(x91003,x91002,x91001)),f639(x91003,x91002,x91001))),x91003))
% 191.21/191.74 [9155]~P1(f773(f773(f334(f854(x91551,x91551)),x91552),f773(f773(f281(x91551,x91551,x91551),x91553),f300(x91551,x91553))))+P1(f773(f773(f334(f854(x91551,x91551)),x91552),f773(f773(f173(f854(x91551,x91551),a841),f638(x91553,x91552,x91551)),x91553)))
% 191.21/191.74 [9156]~P1(f773(x91561,f773(f773(f153(x91562),x91563),f773(f181(f848(x91562)),f162(x91562,x91561,x91563)))))+~P1(f773(f773(f233(a847),f773(f181(f848(x91562)),f162(x91562,x91561,x91563))),f773(f181(f848(x91562)),x91563)))
% 191.21/191.74 [9232]~P1(f773(f773(f232(f855(x92321,a841)),x92322),x92323))+P1(f773(f773(f232(f855(x92321,a841)),f773(f773(f9(x92321,f855(x92321,a841),a841),f334(x92321)),x92322)),f773(f773(f9(x92321,f855(x92321,a841),a841),f334(x92321)),x92323)))
% 191.21/191.74 [9288]~P1(f773(f773(f334(f854(f855(x92881,a841),f855(x92881,a841))),f773(f773(f241(f855(x92881,a841),f855(x92881,a841)),x92882),x92883)),f299(x92881)))+P1(f773(f773(f233(f855(x92881,a841)),x92882),x92883))
% 191.21/191.74 [9314]P54(x93141,x93142,x93143)+~P1(f773(f773(f334(f854(x93141,x93141)),f773(f773(f241(x93141,x93141),f627(x93143,x93142,x93141)),f626(x93143,x93142,x93141))),x93143))
% 191.21/191.74 [9315]P54(x93151,x93152,x93153)+~P1(f773(f773(f334(f854(x93151,x93151)),f773(f773(f241(x93151,x93151),f626(x93153,x93152,x93151)),f627(x93153,x93152,x93151))),x93153))
% 191.21/191.74 [9349]~P1(f773(f773(f334(f854(f848(x93491),f848(x93491))),f773(f773(f241(f848(x93491),f848(x93491)),x93492),x93492)),f137(x93491,x93493)))+P1(f773(f773(f334(f854(x93491,x93491)),f773(f773(f241(x93491,x93491),f754(x93492,x93493,x93491)),f754(x93492,x93493,x93491))),x93493))
% 191.21/191.74 [9394]P1(f773(f773(f232(f855(x93941,a841)),x93942),x93943))+~P1(f773(f773(f232(f855(x93941,a841)),f773(f773(f9(x93941,f855(x93941,a841),a841),f334(x93941)),x93942)),f773(f773(f9(x93941,f855(x93941,a841),a841),f334(x93941)),x93943)))
% 191.21/191.74 [9480]E(f773(f773(f3(a847),f773(f773(f8(a847,a847),x94801),f773(f257(a847),x94802))),f773(f773(f8(a847,a847),x94803),f773(f257(a847),x94802))),f773(f773(f8(a847,a847),f773(f773(f20(a847,a847,a847),f773(f773(f10(a847,f855(a847,a847),a847),f3(a847)),x94801)),x94803)),f773(f257(a847),x94802)))+~P1(f773(f773(f232(a847),f773(x94803,f341(x94802,x94801,x94803))),f773(x94801,f341(x94802,x94801,x94803))))
% 191.21/191.74 [9762]E(f773(f256(f854(x97621,x97622)),f773(f251(x97621,x97622,a841),f773(f773(f9(x97621,f855(x97622,f851(x97622)),f855(x97622,a841)),f773(f773(f10(f855(f851(x97622),a841),f855(f855(x97622,f851(x97622)),f855(x97622,a841)),x97621),f10(f851(x97622),a841,x97622)),f773(f773(f10(f851(x97622),f855(f851(x97622),a841),x97621),a330),f166(x97621,x97622,x97623)))),f227(x97622)))),f773(f158(f854(x97621,x97622)),x97623))+~P1(f773(f127(x97621),f773(f773(f143(f854(x97621,x97622),x97621),f240(x97621,x97622)),x97623)))
% 191.21/191.74 [5508]~P69(x55081)+E(f773(f773(f82(x55081),f773(f773(f3(x55081),x55082),x55083)),x55083),x55082)
% 191.21/191.74 [5509]~P69(x55091)+E(f773(f773(f3(x55091),f773(f773(f82(x55091),x55092),x55093)),x55093),x55092)
% 191.21/191.74 [5735]~P69(x57351)+E(f773(f773(f82(x57351),x57352),f773(f773(f82(x57351),f773(f81(x57351),x57352)),x57353)),x57353)
% 191.21/191.74 [5818]~P75(x58181)+E(f773(f773(f83(x58181),f773(f773(f242(x58181),x58182),x58183)),x58182),f773(f773(f242(x58181),x58182),f773(a114,x58183)))
% 191.21/191.74 [5819]~P85(x58191)+E(f773(f773(f83(x58191),f773(f773(f242(x58191),x58192),x58193)),x58192),f773(f773(f242(x58191),x58192),f773(a114,x58193)))
% 191.21/191.74 [6034]~P110(x60341)+E(f773(f77(x60341),f773(f773(f242(x60341),f773(f81(x60341),x60342)),x60343)),f773(f77(x60341),f773(f773(f242(x60341),x60342),x60343)))
% 191.21/191.74 [6086]~P75(x60861)+E(f773(f773(f83(x60861),f773(f773(f242(x60861),x60862),x60863)),x60862),f773(f773(f83(x60861),x60862),f773(f773(f242(x60861),x60862),x60863)))
% 191.21/191.74 [6146]E(f773(f773(f3(a101),f773(f773(f82(a101),x61461),x61462)),x61463),f269(x61461,x61462,x61463))+~P1(f773(f773(f233(a101),x61462),x61463))
% 191.21/191.74 [6168]~E(f773(f773(f128(x61681),x61683),x61682),f115(x61681))+P1(f773(f773(f232(a847),f773(f181(f848(x61681)),x61682)),x61683))
% 191.21/191.74 [6310]E(f773(f773(f83(a847),f773(f106(a847),x63101)),f773(f773(f83(a847),f773(f106(a847),x63102)),x63103)),f2(a847))+~P1(f773(f773(f233(a1),x63101),a85))
% 191.21/191.74 [6326]~P60(x63261)+E(f773(f773(f242(x63261),f773(f773(f283(x63261),f80(x63261)),x63262)),x63263),f773(f773(f283(x63261),f80(x63261)),f773(f773(f242(x63261),x63262),x63263)))
% 191.21/191.74 [6411]E(f773(f773(f3(a847),f773(f773(f82(a847),x64111),x64112)),x64113),f773(f773(f3(a847),x64111),f773(f773(f3(a847),x64113),x64112)))+~P1(f773(f773(f232(a847),x64112),x64113))
% 191.21/191.74 [6412]E(f773(f773(f3(a847),f773(f773(f82(a847),x64121),x64122)),x64123),f773(f773(f82(a847),x64121),f773(f773(f3(a847),x64122),x64123)))+~P1(f773(f773(f232(a847),x64123),x64122))
% 191.21/191.74 [6452]~P100(x64521)+P1(f773(f773(f232(x64521),f773(f773(f236(x64521),x64522),x64523)),x64523))
% 191.21/191.74 [6453]~P100(x64531)+P1(f773(f773(f232(x64531),f773(f773(f236(x64531),x64532),x64533)),x64532))
% 191.21/191.74 [6454]~P93(x64541)+P1(f773(f773(f232(x64541),f773(f773(f104(x64541),x64542),x64543)),x64543))
% 191.21/191.74 [6455]~P98(x64551)+P1(f773(f773(f232(x64551),f773(f773(f104(x64551),x64552),x64553)),x64553))
% 191.21/191.74 [6456]~P93(x64561)+P1(f773(f773(f232(x64561),f773(f773(f104(x64561),x64562),x64563)),x64562))
% 191.21/191.74 [6457]~P98(x64571)+P1(f773(f773(f232(x64571),f773(f773(f104(x64571),x64572),x64573)),x64572))
% 191.21/191.74 [6472]E(f773(f773(f43(a1),f773(f773(f43(a1),x64721),x64722)),x64723),f773(f773(f43(a1),x64721),f773(f773(f83(a1),x64722),x64723)))+~P1(f773(f773(f233(a1),f2(a1)),x64723))
% 191.21/191.74 [6525]~P85(x65251)+E(f773(f773(f82(x65251),f773(f773(f83(x65251),x65252),x65253)),x65253),f773(f773(f83(x65251),f773(f773(f82(x65251),x65252),f80(x65251))),x65253))
% 191.21/191.74 [6526]~P88(x65261)+E(f773(f773(f83(x65261),f773(f81(x65261),f773(f106(x65261),x65262))),x65263),f773(f773(f83(x65261),f773(f106(x65261),f773(f81(a1),x65262))),x65263))
% 191.21/191.74 [6599]~P67(x65991)+E(f773(f155(x65991),f773(f773(f143(x65992,x65991),f773(f18(x65991,x65992),f2(x65991))),x65993)),f2(x65991))
% 191.21/191.74 [6618]E(f773(f773(f82(a847),f773(f106(a847),x66181)),f773(f773(f82(a847),f773(f106(a847),x66182)),x66183)),f773(f773(f82(a847),f773(f106(a847),x66182)),x66183))+~P1(f773(a186,f773(f106(a1),x66181)))
% 191.21/191.74 [6633]~P9(x66331)+E(f45(x66331,f773(f773(f302(x66331),x66332),f773(f773(f302(x66331),x66333),f180(f855(x66331,a841))))),f773(f773(f104(x66331),x66332),x66333))
% 191.21/191.74 [6634]~P9(x66341)+E(f44(x66341,f773(f773(f302(x66341),x66342),f773(f773(f302(x66341),x66343),f180(f855(x66341,a841))))),f773(f773(f103(x66341),x66342),x66343))
% 191.21/191.74 [6659]E(f773(f773(f159(x66591),x66592),x66593),x66593)+~P1(f773(f773(f232(a847),f773(f181(f848(x66591)),x66593)),x66592))
% 191.21/191.74 [6671]E(f773(f773(f128(x66711),x66712),x66713),f115(x66711))+~P1(f773(f773(f232(a847),f773(f181(f848(x66711)),x66713)),x66712))
% 191.21/191.74 [6683]E(f773(f773(f3(a847),f773(f773(f82(a847),x66831),x66832)),x66833),f773(f773(f82(a847),f773(f773(f3(a847),x66831),x66833)),x66832))+~P1(f773(f773(f232(a847),x66833),x66831))
% 191.21/191.74 [6697]~P1(f773(f773(f233(a847),x66971),x66973))+P1(f773(f773(f233(a847),f773(f773(f3(a847),x66971),x66972)),x66973))
% 191.21/191.74 [6725]~P100(x67251)+E(f151(x67251,x67252,f773(f773(f138(x67251,x67251,f7(x67251)),x67252),x67253)),x67253)
% 191.21/191.74 [6823]E(f773(f773(f3(a847),f773(f773(f82(a847),x68231),x68232)),f773(a114,x68233)),f773(f773(f3(a847),x68231),f773(a114,f773(f773(f3(a847),x68233),x68232))))+~P1(f773(f773(f232(a847),x68232),x68233))
% 191.21/191.74 [6824]~P110(x68241)+P1(f773(f773(f232(x68241),f2(x68241)),f773(f773(f242(x68241),f773(f77(x68241),x68242)),x68243)))
% 191.21/191.74 [6875]P28(x68751,x68752,x68753)+~P1(f773(f773(f232(f855(f846(x68751),a841)),x68753),x68752))
% 191.21/191.74 [6916]~P1(f773(f63(x69161),x69162))+P1(f773(f63(x69161),f773(f773(f3(f855(x69161,a841)),x69162),x69163)))
% 191.21/191.74 [6917]~P1(f773(f63(x69171),x69173))+P1(f773(f63(x69171),f773(f773(f104(f855(x69171,a841)),x69172),x69173)))
% 191.21/191.74 [6918]~P1(f773(f63(x69181),x69182))+P1(f773(f63(x69181),f773(f773(f104(f855(x69181,a841)),x69182),x69183)))
% 191.21/191.74 [7057]~P36(x70571,x70573)+P36(x70571,f773(f773(f104(f855(f854(x70571,x70571),a841)),x70572),x70573))
% 191.21/191.74 [7058]~P36(x70581,x70582)+P36(x70581,f773(f773(f104(f855(f854(x70581,x70581),a841)),x70582),x70583))
% 191.21/191.74 [7178]~P93(x71781)+E(f15(x71781,f773(f158(x71781),f773(f773(f140(x71781),x71782),x71783))),f773(f132(x71781,x71781,f103(x71781),x71782),x71783))
% 191.21/191.74 [7179]~P100(x71791)+E(f16(x71791,f773(f158(x71791),f773(f773(f140(x71791),x71792),x71793))),f773(f132(x71791,x71791,f179(x71791),x71792),x71793))
% 191.21/191.74 [7180]~P100(x71801)+E(f17(x71801,f773(f158(x71801),f773(f773(f140(x71801),x71802),x71803))),f773(f132(x71801,x71801,f236(x71801),x71802),x71803))
% 191.21/191.74 [7181]~P93(x71811)+E(f12(x71811,f773(f158(x71811),f773(f773(f140(x71811),x71812),x71813))),f773(f132(x71811,x71811,f104(x71811),x71812),x71813))
% 191.21/191.74 [7182]~P1(f773(f773(f279(a1),x71821),x71822))+P1(f773(f773(f279(a1),x71821),f773(f773(f82(a1),x71822),f773(f773(f83(a1),x71821),x71823))))
% 191.21/191.74 [7252]~P1(f773(f63(x72521),x72522))+P1(f773(f773(f232(a847),f773(f42(x72521),x72522)),f773(f42(x72521),f773(f773(f302(x72521),x72523),x72522))))
% 191.21/191.74 [7259]E(f773(f773(f103(f855(a847,a841)),f773(f294(a847,x72591),x72592)),f773(f294(a847,x72592),f773(f773(f82(a847),x72592),x72593))),f773(f294(a847,x72591),f773(f773(f82(a847),x72592),x72593)))+~P1(f773(f773(f232(a847),x72591),x72592))
% 191.21/191.74 [7269]P1(f773(f773(f233(a847),x72691),x72692))+~P1(f773(f773(f233(a847),f773(f773(f82(a847),x72691),x72693)),x72692))
% 191.21/191.74 [7272]P1(f773(f773(f232(a847),x72721),x72722))+~P1(f773(f773(f232(a847),f773(f773(f82(a847),x72723),x72721)),x72722))
% 191.21/191.74 [7273]P1(f773(f773(f232(a847),x72731),x72732))+~P1(f773(f773(f232(a847),f773(f773(f82(a847),x72731),x72733)),x72732))
% 191.21/191.74 [7315]~P100(x73151)+E(f13(x73151,f179(x73151),f773(f158(x73151),f773(f773(f140(x73151),x73152),x73153))),f773(f132(x73151,x73151,f179(x73151),x73152),x73153))
% 191.21/191.74 [7316]~P100(x73161)+E(f14(x73161,f236(x73161),f773(f158(x73161),f773(f773(f140(x73161),x73162),x73163))),f773(f132(x73161,x73161,f236(x73161),x73162),x73163))
% 191.21/191.74 [7320]~E(x73202,f180(f855(f854(x73201,x73201),a841)))+P1(f773(f773(f232(f855(f854(x73201,x73201),a841)),x73202),x73203))
% 191.21/191.74 [7429]E(f773(f773(f103(f855(x74291,a841)),x74292),f773(f773(f3(f855(x74291,a841)),x74293),x74292)),x74293)+~P1(f773(f773(f232(f855(x74291,a841)),x74292),x74293))
% 191.21/191.74 [7432]~P1(f773(f773(f233(a847),x74321),f773(f773(f3(a847),x74323),x74322)))+P1(f773(f773(f233(a847),f773(f773(f82(a847),x74321),x74322)),x74323))
% 191.21/191.74 [7433]~P1(f773(f773(f232(a847),x74331),f773(f773(f82(a847),x74333),x74332)))+P1(f773(f773(f232(a847),f773(f773(f3(a847),x74331),x74332)),x74333))
% 191.21/191.74 [7493]E(x74931,f115(x74932))+E(f773(f131(x74932),f773(f773(f773(f173(f848(x74932),f848(x74932)),x74933),f141(x74932)),x74931)),f773(f773(f153(x74932),x74931),f52(a847,x74933,f773(f181(f848(x74932)),x74931))))
% 191.21/191.74 [7502]E(f773(f773(f302(x75021),x75022),f773(f773(f3(f855(x75021,a841)),x75023),f773(f773(f302(x75021),x75022),f180(f855(x75021,a841))))),x75023)+~P1(f773(f773(f334(x75021),x75022),x75023))
% 191.21/191.74 [7666]P1(f773(f773(f233(a847),x76661),f773(f773(f3(a847),x76662),x76663)))+~P1(f773(f773(f233(a847),f773(f773(f82(a847),x76661),x76663)),x76662))
% 191.21/191.74 [7667]P1(f773(f773(f232(a847),x76671),f773(f773(f82(a847),x76672),x76673)))+~P1(f773(f773(f232(a847),f773(f773(f3(a847),x76671),x76673)),x76672))
% 191.21/191.74 [7687]P1(f773(f63(x76871),x76872))+~P1(f773(f63(x76871),f773(f773(f103(f855(x76871,a841)),x76873),x76872)))
% 191.21/191.74 [7688]P1(f773(f63(x76881),x76882))+~P1(f773(f63(x76881),f773(f773(f103(f855(x76881,a841)),x76882),x76883)))
% 191.21/191.74 [7769]~P44(x77691,x77693)+P1(f773(f773(f334(f854(x77691,x77691)),f773(f773(f241(x77691,x77691),x77692),x77692)),x77693))
% 191.21/191.74 [7819]P1(f773(f773(f279(a1),x78191),x78192))+~P1(f773(f773(f279(a1),x78191),f773(f773(f82(a1),x78192),f773(f773(f83(a1),x78191),x78193))))
% 191.21/191.74 [7899]E(f773(f773(f153(a847),f130(a847,f773(f294(a847,x78991),x78992))),x78993),f773(f773(f82(a847),x78991),x78993))+~P1(f773(f773(f233(a847),f773(f773(f82(a847),x78991),x78993)),x78992))
% 191.21/191.74 [7969]~P1(f773(f773(f187(f773(a27,x79691)),x79692),x79693))+P1(f773(f773(f187(f773(f231(a842),f773(a30,x79691))),x79692),x79693))
% 191.21/191.74 [7973]E(f773(f773(f159(a847),x79731),f130(a847,f773(f294(a847,x79732),x79733))),f130(a847,f773(f294(a847,x79732),f773(f773(f82(a847),x79732),x79731))))+~P1(f773(f773(f232(a847),f773(f773(f82(a847),x79732),x79731)),x79733))
% 191.21/191.74 [8022]~P88(x80221)+E(f773(f773(f242(x80221),x80222),f773(f106(a847),f773(f773(f82(a1),x80223),x80223))),f773(f773(f88(x80221,x80221),f773(f773(f242(x80221),x80222),f773(f106(a847),x80223))),f773(f773(f20(x80221,x80221,x80221),f83(x80221)),f7(x80221))))
% 191.21/191.74 [8222]P1(f773(f773(f187(f773(a27,x82221)),x82222),x82223))+~P1(f773(f773(f187(f773(f231(a842),f773(a30,x82221))),x82222),x82223))
% 191.21/191.74 [8279]E(f773(f773(f125(x82791),f773(f773(f159(x82791),x82792),x82793)),f773(f773(f140(x82791),f773(f773(f153(x82791),x82793),x82792)),f773(f773(f128(x82791),f773(a114,x82792)),x82793))),x82793)+~P1(f773(f773(f233(a847),x82792),f773(f181(f848(x82791)),x82793)))
% 191.21/191.74 [8286]P1(f773(f773(f232(f855(x82861,a841)),f321(x82861,x82862)),f321(x82861,x82863)))+~P1(f773(f773(f232(f855(x82861,f855(x82861,a841))),x82863),x82862))
% 191.21/191.74 [8287]~P54(x82871,x82872,x82873)+P54(x82871,x82872,f773(f773(f3(f855(f854(x82871,x82871),a841)),x82873),f300(x82871,f180(f855(f854(x82871,x82871),a841)))))
% 191.21/191.74 [8309]P1(f773(f773(f232(f855(x83091,a841)),f322(x83091,x83092)),f322(x83091,x83093)))+~P1(f773(f773(f232(f855(f854(x83091,x83091),a841)),x83093),x83092))
% 191.21/191.74 [8316]~P118(x83161)+P1(f773(f773(f232(x83161),f2(x83161)),f773(f773(f82(x83161),f773(f773(f83(x83161),x83162),x83162)),f773(f773(f83(x83161),x83163),x83163))))
% 191.21/191.74 [8353]P1(f773(f773(f232(f855(x83531,a841)),f773(f276(x83531),x83532)),f773(f276(x83531),x83533)))+~P1(f773(f773(f232(f855(f854(x83531,x83531),a841)),x83532),x83533))
% 191.21/191.74 [8385]~P48(x83851,x83852)+~P1(f773(f773(f334(f854(x83851,x83851)),f773(f773(f241(x83851,x83851),x83853),x83853)),x83852))
% 191.21/191.74 [8387]~P36(x83871,x83872)+~P1(f773(f773(f334(f854(x83871,x83871)),f773(f773(f241(x83871,x83871),x83873),x83873)),x83872))
% 191.21/191.74 [8448]P1(f773(f773(f232(f855(x84481,a841)),f45(f855(x84481,a841),x84482)),f45(f855(x84481,a841),x84483)))+~P1(f773(f773(f232(f855(f855(x84481,a841),a841)),x84483),x84482))
% 191.21/191.74 [8449]P1(f773(f773(f232(f855(x84491,a841)),f44(f855(x84491,a841),x84492)),f44(f855(x84491,a841),x84493)))+~P1(f773(f773(f232(f855(f855(x84491,a841),a841)),x84492),x84493))
% 191.21/191.74 [8504]~P12(x85041,x85043,x85042)+P1(f773(f773(f232(f855(f854(x85041,x85041),a841)),x85042),f773(f773(f248(x85041,x85041),x85043),f773(f18(f855(x85041,a841),x85041),x85043))))
% 191.21/191.74 [8505]~P47(x85051,x85053,x85052)+P1(f773(f773(f232(f855(f854(x85051,x85051),a841)),x85052),f773(f773(f248(x85051,x85051),x85053),f773(f18(f855(x85051,a841),x85051),x85053))))
% 191.21/191.74 [8543]~P79(x85431)+P1(f773(f773(f232(x85431),f773(f773(f3(x85431),f773(f77(x85431),x85432)),f773(f77(x85431),x85433))),f773(f77(x85431),f773(f773(f3(x85431),x85433),x85432))))
% 191.21/191.74 [8544]~P79(x85441)+P1(f773(f773(f232(x85441),f773(f773(f3(x85441),f773(f77(x85441),x85442)),f773(f77(x85441),x85443))),f773(f77(x85441),f773(f773(f3(x85441),x85442),x85443))))
% 191.21/191.74 [8568]P1(f773(f773(f232(f855(f854(x85681,x85681),a841)),f300(x85681,x85682)),f300(x85681,x85683)))+~P1(f773(f773(f232(f855(f854(x85681,x85681),a841)),x85682),x85683))
% 191.21/191.74 [8714]P54(x87141,x87142,x87143)+~P54(x87141,x87142,f773(f773(f3(f855(f854(x87141,x87141),a841)),x87143),f300(x87141,f180(f855(f854(x87141,x87141),a841)))))
% 191.21/191.74 [8733]P1(f773(f773(f232(f855(f854(f848(x87331),f848(x87331)),a841)),f147(x87331,x87332)),f147(x87331,x87333)))+~P1(f773(f773(f232(f855(f854(x87331,x87331),a841)),x87332),x87333))
% 191.21/191.74 [8734]P1(f773(f773(f232(f855(f854(f848(x87341),f848(x87341)),a841)),f146(x87341,x87342)),f146(x87341,x87343)))+~P1(f773(f773(f232(f855(f854(x87341,x87341),a841)),x87342),x87343))
% 191.21/191.74 [8751]~P47(x87511,x87513,x87512)+P1(f773(f773(f232(f855(f854(x87511,x87511),a841)),x87512),f773(f773(f281(x87511,x87511,x87511),f773(f278(x87511,x87511),x87512)),x87512)))
% 191.21/191.74 [8792]~P1(f773(f127(x87921),x87922))+E(f773(f126(x87921,f773(f773(f9(x87921,f855(x87921,a841),a841),f334(x87921)),f773(f158(x87921),f160(x87921,x87922,x87923)))),x87922),f160(x87921,x87922,x87923))
% 191.21/191.74 [8838]E(x88381,x88382)+~P1(f773(f773(f334(f854(x88383,x88383)),f773(f773(f241(x88383,x88383),x88381),x88382)),f300(x88383,f180(f855(f854(x88383,x88383),a841)))))
% 191.21/191.74 [8920]P1(f773(f773(f334(x89201),x89202),f322(x89201,x89203)))+P1(f773(f773(f334(f854(x89201,x89201)),f773(f773(f241(x89201,x89201),f526(x89203,x89202,x89201)),x89202)),x89203))
% 191.21/191.74 [8921]P1(f773(f773(f334(x89211),x89212),f322(x89211,x89213)))+P1(f773(f773(f334(f854(x89211,x89211)),f773(f773(f241(x89211,x89211),f619(x89213,x89212,x89211)),x89212)),x89213))
% 191.21/191.74 [8922]P1(f773(f773(f334(x89221),x89222),f322(x89221,x89223)))+P1(f773(f773(f334(f854(x89221,x89221)),f773(f773(f241(x89221,x89221),f621(x89223,x89222,x89221)),x89222)),x89223))
% 191.21/191.74 [9026]P1(f773(x90263,x90262))+E(f773(f256(x90261),f773(f773(f20(x90261,a841,a841),f773(f773(f10(a841,f855(a841,a841),x90261),a331),f773(a330,x90262))),x90263)),f180(f855(x90261,a841)))
% 191.21/191.74 [9045]~P79(x90451)+P1(f773(f773(f232(x90451),f773(f77(x90451),f773(f773(f3(x90451),f773(f77(x90451),x90452)),f773(f77(x90451),x90453)))),f773(f77(x90451),f773(f773(f3(x90451),x90452),x90453))))
% 191.21/191.74 [9058]~P1(f773(x90583,x90582))+E(f773(f256(x90581),f773(f773(f20(x90581,a841,a841),f773(f773(f10(a841,f855(a841,a841),x90581),a331),f773(a330,x90582))),x90583)),f773(f773(f302(x90581),x90582),f180(f855(x90581,a841))))
% 191.21/191.74 [9064]~P1(f773(f773(f334(f855(x90641,a841)),x90643),f773(f301(x90641),x90642)))+P1(f773(f245(x90641,f773(f773(f9(x90641,f855(x90641,a841),a841),f334(x90641)),x90642)),x90643))
% 191.21/191.74 [9098]P36(x90981,x90982)+P1(f773(f773(f334(f854(x90981,x90981)),f773(f773(f241(x90981,x90981),f773(f589(x90982,x90981),f773(a114,x90983))),f773(f589(x90982,x90981),x90983))),x90982))
% 191.21/191.74 [9224]P1(f773(f773(f334(f855(x92241,a841)),x92242),f773(f301(x92241),x92243)))+~P1(f773(f245(x92241,f773(f773(f9(x92241,f855(x92241,a841),a841),f334(x92241)),x92243)),x92242))
% 191.21/191.74 [9284]P1(f773(f773(f334(x92841),f773(f265(x92841,x92842),x92843)),f773(f158(x92841),f773(f773(f143(f854(a101,x92841),x92841),f250(a101,x92841)),x92842))))+~P1(f773(f773(f233(a101),x92843),f773(f155(a101),f773(f773(f143(f854(a101,x92841),a101),f240(a101,x92841)),x92842))))
% 191.21/191.74 [9332]P1(f773(f773(f232(f855(f854(f848(x93321),f848(x93321)),a841)),f147(x93321,x93322)),f773(f773(f248(f848(x93321),f848(x93321)),f149(x93321,x93323)),f773(f18(f855(f848(x93321),a841),f848(x93321)),f149(x93321,x93323)))))+~P1(f773(f773(f232(f855(f854(x93321,x93321),a841)),x93322),f773(f773(f248(x93321,x93321),x93323),f773(f18(f855(x93321,a841),x93321),x93323))))
% 191.21/191.74 [9352]P1(f773(f773(f334(x93521),f773(f240(x93521,f854(a101,a101)),f773(f263(x93521,x93522),x93523))),f773(f158(x93521),f773(f773(f143(f854(a101,x93521),x93521),f250(a101,x93521)),x93522))))+~P1(f773(f773(f233(a101),f2(a101)),f773(f155(a101),f773(f773(f143(f854(a101,x93521),a101),f240(a101,x93521)),x93522))))
% 191.21/191.74 [9367]~P1(f773(f773(f232(f855(f854(x93671,x93671),a841)),x93672),f773(f773(f248(x93671,x93671),x93673),f773(f18(f855(x93671,a841),x93671),x93673))))+P1(f773(f773(f232(f855(f854(x93671,x93671),a841)),f773(f773(f281(x93671,x93671,x93671),x93672),f300(x93671,x93672))),f773(f773(f248(x93671,x93671),x93673),f773(f18(f855(x93671,a841),x93671),x93673))))
% 191.21/191.74 [9648]~P36(x96481,x96482)+~P1(f773(f773(f334(f854(x96481,x96481)),f773(f773(f241(x96481,x96481),f773(x96483,f773(a114,f590(x96482,x96481,x96483)))),f773(x96483,f590(x96482,x96481,x96483)))),x96482))
% 191.21/191.74 [9649]~P36(x96491,x96492)+~P1(f773(f773(f334(f854(x96491,x96491)),f773(f773(f241(x96491,x96491),f773(x96493,f773(a114,f635(x96493,x96492,x96491)))),f773(x96493,f635(x96493,x96492,x96491)))),x96492))
% 191.21/191.74 [9904]P1(f773(f773(f232(f855(f854(f855(x99041,a841),f855(x99041,a841)),a841)),f773(f773(f281(f855(x99041,a841),f855(x99041,a841),f855(x99041,a841)),f326(x99041,x99042)),f773(f773(f103(f855(f854(f855(x99041,a841),f855(x99041,a841)),a841)),f326(x99041,x99043)),f773(f773(f302(f854(f855(x99041,a841),f855(x99041,a841))),f773(f773(f241(f855(x99041,a841),f855(x99041,a841)),f180(f855(x99041,a841))),f180(f855(x99041,a841)))),f180(f855(f854(f855(x99041,a841),f855(x99041,a841)),a841)))))),f326(x99041,x99042)))+~P1(f773(f773(f232(f855(f854(x99041,x99041),a841)),f773(f773(f281(x99041,x99041,x99041),x99042),x99043)),x99042))
% 191.21/191.74 [9905]P1(f773(f773(f232(f855(f854(f855(x99051,a841),f855(x99051,a841)),a841)),f773(f773(f281(f855(x99051,a841),f855(x99051,a841),f855(x99051,a841)),f324(x99051,x99052)),f773(f773(f103(f855(f854(f855(x99051,a841),f855(x99051,a841)),a841)),f324(x99051,x99053)),f773(f773(f302(f854(f855(x99051,a841),f855(x99051,a841))),f773(f773(f241(f855(x99051,a841),f855(x99051,a841)),f180(f855(x99051,a841))),f180(f855(x99051,a841)))),f180(f855(f854(f855(x99051,a841),f855(x99051,a841)),a841)))))),f324(x99051,x99052)))+~P1(f773(f773(f232(f855(f854(x99051,x99051),a841)),f773(f773(f281(x99051,x99051,x99051),x99052),x99053)),x99052))
% 191.21/191.74 [7177]~P1(f773(f773(f232(a847),x71772),x71771))+E(f773(f773(f3(a847),f773(a114,f773(f773(f3(a847),x71771),x71772))),x71773),f773(f773(f3(a847),f773(a114,x71771)),f773(f773(f82(a847),x71772),x71773)))
% 191.21/191.74 [7217]~P7(x72171)+E(f773(f773(f82(x72171),f52(x72171,x72172,x72173)),f773(f773(f83(x72171),f773(f773(f43(x72171),x72172),x72173)),x72173)),x72172)
% 191.21/191.74 [7437]E(f773(f773(f83(a847),f773(f106(a847),x74371)),f773(f773(f83(a847),f773(f106(a847),x74372)),x74373)),f773(f773(f83(a847),f773(f106(a847),f773(f773(f83(a1),x74371),x74372))),x74373))+P1(f773(f773(f233(a1),x74371),a85))
% 191.21/191.74 [7910]~P1(f773(f773(f232(a847),x79103),x79102))+P1(f773(f773(f232(a847),x79101),f773(f773(f3(a847),f773(f773(f82(a847),x79102),x79101)),x79103)))
% 191.21/191.74 [8105]~P1(f773(f773(f232(a847),x81051),x81052))+E(f773(f773(f125(a847),f130(a847,f773(f294(a847,x81051),x81052))),f130(a847,f773(f294(a847,x81052),f773(f773(f82(a847),x81052),x81053)))),f130(a847,f773(f294(a847,x81051),f773(f773(f82(a847),x81052),x81053))))
% 191.21/191.74 [8362]~P1(f773(f63(x83621),x83622))+E(f773(a114,f773(f42(x83621),f773(f773(f3(f855(x83621,a841)),x83622),f773(f773(f302(x83621),x83623),f180(f855(x83621,a841)))))),f773(f42(x83621),f773(f773(f302(x83621),x83623),x83622)))
% 191.21/191.74 [8406]~P1(f773(f63(x84061),x84062))+E(f773(f773(f82(a847),f80(a847)),f773(f42(x84061),f773(f773(f3(f855(x84061,a841)),x84062),f773(f773(f302(x84061),x84063),f180(f855(x84061,a841)))))),f773(f42(x84061),f773(f773(f302(x84061),x84063),x84062)))
% 191.21/191.74 [8577]E(f773(f773(f3(a847),f773(f42(x85771),x85772)),f773(f42(x85771),f773(f773(f104(f855(x85771,a841)),x85772),x85773))),f773(f42(x85771),f773(f773(f3(f855(x85771,a841)),x85772),x85773)))+~P1(f773(f63(x85771),f773(f773(f104(f855(x85771,a841)),x85772),x85773)))
% 191.21/191.74 [8789]~P10(f773(x87892,f425(x87892,x87893,x87891)))+E(f773(f102(a1),f773(f773(f8(x87891,a847),f773(f773(f10(a1,a847,x87891),a107),x87892)),x87893)),f773(f773(f8(x87891,a1),x87892),x87893))
% 191.21/191.74 [8790]~P10(f773(x87902,f462(x87902,x87903,x87901)))+E(f773(f102(a1),f773(f773(f11(x87901,a847),f773(f773(f10(a1,a847,x87901),a107),x87902)),x87903)),f773(f773(f11(x87901,a1),x87902),x87903))
% 191.21/191.74 [8822]~P1(f773(f63(x88221),x88223))+P1(f773(f773(f232(a847),f773(f773(f3(a847),f773(f42(x88221),x88222)),f773(f42(x88221),x88223))),f773(f42(x88221),f773(f773(f3(f855(x88221,a841)),x88222),x88223))))
% 191.21/191.74 [8846]P1(f773(f773(f334(x88461),f425(x88462,x88463,x88461)),x88463))+E(f773(f102(a1),f773(f773(f8(x88461,a847),f773(f773(f10(a1,a847,x88461),a107),x88462)),x88463)),f773(f773(f8(x88461,a1),x88462),x88463))
% 191.21/191.74 [8847]P1(f773(f773(f334(x88471),f462(x88472,x88473,x88471)),x88473))+E(f773(f102(a1),f773(f773(f11(x88471,a847),f773(f773(f10(a1,a847,x88471),a107),x88472)),x88473)),f773(f773(f11(x88471,a1),x88472),x88473))
% 191.21/191.74 [8914]E(f87(x89141,f773(f773(f9(x89141,f855(x89141,a841),a841),f334(x89141)),f773(f773(f3(f855(x89141,a841)),x89142),f773(f773(f302(x89141),x89143),f180(f855(x89141,a841)))))),f244(x89141,x89143,x89142))+P1(f773(f773(f232(f855(x89141,a841)),x89142),f773(f773(f302(x89141),x89143),f180(f855(x89141,a841)))))
% 191.21/191.74 [9225]E(f773(f773(f143(f848(x92251),x92251),f773(f773(f9(f848(x92251),a847,x92251),f153(x92251)),x92252)),f773(f126(f848(x92251),f773(f773(f10(a847,a841,f848(x92251)),f773(f233(a847),x92252)),f181(f848(x92251)))),x92253)),f773(f773(f153(f848(x92251)),f164(x92251,x92253)),x92252))+~P1(f773(f773(f233(a847),x92252),f773(f181(f848(f848(x92251))),f164(x92251,x92253))))
% 191.21/191.74 [9524]~P1(f773(f773(f334(f854(x95241,x95241)),x95242),f300(x95241,x95243)))+P1(f773(f773(f334(f854(x95241,x95241)),x95242),f773(f773(f46(a847,f855(f854(x95241,x95241),a841)),f239(f855(a847,a841))),f773(f773(f9(a847,f855(f854(x95241,x95241),a841),f855(f854(x95241,x95241),a841)),f173(f854(x95241,x95241),a841)),x95243))))
% 191.21/191.74 [9577]~P1(f773(f773(f232(f855(x95771,a841)),f773(f773(f46(a847,f855(x95771,a841)),f773(f294(a847,f2(a847)),f397(x95773,x95772,x95771))),x95772)),x95773))+P1(f773(f773(f232(f855(x95771,a841)),f773(f773(f46(a847,f855(x95771,a841)),f239(f855(a847,a841))),x95772)),x95773))
% 191.21/191.74 [9625]~P1(f773(f773(f233(a1),f2(a1)),x96253))+P1(f773(f773(f233(a1),x96251),f773(f773(f82(a1),x96252),f773(f773(f83(a1),f773(f773(f82(a1),f773(f77(a1),f773(f773(f3(a1),x96252),x96251))),f80(a1))),x96253))))
% 191.21/191.74 [9635]~P36(x96351,f773(f773(f103(f855(f854(x96351,x96351),a841)),x96352),x96353))+P36(x96351,f773(f773(f103(f855(f854(x96351,x96351),a841)),f773(f773(f103(f855(f854(x96351,x96351),a841)),f773(f773(f281(x96351,x96351,x96351),x96352),x96352)),f773(f773(f281(x96351,x96351,x96351),x96353),x96352))),x96353))
% 191.21/191.74 [9701]P36(x97011,f773(f773(f103(f855(f854(x97011,x97011),a841)),x97012),x97013))+~P36(x97011,f773(f773(f103(f855(f854(x97011,x97011),a841)),f773(f773(f103(f855(f854(x97011,x97011),a841)),f773(f773(f281(x97011,x97011,x97011),x97012),x97012)),f773(f773(f281(x97011,x97011,x97011),x97013),x97012))),x97013))
% 191.21/191.74 [9306]~P133(x93061)+E(f773(f105(x93061),f773(a91,f773(f277(f854(a847,a847),f854(a847,a847),a111),f773(f773(f302(f854(a847,a847)),f773(f773(f241(a847,a847),x93062),x93063)),f180(f855(f854(a847,a847),a841)))))),f773(f773(f3(x93061),f773(f102(x93061),x93062)),f773(f102(x93061),x93063)))
% 191.21/191.74 [9385]P1(f773(x93853,x93852))+E(f773(f256(x93851),f773(f773(f20(x93851,a841,a841),f773(f773(f10(a841,f855(a841,a841),x93851),a331),f773(f773(f9(x93851,x93851,a841),a330),x93852))),x93853)),f180(f855(x93851,a841)))
% 191.21/191.74 [9387]~P1(f773(x93873,x93872))+E(f773(f256(x93871),f773(f773(f20(x93871,a841,a841),f773(f773(f10(a841,f855(a841,a841),x93871),a331),f773(f773(f9(x93871,x93871,a841),a330),x93872))),x93873)),f773(f773(f302(x93871),x93872),f180(f855(x93871,a841))))
% 191.21/191.74 [9693]~P1(f773(f63(x96931),x96933))+E(f773(f773(f66(x96931,f855(x96931,a841),f773(f773(f10(f855(x96931,a841),f855(f855(x96931,a841),f855(x96931,a841)),x96931),f773(f9(f855(x96931,a841),f855(x96931,a841),f855(x96931,a841)),f3(f855(x96931,a841)))),f773(f773(f9(x96931,f855(x96931,a841),f855(x96931,a841)),f302(x96931)),f180(f855(x96931,a841))))),x96932),x96933),f773(f773(f3(f855(x96931,a841)),x96932),x96933))
% 191.21/191.74 [9726]~P1(f773(f773(f233(a1),f2(a1)),x97263))+P1(f773(f773(f233(a1),f773(f773(f3(a1),x97261),f773(f773(f83(a1),f773(f773(f82(a1),f773(f77(a1),f773(f773(f3(a1),x97261),x97262))),f80(a1))),x97263))),x97262))
% 191.21/191.74 [9972]~P1(f773(f773(f334(x99721),x99723),f322(x99721,x99722)))+P1(f773(f321(x99721,f773(f773(f9(x99721,f855(f854(x99721,x99721),a841),f855(x99721,a841)),f773(f773(f10(f855(x99721,f855(f855(f854(x99721,x99721),a841),a841)),f855(f855(f854(x99721,x99721),a841),f855(x99721,a841)),x99721),f9(x99721,f855(f854(x99721,x99721),a841),a841)),f773(f773(f10(f855(x99721,f854(x99721,x99721)),f855(x99721,f855(f855(f854(x99721,x99721),a841),a841)),x99721),f773(f10(f854(x99721,x99721),f855(f855(f854(x99721,x99721),a841),a841),x99721),f334(f854(x99721,x99721)))),f241(x99721,x99721)))),x99722)),x99723))
% 191.21/191.74 [9984]P1(f773(f773(f334(x99841),x99842),f322(x99841,x99843)))+~P1(f773(f321(x99841,f773(f773(f9(x99841,f855(f854(x99841,x99841),a841),f855(x99841,a841)),f773(f773(f10(f855(x99841,f855(f855(f854(x99841,x99841),a841),a841)),f855(f855(f854(x99841,x99841),a841),f855(x99841,a841)),x99841),f9(x99841,f855(f854(x99841,x99841),a841),a841)),f773(f773(f10(f855(x99841,f854(x99841,x99841)),f855(x99841,f855(f855(f854(x99841,x99841),a841),a841)),x99841),f773(f10(f854(x99841,x99841),f855(f855(f854(x99841,x99841),a841),a841),x99841),f334(f854(x99841,x99841)))),f241(x99841,x99841)))),x99843)),x99842))
% 191.21/191.74 [9575]~P1(f773(f63(x95751),f773(f256(x95751),x95753)))+P1(f773(f63(x95751),f773(f256(x95751),f773(f773(f20(x95751,a841,a841),f773(f773(f10(a841,f855(a841,a841),x95751),a331),x95752)),x95753))))
% 191.21/191.74 [9576]~P1(f773(f63(x95761),f773(f256(x95761),x95762)))+P1(f773(f63(x95761),f773(f256(x95761),f773(f773(f20(x95761,a841,a841),f773(f773(f10(a841,f855(a841,a841),x95761),a331),x95762)),x95763))))
% 191.21/191.74 [9660]P1(f773(f63(x96601),f773(f256(x96601),x96602)))+~P1(f773(f63(x96601),f773(f256(x96601),f773(f773(f20(x96601,a841,a841),f773(f773(f10(a841,f855(a841,a841),x96601),a332),x96603)),x96602))))
% 191.21/191.74 [9661]P1(f773(f63(x96611),f773(f256(x96611),x96612)))+~P1(f773(f63(x96611),f773(f256(x96611),f773(f773(f20(x96611,a841,a841),f773(f773(f10(a841,f855(a841,a841),x96611),a332),x96612)),x96613))))
% 191.21/191.74 [9957]~P1(f773(f63(x99571),x99572))+P1(f773(f63(f848(x99571)),f773(f256(f848(x99571)),f773(f773(f20(f848(x99571),a841,a841),f773(f773(f10(a841,f855(a841,a841),f848(x99571)),a331),f773(f773(f9(f848(x99571),f855(x99571,a841),a841),f773(f773(f10(f855(x99571,a841),f855(f855(x99571,a841),a841),f848(x99571)),f232(f855(x99571,a841))),f158(x99571))),x99572))),f773(f773(f9(f848(x99571),a847,a841),f773(f773(f10(a847,f855(a847,a841),f848(x99571)),a330),f181(f848(x99571)))),x99573)))))
% 191.21/191.74 [9958]~P1(f773(f63(x99581),x99582))+P1(f773(f63(f848(x99581)),f773(f256(f848(x99581)),f773(f773(f20(f848(x99581),a841,a841),f773(f773(f10(a841,f855(a841,a841),f848(x99581)),a331),f773(f773(f9(f848(x99581),f855(x99581,a841),a841),f773(f773(f10(f855(x99581,a841),f855(f855(x99581,a841),a841),f848(x99581)),f232(f855(x99581,a841))),f158(x99581))),x99582))),f773(f773(f9(f848(x99581),a847,a841),f773(f773(f10(a847,f855(a847,a841),f848(x99581)),f232(a847)),f181(f848(x99581)))),x99583)))))
% 191.21/191.74 [9674]~P85(x96741)+E(f773(f773(f242(x96741),x96742),f773(f773(f83(a847),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),x96743)),f773(f773(f83(x96741),f773(f773(f242(x96741),x96742),x96743)),f773(f773(f242(x96741),x96742),x96743)))
% 191.21/191.74 [9705]~P75(x97051)+E(f773(f773(f242(x97051),f773(f773(f242(x97051),x97052),x97053)),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),f773(f773(f242(x97051),x97052),f773(f773(f83(a847),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),x97053)))
% 191.21/191.74 [9766]~P133(x97661)+E(f773(f773(f242(x97661),f773(f81(x97661),x97662)),f773(f773(f83(a847),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),x97663)),f773(f773(f242(x97661),x97662),f773(f773(f83(a847),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),x97663)))
% 191.21/191.74 [9909]~P110(x99091)+P1(f773(f773(f232(x99091),f2(x99091)),f773(f773(f82(x99091),f773(f773(f242(x99091),x99092),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))),f773(f773(f242(x99091),x99093),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))))))
% 191.21/191.74 [9776]~P85(x97761)+E(f773(f773(f242(x97761),x97762),f773(a114,f773(f773(f83(a847),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),x97763))),f773(f773(f83(x97761),x97762),f773(f773(f83(x97761),f773(f773(f242(x97761),x97762),x97763)),f773(f773(f242(x97761),x97762),x97763))))
% 191.21/191.74 [9825]~P75(x98251)+E(f773(f773(f83(x98251),x98252),f773(f773(f242(x98251),f773(f773(f242(x98251),x98252),x98253)),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))),f773(f773(f242(x98251),x98252),f773(a114,f773(f773(f83(a847),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),x98253))))
% 191.21/191.74 [9869]~P110(x98691)+P1(f773(f773(f232(x98691),f2(x98691)),f773(f773(f242(x98691),x98692),f773(f773(f83(a847),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),x98693))))
% 191.21/191.74 [9938]~P88(x99381)+E(f773(f773(f82(x99381),f773(f773(f82(x99381),f773(f773(f242(x99381),x99382),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))),f773(f773(f242(x99381),x99383),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))))),f773(f773(f83(x99381),f773(f773(f83(x99381),f773(f106(x99381),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),x99382)),x99383)),f773(f773(f242(x99381),f773(f773(f82(x99381),x99382),x99383)),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))))
% 191.21/191.74 [9939]~P88(x99391)+E(f773(f773(f3(x99391),f773(f773(f82(x99391),f773(f773(f242(x99391),x99392),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))),f773(f773(f242(x99391),x99393),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))))),f773(f773(f83(x99391),f773(f773(f83(x99391),f773(f106(x99391),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),x99392)),x99393)),f773(f773(f242(x99391),f773(f773(f3(x99391),x99392),x99393)),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))))
% 191.21/191.74 [4578]E(x45781,x45782)+~E(f35(x45783,x45781),f35(x45784,x45782))
% 191.21/191.74 [4579]E(x45791,x45792)+~E(f35(x45791,x45793),f35(x45792,x45794))
% 191.21/191.74 [4580]E(x45801,x45802)+~E(f36(x45803,x45801),f36(x45804,x45802))
% 191.21/191.74 [4581]E(x45811,x45812)+~E(f36(x45811,x45813),f36(x45812,x45814))
% 191.21/191.74 [4582]E(x45821,x45822)+~E(f28(x45823,x45821),f28(x45824,x45822))
% 191.21/191.74 [4583]E(x45831,x45832)+~E(f28(x45831,x45833),f28(x45832,x45834))
% 191.21/191.74 [5700]P39(f35(x57001,x57003),x57002,x57004,x57002)+P1(f773(x57001,x57002))
% 191.21/191.74 [6862]~P39(x68621,x68622,x68623,x68624)+P39(x68621,x68622,f773(a114,x68623),x68624)
% 191.21/191.74 [7707]P29(x77071,x77072,x77073,x77074)+~E(f505(x77074,x77073,x77072,x77071),f519(x77074,x77073,x77072,x77071))
% 191.21/191.74 [8207]~P29(x82071,f851(x82072),x82074,f169(x82071,x82072,x82074))+P29(x82071,f851(x82072),f170(x82071,x82072,x82073,x82074),f169(x82071,x82072,x82074))
% 191.21/191.74 [8421]~P29(x84211,f851(x84212),f170(x84211,x84212,x84214,x84213),f169(x84211,x84212,x84213))+P29(x84211,f851(x84212),x84213,f169(x84211,x84212,x84213))
% 191.21/191.74 [4945]~P21(x49453,x49451,x49454)+E(f773(f773(x49451,x49452),x49452),x49452)
% 191.21/191.74 [4948]E(x49481,x49482)+~E(f773(f304(x49483,x49484),x49481),f773(f304(x49483,x49484),x49482))
% 191.21/191.74 [4950]E(x49501,x49502)+~E(f773(f313(x49503,x49504),x49501),f773(f313(x49503,x49504),x49502))
% 191.21/191.74 [5227]~E(x52274,f180(f855(x52271,a841)))+E(f773(f303(x52271,x52272,x52273),x52274),f180(f855(x52272,a841)))
% 191.21/191.74 [5490]~E(f773(f303(x54902,x54903,x54904),x54901),f180(f855(x54903,a841)))+E(x54901,f180(f855(x54902,a841)))
% 191.21/191.74 [5781]~P100(x57812)+E(f773(f773(f138(x57811,x57812,x57813),x57814),f115(x57811)),f773(f773(f140(x57811),x57814),f115(x57811)))
% 191.21/191.74 [5816]E(f773(x58161,x58162),f183(x58163))+P1(f773(f773(f334(x58164),x58162),f169(x58164,x58163,x58161)))
% 191.21/191.74 [6140]~E(x61401,f180(f855(x61402,a841)))+~P1(f773(f64(x61402,x61403,x61401),x61404))
% 191.21/191.74 [6161]~P57(x61611,x61613,x61614,x61612)+P1(f773(f63(x61611),x61612))
% 191.21/191.74 [6162]~P57(x61621,x61623,x61622,x61624)+P1(f773(f63(x61621),x61622))
% 191.21/191.74 [6169]~P57(x61692,x61693,x61694,x61691)+~E(x61691,f180(f855(x61692,a841)))
% 191.21/191.74 [6201]~P99(x62011)+E(f773(f773(f104(f855(x62011,a841)),f773(f294(x62011,x62012),x62013)),f295(x62011,x62013,x62014)),f180(f855(x62011,a841)))
% 191.21/191.74 [6230]~P1(f773(f773(x62303,x62304),x62302))+P1(f773(f773(f334(x62301),x62302),f287(x62301,x62303,x62304)))
% 191.21/191.74 [6231]~P1(f773(f773(x62313,x62314),x62312))+P1(f773(f773(f334(x62311),x62312),f286(x62311,x62313,x62314)))
% 191.21/191.74 [6232]~P1(f773(f773(x62323,x62322),x62324))+P1(f773(f773(f334(x62321),x62322),f290(x62321,x62323,x62324)))
% 191.21/191.74 [6233]~P1(f773(f773(x62333,x62332),x62334))+P1(f773(f773(f334(x62331),x62332),f288(x62331,x62333,x62334)))
% 191.21/191.74 [6385]~P99(x63851)+E(f773(f773(f104(f855(x63851,a841)),f295(x63851,x63852,x63853)),f297(x63851,x63853,x63854)),f180(f855(x63851,a841)))
% 191.21/191.74 [6386]~P99(x63861)+E(f773(f773(f104(f855(x63861,a841)),f295(x63861,x63862,x63863)),f298(x63861,x63863,x63864)),f180(f855(x63861,a841)))
% 191.21/191.74 [6387]~P99(x63871)+E(f773(f773(f104(f855(x63871,a841)),f297(x63871,x63872,x63873)),f297(x63871,x63873,x63874)),f180(f855(x63871,a841)))
% 191.21/191.74 [6388]~P99(x63881)+E(f773(f773(f104(f855(x63881,a841)),f297(x63881,x63882,x63883)),f298(x63881,x63883,x63884)),f180(f855(x63881,a841)))
% 191.21/191.74 [6389]~P99(x63891)+E(f773(f773(f104(f855(x63891,a841)),f298(x63891,x63892,x63893)),f295(x63891,x63893,x63894)),f180(f855(x63891,a841)))
% 191.21/191.74 [6427]P1(f773(f773(x64271,x64272),f596(x64272,x64271)))+~P1(f773(f246(x64273,x64274,x64271),x64272))
% 191.21/191.74 [6481]~E(f773(x64811,x64812),f183(x64813))+~P1(f773(f773(f334(x64814),x64812),f169(x64814,x64813,x64811)))
% 191.21/191.74 [6563]~P2(x65631)+E(f182(x65631,x65632,f773(a114,x65633),x65634),f182(x65631,x65632,x65633,f773(x65632,x65634)))
% 191.21/191.74 [6627]~P1(f773(f773(f334(x66274),x66273),f287(x66274,x66271,x66272)))+P1(f773(f773(x66271,x66272),x66273))
% 191.21/191.74 [6628]~P1(f773(f773(f334(x66284),x66283),f286(x66284,x66281,x66282)))+P1(f773(f773(x66281,x66282),x66283))
% 191.21/191.74 [6629]~P1(f773(f773(f334(x66294),x66292),f290(x66294,x66291,x66293)))+P1(f773(f773(x66291,x66292),x66293))
% 191.21/191.74 [6630]~P1(f773(f773(f334(x66304),x66302),f288(x66304,x66301,x66303)))+P1(f773(f773(x66301,x66302),x66303))
% 191.21/191.74 [6712]E(f773(f42(f856(x67121,x67122)),f314(x67121,x67122,x67123,x67124)),f2(a847))+P1(f773(f63(x67122),x67124))
% 191.21/191.74 [6713]E(f773(f42(f856(x67131,x67132)),f314(x67131,x67132,x67133,x67134)),f2(a847))+P1(f773(f63(x67131),x67133))
% 191.21/191.74 [6924]~P19(x69244,x69241,x69242)+E(f773(f75(x69241,x69241,x69241,f773(x69242,x69243)),f773(x69242,x69243)),f773(x69242,x69243))
% 191.21/191.74 [7162]E(f272(x71621,x71622,x71623,x71624),f773(f241(f855(a101,f855(a841,f851(f849(x71621)))),f854(a101,a101)),f48(x71621)))+~P1(f773(f773(f232(a101),x71623),f2(a101)))
% 191.21/191.74 [7228]~P39(f773(a27,x72281),x72282,f773(a114,x72283),x72284)+P39(f773(f231(a842),f773(a30,x72281)),x72282,x72283,x72284)
% 191.21/191.74 [7265]P39(f773(a27,x72651),x72652,f773(a114,x72653),x72654)+~P39(f773(f231(a842),f773(a30,x72651)),x72652,x72653,x72654)
% 191.21/191.74 [7565]~P39(f773(a27,x75654),x75653,x75652,x75651)+E(f773(a114,f442(x75651,x75652,x75653,x75654)),x75652)
% 191.21/191.74 [7835]~E(x78352,x78353)+P1(f773(f773(f334(f854(x78351,x78351)),f773(f773(f241(x78351,x78351),x78352),x78353)),f300(x78351,x78354)))
% 191.21/191.74 [7861]~P29(x78611,x78612,x78613,f239(f855(x78611,a841)))+E(f773(f79(x78611,x78612,f239(f855(x78611,a841)),x78613),f773(x78613,x78614)),x78614)
% 191.21/191.74 [7953]~P1(f773(f773(f334(f848(x79531)),f773(f773(f140(x79531),x79534),x79532)),f149(x79531,x79533)))+P1(f773(f773(f334(f848(x79531)),x79532),f149(x79531,x79533)))
% 191.21/191.74 [7954]~P1(f773(f773(f334(f848(x79541)),f773(f773(f125(x79541),x79544),x79542)),f149(x79541,x79543)))+P1(f773(f773(f334(f848(x79541)),x79542),f149(x79541,x79543)))
% 191.21/191.74 [7955]~P1(f773(f773(f334(f848(x79551)),f773(f773(f125(x79551),x79552),x79554)),f149(x79551,x79553)))+P1(f773(f773(f334(f848(x79551)),x79552),f149(x79551,x79553)))
% 191.21/191.74 [8029]~P39(f773(a27,x80291),x80292,x80294,x80293)+P39(f773(f231(a842),f773(a30,x80291)),x80292,f442(x80293,x80294,x80292,x80291),x80293)
% 191.21/191.74 [8066]P29(x80664,x80663,x80661,x80662)+E(f773(x80661,f505(x80662,x80661,x80663,x80664)),f773(x80661,f519(x80662,x80661,x80663,x80664)))
% 191.21/191.74 [8075]E(f170(x80751,x80752,x80753,x80754),f170(x80751,x80752,x80754,x80753))+~E(f773(f773(f104(f855(x80751,a841)),f169(x80751,x80752,x80753)),f169(x80751,x80752,x80754)),f180(f855(x80751,a841)))
% 191.21/191.74 [8172]~P29(x81722,x81721,x81724,x81723)+P29(x81721,x81722,f79(x81722,x81721,x81723,x81724),f773(f303(x81722,x81721,x81724),x81723))
% 191.21/191.74 [8307]P36(f854(x83072,x83074),f275(x83072,x83074,x83071,x83073))+P1(f773(x83071,f593(x83072,x83073,x83074,x83071)))
% 191.21/191.74 [8428]E(x84281,x84282)+~P1(f773(f773(f334(f854(x84283,x84283)),f773(f773(f241(x84283,x84283),x84281),x84282)),f260(x84283,x84284)))
% 191.21/191.74 [8462]~E(f773(x84621,f515(x84623,x84622,x84624,x84621)),f773(f174(x84624,x84622,x84623),f515(x84623,x84622,x84624,x84621)))+E(f773(x84621,f2(a847)),x84622)
% 191.21/191.74 [8496]~P1(f773(f63(f856(x84963,x84961)),f314(x84963,x84961,x84964,x84962)))+P1(f773(f63(x84961),x84962))
% 191.21/191.74 [8497]~P1(f773(f63(f856(x84971,x84973)),f314(x84971,x84973,x84972,x84974)))+P1(f773(f63(x84971),x84972))
% 191.21/191.74 [8658]P36(f854(x86581,x86582),f275(x86581,x86582,x86583,x86584))+~P36(x86582,f773(x86584,f593(x86581,x86584,x86582,x86583)))
% 191.21/191.74 [9159]E(f773(f773(f148(x91591,x91592),f737(x91593,x91594,x91592,x91591)),f738(x91593,x91594,x91592,x91591)),x91594)+~P1(f773(f773(f334(f854(f848(x91591),f848(x91591))),f773(f773(f241(f848(x91591),f848(x91591)),x91592),x91594)),f146(x91591,x91593)))
% 191.21/191.74 [9163]~P1(f773(f773(f334(f854(f848(x91631),f848(x91631))),f773(f773(f241(f848(x91631),f848(x91631)),x91632),x91633)),f135(x91631,x91634)))+P1(f773(f773(f334(f854(f848(x91631),f848(x91631))),f773(f773(f241(f848(x91631),f848(x91631)),x91632),x91633)),f137(x91631,x91634)))
% 191.21/191.74 [9260]P1(f773(f63(x92601),x92602))+~P1(f773(f773(f334(f854(f855(x92601,a841),f855(x92601,a841))),f773(f773(f241(f855(x92601,a841),f855(x92601,a841)),x92603),x92602)),f324(x92601,x92604)))
% 191.21/191.74 [9261]P1(f773(f63(x92611),x92612))+~P1(f773(f773(f334(f854(f855(x92611,a841),f855(x92611,a841))),f773(f773(f241(f855(x92611,a841),f855(x92611,a841)),x92612),x92613)),f324(x92611,x92614)))
% 191.21/191.74 [9264]~E(x92641,f180(f855(x92642,a841)))+~P1(f773(f773(f334(f854(f855(x92642,a841),f855(x92642,a841))),f773(f773(f241(f855(x92642,a841),f855(x92642,a841)),x92643),x92641)),f324(x92642,x92644)))
% 191.21/191.74 [9880]P16(x98801,x98802,x98803,x98804)+~P1(f773(f773(f251(x98801,x98801,a841),f773(f773(f9(x98801,f855(x98801,x98802),f855(x98801,a841)),f773(f773(f10(f855(x98802,a841),f855(f855(x98801,x98802),f855(x98801,a841)),x98801),f10(x98802,a841,x98801)),f773(f773(f10(x98802,f855(x98802,a841),x98801),a330),x98804))),x98804)),f498(x98804,x98803,x98802,x98801)))
% 191.21/191.74 [4848]~E(x48484,f115(x48481))+E(f773(f773(f143(x48481,x48482),x48483),x48484),f115(x48482))
% 191.21/191.74 [4849]~E(x48494,f183(x48491))+E(f773(f773(f196(x48491,x48492),x48493),x48494),f183(x48492))
% 191.21/191.74 [4850]~E(x48502,f115(x48501))+E(f773(f773(f148(x48501,x48502),x48503),x48504),f115(x48501))
% 191.21/191.74 [5087]E(x50871,f183(x50872))+~E(f773(f773(f196(x50872,x50873),x50874),x50871),f183(x50873))
% 191.21/191.74 [5088]E(x50881,f115(x50882))+~E(f773(f773(f143(x50882,x50883),x50884),x50881),f115(x50883))
% 191.21/191.74 [5089]E(x50891,f115(x50892))+~E(f773(f773(f148(x50892,x50891),x50893),x50894),f115(x50892))
% 191.21/191.74 [5119]E(x51191,x51192)+~E(f773(f773(f125(x51193),x51194),x51191),f773(f773(f125(x51193),x51194),x51192))
% 191.21/191.74 [5120]E(x51201,x51202)+~E(f773(f773(f125(x51203),x51201),x51204),f773(f773(f125(x51203),x51202),x51204))
% 191.21/191.74 [5262]P1(f773(x52623,x52622))+E(f151(x52621,x52622,f773(f126(x52621,x52623),x52624)),f773(f126(x52621,x52623),x52624))
% 191.21/191.74 [5273]E(x52731,x52732)+~E(f130(a847,f773(f294(a847,x52731),x52733)),f773(f773(f140(a847),x52732),x52734))
% 191.21/191.74 [5320]~P30(x53202,x53203)+P30(x53201,f773(f773(f76(x53202,x53201),x53203),x53204))
% 191.21/191.74 [5321]~P36(x53212,x53213)+P36(x53211,f773(f773(f280(x53212,x53211),x53213),x53214))
% 191.21/191.74 [5530]~E(x55301,f115(x55302))+~E(f773(f773(f125(x55302),x55303),f773(f773(f140(x55302),x55304),f115(x55302))),x55301)
% 191.21/191.74 [5563]E(f134(x55631,x55632),x55633)+~E(f773(f773(f125(x55631),x55634),f773(f773(f140(x55631),x55633),f115(x55631))),x55632)
% 191.21/191.74 [5564]E(f116(x55641,x55642),x55643)+~E(f773(f773(f125(x55641),x55643),f773(f773(f140(x55641),x55644),f115(x55641))),x55642)
% 191.21/191.74 [5672]~E(f130(a847,f773(f294(a847,x56721),x56722)),f773(f773(f140(a847),x56723),x56724))+P1(f773(f773(f233(a847),x56721),x56722))
% 191.21/191.74 [5879]E(x58791,f773(f773(f125(x58792),f773(f142(x58792),x58793)),f773(f773(f140(x58792),x58794),f115(x58792))))+~E(f773(f142(x58792),x58791),f773(f773(f140(x58792),x58794),x58793))
% 191.21/191.74 [6062]~P99(x60621)+E(f773(f773(f104(f855(x60621,a841)),f773(f294(x60621,x60622),x60623)),f773(f294(x60621,x60623),x60624)),f180(f855(x60621,a841)))
% 191.21/191.74 [6097]~P66(x60971)+E(f773(f155(x60971),f773(f773(f143(a1,x60971),x60972),f163(x60973,x60974))),f773(f773(f8(a1,x60971),x60972),f773(f158(a1),f163(x60973,x60974))))
% 191.21/191.74 [6098]~P66(x60981)+E(f773(f773(f8(a1,x60981),x60982),f773(f158(a1),f163(x60983,x60984))),f773(f155(x60981),f773(f773(f143(a1,x60981),x60982),f163(x60983,x60984))))
% 191.21/191.74 [6245]~E(x62452,f773(f773(f125(x62451),f773(f142(x62451),x62454)),f773(f773(f140(x62451),x62453),f115(x62451))))+E(f773(f142(x62451),x62452),f773(f773(f140(x62451),x62453),x62454))
% 191.21/191.74 [6261]~P23(x62612,x62613,x62614,x62611)+E(f773(x62611,f180(f855(x62612,a841))),f39(x62613))
% 191.21/191.74 [6291]~P99(x62911)+E(f773(f773(f104(f855(x62911,a841)),f298(x62911,x62912,x62913)),f773(f294(x62911,x62913),x62914)),f180(f855(x62911,a841)))
% 191.21/191.74 [6378]~P39(x63781,x63782,x63784,x63783)+P1(f773(f773(f187(x63781),x63782),x63783))
% 191.21/191.74 [6512]E(x65121,f180(f855(x65122,a841)))+~E(f314(x65123,x65122,x65124,x65121),f180(f855(f856(x65123,x65122),a841)))
% 191.21/191.74 [6513]E(x65131,f180(f855(x65132,a841)))+~E(f314(x65132,x65133,x65131,x65134),f180(f855(f856(x65132,x65133),a841)))
% 191.21/191.74 [6593]~P1(f773(f247(x65933,x65934,x65931),x65932))+P1(f773(f773(x65931,f592(x65932,x65931)),x65932))
% 191.21/191.74 [6641]~P1(f773(f63(x66412),x66414))+P1(f773(f63(x66411),f773(f303(x66412,x66411,x66413),x66414)))
% 191.21/191.74 [6883]~P29(x68832,x68831,x68833,x68834)+E(f773(f42(x68831),f773(f303(x68832,x68831,x68833),x68834)),f773(f42(x68832),x68834))
% 191.21/191.74 [6903]E(f773(f303(x69031,x69032,x69033),f773(f305(x69031,x69032,x69033),x69034)),x69034)+~E(f773(f303(x69031,x69032,x69033),f239(f855(x69031,a841))),f239(f855(x69032,a841)))
% 191.21/191.74 [7329]~P29(x73291,x73292,x73293,f239(f855(x73291,a841)))+E(f773(f305(x73291,x73292,x73293),f773(f303(x73291,x73292,x73293),x73294)),x73294)
% 191.21/191.74 [7669]P1(f773(x76691,x76692))+~P1(f773(f773(f334(x76693),x76692),f773(f158(x76693),f162(x76693,x76691,x76694))))
% 191.21/191.74 [7779]~P1(f773(f773(f334(f848(x77791)),f773(f773(f140(x77791),x77792),x77794)),f149(x77791,x77793)))+P1(f773(f773(f334(x77791),x77792),x77793))
% 191.21/191.74 [7906]~P1(f773(f773(f334(x79061),x79062),f773(f158(x79061),f151(x79061,x79064,x79063))))+P1(f773(f773(f334(x79061),x79062),f773(f158(x79061),x79063)))
% 191.21/191.74 [7908]~P1(f773(f773(f334(x79081),x79082),f773(f158(x79081),f160(x79081,x79083,x79084))))+P1(f773(f773(f334(x79081),x79082),f773(f158(x79081),x79083)))
% 191.21/191.74 [7909]~P1(f773(f773(f334(x79091),x79092),f773(f158(x79091),f162(x79091,x79094,x79093))))+P1(f773(f773(f334(x79091),x79092),f773(f158(x79091),x79093)))
% 191.21/191.74 [8122]E(f773(f773(f153(x81221),f162(x81221,x81222,x81223)),x81224),f773(f773(f153(x81221),x81223),x81224))+~P1(f773(f773(f233(a847),x81224),f773(f181(f848(x81221)),f162(x81221,x81222,x81223))))
% 191.21/191.74 [8205]~P66(x82051)+E(f773(f773(f8(a847,x82051),f773(f773(f10(a847,x82051,a847),x82052),a114)),f773(f294(a847,x82053),x82054)),f773(f773(f8(a847,x82051),x82052),f773(f294(a847,f773(a114,x82053)),f773(a114,x82054))))
% 191.21/191.74 [8214]~P66(x82141)+E(f773(f773(f8(a847,x82141),f773(f773(f10(a847,x82141,a847),x82142),a114)),f295(a847,x82143,x82144)),f773(f773(f8(a847,x82141),x82142),f295(a847,f773(a114,x82143),f773(a114,x82144))))
% 191.21/191.74 [8346]~P29(x83461,x83463,x83464,f239(f855(x83461,a841)))+P29(x83461,f855(x83462,x83463),f773(f773(f10(x83463,f855(x83462,x83463),x83461),f18(x83463,x83462)),x83464),f239(f855(x83461,a841)))
% 191.21/191.74 [8437]~P29(x84372,x84371,x84374,x84373)+E(f773(f303(x84371,x84372,f79(x84372,x84371,x84373,x84374)),f773(f303(x84372,x84371,x84374),x84373)),x84373)
% 191.21/191.74 [8498]~P1(f773(f773(f334(f854(x84981,x84981)),f773(f773(f241(x84981,x84981),x84982),x84984)),f260(x84981,x84983)))+P1(f773(f773(f334(x84981),x84982),x84983))
% 191.21/191.74 [8573]E(f773(f773(f773(f74(x85731,f851(x85732)),f773(f18(f851(x85732),x85731),f183(x85732))),x85733),f773(f227(x85732),f529(x85733,x85734,x85732,x85731))),x85734)+~E(f169(x85731,x85732,x85734),f773(f773(f302(x85731),x85733),f180(f855(x85731,a841))))
% 191.21/191.74 [8691]~E(f773(f773(f8(x86911,a847),x86914),x86913),f773(a114,x86912))+P1(f773(f773(f334(x86911),f356(x86912,x86913,x86914,x86911)),x86913))
% 191.21/191.74 [8707]~E(f773(f773(f8(x87074,a847),x87071),x87073),f773(a114,x87072))+P1(f773(f773(f233(a847),f2(a847)),f773(x87071,f356(x87072,x87073,x87071,x87074))))
% 191.21/191.74 [8717]~P1(f773(f63(x87172),x87174))+P1(f773(f773(f232(a847),f773(f42(x87171),f773(f303(x87172,x87171,x87173),x87174))),f773(f42(x87172),x87174)))
% 191.21/191.74 [8718]E(f773(f773(f241(x87181,x87182),f700(x87183,x87184,x87182,x87181)),f701(x87183,x87184,x87182,x87181)),x87184)+~P1(f773(f773(f334(f854(x87181,x87182)),x87184),f773(f278(x87182,x87181),x87183)))
% 191.21/191.74 [8727]P29(x87271,x87272,x87273,x87274)+P1(f773(f773(f334(x87271),f505(x87274,x87273,x87272,x87271)),x87274))
% 191.21/191.74 [8728]P29(x87281,x87282,x87283,x87284)+P1(f773(f773(f334(x87281),f519(x87284,x87283,x87282,x87281)),x87284))
% 191.21/191.74 [8781]P16(x87811,x87812,x87813,x87814)+P1(f773(f773(f334(f854(x87811,x87811)),f498(x87814,x87813,x87812,x87811)),x87813))
% 191.21/191.74 [8828]P1(f773(x88281,x88282))+~P1(f773(x88281,f773(f773(f241(x88283,x88284),f827(x88284,x88283,x88281)),f828(x88284,x88283,x88281))))
% 191.21/191.74 [8841]E(f773(f181(f848(x88411)),x88412),f773(f181(f848(x88411)),x88413))+~P1(f773(f773(f334(f854(f848(x88411),f848(x88411))),f773(f773(f241(f848(x88411),f848(x88411)),x88412),x88413)),f135(x88411,x88414)))
% 191.21/191.74 [8844]E(f773(f181(f848(x88441)),x88442),f773(f181(f848(x88441)),x88443))+~P1(f773(f773(f334(f854(f848(x88441),f848(x88441))),f773(f773(f241(f848(x88441),f848(x88441)),x88442),x88443)),f147(x88441,x88444)))
% 191.21/191.74 [8845]E(f773(f181(f848(x88451)),x88452),f773(f181(f848(x88451)),x88453))+~P1(f773(f773(f334(f854(f848(x88451),f848(x88451))),f773(f773(f241(f848(x88451),f848(x88451)),x88452),x88453)),f146(x88451,x88454)))
% 191.21/191.74 [8918]P1(f773(f773(f232(a847),f144(x89181,x89182,x89183)),f144(x89181,x89184,x89183)))+P1(f773(f773(f334(x89181),f757(x89184,x89182,x89183,x89181)),f773(f158(x89181),x89183)))
% 191.21/191.74 [8919]E(f773(f181(f848(x89191)),x89192),f773(f181(f848(x89191)),x89193))+~P1(f773(f773(f334(f854(f848(x89191),f848(x89191))),f773(f773(f241(f848(x89191),f848(x89191)),x89192),x89193)),f300(f848(x89191),f146(x89191,x89194))))
% 191.21/191.74 [9031]P1(f773(f773(f279(a847),x90311),x90312))+P1(f773(f773(f232(f855(a847,a841)),f282(a847,f279(a847),x90311,x90312)),f282(a847,f279(a847),x90313,x90314)))
% 191.21/191.74 [9139]~P29(x91391,x91392,x91393,x91394)+~P1(f773(f773(f233(a847),f773(f42(x91392),f773(f303(x91391,x91392,x91393),x91394))),f773(f42(x91391),x91394)))
% 191.21/191.74 [9169]~P1(f773(f773(f334(f854(f848(x91691),f848(x91691))),f773(f773(f241(f848(x91691),f848(x91691)),x91692),x91693)),f146(x91691,x91694)))+P1(f773(f773(f334(f854(f848(x91691),f848(x91691))),f773(f773(f241(f848(x91691),f848(x91691)),x91692),x91693)),f147(x91691,f300(x91691,x91694))))
% 191.21/191.74 [9172]~P1(f773(f773(f334(f854(f848(x91721),f848(x91721))),f773(f773(f241(f848(x91721),f848(x91721)),x91722),x91723)),f147(x91721,x91724)))+P1(f773(f773(f334(f854(f848(x91721),f848(x91721))),f773(f773(f241(f848(x91721),f848(x91721)),x91722),x91723)),f300(f848(x91721),f146(x91721,x91724))))
% 191.21/191.74 [9187]P1(f773(f773(f334(f854(x91871,x91871)),f773(f773(f241(x91871,x91871),x91872),x91873)),f300(x91871,x91874)))+~P1(f773(f773(f334(f854(x91871,x91871)),f773(f773(f241(x91871,x91871),x91872),x91873)),f773(f773(f281(x91871,x91871,x91871),x91874),f300(x91871,x91874))))
% 191.21/191.74 [9256]P1(f773(f773(f279(a847),x92561),x92562))+~P1(f773(f773(f233(f855(a847,a841)),f282(a847,f279(a847),x92563,x92564)),f282(a847,f279(a847),x92561,x92562)))
% 191.21/191.74 [9368]E(f773(f773(f125(x93681),f741(x93682,x93683,x93684,x93681)),f773(f773(f140(x93681),f742(x93682,x93683,x93684,x93681)),f744(x93682,x93683,x93684,x93681))),x93684)+~P1(f773(f773(f334(f854(f848(x93681),f848(x93681))),f773(f773(f241(f848(x93681),f848(x93681)),x93684),x93683)),f146(x93681,x93682)))
% 191.21/191.74 [9369]E(f773(f773(f125(x93691),f741(x93692,x93693,x93694,x93691)),f773(f773(f140(x93691),f743(x93692,x93693,x93694,x93691)),f744(x93692,x93693,x93694,x93691))),x93693)+~P1(f773(f773(f334(f854(f848(x93691),f848(x93691))),f773(f773(f241(f848(x93691),f848(x93691)),x93694),x93693)),f146(x93691,x93692)))
% 191.21/191.74 [9442]P1(f773(f773(f334(f854(x94421,x94421)),f773(f773(f241(x94421,x94421),x94422),f655(x94423,x94424,x94422,x94421))),f300(x94421,x94423)))+~P1(f773(f773(f334(f854(x94421,x94421)),f773(f773(f241(x94421,x94421),x94422),x94424)),f773(f773(f281(x94421,x94421,x94421),x94423),f300(x94421,x94423))))
% 191.21/191.74 [9507]P1(f773(f773(f232(a847),f144(x95071,x95072,x95073)),f144(x95071,x95074,x95073)))+~P1(f773(f773(f233(a847),f773(x95072,f757(x95074,x95072,x95073,x95071))),f773(x95074,f757(x95074,x95072,x95073,x95071))))
% 191.21/191.74 [9573]P1(f773(f773(f334(f854(x95731,x95731)),f773(f773(f241(x95731,x95731),f654(x95732,x95733,x95734,x95731)),x95733)),f300(x95731,x95732)))+~P1(f773(f773(f334(f854(x95731,x95731)),f773(f773(f241(x95731,x95731),x95734),x95733)),f773(f773(f281(x95731,x95731,x95731),x95732),f300(x95731,x95732))))
% 191.21/191.74 [5099]~E(x50992,x50993)+E(f151(x50991,x50992,f773(f773(f140(x50991),x50993),x50994)),x50994)
% 191.21/191.74 [5219]P1(f773(x52192,x52193))+E(f162(x52191,x52192,f773(f773(f140(x52191),x52193),x52194)),f115(x52191))
% 191.21/191.74 [5285]~P84(x52852)+E(f773(f773(f81(f855(x52851,x52852)),x52853),x52854),f773(f81(x52852),f773(x52853,x52854)))
% 191.21/191.74 [5297]~E(x52972,f2(a847))+E(f773(f773(f128(x52971),x52972),f773(f773(f140(x52971),x52973),x52974)),f773(f773(f140(x52971),x52973),x52974))
% 191.21/191.74 [5298]P1(f773(x52982,x52983))+E(f773(f126(x52981,x52982),f773(f773(f140(x52981),x52983),x52984)),f773(f126(x52981,x52982),x52984))
% 191.21/191.74 [5431]~E(x54312,x54314)+P1(f773(f773(f773(f302(x54311),x54312),x54313),x54314))
% 191.21/191.74 [5439]E(x54391,f115(x54392))+E(f134(x54393,f773(f773(f143(x54392,x54393),x54394),x54391)),f773(x54394,f134(x54392,x54391)))
% 191.21/191.74 [5450]~E(x54501,f65(x54502,x54504))+E(f773(x54501,f773(f773(f302(x54502),x54503),f180(f855(x54502,a841)))),x54503)
% 191.21/191.74 [5485]E(x54851,f115(x54852))+E(f773(f131(x54853),f773(f773(f143(x54852,x54853),x54854),x54851)),f773(x54854,f773(f131(x54852),x54851)))
% 191.21/191.74 [5582]~P1(f773(x55823,x55824))+P1(f773(f773(f773(f302(x55821),x55822),x55823),x55824))
% 191.21/191.74 [5707]~P22(x57072,x57074,x57071)+E(f773(x57071,f773(f773(f302(x57072),x57073),f180(f855(x57072,a841)))),x57073)
% 191.21/191.74 [5732]~E(x57322,x57323)+P1(f773(f773(f334(x57321),x57322),f773(f773(f302(x57321),x57323),x57324)))
% 191.21/191.74 [5736]~P85(x57361)+E(f773(f773(f82(x57361),x57362),f773(f773(f82(x57361),x57363),x57364)),f773(f773(f82(x57361),x57363),f773(f773(f82(x57361),x57362),x57364)))
% 191.21/191.74 [5737]~P85(x57371)+E(f773(f773(f83(x57371),x57372),f773(f773(f83(x57371),x57373),x57374)),f773(f773(f83(x57371),x57373),f773(f773(f83(x57371),x57372),x57374)))
% 191.21/191.74 [5739]~P100(x57391)+E(f773(f773(f236(x57391),x57392),f773(f773(f236(x57391),x57393),x57394)),f773(f773(f236(x57391),x57393),f773(f773(f236(x57391),x57392),x57394)))
% 191.21/191.74 [5741]~P100(x57411)+E(f773(f773(f179(x57411),x57412),f773(f773(f179(x57411),x57413),x57414)),f773(f773(f179(x57411),x57413),f773(f773(f179(x57411),x57412),x57414)))
% 191.21/191.74 [5743]~P92(x57431)+E(f773(f773(f103(x57431),x57432),f773(f773(f103(x57431),x57433),x57434)),f773(f773(f103(x57431),x57433),f773(f773(f103(x57431),x57432),x57434)))
% 191.21/191.74 [5744]~P93(x57441)+E(f773(f773(f103(x57441),x57442),f773(f773(f103(x57441),x57443),x57444)),f773(f773(f103(x57441),x57443),f773(f773(f103(x57441),x57442),x57444)))
% 191.21/191.74 [5745]~P93(x57451)+E(f773(f773(f104(x57451),x57452),f773(f773(f104(x57451),x57453),x57454)),f773(f773(f104(x57451),x57453),f773(f773(f104(x57451),x57452),x57454)))
% 191.21/191.74 [5747]~P98(x57471)+E(f773(f773(f104(x57471),x57472),f773(f773(f104(x57471),x57473),x57474)),f773(f773(f104(x57471),x57473),f773(f773(f104(x57471),x57472),x57474)))
% 191.21/191.74 [5754]E(x57541,x57542)+E(f151(x57543,x57541,f773(f773(f140(x57543),x57542),x57544)),f773(f773(f140(x57543),x57542),f151(x57543,x57541,x57544)))
% 191.21/191.74 [5769]~P1(f773(x57692,x57693))+E(f773(f126(x57691,x57692),f773(f773(f140(x57691),x57693),x57694)),f773(f773(f140(x57691),x57693),f773(f126(x57691,x57692),x57694)))
% 191.21/191.74 [5900]~P1(f773(x59002,x59003))+E(f162(x59001,x59002,f773(f773(f140(x59001),x59003),x59004)),f773(f773(f140(x59001),x59003),f162(x59001,x59002,x59004)))
% 191.21/191.74 [5952]P28(x59521,x59522,x59523)+~P28(x59521,x59522,f773(f773(f302(f846(x59521)),x59524),x59523))
% 191.21/191.74 [5965]E(x59651,f180(f855(x59652,a841)))+E(f773(f773(f46(x59652,f855(x59653,a841)),x59651),f773(f18(f855(x59653,a841),x59652),x59654)),x59654)
% 191.21/191.74 [5966]E(x59661,f180(f855(x59662,a841)))+E(f773(f773(f47(x59662,f855(x59663,a841)),x59661),f773(f18(f855(x59663,a841),x59662),x59664)),x59664)
% 191.21/191.74 [5975]~E(x59754,f180(f855(x59752,a841)))+E(f773(f773(f248(x59751,x59752),x59753),f773(f18(f855(x59752,a841),x59751),x59754)),f180(f855(f854(x59751,x59752),a841)))
% 191.21/191.74 [5976]~E(x59763,f180(f855(x59761,a841)))+E(f773(f773(f248(x59761,x59762),x59763),f773(f18(f855(x59762,a841),x59761),x59764)),f180(f855(f854(x59761,x59762),a841)))
% 191.21/191.74 [6027]E(x60271,f2(a847))+E(f773(f773(f128(x60272),x60271),f773(f773(f140(x60272),x60273),x60274)),f773(f773(f128(x60272),f773(f773(f3(a847),x60271),f80(a847))),x60274))
% 191.21/191.74 [6054]E(x60541,f180(f855(x60542,a841)))+E(f773(f303(x60542,x60543,f773(f18(x60543,x60542),x60544)),x60541),f773(f773(f302(x60543),x60544),f180(f855(x60543,a841))))
% 191.21/191.74 [6057]E(f773(f305(x60571,x60572,f773(f18(x60572,x60571),x60573)),x60574),f180(f855(x60571,a841)))+P1(f773(f773(f334(x60572),x60573),x60574))
% 191.21/191.74 [6124]~E(x61243,f180(f855(x61241,a841)))+E(f773(f773(f46(x61241,f855(x61242,a841)),x61243),f773(f18(f855(x61242,a841),x61241),x61244)),f180(f855(x61242,a841)))
% 191.21/191.74 [6125]~E(x61253,f180(f855(x61251,a841)))+E(f773(f773(f47(x61251,f855(x61252,a841)),x61253),f773(f18(f855(x61252,a841),x61251),x61254)),f239(f855(x61252,a841)))
% 191.21/191.74 [6127]~P7(x61271)+E(f52(x61271,f773(f773(f83(x61271),x61272),x61273),f773(f773(f83(x61271),x61272),x61274)),f773(f773(f83(x61271),x61272),f52(x61271,x61273,x61274)))
% 191.21/191.74 [6301]E(f773(f305(x63011,x63012,f773(f18(x63012,x63011),x63013)),x63014),f239(f855(x63011,a841)))+~P1(f773(f773(f334(x63012),x63013),x63014))
% 191.21/191.74 [6324]~P1(f773(f773(f334(x63241),x63242),x63244))+P1(f773(f773(f334(x63241),x63242),f773(f773(f302(x63241),x63243),x63244)))
% 191.21/191.74 [6337]~E(x63373,f773(f773(f3(a847),f773(f181(f848(x63371)),x63372)),f80(a847)))+E(f116(x63371,f773(f773(f148(x63371,x63372),x63373),x63374)),f116(x63371,x63372))
% 191.21/191.74 [6362]~P100(x63621)+E(f773(f773(f104(f855(x63621,a841)),f773(f293(x63621),x63622)),f295(x63621,x63623,x63624)),f295(x63621,x63623,f773(f773(f236(x63621),x63622),x63624)))
% 191.21/191.74 [6363]~P100(x63631)+E(f773(f773(f104(f855(x63631,a841)),f773(f258(x63631),x63632)),f295(x63631,x63633,x63634)),f295(x63631,f773(f773(f179(x63631),x63632),x63633),x63634))
% 191.21/191.74 [6380]E(f773(f773(f104(f855(x63801,a841)),x63802),f773(f773(f302(x63801),x63803),x63804)),f773(f773(f104(f855(x63801,a841)),x63802),x63804))+P1(f773(f773(f334(x63801),x63803),x63802))
% 191.21/191.74 [6392]E(f151(x63921,x63922,f773(f773(f125(x63921),x63923),x63924)),f773(f773(f125(x63921),x63923),f151(x63921,x63922,x63924)))+P1(f773(f773(f334(x63921),x63922),f773(f158(x63921),x63923)))
% 191.21/191.74 [6397]~P75(x63971)+E(f773(f773(f83(x63971),f773(f773(f242(x63971),x63972),x63973)),f773(f773(f242(x63971),x63972),x63974)),f773(f773(f242(x63971),x63972),f773(f773(f82(a847),x63973),x63974)))
% 191.21/191.74 [6398]~P85(x63981)+E(f773(f773(f83(x63981),f773(f773(f242(x63981),x63982),x63983)),f773(f773(f242(x63981),x63982),x63984)),f773(f773(f242(x63981),x63982),f773(f773(f82(a847),x63983),x63984)))
% 191.21/191.74 [6434]~P85(x64341)+E(f773(f773(f82(x64341),f773(f773(f83(x64341),x64342),x64343)),f773(f773(f83(x64341),x64342),x64344)),f773(f773(f83(x64341),x64342),f773(f773(f82(x64341),x64343),x64344)))
% 191.21/191.74 [6435]~P100(x64351)+E(f773(f773(f179(x64351),f773(f773(f236(x64351),x64352),x64353)),f773(f773(f236(x64351),x64352),x64354)),f773(f773(f236(x64351),x64352),f773(f773(f179(x64351),x64353),x64354)))
% 191.21/191.74 [6436]~P100(x64361)+E(f773(f773(f236(x64361),f773(f773(f179(x64361),x64362),x64363)),f773(f773(f179(x64361),x64362),x64364)),f773(f773(f179(x64361),x64362),f773(f773(f236(x64361),x64363),x64364)))
% 191.21/191.74 [6437]~P97(x64371)+E(f773(f773(f104(x64371),f773(f773(f103(x64371),x64372),x64373)),f773(f773(f103(x64371),x64372),x64374)),f773(f773(f103(x64371),x64372),f773(f773(f104(x64371),x64373),x64374)))
% 191.21/191.74 [6438]~P97(x64381)+E(f773(f773(f103(x64381),f773(f773(f104(x64381),x64382),x64383)),f773(f773(f104(x64381),x64382),x64384)),f773(f773(f104(x64381),x64382),f773(f773(f103(x64381),x64383),x64384)))
% 191.21/191.74 [6475]~P7(x64751)+E(f52(x64751,f773(f773(f83(x64751),x64752),x64753),f773(f773(f83(x64751),x64754),x64753)),f773(f773(f83(x64751),f52(x64751,x64752,x64754)),x64753))
% 191.21/191.74 [6478]~E(f773(f181(f848(x64781)),x64783),f773(f181(f848(x64782)),x64784))+E(f773(f773(f143(f854(x64781,x64782),x64782),f250(x64781,x64782)),f773(f773(f167(x64781,x64782),x64783),x64784)),x64784)
% 191.21/191.74 [6479]~E(f773(f181(f848(x64791)),x64793),f773(f181(f848(x64792)),x64794))+E(f773(f773(f143(f854(x64791,x64792),x64791),f240(x64791,x64792)),f773(f773(f167(x64791,x64792),x64793),x64794)),x64793)
% 191.21/191.74 [6490]~P7(x64901)+E(f52(x64901,f773(f773(f83(x64901),x64902),f52(x64901,x64903,x64904)),x64904),f52(x64901,f773(f773(f83(x64901),x64902),x64903),x64904))
% 191.21/191.74 [6491]~P8(x64911)+E(f52(x64911,f773(f773(f3(x64911),x64912),f52(x64911,x64913,x64914)),x64914),f52(x64911,f773(f773(f3(x64911),x64912),x64913),x64914))
% 191.21/191.74 [6492]~P7(x64921)+E(f52(x64921,f773(f773(f82(x64921),x64922),f52(x64921,x64923,x64924)),x64924),f52(x64921,f773(f773(f82(x64921),x64922),x64923),x64924))
% 191.21/191.74 [6575]~P100(x65751)+E(f773(f773(f104(f855(x65751,a841)),f295(x65751,x65752,x65753)),f773(f293(x65751),x65754)),f295(x65751,x65752,f773(f773(f236(x65751),x65753),x65754)))
% 191.21/191.74 [6576]~P100(x65761)+E(f773(f773(f104(f855(x65761,a841)),f295(x65761,x65762,x65763)),f773(f258(x65761),x65764)),f295(x65761,f773(f773(f179(x65761),x65762),x65764),x65763))
% 191.21/191.74 [6580]~E(f773(f181(f848(x65801)),x65803),f773(f181(f848(x65802)),x65804))+E(f773(f773(f167(x65801,x65802),f773(f142(x65801),x65803)),f773(f142(x65802),x65804)),f773(f142(f854(x65801,x65802)),f773(f773(f167(x65801,x65802),x65803),x65804)))
% 191.21/191.74 [6589]E(x65891,f773(f773(f3(a847),f773(f181(f848(x65892)),x65893)),f80(a847)))+E(f116(x65892,f773(f773(f148(x65892,x65893),x65891),x65894)),f773(f773(f148(x65892,f116(x65892,x65893)),x65891),x65894))
% 191.21/191.74 [6606]~P1(f773(f127(x66062),x66064))+P1(f773(f127(f854(x66061,x66062)),f773(f773(f167(x66061,x66062),x66063),x66064)))
% 191.21/191.74 [6607]~P1(f773(f127(x66071),x66073))+P1(f773(f127(f854(x66071,x66072)),f773(f773(f167(x66071,x66072),x66073),x66074)))
% 191.21/191.74 [6705]E(x67051,f773(f773(f773(a189,x67052),x67053),f773(x67054,x67052)))+~P1(f773(f773(f187(f28(x67053,x67054)),x67052),x67051))
% 191.21/191.74 [6886]E(f773(f773(f43(a847),x68861),x68862),x68863)+~P1(f773(f55(x68861,x68862),f773(f773(f241(a847,a847),x68863),x68864)))
% 191.21/191.74 [6912]E(f52(a847,x69121,x69122),x69123)+~P1(f773(f55(x69121,x69122),f773(f773(f241(a847,a847),x69124),x69123)))
% 191.21/191.74 [6915]P1(f773(f127(x69151),x69152))+~P1(f773(f127(x69153),f773(f773(f143(x69151,x69153),x69154),x69152)))
% 191.21/191.74 [6923]~P28(x69231,x69232,f773(f773(f302(f846(x69231)),x69233),x69234))+P28(x69231,x69232,f773(f773(f302(f846(x69231)),x69233),f180(f855(f846(x69231),a841))))
% 191.21/191.74 [6995]E(f151(x69951,x69952,f773(f773(f125(x69951),x69953),x69954)),f773(f773(f125(x69951),f151(x69951,x69952,x69953)),x69954))+~P1(f773(f773(f334(x69951),x69952),f773(f158(x69951),x69953)))
% 191.21/191.74 [7091]~P8(x70911)+E(f52(x70911,f773(f773(f3(x70911),f52(x70911,x70912,x70913)),x70914),x70913),f52(x70911,f773(f773(f3(x70911),x70912),x70914),x70913))
% 191.21/191.74 [7092]~P7(x70921)+E(f52(x70921,f773(f773(f82(x70921),f52(x70921,x70922,x70923)),x70924),x70923),f52(x70921,f773(f773(f82(x70921),x70922),x70924),x70923))
% 191.21/191.74 [7093]~P7(x70931)+E(f52(x70931,f773(f773(f83(x70931),f52(x70931,x70932,x70933)),x70934),x70933),f52(x70931,f773(f773(f83(x70931),x70932),x70934),x70933))
% 191.21/191.74 [7299]~E(x72991,f773(f773(f140(x72992),x72993),x72994))+~P1(f773(f773(f232(a847),f773(f181(f848(x72992)),x72991)),f773(f181(f848(x72992)),x72994)))
% 191.21/191.74 [7471]~E(f166(x74711,x74712,x74713),f166(x74711,x74712,x74714))+E(f773(f303(f854(x74711,x74712),x74711,f240(x74711,x74712)),f773(f158(f854(x74711,x74712)),x74713)),f773(f303(f854(x74711,x74712),x74711,f240(x74711,x74712)),f773(f158(f854(x74711,x74712)),x74714)))
% 191.21/191.74 [7514]P29(x75141,x75142,x75143,f773(f158(x75141),x75144))+~P1(f773(f127(x75142),f773(f773(f143(x75141,x75142),x75143),x75144)))
% 191.21/191.74 [7591]~P1(f773(f773(f232(f855(x75911,a841)),x75912),x75914))+P1(f773(f773(f232(f855(x75911,a841)),x75912),f773(f773(f302(x75911),x75913),x75914)))
% 191.21/191.74 [7626]~P7(x76261)+E(f52(x76261,f773(f773(f82(x76261),f52(x76261,x76262,x76263)),f52(x76261,x76264,x76263)),x76263),f52(x76261,f773(f773(f82(x76261),x76262),x76264),x76263))
% 191.21/191.74 [7627]~P7(x76271)+E(f52(x76271,f773(f773(f83(x76271),f52(x76271,x76272,x76273)),f52(x76271,x76274,x76273)),x76273),f52(x76271,f773(f773(f83(x76271),x76272),x76274),x76273))
% 191.21/191.74 [7628]~P8(x76281)+E(f52(x76281,f773(f773(f3(x76281),f52(x76281,x76282,x76283)),f52(x76281,x76284,x76283)),x76283),f52(x76281,f773(f773(f3(x76281),x76282),x76284),x76283))
% 191.21/191.74 [7729]~E(f773(x77294,f651(x77294,x77293,x77291,x77292)),f239(f855(x77292,a841)))+E(f773(f773(f47(x77291,f855(x77292,a841)),x77293),x77294),f239(f855(x77292,a841)))
% 191.21/191.74 [7730]~E(f773(x77304,f410(x77304,x77303,x77301,x77302)),f180(f855(x77302,a841)))+E(f773(f773(f46(x77301,f855(x77302,a841)),x77303),x77304),f180(f855(x77302,a841)))
% 191.21/191.74 [7731]~E(f773(x77314,f411(x77314,x77313,x77312,x77311)),f180(f855(x77312,a841)))+E(f773(f773(f46(x77311,f855(x77312,a841)),x77313),x77314),f180(f855(x77312,a841)))
% 191.21/191.74 [7732]~E(f773(x77324,f652(x77324,x77323,x77322,x77321)),f239(f855(x77322,a841)))+E(f773(f773(f47(x77321,f855(x77322,a841)),x77323),x77324),f239(f855(x77322,a841)))
% 191.21/191.74 [8123]P1(f773(x81231,x81232))+~P1(f773(f773(f334(x81233),x81232),f773(f773(f104(f855(x81233,a841)),x81234),f773(f256(x81233),x81231))))
% 191.21/191.74 [8162]~P1(f773(f773(f232(f855(x81621,a841)),x81623),x81624))+P1(f773(f773(f232(f855(x81621,a841)),f773(f773(f302(x81621),x81622),x81623)),f773(f773(f302(x81621),x81622),x81624)))
% 191.21/191.74 [8329]P1(f773(f773(f187(x83291),x83292),f435(x83293,x83292,x83294,x83291)))+~P1(f773(f773(f187(f36(x83291,x83294)),x83292),x83293))
% 191.21/191.74 [8330]P1(f773(f773(f187(x83301),x83302),f461(x83303,x83302,x83304,x83301)))+~P1(f773(f773(f187(f36(x83301,x83304)),x83302),x83303))
% 191.21/191.74 [8451]~P1(f773(f773(f233(a847),f773(x84514,x84512)),f773(x84514,x84513)))+P1(f773(f773(f334(f854(x84511,x84511)),f773(f773(f241(x84511,x84511),x84512),x84513)),f773(f773(f280(a847,x84511),a237),x84514)))
% 191.21/191.74 [8598]P29(f848(x85981),f848(x85982),f773(f143(x85981,x85982),x85983),x85984)+~P29(x85981,x85982,x85983,f44(f855(x85981,a841),f773(f303(f848(x85981),f855(x85981,a841),f158(x85981)),x85984)))
% 191.21/191.74 [8708]E(f773(f773(f47(x87081,f855(x87082,a841)),x87083),x87084),f239(f855(x87082,a841)))+P1(f773(f773(f334(x87081),f651(x87084,x87083,x87081,x87082)),x87083))
% 191.21/191.74 [8709]E(f773(f773(f46(x87091,f855(x87092,a841)),x87093),x87094),f180(f855(x87092,a841)))+P1(f773(f773(f334(x87091),f410(x87094,x87093,x87091,x87092)),x87093))
% 191.21/191.74 [8710]E(f773(f773(f46(x87101,f855(x87102,a841)),x87103),x87104),f180(f855(x87102,a841)))+P1(f773(f773(f334(x87101),f411(x87104,x87103,x87102,x87101)),x87103))
% 191.21/191.74 [8711]E(f773(f773(f47(x87111,f855(x87112,a841)),x87113),x87114),f239(f855(x87112,a841)))+P1(f773(f773(f334(x87111),f652(x87114,x87113,x87112,x87111)),x87113))
% 191.21/191.74 [8746]P1(f773(f773(f233(a847),f773(x87461,x87462)),f773(x87461,x87463)))+~P1(f773(f773(f334(f854(x87464,x87464)),f773(f773(f241(x87464,x87464),x87462),x87463)),f773(f773(f280(a847,x87464),a237),x87461)))
% 191.21/191.74 [8795]P1(f773(f773(f187(x87951),f435(x87952,x87953,x87951,x87954)),x87952))+~P1(f773(f773(f187(f36(x87954,x87951)),x87953),x87952))
% 191.21/191.74 [8796]P1(f773(f773(f187(x87961),f461(x87962,x87963,x87961,x87964)),x87962))+~P1(f773(f773(f187(f36(x87964,x87961)),x87963),x87962))
% 191.21/191.74 [8907]P1(f773(f773(f334(x89071),f494(x89072,x89073,x89074,x89071)),x89073))+~P1(f773(f773(f334(f855(x89071,a841)),x89074),f773(f773(f61(x89071),x89073),x89072)))
% 191.21/191.74 [8910]E(x89101,x89102)+~P1(f773(f773(f334(f854(x89103,x89103)),f773(f773(f241(x89103,x89103),x89101),x89102)),f773(f773(f173(f854(x89103,x89103),a841),f2(a847)),x89104)))
% 191.21/191.74 [8982]E(f773(f277(x89821,x89821,x89822),f773(f773(f302(x89821),f494(x89822,x89823,x89824,x89821)),f180(f855(x89821,a841)))),x89824)+~P1(f773(f773(f334(f855(x89821,a841)),x89824),f773(f773(f61(x89821),x89823),x89822)))
% 191.21/191.74 [8993]~P1(f773(f773(f334(f854(x89931,x89931)),f773(f773(f241(x89931,x89931),x89933),x89932)),f300(x89931,x89934)))+P1(f773(f773(f334(f854(x89931,x89931)),f773(f773(f241(x89931,x89931),x89932),x89933)),f300(x89931,f773(f278(x89931,x89931),x89934))))
% 191.21/191.74 [9006]~P7(x90061)+E(f773(f773(f82(x90061),f773(f773(f82(x90061),f773(f773(f83(x90061),x90062),f773(f773(f43(x90061),x90063),x90062))),f52(x90061,x90063,x90062))),x90064),f773(f773(f82(x90061),x90063),x90064))
% 191.21/191.74 [9013]~P1(f773(f773(f334(x90131),x90133),x90134))+P1(f773(f773(f334(f855(x90131,a841)),f773(f277(x90131,x90131,x90132),f773(f773(f302(x90131),x90133),f180(f855(x90131,a841))))),f773(f773(f61(x90131),x90134),x90132)))
% 191.21/191.74 [9023]P1(f773(f773(f334(f854(x90231,x90231)),f773(f773(f241(x90231,x90231),x90232),x90233)),f300(x90231,x90234)))+~P1(f773(f773(f334(f854(x90231,x90231)),f773(f773(f241(x90231,x90231),x90233),x90232)),f300(x90231,f773(f278(x90231,x90231),x90234))))
% 191.21/191.74 [9106]E(f773(f773(f148(x91061,f773(f142(x91061),x91062)),f773(f773(f3(a847),f773(f773(f3(a847),f773(f181(f848(x91061)),x91062)),x91063)),f80(a847))),x91064),f773(f142(x91061),f773(f773(f148(x91061,x91062),x91063),x91064)))+~P1(f773(f773(f233(a847),x91063),f773(f181(f848(x91061)),x91062)))
% 191.21/191.74 [9143]~P29(x91432,x91431,x91433,f239(f855(x91432,a841)))+P1(f773(f773(f232(f855(x91431,a841)),f773(f303(x91432,x91431,x91433),f773(f81(f855(x91432,a841)),x91434))),f773(f81(f855(x91431,a841)),f773(f303(x91432,x91431,x91433),x91434))))
% 191.21/191.74 [9151]~P9(x91511)+E(f773(f132(x91511,x91512,f773(f9(x91512,x91511,x91511),f773(f773(f10(x91511,f855(x91511,x91511),x91512),f103(x91511)),x91513)),f180(x91511)),x91514),f773(f773(f46(x91512,x91511),f773(f158(x91512),x91514)),x91513))
% 191.21/191.74 [9152]~P9(x91521)+E(f773(f132(x91521,x91522,f773(f9(x91522,x91521,x91521),f773(f773(f10(x91521,f855(x91521,x91521),x91522),f104(x91521)),x91523)),f239(x91521)),x91524),f773(f773(f47(x91522,x91521),f773(f158(x91522),x91524)),x91523))
% 191.21/191.74 [9218]~P1(f773(f773(f334(f854(f848(x92184),f848(x92184))),f773(f773(f241(f848(x92184),f848(x92184)),x92183),x92182)),f146(x92184,x92181)))+P1(f773(f773(f233(a847),f737(x92181,x92182,x92183,x92184)),f773(f181(f848(x92184)),x92183)))
% 191.21/191.74 [9219]~P7(x92191)+E(f773(f773(f82(x92191),f773(f773(f82(x92191),f773(f773(f83(x92191),f773(f773(f43(x92191),x92192),x92193)),x92193)),f52(x92191,x92192,x92193))),x92194),f773(f773(f82(x92191),x92192),x92194))
% 191.21/191.74 [9248]~P1(f773(f773(f334(f854(f848(x92481),f848(x92481))),f773(f773(f241(f848(x92481),f848(x92481)),x92482),x92483)),f773(f278(f848(x92481),f848(x92481)),f146(x92481,x92484))))+P1(f773(f773(f334(f854(f848(x92481),f848(x92481))),f773(f773(f241(f848(x92481),f848(x92481)),x92482),x92483)),f146(x92481,f773(f278(x92481,x92481),x92484))))
% 191.21/191.74 [9249]P1(f773(f773(f334(f854(f848(x92491),f848(x92491))),f773(f773(f241(f848(x92491),f848(x92491)),x92492),x92493)),f773(f278(f848(x92491),f848(x92491)),f146(x92491,x92494))))+~P1(f773(f773(f334(f854(f848(x92491),f848(x92491))),f773(f773(f241(f848(x92491),f848(x92491)),x92492),x92493)),f146(x92491,f773(f278(x92491,x92491),x92494))))
% 191.21/191.74 [9286]~P1(f773(f773(f334(x92861),x92863),f773(f261(x92861,x92862),x92864)))+P1(f773(f773(f334(f854(x92861,x92862)),f773(f773(f241(x92861,x92862),x92863),f597(x92864,x92862,x92863,x92861))),x92864))
% 191.21/191.74 [9287]~P1(f773(f773(f334(x92871),x92873),f773(f261(x92871,x92872),x92874)))+P1(f773(f773(f334(f854(x92871,x92872)),f773(f773(f241(x92871,x92872),x92873),f598(x92874,x92872,x92873,x92871))),x92874))
% 191.21/191.74 [9413]~P1(f773(f63(f851(x94131)),f773(f303(x94132,f851(x94131),x94133),f239(f855(x94132,a841)))))+P1(f773(f63(f851(x94131)),f773(f303(x94132,f851(x94131),f170(x94132,x94131,x94133,f166(x94132,x94131,x94134))),f239(f855(x94132,a841)))))
% 191.21/191.74 [9437]~P1(f773(f773(f334(f854(x94371,x94371)),f773(f773(f241(x94371,x94371),x94372),x94374)),f773(f773(f281(x94371,x94371,x94371),x94373),f300(x94371,x94373))))+P1(f773(f773(f334(f854(x94371,x94371)),f773(f773(f241(x94371,x94371),x94372),f654(x94373,x94374,x94372,x94371))),x94373))
% 191.21/191.74 [9595]~P1(f773(f773(f334(f854(x95952,x95951)),x95954),f773(f278(x95951,x95952),x95953)))+P1(f773(f773(f334(f854(x95951,x95952)),f773(f773(f241(x95951,x95952),f701(x95953,x95954,x95951,x95952)),f700(x95953,x95954,x95951,x95952))),x95953))
% 191.21/191.74 [9619]~P1(f773(f773(f334(f854(f848(x96191),f848(x96191))),f773(f773(f241(f848(x96191),f848(x96191)),x96194),x96193)),f146(x96191,x96192)))+P1(f773(f773(f334(f854(x96191,x96191)),f773(f773(f241(x96191,x96191),f742(x96192,x96193,x96194,x96191)),f743(x96192,x96193,x96194,x96191))),x96192))
% 191.21/191.74 [9695]~P1(f773(f773(f334(f854(f848(x96951),f848(x96951))),f773(f773(f241(f848(x96951),f848(x96951)),x96952),x96954)),f146(x96951,x96953)))+P1(f773(f773(f334(f854(x96951,x96951)),f773(f773(f241(x96951,x96951),f773(f773(f153(x96951),x96952),f737(x96953,x96954,x96952,x96951))),f738(x96953,x96954,x96952,x96951))),x96953))
% 191.21/191.74 [9716]~P1(f773(f63(x97162),x97164))+E(f773(f773(f773(f67(f855(x97161,a841),x97162,f103(f855(x97161,a841))),f773(f773(f9(x97162,f855(x97161,a841),f855(x97161,a841)),f773(f773(f10(x97161,f855(f855(x97161,a841),f855(x97161,a841)),x97162),f302(x97161)),x97163)),f180(f855(x97161,a841)))),f180(f855(x97161,a841))),x97164),f773(f303(x97162,x97161,x97163),x97164))
% 191.21/191.74 [9832]~P29(x98321,x98322,x98323,f239(f855(x98321,a841)))+P1(f773(f773(f232(f855(x98321,a841)),f773(f305(x98321,x98322,x98323),f773(f773(f302(x98322),x98324),f180(f855(x98322,a841))))),f773(f773(f302(x98321),f87(x98321,f773(f773(f9(x98321,x98322,a841),f773(f773(f10(x98322,f855(x98322,a841),x98321),a330),x98323)),x98324))),f180(f855(x98321,a841)))))
% 191.21/191.74 [5494]~E(f773(f773(f125(x54941),x54942),x54944),x54943)+E(f773(f773(f159(x54941),f773(f181(f848(x54941)),x54942)),x54943),x54942)
% 191.21/191.74 [5495]~E(f773(f773(f125(x54952),x54953),x54951),x54954)+E(x54951,f773(f773(f128(x54952),f773(f181(f848(x54952)),x54953)),x54954))
% 191.21/191.74 [5506]~E(x55064,f2(a847))+E(f773(f773(f153(x55061),f773(f773(f140(x55061),x55062),x55063)),x55064),x55062)
% 191.21/191.74 [6038]~P85(x60381)+E(f773(f773(f242(x60381),f773(f773(f242(x60381),x60382),x60383)),x60384),f773(f773(f242(x60381),x60382),f773(f773(f83(a847),x60383),x60384)))
% 191.21/191.74 [6039]~P75(x60391)+E(f773(f773(f242(x60391),f773(f773(f242(x60391),x60392),x60393)),x60394),f773(f773(f242(x60391),x60392),f773(f773(f83(a847),x60393),x60394)))
% 191.21/191.74 [6055]E(x60551,f2(a847))+E(f773(f773(f153(x60552),f773(f773(f140(x60552),x60553),x60554)),x60551),f773(f773(f153(x60552),x60554),f773(f773(f3(a847),x60551),f80(a847))))
% 191.21/191.74 [6081]~P113(x60811)+E(f773(f773(f283(x60811),f773(f773(f83(x60811),x60812),x60813)),x60814),f773(f773(f83(x60811),x60812),f773(f773(f283(x60811),x60813),x60814)))
% 191.21/191.74 [6082]~P5(x60821)+E(f773(f773(f82(x60821),f773(f773(f82(x60821),x60822),x60823)),x60824),f773(f773(f82(x60821),x60822),f773(f773(f82(x60821),x60823),x60824)))
% 191.21/191.74 [6083]~P85(x60831)+E(f773(f773(f82(x60831),f773(f773(f82(x60831),x60832),x60833)),x60834),f773(f773(f82(x60831),x60832),f773(f773(f82(x60831),x60833),x60834)))
% 191.21/191.74 [6084]~P85(x60841)+E(f773(f773(f83(x60841),f773(f773(f83(x60841),x60842),x60843)),x60844),f773(f773(f83(x60841),x60842),f773(f773(f83(x60841),x60843),x60844)))
% 191.21/191.74 [6085]~P64(x60851)+E(f773(f773(f83(x60851),f773(f773(f83(x60851),x60852),x60853)),x60854),f773(f773(f83(x60851),x60852),f773(f773(f83(x60851),x60853),x60854)))
% 191.21/191.74 [6088]~P100(x60881)+E(f773(f773(f236(x60881),f773(f773(f236(x60881),x60882),x60883)),x60884),f773(f773(f236(x60881),x60882),f773(f773(f236(x60881),x60883),x60884)))
% 191.21/191.74 [6090]~P100(x60901)+E(f773(f773(f179(x60901),f773(f773(f179(x60901),x60902),x60903)),x60904),f773(f773(f179(x60901),x60902),f773(f773(f179(x60901),x60903),x60904)))
% 191.21/191.74 [6092]~P92(x60921)+E(f773(f773(f103(x60921),f773(f773(f103(x60921),x60922),x60923)),x60924),f773(f773(f103(x60921),x60922),f773(f773(f103(x60921),x60923),x60924)))
% 191.21/191.74 [6093]~P93(x60931)+E(f773(f773(f103(x60931),f773(f773(f103(x60931),x60932),x60933)),x60934),f773(f773(f103(x60931),x60932),f773(f773(f103(x60931),x60933),x60934)))
% 191.21/191.74 [6094]~P93(x60941)+E(f773(f773(f104(x60941),f773(f773(f104(x60941),x60942),x60943)),x60944),f773(f773(f104(x60941),x60942),f773(f773(f104(x60941),x60943),x60944)))
% 191.21/191.74 [6096]~P98(x60961)+E(f773(f773(f104(x60961),f773(f773(f104(x60961),x60962),x60963)),x60964),f773(f773(f104(x60961),x60962),f773(f773(f104(x60961),x60963),x60964)))
% 191.21/191.74 [6107]~P7(x61071)+E(f52(x61071,f773(f773(f82(x61071),x61072),f773(f773(f83(x61071),x61073),x61074)),x61074),f52(x61071,x61072,x61074))
% 191.21/191.74 [6108]~P7(x61081)+E(f52(x61081,f773(f773(f82(x61081),x61082),f773(f773(f83(x61081),x61083),x61084)),x61083),f52(x61081,x61082,x61083))
% 191.21/191.74 [6246]E(f773(f773(f153(x62461),f773(f773(f159(x62461),x62462),x62463)),x62464),f773(f773(f153(x62461),x62463),x62464))+~P1(f773(f773(f233(a847),x62464),x62462))
% 191.21/191.74 [6432]~P85(x64321)+E(f773(f773(f82(x64321),f773(f773(f82(x64321),x64322),x64323)),x64324),f773(f773(f82(x64321),f773(f773(f82(x64321),x64322),x64324)),x64323))
% 191.21/191.74 [6433]~P85(x64331)+E(f773(f773(f83(x64331),f773(f773(f83(x64331),x64332),x64333)),x64334),f773(f773(f83(x64331),f773(f773(f83(x64331),x64332),x64334)),x64333))
% 191.21/191.74 [6495]~P2(x64952)+E(f773(f773(f8(x64951,x64952),f773(f18(x64952,x64951),x64953)),x64954),f773(f773(f83(x64952),f773(f102(x64952),f773(f42(x64951),x64954))),x64953))
% 191.21/191.74 [6674]E(f773(f773(f104(f855(x66741,a841)),f773(f773(f302(x66741),x66742),x66743)),x66744),f773(f773(f104(f855(x66741,a841)),x66743),x66744))+P1(f773(f773(f334(x66741),x66742),x66744))
% 191.21/191.74 [6749]~P74(x67491)+E(f773(f773(f236(x67491),f773(f773(f82(x67491),x67492),x67493)),f773(f773(f82(x67491),x67494),x67493)),f773(f773(f82(x67491),f773(f773(f236(x67491),x67492),x67494)),x67493))
% 191.21/191.74 [6750]~P74(x67501)+E(f773(f773(f179(x67501),f773(f773(f82(x67501),x67502),x67503)),f773(f773(f82(x67501),x67504),x67503)),f773(f773(f82(x67501),f773(f773(f179(x67501),x67502),x67504)),x67503))
% 191.21/191.74 [6752]~P109(x67521)+E(f773(f773(f82(x67521),f773(f773(f83(x67521),x67522),x67523)),f773(f773(f83(x67521),x67524),x67523)),f773(f773(f83(x67521),f773(f773(f82(x67521),x67522),x67524)),x67523))
% 191.21/191.74 [6753]~P77(x67531)+E(f773(f773(f236(x67531),f773(f773(f3(x67531),x67532),x67533)),f773(f773(f3(x67531),x67534),x67533)),f773(f773(f3(x67531),f773(f773(f236(x67531),x67532),x67534)),x67533))
% 191.21/191.74 [6754]~P77(x67541)+E(f773(f773(f179(x67541),f773(f773(f3(x67541),x67542),x67543)),f773(f773(f3(x67541),x67544),x67543)),f773(f773(f3(x67541),f773(f773(f179(x67541),x67542),x67544)),x67543))
% 191.21/191.74 [6755]~P85(x67551)+E(f773(f773(f83(x67551),f773(f773(f242(x67551),x67552),x67553)),f773(f773(f242(x67551),x67554),x67553)),f773(f773(f242(x67551),f773(f773(f83(x67551),x67552),x67554)),x67553))
% 191.21/191.74 [6756]~P70(x67561)+E(f773(f773(f83(x67561),f773(f773(f242(x67561),x67562),x67563)),f773(f773(f242(x67561),x67564),x67563)),f773(f773(f242(x67561),f773(f773(f83(x67561),x67562),x67564)),x67563))
% 191.21/191.74 [6757]~P60(x67571)+E(f773(f773(f283(x67571),f773(f773(f242(x67571),x67572),x67573)),f773(f773(f242(x67571),x67574),x67573)),f773(f773(f242(x67571),f773(f773(f283(x67571),x67572),x67574)),x67573))
% 191.21/191.74 [6758]~P113(x67581)+E(f773(f773(f82(x67581),f773(f773(f283(x67581),x67582),x67583)),f773(f773(f283(x67581),x67584),x67583)),f773(f773(f283(x67581),f773(f773(f82(x67581),x67582),x67584)),x67583))
% 191.21/191.74 [6759]~P113(x67591)+E(f773(f773(f3(x67591),f773(f773(f283(x67591),x67592),x67593)),f773(f773(f283(x67591),x67594),x67593)),f773(f773(f283(x67591),f773(f773(f3(x67591),x67592),x67594)),x67593))
% 191.21/191.74 [6760]~P100(x67601)+E(f773(f773(f179(x67601),f773(f773(f236(x67601),x67602),x67603)),f773(f773(f236(x67601),x67604),x67603)),f773(f773(f236(x67601),f773(f773(f179(x67601),x67602),x67604)),x67603))
% 191.21/191.74 [6761]~P100(x67611)+E(f773(f773(f236(x67611),f773(f773(f179(x67611),x67612),x67613)),f773(f773(f179(x67611),x67614),x67613)),f773(f773(f179(x67611),f773(f773(f236(x67611),x67612),x67614)),x67613))
% 191.21/191.74 [6762]~P97(x67621)+E(f773(f773(f104(x67621),f773(f773(f103(x67621),x67622),x67623)),f773(f773(f103(x67621),x67624),x67623)),f773(f773(f103(x67621),f773(f773(f104(x67621),x67622),x67624)),x67623))
% 191.21/191.74 [6763]~P97(x67631)+E(f773(f773(f103(x67631),f773(f773(f104(x67631),x67632),x67633)),f773(f773(f104(x67631),x67634),x67633)),f773(f773(f104(x67631),f773(f773(f103(x67631),x67632),x67634)),x67633))
% 191.21/191.74 [6764]~P85(x67641)+E(f773(f773(f82(x67641),f773(f773(f83(x67641),x67642),x67643)),f773(f773(f83(x67641),x67644),x67643)),f773(f773(f83(x67641),f773(f773(f82(x67641),x67642),x67644)),x67643))
% 191.21/191.74 [6799]E(f773(f773(f148(x67991,x67992),x67993),x67994),x67992)+~P1(f773(f773(f232(a847),f773(f181(f848(x67991)),x67992)),x67993))
% 191.21/191.74 [6826]~P1(f773(x68263,x68264))+P1(f773(f773(f773(f103(f855(x68261,a841)),x68262),x68263),x68264))
% 191.21/191.74 [6828]~P1(f773(x68282,x68284))+P1(f773(f773(f773(f103(f855(x68281,a841)),x68282),x68283),x68284))
% 191.21/191.74 [6850]E(f773(f773(f153(x68501),f773(f773(f125(x68501),x68502),x68503)),x68504),f773(f773(f153(x68501),x68502),x68504))+~P1(f773(f773(f233(a847),x68504),f773(f181(f848(x68501)),x68502)))
% 191.21/191.74 [6860]E(f773(f773(f3(f855(x68601,a841)),f773(f773(f302(x68601),x68602),x68603)),x68604),f773(f773(f3(f855(x68601,a841)),x68603),x68604))+~P1(f773(f773(f334(x68601),x68602),x68604))
% 191.21/191.74 [6901]~E(f130(a847,f773(f294(a847,x69011),x69012)),f773(f773(f140(a847),x69014),x69013))+E(f130(a847,f773(f294(a847,f773(f773(f82(a847),x69011),f80(a847))),x69012)),x69013)
% 191.21/191.74 [6970]E(x69701,f2(a847))+E(f773(f773(f140(x69702),x69703),f773(f773(f159(x69702),f773(f773(f3(a847),x69701),f80(a847))),x69704)),f773(f773(f159(x69702),x69701),f773(f773(f140(x69702),x69703),x69704)))
% 191.21/191.74 [7074]E(f773(f773(f153(x70741),x70742),f773(f773(f3(a847),x70743),f773(f181(f848(x70741)),x70744))),f773(f773(f153(x70741),f773(f773(f125(x70741),x70744),x70742)),x70743))+P1(f773(f773(f233(a847),x70743),f773(f181(f848(x70741)),x70744)))
% 191.21/191.74 [7102]E(f773(f773(f104(f855(x71021,a841)),x71022),f773(f773(f302(x71021),x71023),x71024)),f773(f773(f302(x71021),x71023),f773(f773(f104(f855(x71021,a841)),x71022),x71024)))+~P1(f773(f773(f334(x71021),x71023),x71022))
% 191.21/191.74 [7136]E(f773(f773(f153(x71361),f773(f773(f148(x71361,x71362),x71363),x71364)),x71363),x71364)+~P1(f773(f773(f233(a847),x71363),f773(f181(f848(x71361)),x71362)))
% 191.21/191.74 [7157]E(x71571,f180(f855(x71572,a841)))+E(f773(f303(f854(x71573,x71572),x71573,f240(x71573,x71572)),f773(f773(f248(x71573,x71572),x71574),f773(f18(f855(x71572,a841),x71573),x71571))),x71574)
% 191.21/191.74 [7158]E(x71581,f180(f855(x71582,a841)))+E(f773(f303(f854(x71582,x71583),x71583,f250(x71582,x71583)),f773(f773(f248(x71582,x71583),x71581),f773(f18(f855(x71583,a841),x71582),x71584))),x71584)
% 191.21/191.74 [7242]E(f773(f773(f3(f855(x72421,a841)),f773(f773(f302(x72421),x72422),x72423)),x72424),f773(f773(f302(x72421),x72422),f773(f773(f3(f855(x72421,a841)),x72423),x72424)))+P1(f773(f773(f334(x72421),x72422),x72424))
% 191.21/191.74 [7283]~E(x72834,f180(f855(x72832,a841)))+E(f773(f303(f854(x72831,x72832),x72831,f240(x72831,x72832)),f773(f773(f248(x72831,x72832),x72833),f773(f18(f855(x72832,a841),x72831),x72834))),f180(f855(x72831,a841)))
% 191.21/191.74 [7284]~E(x72843,f180(f855(x72841,a841)))+E(f773(f303(f854(x72841,x72842),x72842,f250(x72841,x72842)),f773(f773(f248(x72841,x72842),x72843),f773(f18(f855(x72842,a841),x72841),x72844))),f180(f855(x72842,a841)))
% 191.21/191.74 [7343]~P1(f773(f773(f334(x73431),x73432),x73434))+P1(f773(f773(f334(x73431),x73432),f773(f773(f103(f855(x73431,a841)),x73433),x73434)))
% 191.21/191.74 [7346]~P1(f773(f773(f334(x73461),x73462),x73463))+P1(f773(f773(f334(x73461),x73462),f773(f773(f103(f855(x73461,a841)),x73463),x73464)))
% 191.21/191.74 [7368]E(f773(f773(f104(f855(x73681,a841)),f773(f773(f302(x73681),x73682),x73683)),x73684),f773(f773(f302(x73681),x73682),f773(f773(f104(f855(x73681,a841)),x73683),x73684)))+~P1(f773(f773(f334(x73681),x73682),x73684))
% 191.21/191.74 [7647]P1(f773(x76471,x76472))+~P1(f773(f773(f773(f104(f855(x76473,a841)),x76474),x76471),x76472))
% 191.21/191.74 [7648]P1(f773(x76481,x76482))+~P1(f773(f773(f773(f104(f855(x76483,a841)),x76481),x76484),x76482))
% 191.21/191.74 [7651]E(f773(f773(f8(x76511,a847),x76512),f773(f773(f3(f855(x76511,a841)),x76513),f773(f773(f302(x76511),x76514),f180(f855(x76511,a841))))),f773(f773(f8(x76511,a847),x76512),x76513))+P1(f773(f773(f334(x76511),x76514),x76513))
% 191.21/191.74 [7657]~P66(x76571)+E(f773(f155(x76571),f773(f773(f143(a847,x76571),x76572),f130(a847,f773(f294(a847,x76573),x76574)))),f773(f773(f8(a847,x76571),x76572),f773(f158(a847),f130(a847,f773(f294(a847,x76573),x76574)))))
% 191.21/191.74 [7658]~P66(x76581)+E(f773(f773(f8(a847,x76581),x76582),f773(f158(a847),f130(a847,f773(f294(a847,x76583),x76584)))),f773(f155(x76581),f773(f773(f143(a847,x76581),x76582),f130(a847,f773(f294(a847,x76583),x76584)))))
% 191.21/191.74 [7772]~E(x77723,x77724)+P1(f773(f64(x77721,x77722,f773(f773(f302(x77721),x77723),f180(f855(x77721,a841)))),x77724))
% 191.21/191.74 [7868]P1(f773(f773(f334(x78681),x78682),f773(f158(x78681),x78683)))+~P1(f773(f773(f334(x78681),x78682),f773(f158(x78681),f773(f773(f159(x78681),x78684),x78683))))
% 191.21/191.74 [7869]P1(f773(f773(f334(x78691),x78692),f773(f158(x78691),x78693)))+~P1(f773(f773(f334(x78691),x78692),f773(f158(x78691),f773(f773(f128(x78691),x78694),x78693))))
% 191.21/191.74 [7943]P1(f773(f773(f334(x79431),x79432),x79433))+~P1(f773(f773(f334(x79431),x79432),f773(f773(f3(f855(x79431,a841)),x79433),x79434)))
% 191.21/191.74 [7945]P1(f773(f773(f334(x79451),x79452),x79453))+~P1(f773(f773(f334(x79451),x79452),f773(f773(f104(f855(x79451,a841)),x79454),x79453)))
% 191.21/191.74 [7948]P1(f773(f773(f334(x79481),x79482),x79483))+~P1(f773(f773(f334(x79481),x79482),f773(f773(f104(f855(x79481,a841)),x79483),x79484)))
% 191.21/191.74 [7965]E(f773(f773(f125(x79651),f773(f773(f159(x79651),x79652),x79653)),f773(f773(f140(x79651),x79654),f773(f773(f128(x79651),f773(a114,x79652)),x79653))),f773(f773(f148(x79651,x79653),x79652),x79654))+~P1(f773(f773(f233(a847),x79652),f773(f181(f848(x79651)),x79653)))
% 191.21/191.74 [7988]P1(f773(f773(f334(x79881),x79882),x79883))+~P1(f773(f773(f232(f855(x79881,a841)),f773(f773(f302(x79881),x79882),x79884)),x79883))
% 191.21/191.74 [8018]~P1(f773(f773(f334(x80181),x80182),x80183))+~P1(f773(f773(f334(x80181),x80182),f773(f773(f3(f855(x80181,a841)),x80184),x80183)))
% 191.21/191.74 [8051]~P1(f773(f773(f233(a847),x80514),f773(f181(f848(x80511)),x80513)))+P1(f773(f773(f334(x80511),x80512),f773(f158(x80511),f773(f773(f148(x80511,x80513),x80514),x80512))))
% 191.21/191.74 [8101]E(f773(f773(f153(x81011),f773(f773(f128(x81011),x81012),x81013)),x81014),f773(f773(f153(x81011),x81013),f773(f773(f82(a847),x81012),x81014)))+~P1(f773(f773(f232(a847),f773(f773(f82(a847),x81012),x81014)),f773(f181(f848(x81011)),x81013)))
% 191.21/191.74 [8110]~P2(x81102)+E(f773(f773(f8(x81101,x81102),f773(f773(f10(a847,x81102,x81101),f102(x81102)),x81103)),x81104),f773(f102(x81102),f773(f773(f8(x81101,a847),x81103),x81104)))
% 191.21/191.74 [8111]~P133(x81112)+E(f773(f773(f8(x81111,x81112),f773(f773(f10(a1,x81112,x81111),f105(x81112)),x81113)),x81114),f773(f105(x81112),f773(f773(f8(x81111,a1),x81113),x81114)))
% 191.21/191.74 [8164]~P63(x81642)+E(f773(f773(f11(x81641,x81642),f773(f773(f10(x81642,x81642,x81641),f77(x81642)),x81643)),x81644),f773(f77(x81642),f773(f773(f11(x81641,x81642),x81643),x81644)))
% 191.21/191.74 [8165]~P6(x81652)+E(f773(f773(f8(x81651,x81652),f773(f773(f10(x81652,x81652,x81651),f81(x81652)),x81653)),x81654),f773(f81(x81652),f773(f773(f8(x81651,x81652),x81653),x81654)))
% 191.21/191.74 [8167]E(f773(f773(f8(x81671,a847),x81672),f773(f773(f3(f855(x81671,a841)),x81673),f773(f773(f302(x81671),x81674),f180(f855(x81671,a841))))),f773(f773(f3(a847),f773(f773(f8(x81671,a847),x81672),x81673)),f773(x81672,x81674)))+~P1(f773(f773(f334(x81671),x81674),x81673))
% 191.21/191.74 [8186]P1(f773(f773(f232(f855(x81861,a841)),x81862),x81863))+~P1(f773(f773(f232(f855(x81861,a841)),f773(f773(f302(x81861),x81864),x81862)),x81863))
% 191.21/191.74 [8394]P36(x83941,x83942)+~P36(x83941,f773(f773(f302(f854(x83941,x83941)),f773(f773(f241(x83941,x83941),x83943),x83944)),x83942))
% 191.21/191.74 [8395]P56(x83951,x83952)+~P56(x83951,f773(f773(f302(f854(x83951,x83951)),f773(f773(f241(x83951,x83951),x83953),x83954)),x83952))
% 191.21/191.74 [8403]~P100(x84031)+E(f773(f773(f138(x84031,x84031,f7(x84031)),x84032),f773(f773(f138(x84031,x84031,f7(x84031)),x84033),x84034)),f773(f773(f138(x84031,x84031,f7(x84031)),x84033),f773(f773(f138(x84031,x84031,f7(x84031)),x84032),x84034)))
% 191.21/191.74 [8413]E(x84131,x84132)+~P1(f773(f64(x84133,x84134,f773(f773(f302(x84133),x84131),f180(f855(x84133,a841)))),x84132))
% 191.21/191.74 [8418]E(f773(f166(x84181,x84182,x84183),x84184),f183(x84182))+P1(f773(f773(f334(x84181),x84184),f773(f303(f854(x84181,x84182),x84181,f240(x84181,x84182)),f773(f158(f854(x84181,x84182)),x84183))))
% 191.21/191.74 [8424]E(f773(f773(f125(x84241),f773(f773(f159(x84241),x84242),x84243)),f773(f773(f159(x84241),x84244),f773(f773(f128(x84241),x84242),x84243))),f773(f773(f159(x84241),f773(f773(f82(a847),x84242),x84244)),x84243))+~P1(f773(f773(f232(a847),f773(f773(f82(a847),x84242),x84244)),f773(f181(f848(x84241)),x84243)))
% 191.21/191.74 [8468]P1(f773(f63(x84681),x84682))+~E(x84682,f773(f303(a847,x84681,x84683),f773(f256(a847),f773(f773(f9(a847,a847,a841),f233(a847)),x84684))))
% 191.21/191.74 [8488]~P83(x84881)+E(f773(f132(x84881,x84881,f82(x84881),f773(f773(f82(x84881),x84882),x84883)),x84884),f773(f773(f82(x84881),x84882),f773(f132(x84881,x84881,f82(x84881),x84883),x84884)))
% 191.21/191.74 [8520]P1(f773(f773(f232(f855(x85201,a841)),f773(f261(x85201,x85202),x85203)),f773(f261(x85201,x85202),x85204)))+~P1(f773(f773(f232(f855(f854(x85201,x85202),a841)),x85203),x85204))
% 191.21/191.74 [8531]~P1(f773(f773(f232(a847),x85312),x85314))+P1(f773(f773(f232(f855(x85311,a841)),f773(f158(x85311),f773(f773(f159(x85311),x85312),x85313))),f773(f158(x85311),f773(f773(f159(x85311),x85314),x85313))))
% 191.21/191.74 [8532]~P1(f773(f773(f232(a847),x85324),x85322))+P1(f773(f773(f232(f855(x85321,a841)),f773(f158(x85321),f773(f773(f128(x85321),x85322),x85323))),f773(f158(x85321),f773(f773(f128(x85321),x85324),x85323))))
% 191.21/191.74 [8575]~P1(f773(f63(x85751),f773(f773(f3(f855(x85751,a841)),x85752),x85754)))+P1(f773(f63(x85751),f773(f773(f3(f855(x85751,a841)),x85752),f773(f773(f302(x85751),x85753),x85754))))
% 191.21/191.74 [8609]P1(f773(f773(f334(f854(x86091,x86091)),x86092),f300(x86091,x86093)))+~P1(f773(f773(f334(f854(x86091,x86091)),x86092),f773(f773(f173(f854(x86091,x86091),a841),x86094),x86093)))
% 191.21/191.74 [8684]~P1(f773(f63(x86841),f773(f773(f3(f855(x86841,a841)),x86842),f773(f773(f302(x86841),x86844),x86843))))+P1(f773(f63(x86841),f773(f773(f3(f855(x86841,a841)),x86842),x86843)))
% 191.21/191.74 [8827]~E(f773(f166(x88271,x88272,x88273),x88274),f183(x88272))+~P1(f773(f773(f334(x88271),x88274),f773(f303(f854(x88271,x88272),x88271,f240(x88271,x88272)),f773(f158(f854(x88271,x88272)),x88273))))
% 191.21/191.74 [8864]~P100(x88641)+P1(f773(f773(f232(x88641),f773(f773(f179(x88641),x88642),f773(f773(f236(x88641),x88643),x88644))),f773(f773(f236(x88641),f773(f773(f179(x88641),x88642),x88643)),f773(f773(f179(x88641),x88642),x88644))))
% 191.21/191.74 [8865]~P93(x88651)+P1(f773(f773(f232(x88651),f773(f773(f103(x88651),x88652),f773(f773(f104(x88651),x88653),x88654))),f773(f773(f104(x88651),f773(f773(f103(x88651),x88652),x88653)),f773(f773(f103(x88651),x88652),x88654))))
% 191.21/191.74 [9009]E(x90091,x90092)+~P1(f773(f773(f334(f854(x90093,x90093)),f773(f773(f241(x90093,x90093),x90091),x90092)),f773(f158(f854(x90093,x90093)),f773(f773(f167(x90093,x90093),x90094),x90094))))
% 191.21/191.74 [9039]~P1(f773(f773(f334(f854(x90391,x90391)),f773(f773(f241(x90391,x90391),x90393),x90392)),f300(x90391,x90394)))+~P36(x90391,f773(f773(f302(f854(x90391,x90391)),f773(f773(f241(x90391,x90391),x90392),x90393)),x90394))
% 191.21/191.74 [9040]~P1(f773(f773(f334(f854(x90401,x90401)),f773(f773(f241(x90401,x90401),x90403),x90402)),f300(x90401,x90404)))+~P56(x90401,f773(f773(f302(f854(x90401,x90401)),f773(f773(f241(x90401,x90401),x90402),x90403)),x90404))
% 191.21/191.74 [9084]~P100(x90841)+P1(f773(f773(f232(x90841),f773(f773(f179(x90841),f773(f773(f236(x90841),x90842),x90843)),f773(f773(f236(x90841),x90842),x90844))),f773(f773(f236(x90841),x90842),f773(f773(f179(x90841),x90843),x90844))))
% 191.21/191.74 [9085]~P93(x90851)+P1(f773(f773(f232(x90851),f773(f773(f103(x90851),f773(f773(f104(x90851),x90852),x90853)),f773(f773(f104(x90851),x90852),x90854))),f773(f773(f104(x90851),x90852),f773(f773(f103(x90851),x90853),x90854))))
% 191.21/191.74 [9148]~E(f773(f303(x91482,x91481,x91483),f239(f855(x91482,a841))),f239(f855(x91481,a841)))+P1(f773(f773(f232(f855(x91481,a841)),f773(f81(f855(x91481,a841)),f773(f303(x91482,x91481,x91483),x91484))),f773(f303(x91482,x91481,x91483),f773(f81(f855(x91482,a841)),x91484))))
% 191.21/191.74 [9451]P1(f773(f773(f334(f854(x94511,x94511)),f773(f773(f241(x94511,x94511),x94512),x94513)),f773(f278(x94511,x94511),f773(f773(f281(x94511,x94511,x94511),x94514),f300(x94511,x94514)))))+~P1(f773(f773(f334(f854(x94511,x94511)),f773(f773(f241(x94511,x94511),x94512),x94513)),f773(f773(f281(x94511,x94511,x94511),f773(f278(x94511,x94511),x94514)),f300(x94511,f773(f278(x94511,x94511),x94514)))))
% 191.21/191.74 [9452]~P1(f773(f773(f334(f854(x94521,x94521)),f773(f773(f241(x94521,x94521),x94522),x94523)),f773(f278(x94521,x94521),f773(f773(f281(x94521,x94521,x94521),x94524),f300(x94521,x94524)))))+P1(f773(f773(f334(f854(x94521,x94521)),f773(f773(f241(x94521,x94521),x94522),x94523)),f773(f773(f281(x94521,x94521,x94521),f773(f278(x94521,x94521),x94524)),f300(x94521,f773(f278(x94521,x94521),x94524)))))
% 191.21/191.74 [9477]~P1(f773(f773(f334(x94772),x94774),f773(f259(x94771,x94772),x94773)))+P1(f773(f773(f334(f854(x94771,x94772)),f773(f773(f241(x94771,x94772),f594(x94773,x94771,x94774,x94772)),x94774)),x94773))
% 191.21/191.74 [9478]~P1(f773(f773(f334(x94782),x94784),f773(f259(x94781,x94782),x94783)))+P1(f773(f773(f334(f854(x94781,x94782)),f773(f773(f241(x94781,x94782),f595(x94783,x94781,x94784,x94782)),x94784)),x94783))
% 191.21/191.74 [9497]~P1(f773(f773(f334(x94971),x94974),f773(f773(f103(f855(x94971,a841)),x94972),x94973)))+P1(f773(f773(f773(f103(f855(x94971,a841)),f773(f773(f9(x94971,f855(x94971,a841),a841),f334(x94971)),x94972)),f773(f773(f9(x94971,f855(x94971,a841),a841),f334(x94971)),x94973)),x94974))
% 191.21/191.74 [9498]~P1(f773(f773(f334(x94981),x94984),f773(f773(f104(f855(x94981,a841)),x94982),x94983)))+P1(f773(f773(f773(f104(f855(x94981,a841)),f773(f773(f9(x94981,f855(x94981,a841),a841),f334(x94981)),x94982)),f773(f773(f9(x94981,f855(x94981,a841),a841),f334(x94981)),x94983)),x94984))
% 191.21/191.74 [9571]~P1(f773(f773(f334(f854(x95711,x95711)),f773(f773(f241(x95711,x95711),x95714),x95713)),f773(f773(f281(x95711,x95711,x95711),x95712),f300(x95711,x95712))))+P1(f773(f773(f334(f854(x95711,x95711)),f773(f773(f241(x95711,x95711),f655(x95712,x95713,x95714,x95711)),x95713)),x95712))
% 191.21/191.74 [9606]P1(f773(f773(f334(x96061),x96062),f773(f773(f103(f855(x96061,a841)),x96063),x96064)))+~P1(f773(f773(f773(f103(f855(x96061,a841)),f773(f773(f9(x96061,f855(x96061,a841),a841),f334(x96061)),x96063)),f773(f773(f9(x96061,f855(x96061,a841),a841),f334(x96061)),x96064)),x96062))
% 191.21/191.74 [9607]P1(f773(f773(f334(x96071),x96072),f773(f773(f104(f855(x96071,a841)),x96073),x96074)))+~P1(f773(f773(f773(f104(f855(x96071,a841)),f773(f773(f9(x96071,f855(x96071,a841),a841),f334(x96071)),x96073)),f773(f773(f9(x96071,f855(x96071,a841),a841),f334(x96071)),x96074)),x96072))
% 191.21/191.74 [9885]P34(x98851,f773(f773(f9(x98851,f855(f854(x98851,x98851),a841),f855(x98851,a841)),f773(f773(f10(f855(x98851,f855(f855(f854(x98851,x98851),a841),a841)),f855(f855(f854(x98851,x98851),a841),f855(x98851,a841)),x98851),f9(x98851,f855(f854(x98851,x98851),a841),a841)),f773(f773(f10(f855(x98851,f854(x98851,x98851)),f855(x98851,f855(f855(f854(x98851,x98851),a841),a841)),x98851),f773(f10(f854(x98851,x98851),f855(f855(f854(x98851,x98851),a841),a841),x98851),f334(f854(x98851,x98851)))),f241(x98851,x98851)))),x98852),x98853,x98854)+~P1(f773(f773(f334(f854(f848(x98851),f848(x98851))),f773(f773(f241(f848(x98851),f848(x98851)),x98853),x98854)),f147(x98851,x98852)))
% 191.21/191.74 [9889]P57(x98891,f773(f773(f9(x98891,f855(f854(x98891,x98891),a841),f855(x98891,a841)),f773(f773(f10(f855(x98891,f855(f855(f854(x98891,x98891),a841),a841)),f855(f855(f854(x98891,x98891),a841),f855(x98891,a841)),x98891),f9(x98891,f855(f854(x98891,x98891),a841),a841)),f773(f773(f10(f855(x98891,f854(x98891,x98891)),f855(x98891,f855(f855(f854(x98891,x98891),a841),a841)),x98891),f773(f10(f854(x98891,x98891),f855(f855(f854(x98891,x98891),a841),a841),x98891),f334(f854(x98891,x98891)))),f241(x98891,x98891)))),x98892),x98893,x98894)+~P1(f773(f773(f334(f854(f855(x98891,a841),f855(x98891,a841))),f773(f773(f241(f855(x98891,a841),f855(x98891,a841)),x98893),x98894)),f324(x98891,x98892)))
% 191.21/191.74 [9918]E(x99181,x99182)+~E(f773(f773(f9(x99183,f855(f854(x99183,x99184),a841),f855(x99184,a841)),f773(f773(f10(f855(x99184,f855(f855(f854(x99183,x99184),a841),a841)),f855(f855(f854(x99183,x99184),a841),f855(x99184,a841)),x99183),f9(x99184,f855(f854(x99183,x99184),a841),a841)),f773(f773(f10(f855(x99184,f854(x99183,x99184)),f855(x99184,f855(f855(f854(x99183,x99184),a841),a841)),x99183),f773(f10(f854(x99183,x99184),f855(f855(f854(x99183,x99184),a841),a841),x99184),f334(f854(x99183,x99184)))),f241(x99183,x99184)))),x99181),f773(f773(f9(x99183,f855(f854(x99183,x99184),a841),f855(x99184,a841)),f773(f773(f10(f855(x99184,f855(f855(f854(x99183,x99184),a841),a841)),f855(f855(f854(x99183,x99184),a841),f855(x99184,a841)),x99183),f9(x99184,f855(f854(x99183,x99184),a841),a841)),f773(f773(f10(f855(x99184,f854(x99183,x99184)),f855(x99184,f855(f855(f854(x99183,x99184),a841),a841)),x99183),f773(f10(f854(x99183,x99184),f855(f855(f854(x99183,x99184),a841),a841),x99184),f334(f854(x99183,x99184)))),f241(x99183,x99184)))),x99182))
% 191.21/191.74 [9921]~P34(x99211,f773(f773(f9(x99211,f855(f854(x99211,x99211),a841),f855(x99211,a841)),f773(f773(f10(f855(x99211,f855(f855(f854(x99211,x99211),a841),a841)),f855(f855(f854(x99211,x99211),a841),f855(x99211,a841)),x99211),f9(x99211,f855(f854(x99211,x99211),a841),a841)),f773(f773(f10(f855(x99211,f854(x99211,x99211)),f855(x99211,f855(f855(f854(x99211,x99211),a841),a841)),x99211),f773(f10(f854(x99211,x99211),f855(f855(f854(x99211,x99211),a841),a841),x99211),f334(f854(x99211,x99211)))),f241(x99211,x99211)))),x99214),x99212,x99213)+P1(f773(f773(f334(f854(f848(x99211),f848(x99211))),f773(f773(f241(f848(x99211),f848(x99211)),x99212),x99213)),f147(x99211,x99214)))
% 191.21/191.74 [9922]~P57(x99221,f773(f773(f9(x99221,f855(f854(x99221,x99221),a841),f855(x99221,a841)),f773(f773(f10(f855(x99221,f855(f855(f854(x99221,x99221),a841),a841)),f855(f855(f854(x99221,x99221),a841),f855(x99221,a841)),x99221),f9(x99221,f855(f854(x99221,x99221),a841),a841)),f773(f773(f10(f855(x99221,f854(x99221,x99221)),f855(x99221,f855(f855(f854(x99221,x99221),a841),a841)),x99221),f773(f10(f854(x99221,x99221),f855(f855(f854(x99221,x99221),a841),a841),x99221),f334(f854(x99221,x99221)))),f241(x99221,x99221)))),x99224),x99222,x99223)+P1(f773(f773(f334(f854(f855(x99221,a841),f855(x99221,a841))),f773(f773(f241(f855(x99221,a841),f855(x99221,a841)),x99222),x99223)),f324(x99221,x99224)))
% 191.21/191.74 [7416]~P88(x74161)+E(f773(f773(f82(x74161),f773(f106(x74161),x74162)),f773(f773(f82(x74161),f773(f106(x74161),x74163)),x74164)),f773(f773(f82(x74161),f773(f106(x74161),f773(f773(f82(a1),x74162),x74163))),x74164))
% 191.21/191.74 [7417]~P88(x74171)+E(f773(f773(f82(x74171),f773(f106(x74171),x74172)),f773(f773(f3(x74171),f773(f106(x74171),x74173)),x74174)),f773(f773(f3(x74171),f773(f106(x74171),f773(f773(f82(a1),x74172),x74173))),x74174))
% 191.21/191.74 [7418]~P88(x74181)+E(f773(f773(f83(x74181),f773(f106(x74181),x74182)),f773(f773(f83(x74181),f773(f106(x74181),x74183)),x74184)),f773(f773(f83(x74181),f773(f106(x74181),f773(f773(f83(a1),x74182),x74183))),x74184))
% 191.21/191.74 [7465]~P2(x74651)+E(f773(f155(x74651),f773(f773(f143(x74652,x74651),f773(f18(x74651,x74652),x74653)),x74654)),f773(f773(f83(x74651),f773(f102(x74651),f773(f181(f848(x74652)),x74654))),x74653))
% 191.21/191.74 [7701]E(f773(f265(x77011,f773(f773(f140(f854(a101,x77011)),x77012),x77013)),x77014),f773(f250(a101,x77011),x77012))+~P1(f773(f773(f233(a101),x77014),f773(f240(a101,x77011),x77012)))
% 191.21/191.74 [7749]~P88(x77491)+E(f773(f773(f82(x77491),f773(f106(x77491),x77492)),f773(f773(f3(x77491),x77493),f773(f106(x77491),x77494))),f773(f773(f82(x77491),f773(f106(x77491),f773(f773(f82(a1),x77492),f773(f81(a1),x77494)))),x77493))
% 191.21/191.74 [7880]E(f773(f265(x78801,x78802),f773(f773(f3(a101),x78803),f773(f240(a101,x78801),x78804))),f773(f265(x78801,f773(f773(f140(f854(a101,x78801)),x78804),x78802)),x78803))+P1(f773(f773(f233(a101),x78803),f773(f240(a101,x78801),x78804)))
% 191.21/191.74 [8311]~P1(f773(f773(f334(x83111),x83112),f773(f158(x83111),f116(x83111,x83114))))+P1(f773(f773(f334(x83111),x83112),f773(f158(x83111),f116(x83111,f773(f773(f125(x83111),x83113),x83114)))))
% 191.21/191.74 [8312]~P1(f773(f773(f334(x83121),x83122),f773(f158(x83121),f116(x83121,x83123))))+P1(f773(f773(f334(x83121),x83122),f773(f158(x83121),f116(x83121,f773(f773(f125(x83121),x83123),x83124)))))
% 191.21/191.74 [8335]E(f773(f773(f103(f855(x83351,a841)),f773(f773(f104(f855(x83351,a841)),x83352),x83353)),x83354),f773(f773(f104(f855(x83351,a841)),x83352),f773(f773(f103(f855(x83351,a841)),x83353),x83354)))+~P1(f773(f773(f232(f855(x83351,a841)),x83354),x83352))
% 191.21/191.74 [8622]~E(f773(f773(f103(f855(x86221,a841)),f773(f773(f104(f855(x86221,a841)),x86223),x86224)),x86222),f773(f773(f104(f855(x86221,a841)),x86223),f773(f773(f103(f855(x86221,a841)),x86224),x86222)))+P1(f773(f773(f232(f855(x86221,a841)),x86222),x86223))
% 191.21/191.74 [8871]~P1(f773(f773(f232(f855(x88711,a841)),x88712),f773(f773(f103(f855(x88711,a841)),x88713),x88714)))+P1(f773(f773(f232(f855(x88711,a841)),f773(f773(f3(f855(x88711,a841)),x88712),x88713)),x88714))
% 191.21/191.74 [8990]P1(f773(f773(f232(f855(x89901,a841)),x89902),f773(f773(f103(f855(x89901,a841)),x89903),x89904)))+~P1(f773(f773(f232(f855(x89901,a841)),f773(f773(f3(f855(x89901,a841)),x89902),x89903)),x89904))
% 191.21/191.74 [9066]~P79(x90661)+E(f773(f77(x90661),f773(f773(f8(x90662,x90661),f773(f773(f10(x90661,x90661,x90662),f77(x90661)),x90663)),x90664)),f773(f773(f8(x90662,x90661),f773(f773(f10(x90661,x90661,x90662),f77(x90661)),x90663)),x90664))
% 191.21/191.74 [9211]~P79(x92111)+P1(f773(f773(f232(x92111),f2(x92111)),f773(f773(f8(x92112,x92111),f773(f773(f10(x92111,x92111,x92112),f77(x92111)),x92113)),x92114)))
% 191.21/191.74 [9214]~P6(x92141)+E(f773(f155(x92141),f773(f773(f143(x92142,x92141),f773(f75(x92141,x92141,x92142,f81(x92141)),x92143)),x92144)),f773(f81(x92141),f773(f155(x92141),f773(f773(f143(x92142,x92141),x92143),x92144))))
% 191.21/191.74 [9351]~P79(x93511)+P1(f773(f773(f232(x93511),f773(f77(x93511),f773(f773(f8(x93512,x93511),x93513),x93514))),f773(f773(f8(x93512,x93511),f773(f773(f10(x93511,x93511,x93512),f77(x93511)),x93513)),x93514)))
% 191.21/191.74 [9379]~E(f773(f773(f82(a847),x93791),x93794),f773(f773(f82(a847),x93793),x93792))+P1(f773(f773(f334(f854(f854(a847,a847),f854(a847,a847))),f773(f773(f241(f854(a847,a847),f854(a847,a847)),f773(f773(f241(a847,a847),x93791),x93792)),f773(f773(f241(a847,a847),x93793),x93794))),a111))
% 191.21/191.74 [9380]~P1(f773(f773(f233(a847),x93801),x93803))+P1(f773(f773(f334(f854(f854(a847,a847),f854(a847,a847))),f773(f773(f241(f854(a847,a847),f854(a847,a847)),f773(f773(f241(a847,a847),x93801),x93802)),f773(f773(f241(a847,a847),x93803),x93804))),a40))
% 191.21/191.74 [9381]~P1(f773(f773(f233(a847),x93811),x93813))+P1(f773(f773(f334(f854(f854(a847,a847),f854(a847,a847))),f773(f773(f241(f854(a847,a847),f854(a847,a847)),f773(f773(f241(a847,a847),x93811),x93812)),f773(f773(f241(a847,a847),x93813),x93814))),a72))
% 191.21/191.74 [9520]E(f773(f773(f82(a847),x95201),x95202),f773(f773(f82(a847),x95203),x95204))+~P1(f773(f773(f334(f854(f854(a847,a847),f854(a847,a847))),f773(f773(f241(f854(a847,a847),f854(a847,a847)),f773(f773(f241(a847,a847),x95201),x95204)),f773(f773(f241(a847,a847),x95203),x95202))),a111))
% 191.21/191.74 [9564]~P1(f773(f773(f334(x95642),x95644),f773(f773(f46(x95641,f855(x95642,a841)),f239(f855(x95641,a841))),x95643)))+P1(f773(f773(f773(f46(x95641,f855(x95642,a841)),f239(f855(x95641,a841))),f773(f773(f10(f855(x95642,a841),f855(x95642,a841),x95641),f773(f9(x95642,f855(x95642,a841),a841),f334(x95642))),x95643)),x95644))
% 191.21/191.74 [9565]~P1(f773(f773(f334(x95652),x95654),f773(f773(f47(x95651,f855(x95652,a841)),f239(f855(x95651,a841))),x95653)))+P1(f773(f773(f773(f47(x95651,f855(x95652,a841)),f239(f855(x95651,a841))),f773(f773(f10(f855(x95652,a841),f855(x95652,a841),x95651),f773(f9(x95652,f855(x95652,a841),a841),f334(x95652))),x95653)),x95654))
% 191.21/191.74 [9631]~P1(f773(f56(x96311,x96312),f773(f773(f241(a1,a1),x96314),x96313)))+P1(f773(f56(f773(f81(a1),x96311),x96312),f773(f773(f241(a1,a1),f773(f773(f773(f98(a1),f773(f773(a330,x96313),f2(a1))),f773(f81(a1),x96314)),f773(f773(f3(a1),f773(f81(a1),x96314)),f80(a1)))),f773(f773(f773(f98(a1),f773(f773(a330,x96313),f2(a1))),f2(a1)),f773(f773(f3(a1),x96312),x96313)))))
% 191.21/191.74 [9640]P1(f773(f773(f334(x96401),x96402),f773(f773(f46(x96403,f855(x96401,a841)),f239(f855(x96403,a841))),x96404)))+~P1(f773(f773(f773(f46(x96403,f855(x96401,a841)),f239(f855(x96403,a841))),f773(f773(f10(f855(x96401,a841),f855(x96401,a841),x96403),f773(f9(x96401,f855(x96401,a841),a841),f334(x96401))),x96404)),x96402))
% 191.21/191.74 [9641]P1(f773(f773(f334(x96411),x96412),f773(f773(f47(x96413,f855(x96411,a841)),f239(f855(x96413,a841))),x96414)))+~P1(f773(f773(f773(f47(x96413,f855(x96411,a841)),f239(f855(x96413,a841))),f773(f773(f10(f855(x96411,a841),f855(x96411,a841),x96413),f773(f9(x96411,f855(x96411,a841),a841),f334(x96411))),x96414)),x96412))
% 191.21/191.74 [9652]E(f773(f773(f46(a847,f855(x96521,a841)),f239(f855(a847,a841))),x96522),f773(f773(f46(a847,f855(x96521,a841)),f239(f855(a847,a841))),x96523))+~E(f773(f773(f46(a847,f855(x96521,a841)),f773(f294(a847,f2(a847)),f398(x96522,x96524,x96523,x96521))),x96523),f773(f773(f46(a847,f855(x96521,a841)),f773(f294(a847,f2(a847)),f773(f773(f82(a847),f398(x96522,x96524,x96523,x96521)),x96524))),x96522))
% 191.21/191.74 [9982]~P1(f773(f773(f232(f855(f854(x99821,x99822),a841)),x99823),x99824))+P1(f773(f773(f232(f855(x99821,f855(x99822,a841))),f773(f773(f9(x99821,f855(f854(x99821,x99822),a841),f855(x99822,a841)),f773(f773(f10(f855(x99822,f855(f855(f854(x99821,x99822),a841),a841)),f855(f855(f854(x99821,x99822),a841),f855(x99822,a841)),x99821),f9(x99822,f855(f854(x99821,x99822),a841),a841)),f773(f773(f10(f855(x99822,f854(x99821,x99822)),f855(x99822,f855(f855(f854(x99821,x99822),a841),a841)),x99821),f773(f10(f854(x99821,x99822),f855(f855(f854(x99821,x99822),a841),a841),x99822),f334(f854(x99821,x99822)))),f241(x99821,x99822)))),x99823)),f773(f773(f9(x99821,f855(f854(x99821,x99822),a841),f855(x99822,a841)),f773(f773(f10(f855(x99822,f855(f855(f854(x99821,x99822),a841),a841)),f855(f855(f854(x99821,x99822),a841),f855(x99822,a841)),x99821),f9(x99822,f855(f854(x99821,x99822),a841),a841)),f773(f773(f10(f855(x99822,f854(x99821,x99822)),f855(x99822,f855(f855(f854(x99821,x99822),a841),a841)),x99821),f773(f10(f854(x99821,x99822),f855(f855(f854(x99821,x99822),a841),a841),x99822),f334(f854(x99821,x99822)))),f241(x99821,x99822)))),x99824)))
% 191.21/191.74 [9998]P1(f773(f773(f232(f855(f854(x99981,x99982),a841)),x99983),x99984))+~P1(f773(f773(f232(f855(x99981,f855(x99982,a841))),f773(f773(f9(x99981,f855(f854(x99981,x99982),a841),f855(x99982,a841)),f773(f773(f10(f855(x99982,f855(f855(f854(x99981,x99982),a841),a841)),f855(f855(f854(x99981,x99982),a841),f855(x99982,a841)),x99981),f9(x99982,f855(f854(x99981,x99982),a841),a841)),f773(f773(f10(f855(x99982,f854(x99981,x99982)),f855(x99982,f855(f855(f854(x99981,x99982),a841),a841)),x99981),f773(f10(f854(x99981,x99982),f855(f855(f854(x99981,x99982),a841),a841),x99982),f334(f854(x99981,x99982)))),f241(x99981,x99982)))),x99983)),f773(f773(f9(x99981,f855(f854(x99981,x99982),a841),f855(x99982,a841)),f773(f773(f10(f855(x99982,f855(f855(f854(x99981,x99982),a841),a841)),f855(f855(f854(x99981,x99982),a841),f855(x99982,a841)),x99981),f9(x99982,f855(f854(x99981,x99982),a841),a841)),f773(f773(f10(f855(x99982,f854(x99981,x99982)),f855(x99982,f855(f855(f854(x99981,x99982),a841),a841)),x99981),f773(f10(f854(x99981,x99982),f855(f855(f854(x99981,x99982),a841),a841),x99982),f334(f854(x99981,x99982)))),f241(x99981,x99982)))),x99984)))
% 191.21/191.74 [9111]~P1(f773(f773(f334(f854(x91111,x91111)),x91112),f300(x91111,x91114)))+P1(f773(f773(f334(f854(x91111,x91111)),x91112),f300(x91111,f773(f773(f103(f855(f854(x91111,x91111),a841)),x91113),x91114))))
% 191.21/191.74 [9112]~P1(f773(f773(f334(f854(x91121,x91121)),x91122),f300(x91121,x91123)))+P1(f773(f773(f334(f854(x91121,x91121)),x91122),f300(x91121,f773(f773(f103(f855(f854(x91121,x91121),a841)),x91123),x91124))))
% 191.21/191.74 [9443]~E(f773(f158(x94431),x94434),f169(x94431,x94432,x94433))+E(f166(x94431,x94432,f773(f773(f143(x94431,f854(x94431,x94432)),f773(f773(f20(x94431,x94432,f854(x94431,x94432)),f241(x94431,x94432)),f773(f773(f10(f851(x94432),x94432,x94431),f231(x94432)),x94433))),x94434)),x94433)
% 191.21/191.74 [9734]~P1(f773(f773(f233(a847),f773(f773(f82(a847),x97341),x97344)),f773(f773(f82(a847),x97343),x97342)))+P1(f773(f773(f233(a1),f773(a91,f773(f277(f854(a847,a847),f854(a847,a847),a111),f773(f773(f302(f854(a847,a847)),f773(f773(f241(a847,a847),x97341),x97342)),f180(f855(f854(a847,a847),a841)))))),f773(a91,f773(f277(f854(a847,a847),f854(a847,a847),a111),f773(f773(f302(f854(a847,a847)),f773(f773(f241(a847,a847),x97343),x97344)),f180(f855(f854(a847,a847),a841)))))))
% 191.21/191.74 [9735]~P1(f773(f773(f232(a847),f773(f773(f82(a847),x97351),x97354)),f773(f773(f82(a847),x97353),x97352)))+P1(f773(f773(f232(a1),f773(a91,f773(f277(f854(a847,a847),f854(a847,a847),a111),f773(f773(f302(f854(a847,a847)),f773(f773(f241(a847,a847),x97351),x97352)),f180(f855(f854(a847,a847),a841)))))),f773(a91,f773(f277(f854(a847,a847),f854(a847,a847),a111),f773(f773(f302(f854(a847,a847)),f773(f773(f241(a847,a847),x97353),x97354)),f180(f855(f854(a847,a847),a841)))))))
% 191.21/191.74 [9823]P1(f773(f773(f233(a847),f773(f773(f82(a847),x98231),x98232)),f773(f773(f82(a847),x98233),x98234)))+~P1(f773(f773(f233(a1),f773(a91,f773(f277(f854(a847,a847),f854(a847,a847),a111),f773(f773(f302(f854(a847,a847)),f773(f773(f241(a847,a847),x98231),x98234)),f180(f855(f854(a847,a847),a841)))))),f773(a91,f773(f277(f854(a847,a847),f854(a847,a847),a111),f773(f773(f302(f854(a847,a847)),f773(f773(f241(a847,a847),x98233),x98232)),f180(f855(f854(a847,a847),a841)))))))
% 191.21/191.74 [9824]P1(f773(f773(f232(a847),f773(f773(f82(a847),x98241),x98242)),f773(f773(f82(a847),x98243),x98244)))+~P1(f773(f773(f232(a1),f773(a91,f773(f277(f854(a847,a847),f854(a847,a847),a111),f773(f773(f302(f854(a847,a847)),f773(f773(f241(a847,a847),x98241),x98244)),f180(f855(f854(a847,a847),a841)))))),f773(a91,f773(f277(f854(a847,a847),f854(a847,a847),a111),f773(f773(f302(f854(a847,a847)),f773(f773(f241(a847,a847),x98243),x98242)),f180(f855(f854(a847,a847),a841)))))))
% 191.21/191.74 [9871]P1(f773(f773(f232(f855(x98711,a841)),f773(f773(f46(a847,f855(x98711,a841)),f239(f855(a847,a841))),x98712)),f773(f773(f46(a847,f855(x98711,a841)),f239(f855(a847,a841))),x98713)))+~P1(f773(f773(f232(f855(x98711,a841)),f773(f773(f46(a847,f855(x98711,a841)),f773(f294(a847,f2(a847)),f399(x98713,x98714,x98712,x98711))),x98712)),f773(f773(f46(a847,f855(x98711,a841)),f773(f294(a847,f2(a847)),f773(f773(f82(a847),f399(x98713,x98714,x98712,x98711)),x98714))),x98713)))
% 191.21/191.74 [9924]P1(f773(f773(f232(a101),x99244),f2(a101)))+E(f773(f773(f253(f854(a101,a101),f854(x99241,f855(a850,a839)),f854(a101,a101),f854(f855(a101,f855(a841,f851(f849(x99241)))),f854(a101,a101))),f773(x99242,x99243)),f773(f773(f10(f855(f855(a101,f855(a841,f851(f849(x99241)))),f855(f854(a101,a101),f854(f855(a101,f855(a841,f851(f849(x99241)))),f854(a101,a101)))),f855(f854(a101,a101),f854(f855(a101,f855(a841,f851(f849(x99241)))),f854(a101,a101))),f854(x99241,f855(a850,a839))),f773(f253(f854(a101,a101),f855(a101,f855(a841,f851(f849(x99241)))),f854(a101,a101),f854(f855(a101,f855(a841,f851(f849(x99241)))),f854(a101,a101))),f272(x99241,x99242,f773(f773(f3(a101),x99244),f80(a101)),x99243))),f773(f773(f10(f855(f855(a101,f855(a841,f851(f849(x99241)))),f855(a101,f855(a841,f851(f849(x99241))))),f855(f855(a101,f855(a841,f851(f849(x99241)))),f855(f854(a101,a101),f854(f855(a101,f855(a841,f851(f849(x99241)))),f854(a101,a101)))),f854(x99241,f855(a850,a839))),f773(f10(f855(a101,f855(a841,f851(f849(x99241)))),f855(f854(a101,a101),f854(f855(a101,f855(a841,f851(f849(x99241)))),f854(a101,a101))),f855(a101,f855(a841,f851(f849(x99241))))),f241(f855(a101,f855(a841,f851(f849(x99241)))),f854(a101,a101)))),f773(f773(f10(f855(a101,f855(a841,f851(f849(x99241)))),f855(f855(a101,f855(a841,f851(f849(x99241)))),f855(a101,f855(a841,f851(f849(x99241))))),f854(x99241,f855(a850,a839))),f51(x99241)),f773(f773(f10(x99241,f855(a101,f855(a841,f851(f849(x99241)))),f854(x99241,f855(a850,a839))),f49(x99241)),f240(x99241,f855(a850,a839))))))),f272(x99241,x99242,x99244,x99243))
% 191.21/191.74 [9973]~P1(f773(f773(f334(x99732),x99734),f773(f259(x99731,x99732),x99733)))+P1(f773(f247(x99731,x99732,f773(f773(f9(x99731,f855(f854(x99731,x99732),a841),f855(x99732,a841)),f773(f773(f10(f855(x99732,f855(f855(f854(x99731,x99732),a841),a841)),f855(f855(f854(x99731,x99732),a841),f855(x99732,a841)),x99731),f9(x99732,f855(f854(x99731,x99732),a841),a841)),f773(f773(f10(f855(x99732,f854(x99731,x99732)),f855(x99732,f855(f855(f854(x99731,x99732),a841),a841)),x99731),f773(f10(f854(x99731,x99732),f855(f855(f854(x99731,x99732),a841),a841),x99732),f334(f854(x99731,x99732)))),f241(x99731,x99732)))),x99733)),x99734))
% 191.21/191.74 [9974]~P1(f773(f773(f334(x99741),x99744),f773(f261(x99741,x99742),x99743)))+P1(f773(f246(x99741,x99742,f773(f773(f9(x99741,f855(f854(x99741,x99742),a841),f855(x99742,a841)),f773(f773(f10(f855(x99742,f855(f855(f854(x99741,x99742),a841),a841)),f855(f855(f854(x99741,x99742),a841),f855(x99742,a841)),x99741),f9(x99742,f855(f854(x99741,x99742),a841),a841)),f773(f773(f10(f855(x99742,f854(x99741,x99742)),f855(x99742,f855(f855(f854(x99741,x99742),a841),a841)),x99741),f773(f10(f854(x99741,x99742),f855(f855(f854(x99741,x99742),a841),a841),x99742),f334(f854(x99741,x99742)))),f241(x99741,x99742)))),x99743)),x99744))
% 191.21/191.74 [9985]P1(f773(f773(f334(x99851),x99852),f773(f259(x99853,x99851),x99854)))+~P1(f773(f247(x99853,x99851,f773(f773(f9(x99853,f855(f854(x99853,x99851),a841),f855(x99851,a841)),f773(f773(f10(f855(x99851,f855(f855(f854(x99853,x99851),a841),a841)),f855(f855(f854(x99853,x99851),a841),f855(x99851,a841)),x99853),f9(x99851,f855(f854(x99853,x99851),a841),a841)),f773(f773(f10(f855(x99851,f854(x99853,x99851)),f855(x99851,f855(f855(f854(x99853,x99851),a841),a841)),x99853),f773(f10(f854(x99853,x99851),f855(f855(f854(x99853,x99851),a841),a841),x99851),f334(f854(x99853,x99851)))),f241(x99853,x99851)))),x99854)),x99852))
% 191.21/191.74 [9986]P1(f773(f773(f334(x99861),x99862),f773(f261(x99861,x99863),x99864)))+~P1(f773(f246(x99861,x99863,f773(f773(f9(x99861,f855(f854(x99861,x99863),a841),f855(x99863,a841)),f773(f773(f10(f855(x99863,f855(f855(f854(x99861,x99863),a841),a841)),f855(f855(f854(x99861,x99863),a841),f855(x99863,a841)),x99861),f9(x99863,f855(f854(x99861,x99863),a841),a841)),f773(f773(f10(f855(x99863,f854(x99861,x99863)),f855(x99863,f855(f855(f854(x99861,x99863),a841),a841)),x99861),f773(f10(f854(x99861,x99863),f855(f855(f854(x99861,x99863),a841),a841),x99863),f334(f854(x99861,x99863)))),f241(x99861,x99863)))),x99864)),x99862))
% 191.21/191.74 [9748]~P85(x97481)+E(f773(f773(f83(x97481),f773(f773(f82(x97481),f80(x97481)),f80(x97481))),f773(f773(f8(a847,x97481),f773(f773(f10(x97481,x97481,a847),f773(f82(x97481),x97482)),f773(f773(f9(a847,x97481,x97481),f773(f773(f10(x97481,f855(x97481,x97481),a847),f83(x97481)),f102(x97481))),x97483))),f773(f257(a847),x97484))),f773(f773(f83(x97481),f773(f102(x97481),x97484)),f773(f773(f82(x97481),x97482),f773(f773(f82(x97481),x97482),f773(f773(f83(x97481),f773(f102(x97481),f773(f773(f3(a847),x97484),f80(a847)))),x97483)))))
% 191.21/191.74 [9892]P1(f773(x98921,f591(x98922,x98923,x98924,x98921)))+P36(x98922,f773(f256(f854(x98922,x98922)),f773(f251(x98922,x98922,a841),f773(f773(f10(f855(x98922,a841),f855(x98922,a841),x98922),f773(f20(x98922,a841,a841),f773(f773(f10(a841,f855(a841,a841),x98922),a331),x98921))),f773(f773(f9(x98922,f855(x98922,x98922),f855(x98922,a841)),f773(f773(f10(f855(x98922,a841),f855(f855(x98922,x98922),f855(x98922,a841)),x98922),f10(x98922,a841,x98922)),a330)),x98923)))))
% 191.21/191.74 [9906]~P1(f773(f773(f233(a847),f773(x99064,f773(x99063,f591(x99061,x99063,x99064,x99062)))),f773(x99064,f591(x99061,x99063,x99064,x99062))))+P36(x99061,f773(f256(f854(x99061,x99061)),f773(f251(x99061,x99061,a841),f773(f773(f10(f855(x99061,a841),f855(x99061,a841),x99061),f773(f20(x99061,a841,a841),f773(f773(f10(a841,f855(a841,a841),x99061),a331),x99062))),f773(f773(f9(x99061,f855(x99061,x99061),f855(x99061,a841)),f773(f773(f10(f855(x99061,a841),f855(f855(x99061,x99061),f855(x99061,a841)),x99061),f10(x99061,a841,x99061)),a330)),x99063)))))
% 191.21/191.74 [10010]~P1(f773(f773(f334(f854(x100101,x100101)),f773(f773(f241(x100101,x100101),x100103),x100104)),f773(f773(f103(f855(f854(x100101,x100101),a841)),x100102),f300(x100101,f180(f855(f854(x100101,x100101),a841))))))+P1(f773(f773(f773(f773(f103(f855(x100101,f855(x100101,a841))),f773(f773(f9(x100101,f855(f854(x100101,x100101),a841),f855(x100101,a841)),f773(f773(f10(f855(x100101,f855(f855(f854(x100101,x100101),a841),a841)),f855(f855(f854(x100101,x100101),a841),f855(x100101,a841)),x100101),f9(x100101,f855(f854(x100101,x100101),a841),a841)),f773(f773(f10(f855(x100101,f854(x100101,x100101)),f855(x100101,f855(f855(f854(x100101,x100101),a841),a841)),x100101),f773(f10(f854(x100101,x100101),f855(f855(f854(x100101,x100101),a841),a841),x100101),f334(f854(x100101,x100101)))),f241(x100101,x100101)))),x100102)),a330),x100103),x100104))
% 191.21/191.74 [10018]P1(f773(f773(f334(f854(x100181,x100181)),f773(f773(f241(x100181,x100181),x100182),x100183)),f773(f773(f103(f855(f854(x100181,x100181),a841)),x100184),f300(x100181,f180(f855(f854(x100181,x100181),a841))))))+~P1(f773(f773(f773(f773(f103(f855(x100181,f855(x100181,a841))),f773(f773(f9(x100181,f855(f854(x100181,x100181),a841),f855(x100181,a841)),f773(f773(f10(f855(x100181,f855(f855(f854(x100181,x100181),a841),a841)),f855(f855(f854(x100181,x100181),a841),f855(x100181,a841)),x100181),f9(x100181,f855(f854(x100181,x100181),a841),a841)),f773(f773(f10(f855(x100181,f854(x100181,x100181)),f855(x100181,f855(f855(f854(x100181,x100181),a841),a841)),x100181),f773(f10(f854(x100181,x100181),f855(f855(f854(x100181,x100181),a841),a841),x100181),f334(f854(x100181,x100181)))),f241(x100181,x100181)))),x100184)),a330),x100182),x100183))
% 191.21/191.74 [9970]E(f773(f773(f140(f848(x99701)),f773(f773(f140(x99701),x99702),f773(f132(f848(x99701),f848(x99701),f125(x99701),f115(x99701)),f773(f773(f143(f848(x99701),f848(x99701)),f145(f848(x99701),x99701,f115(x99701),f773(f773(f10(f848(x99701),f855(f848(x99701),f848(x99701)),x99701),f18(f848(x99701),f848(x99701))),f773(f773(f9(x99701,f848(x99701),f848(x99701)),f140(x99701)),f115(x99701))))),x99703)))),f164(x99701,f773(f773(f140(f848(x99701)),x99704),f773(f132(f848(f848(x99701)),f848(f848(x99701)),f125(f848(x99701)),f115(f848(x99701))),f773(f773(f143(f848(x99701),f848(f848(x99701))),f145(f848(f848(x99701)),x99701,f115(f848(x99701)),f773(f18(f855(f848(x99701),f848(f848(x99701))),x99701),f773(f773(f9(f848(x99701),f848(f848(x99701)),f848(f848(x99701))),f140(f848(x99701))),f115(f848(x99701)))))),x99703))))),f164(x99701,f773(f773(f140(f848(x99701)),f773(f773(f140(x99701),x99702),x99704)),x99703)))+~P1(f773(f321(f848(f848(x99701)),f165(x99701)),f773(f773(f140(f848(x99701)),f773(f773(f140(x99701),x99702),x99704)),x99703)))
% 191.21/191.74 [10009]~P1(f773(f63(x100092),f773(f256(x100092),x100094)))+P1(f773(f63(x100091),f773(f256(x100091),f773(f773(f10(f855(x100092,a841),a841,x100091),f89(x100092)),f773(f773(f9(x100091,f855(x100092,a841),f855(x100092,a841)),f773(f773(f10(f855(x100092,f855(a841,a841)),f855(f855(x100092,a841),f855(x100092,a841)),x100091),f20(x100092,a841,a841)),f773(f773(f10(f855(x100092,a841),f855(x100092,f855(a841,a841)),x100091),f773(f10(a841,f855(a841,a841),x100092),a331)),f773(f773(f9(x100091,f855(x100092,x100091),f855(x100092,a841)),f773(f773(f10(f855(x100091,a841),f855(f855(x100092,x100091),f855(x100092,a841)),x100091),f10(x100091,a841,x100092)),a330)),x100093)))),x100094)))))
% 191.21/191.74 [7171]E(x71711,x71712)+~E(f316(x71713,x71714,x71715,x71711),f316(x71713,x71714,x71715,x71712))
% 191.21/191.74 [7172]E(x71721,x71722)+~E(f317(x71723,x71724,x71725,x71721),f317(x71723,x71724,x71725,x71722))
% 191.21/191.74 [8984]~P39(f36(x89841,x89845),x89842,x89843,x89844)+P39(x89841,x89842,x89843,f371(x89844,x89843,x89842,x89845,x89841))
% 191.21/191.74 [8985]~P39(f36(x89851,x89855),x89852,x89853,x89854)+P39(x89851,x89852,x89853,f383(x89854,x89853,x89852,x89855,x89851))
% 191.21/191.74 [8986]~P39(f36(x89865,x89861),x89864,x89863,x89862)+P39(x89861,f371(x89862,x89863,x89864,x89861,x89865),x89863,x89862)
% 191.21/191.74 [8987]~P39(f36(x89875,x89871),x89874,x89873,x89872)+P39(x89871,f383(x89872,x89873,x89874,x89871,x89875),x89873,x89872)
% 191.21/191.74 [5518]E(f773(f773(f302(x55181),x55182),f169(x55181,x55183,x55184)),f169(x55181,x55183,x55184))+~E(f773(x55184,x55182),f773(f227(x55183),x55185))
% 191.21/191.74 [5932]P1(f773(f247(x59321,x59322,x59323),x59324))+~P1(f773(f773(x59323,x59325),x59324))
% 191.21/191.74 [5934]P1(f773(f246(x59341,x59342,x59343),x59344))+~P1(f773(f773(x59343,x59344),x59345))
% 191.21/191.74 [5937]~E(f773(x59374,x59372),f773(f227(x59373),x59375))+P1(f773(f773(f334(x59371),x59372),f169(x59371,x59373,x59374)))
% 191.21/191.74 [5938]~E(f773(x59384,x59385),f773(f227(x59381),x59382))+P1(f773(f773(f334(x59381),x59382),f171(x59383,x59381,x59384)))
% 191.21/191.74 [6422]~E(x64225,f2(a101))+E(f773(f193(x64221,x64222,x64223,x64224),x64225),f117(x64222))
% 191.21/191.74 [6423]~E(x64235,f2(a101))+E(f773(f191(x64231,x64232,x64233,x64234),x64235),f124(x64232))
% 191.21/191.74 [6519]~P39(f28(x65193,x65194),x65192,x65195,x65191)+E(x65191,f773(f773(f773(a189,x65192),x65193),f773(x65194,x65192)))
% 191.21/191.74 [6564]~E(x65643,f2(a101))+E(f773(f268(x65641,x65642,x65643,x65644),x65645),f773(f241(x65641,x65642),x65645))
% 191.21/191.74 [6644]~E(f773(x66444,x66445),f183(x66442))+E(f773(f229(f851(x66441),x66442,f183(x66441),x66443),f773(x66444,x66445)),f183(x66441))
% 191.21/191.74 [7294]E(f773(x72941,x72942),f183(x72943))+~E(f773(f170(x72944,x72943,x72945,x72941),x72942),f183(x72943))
% 191.21/191.74 [7295]E(f773(x72951,x72952),f183(x72953))+~E(f773(f170(x72954,x72953,x72951,x72955),x72952),f183(x72953))
% 191.21/191.74 [7335]E(f773(f170(x73351,x73352,x73353,x73354),x73355),f773(x73353,x73355))+P1(f773(f773(f334(x73351),x73355),f169(x73351,x73352,x73354)))
% 191.21/191.74 [7336]E(f773(f170(x73361,x73362,x73363,x73364),x73365),f773(x73364,x73365))+P1(f773(f773(f334(x73361),x73365),f169(x73361,x73362,x73363)))
% 191.21/191.74 [7662]~P24(x76624,x76621,x76622,x76625)+E(f773(f75(x76621,x76621,x76621,f773(x76622,x76623)),f773(x76622,x76623)),f773(x76622,x76623))
% 191.21/191.74 [7705]E(f773(f170(x77051,x77052,x77053,x77054),x77055),f773(x77054,x77055))+~P1(f773(f773(f334(x77051),x77055),f169(x77051,x77052,x77054)))
% 191.21/191.74 [8052]~P20(x80525,x80521,x80522)+E(f773(f75(x80521,x80521,x80521,f773(x80522,x80523)),f773(x80522,x80524)),f773(f75(x80521,x80521,x80521,f773(x80522,x80524)),f773(x80522,x80523)))
% 191.21/191.74 [8374]P1(f773(f773(f334(f854(x83741,x83741)),f773(f773(f241(x83741,x83741),x83742),x83743)),f327(x83741,x83744,x83745)))+~P1(f773(f773(f233(a847),f773(x83744,x83742)),f773(x83744,x83743)))
% 191.21/191.74 [8474]~P1(f773(f773(f334(x84744),x84743),f282(x84744,x84741,x84742,x84745)))+P1(f773(f773(x84741,x84742),x84743))
% 191.21/191.74 [8475]~P1(f773(f773(f334(x84754),x84753),f291(x84754,x84751,x84752,x84755)))+P1(f773(f773(x84751,x84752),x84753))
% 191.21/191.74 [8476]~P1(f773(f773(f334(x84764),x84762),f282(x84764,x84761,x84765,x84763)))+P1(f773(f773(x84761,x84762),x84763))
% 191.21/191.74 [8477]~P1(f773(f773(f334(x84774),x84772),f291(x84774,x84771,x84775,x84773)))+P1(f773(f773(x84771,x84772),x84773))
% 191.21/191.74 [8599]~P55(x85992,x85991,x85995,x85993,x85994)+E(f773(f303(x85991,x85992,x85993),x85994),f239(f855(x85992,a841)))
% 191.21/191.74 [9370]P1(f773(f773(f334(f854(f848(x93701),f848(x93701))),f773(f773(f241(f848(x93701),f848(x93701)),f773(f773(f140(x93701),x93702),x93703)),f773(f773(f140(x93701),x93702),x93704))),f146(x93701,x93705)))+~P1(f773(f773(f334(f854(f848(x93701),f848(x93701))),f773(f773(f241(f848(x93701),f848(x93701)),x93703),x93704)),f146(x93701,x93705)))
% 191.21/191.74 [9371]P1(f773(f773(f334(f854(f848(x93711),f848(x93711))),f773(f773(f241(f848(x93711),f848(x93711)),f773(f773(f125(x93711),x93712),x93713)),f773(f773(f125(x93711),x93712),x93714))),f137(x93711,x93715)))+~P1(f773(f773(f334(f854(f848(x93711),f848(x93711))),f773(f773(f241(f848(x93711),f848(x93711)),x93713),x93714)),f137(x93711,x93715)))
% 191.21/191.74 [9422]~E(f773(x94223,f396(x94222,x94221,x94224,x94225,x94223)),f773(f174(x94225,x94224,x94221),f396(x94222,x94221,x94224,x94225,x94223)))+E(f773(f773(x94221,x94222),f773(x94223,x94222)),f773(x94223,f773(a114,x94222)))
% 191.21/191.74 [9547]E(f773(f773(f140(x95471),f717(x95472,x95473,x95474,x95475,x95471)),f720(x95472,x95473,x95474,x95475,x95471)),x95475)+~P1(f773(f773(f334(f854(f848(x95471),f848(x95471))),f773(f773(f241(f848(x95471),f848(x95471)),x95475),f773(f773(f140(x95471),x95474),x95473))),f147(x95471,x95472)))
% 191.21/191.74 [9574]E(f773(f773(f140(x95741),f718(x95742,x95743,x95744,x95745,x95741)),f719(x95742,x95743,x95744,x95745,x95741)),x95743)+~P1(f773(f773(f334(f854(f848(x95741),f848(x95741))),f773(f773(f241(f848(x95741),f848(x95741)),f773(f773(f140(x95741),x95745),x95744)),x95743)),f147(x95741,x95742)))
% 191.21/191.74 [9706]~P1(f773(f773(f334(f854(f848(x97061),f848(x97061))),f773(f773(f241(f848(x97061),f848(x97061)),f773(f773(f140(x97061),x97065),x97062)),x97064)),f147(x97061,x97063)))+P1(f773(f773(f334(f854(f848(x97061),f848(x97061))),f773(f773(f241(f848(x97061),f848(x97061)),x97062),f719(x97063,x97064,x97062,x97065,x97061))),f147(x97061,x97063)))
% 191.21/191.74 [9791]~P1(f773(f773(f334(f854(f848(x97911),f848(x97911))),f773(f773(f241(f848(x97911),f848(x97911)),x97915),f773(f773(f140(x97911),x97914),x97913))),f147(x97911,x97912)))+P1(f773(f773(f334(f854(f848(x97911),f848(x97911))),f773(f773(f241(f848(x97911),f848(x97911)),f720(x97912,x97913,x97914,x97915,x97911)),x97913)),f147(x97911,x97912)))
% 191.21/191.74 [9964]P1(f773(f773(f334(f854(x99641,x99641)),f773(f773(f241(x99641,x99641),f773(x99642,f773(f773(f82(a847),x99643),x99644))),f773(x99642,x99643))),f300(x99641,x99645)))+~P1(f773(f773(f334(f854(x99641,x99641)),f773(f773(f241(x99641,x99641),f773(x99642,f773(a114,f637(x99644,x99643,x99645,x99642,x99641)))),f773(x99642,f637(x99644,x99643,x99645,x99642,x99641)))),f300(x99641,x99645)))
% 191.21/191.74 [9988]E(x99881,f2(a101))+E(f773(f229(f854(f848(x99882),x99883),f854(x99882,x99883),f773(f773(f241(f848(x99882),x99883),f115(x99882)),x99884),f773(f251(x99882,x99883,f854(f848(x99882),x99883)),f773(f773(f9(x99882,f855(x99883,f854(f848(x99882),x99883)),f855(x99883,f854(f848(x99882),x99883))),f773(f773(f10(f855(f854(f848(x99882),x99883),f854(f848(x99882),x99883)),f855(f855(x99883,f854(f848(x99882),x99883)),f855(x99883,f854(f848(x99882),x99883))),x99882),f10(f854(f848(x99882),x99883),f854(f848(x99882),x99883),x99883)),f773(f773(f10(f855(f848(x99882),f855(x99883,f854(f848(x99882),x99883))),f855(f854(f848(x99882),x99883),f854(f848(x99882),x99883)),x99882),f251(f848(x99882),x99883,f854(f848(x99882),x99883))),f773(f773(f10(f855(f848(x99882),f848(x99882)),f855(f848(x99882),f855(x99883,f854(f848(x99882),x99883))),x99882),f773(f10(f848(x99882),f855(x99883,f854(f848(x99882),x99883)),f848(x99882)),f241(f848(x99882),x99883))),f140(x99882))))),f119(x99883,x99882,x99885,f773(f773(f3(a101),x99881),f80(a101)))))),f773(x99885,x99884)),f773(f119(x99883,x99882,x99885,x99881),x99884))
% 191.21/191.74 [5121]E(x51211,x51212)+~E(f773(f773(f140(x51213),x51214),x51211),f773(f773(f140(x51213),x51215),x51212))
% 191.21/191.74 [5122]E(x51221,x51222)+~E(f773(f773(f140(x51223),x51221),x51224),f773(f773(f140(x51223),x51222),x51225))
% 191.21/191.74 [5316]~E(f773(f773(f128(x53161),x53163),x53162),f773(f773(f140(x53161),x53164),x53165))+E(f773(f773(f153(x53161),x53162),x53163),x53164)
% 191.21/191.74 [5449]~P19(x54494,x54495,x54491)+E(f773(f773(x54491,x54492),f773(f773(x54491,x54492),x54493)),f773(f773(x54491,x54492),x54493))
% 191.21/191.74 [6065]~P100(x60652)+~E(f773(f773(f138(x60651,x60652,x60653),x60654),x60655),f115(x60651))
% 191.21/191.74 [6464]E(x64641,x64642)+~E(f773(f773(f125(x64643),x64644),f773(f773(f140(x64643),x64641),f115(x64643))),f773(f773(f125(x64643),x64645),f773(f773(f140(x64643),x64642),f115(x64643))))
% 191.21/191.74 [6465]E(x64651,x64652)+~E(f773(f773(f125(x64653),x64651),f773(f773(f140(x64653),x64654),f115(x64653))),f773(f773(f125(x64653),x64652),f773(f773(f140(x64653),x64655),f115(x64653))))
% 191.21/191.74 [6727]E(f773(f172(x67271,x67272,x67273,x67274),x67275),f183(x67272))+P1(f773(f773(f334(x67271),x67275),x67274))
% 191.21/191.74 [6797]E(f773(f773(f302(x67971),f773(x67972,x67973)),f773(f303(x67974,x67971,x67972),x67975)),f773(f303(x67974,x67971,x67972),x67975))+~P1(f773(f773(f334(x67974),x67973),x67975))
% 191.21/191.74 [6806]~P1(f773(x68064,f773(x68063,x68065)))+P1(f773(f773(f305(x68061,x68062,x68063),x68064),x68065))
% 191.21/191.74 [6811]~E(x68114,f2(a101))+E(f773(f119(x68111,x68112,x68113,x68114),x68115),f773(f773(f241(f848(x68112),x68111),f115(x68112)),x68115))
% 191.21/191.74 [6905]~E(f773(f303(x69051,x69052,x69053),x69054),x69055)+E(f773(f303(f855(x69051,a841),f855(x69052,a841),f303(x69051,x69052,x69053)),f773(f301(x69051),x69054)),f773(f301(x69052),x69055))
% 191.21/191.74 [6936]E(f773(f172(x69361,x69362,x69363,x69364),x69365),f773(x69363,x69365))+~P1(f773(f773(f334(x69361),x69365),x69364))
% 191.21/191.74 [7251]P29(x72511,x72512,x72513,x72514)+~P29(x72511,x72512,x72513,f773(f773(f302(x72511),x72515),x72514))
% 191.21/191.74 [7322]P1(f773(x73221,x73222))+~P1(f773(f773(f94(x73223,x73224,x73221),x73225),x73222))
% 191.21/191.74 [7373]~P1(f773(f773(f334(x73734),x73733),x73735))+P1(f773(f773(f334(x73731),f773(x73732,x73733)),f773(f303(x73734,x73731,x73732),x73735)))
% 191.21/191.74 [7425]P1(f773(x74251,f773(x74252,x74253)))+~P1(f773(f773(f305(x74254,x74255,x74252),x74251),x74253))
% 191.21/191.74 [7426]P1(f773(f773(x74261,x74262),x74263))+~P1(f773(f773(f94(x74264,x74261,x74265),x74262),x74263))
% 191.21/191.74 [7495]~P1(f773(f773(f334(x74953),f773(x74954,x74952)),x74955))+P1(f773(f773(f334(x74951),x74952),f773(f305(x74951,x74953,x74954),x74955)))
% 191.21/191.74 [7894]~P1(f773(f773(f334(x78945),x78943),f773(f305(x78945,x78941,x78942),x78944)))+P1(f773(f773(f334(x78941),f773(x78942,x78943)),x78944))
% 191.21/191.74 [8112]~E(x81123,f773(f773(f773(f74(x81121,f851(x81122)),f773(f18(f851(x81122),x81121),f183(x81122))),x81124),f773(f227(x81122),x81125)))+E(f169(x81121,x81122,x81123),f773(f773(f302(x81121),x81124),f180(f855(x81121,a841))))
% 191.21/191.74 [8208]E(f773(x82081,f416(x82082,x82081,x82083,x82084)),x82084)+~P1(f773(f773(f334(x82085),x82084),f773(f303(x82083,x82085,x82081),x82082)))
% 191.21/191.74 [8460]P1(f773(f773(f334(f856(x84601,x84602)),f773(f313(x84602,x84601),x84603)),f314(x84601,x84602,x84604,x84605)))+~P1(f773(f773(f334(x84602),x84603),x84605))
% 191.21/191.74 [8461]P1(f773(f773(f334(f856(x84611,x84612)),f773(f304(x84611,x84612),x84613)),f314(x84611,x84612,x84614,x84615)))+~P1(f773(f773(f334(x84611),x84613),x84614))
% 191.21/191.74 [8518]~E(x85182,f773(f773(f140(x85181),x85184),x85185))+P1(f773(f773(f334(f854(f848(x85181),f848(x85181))),f773(f773(f241(f848(x85181),f848(x85181)),f115(x85181)),x85182)),f137(x85181,x85183)))
% 191.21/191.74 [8569]P1(f773(f773(f232(f855(x85691,a841)),f773(f773(f47(x85692,f855(x85691,a841)),x85693),x85694)),f773(x85694,x85695)))+~P1(f773(f773(f334(x85692),x85695),x85693))
% 191.21/191.74 [8615]~P55(x86151,x86152,x86153,x86155,x86154)+E(f773(f303(x86151,x86152,x86153),f239(f855(x86151,a841))),x86154)
% 191.21/191.74 [8804]E(f773(f773(f773(f74(x88041,f851(x88042)),f172(x88041,x88042,x88043,x88044)),x88045),f183(x88042)),f172(x88041,x88042,x88043,x88044))+P1(f773(f773(f334(x88041),x88045),x88044))
% 191.21/191.74 [8807]E(f773(x88071,f702(x88072,x88073,x88071,x88074,x88075)),x88072)+~E(f773(f773(f196(x88075,x88074),x88071),x88073),f773(f227(x88074),x88072))
% 191.21/191.74 [8810]E(f773(f227(x88101),f702(x88102,x88103,x88104,x88105,x88101)),x88103)+~E(f773(f773(f196(x88101,x88105),x88104),x88103),f773(f227(x88105),x88102))
% 191.21/191.74 [8894]E(f773(f181(f848(x88941)),x88942),x88943)+~P1(f773(f773(f334(f854(f848(x88941),f848(x88941))),f773(f773(f241(f848(x88941),f848(x88941)),x88944),x88942)),f773(f133(x88941,x88945),x88943)))
% 191.21/191.74 [8895]E(f773(f181(f848(x88951)),x88952),x88953)+~P1(f773(f773(f334(f854(f848(x88951),f848(x88951))),f773(f773(f241(f848(x88951),f848(x88951)),x88952),x88954)),f773(f133(x88951,x88955),x88953)))
% 191.21/191.74 [8956]P1(f773(f773(f334(x89561),f416(x89562,x89563,x89561,x89564)),x89562))+~P1(f773(f773(f334(x89565),x89564),f773(f303(x89561,x89565,x89563),x89562)))
% 191.21/191.74 [9109]E(f773(f303(x91091,x91092,x91093),f362(x91094,x91093,x91091,x91095,x91092)),x91095)+~P1(f773(f773(f232(f855(x91092,a841)),x91095),f773(f303(x91091,x91092,x91093),x91094)))
% 191.21/191.74 [9342]E(f773(x93421,f536(x93422,x93421,x93423,x93424,x93425)),f773(f227(x93425),x93424))+~P1(f773(f773(f334(x93425),x93424),f171(x93423,x93425,f172(x93423,x93425,x93421,x93422))))
% 191.21/191.74 [9386]P1(f773(f773(f334(f854(f848(x93861),f848(x93861))),f773(f773(f241(f848(x93861),f848(x93861)),f773(f773(f140(x93861),x93862),x93863)),f773(f773(f140(x93861),x93862),x93864))),f300(f848(x93861),f146(x93861,x93865))))+~P1(f773(f773(f334(f854(f848(x93861),f848(x93861))),f773(f773(f241(f848(x93861),f848(x93861)),x93863),x93864)),f300(f848(x93861),f146(x93861,x93865))))
% 191.21/191.74 [9415]~E(f773(x94153,f703(x94155,x94154,x94153,x94152,x94151)),f773(x94155,f703(x94155,x94154,x94153,x94152,x94151)))+E(f773(f773(f143(x94151,x94152),x94153),x94154),f773(f773(f143(x94151,x94152),x94155),x94154))
% 191.21/191.74 [9493]E(f773(f773(f143(x94931,x94932),x94933),x94934),f773(f773(f143(x94931,x94932),x94935),x94934))+P1(f773(f773(f334(x94931),f703(x94933,x94934,x94935,x94932,x94931)),f773(f158(x94931),x94934)))
% 191.21/191.74 [9521]~P1(f773(f773(f334(x95215),x95214),f773(f277(x95211,x95215,x95213),x95212)))+P1(f773(f773(f334(x95211),f488(x95212,x95213,x95211,x95214,x95215)),x95212))
% 191.21/191.74 [9522]~P1(f773(f773(f334(x95225),x95224),f773(f277(x95221,x95225,x95223),x95222)))+P1(f773(f773(f334(x95221),f534(x95222,x95223,x95221,x95224,x95225)),x95222))
% 191.21/191.74 [9545]~P1(f773(f773(f232(f855(x95455,a841)),x95454),f773(f303(x95451,x95455,x95453),x95452)))+P1(f773(f773(f232(f855(x95451,a841)),f362(x95452,x95453,x95451,x95454,x95455)),x95452))
% 191.21/191.74 [9589]~P1(f773(f773(f334(x95895),x95894),f171(x95891,x95895,f172(x95891,x95895,x95893,x95892))))+P1(f773(f773(f334(x95891),f536(x95892,x95893,x95891,x95894,x95895)),x95892))
% 191.21/191.74 [5330]~E(f773(x53303,x53304),x53305)+E(f773(f773(f773(f74(x53301,x53302),x53303),x53304),x53305),x53303)
% 191.21/191.74 [5779]E(f773(x57791,x57792),x57793)+~E(f773(f773(f773(f74(x57794,x57795),x57791),x57792),x57793),x57791)
% 191.21/191.74 [5868]E(x58681,x58682)+~E(f773(f250(x58683,x58684),f773(f773(f241(x58683,x58684),x58685),x58681)),x58682)
% 191.21/191.74 [5869]E(x58691,x58692)+~E(f773(f240(x58693,x58694),f773(f773(f241(x58693,x58694),x58691),x58695)),x58692)
% 191.21/191.74 [6552]E(f773(f303(x65521,x65522,f773(f18(x65522,x65521),x65523)),x65524),f773(f773(f302(x65522),x65523),f180(f855(x65522,a841))))+~P1(f773(f773(f334(x65521),x65525),x65524))
% 191.21/191.74 [6626]E(f773(f773(f103(f855(x66261,a841)),f773(f158(x66261),x66262)),f773(f158(x66261),x66263)),f773(f158(x66261),x66264))+~E(f156(x66261,x66265,x66264),f773(f773(f241(f848(x66261),f848(x66261)),x66262),x66263))
% 191.21/191.74 [6733]~P100(x67332)+E(f773(f181(f848(x67331)),f773(f773(f138(x67331,x67332,x67333),x67334),x67335)),f773(a114,f773(f181(f848(x67331)),x67335)))
% 191.21/191.74 [6748]~P100(x67482)+E(f773(f158(x67481),f773(f773(f138(x67481,x67482,x67483),x67484),x67485)),f773(f773(f302(x67481),x67484),f773(f158(x67481),x67485)))
% 191.21/191.74 [7026]~P85(x70261)+E(f773(f773(f82(x70261),f773(f773(f82(x70261),x70262),x70263)),f773(f773(f82(x70261),x70264),x70265)),f773(f773(f82(x70261),f773(f773(f82(x70261),x70262),x70264)),f773(f773(f82(x70261),x70263),x70265)))
% 191.21/191.74 [7027]~P85(x70271)+E(f773(f773(f83(x70271),f773(f773(f83(x70271),x70272),x70273)),f773(f773(f83(x70271),x70274),x70275)),f773(f773(f83(x70271),f773(f773(f83(x70271),x70272),x70274)),f773(f773(f83(x70271),x70273),x70275)))
% 191.21/191.74 [7028]~P60(x70281)+E(f773(f773(f283(x70281),f773(f773(f83(x70281),x70282),x70283)),f773(f773(f83(x70281),x70284),x70285)),f773(f773(f83(x70281),f773(f773(f283(x70281),x70282),x70284)),f773(f773(f283(x70281),x70283),x70285)))
% 191.21/191.74 [7042]~P100(x70421)+E(f295(x70421,f773(f773(f179(x70421),x70422),x70423),f773(f773(f236(x70421),x70424),x70425)),f773(f773(f104(f855(x70421,a841)),f295(x70421,x70422,x70424)),f295(x70421,x70423,x70425)))
% 191.21/191.74 [7043]~P100(x70431)+E(f297(x70431,f773(f773(f179(x70431),x70432),x70433),f773(f773(f236(x70431),x70434),x70435)),f773(f773(f104(f855(x70431,a841)),f297(x70431,x70432,x70434)),f297(x70431,x70433,x70435)))
% 191.21/191.74 [7044]~P100(x70441)+E(f298(x70441,f773(f773(f179(x70441),x70442),x70443),f773(f773(f236(x70441),x70444),x70445)),f773(f773(f104(f855(x70441,a841)),f298(x70441,x70442,x70444)),f298(x70441,x70443,x70445)))
% 191.21/191.74 [7045]~P100(x70451)+E(f773(f773(f104(f855(x70451,a841)),f773(f294(x70451,x70452),x70453)),f773(f294(x70451,x70454),x70455)),f773(f294(x70451,f773(f773(f179(x70451),x70452),x70454)),f773(f773(f236(x70451),x70453),x70455)))
% 191.21/191.74 [7163]~P1(f773(x71631,f821(x71633,x71632,x71631)))+P1(f773(x71631,f773(f773(f241(x71632,x71633),x71634),x71635)))
% 191.21/191.74 [7263]~E(f773(x72633,x72634),f183(x72632))+E(f171(x72631,x72632,f773(f773(f773(f74(x72631,f851(x72632)),x72633),x72634),f773(f227(x72632),x72635))),f773(f773(f302(x72632),x72635),f171(x72631,x72632,x72633)))
% 191.21/191.74 [7286]~E(x72862,f773(x72864,x72865))+P1(f773(f773(f334(x72861),x72862),f773(f303(x72863,x72861,x72864),f239(f855(x72863,a841)))))
% 191.21/191.74 [7347]~E(f773(x73473,x73474),f183(x73472))+E(f773(f773(f3(f855(x73471,a841)),f169(x73471,x73472,x73473)),f773(f773(f302(x73471),x73474),x73475)),f773(f773(f3(f855(x73471,a841)),f169(x73471,x73472,x73473)),x73475))
% 191.21/191.74 [7369]~P19(x73693,x73692,x73694)+P19(x73691,x73692,f773(f773(f10(x73693,f855(x73692,x73692),x73691),x73694),x73695))
% 191.21/191.74 [7370]~P20(x73703,x73702,x73704)+P20(x73701,x73702,f773(f773(f10(x73703,f855(x73702,x73702),x73701),x73704),x73705))
% 191.21/191.74 [7511]~P29(x75111,x75112,x75113,x75114)+P29(x75111,x75112,x75113,f773(f773(f3(f855(x75111,a841)),x75114),x75115))
% 191.21/191.74 [7671]~P1(f773(f773(x76713,x76714),x76715))+P1(f773(f773(f251(x76711,x76712,a841),x76713),f773(f773(f241(x76711,x76712),x76714),x76715)))
% 191.21/191.74 [7805]P29(x78051,x78052,x78053,x78054)+~P29(x78051,x78052,x78053,f773(f773(f103(f855(x78051,a841)),x78055),x78054))
% 191.21/191.74 [7806]P29(x78061,x78062,x78063,x78064)+~P29(x78061,x78062,x78063,f773(f773(f103(f855(x78061,a841)),x78064),x78065))
% 191.21/191.74 [8011]~P31(x80111,f773(a114,x80112),f773(f773(f773(f93(x80111),x80113),f773(a27,x80114)),x80115))+P31(x80111,x80112,f773(f773(f773(f93(x80111),x80113),f773(f231(a842),f773(a30,x80114))),x80115))
% 191.21/191.74 [8139]P31(x81391,f773(a114,x81392),f773(f773(f773(f93(x81391),x81393),f773(a27,x81394)),x81395))+~P31(x81391,x81392,f773(f773(f773(f93(x81391),x81393),f773(f231(a842),f773(a30,x81394))),x81395))
% 191.21/191.74 [8168]~P19(x81682,x81681,x81683)+E(f773(f132(x81681,x81682,f773(f9(x81682,x81681,x81681),x81683),x81684),x81685),f773(f773(f66(x81682,x81681,x81683),x81684),f773(f158(x81682),x81685)))
% 191.21/191.74 [8218]P1(f773(f773(x82181,x82182),x82183))+~P1(f773(f773(f251(x82184,x82185,a841),x82181),f773(f773(f241(x82184,x82185),x82182),x82183)))
% 191.21/191.74 [8289]P39(x82894,f838(x82895,x82894,x82893,x82892),x82892,f345(x82895,x82894,x82893,x82892))+P31(x82891,x82892,f773(f773(f773(f93(x82891),x82893),x82894),x82895))
% 191.21/191.74 [8305]~E(f773(f166(x83051,x83052,x83055),x83053),f773(f227(x83052),x83054))+P1(f773(f773(f334(f854(x83051,x83052)),f773(f773(f241(x83051,x83052),x83053),x83054)),f773(f158(f854(x83051,x83052)),x83055)))
% 191.21/191.74 [8668]P1(f773(f773(f232(f855(x86681,a841)),f773(f303(x86682,x86681,x86683),x86684)),f773(f303(x86682,x86681,x86683),x86685)))+~P1(f773(f773(f232(f855(x86682,a841)),x86684),x86685))
% 191.21/191.74 [8669]P1(f773(f773(f232(f855(x86691,a841)),f773(f305(x86691,x86692,x86693),x86694)),f773(f305(x86691,x86692,x86693),x86695)))+~P1(f773(f773(f232(f855(x86692,a841)),x86694),x86695))
% 191.21/191.74 [8740]E(x87401,f2(a101))+E(f773(f773(f253(x87402,x87403,x87402,f854(x87403,x87402)),f773(x87404,x87405)),f268(x87403,x87402,f773(f773(f3(a101),x87401),f80(a101)),x87404)),f773(f268(x87403,x87402,x87401,x87404),x87405))
% 191.21/191.74 [8826]P1(f773(f773(f249(x88261,x88262,a841,x88263),x88264),x88265))+~P1(f773(x88263,f773(f773(f241(x88261,x88262),x88264),x88265)))
% 191.21/191.74 [9027]P31(x90271,x90272,f773(f773(f773(f93(x90271),x90273),x90274),x90275))+P1(f773(f773(x90273,f831(x90275,x90274,x90273,x90272)),f838(x90275,x90274,x90273,x90272)))
% 191.21/191.74 [9088]~P1(f773(f773(f249(x90882,x90883,a841,x90881),x90884),x90885))+P1(f773(x90881,f773(f773(f241(x90882,x90883),x90884),x90885)))
% 191.21/191.74 [9197]E(f773(f227(x91971),f714(x91972,x91973,x91974,x91971,x91975)),f773(f166(x91975,x91971,x91972),x91974))+~P1(f773(f773(f334(f854(x91975,x91971)),f773(f773(f241(x91975,x91971),x91974),x91973)),f773(f158(f854(x91975,x91971)),x91972)))
% 191.21/191.74 [9240]P31(x92401,x92402,f773(f773(f773(f93(x92401),x92403),x92404),x92405))+~P1(f773(f773(x92405,f831(x92405,x92404,x92403,x92402)),f345(x92405,x92404,x92403,x92402)))
% 191.21/191.74 [9307]~P28(x93071,x93072,f773(f773(f302(f846(x93071)),f773(f773(f773(f93(x93071),x93073),f773(f231(a842),f773(a30,x93074))),x93075)),f180(f855(f846(x93071),a841))))+P28(x93071,x93072,f773(f773(f302(f846(x93071)),f773(f773(f773(f93(x93071),x93073),f773(a27,x93074)),x93075)),f180(f855(f846(x93071),a841))))
% 191.21/191.74 [9334]~P1(f773(f63(x93343),f773(f303(x93342,x93343,x93345),f239(f855(x93342,a841)))))+P1(f773(f63(x93341),f773(f303(x93342,x93341,f773(f773(f10(x93343,x93341,x93342),x93344),x93345)),f239(f855(x93342,a841)))))
% 191.21/191.74 [9356]P1(f773(f773(f232(f855(f855(x93561,a841),a841)),f773(f303(f855(x93562,a841),f855(x93561,a841),f303(x93562,x93561,x93563)),f773(f301(x93562),x93564))),f773(f301(x93561),x93565)))+~P1(f773(f773(f232(f855(x93561,a841)),f773(f303(x93562,x93561,x93563),x93564)),x93565))
% 191.21/191.74 [9366]~P1(f773(f63(f851(x93661)),f773(f303(x93662,f851(x93661),x93663),f239(f855(x93662,a841)))))+P1(f773(f63(f851(x93661)),f773(f303(x93662,f851(x93661),f773(f773(f773(f74(x93662,f851(x93661)),x93663),x93664),f773(f227(x93661),x93665))),f239(f855(x93662,a841)))))
% 191.21/191.74 [9425]E(x94251,x94252)+~P1(f773(f68(x94253,x94254,x94255,x94251,f180(f855(x94253,a841))),x94252))
% 191.21/191.74 [9438]E(f773(f773(f241(x94381,x94382),f569(x94383,x94384,x94385,x94382,x94381)),f570(x94383,x94384,x94385,x94382,x94381)),x94385)+~P1(f773(f773(f334(f854(x94381,x94382)),x94385),f773(f773(f248(x94381,x94382),x94384),x94383)))
% 191.21/191.74 [9526]P1(f773(f773(f334(x95261),f569(x95262,x95263,x95264,x95265,x95261)),x95263))+~P1(f773(f773(f334(f854(x95261,x95265)),x95264),f773(f773(f248(x95261,x95265),x95263),x95262)))
% 191.21/191.74 [9622]P28(x96225,x96224,f773(f773(f302(f846(x96225)),f773(f773(f773(f93(x96225),x96221),x96223),x96222)),f180(f855(f846(x96225),a841))))+P1(f773(f773(x96221,f484(x96222,x96223,x96224,x96225,x96221)),f485(x96222,x96223,x96224,x96225,x96221)))
% 191.21/191.74 [9664]P1(f773(f773(f334(x96641),f570(x96642,x96643,x96644,x96641,x96645)),f773(x96642,f569(x96642,x96643,x96644,x96641,x96645))))+~P1(f773(f773(f334(f854(x96645,x96641)),x96644),f773(f773(f248(x96645,x96641),x96643),x96642)))
% 191.21/191.74 [9683]P1(f773(f773(f334(f854(x96831,x96831)),f773(f773(f241(x96831,x96831),x96832),f658(x96833,x96834,x96835,x96832,x96831))),x96833))+~P1(f773(f773(f334(f854(x96831,x96831)),f773(f773(f241(x96831,x96831),x96832),x96835)),f773(f773(f173(f854(x96831,x96831),a841),f773(a114,x96834)),x96833)))
% 191.21/191.74 [9684]P1(f773(f773(f334(f854(x96841,x96841)),f773(f773(f241(x96841,x96841),x96842),f660(x96843,x96844,x96845,x96842,x96841))),x96843))+~P1(f773(f773(f334(f854(x96841,x96841)),f773(f773(f241(x96841,x96841),x96842),x96845)),f773(f773(f173(f854(x96841,x96841),a841),f773(a114,x96844)),x96843)))
% 191.21/191.74 [9702]~P1(f773(f773(f334(f854(f848(x97021),f848(x97021))),f773(f773(f241(f848(x97021),f848(x97021)),f773(f773(f140(x97021),x97022),x97025)),x97024)),f147(x97021,x97023)))+P1(f773(f773(f334(f854(x97021,x97021)),f773(f773(f241(x97021,x97021),x97022),f718(x97023,x97024,x97025,x97022,x97021))),x97023))
% 191.21/191.74 [9704]~P28(x97041,x97042,f773(f773(f302(f846(x97041)),f773(f773(f773(f93(x97041),f94(x97041,x97043,x97044)),x97045),x97043)),f180(f855(f846(x97041),a841))))+P28(x97041,x97042,f773(f773(f302(f846(x97041)),f773(f773(f773(f93(x97041),x97043),f35(x97044,x97045)),f94(x97041,x97043,f773(f75(a841,a841,a844,a328),x97044)))),f180(f855(f846(x97041),a841))))
% 191.21/191.74 [9989]P28(x99891,x99892,f773(f773(f302(f846(x99891)),f773(f773(f773(f93(x99891),x99893),x99894),x99895)),f180(f855(f846(x99891),a841))))+~P28(x99891,x99892,f773(f773(f302(f846(x99891)),f773(f773(f773(f93(x99891),f773(f18(f855(a844,a841),x99891),f773(f773(f9(a844,a844,a841),a330),f485(x99895,x99894,x99892,x99891,x99893)))),x99894),f773(f18(f855(a844,a841),x99891),f773(x99895,f484(x99895,x99894,x99892,x99891,x99893))))),f180(f855(f846(x99891),a841))))
% 191.21/191.74 [6216]P1(f773(x62162,x62164))+E(f162(x62161,x62162,f773(f773(f125(x62161),x62163),f773(f773(f140(x62161),x62164),x62165))),f162(x62161,x62162,x62163))
% 191.21/191.74 [6266]~P71(x62662)+E(f773(f773(f773(f3(f855(x62661,x62662)),x62663),x62664),x62665),f773(f773(f3(x62662),f773(x62663,x62665)),f773(x62664,x62665)))
% 191.21/191.74 [6268]~P93(x62682)+E(f773(f773(f773(f103(f855(x62681,x62682)),x62683),x62684),x62685),f773(f773(f103(x62682),f773(x62683,x62685)),f773(x62684,x62685)))
% 191.21/191.74 [6270]~P93(x62702)+E(f773(f773(f773(f104(f855(x62701,x62702)),x62703),x62704),x62705),f773(f773(f104(x62702),f773(x62703,x62705)),f773(x62704,x62705)))
% 191.21/191.74 [6292]E(x62921,x62922)+E(f773(f773(f153(x62923),f773(f773(f148(x62923,x62924),x62921),x62925)),x62922),f773(f773(f153(x62923),x62924),x62922))
% 191.21/191.74 [6569]~E(x65694,f180(f855(x65693,a841)))+E(f773(f773(f3(f855(x65691,a841)),x65692),f773(f773(f46(x65693,f855(x65691,a841)),x65694),x65695)),x65692)
% 191.21/191.74 [6570]~E(x65704,f180(f855(x65703,a841)))+E(f773(f773(f103(f855(x65701,a841)),x65702),f773(f773(f46(x65703,f855(x65701,a841)),x65704),x65705)),x65702)
% 191.21/191.74 [6571]~E(x65714,f180(f855(x65713,a841)))+E(f773(f773(f104(f855(x65711,a841)),x65712),f773(f773(f47(x65713,f855(x65711,a841)),x65714),x65715)),x65712)
% 191.21/191.74 [6585]~E(x65854,f180(f855(x65853,a841)))+E(f773(f773(f302(x65851),x65852),f773(f773(f46(x65853,f855(x65851,a841)),x65854),x65855)),f773(f773(f302(x65851),x65852),f180(f855(x65851,a841))))
% 191.21/191.74 [7414]E(f773(f773(f153(x74141),f773(f773(f143(x74142,x74141),x74143),x74144)),x74145),f773(x74143,f773(f773(f153(x74142),x74144),x74145)))+~P1(f773(f773(f233(a847),x74145),f773(f181(f848(x74142)),x74144)))
% 191.21/191.74 [7483]E(f773(f773(f103(f855(x74831,a841)),f773(x74832,x74833)),f773(f773(f46(x74834,f855(x74831,a841)),x74835),x74832)),f773(f773(f46(x74834,f855(x74831,a841)),x74835),x74832))+~P1(f773(f773(f334(x74834),x74833),x74835))
% 191.21/191.74 [7484]E(f773(f773(f104(f855(x74841,a841)),f773(x74842,x74843)),f773(f773(f47(x74844,f855(x74841,a841)),x74845),x74842)),f773(f773(f47(x74844,f855(x74841,a841)),x74845),x74842))+~P1(f773(f773(f334(x74844),x74843),x74845))
% 191.21/191.74 [8087]~E(x80873,f180(f855(x80871,a841)))+E(f773(f773(f46(x80871,f855(x80872,a841)),x80873),f773(f773(f10(f855(x80872,a841),f855(x80872,a841),x80871),f773(f302(x80872),x80874)),x80875)),f180(f855(x80872,a841)))
% 191.21/191.74 [8093]~P1(f773(f773(f334(x80934),x80933),x80935))+P1(f773(f773(f232(f855(x80931,a841)),f773(x80932,x80933)),f773(f773(f46(x80934,f855(x80931,a841)),x80935),x80932)))
% 191.21/191.74 [8217]~E(f773(x82174,x82172),x82175)+P1(f773(f773(f334(x82171),x82172),f773(f305(x82171,x82173,x82174),f773(f773(f302(x82173),x82175),f180(f855(x82173,a841))))))
% 191.21/191.74 [8263]~P53(x82631,x82632,f773(f278(x82632,x82631),x82633))+E(f773(f773(f104(f855(x82631,a841)),f773(f277(x82632,x82631,x82633),x82634)),f773(f277(x82632,x82631,x82633),x82635)),f773(f277(x82632,x82631,x82633),f773(f773(f104(f855(x82632,a841)),x82634),x82635)))
% 191.21/191.74 [8288]E(x82881,f2(a101))+E(f118(x82882,x82883,f773(x82884,f773(f773(f3(a101),x82881),f80(a101))),f773(f773(f9(x82882,a101,f849(x82883)),x82885),x82881)),f773(f193(x82882,x82883,x82884,x82885),x82881))
% 191.21/191.74 [8384]E(x83841,f180(f855(x83842,a841)))+E(f773(f773(f46(x83842,f855(x83843,a841)),x83841),f773(f773(f10(f855(x83843,a841),f855(x83843,a841),x83842),f773(f302(x83843),x83844)),x83845)),f773(f773(f302(x83843),x83844),f773(f773(f46(x83842,f855(x83843,a841)),x83841),x83845)))
% 191.21/191.74 [8438]~P29(x84382,x84381,x84383,f239(f855(x84382,a841)))+E(f773(f773(f3(f855(x84381,a841)),f773(f303(x84382,x84381,x84383),x84384)),f773(f303(x84382,x84381,x84383),x84385)),f773(f303(x84382,x84381,x84383),f773(f773(f3(f855(x84382,a841)),x84384),x84385)))
% 191.21/191.74 [8439]~P29(x84392,x84391,x84393,f239(f855(x84392,a841)))+E(f773(f773(f104(f855(x84391,a841)),f773(f303(x84392,x84391,x84393),x84394)),f773(f303(x84392,x84391,x84393),x84395)),f773(f303(x84392,x84391,x84393),f773(f773(f104(f855(x84392,a841)),x84394),x84395)))
% 191.21/191.74 [8506]~P1(f773(f773(f69(x85061,x85062,x85065),x85063),x85064))+P1(f773(f773(f334(f854(x85061,x85062)),f773(f773(f241(x85061,x85062),x85063),x85064)),x85065))
% 191.21/191.74 [8534]P1(f773(f773(f334(x85341),x85342),f773(f259(x85343,x85341),x85344)))+~P1(f773(f773(f334(f854(x85343,x85341)),f773(f773(f241(x85343,x85341),x85345),x85342)),x85344))
% 191.21/191.74 [8536]P1(f773(f773(f334(x85361),x85362),f773(f261(x85361,x85363),x85364)))+~P1(f773(f773(f334(f854(x85361,x85363)),f773(f773(f241(x85361,x85363),x85362),x85365)),x85364))
% 191.21/191.74 [8657]P1(f773(f773(f69(x86571,x86572,x86573),x86574),x86575))+~P1(f773(f773(f334(f854(x86571,x86572)),f773(f773(f241(x86571,x86572),x86574),x86575)),x86573))
% 191.21/191.74 [8690]E(f773(x86901,x86902),x86903)+~P1(f773(f773(f334(x86904),x86902),f773(f305(x86904,x86905,x86901),f773(f773(f302(x86905),x86903),f180(f855(x86905,a841))))))
% 191.21/191.74 [8891]P1(f773(f773(f334(f854(x88911,x88912)),f773(f773(f241(x88911,x88912),x88913),x88914)),f773(f278(x88912,x88911),x88915)))+~P1(f773(f773(f334(f854(x88912,x88911)),f773(f773(f241(x88912,x88911),x88914),x88913)),x88915))
% 191.21/191.74 [8909]~P1(f773(f773(x89091,x89095),x89094))+P1(f773(f773(x89091,f773(f250(x89092,x89093),f773(f773(f241(x89092,x89093),x89094),x89095))),f773(f240(x89092,x89093),f773(f773(f241(x89092,x89093),x89094),x89095))))
% 191.21/191.74 [8936]~P1(f773(f773(f334(f854(x89362,x89361)),f773(f773(f241(x89362,x89361),x89364),x89363)),f773(f278(x89361,x89362),x89365)))+P1(f773(f773(f334(f854(x89361,x89362)),f773(f773(f241(x89361,x89362),x89363),x89364)),x89365))
% 191.21/191.74 [8964]~P1(f773(f773(f334(f854(x89643,x89641)),f773(f773(f241(x89643,x89641),x89645),x89642)),x89644))+P1(f773(f773(f334(x89641),x89642),f773(f277(x89643,x89641,x89644),f773(f773(f302(x89643),x89645),f180(f855(x89643,a841))))))
% 191.21/191.74 [9011]P1(f773(f773(f334(f854(x90111,x90112)),f773(f773(f241(x90111,x90112),x90113),x90114)),x90115))+~P1(f773(f773(f334(x90112),x90114),f773(f277(x90111,x90112,x90115),f773(f773(f302(x90111),x90113),f180(f855(x90111,a841))))))
% 191.21/191.74 [9030]E(f773(f773(f773(f74(x90301,f851(x90302)),f172(x90301,x90302,x90303,x90304)),x90305),f183(x90302)),f172(x90301,x90302,x90303,f773(f773(f3(f855(x90301,a841)),x90304),f773(f773(f302(x90301),x90305),f180(f855(x90301,a841))))))+~P1(f773(f773(f334(x90301),x90305),x90304))
% 191.21/191.74 [9094]~P66(x90941)+E(f773(f773(f8(a847,x90941),x90942),f295(a847,f773(f773(f82(a847),x90943),x90944),f773(f773(f82(a847),x90945),x90944))),f773(f773(f8(a847,x90941),f773(f773(f10(a847,x90941,a847),x90942),f773(f773(f9(a847,a847,a847),f82(a847)),x90944))),f295(a847,x90943,x90945)))
% 191.21/191.74 [9113]~P66(x91131)+E(f773(f773(f8(a847,x91131),x91132),f773(f294(a847,f773(f773(f82(a847),x91133),x91134)),f773(f773(f82(a847),x91135),x91134))),f773(f773(f8(a847,x91131),f773(f773(f10(a847,x91131,a847),x91132),f773(f773(f9(a847,a847,a847),f82(a847)),x91134))),f773(f294(a847,x91133),x91135)))
% 191.21/191.74 [9322]P1(f773(f773(f334(f854(f848(x93221),f848(x93221))),f773(f773(f241(f848(x93221),f848(x93221)),f773(f773(f140(x93221),x93222),x93223)),f773(f773(f140(x93221),x93224),x93223))),f146(x93221,x93225)))+~P1(f773(f773(f334(f854(x93221,x93221)),f773(f773(f241(x93221,x93221),x93222),x93224)),x93225))
% 191.21/191.74 [9423]P28(x94231,x94232,f773(f773(f302(f846(x94231)),f773(f773(f773(f93(x94231),x94233),f773(a27,x94234)),x94235)),f180(f855(f846(x94231),a841))))+~P28(x94231,f773(f773(f302(f846(x94231)),f773(f773(f773(f93(x94231),x94233),f773(a27,x94234)),x94235)),x94232),f773(f773(f302(f846(x94231)),f773(f773(f773(f93(x94231),x94233),f773(f231(a842),f773(a30,x94234))),x94235)),f180(f855(f846(x94231),a841))))
% 191.21/191.74 [9434]E(f773(f773(f302(x94341),f540(x94342,x94343,x94344,x94345,x94341)),f545(x94342,x94343,x94344,x94345,x94341)),f773(f773(f302(x94341),x94344),x94343))+~P1(f773(f64(x94341,x94345,f773(f773(f302(x94341),x94344),x94343)),x94342))
% 191.21/191.74 [9435]E(f773(f773(f302(x94351),f546(x94352,x94353,x94354,x94355,x94351)),f551(x94352,x94353,x94354,x94355,x94351)),f773(f773(f302(x94351),x94354),x94353))+~P1(f773(f64(x94351,x94355,f773(f773(f302(x94351),x94354),x94353)),x94352))
% 191.21/191.74 [9512]P1(f773(f773(f334(x95121),f666(x95122,x95123,x95124,x95125,x95121)),x95124))+P1(f773(f773(f773(f47(x95121,f855(x95125,a841)),x95124),x95123),x95122))
% 191.21/191.74 [9517]P1(f773(f773(f334(x95171),f665(x95172,x95173,x95171,x95174,x95175)),x95173))+P1(f773(f773(f334(x95175),x95174),f773(f773(f47(x95171,f855(x95175,a841)),x95173),x95172)))
% 191.21/191.74 [9525]P1(f773(f773(f334(x95251),f667(x95252,x95253,x95251,x95254,x95255)),x95253))+P1(f773(f773(f232(f855(x95255,a841)),x95254),f773(f773(f47(x95251,f855(x95255,a841)),x95253),x95252)))
% 191.21/191.74 [9527]P1(f773(f773(x95271,f386(x95272,x95271,x95273,x95274,x95275)),x95272))+~P1(f773(f773(f773(f46(x95275,f855(x95274,a841)),x95273),x95271),x95272))
% 191.21/191.74 [9529]P1(f773(f773(f334(x95291),f386(x95292,x95293,x95294,x95295,x95291)),x95294))+~P1(f773(f773(f773(f46(x95291,f855(x95295,a841)),x95294),x95293),x95292))
% 191.21/191.74 [9539]P1(f773(f773(f334(x95391),f417(x95392,x95393,x95391,x95394,x95395)),x95393))+~P1(f773(f773(f334(x95395),x95394),f773(f773(f46(x95391,f855(x95395,a841)),x95393),x95392)))
% 191.21/191.74 [9544]P1(f773(f773(f334(x95441),x95442),f773(x95443,f417(x95443,x95444,x95445,x95442,x95441))))+~P1(f773(f773(f334(x95441),x95442),f773(f773(f46(x95445,f855(x95441,a841)),x95444),x95443)))
% 191.21/191.74 [9626]~P1(f773(f773(x96264,f666(x96265,x96264,x96263,x96262,x96261)),x96265))+P1(f773(f773(f773(f47(x96261,f855(x96262,a841)),x96263),x96264),x96265))
% 191.21/191.74 [9629]~P1(f773(f773(f334(x96291),x96292),f773(x96295,f665(x96295,x96294,x96293,x96292,x96291))))+P1(f773(f773(f334(x96291),x96292),f773(f773(f47(x96293,f855(x96291,a841)),x96294),x96295)))
% 191.21/191.74 [9632]~P1(f773(f773(f232(f855(x96321,a841)),x96322),f773(x96325,f667(x96325,x96324,x96323,x96322,x96321))))+P1(f773(f773(f232(f855(x96321,a841)),x96322),f773(f773(f47(x96323,f855(x96321,a841)),x96324),x96325)))
% 191.21/191.74 [9687]~P1(f773(f773(f334(x96871),f540(x96875,x96874,x96873,x96872,x96871)),f545(x96875,x96874,x96873,x96872,x96871)))+~P1(f773(f64(x96871,x96872,f773(f773(f302(x96871),x96873),x96874)),x96875))
% 191.21/191.74 [9688]~P1(f773(f773(f334(x96881),f546(x96885,x96884,x96883,x96882,x96881)),f551(x96885,x96884,x96883,x96882,x96881)))+~P1(f773(f64(x96881,x96882,f773(f773(f302(x96881),x96883),x96884)),x96885))
% 191.21/191.74 [9689]~P1(f773(f773(f334(f854(x96891,x96891)),f773(f773(f241(x96891,x96891),x96892),x96895)),f773(f773(f173(f854(x96891,x96891),a841),f773(a114,x96894)),x96893)))+P1(f773(f773(f334(f854(x96891,x96891)),f773(f773(f241(x96891,x96891),x96892),f659(x96893,x96894,x96895,x96892,x96891))),f773(f773(f173(f854(x96891,x96891),a841),x96894),x96893)))
% 191.21/191.74 [9696]P1(f773(f68(x96961,x96961,x96962,f540(x96963,x96964,x96965,x96962,x96961),f545(x96963,x96964,x96965,x96962,x96961)),x96963))+~P1(f773(f64(x96961,x96962,f773(f773(f302(x96961),x96965),x96964)),x96963))
% 191.21/191.74 [9697]P1(f773(f68(x96971,x96971,x96972,f546(x96973,x96974,x96975,x96972,x96971),f551(x96973,x96974,x96975,x96972,x96971)),x96973))+~P1(f773(f64(x96971,x96972,f773(f773(f302(x96971),x96975),x96974)),x96973))
% 191.21/191.74 [9708]~P100(x97081)+P18(x97081,f773(f773(f143(x97082,x97081),x97083),f773(f126(x97082,f773(f773(f9(x97082,x97081,a841),f773(f773(f10(x97081,f855(x97081,a841),x97082),a330),x97083)),f773(x97084,x97085))),x97085)))
% 191.21/191.74 [9763]~P1(f773(f773(f334(x97632),x97635),f773(f277(x97631,x97632,x97634),x97633)))+P1(f773(f773(f334(f854(x97631,x97632)),f773(f773(f241(x97631,x97632),f488(x97633,x97634,x97631,x97635,x97632)),x97635)),x97634))
% 191.21/191.74 [9764]~P1(f773(f773(f334(x97642),x97645),f773(f277(x97641,x97642,x97644),x97643)))+P1(f773(f773(f334(f854(x97641,x97642)),f773(f773(f241(x97641,x97642),f534(x97643,x97644,x97641,x97645,x97642)),x97645)),x97644))
% 191.21/191.74 [9784]~P1(f773(f773(f334(f854(x97841,x97841)),f773(f773(f241(x97841,x97841),x97845),x97844)),f773(f773(f173(f854(x97841,x97841),a841),f773(a114,x97843)),x97842)))+P1(f773(f773(f334(f854(x97841,x97841)),f773(f773(f241(x97841,x97841),f659(x97842,x97843,x97844,x97845,x97841)),x97844)),x97842))
% 191.21/191.74 [9787]~P1(f773(f773(f334(f854(x97871,x97871)),f773(f773(f241(x97871,x97871),x97875),x97874)),f773(f773(f173(f854(x97871,x97871),a841),f773(a114,x97873)),x97872)))+P1(f773(f773(f334(f854(x97871,x97871)),f773(f773(f241(x97871,x97871),f658(x97872,x97873,x97874,x97875,x97871)),x97874)),f773(f773(f173(f854(x97871,x97871),a841),x97873),x97872)))
% 191.21/191.74 [9788]~P1(f773(f773(f334(f854(x97881,x97881)),f773(f773(f241(x97881,x97881),x97885),x97884)),f773(f773(f173(f854(x97881,x97881),a841),f773(a114,x97883)),x97882)))+P1(f773(f773(f334(f854(x97881,x97881)),f773(f773(f241(x97881,x97881),f660(x97882,x97883,x97884,x97885,x97881)),x97884)),f773(f773(f173(f854(x97881,x97881),a841),x97883),x97882)))
% 191.21/191.74 [9789]~P1(f773(f773(f334(f854(f848(x97891),f848(x97891))),f773(f773(f241(f848(x97891),f848(x97891)),x97895),f773(f773(f140(x97891),x97894),x97893))),f147(x97891,x97892)))+P1(f773(f773(f334(f854(x97891,x97891)),f773(f773(f241(x97891,x97891),f717(x97892,x97893,x97894,x97895,x97891)),x97894)),x97892))
% 191.21/191.74 [6985]E(x69851,f183(x69852))+E(f169(x69853,x69852,f773(f773(f773(f74(x69853,f851(x69852)),x69854),x69855),x69851)),f773(f773(f302(x69853),x69855),f169(x69853,x69852,x69854)))
% 191.21/191.74 [7504]~E(x75043,f180(f855(x75042,a841)))+E(f773(f773(f103(f855(x75041,a841)),f773(f773(f46(x75042,f855(x75041,a841)),x75043),x75044)),x75045),x75045)
% 191.21/191.74 [7505]~E(x75053,f180(f855(x75052,a841)))+E(f773(f773(f104(f855(x75051,a841)),f773(f773(f47(x75052,f855(x75051,a841)),x75053),x75054)),x75055),x75055)
% 191.21/191.74 [7867]~E(x78675,f183(x78672))+E(f169(x78671,x78672,f773(f773(f773(f74(x78671,f851(x78672)),x78673),x78674),x78675)),f773(f773(f3(f855(x78671,a841)),f169(x78671,x78672,x78673)),f773(f773(f302(x78671),x78674),f180(f855(x78671,a841)))))
% 191.21/191.74 [7937]~E(x79373,f180(f855(x79372,a841)))+E(f773(f773(f3(f855(x79371,a841)),f773(f773(f47(x79372,f855(x79371,a841)),x79373),x79374)),x79375),f773(f773(f3(f855(x79371,a841)),f239(f855(x79371,a841))),x79375))
% 191.21/191.74 [8065]E(f773(f773(f148(x80651,f773(f773(f125(x80651),x80652),x80653)),x80654),x80655),f773(f773(f125(x80651),f773(f773(f148(x80651,x80652),x80654),x80655)),x80653))+~P1(f773(f773(f233(a847),x80654),f773(f181(f848(x80651)),x80652)))
% 191.21/191.74 [8195]P1(f773(f773(f334(x81951),x81955),f773(f158(x81951),x81953)))+E(f773(f166(x81951,x81952,f773(f773(f167(x81951,x81952),x81953),f773(f773(f143(x81951,x81952),x81954),x81953))),x81955),f183(x81952))
% 191.21/191.74 [8303]~P1(f773(f773(f334(x83031),x83035),f773(f158(x83031),x83033)))+E(f773(f166(x83031,x83032,f773(f773(f167(x83031,x83032),x83033),f773(f773(f143(x83031,x83032),x83034),x83033))),x83035),f773(f227(x83032),f773(x83034,x83035)))
% 191.21/191.74 [8334]E(f773(f773(f153(x83341),f773(f773(f143(a847,x83341),x83342),f130(a847,f773(f294(a847,x83343),x83344)))),x83345),f773(x83342,f773(f773(f82(a847),x83343),x83345)))+~P1(f773(f773(f233(a847),x83345),f773(f773(f3(a847),x83344),x83343)))
% 191.21/191.74 [8347]E(x83471,f2(a101))+E(f121(x83472,x83473,f773(x83474,f773(f773(f3(a101),x83471),f80(a101))),f773(f773(f9(x83472,a101,f849(f851(x83473))),x83475),x83471)),f773(f191(x83472,x83473,x83474,x83475),x83471))
% 191.21/191.74 [8371]~E(x83713,f180(f855(x83711,a841)))+E(f773(f773(f46(x83711,f855(x83712,a841)),x83713),f773(f773(f10(f855(x83712,a841),f855(x83712,a841),x83711),f773(f103(f855(x83712,a841)),x83714)),x83715)),f180(f855(x83712,a841)))
% 191.21/191.74 [8372]~E(x83723,f180(f855(x83721,a841)))+E(f773(f773(f47(x83721,f855(x83722,a841)),x83723),f773(f773(f10(f855(x83722,a841),f855(x83722,a841),x83721),f773(f3(f855(x83722,a841)),x83724)),x83725)),f239(f855(x83722,a841)))
% 191.21/191.74 [8373]~E(x83733,f180(f855(x83731,a841)))+E(f773(f773(f47(x83731,f855(x83732,a841)),x83733),f773(f773(f10(f855(x83732,a841),f855(x83732,a841),x83731),f773(f104(f855(x83732,a841)),x83734)),x83735)),f239(f855(x83732,a841)))
% 191.21/191.74 [8378]~P136(x83782)+E(f773(f773(f8(x83781,x83782),f773(f773(f10(x83782,x83782,x83781),f773(f83(x83782),x83783)),x83784)),x83785),f773(f773(f83(x83782),x83783),f773(f773(f8(x83781,x83782),x83784),x83785)))
% 191.21/191.74 [8642]E(x86421,f180(f855(x86422,a841)))+E(f773(f773(f46(x86422,f855(x86423,a841)),x86421),f773(f773(f10(f855(x86423,a841),f855(x86423,a841),x86422),f773(f103(f855(x86423,a841)),x86424)),x86425)),f773(f773(f103(f855(x86423,a841)),x86424),f773(f773(f46(x86422,f855(x86423,a841)),x86421),x86425)))
% 191.21/191.74 [8643]E(x86431,f180(f855(x86432,a841)))+E(f773(f773(f47(x86432,f855(x86433,a841)),x86431),f773(f773(f10(f855(x86433,a841),f855(x86433,a841),x86432),f773(f3(f855(x86433,a841)),x86434)),x86435)),f773(f773(f3(f855(x86433,a841)),x86434),f773(f773(f46(x86432,f855(x86433,a841)),x86431),x86435)))
% 191.21/191.74 [8644]E(x86441,f180(f855(x86442,a841)))+E(f773(f773(f47(x86442,f855(x86443,a841)),x86441),f773(f773(f10(f855(x86443,a841),f855(x86443,a841),x86442),f773(f104(f855(x86443,a841)),x86444)),x86445)),f773(f773(f104(f855(x86443,a841)),x86444),f773(f773(f47(x86442,f855(x86443,a841)),x86441),x86445)))
% 191.21/191.74 [9063]~P29(x90632,x90631,x90633,f773(f773(f103(f855(x90632,a841)),x90634),x90635))+E(f773(f773(f104(f855(x90631,a841)),f773(f303(x90632,x90631,x90633),f773(f773(f3(f855(x90632,a841)),x90634),x90635))),f773(f303(x90632,x90631,x90633),f773(f773(f3(f855(x90632,a841)),x90635),x90634))),f180(f855(x90631,a841)))
% 191.21/191.74 [9318]~P1(f773(f773(f232(f855(x93183,a841)),f773(f277(x93181,x93183,x93184),x93182)),x93185))+P1(f773(f773(f232(f855(x93181,a841)),x93182),f773(f81(f855(x93181,a841)),f773(f277(x93183,x93181,f773(f278(x93181,x93183),x93184)),f773(f81(f855(x93183,a841)),x93185)))))
% 191.21/191.74 [9341]~P29(x93411,x93412,x93413,f773(f773(f302(x93411),x93414),x93415))+~P1(f773(f773(f334(x93412),f773(x93413,x93414)),f773(f303(x93411,x93412,x93413),f773(f773(f3(f855(x93411,a841)),x93415),f773(f773(f302(x93411),x93414),f180(f855(x93411,a841)))))))
% 191.21/191.74 [9390]P1(f773(f773(f232(f855(x93901,a841)),f773(f277(x93902,x93901,x93903),x93904)),x93905))+~P1(f773(f773(f232(f855(x93902,a841)),x93904),f773(f81(f855(x93902,a841)),f773(f277(x93901,x93902,f773(f278(x93902,x93901),x93903)),f773(f81(f855(x93901,a841)),x93905)))))
% 191.21/191.74 [9463]~P79(x94631)+P1(f773(f773(f232(x94631),f773(f77(x94631),f773(f773(f3(x94631),f773(f773(f82(x94631),x94632),x94633)),f773(f773(f82(x94631),x94634),x94635)))),f773(f773(f82(x94631),f773(f77(x94631),f773(f773(f3(x94631),x94632),x94634))),f773(f77(x94631),f773(f773(f3(x94631),x94633),x94635)))))
% 191.21/191.74 [9556]P1(f773(f773(f334(x95561),f392(x95562,x95563,x95564,x95561,x95565)),x95564))+P1(f773(f773(f232(f855(x95565,a841)),f773(f773(f46(x95561,f855(x95565,a841)),x95564),x95563)),x95562))
% 191.21/191.74 [9728]~P1(f773(f773(f232(f855(x97281,a841)),f773(x97284,f392(x97285,x97284,x97283,x97282,x97281))),x97285))+P1(f773(f773(f232(f855(x97281,a841)),f773(f773(f46(x97282,f855(x97281,a841)),x97283),x97284)),x97285))
% 191.21/191.74 [8487]E(f773(f773(f125(x84871),x84872),f773(f773(f148(x84871,x84873),f773(f773(f3(a847),x84874),f773(f181(f848(x84871)),x84872))),x84875)),f773(f773(f148(x84871,f773(f773(f125(x84871),x84872),x84873)),x84874),x84875))+P1(f773(f773(f233(a847),x84874),f773(f181(f848(x84871)),x84872)))
% 191.21/191.74 [8512]~P135(x85121)+E(f773(f773(f82(x85121),f773(f773(f83(x85121),x85122),x85123)),f773(f773(f82(x85121),f773(f773(f83(x85121),x85124),x85123)),x85125)),f773(f773(f82(x85121),f773(f773(f83(x85121),f773(f773(f82(x85121),x85122),x85124)),x85123)),x85125))
% 191.21/191.74 [9020]~P136(x90201)+E(f773(f155(x90201),f773(f773(f143(x90202,x90201),f773(f773(f10(x90201,x90201,x90202),f773(f83(x90201),x90203)),x90204)),x90205)),f773(f773(f83(x90201),x90203),f773(f155(x90201),f773(f773(f143(x90202,x90201),x90204),x90205))))
% 191.21/191.74 [9397]~P136(x93972)+E(f773(f773(f8(x93971,x93972),f773(f773(f9(x93971,x93972,x93972),f773(f773(f10(x93972,f855(x93972,x93972),x93971),f83(x93972)),x93973)),x93974)),x93975),f773(f773(f83(x93972),f773(f773(f8(x93971,x93972),x93973),x93975)),x93974))
% 191.21/191.74 [9398]~P61(x93982)+E(f773(f773(f8(x93981,x93982),f773(f773(f9(x93981,x93982,x93982),f773(f773(f10(x93982,f855(x93982,x93982),x93981),f283(x93982)),x93983)),x93984)),x93985),f773(f773(f283(x93982),f773(f773(f8(x93981,x93982),x93983),x93985)),x93984))
% 191.21/191.74 [9405]~P66(x94052)+E(f773(f773(f8(x94051,x94052),f773(f773(f20(x94051,x94052,x94052),f773(f773(f10(x94052,f855(x94052,x94052),x94051),f82(x94052)),x94053)),x94054)),x94055),f773(f773(f82(x94052),f773(f773(f8(x94051,x94052),x94053),x94055)),f773(f773(f8(x94051,x94052),x94054),x94055)))
% 191.21/191.74 [9406]~P6(x94062)+E(f773(f773(f8(x94061,x94062),f773(f773(f20(x94061,x94062,x94062),f773(f773(f10(x94062,f855(x94062,x94062),x94061),f3(x94062)),x94063)),x94064)),x94065),f773(f773(f3(x94062),f773(f773(f8(x94061,x94062),x94063),x94065)),f773(f773(f8(x94061,x94062),x94064),x94065)))
% 191.21/191.74 [9407]~P70(x94072)+E(f773(f773(f11(x94071,x94072),f773(f773(f20(x94071,x94072,x94072),f773(f773(f10(x94072,f855(x94072,x94072),x94071),f83(x94072)),x94073)),x94074)),x94075),f773(f773(f83(x94072),f773(f773(f11(x94071,x94072),x94073),x94075)),f773(f773(f11(x94071,x94072),x94074),x94075)))
% 191.21/191.74 [9446]~E(x94463,f180(f855(x94461,a841)))+E(f773(f773(f46(x94461,f855(x94462,a841)),x94463),f773(f773(f9(x94461,f855(x94462,a841),f855(x94462,a841)),f773(f773(f10(f855(x94462,a841),f855(f855(x94462,a841),f855(x94462,a841)),x94461),f103(f855(x94462,a841))),x94464)),x94465)),f180(f855(x94462,a841)))
% 191.21/191.74 [9447]~E(x94473,f180(f855(x94471,a841)))+E(f773(f773(f47(x94471,f855(x94472,a841)),x94473),f773(f773(f9(x94471,f855(x94472,a841),f855(x94472,a841)),f773(f773(f10(f855(x94472,a841),f855(f855(x94472,a841),f855(x94472,a841)),x94471),f3(f855(x94472,a841))),x94474)),x94475)),f239(f855(x94472,a841)))
% 191.21/191.74 [9448]~E(x94483,f180(f855(x94481,a841)))+E(f773(f773(f47(x94481,f855(x94482,a841)),x94483),f773(f773(f9(x94481,f855(x94482,a841),f855(x94482,a841)),f773(f773(f10(f855(x94482,a841),f855(f855(x94482,a841),f855(x94482,a841)),x94481),f104(f855(x94482,a841))),x94484)),x94485)),f239(f855(x94482,a841)))
% 191.21/191.74 [9473]E(x94731,f180(f855(x94732,a841)))+E(f773(f773(f46(x94732,f855(x94733,a841)),x94731),f773(f773(f9(x94732,f855(x94733,a841),f855(x94733,a841)),f773(f773(f10(f855(x94733,a841),f855(f855(x94733,a841),f855(x94733,a841)),x94732),f103(f855(x94733,a841))),x94734)),x94735)),f773(f773(f103(f855(x94733,a841)),f773(f773(f46(x94732,f855(x94733,a841)),x94731),x94734)),x94735))
% 191.21/191.74 [9474]E(x94741,f180(f855(x94742,a841)))+E(f773(f773(f47(x94742,f855(x94743,a841)),x94741),f773(f773(f9(x94742,f855(x94743,a841),f855(x94743,a841)),f773(f773(f10(f855(x94743,a841),f855(f855(x94743,a841),f855(x94743,a841)),x94742),f3(f855(x94743,a841))),x94744)),x94745)),f773(f773(f3(f855(x94743,a841)),f773(f773(f47(x94742,f855(x94743,a841)),x94741),x94744)),x94745))
% 191.21/191.74 [9475]E(x94751,f180(f855(x94752,a841)))+E(f773(f773(f47(x94752,f855(x94753,a841)),x94751),f773(f773(f9(x94752,f855(x94753,a841),f855(x94753,a841)),f773(f773(f10(f855(x94753,a841),f855(f855(x94753,a841),f855(x94753,a841)),x94752),f104(f855(x94753,a841))),x94754)),x94755)),f773(f773(f104(f855(x94753,a841)),f773(f773(f47(x94752,f855(x94753,a841)),x94751),x94754)),x94755))
% 191.21/191.74 [9067]~P1(f773(f773(f232(a847),x90671),x90674))+E(f773(f773(f3(a847),f773(f773(f82(a847),f773(f773(f83(a847),x90671),x90672)),x90673)),f773(f773(f82(a847),f773(f773(f83(a847),x90674),x90672)),x90675)),f773(f773(f3(a847),x90673),f773(f773(f82(a847),f773(f773(f83(a847),f773(f773(f3(a847),x90674),x90671)),x90672)),x90675)))
% 191.21/191.74 [9609]~P136(x96091)+E(f773(f155(x96091),f773(f773(f143(x96092,x96091),f773(f773(f9(x96092,x96091,x96091),f773(f773(f10(x96091,f855(x96091,x96091),x96092),f83(x96091)),x96093)),x96094)),x96095)),f773(f773(f83(x96091),f773(f155(x96091),f773(f773(f143(x96092,x96091),x96093),x96095))),x96094))
% 191.21/191.74 [9615]~P66(x96151)+E(f773(f155(x96151),f773(f773(f143(x96152,x96151),f773(f773(f20(x96152,x96151,x96151),f773(f773(f10(x96151,f855(x96151,x96151),x96152),f82(x96151)),x96153)),x96154)),x96155)),f773(f773(f82(x96151),f773(f155(x96151),f773(f773(f143(x96152,x96151),x96153),x96155))),f773(f155(x96151),f773(f773(f143(x96152,x96151),x96154),x96155))))
% 191.21/191.74 [9616]~P6(x96161)+E(f773(f155(x96161),f773(f773(f143(x96162,x96161),f773(f773(f20(x96162,x96161,x96161),f773(f773(f10(x96161,f855(x96161,x96161),x96162),f3(x96161)),x96163)),x96164)),x96165)),f773(f773(f3(x96161),f773(f155(x96161),f773(f773(f143(x96162,x96161),x96163),x96165))),f773(f155(x96161),f773(f773(f143(x96162,x96161),x96164),x96165))))
% 191.21/191.74 [9285]~P1(f773(f773(f232(a847),x92854),x92851))+E(f773(f773(f3(a847),f773(f773(f82(a847),f773(f773(f83(a847),x92851),x92852)),x92853)),f773(f773(f82(a847),f773(f773(f83(a847),x92854),x92852)),x92855)),f773(f773(f3(a847),f773(f773(f82(a847),f773(f773(f83(a847),f773(f773(f3(a847),x92851),x92854)),x92852)),x92853)),x92855))
% 191.21/191.74 [10013]P28(x100131,x100132,f773(f303(a843,f846(x100131),f773(f773(f20(a843,f855(x100131,f855(a844,a841)),f846(x100131)),f773(f773(f20(a843,a842,f855(f855(x100131,f855(a844,a841)),f846(x100131))),f773(f773(f10(f855(x100131,f855(a844,a841)),f855(a842,f855(f855(x100131,f855(a844,a841)),f846(x100131))),a843),f93(x100131)),x100133)),a27)),x100134)),x100135))+~P28(x100131,f773(f773(f103(f855(f846(x100131),a841)),x100132),f773(f303(a843,f846(x100131),f773(f773(f20(a843,f855(x100131,f855(a844,a841)),f846(x100131)),f773(f773(f20(a843,a842,f855(f855(x100131,f855(a844,a841)),f846(x100131))),f773(f773(f10(f855(x100131,f855(a844,a841)),f855(a842,f855(f855(x100131,f855(a844,a841)),f846(x100131))),a843),f93(x100131)),x100133)),a27)),x100134)),x100135)),f773(f303(a843,f846(x100131),f773(f773(f20(a843,f855(x100131,f855(a844,a841)),f846(x100131)),f773(f773(f20(a843,a842,f855(f855(x100131,f855(a844,a841)),f846(x100131))),f773(f773(f10(f855(x100131,f855(a844,a841)),f855(a842,f855(f855(x100131,f855(a844,a841)),f846(x100131))),a843),f93(x100131)),x100133)),f773(f773(f10(f851(a842),a842,a843),f231(a842)),a30))),x100134)),x100135))
% 191.21/191.74 [5146]E(x51461,x51462)+~E(f33(x51463,x51464,x51461),f33(x51465,x51466,x51462))
% 191.21/191.74 [5147]E(x51471,x51472)+~E(f33(x51473,x51471,x51474),f33(x51475,x51472,x51476))
% 191.21/191.74 [5148]E(x51481,x51482)+~E(f33(x51481,x51483,x51484),f33(x51482,x51485,x51486))
% 191.21/191.74 [5149]E(x51491,x51492)+~E(f32(x51493,x51494,x51491),f32(x51495,x51496,x51492))
% 191.21/191.74 [5150]E(x51501,x51502)+~E(f32(x51503,x51501,x51504),f32(x51505,x51502,x51506))
% 191.21/191.74 [5151]E(x51511,x51512)+~E(f32(x51511,x51513,x51514),f32(x51512,x51515,x51516))
% 191.21/191.74 [5152]E(x51521,x51522)+~E(f31(x51523,x51524,x51521),f31(x51525,x51526,x51522))
% 191.21/191.74 [5153]E(x51531,x51532)+~E(f31(x51533,x51531,x51534),f31(x51535,x51532,x51536))
% 191.21/191.74 [5154]E(x51541,x51542)+~E(f31(x51541,x51543,x51544),f31(x51542,x51545,x51546))
% 191.21/191.74 [7173]E(x71731,x71732)+~E(f215(x71733,x71734,x71735,x71731),f215(x71733,x71734,x71736,x71732))
% 191.21/191.74 [7174]E(x71741,x71742)+~E(f215(x71743,x71744,x71741,x71745),f215(x71743,x71744,x71742,x71746))
% 191.21/191.74 [6616]E(f773(f170(x66161,x66162,x66163,x66164),x66165),f773(f227(x66162),x66166))+~E(f773(x66164,x66165),f773(f227(x66162),x66166))
% 191.21/191.74 [6768]E(f773(f229(f851(x67681),x67682,f183(x67681),x67683),f773(x67684,x67685)),f773(x67683,x67686))+~E(f773(x67684,x67685),f773(f227(x67682),x67686))
% 191.21/191.74 [8314]~P23(x83145,x83141,x83142,x83146)+E(f773(f75(x83141,x83141,x83141,f773(x83142,x83143)),f773(x83142,x83144)),f773(f75(x83141,x83141,x83141,f773(x83142,x83144)),f773(x83142,x83143)))
% 191.21/191.74 [8547]~P55(x85474,x85475,x85472,x85471,x85476)+E(f773(x85471,f773(x85472,x85473)),x85473)
% 191.21/191.74 [8688]P29(x86881,x86882,x86883,x86884)+~P29(x86881,x86885,f773(f75(x86882,x86885,x86881,x86886),x86883),x86884)
% 191.21/191.74 [8765]~P29(x87654,x87652,f773(f75(x87651,x87652,x87654,x87653),x87655),x87656)+P29(x87651,x87652,x87653,f773(f303(x87654,x87651,x87655),x87656))
% 191.21/191.74 [9408]P1(f773(f63(x94081),x94082))+~P1(f773(f68(x94081,x94083,x94084,x94085,x94082),x94086))
% 191.21/191.74 [9418]~P1(f773(f773(f334(x94184),x94183),f292(x94184,x94185,x94181,x94182,x94186)))+P1(f773(f773(x94181,x94182),x94183))
% 191.21/191.74 [9419]~P1(f773(f773(f334(x94194),x94193),f289(x94194,x94191,x94195,x94192,x94196)))+P1(f773(f773(x94191,x94192),x94193))
% 191.21/191.74 [9420]~P1(f773(f773(f334(x94204),x94202),f292(x94204,x94201,x94205,x94206,x94203)))+P1(f773(f773(x94201,x94202),x94203))
% 191.21/191.74 [9421]~P1(f773(f773(f334(x94214),x94212),f289(x94214,x94215,x94211,x94216,x94213)))+P1(f773(f773(x94211,x94212),x94213))
% 191.21/191.74 [5633]E(x56331,x56332)+~E(f773(f773(f241(x56333,x56334),x56335),x56331),f773(f773(f241(x56333,x56334),x56336),x56332))
% 191.21/191.74 [5635]E(x56351,x56352)+~E(f773(f773(f241(x56353,x56354),x56351),x56355),f773(f773(f241(x56353,x56354),x56352),x56356))
% 191.21/191.74 [5774]~P20(x57745,x57746,x57741)+E(f773(f773(x57741,x57742),f773(f773(x57741,x57743),x57744)),f773(f773(x57741,x57743),f773(f773(x57741,x57742),x57744)))
% 191.21/191.74 [7244]~P34(x72444,x72441,f773(f773(f140(x72444),x72442),x72445),f773(f773(f140(x72444),x72443),x72446))+P1(f773(f773(x72441,x72442),x72443))
% 191.21/191.74 [7623]P34(x76231,x76232,x76233,x76234)+~P34(x76231,x76232,f773(f773(f140(x76231),x76235),x76233),f773(f773(f140(x76231),x76236),x76234))
% 191.21/191.74 [8633]~P55(x86335,x86331,x86332,x86336,x86334)+P1(f773(f773(f334(x86331),f773(x86332,x86333)),x86334))
% 191.21/191.74 [8787]E(f773(f78(x87871,x87872,x87873,x87874,x87875),x87876),f773(x87873,x87876))+P1(f773(f773(f334(x87871),x87876),x87875))
% 191.21/191.74 [8805]~E(x88053,f773(f773(f140(x88051),x88055),x88056))+P1(f773(f773(f334(f854(f848(x88051),f848(x88051))),f773(f773(f241(f848(x88051),f848(x88051)),x88052),f773(f773(f125(x88051),x88052),x88053))),f137(x88051,x88054)))
% 191.21/191.74 [8809]E(f773(f78(x88091,x88092,x88093,x88094,x88095),x88096),f773(x88094,x88096))+~P1(f773(f773(f334(x88091),x88096),x88095))
% 191.21/191.74 [9485]~P27(x94854,x94852,x94855,x94853,x94856,x94851)+E(f773(x94851,f180(f855(x94852,a841))),x94853)
% 191.21/191.74 [9690]~E(f773(x96904,f773(f240(x96901,x96903),x96905)),f773(x96906,f773(f240(x96901,x96903),x96905)))+E(f773(f252(x96901,x96902,x96903,x96903,x96904,f39(x96903)),x96905),f773(f252(x96901,x96902,x96903,x96903,x96906,f39(x96903)),x96905))
% 191.21/191.74 [9691]~E(f773(x96914,f773(f250(x96911,x96912),x96915)),f773(x96916,f773(f250(x96911,x96912),x96915)))+E(f773(f252(x96911,x96911,x96912,x96913,f39(x96911),x96914),x96915),f773(f252(x96911,x96911,x96912,x96913,f39(x96911),x96916),x96915))
% 191.21/191.74 [9751]~E(f773(f252(x97512,x97516,x97513,x97513,x97511,f39(x97513)),x97514),f773(f252(x97512,x97516,x97513,x97513,x97515,f39(x97513)),x97514))+E(f773(x97511,f773(f240(x97512,x97513),x97514)),f773(x97515,f773(f240(x97512,x97513),x97514)))
% 191.21/191.74 [9752]~E(f773(f252(x97522,x97522,x97523,x97526,f39(x97522),x97521),x97524),f773(f252(x97522,x97522,x97523,x97526,f39(x97522),x97525),x97524))+E(f773(x97521,f773(f250(x97522,x97523),x97524)),f773(x97525,f773(f250(x97522,x97523),x97524)))
% 191.21/191.74 [8722]P1(f773(f773(f334(x87221),x87222),x87223))+~P1(f773(f773(f334(f854(x87221,x87224)),f773(f773(f241(x87221,x87224),x87222),x87225)),f773(f773(f248(x87221,x87224),x87223),x87226)))
% 191.21/191.74 [8737]P1(f773(f773(f334(x87371),x87372),f773(x87373,x87374)))+~P1(f773(f773(f334(f854(x87375,x87371)),f773(f773(f241(x87375,x87371),x87374),x87372)),f773(f773(f248(x87375,x87371),x87376),x87373)))
% 191.21/191.74 [9043]P1(f773(f773(f334(x90431),x90434),f169(x90431,x90432,x90436)))+E(f170(x90431,x90432,f773(f773(f773(f74(x90431,f851(x90432)),x90433),x90434),f773(f227(x90432),x90435)),x90436),f773(f773(f773(f74(x90431,f851(x90432)),f170(x90431,x90432,x90433,x90436)),x90434),f773(f227(x90432),x90435)))
% 191.21/191.74 [9134]P1(f773(f773(f334(f854(x91341,x91341)),f773(f773(f241(x91341,x91341),f773(x91342,x91343)),f773(x91342,x91344))),x91345))+~P1(f773(f773(f334(f854(x91346,x91346)),f773(f773(f241(x91346,x91346),x91343),x91344)),f773(f773(f280(x91341,x91346),x91345),x91342)))
% 191.21/191.74 [9146]~P1(f773(f773(f334(f854(x91464,x91464)),f773(f773(f241(x91464,x91464),f773(x91466,x91462)),f773(x91466,x91463))),x91465))+P1(f773(f773(f334(f854(x91461,x91461)),f773(f773(f241(x91461,x91461),x91462),x91463)),f773(f773(f280(x91464,x91461),x91465),x91466)))
% 191.21/191.74 [9754]E(f773(f773(f241(x97541,x97542),f705(x97543,x97544,x97545,x97546,x97542,x97541)),f708(x97543,x97544,x97545,x97546,x97542,x97541)),x97546)+~P1(f773(f773(f334(f854(x97541,x97542)),x97546),f773(f773(f281(x97541,x97545,x97542),x97544),x97543)))
% 191.21/191.74 [9962]~P1(f773(f773(f334(f854(x99621,x99626)),x99625),f773(f773(f281(x99621,x99622,x99626),x99624),x99623)))+P1(f773(f773(f334(f854(x99621,x99622)),f773(f773(f241(x99621,x99622),f705(x99623,x99624,x99622,x99625,x99626,x99621)),f709(x99623,x99624,x99622,x99625,x99626,x99621))),x99624))
% 191.21/191.74 [9963]~P1(f773(f773(f334(f854(x99636,x99632)),x99635),f773(f773(f281(x99636,x99631,x99632),x99634),x99633)))+P1(f773(f773(f334(f854(x99631,x99632)),f773(f773(f241(x99631,x99632),f709(x99633,x99634,x99631,x99635,x99632,x99636)),f708(x99633,x99634,x99631,x99635,x99632,x99636))),x99633))
% 191.21/191.74 [6052]~E(x60526,x60524)+E(f773(f773(f773(f773(f74(x60521,x60522),x60523),x60524),x60525),x60526),x60525)
% 191.21/191.74 [6101]E(x61011,x61012)+E(f773(f773(f773(f773(f74(x61013,x61014),x61015),x61012),x61016),x61011),f773(x61015,x61011))
% 191.21/191.74 [7689]~P9(x76892)+E(f773(f773(f46(x76891,x76892),x76893),f773(f773(f9(x76891,x76894,x76892),x76895),x76896)),f773(f773(f773(f46(x76891,f855(x76894,x76892)),x76893),x76895),x76896))
% 191.21/191.74 [7690]~P9(x76902)+E(f773(f773(f47(x76901,x76902),x76903),f773(f773(f9(x76901,x76904,x76902),x76905),x76906)),f773(f773(f773(f47(x76901,f855(x76904,x76902)),x76903),x76905),x76906))
% 191.21/191.74 [8469]E(f773(f773(f46(x84691,f855(x84692,a841)),x84693),f773(f773(f10(f855(x84692,a841),f855(x84692,a841),x84691),f773(f302(x84692),x84694)),x84695)),f773(f773(f302(x84692),x84694),f773(f773(f46(x84691,f855(x84692,a841)),x84693),x84695)))+~P1(f773(f773(f334(x84691),x84696),x84693))
% 191.21/191.74 [8849]~P9(x88492)+E(f773(f773(f46(x88491,x88492),x88493),f773(f773(f10(f855(x88494,x88492),x88492,x88491),f773(f46(x88494,x88492),x88495)),f773(f9(x88494,x88491,x88492),x88496))),f773(f773(f46(x88494,x88492),x88495),f773(f773(f10(f855(x88491,x88492),x88492,x88494),f773(f46(x88491,x88492),x88493)),x88496)))
% 191.21/191.74 [8850]~P9(x88502)+E(f773(f773(f47(x88501,x88502),x88503),f773(f773(f10(f855(x88504,x88502),x88502,x88501),f773(f47(x88504,x88502),x88505)),f773(f9(x88504,x88501,x88502),x88506))),f773(f773(f47(x88504,x88502),x88505),f773(f773(f10(f855(x88501,x88502),x88502,x88504),f773(f47(x88501,x88502),x88503)),x88506)))
% 191.21/191.74 [9051]P1(f773(f773(f334(x90511),x90512),f773(f158(x90511),x90513)))+~P1(f773(f773(f334(f854(x90514,x90511)),f773(f773(f241(x90514,x90511),x90515),x90512)),f773(f158(f854(x90514,x90511)),f773(f773(f167(x90514,x90511),x90516),x90513))))
% 191.21/191.74 [9052]P1(f773(f773(f334(x90521),x90522),f773(f158(x90521),x90523)))+~P1(f773(f773(f334(f854(x90521,x90524)),f773(f773(f241(x90521,x90524),x90522),x90525)),f773(f158(f854(x90521,x90524)),f773(f773(f167(x90521,x90524),x90523),x90526))))
% 191.21/191.74 [9144]P1(f773(f773(f232(f855(x91441,a841)),f773(f277(x91442,x91441,x91443),x91444)),x91445))+~P1(f773(f773(f232(f855(f854(x91442,x91441),a841)),x91443),f773(f773(f248(x91442,x91441),x91446),f773(f18(f855(x91441,a841),x91442),x91445))))
% 191.21/191.74 [9321]P1(f773(f773(f334(f854(f848(x93211),f848(x93211))),f773(f773(f241(f848(x93211),f848(x93211)),f773(f773(f140(x93211),x93212),x93213)),f773(f773(f140(x93211),x93214),x93215))),f137(x93211,x93216)))+~P1(f773(f773(f334(f854(x93211,x93211)),f773(f773(f241(x93211,x93211),x93212),x93214)),x93216))
% 191.21/191.74 [9750]E(f773(f773(f241(x97501,x97502),f612(x97503,x97504,x97505,x97502,x97501,x97506)),f615(x97503,x97504,x97505,x97502,x97501,x97506)),x97506)+P1(f773(f773(f334(x97505),x97504),f773(f773(f251(x97501,x97502,f855(x97505,a841)),x97503),x97506)))
% 191.21/191.74 [9755]E(f773(f773(f241(x97551,x97552),f613(x97553,x97554,x97552,x97551,x97555,x97556)),f614(x97553,x97554,x97552,x97551,x97555,x97556)),x97553)+~P1(f773(f773(f334(x97556),x97555),f773(f773(f251(x97551,x97552,f855(x97556,a841)),x97554),x97553)))
% 191.21/191.74 [9917]P1(f773(f773(f334(x99171),x99172),f773(f773(x99173,f613(x99174,x99173,x99175,x99176,x99172,x99171)),f614(x99174,x99173,x99175,x99176,x99172,x99171))))+~P1(f773(f773(f334(x99171),x99172),f773(f773(f251(x99176,x99175,f855(x99171,a841)),x99173),x99174)))
% 191.21/191.74 [9941]~P1(f773(f773(f334(x99411),x99412),f773(f773(x99415,f612(x99415,x99412,x99411,x99414,x99413,x99416)),f615(x99415,x99412,x99411,x99414,x99413,x99416))))+P1(f773(f773(f334(x99411),x99412),f773(f773(f251(x99413,x99414,f855(x99411,a841)),x99415),x99416)))
% 191.21/191.74 [7814]P1(f773(f773(f334(x78141),x78144),x78146))+E(f172(x78141,x78142,f773(f773(f773(f74(x78141,f851(x78142)),x78143),x78144),x78145),x78146),f172(x78141,x78142,x78143,x78146))
% 191.21/191.74 [7889]P1(f773(f773(f334(x78891),x78894),x78896))+E(f773(f303(x78891,x78892,f773(f773(f773(f74(x78891,x78892),x78893),x78894),x78895)),x78896),f773(f303(x78891,x78892,x78893),x78896))
% 191.21/191.74 [7917]P1(f773(f773(f334(x79171),x79174),f773(f158(x79171),x79176)))+E(f773(f773(f143(x79171,x79172),f773(f773(f773(f74(x79171,x79172),x79173),x79174),x79175)),x79176),f773(f773(f143(x79171,x79172),x79173),x79176))
% 191.21/191.74 [8364]E(x83641,x83642)+E(f773(f773(f148(x83643,f773(f773(f148(x83643,x83644),x83641),x83645)),x83642),x83646),f773(f773(f148(x83643,f773(f773(f148(x83643,x83644),x83642),x83646)),x83641),x83645))
% 191.21/191.74 [8855]~P1(f773(f773(f334(x88553),x88556),x88555))+E(f773(f773(f302(x88551),x88552),f773(f303(x88553,x88551,x88554),f773(f773(f3(f855(x88553,a841)),x88555),f773(f773(f302(x88553),x88556),f180(f855(x88553,a841)))))),f773(f303(x88553,x88551,f773(f773(f773(f74(x88553,x88551),x88554),x88556),x88552)),x88555))
% 191.21/191.74 [8683]~E(x86833,x86836)+E(f773(f166(x86831,x86832,f773(f773(f140(f854(x86831,x86832)),f773(f773(f241(x86831,x86832),x86833),x86834)),x86835)),x86836),f773(f227(x86832),x86834))
% 191.21/191.74 [8724]E(x87241,x87242)+E(f773(f166(x87243,x87244,f773(f773(f140(f854(x87243,x87244)),f773(f773(f241(x87243,x87244),x87241),x87245)),x87246)),x87242),f773(f166(x87243,x87244,x87246),x87242))
% 191.21/191.74 [8930]~P1(f773(f773(x89304,x89305),x89306))+P1(f773(f773(f773(f773(f103(f855(x89301,f855(x89302,a841))),x89303),x89304),x89305),x89306))
% 191.21/191.74 [8932]~P1(f773(f773(x89323,x89325),x89326))+P1(f773(f773(f773(f773(f103(f855(x89321,f855(x89322,a841))),x89323),x89324),x89325),x89326))
% 191.21/191.74 [8948]P1(f773(f773(f334(x89481),x89486),f773(f158(x89481),x89484)))+E(f773(f170(x89481,x89482,x89483,f166(x89481,x89482,f773(f142(f854(x89481,x89482)),f773(f773(f167(x89481,x89482),x89484),x89485)))),x89486),f773(x89483,x89486))
% 191.21/191.74 [9097]~E(f773(f181(f848(x90971)),x90974),f773(f181(f848(x90972)),x90975))+E(f170(x90971,x90972,x90973,f166(x90971,x90972,f773(f142(f854(x90971,x90972)),f773(f773(f167(x90971,x90972),x90974),f773(f773(f125(x90972),x90975),x90976))))),f170(x90971,x90972,x90973,f166(x90971,x90972,f773(f142(f854(x90971,x90972)),f773(f773(f167(x90971,x90972),x90974),x90975)))))
% 191.21/191.74 [9184]P1(f773(f773(x91841,x91842),x91843))+~P1(f773(f773(f773(f773(f104(f855(x91844,f855(x91845,a841))),x91846),x91841),x91842),x91843))
% 191.21/191.74 [9185]P1(f773(f773(x91851,x91852),x91853))+~P1(f773(f773(f773(f773(f104(f855(x91854,f855(x91855,a841))),x91851),x91856),x91852),x91853))
% 191.21/191.74 [9598]~P66(x95982)+E(f773(f773(f8(x95981,x95982),f773(f773(f9(x95981,f855(x95983,a841),x95982),f773(f773(f10(f855(x95983,x95982),f855(f855(x95983,a841),x95982),x95981),f8(x95983,x95982)),x95984)),x95985)),x95986),f773(f773(f8(f854(x95981,x95983),x95982),f773(f251(x95981,x95983,x95982),x95984)),f773(f773(f248(x95981,x95983),x95986),f773(f18(f855(x95983,a841),x95981),x95985))))
% 191.21/191.74 [9599]~P70(x95992)+E(f773(f773(f11(x95991,x95992),f773(f773(f9(x95991,f855(x95993,a841),x95992),f773(f773(f10(f855(x95993,x95992),f855(f855(x95993,a841),x95992),x95991),f11(x95993,x95992)),x95994)),x95995)),x95996),f773(f773(f11(f854(x95991,x95993),x95992),f773(f251(x95991,x95993,x95992),x95994)),f773(f773(f248(x95991,x95993),x95996),f773(f18(f855(x95993,a841),x95991),x95995))))
% 191.21/191.74 [9717]~P66(x97172)+E(f773(f773(f8(x97171,x97172),f773(f773(f9(x97171,f855(x97173,a841),x97172),f773(f773(f10(f855(x97173,x97172),f855(f855(x97173,a841),x97172),x97171),f8(x97173,x97172)),f773(f9(x97173,x97171,x97172),x97174))),x97175)),x97176),f773(f773(f8(x97173,x97172),f773(f773(f9(x97173,f855(x97171,a841),x97172),f773(f773(f10(f855(x97171,x97172),f855(f855(x97171,a841),x97172),x97173),f8(x97171,x97172)),x97174)),x97176)),x97175))
% 191.21/191.74 [9186]~E(f773(f181(f848(x91861)),x91864),f773(f181(f848(x91862)),x91866))+E(f170(x91861,x91862,x91863,f166(x91861,x91862,f773(f142(f854(x91861,x91862)),f773(f773(f167(x91861,x91862),f773(f773(f125(x91861),x91864),x91865)),x91866)))),f170(x91861,x91862,x91863,f166(x91861,x91862,f773(f142(f854(x91861,x91862)),f773(f773(f167(x91861,x91862),x91864),x91866)))))
% 191.21/191.74 [9450]~P1(f773(f773(f334(x94501),x94505),x94504))+E(f773(f773(f773(f74(x94501,f851(x94502)),f172(x94501,x94502,x94503,f773(f773(f3(f855(x94501,a841)),x94504),f773(f773(f302(x94501),x94505),f180(f855(x94501,a841)))))),x94505),x94506),f172(x94501,x94502,f773(f773(f773(f74(x94501,f851(x94502)),x94503),x94505),x94506),x94504))
% 191.21/191.74 [9657]E(f170(x96571,x96572,x96573,f166(x96571,x96572,f773(f142(f854(x96571,x96572)),f773(f773(f167(x96571,x96572),f773(f773(f125(x96571),x96574),f773(f773(f140(x96571),x96575),f115(x96571)))),x96576)))),f773(f773(f773(f74(x96571,f851(x96572)),f170(x96571,x96572,x96573,f166(x96571,x96572,f773(f142(f854(x96571,x96572)),f773(f773(f167(x96571,x96572),x96574),x96576))))),x96575),f773(f227(x96572),f773(f773(f153(x96572),x96576),f773(f181(f848(x96571)),x96574)))))+~P1(f773(f773(f233(a847),f773(f181(f848(x96571)),x96574)),f773(f181(f848(x96572)),x96576)))
% 191.21/191.74 [10016]~P1(f773(f773(f334(f854(x100161,x100162)),f773(f773(f241(x100161,x100162),x100165),x100166)),f773(f773(f103(f855(f854(x100161,x100162),a841)),x100163),x100164)))+P1(f773(f773(f773(f773(f103(f855(x100161,f855(x100162,a841))),f773(f773(f9(x100161,f855(f854(x100161,x100162),a841),f855(x100162,a841)),f773(f773(f10(f855(x100162,f855(f855(f854(x100161,x100162),a841),a841)),f855(f855(f854(x100161,x100162),a841),f855(x100162,a841)),x100161),f9(x100162,f855(f854(x100161,x100162),a841),a841)),f773(f773(f10(f855(x100162,f854(x100161,x100162)),f855(x100162,f855(f855(f854(x100161,x100162),a841),a841)),x100161),f773(f10(f854(x100161,x100162),f855(f855(f854(x100161,x100162),a841),a841),x100162),f334(f854(x100161,x100162)))),f241(x100161,x100162)))),x100163)),f773(f773(f9(x100161,f855(f854(x100161,x100162),a841),f855(x100162,a841)),f773(f773(f10(f855(x100162,f855(f855(f854(x100161,x100162),a841),a841)),f855(f855(f854(x100161,x100162),a841),f855(x100162,a841)),x100161),f9(x100162,f855(f854(x100161,x100162),a841),a841)),f773(f773(f10(f855(x100162,f854(x100161,x100162)),f855(x100162,f855(f855(f854(x100161,x100162),a841),a841)),x100161),f773(f10(f854(x100161,x100162),f855(f855(f854(x100161,x100162),a841),a841),x100162),f334(f854(x100161,x100162)))),f241(x100161,x100162)))),x100164)),x100165),x100166))
% 191.21/191.74 [10017]~P1(f773(f773(f334(f854(x100171,x100172)),f773(f773(f241(x100171,x100172),x100175),x100176)),f773(f773(f104(f855(f854(x100171,x100172),a841)),x100173),x100174)))+P1(f773(f773(f773(f773(f104(f855(x100171,f855(x100172,a841))),f773(f773(f9(x100171,f855(f854(x100171,x100172),a841),f855(x100172,a841)),f773(f773(f10(f855(x100172,f855(f855(f854(x100171,x100172),a841),a841)),f855(f855(f854(x100171,x100172),a841),f855(x100172,a841)),x100171),f9(x100172,f855(f854(x100171,x100172),a841),a841)),f773(f773(f10(f855(x100172,f854(x100171,x100172)),f855(x100172,f855(f855(f854(x100171,x100172),a841),a841)),x100171),f773(f10(f854(x100171,x100172),f855(f855(f854(x100171,x100172),a841),a841),x100172),f334(f854(x100171,x100172)))),f241(x100171,x100172)))),x100173)),f773(f773(f9(x100171,f855(f854(x100171,x100172),a841),f855(x100172,a841)),f773(f773(f10(f855(x100172,f855(f855(f854(x100171,x100172),a841),a841)),f855(f855(f854(x100171,x100172),a841),f855(x100172,a841)),x100171),f9(x100172,f855(f854(x100171,x100172),a841),a841)),f773(f773(f10(f855(x100172,f854(x100171,x100172)),f855(x100172,f855(f855(f854(x100171,x100172),a841),a841)),x100171),f773(f10(f854(x100171,x100172),f855(f855(f854(x100171,x100172),a841),a841),x100172),f334(f854(x100171,x100172)))),f241(x100171,x100172)))),x100174)),x100175),x100176))
% 191.21/191.74 [10021]P1(f773(f773(f334(f854(x100211,x100212)),f773(f773(f241(x100211,x100212),x100213),x100214)),f773(f773(f103(f855(f854(x100211,x100212),a841)),x100215),x100216)))+~P1(f773(f773(f773(f773(f103(f855(x100211,f855(x100212,a841))),f773(f773(f9(x100211,f855(f854(x100211,x100212),a841),f855(x100212,a841)),f773(f773(f10(f855(x100212,f855(f855(f854(x100211,x100212),a841),a841)),f855(f855(f854(x100211,x100212),a841),f855(x100212,a841)),x100211),f9(x100212,f855(f854(x100211,x100212),a841),a841)),f773(f773(f10(f855(x100212,f854(x100211,x100212)),f855(x100212,f855(f855(f854(x100211,x100212),a841),a841)),x100211),f773(f10(f854(x100211,x100212),f855(f855(f854(x100211,x100212),a841),a841),x100212),f334(f854(x100211,x100212)))),f241(x100211,x100212)))),x100215)),f773(f773(f9(x100211,f855(f854(x100211,x100212),a841),f855(x100212,a841)),f773(f773(f10(f855(x100212,f855(f855(f854(x100211,x100212),a841),a841)),f855(f855(f854(x100211,x100212),a841),f855(x100212,a841)),x100211),f9(x100212,f855(f854(x100211,x100212),a841),a841)),f773(f773(f10(f855(x100212,f854(x100211,x100212)),f855(x100212,f855(f855(f854(x100211,x100212),a841),a841)),x100211),f773(f10(f854(x100211,x100212),f855(f855(f854(x100211,x100212),a841),a841),x100212),f334(f854(x100211,x100212)))),f241(x100211,x100212)))),x100216)),x100213),x100214))
% 191.21/191.74 [10022]P1(f773(f773(f334(f854(x100221,x100222)),f773(f773(f241(x100221,x100222),x100223),x100224)),f773(f773(f104(f855(f854(x100221,x100222),a841)),x100225),x100226)))+~P1(f773(f773(f773(f773(f104(f855(x100221,f855(x100222,a841))),f773(f773(f9(x100221,f855(f854(x100221,x100222),a841),f855(x100222,a841)),f773(f773(f10(f855(x100222,f855(f855(f854(x100221,x100222),a841),a841)),f855(f855(f854(x100221,x100222),a841),f855(x100222,a841)),x100221),f9(x100222,f855(f854(x100221,x100222),a841),a841)),f773(f773(f10(f855(x100222,f854(x100221,x100222)),f855(x100222,f855(f855(f854(x100221,x100222),a841),a841)),x100221),f773(f10(f854(x100221,x100222),f855(f855(f854(x100221,x100222),a841),a841),x100222),f334(f854(x100221,x100222)))),f241(x100221,x100222)))),x100225)),f773(f773(f9(x100221,f855(f854(x100221,x100222),a841),f855(x100222,a841)),f773(f773(f10(f855(x100222,f855(f855(f854(x100221,x100222),a841),a841)),f855(f855(f854(x100221,x100222),a841),f855(x100222,a841)),x100221),f9(x100222,f855(f854(x100221,x100222),a841),a841)),f773(f773(f10(f855(x100222,f854(x100221,x100222)),f855(x100222,f855(f855(f854(x100221,x100222),a841),a841)),x100221),f773(f10(f854(x100221,x100222),f855(f855(f854(x100221,x100222),a841),a841),x100222),f334(f854(x100221,x100222)))),f241(x100221,x100222)))),x100226)),x100223),x100224))
% 191.21/191.74 [10011]~P1(f773(f773(f334(f854(x100112,x100113)),f773(f773(f241(x100112,x100113),x100115),x100116)),f773(f773(f46(x100111,f855(f854(x100112,x100113),a841)),f239(f855(x100111,a841))),x100114)))+P1(f773(f773(f773(f773(f46(x100111,f855(x100112,f855(x100113,a841))),f239(f855(x100111,a841))),f773(f773(f10(f855(f854(x100112,x100113),a841),f855(x100112,f855(x100113,a841)),x100111),f773(f9(x100112,f855(f854(x100112,x100113),a841),f855(x100113,a841)),f773(f773(f10(f855(x100113,f855(f855(f854(x100112,x100113),a841),a841)),f855(f855(f854(x100112,x100113),a841),f855(x100113,a841)),x100112),f9(x100113,f855(f854(x100112,x100113),a841),a841)),f773(f773(f10(f855(x100113,f854(x100112,x100113)),f855(x100113,f855(f855(f854(x100112,x100113),a841),a841)),x100112),f773(f10(f854(x100112,x100113),f855(f855(f854(x100112,x100113),a841),a841),x100113),f334(f854(x100112,x100113)))),f241(x100112,x100113))))),x100114)),x100115),x100116))
% 191.21/191.74 [10012]~P1(f773(f773(f334(f854(x100122,x100123)),f773(f773(f241(x100122,x100123),x100125),x100126)),f773(f773(f47(x100121,f855(f854(x100122,x100123),a841)),f239(f855(x100121,a841))),x100124)))+P1(f773(f773(f773(f773(f47(x100121,f855(x100122,f855(x100123,a841))),f239(f855(x100121,a841))),f773(f773(f10(f855(f854(x100122,x100123),a841),f855(x100122,f855(x100123,a841)),x100121),f773(f9(x100122,f855(f854(x100122,x100123),a841),f855(x100123,a841)),f773(f773(f10(f855(x100123,f855(f855(f854(x100122,x100123),a841),a841)),f855(f855(f854(x100122,x100123),a841),f855(x100123,a841)),x100122),f9(x100123,f855(f854(x100122,x100123),a841),a841)),f773(f773(f10(f855(x100123,f854(x100122,x100123)),f855(x100123,f855(f855(f854(x100122,x100123),a841),a841)),x100122),f773(f10(f854(x100122,x100123),f855(f855(f854(x100122,x100123),a841),a841),x100123),f334(f854(x100122,x100123)))),f241(x100122,x100123))))),x100124)),x100125),x100126))
% 191.21/191.74 [10019]P1(f773(f773(f334(f854(x100191,x100192)),f773(f773(f241(x100191,x100192),x100193),x100194)),f773(f773(f46(x100195,f855(f854(x100191,x100192),a841)),f239(f855(x100195,a841))),x100196)))+~P1(f773(f773(f773(f773(f46(x100195,f855(x100191,f855(x100192,a841))),f239(f855(x100195,a841))),f773(f773(f10(f855(f854(x100191,x100192),a841),f855(x100191,f855(x100192,a841)),x100195),f773(f9(x100191,f855(f854(x100191,x100192),a841),f855(x100192,a841)),f773(f773(f10(f855(x100192,f855(f855(f854(x100191,x100192),a841),a841)),f855(f855(f854(x100191,x100192),a841),f855(x100192,a841)),x100191),f9(x100192,f855(f854(x100191,x100192),a841),a841)),f773(f773(f10(f855(x100192,f854(x100191,x100192)),f855(x100192,f855(f855(f854(x100191,x100192),a841),a841)),x100191),f773(f10(f854(x100191,x100192),f855(f855(f854(x100191,x100192),a841),a841),x100192),f334(f854(x100191,x100192)))),f241(x100191,x100192))))),x100196)),x100193),x100194))
% 191.21/191.74 [10020]P1(f773(f773(f334(f854(x100201,x100202)),f773(f773(f241(x100201,x100202),x100203),x100204)),f773(f773(f47(x100205,f855(f854(x100201,x100202),a841)),f239(f855(x100205,a841))),x100206)))+~P1(f773(f773(f773(f773(f47(x100205,f855(x100201,f855(x100202,a841))),f239(f855(x100205,a841))),f773(f773(f10(f855(f854(x100201,x100202),a841),f855(x100201,f855(x100202,a841)),x100205),f773(f9(x100201,f855(f854(x100201,x100202),a841),f855(x100202,a841)),f773(f773(f10(f855(x100202,f855(f855(f854(x100201,x100202),a841),a841)),f855(f855(f854(x100201,x100202),a841),f855(x100202,a841)),x100201),f9(x100202,f855(f854(x100201,x100202),a841),a841)),f773(f773(f10(f855(x100202,f854(x100201,x100202)),f855(x100202,f855(f855(f854(x100201,x100202),a841),a841)),x100201),f773(f10(f854(x100201,x100202),f855(f855(f854(x100201,x100202),a841),a841),x100202),f334(f854(x100201,x100202)))),f241(x100201,x100202))))),x100206)),x100203),x100204))
% 191.21/191.74 [9119]E(x91191,x91192)+~E(f319(x91193,x91194,x91195,x91196,x91191),f319(x91193,x91194,x91195,x91197,x91192))
% 191.21/191.74 [9120]E(x91201,x91202)+~E(f319(x91203,x91204,x91205,x91201,x91206),f319(x91203,x91204,x91205,x91202,x91207))
% 191.21/191.74 [7362]E(f773(x73621,f773(x73622,x73623)),f773(x73624,x73623))+~E(f773(f75(x73625,x73626,x73627,x73621),x73622),x73624)
% 191.21/191.74 [9484]~P26(x94843,x94844,x94841,x94845,x94846,x94847)+E(f773(f773(x94841,x94842),x94842),x94842)
% 191.21/191.74 [9810]~P51(x98105,x98106,x98107,x98101,x98104,x98102,x98103)+P1(f773(f773(x98101,x98102),f588(x98103,x98102,x98104,x98101)))
% 191.21/191.74 [9835]~E(f773(f229(f851(x98357),x98351,f183(x98357),x98355),f773(x98354,x98353)),f773(f227(x98357),x98352))+E(f773(f227(x98351),f712(x98352,x98353,x98354,x98355,x98356,x98357,x98351)),f773(x98354,x98353))
% 191.21/191.74 [9836]~E(f773(f229(f851(x98366),x98367,f183(x98366),x98361),f773(x98364,x98363)),f773(f227(x98366),x98362))+E(f773(x98361,f712(x98362,x98363,x98364,x98361,x98365,x98366,x98367)),f773(f227(x98366),x98362))
% 191.21/191.74 [5870]~E(f773(f773(f143(x58701,x58705),x58706),x58702),f773(f773(f143(x58703,x58705),x58707),x58704))+E(f773(f181(f848(x58701)),x58702),f773(f181(f848(x58703)),x58704))
% 191.21/191.74 [7438]E(x74381,x74382)+~E(f773(f773(f773(f74(x74383,f851(x74384)),x74385),x74386),f773(f227(x74384),x74381)),f773(f773(f773(f74(x74383,f851(x74384)),x74387),x74386),f773(f227(x74384),x74382)))
% 191.21/191.74 [8399]E(f773(x83991,f773(x83992,x83993)),f773(x83994,x83993))+~E(f773(f75(x83995,x83996,x83997,x83991),x83992),f773(f75(x83996,x83996,x83997,f39(x83996)),x83994))
% 191.21/191.74 [9815]~P51(x98155,x98156,x98157,x98154,x98151,x98153,x98152)+P1(f773(f773(x98151,f588(x98152,x98153,x98151,x98154)),x98152))
% 191.21/191.74 [5917]E(x59171,x59172)+~E(f773(f773(f773(f93(x59173),x59174),x59175),x59171),f773(f773(f773(f93(x59173),x59176),x59177),x59172))
% 191.21/191.74 [5918]E(x59181,x59182)+~E(f773(f773(f773(f93(x59183),x59184),x59181),x59185),f773(f773(f773(f93(x59183),x59186),x59182),x59187))
% 191.21/191.74 [5919]E(x59191,x59192)+~E(f773(f773(f773(f93(x59193),x59191),x59194),x59195),f773(f773(f773(f93(x59193),x59192),x59196),x59197))
% 191.21/191.74 [8812]~P24(x88126,x88121,x88123,x88127)+E(f773(f75(x88121,x88121,x88122,f773(x88123,x88124)),f773(f75(x88121,x88121,x88122,f773(x88123,x88124)),x88125)),f773(f75(x88121,x88121,x88122,f773(x88123,x88124)),x88125))
% 191.21/191.74 [8811]~P1(f773(f773(f334(x88111),x88112),f773(f773(x88115,x88116),x88117)))+P1(f773(f773(f334(x88111),x88112),f773(f773(f251(x88113,x88114,f855(x88111,a841)),x88115),f773(f773(f241(x88113,x88114),x88116),x88117))))
% 191.21/191.74 [9078]P1(f773(f773(f773(x90781,x90782),x90783),x90784))+~P1(f773(f773(f773(f251(x90785,x90786,f855(x90787,a841)),x90781),f773(f773(f241(x90785,x90786),x90782),x90783)),x90784))
% 191.21/191.74 [9198]P1(f773(f773(f334(x91981),f773(f773(x91982,x91983),x91984)),f773(f303(f854(x91985,x91986),x91981,f773(f251(x91985,x91986,x91981),x91982)),x91987)))+~P1(f773(f773(f334(f854(x91985,x91986)),f773(f773(f241(x91985,x91986),x91983),x91984)),x91987))
% 191.21/191.74 [9523]P1(f773(f773(f334(f854(f848(x95231),f848(x95231))),f773(f773(f241(f848(x95231),f848(x95231)),f773(f773(f125(x95231),x95232),f773(f773(f140(x95231),x95233),x95234))),f773(f773(f125(x95231),x95232),f773(f773(f140(x95231),x95235),x95236)))),f137(x95231,x95237)))+~P1(f773(f773(f334(f854(x95231,x95231)),f773(f773(f241(x95231,x95231),x95233),x95235)),x95237))
% 191.21/191.74 [9940]P51(x99401,x99402,x99403,f773(f773(f9(x99401,f855(f854(x99401,x99402),a841),f855(x99402,a841)),f773(f773(f10(f855(x99402,f855(f855(f854(x99401,x99402),a841),a841)),f855(f855(f854(x99401,x99402),a841),f855(x99402,a841)),x99401),f9(x99402,f855(f854(x99401,x99402),a841),a841)),f773(f773(f10(f855(x99402,f854(x99401,x99402)),f855(x99402,f855(f855(f854(x99401,x99402),a841),a841)),x99401),f773(f10(f854(x99401,x99402),f855(f855(f854(x99401,x99402),a841),a841),x99402),f334(f854(x99401,x99402)))),f241(x99401,x99402)))),x99404),f773(f773(f9(x99402,f855(f854(x99402,x99403),a841),f855(x99403,a841)),f773(f773(f10(f855(x99403,f855(f855(f854(x99402,x99403),a841),a841)),f855(f855(f854(x99402,x99403),a841),f855(x99403,a841)),x99402),f9(x99403,f855(f854(x99402,x99403),a841),a841)),f773(f773(f10(f855(x99403,f854(x99402,x99403)),f855(x99403,f855(f855(f854(x99402,x99403),a841),a841)),x99402),f773(f10(f854(x99402,x99403),f855(f855(f854(x99402,x99403),a841),a841),x99403),f334(f854(x99402,x99403)))),f241(x99402,x99403)))),x99405),x99406,x99407)+~P1(f773(f773(f334(f854(x99401,x99403)),f773(f773(f241(x99401,x99403),x99406),x99407)),f773(f773(f281(x99401,x99402,x99403),x99404),x99405)))
% 191.21/191.74 [9969]~P51(x99691,x99695,x99692,f773(f773(f9(x99691,f855(f854(x99691,x99695),a841),f855(x99695,a841)),f773(f773(f10(f855(x99695,f855(f855(f854(x99691,x99695),a841),a841)),f855(f855(f854(x99691,x99695),a841),f855(x99695,a841)),x99691),f9(x99695,f855(f854(x99691,x99695),a841),a841)),f773(f773(f10(f855(x99695,f854(x99691,x99695)),f855(x99695,f855(f855(f854(x99691,x99695),a841),a841)),x99691),f773(f10(f854(x99691,x99695),f855(f855(f854(x99691,x99695),a841),a841),x99695),f334(f854(x99691,x99695)))),f241(x99691,x99695)))),x99696),f773(f773(f9(x99695,f855(f854(x99695,x99692),a841),f855(x99692,a841)),f773(f773(f10(f855(x99692,f855(f855(f854(x99695,x99692),a841),a841)),f855(f855(f854(x99695,x99692),a841),f855(x99692,a841)),x99695),f9(x99692,f855(f854(x99695,x99692),a841),a841)),f773(f773(f10(f855(x99692,f854(x99695,x99692)),f855(x99692,f855(f855(f854(x99695,x99692),a841),a841)),x99695),f773(f10(f854(x99695,x99692),f855(f855(f854(x99695,x99692),a841),a841),x99692),f334(f854(x99695,x99692)))),f241(x99695,x99692)))),x99697),x99693,x99694)+P1(f773(f773(f334(f854(x99691,x99692)),f773(f773(f241(x99691,x99692),x99693),x99694)),f773(f773(f281(x99691,x99695,x99692),x99696),x99697)))
% 191.21/191.74 [9587]P1(f773(f773(f334(x95871),x95874),f773(f158(x95871),x95876)))+E(f170(x95871,x95872,f773(f773(f773(f74(x95871,f851(x95872)),x95873),x95874),f773(f227(x95872),x95875)),f166(x95871,x95872,f773(f142(f854(x95871,x95872)),f773(f773(f167(x95871,x95872),x95876),x95877)))),f773(f773(f773(f74(x95871,f851(x95872)),f170(x95871,x95872,x95873,f166(x95871,x95872,f773(f142(f854(x95871,x95872)),f773(f773(f167(x95871,x95872),x95876),x95877))))),x95874),f773(f227(x95872),x95875)))
% 191.21/191.74 [9073]E(x90731,x90732)+E(f773(f773(f773(f74(x90733,x90734),f773(f773(f773(f74(x90733,x90734),x90735),x90731),x90736)),x90732),x90737),f773(f773(f773(f74(x90733,x90734),f773(f773(f773(f74(x90733,x90734),x90735),x90732),x90737)),x90731),x90736))
% 191.21/191.74 [9325]E(f170(x93251,x93252,f773(f773(f773(f74(x93251,f851(x93252)),x93253),x93254),f773(f227(x93252),x93255)),f166(x93251,x93252,f773(f142(f854(x93251,x93252)),f773(f773(f167(x93251,x93252),x93256),x93257)))),f170(x93251,x93252,x93253,f166(x93251,x93252,f773(f142(f854(x93251,x93252)),f773(f773(f167(x93251,x93252),x93256),x93257)))))+~P1(f773(f773(f334(x93251),x93254),f773(f158(x93251),f773(f773(f159(x93251),f773(f181(f848(x93252)),x93257)),x93256))))
% 191.21/191.74 [9605]E(f170(x96051,x96052,f773(f773(f773(f74(x96051,f851(x96052)),x96053),x96054),f773(f227(x96052),x96055)),f166(x96051,x96052,f773(f142(f854(x96051,x96052)),f773(f773(f167(x96051,x96052),x96056),x96057)))),f773(f773(f773(f74(x96051,f851(x96052)),f170(x96051,x96052,x96053,f166(x96051,x96052,f773(f142(f854(x96051,x96052)),f773(f773(f167(x96051,x96052),x96056),x96057))))),x96054),f773(f227(x96052),x96055)))+P1(f773(f773(f334(x96051),x96054),f773(f158(x96051),f773(f773(f159(x96051),f773(f181(f848(x96052)),x96057)),x96056))))
% 191.21/191.74 [9951]P1(f773(f773(f334(x99511),f668(x99512,x99513,x99514,x99515,x99516,x99517,x99511)),x99515))+P1(f773(f773(f773(f773(f47(x99511,f855(x99517,f855(x99516,a841))),x99515),x99514),x99513),x99512))
% 191.21/191.74 [9952]P1(f773(f773(f334(x99521),f430(x99522,x99523,x99524,x99525,x99526,x99527,x99521)),x99525))+~P1(f773(f773(f773(f773(f46(x99521,f855(x99527,f855(x99526,a841))),x99525),x99524),x99523),x99522))
% 191.21/191.74 [9979]P1(f773(f773(f773(x99791,f430(x99792,x99793,x99791,x99794,x99795,x99796,x99797)),x99793),x99792))+~P1(f773(f773(f773(f773(f46(x99797,f855(x99796,f855(x99795,a841))),x99794),x99791),x99793),x99792))
% 191.21/191.74 [9996]~P1(f773(f773(f773(x99965,f668(x99967,x99966,x99965,x99964,x99963,x99962,x99961)),x99966),x99967))+P1(f773(f773(f773(f773(f47(x99961,f855(x99962,f855(x99963,a841))),x99964),x99965),x99966),x99967))
% 191.21/191.74 [9961]~P136(x99612)+E(f773(f773(f8(x99611,x99612),f773(f773(f9(x99611,f855(x99613,a841),x99612),f773(f773(f10(f855(x99613,x99612),f855(f855(x99613,a841),x99612),x99611),f8(x99613,x99612)),f773(f773(f9(x99611,f855(x99613,x99612),f855(x99613,x99612)),f773(f773(f10(f855(x99612,x99612),f855(f855(x99613,x99612),f855(x99613,x99612)),x99611),f10(x99612,x99612,x99613)),f773(f773(f10(x99612,f855(x99612,x99612),x99611),f83(x99612)),x99614))),x99615))),x99616)),x99617),f773(f773(f83(x99612),f773(f773(f8(x99611,x99612),x99614),x99617)),f773(f773(f8(x99613,x99612),x99615),x99616)))
% 191.21/191.74 [9110]~P23(x91107,x91101,x91103,x91108)+E(f773(f75(x91101,x91101,x91102,f773(x91103,x91104)),f773(f75(x91101,x91101,x91102,f773(x91103,x91105)),x91106)),f773(f75(x91101,x91101,x91102,f773(x91103,x91105)),f773(f75(x91101,x91101,x91102,f773(x91103,x91104)),x91106)))
% 191.21/191.74 [10014]E(f773(f773(f241(x100141,x100142),f773(x100143,f573(x100144,x100145,x100143,x100146,x100147,x100148,x100142,x100141))),f773(x100145,f574(x100144,x100145,x100143,x100146,x100147,x100148,x100142,x100141))),x100148)+~P1(f773(f773(f334(f854(x100141,x100142)),x100148),f773(f303(f854(x100147,x100146),f854(x100141,x100142),f252(x100147,x100141,x100146,x100142,x100143,x100145)),x100144)))
% 191.21/191.74 [10026]~P1(f773(f773(f334(f854(x100268,x100267)),x100266),f773(f303(f854(x100261,x100262),f854(x100268,x100267),f252(x100261,x100268,x100262,x100267,x100265,x100264)),x100263)))+P1(f773(f773(f334(f854(x100261,x100262)),f773(f773(f241(x100261,x100262),f573(x100263,x100264,x100265,x100262,x100261,x100266,x100267,x100268)),f574(x100263,x100264,x100265,x100262,x100261,x100266,x100267,x100268))),x100263))
% 191.21/191.74 [9513]P1(f773(f773(f334(f854(f854(x95131,x95132),f854(x95131,x95132))),f773(f773(f241(f854(x95131,x95132),f854(x95131,x95132)),f773(f773(f241(x95131,x95132),x95133),x95134)),f773(f773(f241(x95131,x95132),x95135),x95136))),f325(x95131,x95132,x95137,x95138)))+~P1(f773(f773(f334(f854(x95131,x95131)),f773(f773(f241(x95131,x95131),x95133),x95135)),x95137))
% 191.21/191.74 [8405]E(f773(x84051,f773(x84052,x84053)),f773(x84054,f773(x84055,x84053)))+~E(f773(f75(x84056,x84057,x84058,x84051),x84052),f773(f75(x84059,x84057,x84058,x84054),x84055))
% 191.21/191.74 [9886]P1(f773(f773(f334(f854(x98861,x98862)),f773(f773(f241(x98861,x98862),f773(x98863,x98864)),f773(x98865,x98866))),f773(f303(f854(x98867,x98868),f854(x98861,x98862),f252(x98867,x98861,x98868,x98862,x98863,x98865)),x98869)))+~P1(f773(f773(f334(f854(x98867,x98868)),f773(f773(f241(x98867,x98868),x98864),x98866)),x98869))
% 191.21/191.74 [8664]~E(f773(x86644,f773(x86645,x86646)),f773(x86649,f773(x866410,x866411)))+E(f773(f773(f75(x86641,x86642,x86643,x86644),x86645),x86646),f773(f773(f75(x86647,x86642,x86648,x86649),x866410),x866411))
% 191.21/191.74 [4492]~P100(x44921)+~P92(x44921)+E(f179(x44921),f103(x44921))
% 191.21/191.74 [4493]~P100(x44931)+~P98(x44931)+E(f236(x44931),f104(x44931))
% 191.21/191.74 [4727]~P110(x47271)+~P88(x47271)+E(f773(f77(x47271),f773(f106(x47271),a99)),f80(x47271))
% 191.21/191.74 [5002]E(x50021,f2(a1))+E(f84(a1,x50021),f773(f81(a1),f80(a1)))+P1(f773(f773(f233(a1),f2(a1)),x50021))
% 191.21/191.74 [5204]E(x52041,f2(a1))+E(f84(a1,x52041),f80(a1))+~P1(f773(f773(f233(a1),f2(a1)),x52041))
% 191.21/191.74 [7249]~P38(x72491)+P1(f773(f63(a1),x72491))+~P1(f773(f63(a847),f773(f303(a1,a847,a107),x72491)))
% 191.21/191.74 [8511]~P13(a5000)+~P1(f773(f773(f334(f854(a843,a842)),x85111),f773(f158(f854(a843,a842)),a29)))+P1(f773(f773(f251(a843,a842,a841),f773(f18(f855(a842,a841),a843),a26)),x85111))
% 191.21/191.74 [9483]E(x94831,f180(f855(f854(a847,a847),a841)))+~P1(f773(f63(f854(a847,a847)),x94831))+P1(f773(f773(f334(f854(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841))),f773(f773(f241(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841)),f180(f855(f854(a847,a847),a841))),x94831)),a41))
% 191.21/191.74 [9630]E(x96301,f2(a847))+E(x96301,f773(a114,f2(a847)))+~P1(f773(f773(f233(a847),x96301),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))))
% 191.21/191.74 [9912]E(x99121,f2(a101))+E(f773(f773(f82(a1),f773(f773(f83(a1),f773(f106(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),f773(a23,f773(f773(f43(a101),x99121),f773(f106(a101),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))))),f80(a1)),f773(a23,x99121))+E(f52(a101,x99121,f773(f106(a101),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),f2(a101))
% 191.21/191.74 [9759]E(x97591,f2(a101))+~E(f52(a101,x97591,f773(f106(a101),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),f2(a101))+E(f773(f773(f83(a1),f773(f106(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),f773(a23,f773(f773(f43(a101),x97591),f773(f106(a101),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))))),f773(a23,x97591))
% 191.21/191.74 [4563]~P56(x45631,x45632)+P42(x45631,x45632)+~P43(a841)
% 191.21/191.74 [4503]~P2(x45031)+P33(x45031,x45032)+~E(x45032,f2(x45031))
% 191.21/191.74 [4512]~P110(x45121)+~E(x45122,f2(x45121))+E(f84(x45121,x45122),f2(x45121))
% 191.21/191.74 [4513]~P82(x45131)+~E(x45132,f2(x45131))+E(f84(x45131,x45132),f2(x45131))
% 191.21/191.74 [4519]~P2(x45192)+~P33(x45192,x45191)+E(x45191,f2(x45192))
% 191.21/191.74 [4553]~P110(x45532)+~E(f84(x45532,x45531),f2(x45532))+E(x45531,f2(x45532))
% 191.21/191.74 [4571]~P10(x45712)+~P10(x45711)+P10(f188(x45711,x45712))
% 191.21/191.74 [4572]~P59(x45722)+~P59(x45721)+P59(f856(x45721,x45722))
% 191.21/191.74 [4573]~P59(x45732)+~P59(x45731)+P59(f855(x45731,x45732))
% 191.21/191.74 [4574]~P59(x45742)+~P59(x45741)+P59(f854(x45741,x45742))
% 191.21/191.74 [4575]~P139(x45752)+~P139(x45751)+P139(f854(x45751,x45752))
% 191.21/191.74 [4930]~P10(x49302)+~P10(x49301)+P10(f52(a1,x49301,x49302))
% 191.21/191.74 [4521]~P68(x45211)+~E(x45212,f2(x45211))+E(f773(f81(x45211),x45212),x45212)
% 191.21/191.74 [4525]~P87(x45251)+~E(x45252,f2(a1))+E(f773(f105(x45251),x45252),f2(x45251))
% 191.21/191.74 [4526]~P133(x45261)+~E(x45262,f2(a1))+E(f773(f105(x45261),x45262),f2(x45261))
% 191.21/191.74 [4550]~P69(x45501)+~E(f2(x45501),x45502)+E(f773(f81(x45501),x45502),f2(x45501))
% 191.21/191.74 [4551]~P69(x45511)+~E(x45512,f2(x45511))+E(f773(f81(x45511),x45512),f2(x45511))
% 191.21/191.74 [4552]~P79(x45521)+~E(x45522,f2(x45521))+E(f773(f77(x45521),x45522),f2(x45521))
% 191.21/191.74 [4577]~P68(x45772)+E(x45771,f2(x45772))+~E(f773(f81(x45772),x45771),x45771)
% 191.21/191.74 [4585]E(x45851,f773(a107,x45852))+~E(x45851,f2(a847))+~E(x45852,f773(f102(a1),x45851))
% 191.21/191.74 [4586]E(f773(a107,x45861),x45862)+~E(x45862,f2(a847))+~E(x45861,f773(f102(a1),x45862))
% 191.21/191.74 [4590]~P87(x45902)+E(x45901,f2(a1))+~E(f773(f105(x45902),x45901),f2(x45902))
% 191.21/191.74 [4595]~P69(x45952)+E(x45951,f2(x45952))+~E(f773(f81(x45952),x45951),f2(x45952))
% 191.21/191.74 [4596]~P79(x45962)+E(x45961,f2(x45962))+~E(f773(f77(x45962),x45961),f2(x45962))
% 191.21/191.74 [4597]~P69(x45971)+E(f2(x45971),x45972)+~E(f773(f81(x45971),x45972),f2(x45971))
% 191.21/191.74 [4731]~P13(a5000)+~E(f773(a30,x47312),f773(f227(a842),x47311))+P1(f773(a26,x47311))
% 191.21/191.74 [4770]~P100(x47701)+~P18(x47701,x47702)+P18(x47701,f773(f157(x47701),x47702))
% 191.21/191.74 [4796]~P1(x47962)+~P1(x47961)+P1(f773(f773(a331,x47961),x47962))
% 191.21/191.74 [4830]~E(f80(a847),f2(a847))+E(f773(f42(x48301),x48302),f2(a847))+~P1(f773(f63(x48301),x48302))
% 191.21/191.74 [4861]~P105(x48611)+~P136(x48611)+E(f773(f773(f242(x48611),f2(x48611)),f773(a114,x48612)),f2(x48611))
% 191.21/191.74 [4901]~P100(x49011)+P18(x49011,f130(x49011,x49012))+~P1(f773(f63(x49011),x49012))
% 191.21/191.74 [4921]~P100(x49211)+E(f773(f158(x49211),f130(x49211,x49212)),x49212)+~P1(f773(f63(x49211),x49212))
% 191.21/191.74 [4955]P1(x49551)+P1(x49552)+~P1(f773(f773(a332,x49552),x49551))
% 191.21/191.74 [4967]E(x49671,f180(f855(x49672,a841)))+~E(f773(f42(x49672),x49671),f2(a847))+~P1(f773(f63(x49672),x49671))
% 191.21/191.74 [4972]P1(x49721)+~P1(x49722)+~P1(f773(f773(a335,x49722),x49721))
% 191.21/191.74 [5020]~P65(x50201)+E(f773(f77(x50201),x50202),x50202)+P1(f773(f773(f233(x50201),x50202),f2(x50201)))
% 191.21/191.74 [5117]~P1(f773(a26,x51172))+~P1(f773(a26,x51171))+P1(f773(a26,f36(x51171,x51172)))
% 191.21/191.74 [5124]E(x51241,f115(x51242))+P1(f773(f127(x51242),f116(x51242,x51241)))+~P1(f773(f127(x51242),x51241))
% 191.21/191.74 [5129]~P100(x51291)+~P1(f773(f63(x51291),x51292))+P1(f773(f127(x51291),f130(x51291,x51292)))
% 191.21/191.74 [5135]~P133(x51351)+E(f773(f102(x51351),f773(a107,x51352)),f773(f105(x51351),x51352))+P1(f773(f773(f233(a1),x51352),f2(a1)))
% 191.21/191.74 [5161]P11(x51612,x51611)+E(f773(x51611,f504(x51611)),f773(x51611,f520(x51611)))+P1(f773(f773(x51611,f504(x51611)),f520(x51611)))
% 191.21/191.74 [5174]E(f773(f102(a1),f616(x51741,x51742)),x51741)+P1(f773(x51742,f773(a107,x51741)))+~P1(f773(x51742,f2(a847)))
% 191.21/191.74 [5214]~P110(x52141)+~E(f84(x52141,x52142),f773(f81(x52141),f80(x52141)))+P1(f773(f773(f233(x52141),x52142),f2(x52141)))
% 191.21/191.74 [5287]~E(x52872,f2(a1))+E(f210(x52871,x52872),f773(f773(f241(a1,a1),f2(a1)),f80(a1)))+P1(f773(f773(f233(a1),x52872),f2(a1)))
% 191.21/191.74 [5288]~E(x52881,f2(a1))+E(f210(x52881,x52882),f773(f773(f241(a1,a1),f2(a1)),f80(a1)))+P1(f773(f773(f233(a1),x52882),f2(a1)))
% 191.21/191.74 [5339]E(f773(f102(a1),f616(x53391,x53392)),x53391)+P1(f773(x53392,f773(a107,x53391)))+P1(f773(f773(f233(a1),x53391),f2(a1)))
% 191.21/191.74 [5405]~P110(x54051)+E(f84(x54051,x54052),f773(f81(x54051),f80(x54051)))+~P1(f773(f773(f233(x54051),x54052),f2(x54051)))
% 191.21/191.74 [5406]~P79(x54061)+E(f773(f77(x54061),x54062),f773(f81(x54061),x54062))+~P1(f773(f773(f233(x54061),x54062),f2(x54061)))
% 191.21/191.74 [5407]~P79(x54071)+E(f773(f77(x54071),x54072),f773(f81(x54071),x54072))+~P1(f773(f773(f232(x54071),x54072),f2(x54071)))
% 191.21/191.74 [5408]~P65(x54081)+E(f773(f77(x54081),x54082),f773(f81(x54081),x54082))+~P1(f773(f773(f233(x54081),x54082),f2(x54081)))
% 191.21/191.74 [5500]~P1(f773(x55001,f616(x55002,x55001)))+P1(f773(x55001,f773(a107,x55002)))+~P1(f773(x55001,f2(a847)))
% 191.21/191.74 [5507]E(x55071,f2(a847))+E(f773(a114,f559(x55072,x55071)),x55071)+~P1(f773(f773(f233(a847),x55071),f773(a114,x55072)))
% 191.21/191.74 [5510]P11(x55101,x55102)+~E(f773(x55102,f504(x55102)),f773(x55102,f520(x55102)))+~P1(f773(f773(x55102,f504(x55102)),f520(x55102)))
% 191.21/191.74 [5529]~P100(x55291)+P18(x55291,x55292)+P1(f773(f773(f232(a847),f760(x55292,x55291)),f761(x55292,x55291)))
% 191.21/191.74 [5615]~P79(x56151)+~E(x56152,f2(x56151))+P1(f773(f773(f232(x56151),f773(f77(x56151),x56152)),f2(x56151)))
% 191.21/191.74 [5704]~P1(f773(x57041,f616(x57042,x57041)))+P1(f773(x57041,f773(a107,x57042)))+P1(f773(f773(f233(a1),x57042),f2(a1)))
% 191.21/191.74 [5730]~P1(f773(x57301,f773(a107,x57302)))+P1(f773(x57301,f2(a847)))+~P1(f773(f773(f233(a1),x57302),f2(a1)))
% 191.21/191.74 [6074]~P110(x60741)+~P1(f773(f773(f233(x60741),x60742),f2(x60741)))+P1(f773(f773(f233(x60741),f84(x60741,x60742)),f2(x60741)))
% 191.21/191.74 [6191]~P110(x61911)+P1(f773(f773(f233(x61911),f773(f105(x61911),x61912)),f2(x61911)))+~P1(f773(f773(f233(a1),x61912),f2(a1)))
% 191.21/191.74 [6192]~P110(x61921)+P1(f773(f773(f232(x61921),f773(f105(x61921),x61922)),f2(x61921)))+~P1(f773(f773(f232(a1),x61922),f2(a1)))
% 191.21/191.74 [6197]~P79(x61972)+E(x61971,f2(x61972))+~P1(f773(f773(f232(x61972),f773(f77(x61972),x61971)),f2(x61972)))
% 191.21/191.74 [6282]~P133(x62821)+~P1(f773(f773(f334(x62821),x62822),f112(x62821)))+P1(f773(f773(f334(x62821),f773(f81(x62821),x62822)),f112(x62821)))
% 191.21/191.74 [6314]~P110(x63141)+~P1(f773(f773(f233(x63141),f84(x63141,x63142)),f2(x63141)))+P1(f773(f773(f233(x63141),x63142),f2(x63141)))
% 191.21/191.74 [6395]~P99(x63951)+P50(a847,x63951,f279(a847),x63952)+P1(f773(f773(f279(a847),f377(x63952,x63951)),f393(x63952,x63951)))
% 191.21/191.74 [6493]~P110(x64932)+~P1(f773(f773(f233(x64932),f773(f105(x64932),x64931)),f2(x64932)))+P1(f773(f773(f233(a1),x64931),f2(a1)))
% 191.21/191.74 [6494]~P110(x64942)+~P1(f773(f773(f232(x64942),f773(f105(x64942),x64941)),f2(x64942)))+P1(f773(f773(f232(a1),x64941),f2(a1)))
% 191.21/191.74 [7019]~P68(x70191)+~P1(f773(f773(f233(x70191),x70192),f2(x70191)))+P1(f773(f773(f233(x70191),f773(f773(f82(x70191),x70192),x70192)),f2(x70191)))
% 191.21/191.74 [7020]~P110(x70201)+~P1(f773(f773(f233(x70201),x70202),f2(x70201)))+P1(f773(f773(f233(x70201),f773(f773(f82(x70201),x70202),x70202)),f2(x70201)))
% 191.21/191.74 [7021]~P68(x70211)+~P1(f773(f773(f232(x70211),x70212),f2(x70211)))+P1(f773(f773(f232(x70211),f773(f773(f82(x70211),x70212),x70212)),f2(x70211)))
% 191.21/191.74 [7616]~P68(x76161)+~P1(f773(f773(f233(x76161),f773(f773(f82(x76161),x76162),x76162)),f2(x76161)))+P1(f773(f773(f233(x76161),x76162),f2(x76161)))
% 191.21/191.74 [7617]~P110(x76171)+~P1(f773(f773(f233(x76171),f773(f773(f82(x76171),x76172),x76172)),f2(x76171)))+P1(f773(f773(f233(x76171),x76172),f2(x76171)))
% 191.21/191.74 [7618]~P68(x76181)+~P1(f773(f773(f232(x76181),f773(f773(f82(x76181),x76182),x76182)),f2(x76181)))+P1(f773(f773(f232(x76181),x76182),f2(x76181)))
% 191.21/191.74 [4634]~E(x46342,f2(a847))+~E(x46341,f2(a847))+E(f773(f773(f82(a847),x46341),x46342),f2(a847))
% 191.21/191.74 [4635]~E(x46352,f80(a847))+~E(x46351,f80(a847))+E(f773(f773(f83(a847),x46351),x46352),f80(a847))
% 191.21/191.74 [4636]~E(x46362,f80(a1))+~E(x46361,f80(a1))+E(f773(f773(f83(a1),x46361),x46362),f80(a1))
% 191.21/191.74 [4686]~P7(x46862)+E(x46861,f2(x46862))+E(f773(f773(f43(x46862),x46861),x46861),f80(x46862))
% 191.21/191.74 [4687]~P113(x46872)+E(x46871,f2(x46872))+E(f773(f773(f283(x46872),x46871),x46871),f80(x46872))
% 191.21/191.74 [4688]~P114(x46882)+E(x46881,f2(x46882))+E(f773(f773(f283(x46882),x46881),x46881),f80(x46882))
% 191.21/191.74 [4703]~P68(x47031)+~E(x47032,f2(x47031))+E(f773(f773(f82(x47031),x47032),x47032),f2(x47031))
% 191.21/191.74 [4706]~P120(x47061)+~E(x47062,f80(x47061))+E(f773(f773(f83(x47061),x47062),x47062),f80(x47061))
% 191.21/191.74 [4707]~P114(x47071)+~E(x47072,f2(x47071))+E(f773(f773(f283(x47071),x47072),x47072),f2(x47071))
% 191.21/191.74 [4751]~E(x47512,f2(a847))+~E(x47511,f2(a847))+E(f773(f81(a1),f773(f102(a1),x47511)),f773(f102(a1),x47512))
% 191.21/191.74 [4769]E(x47691,f80(a847))+E(x47692,f2(a847))+~E(f773(f773(f83(a847),x47692),x47691),x47692)
% 191.21/191.74 [4777]E(x47771,f2(a847))+E(x47772,f2(a847))+~E(f773(f773(f83(a847),x47772),x47771),f2(a847))
% 191.21/191.74 [4805]~E(x48052,f2(a847))+~E(x48051,f773(a114,f2(a847)))+E(f773(f773(f82(a847),x48051),x48052),f773(a114,f2(a847)))
% 191.21/191.74 [4806]~E(x48061,f2(a847))+~E(x48062,f773(a114,f2(a847)))+E(f773(f773(f82(a847),x48061),x48062),f773(a114,f2(a847)))
% 191.21/191.74 [4811]E(x48111,f80(a1))+E(x48112,f773(f106(a1),a99))+~E(f773(f773(f83(a1),x48111),x48112),f80(a1))
% 191.21/191.74 [4812]E(x48121,f80(a1))+E(x48122,f773(f106(a1),a99))+~E(f773(f773(f83(a1),x48122),x48121),f80(a1))
% 191.21/191.74 [4813]E(x48131,f80(a1))+E(x48131,f773(f106(a1),a99))+~E(f773(f773(f83(a1),x48132),x48131),f80(a1))
% 191.21/191.74 [4815]E(x48151,f80(a1))+E(x48151,f773(f106(a1),a99))+~E(f773(f773(f83(a1),x48151),x48152),f80(a1))
% 191.21/191.74 [4834]~P68(x48342)+E(x48341,f2(x48342))+~E(f773(f773(f82(x48342),x48341),x48341),f2(x48342))
% 191.21/191.74 [4840]~E(x48401,f773(f106(a1),a99))+~E(x48402,f773(f106(a1),a99))+E(f773(f773(f83(a1),x48401),x48402),f80(a1))
% 191.21/191.74 [4852]E(x48521,f2(a847))+E(x48522,f2(a847))+~E(f773(f773(f82(a847),x48522),x48521),f773(a114,f2(a847)))
% 191.21/191.74 [4860]~P88(x48601)+~P60(x48601)+E(f773(f773(f283(x48601),x48602),f773(f106(x48601),a85)),f2(x48601))
% 191.21/191.74 [4867]~P120(x48671)+~E(x48672,f773(f81(x48671),f80(x48671)))+E(f773(f773(f83(x48671),x48672),x48672),f80(x48671))
% 191.21/191.74 [4872]~P10(x48722)+~P10(x48721)+P10(f773(f773(f82(a1),x48721),x48722))
% 191.21/191.74 [4873]~P10(x48732)+~P10(x48731)+P10(f773(f773(f83(a1),x48731),x48732))
% 191.21/191.74 [4874]~P10(x48742)+~P10(x48741)+P10(f773(f773(f43(a1),x48741),x48742))
% 191.21/191.74 [4876]~E(x48762,f2(a1))+E(x48761,f2(a1))+E(f53(x48761,x48762),f773(f773(f241(a1,a1),f2(a1)),x48761))
% 191.21/191.74 [4899]~E(x48992,f773(a114,f2(a847)))+~E(x48991,f773(a114,f2(a847)))+E(f773(f773(f83(a847),x48991),x48992),f773(a114,f2(a847)))
% 191.21/191.74 [4912]E(x49121,f2(a847))+E(x49122,f773(a114,f2(a847)))+~E(f773(f773(f242(a847),x49122),x49121),f773(a114,f2(a847)))
% 191.21/191.74 [4913]E(x49131,f2(a847))+E(x49131,f773(a114,f2(a847)))+~E(f773(f773(f82(a847),x49132),x49131),f773(a114,f2(a847)))
% 191.21/191.74 [4914]E(x49141,f2(a847))+E(x49141,f773(a114,f2(a847)))+~E(f773(f773(f82(a847),x49141),x49142),f773(a114,f2(a847)))
% 191.21/191.74 [4922]~P88(x49221)+~P60(x49221)+E(f773(f773(f283(x49221),x49222),f773(f106(x49221),a99)),f773(f81(x49221),x49222))
% 191.21/191.74 [4943]E(x49431,f773(a107,x49432))+~E(x49431,f2(a847))+P1(f773(f773(f232(a1),f2(a1)),x49432))
% 191.21/191.74 [4944]E(f773(a107,x49441),x49442)+~E(x49442,f2(a847))+P1(f773(f773(f232(a1),f2(a1)),x49441))
% 191.21/191.74 [4963]E(x49631,f773(a114,f2(a847)))+E(x49632,f773(a114,f2(a847)))+~E(f773(f773(f82(a847),x49631),x49632),f773(a114,f2(a847)))
% 191.21/191.74 [4974]~E(x49741,f773(a107,x49742))+E(x49741,f2(a847))+P1(f773(f773(f232(a1),f2(a1)),x49742))
% 191.21/191.74 [4975]~E(f773(a107,x49752),x49751)+E(x49751,f2(a847))+P1(f773(f773(f232(a1),f2(a1)),x49752))
% 191.21/191.74 [4998]~P93(x49981)+E(f773(f65(x49981,f103(x49981)),x49982),f15(x49981,x49982))+~P1(f773(f63(x49981),x49982))
% 191.21/191.74 [4999]~P100(x49991)+E(f773(f65(x49991,f179(x49991)),x49992),f16(x49991,x49992))+~P1(f773(f63(x49991),x49992))
% 191.21/191.74 [5000]~P100(x50001)+E(f773(f65(x50001,f236(x50001)),x50002),f17(x50001,x50002))+~P1(f773(f63(x50001),x50002))
% 191.21/191.74 [5001]~P93(x50011)+E(f773(f65(x50011,f104(x50011)),x50012),f12(x50011,x50012))+~P1(f773(f63(x50011),x50012))
% 191.21/191.74 [5084]E(x50841,x50842)+~E(f773(f773(f3(a847),x50842),x50841),f2(a847))+~E(f773(f773(f3(a847),x50841),x50842),f2(a847))
% 191.21/191.74 [5094]P10(x50941)+~P38(x50942)+~P1(f773(f773(f334(a1),x50941),x50942))
% 191.21/191.74 [5125]~P110(x51251)+~E(f84(x51251,x51252),f80(x51251))+P1(f773(f773(f233(x51251),f2(x51251)),x51252))
% 191.21/191.74 [5136]~P88(x51361)+E(f773(f102(x51361),f773(f106(a847),x51362)),f773(f106(x51361),x51362))+P1(f773(a186,f773(f106(a1),x51362)))
% 191.21/191.74 [5141]~P42(x51411,x51412)+P43(a841)+P1(f773(f63(f854(x51411,x51411)),x51412))
% 191.21/191.74 [5206]~P100(x52061)+E(f773(f65(x52061,f179(x52061)),x52062),f13(x52061,f179(x52061),x52062))+~P1(f773(f63(x52061),x52062))
% 191.21/191.74 [5207]~P100(x52071)+E(f773(f65(x52071,f236(x52071)),x52072),f14(x52071,f236(x52071),x52072))+~P1(f773(f63(x52071),x52072))
% 191.21/191.74 [5221]E(x52211,x52212)+P1(f773(f773(f233(a847),x52212),x52211))+P1(f773(f773(f233(a847),x52211),x52212))
% 191.21/191.74 [5222]E(x52221,x52222)+P1(f773(f773(f233(a1),x52222),x52221))+P1(f773(f773(f233(a1),x52221),x52222))
% 191.21/191.74 [5274]~P88(x52741)+E(f773(f102(x52741),f773(f106(a847),x52742)),f2(x52741))+~P1(f773(a186,f773(f106(a1),x52742)))
% 191.21/191.74 [5277]~E(x52772,f773(a107,x52771))+E(x52771,f773(f102(a1),x52772))+~P1(f773(f773(f232(a1),f2(a1)),x52771))
% 191.21/191.74 [5278]~E(f773(a107,x52781),x52782)+E(x52781,f773(f102(a1),x52782))+~P1(f773(f773(f232(a1),f2(a1)),x52781))
% 191.21/191.74 [5279]~E(x52791,f773(a107,x52792))+E(f773(f102(a1),x52791),x52792)+~P1(f773(f773(f232(a1),f2(a1)),x52792))
% 191.21/191.74 [5289]E(x52891,f773(a107,x52892))+~E(x52892,f773(f102(a1),x52891))+~P1(f773(f773(f232(a1),f2(a1)),x52892))
% 191.21/191.74 [5290]E(f773(a107,x52901),x52902)+~E(x52901,f773(f102(a1),x52902))+~P1(f773(f773(f232(a1),f2(a1)),x52901))
% 191.21/191.74 [5319]~P85(x53192)+E(x53191,f2(x53192))+~P1(f773(f773(f279(x53192),f2(x53192)),x53191))
% 191.21/191.74 [5328]~P79(x53282)+E(x53281,f2(x53282))+P1(f773(f773(f233(x53282),f2(x53282)),f773(f77(x53282),x53281)))
% 191.21/191.74 [5396]~P110(x53961)+E(f84(x53961,x53962),f80(x53961))+~P1(f773(f773(f233(x53961),f2(x53961)),x53962))
% 191.21/191.74 [5402]~P88(x54021)+E(f773(f102(x54021),f773(f106(a847),x54022)),f2(x54021))+P1(f773(f773(f232(a1),f2(a1)),f773(f106(a1),x54022)))
% 191.21/191.74 [5409]~P79(x54091)+E(f773(f77(x54091),x54092),x54092)+~P1(f773(f773(f233(x54091),f2(x54091)),x54092))
% 191.21/191.74 [5410]~P79(x54101)+E(f773(f77(x54101),x54102),x54102)+~P1(f773(f773(f232(x54101),f2(x54101)),x54102))
% 191.21/191.74 [5417]E(x54171,f2(a847))+~E(f130(a847,f773(f294(a847,x54172),x54171)),f115(a847))+P1(f773(f773(f232(a847),x54171),x54172))
% 191.21/191.74 [5427]~P66(x54271)+E(f773(f773(f8(x54271,x54271),f7(x54271)),f773(f158(x54271),x54272)),f773(f155(x54271),x54272))+~P1(f773(f127(x54271),x54272))
% 191.21/191.74 [5430]~P133(x54301)+E(f773(f102(x54301),f773(a107,x54302)),f773(f105(x54301),x54302))+~P1(f773(f773(f232(a1),f2(a1)),x54302))
% 191.21/191.74 [5453]E(x54531,x54532)+P1(f773(f773(f233(a847),x54531),x54532))+~P1(f773(f773(f232(a847),x54531),x54532))
% 191.21/191.74 [5454]E(x54541,x54542)+P1(f773(f773(f233(a1),x54541),x54542))+~P1(f773(f773(f232(a1),x54541),x54542))
% 191.21/191.74 [5457]E(x54571,f80(a1))+~E(f773(f773(f83(a1),x54572),x54571),f80(a1))+~P1(f773(f773(f233(a1),f2(a1)),x54572))
% 191.21/191.74 [5458]E(x54581,f80(a1))+~E(f773(f773(f83(a1),x54581),x54582),f80(a1))+~P1(f773(f773(f233(a1),f2(a1)),x54581))
% 191.21/191.74 [5497]~P38(x54972)+P1(f773(f773(f232(a1),f2(a1)),x54971))+~P1(f773(f773(f334(a1),x54971),x54972))
% 191.21/191.74 [5515]~P56(x55151,x55152)+P36(x55151,x55152)+~P1(f773(f63(f854(x55151,x55151)),x55152))
% 191.21/191.74 [5517]~P56(x55171,x55172)+P42(x55171,x55172)+~P1(f773(f63(f854(x55171,x55171)),x55172))
% 191.21/191.74 [5557]E(x55571,f180(f855(x55572,a841)))+~P1(f773(f63(x55572),x55571))+P1(f773(f773(f233(a847),f2(a847)),f773(f42(x55572),x55571)))
% 191.21/191.74 [5583]~P1(f773(x55831,x55832))+P1(f773(x55831,f2(a847)))+P1(f773(f773(f233(a847),f789(x55832,x55831)),x55832))
% 191.21/191.74 [5608]E(x56081,f2(a847))+~E(f773(f155(a847),x56082),f2(a847))+~P1(f773(f773(f334(a847),x56081),f773(f158(a847),x56082)))
% 191.21/191.74 [5670]~E(x56702,f2(a847))+P1(f773(f773(f232(a1),f2(a1)),x56701))+P1(f773(f773(f279(a847),f773(a107,x56701)),x56702))
% 191.21/191.74 [5673]E(x56731,x56732)+~P1(f773(f773(f232(a847),x56732),x56731))+~P1(f773(f773(f232(a847),x56731),x56732))
% 191.21/191.74 [5674]E(x56741,x56742)+~P1(f773(f773(f232(a1),x56742),x56741))+~P1(f773(f773(f232(a1),x56741),x56742))
% 191.21/191.74 [5683]E(x56831,x56832)+~P1(f773(f773(f279(a847),x56832),x56831))+~P1(f773(f773(f279(a847),x56831),x56832))
% 191.21/191.74 [5684]E(f773(f42(x56841),x56842),f2(a847))+~P1(f773(f63(x56841),x56842))+P1(f773(f773(f334(x56841),f618(x56842,x56841)),x56842))
% 191.21/191.74 [5690]E(f57(x56901,x56902),f53(x56901,x56902))+P1(f773(f773(f232(a1),f2(a1)),x56901))+~P1(f773(f773(f233(a1),f2(a1)),x56902))
% 191.21/191.74 [5719]~P1(f773(x57191,f775(x57191)))+P1(f773(x57191,f773(a107,x57192)))+~P1(f773(f773(f232(a1),f2(a1)),x57192))
% 191.21/191.74 [5721]P1(f773(f773(f233(a847),x57211),f401(x57212)))+~P1(f773(f63(a847),x57212))+~P1(f773(f773(f334(a847),x57211),x57212))
% 191.21/191.74 [5722]P1(f773(f773(f232(a847),x57221),f376(x57222)))+~P1(f773(f63(a847),x57222))+~P1(f773(f773(f334(a847),x57221),x57222))
% 191.21/191.74 [5751]E(x57511,x57512)+~P1(f773(f773(f233(a847),x57511),f773(a114,x57512)))+P1(f773(f773(f233(a847),x57511),x57512))
% 191.21/191.74 [5789]E(x57891,f773(a114,x57892))+~P1(f773(f773(f232(a847),x57891),f773(a114,x57892)))+P1(f773(f773(f232(a847),x57891),x57892))
% 191.21/191.74 [5799]P1(f773(x57991,f776(x57991)))+~P1(f773(x57991,f773(a107,x57992)))+~P1(f773(f773(f232(a1),f2(a1)),x57992))
% 191.21/191.74 [5801]E(f773(f77(a1),x58011),f773(f77(a1),x58012))+~P1(f773(f773(f279(a1),x58012),x58011))+~P1(f773(f773(f279(a1),x58011),x58012))
% 191.21/191.74 [5813]~P1(f773(x58131,x58132))+~P1(f773(f773(f232(a1),f2(a1)),x58132))+P1(f773(x58131,f773(f102(a1),f723(x58131))))
% 191.21/191.74 [5825]~P79(x58252)+~E(x58251,f2(x58252))+~P1(f773(f773(f233(x58252),f2(x58252)),f773(f77(x58252),x58251)))
% 191.21/191.74 [5850]~P56(x58501,x58502)+P36(x58501,f773(f278(x58501,x58501),x58502))+~P1(f773(f63(f854(x58501,x58501)),x58502))
% 191.21/191.74 [5858]~P88(x58581)+E(f773(f102(x58581),f773(f106(a847),x58582)),f773(f106(x58581),x58582))+~P1(f773(f773(f232(a1),f2(a1)),f773(f106(a1),x58582)))
% 191.21/191.74 [5862]E(f773(a114,x58621),x58622)+~P1(f773(f773(f233(a847),x58621),x58622))+P1(f773(f773(f233(a847),f773(a114,x58621)),x58622))
% 191.21/191.74 [5875]E(f773(f773(f43(a1),x58751),x58752),f2(a1))+~P1(f773(f773(f232(a1),x58751),f2(a1)))+~P1(f773(f773(f233(a1),x58752),x58751))
% 191.21/191.74 [5888]E(f52(a1,x58881,x58882),x58881)+~P1(f773(f773(f232(a1),x58881),f2(a1)))+~P1(f773(f773(f233(a1),x58882),x58881))
% 191.21/191.74 [5901]E(f54(x59011,x59012),f53(x59011,x59012))+~P1(f773(f773(f232(a1),f2(a1)),x59011))+~P1(f773(f773(f232(a1),f2(a1)),x59012))
% 191.21/191.74 [5909]E(f773(f773(f43(a1),x59091),x59092),f2(a1))+~P1(f773(f773(f232(a1),f2(a1)),x59091))+~P1(f773(f773(f233(a1),x59091),x59092))
% 191.21/191.74 [5923]E(f52(a847,f773(f106(a847),x59231),f773(f106(a847),x59232)),f773(f106(a847),x59231))+P1(f773(a186,f773(f106(a1),x59231)))+~P1(f773(a186,f773(f106(a1),x59232)))
% 191.21/191.74 [5925]E(f52(a1,x59251,x59252),x59251)+~P1(f773(f773(f232(a1),f2(a1)),x59251))+~P1(f773(f773(f233(a1),x59251),x59252))
% 191.21/191.74 [5927]E(x59271,x59272)+~P1(f773(f773(f233(a847),x59271),f773(a114,x59272)))+~P1(f773(f773(f232(a847),x59272),x59271))
% 191.21/191.74 [5943]~P110(x59431)+~P1(f773(f773(f233(x59431),x59432),f2(x59431)))+P1(f773(f773(f233(x59431),x59432),f773(f81(x59431),x59432)))
% 191.21/191.74 [5944]~P68(x59441)+~P1(f773(f773(f232(x59441),x59442),f2(x59441)))+P1(f773(f773(f232(x59441),x59442),f773(f81(x59441),x59442)))
% 191.21/191.74 [5953]~P9(x59531)+E(f773(f773(f66(x59531,x59531,f104(x59531)),f239(x59531)),x59532),f45(x59531,x59532))+~P1(f773(f63(x59531),x59532))
% 191.21/191.74 [5954]~P9(x59541)+E(f773(f773(f66(x59541,x59541,f103(x59541)),f180(x59541)),x59542),f44(x59541,x59542))+~P1(f773(f63(x59541),x59542))
% 191.21/191.74 [5968]~P117(x59681)+~P1(f773(f773(f233(a847),f2(a847)),x59682))+P1(f773(f773(f233(x59681),f2(x59681)),f773(f102(x59681),x59682)))
% 191.21/191.74 [5969]~P110(x59691)+~P1(f773(f773(f233(a1),f2(a1)),x59692))+P1(f773(f773(f233(x59691),f2(x59691)),f773(f105(x59691),x59692)))
% 191.21/191.74 [5970]~P110(x59701)+~P1(f773(f773(f232(a1),f2(a1)),x59702))+P1(f773(f773(f232(x59701),f2(x59701)),f773(f105(x59701),x59702)))
% 191.21/191.74 [5973]~P10(x59732)+~P10(x59731)+E(f773(f303(a847,a1,f102(a1)),f295(a847,f773(a107,x59731),f773(a107,x59732))),f295(a1,x59731,x59732))
% 191.21/191.74 [5979]P1(f773(x59791,x59792))+~P1(f773(f773(f232(a1),f2(a1)),x59792))+~P1(f773(x59791,f773(f102(a1),f747(x59791))))
% 191.21/191.74 [6006]E(f773(f773(f82(a847),f773(f106(a847),x60061)),f773(f106(a847),x60062)),f773(f106(a847),x60061))+P1(f773(f773(f233(a1),x60061),a85))+~P1(f773(f773(f233(a1),x60062),a85))
% 191.21/191.74 [6010]~P110(x60101)+P1(f773(f773(f233(x60101),f2(x60101)),f84(x60101,x60102)))+~P1(f773(f773(f233(x60101),f2(x60101)),x60102))
% 191.21/191.74 [6024]~P77(x60241)+~P1(f773(f773(f233(x60241),x60242),f2(x60241)))+P1(f773(f773(f233(x60241),f2(x60241)),f773(f81(x60241),x60242)))
% 191.21/191.74 [6025]~P77(x60251)+~P1(f773(f773(f232(x60251),x60252),f2(x60251)))+P1(f773(f773(f232(x60251),f2(x60251)),f773(f81(x60251),x60252)))
% 191.21/191.74 [6028]E(x60281,f2(a847))+P1(f773(f773(f232(a1),f2(a1)),x60282))+~P1(f773(f773(f279(a847),f773(a107,x60282)),x60281))
% 191.21/191.74 [6029]E(x60291,f239(f855(x60292,a841)))+~E(f773(f42(x60292),x60291),f773(f42(x60292),f239(f855(x60292,a841))))+~P1(f773(f63(x60292),f239(f855(x60292,a841))))
% 191.21/191.74 [6060]~P1(f773(f773(f233(a847),f2(a847)),x60602))+~P1(f773(f773(f279(a847),x60601),x60602))+P1(f773(f773(f232(a847),x60601),x60602))
% 191.21/191.74 [6061]~P1(f773(f773(f233(a1),f2(a1)),x60612))+~P1(f773(f773(f279(a1),x60611),x60612))+P1(f773(f773(f232(a1),x60611),x60612))
% 191.21/191.74 [6067]~P110(x60671)+P1(f773(f773(f233(x60671),x60672),f2(x60671)))+~P1(f773(f773(f233(x60671),x60672),f773(f81(x60671),x60672)))
% 191.21/191.74 [6068]~P68(x60681)+P1(f773(f773(f232(x60681),x60682),f2(x60681)))+~P1(f773(f773(f232(x60681),x60682),f773(f81(x60681),x60682)))
% 191.21/191.74 [6076]~P88(x60761)+P1(f773(f773(f334(x60761),f773(f106(x60761),x60762)),f176(x60761)))+~P1(f773(f773(f232(a1),a85),x60762))
% 191.21/191.74 [6106]E(x61061,f2(a847))+~P1(f773(f773(f233(a847),x61061),f773(a114,x61062)))+P1(f773(f773(f233(a847),f559(x61062,x61061)),x61062))
% 191.21/191.74 [6130]~P110(x61301)+~P1(f773(f773(f233(x61301),f2(x61301)),f84(x61301,x61302)))+P1(f773(f773(f233(x61301),f2(x61301)),x61302))
% 191.21/191.74 [6132]~E(f773(f106(a847),x61322),f773(f106(a847),x61321))+P1(f773(f773(f232(a1),f773(f106(a1),x61321)),f2(a1)))+~P1(f773(a186,f773(f106(a1),x61322)))
% 191.21/191.74 [6160]E(f773(f240(a1,a1),f57(x61601,x61602)),f773(f773(f43(a1),x61601),x61602))+~P1(f773(f773(f233(a1),x61601),f2(a1)))+~P1(f773(f773(f233(a1),f2(a1)),x61602))
% 191.21/191.74 [6194]E(f773(f250(a1,a1),f57(x61941,x61942)),f52(a1,x61941,x61942))+~P1(f773(f773(f233(a1),x61941),f2(a1)))+~P1(f773(f773(f233(a1),f2(a1)),x61942))
% 191.21/191.74 [6196]E(x61961,f2(a1))+~P1(f773(f773(f279(a1),x61962),x61961))+P1(f773(f773(f232(a1),f773(f77(a1),x61962)),f773(f77(a1),x61961)))
% 191.21/191.74 [6198]~P117(x61982)+~P1(f773(f773(f233(x61982),f2(x61982)),f773(f102(x61982),x61981)))+P1(f773(f773(f233(a847),f2(a847)),x61981))
% 191.21/191.74 [6199]~P110(x61992)+~P1(f773(f773(f233(x61992),f2(x61992)),f773(f105(x61992),x61991)))+P1(f773(f773(f233(a1),f2(a1)),x61991))
% 191.21/191.74 [6200]~P110(x62002)+~P1(f773(f773(f232(x62002),f2(x62002)),f773(f105(x62002),x62001)))+P1(f773(f773(f232(a1),f2(a1)),x62001))
% 191.21/191.74 [6204]~E(x62042,f2(a847))+P1(f773(f773(f279(a847),f773(a107,x62041)),x62042))+~P1(f773(f773(f279(a1),x62041),f773(f102(a1),x62042)))
% 191.21/191.74 [6205]E(f773(f240(a1,a1),f54(x62051,x62052)),f773(f773(f43(a1),x62051),x62052))+~P1(f773(f773(f233(a1),f2(a1)),x62051))+~P1(f773(f773(f232(a1),f2(a1)),x62052))
% 191.21/191.74 [6219]E(f773(f250(a1,a1),f54(x62191,x62192)),f52(a1,x62191,x62192))+~P1(f773(f773(f233(a1),f2(a1)),x62191))+~P1(f773(f773(f232(a1),f2(a1)),x62192))
% 191.21/191.74 [6237]~P77(x62371)+P1(f773(f773(f233(x62371),x62372),f2(x62371)))+~P1(f773(f773(f233(x62371),f2(x62371)),f773(f81(x62371),x62372)))
% 191.21/191.74 [6238]~P77(x62381)+P1(f773(f773(f232(x62381),x62382),f2(x62381)))+~P1(f773(f773(f232(x62381),f2(x62381)),f773(f81(x62381),x62382)))
% 191.21/191.74 [6264]P1(f773(f56(x62641,x62642),f57(x62641,x62642)))+~P1(f773(f773(f233(a1),x62641),f2(a1)))+~P1(f773(f773(f233(a1),f2(a1)),x62642))
% 191.21/191.74 [6280]~P1(f773(f773(f233(a847),f2(a847)),x62801))+~P1(f773(f773(f279(a847),x62802),x62801))+~P1(f773(f773(f233(a847),x62801),x62802))
% 191.21/191.74 [6281]~P1(f773(f773(f233(a1),f2(a1)),x62811))+~P1(f773(f773(f279(a1),x62812),x62811))+~P1(f773(f773(f233(a1),x62811),x62812))
% 191.21/191.74 [6293]P1(f773(f56(x62931,x62932),f54(x62931,x62932)))+~P1(f773(f773(f233(a1),f2(a1)),x62932))+~P1(f773(f773(f232(a1),f2(a1)),x62931))
% 191.21/191.74 [6335]~P77(x63351)+P1(f773(f773(f233(x63351),f773(f81(x63351),x63352)),f2(x63351)))+~P1(f773(f773(f233(x63351),f2(x63351)),x63352))
% 191.21/191.74 [6336]~P77(x63361)+P1(f773(f773(f232(x63361),f773(f81(x63361),x63362)),f2(x63361)))+~P1(f773(f773(f232(x63361),f2(x63361)),x63362))
% 191.21/191.74 [6358]E(f773(f773(f3(a847),f773(a107,x63581)),f773(a107,x63582)),f773(a107,f188(x63581,x63582)))+~P1(f773(f773(f232(a1),f2(a1)),x63582))+~P1(f773(f773(f232(a1),f2(a1)),x63581))
% 191.21/191.74 [6376]P1(f773(f773(f232(a1),f2(a1)),f188(x63761,x63762)))+~P1(f773(f773(f232(a1),f2(a1)),x63762))+~P1(f773(f773(f232(a1),f2(a1)),x63761))
% 191.21/191.74 [6415]~P1(f773(x64151,x64152))+P1(f773(x64151,f2(a847)))+P1(f773(x64151,f773(f773(f82(a847),f789(x64152,x64151)),f80(a847))))
% 191.21/191.74 [6501]E(f773(f106(a847),x65011),f773(f106(a847),x65012))+~P1(f773(f773(f232(a1),f773(f106(a1),x65012)),f2(a1)))+~P1(f773(a186,f773(f106(a1),x65011)))
% 191.21/191.74 [6514]~E(x65141,f2(a847))+~E(f736(x65142,x65141),f2(a847))+E(f773(f132(a847,a847,f82(a847),x65141),x65142),f2(a847))
% 191.21/191.74 [6540]~P1(f773(f63(x65401),f670(x65402,x65401)))+~P1(f773(f63(f855(x65401,a841)),x65402))+P1(f773(f63(x65401),f44(f855(x65401,a841),x65402)))
% 191.21/191.74 [6546]E(x65461,x65462)+P1(f773(f773(f233(a1),x65461),x65462))+~P1(f773(f773(f233(a1),x65461),f773(f773(f82(a1),x65462),f80(a1))))
% 191.21/191.74 [6548]P1(f773(f773(f233(a847),f773(a107,x65481)),f773(a107,x65482)))+~P1(f773(f773(f233(a1),f2(a1)),x65482))+~P1(f773(f773(f233(a1),x65481),x65482))
% 191.21/191.74 [6549]P1(f773(f773(f233(a847),f773(a107,x65491)),f773(a107,x65492)))+~P1(f773(f773(f232(a1),f2(a1)),x65491))+~P1(f773(f773(f233(a1),x65491),x65492))
% 191.21/191.74 [6550]P1(f773(f773(f232(a847),f773(a107,x65501)),f773(a107,x65502)))+~P1(f773(f773(f233(a1),f2(a1)),x65501))+~P1(f773(f773(f232(a1),x65501),x65502))
% 191.21/191.74 [6551]P1(f773(f773(f232(a847),f773(a107,x65511)),f773(a107,x65512)))+~P1(f773(f773(f232(a1),f2(a1)),x65512))+~P1(f773(f773(f232(a1),x65511),x65512))
% 191.21/191.74 [6562]E(f52(a847,f773(a107,x65621),f773(a107,x65622)),f773(a107,f52(a1,x65621,x65622)))+~P1(f773(f773(f232(a1),f2(a1)),x65622))+~P1(f773(f773(f232(a1),f2(a1)),x65621))
% 191.21/191.74 [6583]~P77(x65831)+~P1(f773(f773(f233(x65831),f773(f81(x65831),x65832)),f2(x65831)))+P1(f773(f773(f233(x65831),f2(x65831)),x65832))
% 191.21/191.74 [6584]~P77(x65841)+~P1(f773(f773(f232(x65841),f773(f81(x65841),x65842)),f2(x65841)))+P1(f773(f773(f232(x65841),f2(x65841)),x65842))
% 191.21/191.74 [6601]~P1(f773(f773(f233(a1),a85),x66012))+~P1(f773(f773(f233(a1),x66011),x66012))+P1(f773(f773(f233(a847),f773(f106(a847),x66011)),f773(f106(a847),x66012)))
% 191.21/191.74 [6698]~P1(f773(f773(f232(a1),f2(a1)),x66981))+P1(f773(f773(f233(a847),f773(a107,x66981)),x66982))+~P1(f773(f773(f233(a1),x66981),f773(f102(a1),x66982)))
% 191.21/191.74 [6699]~P1(f773(f773(f232(a1),f2(a1)),x66991))+P1(f773(f773(f279(a847),f773(a107,x66991)),x66992))+~P1(f773(f773(f279(a1),x66991),f773(f102(a1),x66992)))
% 191.21/191.74 [6715]E(x67151,f2(a1))+E(f52(a1,x67152,x67151),f2(a1))+E(f773(f773(f3(a1),f773(f81(a1),f773(f773(f43(a1),x67152),x67151))),f80(a1)),f773(f773(f43(a1),x67152),f773(f81(a1),x67151)))
% 191.21/191.74 [6731]~P1(f773(f773(f232(a1),f2(a1)),x67311))+~P1(f773(f773(f233(a847),f773(a107,x67311)),x67312))+P1(f773(f773(f233(a1),x67311),f773(f102(a1),x67312)))
% 191.21/191.74 [6732]~P1(f773(f773(f232(a1),f2(a1)),x67321))+~P1(f773(f773(f279(a847),f773(a107,x67321)),x67322))+P1(f773(f773(f279(a1),x67321),f773(f102(a1),x67322)))
% 191.21/191.74 [6772]~P1(f773(f773(f232(a847),f773(a107,x67721)),f773(a107,x67722)))+~P1(f773(f773(f233(a1),f2(a1)),x67721))+P1(f773(f773(f232(a1),x67721),x67722))
% 191.21/191.74 [6773]~P1(f773(f773(f232(a847),f773(a107,x67731)),f773(a107,x67732)))+~P1(f773(f773(f232(a1),f2(a1)),x67732))+P1(f773(f773(f232(a1),x67731),x67732))
% 191.21/191.74 [6804]P1(f773(f773(f232(a1),x68041),x68042))+~P1(f773(f773(f232(a847),f773(f106(a847),x68041)),f773(f106(a847),x68042)))+P1(f773(f773(f232(a1),x68041),a85))
% 191.21/191.74 [6831]P1(f773(f773(f232(a1),f2(a1)),f52(a1,x68311,x68312)))+~P1(f773(f773(f232(a1),f2(a1)),x68312))+~P1(f773(f773(f232(a1),f2(a1)),x68311))
% 191.21/191.74 [6930]P1(f773(f773(f233(a1),a85),x69301))+~P1(f773(f773(f233(a1),x69302),x69301))+~P1(f773(f773(f233(a847),f773(f106(a847),x69302)),f773(f106(a847),x69301)))
% 191.21/191.74 [6978]E(f773(f773(f241(a1,a1),f773(f773(f43(a1),x69781),x69782)),f52(a1,x69781,x69782)),f57(x69781,x69782))+~P1(f773(f773(f233(a1),x69781),f2(a1)))+~P1(f773(f773(f233(a1),f2(a1)),x69782))
% 191.21/191.74 [6999]E(f773(f773(f241(a1,a1),f773(f773(f43(a1),x69991),x69992)),f52(a1,x69991,x69992)),f54(x69991,x69992))+~P1(f773(f773(f232(a1),f2(a1)),x69992))+~P1(f773(f773(f232(a1),f2(a1)),x69991))
% 191.21/191.74 [7054]~P91(x70542)+E(x70541,f115(x70542))+E(f773(f132(x70542,x70542,f83(x70542),f773(f131(x70542),x70541)),f773(f157(x70542),x70541)),f773(f65(x70542,f83(x70542)),f773(f158(x70542),x70541)))
% 191.21/191.74 [7168]~E(x71681,f2(a847))+E(f773(f132(a847,a847,f82(a847),x71681),x71682),f2(a847))+P1(f773(f773(f334(a847),f736(x71682,x71681)),f773(f158(a847),x71682)))
% 191.21/191.74 [7222]~P1(f773(f773(f233(a1),x72222),f2(a1)))+P1(f773(f773(f233(a1),f773(f773(f43(a1),x72221),x72222)),f2(a1)))+~P1(f773(f773(f233(a1),f2(a1)),x72221))
% 191.21/191.74 [7224]~P1(f773(f773(f233(a1),x72241),f2(a1)))+P1(f773(f773(f233(a1),f773(f773(f43(a1),x72241),x72242)),f2(a1)))+~P1(f773(f773(f233(a1),f2(a1)),x72242))
% 191.21/191.74 [7225]~P1(f773(f773(f233(a1),x72252),f2(a1)))+P1(f773(f773(f232(a1),f773(f773(f43(a1),x72251),x72252)),f2(a1)))+~P1(f773(f773(f232(a1),f2(a1)),x72251))
% 191.21/191.74 [7226]~P1(f773(f773(f232(a1),x72261),f2(a1)))+P1(f773(f773(f232(a1),f773(f773(f43(a1),x72261),x72262)),f2(a1)))+~P1(f773(f773(f233(a1),f2(a1)),x72262))
% 191.21/191.74 [7235]P1(f773(f773(f334(f855(x72351,a841)),f670(x72352,x72351)),x72352))+~P1(f773(f63(f855(x72351,a841)),x72352))+P1(f773(f63(x72351),f44(f855(x72351,a841),x72352)))
% 191.21/191.74 [7340]P29(x73401,x73401,x73402,f239(f855(x73401,a841)))+~E(f773(f303(x73401,x73401,x73402),f239(f855(x73401,a841))),f239(f855(x73401,a841)))+~P1(f773(f63(x73401),f239(f855(x73401,a841))))
% 191.21/191.74 [7469]~P29(x74691,x74691,x74692,f239(f855(x74691,a841)))+E(f773(f303(x74691,x74691,x74692),f239(f855(x74691,a841))),f239(f855(x74691,a841)))+~P1(f773(f63(x74691),f239(f855(x74691,a841))))
% 191.21/191.74 [7610]E(f773(f773(f43(a1),x76101),x76102),f773(f106(a1),a99))+~P1(f773(f773(f232(a1),f773(f773(f82(a1),x76101),x76102)),f2(a1)))+~P1(f773(f773(f233(a1),f2(a1)),x76101))
% 191.21/191.74 [7668]~P1(f773(f773(f233(a1),x76682),f2(a1)))+~P1(f773(f773(f233(a1),f773(f773(f43(a1),x76681),x76682)),f2(a1)))+P1(f773(f773(f233(a1),f2(a1)),x76681))
% 191.21/191.74 [7673]E(f773(f773(f82(a1),x76731),x76732),f52(a1,x76731,x76732))+~P1(f773(f773(f232(a1),f773(f773(f82(a1),x76731),x76732)),f2(a1)))+~P1(f773(f773(f233(a1),f2(a1)),x76731))
% 191.21/191.74 [7675]P1(f773(f773(f233(a1),x76751),f2(a1)))+~P1(f773(f773(f233(a1),f773(f773(f43(a1),x76751),x76752)),f2(a1)))+~P1(f773(f773(f233(a1),f2(a1)),x76752))
% 191.21/191.74 [7927]~P99(x79271)+P50(a847,x79271,f279(a847),x79272)+~P1(f773(f773(f232(x79271),f773(x79272,f377(x79272,x79271))),f773(x79272,f393(x79272,x79271))))
% 191.21/191.74 [8369]~P100(x83691)+P18(x83691,x83692)+~P1(f773(f773(f232(x83691),f773(f773(f153(x83691),x83692),f760(x83692,x83691))),f773(f773(f153(x83691),x83692),f761(x83692,x83691))))
% 191.21/191.74 [5551]E(x55511,f2(a1))+~E(f52(a1,x55512,x55511),f2(a1))+E(f773(f773(f43(a1),x55512),f773(f81(a1),x55511)),f773(f81(a1),f773(f773(f43(a1),x55512),x55511)))
% 191.21/191.74 [5568]~P38(x55682)+~P38(x55681)+P38(f773(f773(f103(f855(a1,a841)),x55681),x55682))
% 191.21/191.74 [5569]~P38(x55692)+~P38(x55691)+P38(f773(f773(f104(f855(a1,a841)),x55691),x55692))
% 191.21/191.74 [5586]~P88(x55861)+~P60(x55861)+E(f773(f81(x55861),f773(f773(f283(x55861),f80(x55861)),x55862)),f773(f773(f283(x55861),f773(f106(x55861),a99)),x55862))
% 191.21/191.74 [5711]E(x57111,f2(a1))+~E(f52(a1,x57112,x57111),f2(a1))+E(f773(f773(f43(a1),f773(f81(a1),x57112)),x57111),f773(f81(a1),f773(f773(f43(a1),x57112),x57111)))
% 191.21/191.74 [5845]~P100(x58451)+P18(x58451,x58452)+P1(f773(f773(f233(a847),f761(x58452,x58451)),f773(f181(f848(x58451)),x58452)))
% 191.21/191.74 [6002]~P88(x60021)+~E(f773(f106(x60021),x60022),f2(x60021))+P33(x60021,f773(f106(x60021),f773(f773(f82(a1),x60022),f773(f81(a1),a85))))
% 191.21/191.74 [6003]~P88(x60031)+~E(f773(f106(x60031),x60032),f2(x60031))+P33(x60031,f773(f106(x60031),f773(f773(f82(a1),a85),f773(f81(a1),x60032))))
% 191.21/191.74 [6005]E(f773(a58,f54(f773(f81(a1),x60051),f773(f81(a1),x60052))),f53(x60051,x60052))+P1(f773(f773(f233(a1),f2(a1)),x60052))+P1(f773(f773(f232(a1),f2(a1)),x60051))
% 191.21/191.74 [6138]~E(x61382,f2(a847))+~E(x61381,f2(a847))+P1(f773(f773(f232(a1),f773(f102(a1),x61381)),f773(f81(a1),f773(f102(a1),x61382))))
% 191.21/191.74 [6164]E(f773(f773(f82(a847),f773(f106(a847),x61641)),f773(f106(a847),x61642)),f773(f106(a847),f773(f773(f82(a1),x61641),x61642)))+P1(f773(f773(f233(a1),x61641),a85))+P1(f773(f773(f233(a1),x61642),a85))
% 191.21/191.74 [6302]~P68(x63021)+~P1(f773(f773(f233(x63021),f2(x63021)),x63022))+P1(f773(f773(f233(x63021),f773(f81(x63021),x63022)),x63022))
% 191.21/191.74 [6303]~P68(x63031)+~P1(f773(f773(f232(x63031),f2(x63031)),x63032))+P1(f773(f773(f232(x63031),f773(f81(x63031),x63032)),x63032))
% 191.21/191.74 [6486]E(f773(f773(f3(a847),f773(a107,x64861)),f773(a107,x64862)),f773(a107,f773(f773(f3(a1),x64861),x64862)))+~P1(f773(f773(f232(a1),f2(a1)),x64862))+~P1(f773(f773(f232(a1),x64862),x64861))
% 191.21/191.74 [6523]E(f773(a107,f52(a1,f773(f106(a1),x65231),f773(f106(a1),x65232))),f52(a847,f773(f106(a847),x65231),f773(f106(a847),x65232)))+P1(f773(a186,f773(f106(a1),x65231)))+P1(f773(a186,f773(f106(a1),x65232)))
% 191.21/191.74 [6541]~P68(x65411)+P1(f773(f773(f233(x65411),f2(x65411)),x65412))+~P1(f773(f773(f233(x65411),f773(f81(x65411),x65412)),x65412))
% 191.21/191.74 [6542]~P68(x65421)+P1(f773(f773(f232(x65421),f2(x65421)),x65422))+~P1(f773(f773(f232(x65421),f773(f81(x65421),x65422)),x65422))
% 191.21/191.74 [6553]~P68(x65531)+~P1(f773(f773(f233(x65531),f2(x65531)),x65532))+P1(f773(f773(f233(x65531),f2(x65531)),f773(f773(f82(x65531),x65532),x65532)))
% 191.21/191.74 [6555]~P68(x65551)+~P1(f773(f773(f232(x65551),f2(x65551)),x65552))+P1(f773(f773(f232(x65551),f2(x65551)),f773(f773(f82(x65551),x65552),x65552)))
% 191.21/191.74 [6566]E(f773(f773(f82(a847),f773(a107,x65661)),f773(a107,x65662)),f773(a107,f773(f773(f82(a1),x65661),x65662)))+~P1(f773(f773(f232(a1),f2(a1)),x65662))+~P1(f773(f773(f232(a1),f2(a1)),x65661))
% 191.21/191.74 [6579]E(x65791,f2(a847))+P1(f773(f773(f233(a847),f2(a847)),x65792))+~P1(f773(f773(f233(a847),f2(a847)),f773(f773(f242(a847),x65792),x65791)))
% 191.21/191.74 [6612]~P88(x66121)+E(f773(f106(x66121),x66122),f2(x66121))+~P33(x66121,f773(f106(x66121),f773(f773(f82(a1),a85),f773(f81(a1),x66122))))
% 191.21/191.74 [6613]~P88(x66131)+E(f773(f106(x66131),x66132),f2(x66131))+~P33(x66131,f773(f106(x66131),f773(f773(f82(a1),x66132),f773(f81(a1),a85))))
% 191.21/191.74 [6675]~P1(f773(f63(x66751),x66752))+~P1(f773(f63(x66751),f239(f855(x66751,a841))))+P1(f773(f63(x66751),f773(f81(f855(x66751,a841)),x66752)))
% 191.21/191.74 [6700]~P1(f773(f773(f233(a1),f2(a1)),x67002))+~P1(f773(f773(f232(a1),x67002),x67001))+P1(f773(f773(f233(a1),f2(a1)),f773(f773(f43(a1),x67001),x67002)))
% 191.21/191.74 [6701]~P1(f773(f773(f233(a1),x67012),f2(a1)))+~P1(f773(f773(f232(a1),x67011),f2(a1)))+P1(f773(f773(f232(a1),f2(a1)),f773(f773(f43(a1),x67011),x67012)))
% 191.21/191.74 [6743]~P1(f773(f773(f233(a847),f2(a847)),x67432))+~P1(f773(f773(f233(a847),f2(a847)),x67431))+P1(f773(f773(f233(a847),f2(a847)),f773(f773(f83(a847),x67431),x67432)))
% 191.21/191.74 [6744]~P1(f773(f773(f232(a1),f2(a1)),x67442))+~P1(f773(f773(f232(a1),f2(a1)),x67441))+P1(f773(f773(f232(a1),f2(a1)),f773(f773(f82(a1),x67441),x67442)))
% 191.21/191.74 [6745]~P1(f773(f773(f232(a1),f2(a1)),x67452))+~P1(f773(f773(f232(a1),f2(a1)),x67451))+P1(f773(f773(f232(a1),f2(a1)),f773(f773(f83(a1),x67451),x67452)))
% 191.21/191.74 [6746]~P1(f773(f773(f233(a1),f2(a1)),x67462))+~P1(f773(f773(f232(a1),f2(a1)),x67461))+P1(f773(f773(f232(a1),f2(a1)),f773(f773(f43(a1),x67461),x67462)))
% 191.21/191.74 [6747]~P1(f773(f773(f232(a1),f2(a1)),x67472))+~P1(f773(f773(f232(a1),f2(a1)),x67471))+P1(f773(f773(f232(a1),f2(a1)),f773(f773(f43(a1),x67471),x67472)))
% 191.21/191.74 [6816]E(x68161,f2(a1))+E(f52(a1,x68162,x68161),f2(a1))+E(f773(f773(f3(a1),f773(f81(a1),f773(f773(f43(a1),x68162),x68161))),f80(a1)),f773(f773(f43(a1),f773(f81(a1),x68162)),x68161))
% 191.21/191.74 [6876]P1(f773(f773(f233(a847),f2(a847)),x68761))+P1(f773(f773(f233(a847),f2(a847)),x68762))+~P1(f773(f773(f233(a847),f2(a847)),f773(f773(f82(a847),x68762),x68761)))
% 191.21/191.74 [6877]~P68(x68771)+P1(f773(f773(f233(x68771),f2(x68771)),x68772))+~P1(f773(f773(f233(x68771),f2(x68771)),f773(f773(f82(x68771),x68772),x68772)))
% 191.21/191.74 [6878]~P68(x68781)+P1(f773(f773(f232(x68781),f2(x68781)),x68782))+~P1(f773(f773(f232(x68781),f2(x68781)),f773(f773(f82(x68781),x68782),x68782)))
% 191.21/191.74 [6931]~P1(f773(f63(x69311),x69312))+P1(f773(f63(x69311),f239(f855(x69311,a841))))+~P1(f773(f63(x69311),f773(f81(f855(x69311,a841)),x69312)))
% 191.21/191.74 [6991]P1(f773(f773(f232(a1),x69911),f2(a1)))+~P1(f773(f773(f233(a1),x69912),f2(a1)))+~P1(f773(f773(f232(a1),f2(a1)),f773(f773(f43(a1),x69911),x69912)))
% 191.21/191.74 [6997]~P1(f773(f773(f233(a1),f2(a1)),x69971))+P1(f773(f773(f232(a1),x69971),x69972))+~P1(f773(f773(f233(a1),f2(a1)),f773(f773(f43(a1),x69972),x69971)))
% 191.21/191.74 [6998]~P1(f773(f773(f232(a1),f2(a1)),x69982))+P1(f773(f773(f232(a1),x69981),x69982))+~P1(f773(f773(f233(a1),f2(a1)),f773(f773(f43(a1),x69982),x69981)))
% 191.21/191.74 [7030]P1(f773(f773(f233(a1),f2(a1)),x70301))+~P1(f773(f773(f232(a1),f2(a1)),x70302))+~P1(f773(f773(f233(a1),f2(a1)),f773(f773(f43(a1),x70302),x70301)))
% 191.21/191.74 [7031]P1(f773(f773(f232(a1),f2(a1)),x70311))+~P1(f773(f773(f233(a1),f2(a1)),x70312))+~P1(f773(f773(f232(a1),f2(a1)),f773(f773(f43(a1),x70311),x70312)))
% 191.21/191.74 [7500]~P1(f773(f63(x75002),f239(f855(x75002,a841))))+~P1(f773(f63(x75001),f239(f855(x75001,a841))))+P1(f773(f63(f856(x75001,x75002)),f239(f855(f856(x75001,x75002),a841))))
% 191.21/191.74 [7501]~P1(f773(f63(x75012),f239(f855(x75012,a841))))+~P1(f773(f63(x75011),f239(f855(x75011,a841))))+P1(f773(f63(f854(x75011,x75012)),f239(f855(f854(x75011,x75012),a841))))
% 191.21/191.74 [7573]~P1(f773(f773(f233(a847),f773(a114,f2(a847))),x75731))+~P1(f773(f773(f233(a847),f773(a114,f2(a847))),x75732))+P1(f773(f773(f233(a847),x75731),f773(f773(f83(a847),x75732),x75731)))
% 191.21/191.74 [7574]~P1(f773(f773(f233(a847),f773(a114,f2(a847))),x75741))+~P1(f773(f773(f233(a847),f773(a114,f2(a847))),x75742))+P1(f773(f773(f233(a847),x75741),f773(f773(f83(a847),x75741),x75742)))
% 191.21/191.74 [7609]E(f773(f42(x76091),f239(f855(x76091,a841))),f773(a114,f2(a847)))+P1(f773(f63(x76092),f239(f855(x76092,a841))))+~P1(f773(f63(f855(x76092,x76091)),f239(f855(f855(x76092,x76091),a841))))
% 191.21/191.74 [7734]~P1(f773(f773(f233(a847),f773(a114,f2(a847))),x77342))+~P1(f773(f773(f233(a847),f773(a114,f2(a847))),x77341))+P1(f773(f773(f233(a847),f773(a114,f2(a847))),f773(f773(f83(a847),x77341),x77342)))
% 191.21/191.74 [7735]~P1(f773(f773(f232(a847),f773(a114,f2(a847))),x77351))+~P1(f773(f773(f232(a847),f773(a114,f2(a847))),x77352))+P1(f773(f773(f232(a847),f773(a114,f2(a847))),f773(f773(f83(a847),x77351),x77352)))
% 191.21/191.74 [8416]E(x84161,f115(x84162))+~P1(f773(f127(x84162),x84161))+E(f162(x84162,f773(f773(f10(a841,a841,x84162),a328),f773(f773(f9(x84162,x84162,a841),a330),f134(x84162,x84161))),x84161),f116(x84162,x84161))
% 191.21/191.74 [8514]~P38(x85142)+~P38(x85141)+E(f773(f303(a847,a1,f102(a1)),f773(f773(f103(f855(a847,a841)),f773(f303(a1,a847,a107),x85141)),f773(f303(a1,a847,a107),x85142))),f773(f773(f103(f855(a1,a841)),x85141),x85142))
% 191.21/191.74 [8515]~P38(x85152)+~P38(x85151)+E(f773(f303(a847,a1,f102(a1)),f773(f773(f104(f855(a847,a841)),f773(f303(a1,a847,a107),x85151)),f773(f303(a1,a847,a107),x85152))),f773(f773(f104(f855(a1,a841)),x85151),x85152))
% 191.21/191.74 [9104]~P88(x91041)+~E(f773(f106(x91041),x91042),f80(x91041))+P33(x91041,f773(f106(x91041),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f81(a1),x91042))))
% 191.21/191.74 [9319]~P88(x93191)+E(f773(f106(x93191),x93192),f80(x93191))+~P33(x93191,f773(f106(x93191),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f81(a1),x93192))))
% 191.21/191.74 [9733]~P99(x97332)+P52(a847,x97332,f773(f773(f20(a847,f855(a847,a841),f855(a847,a841)),f773(f773(f10(f855(a847,f855(a841,a841)),f855(f855(a847,a841),f855(a847,a841)),a847),f20(a847,a841,a841)),f773(f773(f10(f855(a847,a841),f855(a847,f855(a841,a841)),a847),f773(f10(a841,f855(a841,a841),a847),a331)),f279(a847)))),f773(f773(f10(f855(a847,a841),f855(a847,a841),a847),f773(f10(a841,a841,a847),a328)),f773(f9(a847,a847,a841),f279(a847)))),x97331)+P1(f773(f773(f279(a847),f369(x97331,x97332)),f370(x97331,x97332)))
% 191.21/191.74 [9736]~P99(x97361)+P52(a847,x97361,f773(f773(f20(a847,f855(a847,a841),f855(a847,a841)),f773(f773(f10(f855(a847,f855(a841,a841)),f855(f855(a847,a841),f855(a847,a841)),a847),f20(a847,a841,a841)),f773(f773(f10(f855(a847,a841),f855(a847,f855(a841,a841)),a847),f773(f10(a841,f855(a841,a841),a847),a331)),f279(a847)))),f773(f773(f10(f855(a847,a841),f855(a847,a841),a847),f773(f10(a841,a841,a847),a328)),f773(f9(a847,a847,a841),f279(a847)))),x97362)+~P1(f773(f773(f279(a847),f370(x97362,x97361)),f369(x97362,x97361)))
% 191.21/191.74 [9737]~P99(x97371)+P52(a847,x97371,f773(f773(f20(a847,f855(a847,a841),f855(a847,a841)),f773(f773(f10(f855(a847,f855(a841,a841)),f855(f855(a847,a841),f855(a847,a841)),a847),f20(a847,a841,a841)),f773(f773(f10(f855(a847,a841),f855(a847,f855(a841,a841)),a847),f773(f10(a841,f855(a841,a841),a847),a331)),f279(a847)))),f773(f773(f10(f855(a847,a841),f855(a847,a841),a847),f773(f10(a841,a841,a847),a328)),f773(f9(a847,a847,a841),f279(a847)))),x97372)+~P1(f773(f773(f233(x97371),f773(x97372,f369(x97372,x97371))),f773(x97372,f370(x97372,x97371))))
% 191.21/191.74 [9826]~P99(x98261)+P50(a847,x98261,f279(a847),x98262)+~P52(a847,x98261,f773(f773(f20(a847,f855(a847,a841),f855(a847,a841)),f773(f773(f10(f855(a847,f855(a841,a841)),f855(f855(a847,a841),f855(a847,a841)),a847),f20(a847,a841,a841)),f773(f773(f10(f855(a847,a841),f855(a847,f855(a841,a841)),a847),f773(f10(a841,f855(a841,a841),a847),a331)),f279(a847)))),f773(f773(f10(f855(a847,a841),f855(a847,a841),a847),f773(f10(a841,a841,a847),a328)),f773(f9(a847,a847,a841),f279(a847)))),x98262)
% 191.21/191.74 [10024]E(x100241,f2(a1))+E(x100242,f2(a1))+E(f773(f252(a1,a1,a1,a1,f39(a1),f773(f83(a1),f84(a1,x100242))),f773(f773(f773(f98(f854(a1,a1)),f773(f773(a330,f84(a1,x100241)),f84(a1,x100242))),f60(x100241,x100242)),f773(f773(f251(a1,a1,f854(a1,a1)),f773(f773(f20(a1,f855(a1,f854(a1,a1)),f855(a1,f854(a1,a1))),f773(f773(f10(f855(a1,f855(f854(a1,a1),f854(a1,a1))),f855(f855(a1,f854(a1,a1)),f855(a1,f854(a1,a1))),a1),f20(a1,f854(a1,a1),f854(a1,a1))),f773(f773(f10(f854(a1,a1),f855(a1,f855(f854(a1,a1),f854(a1,a1))),a1),f773(f9(a1,f854(a1,a1),f855(f854(a1,a1),f854(a1,a1))),f773(f773(f10(a841,f855(f854(a1,a1),f855(f854(a1,a1),f854(a1,a1))),a1),f98(f854(a1,a1))),f773(f773(f9(a1,a1,a841),a330),f2(a1))))),f773(f773(f9(a1,a1,f854(a1,a1)),f773(f773(f10(a1,f855(a1,f854(a1,a1)),a1),f241(a1,a1)),f81(a1))),f2(a1))))),f773(f773(f9(a1,f855(a1,a1),f855(a1,f854(a1,a1))),f773(f773(f10(f855(a1,f854(a1,a1)),f855(f855(a1,a1),f855(a1,f854(a1,a1))),a1),f10(a1,f854(a1,a1),a1)),f773(f773(f10(a1,f855(a1,f854(a1,a1)),a1),f241(a1,a1)),f773(f773(f9(a1,a1,a1),f773(f773(f10(a1,f855(a1,a1),a1),f3(a1)),f81(a1))),f80(a1))))),f773(f3(a1),f773(f77(a1),x100242))))),f60(x100241,x100242)))),f53(x100241,x100242))
% 191.21/191.74 [10025]E(x100251,f2(a1))+E(x100252,f2(a1))+E(f773(f252(a1,a1,a1,a1,f39(a1),f773(f83(a1),f84(a1,x100252))),f773(f773(f773(f98(f854(a1,a1)),f773(f773(a332,f773(f773(a331,f773(f773(f233(a1),f2(a1)),x100252)),f773(f773(f232(a1),f2(a1)),x100251))),f773(f773(a331,f773(f773(f233(a1),x100252),f2(a1))),f773(f773(f233(a1),x100251),f2(a1))))),f60(x100251,x100252)),f773(f773(f251(a1,a1,f854(a1,a1)),f773(f773(f20(a1,f855(a1,f854(a1,a1)),f855(a1,f854(a1,a1))),f773(f773(f10(f855(a1,f855(f854(a1,a1),f854(a1,a1))),f855(f855(a1,f854(a1,a1)),f855(a1,f854(a1,a1))),a1),f20(a1,f854(a1,a1),f854(a1,a1))),f773(f773(f10(f854(a1,a1),f855(a1,f855(f854(a1,a1),f854(a1,a1))),a1),f773(f9(a1,f854(a1,a1),f855(f854(a1,a1),f854(a1,a1))),f773(f773(f10(a841,f855(f854(a1,a1),f855(f854(a1,a1),f854(a1,a1))),a1),f98(f854(a1,a1))),f773(f773(f9(a1,a1,a841),a330),f2(a1))))),f773(f773(f9(a1,a1,f854(a1,a1)),f773(f773(f10(a1,f855(a1,f854(a1,a1)),a1),f241(a1,a1)),f81(a1))),f2(a1))))),f773(f773(f9(a1,f855(a1,a1),f855(a1,f854(a1,a1))),f773(f773(f10(f855(a1,f854(a1,a1)),f855(f855(a1,a1),f855(a1,f854(a1,a1))),a1),f10(a1,f854(a1,a1),a1)),f773(f773(f10(a1,f855(a1,f854(a1,a1)),a1),f241(a1,a1)),f773(f773(f9(a1,a1,a1),f773(f773(f10(a1,f855(a1,a1),a1),f3(a1)),f81(a1))),f80(a1))))),f773(f3(a1),f773(f77(a1),x100252))))),f60(x100251,x100252)))),f53(x100251,x100252))
% 191.21/191.74 [5576]~P110(x55761)+~P88(x55761)+E(f773(f77(x55761),f773(f773(f242(x55761),f773(f106(x55761),a99)),x55762)),f80(x55761))
% 191.21/191.74 [6077]~P133(x60771)+~P1(f773(f773(f233(a1),x60772),f2(a1)))+E(f773(f81(x60771),f773(f102(x60771),f773(a107,f773(f81(a1),x60772)))),f773(f105(x60771),x60772))
% 191.21/191.74 [6286]P1(f773(f773(f232(a101),x62861),f80(a101)))+E(f773(f773(f82(a101),f80(a101)),f267(x62861,f773(f773(f43(a101),x62862),x62861))),f267(x62861,x62862))+P1(f773(f773(f233(a101),x62862),x62861))
% 191.21/191.74 [6359]E(x63591,f2(a1))+~E(f773(f77(a1),x63592),f80(a1))+P1(f773(f773(f279(a1),f773(f773(f83(a1),x63591),x63592)),x63591))
% 191.21/191.74 [6785]~E(x67852,f80(a847))+~P1(f773(f773(f233(a847),f2(a847)),x67851))+P1(f773(f773(f279(a847),f773(f773(f83(a847),x67851),x67852)),x67851))
% 191.21/191.74 [6786]~E(x67861,f80(a847))+~P1(f773(f773(f233(a847),f2(a847)),x67862))+P1(f773(f773(f279(a847),f773(f773(f83(a847),x67861),x67862)),x67862))
% 191.21/191.74 [6919]~P87(x69191)+~P1(f773(f773(f334(x69191),x69192),f112(x69191)))+~E(f773(f773(f82(x69191),f773(f773(f82(x69191),f80(x69191)),x69192)),x69192),f2(x69191))
% 191.21/191.74 [7032]~P1(f773(f773(f233(a1),x70321),f2(a1)))+~P1(f773(f773(f232(a1),x70322),f2(a1)))+E(f773(f240(a1,a1),f773(a58,f54(f773(f81(a1),x70321),f773(f81(a1),x70322)))),f773(f773(f43(a1),x70321),x70322))
% 191.21/191.74 [7048]~P1(f773(f773(f233(a1),x70481),f2(a1)))+~P1(f773(f773(f232(a1),x70482),f2(a1)))+E(f773(f250(a1,a1),f773(a58,f54(f773(f81(a1),x70481),f773(f81(a1),x70482)))),f52(a1,x70481,x70482))
% 191.21/191.74 [7056]~P1(f773(f773(f233(a1),x70562),f2(a1)))+E(f773(f240(a1,a1),f773(a58,f57(f773(f81(a1),x70561),f773(f81(a1),x70562)))),f773(f773(f43(a1),x70561),x70562))+~P1(f773(f773(f233(a1),f2(a1)),x70561))
% 191.21/191.74 [7060]E(x70601,f2(a1))+E(f773(f77(a1),x70602),f80(a1))+~P1(f773(f773(f279(a1),f773(f773(f83(a1),x70601),x70602)),x70601))
% 191.21/191.74 [7075]~P1(f773(f773(f233(a1),x70752),f2(a1)))+E(f773(f250(a1,a1),f773(a58,f57(f773(f81(a1),x70751),f773(f81(a1),x70752)))),f52(a1,x70751,x70752))+~P1(f773(f773(f233(a1),f2(a1)),x70751))
% 191.21/191.74 [7126]E(f773(f773(f43(a1),f773(f773(f242(a1),x71261),x71262)),x71261),f773(f773(f242(a1),x71261),f773(f773(f3(a847),x71262),f773(a114,f2(a847)))))+~P1(f773(f773(f233(a847),f2(a847)),x71262))+~P1(f773(f773(f233(a1),f2(a1)),x71261))
% 191.21/191.74 [7231]~P1(f773(f773(f233(a847),f2(a847)),x72311))+~P1(f773(f773(f233(a847),f80(a847)),x72312))+P1(f773(f773(f233(a847),f773(f773(f43(a847),x72311),x72312)),x72311))
% 191.21/191.74 [7232]~P1(f773(f773(f233(a847),f2(a847)),x72321))+~P1(f773(f773(f233(a847),f2(a847)),x72322))+P1(f773(f773(f233(a847),f773(f773(f3(a847),x72321),x72322)),x72321))
% 191.21/191.74 [7233]~P1(f773(f773(f233(a1),f2(a1)),x72331))+~P1(f773(f773(f233(a1),f80(a1)),x72332))+P1(f773(f773(f233(a1),f773(f773(f43(a1),x72331),x72332)),x72331))
% 191.21/191.74 [7392]E(x73921,f2(a847))+~E(x73922,f2(a1))+~P1(f773(f773(f233(a1),f2(a1)),f773(f773(f242(a1),f773(f77(a1),x73922)),x73921)))
% 191.21/191.74 [7430]E(x74301,f80(a847))+~P1(f773(f773(f233(a847),f2(a847)),x74302))+~P1(f773(f773(f279(a847),f773(f773(f83(a847),x74302),x74301)),x74302))
% 191.21/191.74 [7431]E(x74311,f80(a847))+~P1(f773(f773(f233(a847),f2(a847)),x74312))+~P1(f773(f773(f279(a847),f773(f773(f83(a847),x74311),x74312)),x74312))
% 191.21/191.74 [7817]~E(x78172,f115(f848(x78171)))+E(f773(f181(f848(f848(x78171))),f164(x78171,x78172)),f2(a847))+~P18(a847,f773(f142(a847),f773(f773(f143(f848(x78171),a847),f181(f848(x78171))),x78172)))
% 191.21/191.74 [8067]P1(f773(x80671,x80672))+~P1(f773(x80671,f773(a109,f575(x80671,x80672))))+~P1(f773(f773(f334(f855(f854(a847,a847),a841)),x80672),a100))
% 191.21/191.74 [8081]E(x80811,f115(f848(x80812)))+E(f773(f181(f848(x80812)),f773(f773(f153(f848(x80812)),x80811),f2(a847))),f773(f181(f848(f848(x80812))),f164(x80812,x80811)))+~P18(a847,f773(f142(a847),f773(f773(f143(f848(x80812),a847),f181(f848(x80812))),x80811)))
% 191.21/191.74 [8753]~P1(f773(f63(x87531),f773(f256(x87531),x87532)))+~P1(f773(f63(x87531),f239(f855(x87531,a841))))+P1(f773(f63(x87531),f773(f256(x87531),f773(f773(f10(a841,a841,x87531),a328),x87532))))
% 191.21/191.74 [8806]E(f773(f773(f241(a847,a847),f773(a114,f773(f773(f43(a847),f773(f773(f3(a847),x88061),x88062)),x88062))),f52(a847,f773(f773(f3(a847),x88061),x88062),x88062)),f87(f854(a847,a847),f55(x88061,x88062)))+~P1(f773(f773(f233(a847),f2(a847)),x88062))+~P1(f773(f773(f232(a847),x88062),x88061))
% 191.21/191.74 [9071]~P1(f773(f63(x90711),f773(f256(x90711),x90712)))+P1(f773(f63(x90711),f239(f855(x90711,a841))))+~P1(f773(f63(x90711),f773(f256(x90711),f773(f773(f10(a841,a841,x90711),a328),x90712))))
% 191.21/191.74 [9730]P30(x97301,x97302)+~P36(x97301,f773(f240(f855(f854(x97301,x97301),a841),f855(f854(x97301,x97301),a841)),x97302))+~P1(f773(f773(f232(f855(f854(x97301,x97301),a841)),f773(f773(f281(x97301,x97301,x97301),f773(f240(f855(f854(x97301,x97301),a841),f855(f854(x97301,x97301),a841)),x97302)),f773(f250(f855(f854(x97301,x97301),a841),f855(f854(x97301,x97301),a841)),x97302))),f773(f240(f855(f854(x97301,x97301),a841),f855(f854(x97301,x97301),a841)),x97302)))
% 191.21/191.74 [9830]~E(f292(a847,f279(a847),f773(f773(f20(a847,f855(a847,a841),f855(a847,a841)),f773(f773(f10(f855(a847,f855(a841,a841)),f855(f855(a847,a841),f855(a847,a841)),a847),f20(a847,a841,a841)),f773(f773(f10(f855(a847,a841),f855(a847,f855(a841,a841)),a847),f773(f10(a841,f855(a841,a841),a847),a331)),f279(a847)))),f773(f773(f10(f855(a847,a841),f855(a847,a841),a847),f773(f10(a841,a841,a847),a328)),f773(f9(a847,a847,a841),f279(a847)))),x98302,x98301),f180(f855(a847,a841)))+~P1(f773(f773(f279(a847),x98302),x98301))+P1(f773(f773(f279(a847),x98301),x98302))
% 191.21/191.74 [9831]~E(f289(a847,f279(a847),f773(f773(f20(a847,f855(a847,a841),f855(a847,a841)),f773(f773(f10(f855(a847,f855(a841,a841)),f855(f855(a847,a841),f855(a847,a841)),a847),f20(a847,a841,a841)),f773(f773(f10(f855(a847,a841),f855(a847,f855(a841,a841)),a847),f773(f10(a841,f855(a841,a841),a847),a331)),f279(a847)))),f773(f773(f10(f855(a847,a841),f855(a847,a841),a847),f773(f10(a841,a841,a847),a328)),f773(f9(a847,a847,a841),f279(a847)))),x98312,x98311),f180(f855(a847,a841)))+~P1(f773(f773(f279(a847),x98312),x98311))+P1(f773(f773(f279(a847),x98311),x98312))
% 191.21/191.74 [7150]~P1(f773(f773(f233(a847),f2(a847)),x71502))+P1(f773(f773(f233(a847),x71501),x71502))+E(f773(a114,f773(f773(f43(a847),f773(f773(f3(a847),x71501),x71502)),x71502)),f773(f773(f43(a847),x71501),x71502))
% 191.21/191.74 [7307]~P1(f773(f773(f233(a847),f2(a847)),x73072))+~P1(f773(f773(f232(a847),x73072),x73071))+E(f773(a114,f773(f773(f43(a847),f773(f773(f3(a847),x73071),x73072)),x73072)),f773(f773(f43(a847),x73071),x73072))
% 191.21/191.74 [8280]~P88(x82801)+~P87(x82801)+~P33(x82801,f773(f106(x82801),f773(f773(f3(a1),f773(f773(f82(a1),x82802),x82802)),a99)))
% 191.21/191.74 [8981]E(x89811,f2(a847))+E(f773(f773(f251(a847,a847,f854(a847,a847)),f773(f773(f10(a847,f855(a847,f854(a847,a847)),a847),f241(a847,a847)),a114)),f87(f854(a847,a847),f55(f773(f773(f3(a847),x89812),x89811),x89811))),f87(f854(a847,a847),f55(x89812,x89811)))+P1(f773(f773(f233(a847),x89812),x89811))
% 191.21/191.74 [9378]P1(f773(x93782,f698(x93782,x93781)))+P1(f773(x93781,f698(x93782,x93781)))+E(f773(f256(a1),f773(f773(f20(a1,a841,a841),f773(f773(f10(a841,f855(a841,a841),a1),a331),f773(f232(a1),f2(a1)))),x93781)),f773(f256(a1),f773(f773(f20(a1,a841,a841),f773(f773(f10(a841,f855(a841,a841),a1),a331),f773(f232(a1),f2(a1)))),x93782)))
% 191.21/191.74 [9382]~P1(f773(x93822,f698(x93822,x93821)))+~P1(f773(x93821,f698(x93822,x93821)))+E(f773(f256(a1),f773(f773(f20(a1,a841,a841),f773(f773(f10(a841,f855(a841,a841),a1),a331),f773(f232(a1),f2(a1)))),x93821)),f773(f256(a1),f773(f773(f20(a1,a841,a841),f773(f773(f10(a841,f855(a841,a841),a1),a331),f773(f232(a1),f2(a1)))),x93822)))
% 191.21/191.74 [9913]~P1(f773(f773(f279(a847),x99132),x99131))+P1(f773(f773(f279(a847),x99131),x99132))+P1(f773(f773(f334(a847),x99131),f287(a847,f773(f773(f20(a847,f855(a847,a841),f855(a847,a841)),f773(f773(f10(f855(a847,f855(a841,a841)),f855(f855(a847,a841),f855(a847,a841)),a847),f20(a847,a841,a841)),f773(f773(f10(f855(a847,a841),f855(a847,f855(a841,a841)),a847),f773(f10(a841,f855(a841,a841),a847),a331)),f279(a847)))),f773(f773(f10(f855(a847,a841),f855(a847,a841),a847),f773(f10(a841,a841,a847),a328)),f773(f9(a847,a847,a841),f279(a847)))),x99132)))
% 191.21/191.74 [9914]~P1(f773(f773(f279(a847),x99142),x99141))+P1(f773(f773(f279(a847),x99141),x99142))+P1(f773(f773(f334(a847),x99142),f290(a847,f773(f773(f20(a847,f855(a847,a841),f855(a847,a841)),f773(f773(f10(f855(a847,f855(a841,a841)),f855(f855(a847,a841),f855(a847,a841)),a847),f20(a847,a841,a841)),f773(f773(f10(f855(a847,a841),f855(a847,f855(a841,a841)),a847),f773(f10(a841,f855(a841,a841),a847),a331)),f279(a847)))),f773(f773(f10(f855(a847,a841),f855(a847,a841),a847),f773(f10(a841,a841,a847),a328)),f773(f9(a847,a847,a841),f279(a847)))),x99141)))
% 191.21/191.74 [7530]~P88(x75301)+~P61(x75301)+E(f773(f773(f283(x75301),x75302),f773(f106(x75301),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))),x75302)
% 191.21/191.74 [9103]~P88(x91031)+~E(f773(f106(x91031),x91032),f80(x91031))+P33(x91031,f773(f106(x91031),f773(f773(f82(a1),x91032),f773(f81(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))))
% 191.21/191.74 [9258]~P120(x92581)+~E(x92582,f2(x92581))+E(f773(f773(f242(x92581),x92582),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),f2(x92581))
% 191.21/191.74 [9259]~P120(x92591)+~E(x92592,f80(x92591))+E(f773(f773(f242(x92591),x92592),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),f80(x92591))
% 191.21/191.74 [9272]~P120(x92721)+~E(x92722,f773(f81(x92721),f80(x92721)))+E(f773(f773(f242(x92721),x92722),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),f80(x92721))
% 191.21/191.74 [9320]~P88(x93201)+E(f773(f106(x93201),x93202),f80(x93201))+~P33(x93201,f773(f106(x93201),f773(f773(f82(a1),x93202),f773(f81(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))))
% 191.21/191.74 [9671]~P110(x96712)+E(x96711,f2(x96712))+P1(f773(f773(f233(x96712),f2(x96712)),f773(f773(f242(x96712),x96711),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))))
% 191.21/191.74 [9729]~P110(x97292)+~E(x97291,f2(x97292))+~P1(f773(f773(f233(x97292),f2(x97292)),f773(f773(f242(x97292),x97291),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))))
% 191.21/191.74 [9768]P1(f773(f773(f232(a1),x97681),f2(a1)))+P1(f773(f773(f233(a1),x97682),x97681))+E(f773(f50(x97681),f54(x97682,f773(f773(f83(a1),f773(f106(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),x97681))),f54(x97682,x97681))
% 191.21/191.74 [9769]~P1(f773(f773(f233(a1),f2(a1)),x97691))+P1(f773(f773(f233(a1),x97692),x97691))+E(f773(f50(x97691),f54(x97692,f773(f773(f83(a1),f773(f106(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),x97691))),f54(x97692,x97691))
% 191.21/191.74 [9770]P1(f773(f773(f232(a1),x97701),f2(a1)))+P1(f773(f773(f232(a1),f2(a1)),f773(f773(f82(a1),x97702),x97701)))+E(f773(f50(x97701),f57(x97702,f773(f773(f83(a1),f773(f106(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),x97701))),f57(x97702,x97701))
% 191.21/191.74 [9771]~P1(f773(f773(f233(a1),f2(a1)),x97711))+P1(f773(f773(f232(a1),f2(a1)),f773(f773(f82(a1),x97712),x97711)))+E(f773(f50(x97711),f57(x97712,f773(f773(f83(a1),f773(f106(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),x97711))),f57(x97712,x97711))
% 191.21/191.74 [9772]~P2(x97721)+~P1(f773(f773(f232(a1),f2(a1)),x97722))+E(f773(f102(x97721),f773(a107,f773(f773(f83(a1),f773(f106(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),x97722))),f773(f773(f82(x97721),f773(f102(x97721),f773(a107,x97722))),f773(f102(x97721),f773(a107,x97722))))
% 191.21/191.74 [4931]~P140(x49311,x49313,x49312)+~E(x49313,f2(a1))+P1(f773(x49311,x49312))
% 191.21/191.74 [5057]~P100(x50571)+~P18(x50571,x50573)+P18(x50571,f151(x50571,x50572,x50573))
% 191.21/191.74 [5058]~P100(x50581)+~P18(x50581,x50583)+P18(x50581,f162(x50581,x50582,x50583))
% 191.21/191.74 [4644]~P69(x46442)+~E(x46443,f773(f81(x46442),x46441))+E(x46441,f773(f81(x46442),x46443))
% 191.21/191.74 [4646]~P69(x46461)+~E(f773(f81(x46461),x46463),x46462)+E(f773(f81(x46461),x46462),x46463)
% 191.21/191.74 [4717]~P86(x47173)+E(x47171,x47172)+~E(f773(f102(x47173),x47171),f773(f102(x47173),x47172))
% 191.21/191.74 [4718]~P87(x47183)+E(x47181,x47182)+~E(f773(f105(x47183),x47181),f773(f105(x47183),x47182))
% 191.21/191.74 [4719]~P69(x47193)+E(x47191,x47192)+~E(f773(f81(x47193),x47191),f773(f81(x47193),x47192))
% 191.21/191.74 [4720]~P90(x47203)+E(x47201,x47202)+~E(f773(f81(x47203),x47201),f773(f81(x47203),x47202))
% 191.21/191.74 [4721]~P100(x47213)+E(x47211,x47212)+~E(f773(f257(x47213),x47211),f773(f257(x47213),x47212))
% 191.21/191.74 [4722]~P100(x47223)+E(x47221,x47222)+~E(f773(f296(x47223),x47221),f773(f296(x47223),x47222))
% 191.21/191.74 [4723]~P100(x47233)+E(x47231,x47232)+~E(f773(f293(x47233),x47231),f773(f293(x47233),x47232))
% 191.21/191.74 [4724]~P100(x47243)+E(x47241,x47242)+~E(f773(f258(x47243),x47241),f773(f258(x47243),x47242))
% 191.21/191.74 [4954]~P141(x49541,x49542,x49543)+~E(x49542,f2(a1))+P1(f773(x49541,f2(a1)))
% 191.21/191.74 [4993]~E(x49931,f2(a847))+E(f374(x49931,x49932,x49933),f180(f855(x49933,a841)))+~E(f773(f42(x49933),x49932),f773(a114,x49931))
% 191.21/191.74 [5140]~E(x51402,f2(a847))+E(f773(f240(a847,a847),x51401),f2(a847))+~P1(f773(f55(x51403,x51402),x51401))
% 191.21/191.74 [5184]P1(f773(x51841,x51842))+~E(x51843,f773(f102(a1),x51842))+~P1(f773(x51841,f773(a107,x51843)))
% 191.21/191.74 [5638]~E(x56383,f2(a847))+~P1(f773(x56381,x56382))+P1(f773(x56381,f52(a847,x56382,x56383)))
% 191.21/191.74 [5785]~P1(f773(a26,x57853))+~P1(f773(a26,x57852))+P1(f773(a26,f33(x57851,x57852,x57853)))
% 191.21/191.74 [6059]~E(x60593,f2(a847))+P1(f773(x60591,x60592))+~P1(f773(x60591,f52(a847,x60592,x60593)))
% 191.21/191.74 [6769]E(x67691,f2(a847))+~P1(f773(x67692,f801(x67691,x67693,x67692)))+P1(f773(x67692,f52(a847,x67693,x67691)))
% 191.21/191.74 [6882]~P9(x68821)+~P1(f773(f773(f232(x68821),x68822),f672(x68823,x68822,x68821)))+P1(f773(f773(f232(x68821),x68822),f45(x68821,x68823)))
% 191.21/191.74 [6884]~P1(f773(x68841,x68842))+~P1(f773(x68841,f801(x68843,x68842,x68841)))+P1(f773(x68841,f52(a847,x68842,x68843)))
% 191.21/191.74 [6984]E(x69841,f115(x69842))+E(f773(f773(f140(x69842),f748(x69843,x69841,x69842)),f755(x69843,x69841,x69842)),x69841)+~P1(f773(f773(f334(f848(x69842)),x69841),f149(x69842,x69843)))
% 191.21/191.74 [7018]~P133(x70181)+~P1(f773(f773(f334(x70181),x70182),f112(x70181)))+P1(f773(f773(f334(x70181),f773(f773(f242(x70181),x70182),x70183)),f112(x70181)))
% 191.21/191.74 [7359]P36(x73591,x73592)+~P1(f773(f773(f334(x73591),x73593),f682(x73592,x73591)))+P1(f773(f773(f334(x73591),f697(x73592,x73591,x73593)),f682(x73592,x73591)))
% 191.21/191.74 [7635]E(x76351,f115(x76352))+~P1(f773(f773(f334(f848(x76352)),x76351),f149(x76352,x76353)))+P1(f773(f773(f334(f848(x76352)),f755(x76353,x76351,x76352)),f149(x76352,x76353)))
% 191.21/191.74 [7685]E(x76851,f2(a847))+E(f773(f773(f82(a847),f773(f773(f83(a847),x76851),f803(x76851,x76852,x76853))),f801(x76851,x76852,x76853)),x76852)+P1(f773(x76853,f52(a847,x76852,x76851)))
% 191.21/191.74 [7728]~P1(f773(x77283,x77282))+E(f773(f773(f82(a847),f773(f773(f83(a847),x77281),f803(x77281,x77282,x77283))),f801(x77281,x77282,x77283)),x77282)+P1(f773(x77283,f52(a847,x77282,x77281)))
% 191.21/191.74 [7872]P1(f773(f773(f233(a1),x78721),f791(x78722,x78723,x78721)))+P1(f773(f773(x78723,f773(f773(f43(a1),x78722),x78721)),f52(a1,x78722,x78721)))+~P1(f773(f773(f233(a1),x78721),f2(a1)))
% 191.21/191.74 [8138]P1(f773(f773(x81382,f773(f773(f43(a1),x81381),x81383)),f52(a1,x81381,x81383)))+~P1(f773(f773(f233(a1),x81383),f2(a1)))+P1(f773(f773(f232(a1),f791(x81381,x81382,x81383)),f2(a1)))
% 191.21/191.74 [8317]E(f773(f773(f82(a1),f773(f773(f83(a1),x83171),f794(x83172,x83173,x83171))),f791(x83172,x83173,x83171)),x83172)+P1(f773(f773(x83173,f773(f773(f43(a1),x83172),x83171)),f52(a1,x83172,x83171)))+~P1(f773(f773(f233(a1),x83171),f2(a1)))
% 191.21/191.74 [8552]~P1(f773(f773(x85521,f794(x85522,x85521,x85523)),f791(x85522,x85521,x85523)))+P1(f773(f773(x85521,f773(f773(f43(a1),x85522),x85523)),f52(a1,x85522,x85523)))+~P1(f773(f773(f233(a1),x85523),f2(a1)))
% 191.21/191.74 [8763]~P100(x87631)+~P18(x87631,x87633)+P18(x87631,f139(x87631,x87631,f7(x87631),x87632,x87633))
% 191.21/191.74 [9208]~P119(x92082)+E(x92081,f2(x92082))+~P1(f773(f773(f232(x92082),f773(f773(f82(x92082),f773(f773(f83(x92082),x92083),x92083)),f773(f773(f83(x92082),x92081),x92081))),f2(x92082)))
% 191.21/191.74 [9209]~P119(x92092)+E(x92091,f2(x92092))+~P1(f773(f773(f232(x92092),f773(f773(f82(x92092),f773(f773(f83(x92092),x92091),x92091)),f773(f773(f83(x92092),x92093),x92093))),f2(x92092)))
% 191.21/191.74 [9967]~P110(x99671)+~P1(f773(f773(f233(x99671),x99672),f2(x99671)))+P1(f773(f773(f233(x99671),f773(f773(f242(x99671),x99672),f773(a114,f773(f773(f83(a847),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),x99673)))),f2(x99671)))
% 191.21/191.74 [9977]~P110(x99772)+E(x99771,f2(x99772))+~P1(f773(f773(f232(x99772),f773(f773(f82(x99772),f773(f773(f242(x99772),x99773),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))),f773(f773(f242(x99772),x99771),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))))),f2(x99772)))
% 191.21/191.74 [9978]~P110(x99782)+E(x99781,f2(x99782))+~P1(f773(f773(f232(x99782),f773(f773(f82(x99782),f773(f773(f242(x99782),x99781),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))),f773(f773(f242(x99782),x99783),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))))),f2(x99782)))
% 191.21/191.74 [4675]~E(x46752,x46753)+~P69(x46751)+E(f773(f773(f3(x46751),x46752),x46753),f2(x46751))
% 191.21/191.74 [4676]~E(x46762,x46763)+~P6(x46761)+E(f773(f773(f3(x46761),x46762),x46763),f2(x46761))
% 191.21/191.74 [4689]~P137(x46891)+~E(x46893,f2(x46891))+E(f773(f773(f82(x46891),x46892),x46893),x46892)
% 191.21/191.74 [4704]~P134(x47041)+~E(x47043,f2(x47041))+E(f773(f773(f83(x47041),x47042),x47043),f2(x47041))
% 191.21/191.74 [4705]~P134(x47051)+~E(x47052,f2(x47051))+E(f773(f773(f83(x47051),x47052),x47053),f2(x47051))
% 191.21/191.74 [4726]~E(x47263,f115(x47261))+~E(x47262,f115(x47261))+E(f773(f773(f125(x47261),x47262),x47263),f115(x47261))
% 191.21/191.74 [4809]~P137(x48092)+E(x48091,f2(x48092))+~E(f773(f773(f82(x48092),x48093),x48091),x48093)
% 191.21/191.74 [4810]~P69(x48101)+~E(x48102,f773(f81(x48101),x48103))+E(f773(f773(f82(x48101),x48102),x48103),f2(x48101))
% 191.21/191.74 [4817]E(x48171,f115(x48172))+E(x48173,f2(a847))+~E(f773(f773(f159(x48172),x48173),x48171),f115(x48172))
% 191.21/191.74 [4825]~P69(x48253)+E(x48251,x48252)+~E(f773(f773(f3(x48253),x48251),x48252),f2(x48253))
% 191.21/191.74 [4826]~P6(x48263)+E(x48261,x48262)+~E(f773(f773(f3(x48263),x48261),x48262),f2(x48263))
% 191.21/191.74 [4835]~P120(x48352)+E(x48351,f2(x48352))+~E(f773(f773(f242(x48352),x48351),x48353),f2(x48352))
% 191.21/191.74 [4836]~P94(x48362)+E(x48361,f239(x48362))+~E(f773(f773(f104(x48362),x48363),x48361),f239(x48362))
% 191.21/191.74 [4837]~P94(x48372)+E(x48371,f239(x48372))+~E(f773(f773(f104(x48372),x48371),x48373),f239(x48372))
% 191.21/191.74 [4838]~P95(x48382)+E(x48381,f180(x48382))+~E(f773(f773(f103(x48382),x48383),x48381),f180(x48382))
% 191.21/191.74 [4839]~P95(x48392)+E(x48391,f180(x48392))+~E(f773(f773(f103(x48392),x48391),x48393),f180(x48392))
% 191.21/191.74 [4904]~P69(x49042)+E(x49041,f773(f81(x49042),x49043))+~E(f773(f773(f82(x49042),x49041),x49043),f2(x49042))
% 191.21/191.74 [4905]~P69(x49051)+E(f773(f81(x49051),x49052),x49053)+~E(f773(f773(f82(x49051),x49052),x49053),f2(x49051))
% 191.21/191.74 [4908]~E(x49082,x49083)+~P99(x49081)+P1(f773(f773(f232(x49081),x49082),x49083))
% 191.21/191.74 [4909]~E(x49092,x49093)+~P103(x49091)+P1(f773(f773(f232(x49091),x49092),x49093))
% 191.21/191.74 [5007]~P111(x50071)+~E(x50072,f773(f81(x50071),x50073))+E(f773(f773(f83(x50071),x50072),x50072),f773(f773(f83(x50071),x50073),x50073))
% 191.21/191.74 [5015]~P100(x50151)+~P18(x50151,x50153)+P18(x50151,f773(f773(f159(x50151),x50152),x50153))
% 191.21/191.74 [5016]~P100(x50161)+~P18(x50161,x50163)+P18(x50161,f773(f773(f128(x50161),x50162),x50163))
% 191.21/191.74 [5055]E(x50551,x50552)+E(x50553,f2(a847))+~E(f773(f773(f83(a847),x50553),x50551),f773(f773(f83(a847),x50553),x50552))
% 191.21/191.74 [5056]E(x50561,x50562)+E(x50563,f2(a847))+~E(f773(f773(f83(a847),x50561),x50563),f773(f773(f83(a847),x50562),x50563))
% 191.21/191.74 [5132]~E(x51322,x51323)+~P99(x51321)+E(f295(x51321,x51322,x51323),f773(f773(f302(x51321),x51322),f180(f855(x51321,a841))))
% 191.21/191.74 [5172]~P110(x51721)+~E(f773(f77(x51721),x51722),f773(f77(x51721),x51723))+P1(f773(f773(f279(x51721),x51722),x51723))
% 191.21/191.74 [5181]~E(x51811,x51812)+~P99(x51813)+~P1(f773(f773(f233(x51813),x51811),x51812))
% 191.21/191.74 [5182]~E(x51821,x51822)+~P100(x51823)+~P1(f773(f773(f233(x51823),x51821),x51822))
% 191.21/191.74 [5189]~P99(x51891)+E(f773(f294(x51891,x51892),x51893),f180(f855(x51891,a841)))+P1(f773(f773(f233(x51891),x51892),x51893))
% 191.21/191.74 [5235]~P99(x52351)+E(f295(x52351,x52352,x52353),f180(f855(x52351,a841)))+P1(f773(f773(f232(x52351),x52352),x52353))
% 191.21/191.74 [5236]~P99(x52361)+E(f297(x52361,x52362,x52363),f180(f855(x52361,a841)))+P1(f773(f773(f233(x52361),x52362),x52363))
% 191.21/191.74 [5237]~P99(x52371)+E(f180(f855(x52371,a841)),f295(x52371,x52372,x52373))+P1(f773(f773(f232(x52371),x52372),x52373))
% 191.21/191.74 [5238]~P99(x52381)+E(f180(f855(x52381,a841)),f297(x52381,x52382,x52383))+P1(f773(f773(f233(x52381),x52382),x52383))
% 191.21/191.74 [5246]~P100(x52461)+~E(f773(f773(f236(x52461),x52462),x52463),x52462)+P1(f773(f773(f232(x52461),x52462),x52463))
% 191.21/191.74 [5247]~P100(x52471)+~E(f773(f773(f179(x52471),x52472),x52473),x52473)+P1(f773(f773(f232(x52471),x52472),x52473))
% 191.21/191.74 [5248]~P92(x52481)+~E(f773(f773(f103(x52481),x52482),x52483),x52483)+P1(f773(f773(f232(x52481),x52482),x52483))
% 191.21/191.74 [5249]~P98(x52491)+~E(f773(f773(f104(x52491),x52492),x52493),x52492)+P1(f773(f773(f232(x52491),x52492),x52493))
% 191.21/191.74 [5265]~P100(x52651)+P18(x52651,x52652)+~P18(x52651,f773(f773(f140(x52651),x52653),x52652))
% 191.21/191.74 [5266]~P100(x52661)+P18(x52661,x52662)+~P18(x52661,f773(f773(f125(x52661),x52663),x52662))
% 191.21/191.74 [5267]~P100(x52671)+P18(x52671,x52672)+~P18(x52671,f773(f773(f125(x52671),x52672),x52673))
% 191.21/191.74 [5272]~P7(x52721)+~E(f52(x52721,x52723,x52722),f2(x52721))+P1(f773(f773(f279(x52721),x52722),x52723))
% 191.21/191.74 [5335]~P100(x53351)+P1(f773(f773(f232(x53351),x53353),x53352))+P1(f773(f773(f233(x53351),x53352),x53353))
% 191.21/191.74 [5337]~P100(x53371)+P1(f773(f773(f232(x53371),x53373),x53372))+P1(f773(f773(f232(x53371),x53372),x53373))
% 191.21/191.74 [5376]~P100(x53761)+E(f773(f773(f236(x53761),x53762),x53763),x53763)+~P1(f773(f773(f232(x53761),x53763),x53762))
% 191.21/191.74 [5378]~P100(x53781)+E(f773(f773(f236(x53781),x53782),x53783),x53782)+~P1(f773(f773(f232(x53781),x53782),x53783))
% 191.21/191.74 [5379]~P100(x53791)+E(f773(f773(f179(x53791),x53792),x53793),x53792)+~P1(f773(f773(f232(x53791),x53793),x53792))
% 191.21/191.74 [5381]~P100(x53811)+E(f773(f773(f179(x53811),x53812),x53813),x53813)+~P1(f773(f773(f232(x53811),x53812),x53813))
% 191.21/191.74 [5382]~P92(x53821)+E(f773(f773(f103(x53821),x53822),x53823),x53822)+~P1(f773(f773(f232(x53821),x53823),x53822))
% 191.21/191.74 [5384]~P92(x53841)+E(f773(f773(f103(x53841),x53842),x53843),x53843)+~P1(f773(f773(f232(x53841),x53842),x53843))
% 191.21/191.74 [5385]~P98(x53851)+E(f773(f773(f104(x53851),x53852),x53853),x53853)+~P1(f773(f773(f232(x53851),x53853),x53852))
% 191.21/191.74 [5387]~P98(x53871)+E(f773(f773(f104(x53871),x53872),x53873),x53872)+~P1(f773(f773(f232(x53871),x53872),x53873))
% 191.21/191.74 [5394]~P113(x53942)+E(x53941,f2(x53942))+E(f773(f773(f283(x53942),f773(f81(x53942),x53943)),f773(f81(x53942),x53941)),f773(f773(f283(x53942),x53943),x53941))
% 191.21/191.74 [5401]~P7(x54011)+E(f52(x54011,x54012,x54013),f2(x54011))+~P1(f773(f773(f279(x54011),x54013),x54012))
% 191.21/191.74 [5441]~P99(x54411)+E(f773(f294(x54411,x54412),x54413),f180(f855(x54411,a841)))+~P1(f773(f773(f232(x54411),x54413),x54412))
% 191.21/191.74 [5470]~P99(x54701)+E(f295(x54701,x54702,x54703),f180(f855(x54701,a841)))+~P1(f773(f773(f233(x54701),x54703),x54702))
% 191.21/191.74 [5471]~P99(x54711)+E(f297(x54711,x54712,x54713),f180(f855(x54711,a841)))+~P1(f773(f773(f232(x54711),x54713),x54712))
% 191.21/191.74 [5472]~P99(x54721)+E(f298(x54721,x54722,x54723),f180(f855(x54721,a841)))+~P1(f773(f773(f232(x54721),x54723),x54722))
% 191.21/191.74 [5521]~E(f773(f773(f3(a847),x55211),x55213),x55212)+E(x55211,f773(f773(f82(a847),x55212),x55213))+~P1(f773(f773(f232(a847),x55213),x55211))
% 191.21/191.74 [5522]~E(x55221,f773(f773(f82(a847),x55223),x55222))+E(f773(f773(f3(a847),x55221),x55222),x55223)+~P1(f773(f773(f232(a847),x55222),x55221))
% 191.21/191.74 [5565]~P1(f773(x55651,x55653))+P1(f773(x55651,f796(x55651,x55652)))+~P1(f773(f773(f232(a847),x55653),x55652))
% 191.21/191.74 [5566]~P1(f773(x55661,x55663))+P1(f773(x55661,f339(x55661,x55662)))+~P1(f773(f773(f233(a847),x55663),x55662))
% 191.21/191.74 [5574]~P99(x55741)+~E(f773(f294(x55741,x55742),x55743),f180(f855(x55741,a841)))+~P1(f773(f773(f233(x55741),x55742),x55743))
% 191.21/191.74 [5578]~P99(x55781)+~P1(f773(f773(f233(x55781),x55782),x55783))+P1(f773(f773(f232(x55781),x55782),x55783))
% 191.21/191.74 [5580]~P103(x55801)+~P1(f773(f773(f233(x55801),x55802),x55803))+P1(f773(f773(f232(x55801),x55802),x55803))
% 191.21/191.74 [5693]~P99(x56931)+~E(f295(x56931,x56932,x56933),f180(f855(x56931,a841)))+~P1(f773(f773(f232(x56931),x56932),x56933))
% 191.21/191.74 [5694]~P99(x56941)+~E(f297(x56941,x56942,x56943),f180(f855(x56941,a841)))+~P1(f773(f773(f233(x56941),x56942),x56943))
% 191.21/191.74 [5695]~P99(x56951)+~E(f180(f855(x56951,a841)),f295(x56951,x56952,x56953))+~P1(f773(f773(f232(x56951),x56952),x56953))
% 191.21/191.74 [5696]~P99(x56961)+~E(f180(f855(x56961,a841)),f297(x56961,x56962,x56963))+~P1(f773(f773(f233(x56961),x56962),x56963))
% 191.21/191.74 [5709]P1(f773(x57091,x57092))+~P1(f773(x57091,f797(x57091,x57093)))+~P1(f773(f773(f232(a847),x57092),x57093))
% 191.21/191.74 [5710]P1(f773(x57101,x57102))+~P1(f773(x57101,f342(x57101,x57103)))+~P1(f773(f773(f233(a847),x57102),x57103))
% 191.21/191.74 [5718]~E(x57181,f773(a114,x57183))+P1(f773(f773(f233(a847),x57181),f773(a114,x57182)))+~P1(f773(f773(f233(a847),x57183),x57182))
% 191.21/191.74 [5734]E(x57341,x57342)+~E(f773(f773(f83(a847),x57343),x57341),f773(f773(f83(a847),x57343),x57342))+~P1(f773(f773(f233(a847),f2(a847)),x57343))
% 191.21/191.74 [5795]E(f773(x57951,f404(x57951,x57952,x57953)),f80(a847))+~E(f773(f773(f8(x57953,a847),x57951),x57952),f80(a847))+~P1(f773(f63(x57953),x57952))
% 191.21/191.74 [5805]~P9(x58051)+P1(f773(f773(f232(x58051),x58052),f44(x58051,x58053)))+~P1(f773(f773(f334(x58051),x58052),x58053))
% 191.21/191.74 [5829]~P99(x58291)+~P1(f773(f773(f233(x58291),x58293),x58292))+~P1(f773(f773(f233(x58291),x58292),x58293))
% 191.21/191.74 [5833]~P103(x58331)+~P1(f773(f773(f233(x58331),x58333),x58332))+~P1(f773(f773(f233(x58331),x58332),x58333))
% 191.21/191.74 [5834]~P103(x58341)+~P1(f773(f773(f232(x58341),x58343),x58342))+~P1(f773(f773(f233(x58341),x58342),x58343))
% 191.21/191.74 [5835]~P100(x58351)+~P1(f773(f773(f233(x58351),x58353),x58352))+~P1(f773(f773(f233(x58351),x58352),x58353))
% 191.21/191.74 [5838]~P100(x58381)+~P1(f773(f773(f232(x58381),x58383),x58382))+~P1(f773(f773(f233(x58381),x58382),x58383))
% 191.21/191.74 [5857]~E(x58572,x58573)+~E(x58571,x58572)+E(f282(a847,f279(a847),x58571,x58572),f773(f773(f302(a847),x58573),f180(f855(a847,a841))))
% 191.21/191.74 [5865]~E(f773(x58652,f405(x58652,x58653,x58651)),f2(a847))+E(f773(f773(f8(x58651,a847),x58652),x58653),f2(a847))+~P1(f773(f63(x58651),x58653))
% 191.21/191.74 [5866]~E(f773(x58662,f450(x58662,x58663,x58661)),f80(a847))+E(f773(f773(f11(x58661,a847),x58662),x58663),f80(a847))+~P1(f773(f63(x58661),x58663))
% 191.21/191.74 [5880]~P102(x58801)+~P1(f773(f773(f233(x58801),x58803),x58802))+P1(f773(f773(f334(x58801),x58802),f773(f296(x58801),x58803)))
% 191.21/191.74 [5881]~P102(x58811)+~P1(f773(f773(f232(x58811),x58813),x58812))+P1(f773(f773(f334(x58811),x58812),f773(f258(x58811),x58813)))
% 191.21/191.74 [5882]~P102(x58821)+~P1(f773(f773(f233(x58821),x58822),x58823))+P1(f773(f773(f334(x58821),x58822),f773(f257(x58821),x58823)))
% 191.21/191.74 [5883]~P102(x58831)+~P1(f773(f773(f232(x58831),x58832),x58833))+P1(f773(f773(f334(x58831),x58832),f773(f293(x58831),x58833)))
% 191.21/191.74 [5884]~P104(x58841)+~P1(f773(f773(f279(x58841),x58842),x58843))+P1(f773(f773(f279(x58841),x58842),f773(f81(x58841),x58843)))
% 191.21/191.74 [5885]~P110(x58851)+~P1(f773(f773(f279(x58851),x58852),x58853))+P1(f773(f773(f279(x58851),x58852),f773(f77(x58851),x58853)))
% 191.21/191.74 [5896]E(f773(x58961,f406(x58961,x58962,x58963)),f773(a114,f2(a847)))+~E(f773(f773(f8(x58963,a847),x58961),x58962),f773(a114,f2(a847)))+~P1(f773(f63(x58963),x58962))
% 191.21/191.74 [5980]~P9(x59801)+~P1(f773(f773(f334(x59801),x59803),x59802))+P1(f773(f773(f232(x59801),f45(x59801,x59802)),x59803))
% 191.21/191.74 [5998]~P1(f773(f773(f232(a847),x59981),x59983))+P1(f773(f773(f232(a847),x59981),x59982))+~P1(f773(f773(f232(a847),x59983),x59982))
% 191.21/191.74 [5999]~P1(f773(f773(f232(a1),x59991),x59993))+P1(f773(f773(f232(a1),x59991),x59992))+~P1(f773(f773(f232(a1),x59993),x59992))
% 191.21/191.74 [6000]~P1(f773(f773(f279(a847),x60001),x60003))+P1(f773(f773(f279(a847),x60001),x60002))+~P1(f773(f773(f279(a847),x60003),x60002))
% 191.21/191.74 [6018]~P102(x60181)+~P1(f773(f773(f334(x60181),x60183),f773(f296(x60181),x60182)))+P1(f773(f773(f233(x60181),x60182),x60183))
% 191.21/191.74 [6019]~P102(x60191)+~P1(f773(f773(f334(x60191),x60192),f773(f257(x60191),x60193)))+P1(f773(f773(f233(x60191),x60192),x60193))
% 191.21/191.74 [6020]~P102(x60201)+~P1(f773(f773(f334(x60201),x60203),f773(f258(x60201),x60202)))+P1(f773(f773(f232(x60201),x60202),x60203))
% 191.21/191.74 [6021]~P102(x60211)+~P1(f773(f773(f334(x60211),x60212),f773(f293(x60211),x60213)))+P1(f773(f773(f232(x60211),x60212),x60213))
% 191.21/191.74 [6022]~P110(x60221)+~P1(f773(f773(f279(x60221),x60222),f773(f77(x60221),x60223)))+P1(f773(f773(f279(x60221),x60222),x60223))
% 191.21/191.74 [6023]~P104(x60231)+~P1(f773(f773(f279(x60231),x60232),f773(f81(x60231),x60233)))+P1(f773(f773(f279(x60231),x60232),x60233))
% 191.21/191.74 [6247]~P62(x62471)+P1(f773(f773(f233(x62471),f2(x62471)),f799(x62473,x62472,x62471)))+P1(f773(f773(f232(x62471),x62472),x62473))
% 191.21/191.74 [6248]~P63(x62481)+P1(f773(f773(f233(x62481),f2(x62481)),f806(x62483,x62482,x62481)))+P1(f773(f773(f232(x62481),x62482),x62483))
% 191.21/191.74 [6319]~P77(x63191)+~P1(f773(f773(f233(x63191),x63193),f773(f81(x63191),x63192)))+P1(f773(f773(f233(x63191),x63192),f773(f81(x63191),x63193)))
% 191.21/191.74 [6321]~P77(x63211)+~P1(f773(f773(f232(x63211),x63213),f773(f81(x63211),x63212)))+P1(f773(f773(f232(x63211),x63212),f773(f81(x63211),x63213)))
% 191.21/191.74 [6332]~P1(f773(f773(f233(a847),x63321),x63323))+~P1(f773(f773(f233(a847),x63323),x63322))+P1(f773(f773(f233(a847),f773(a114,x63321)),x63322))
% 191.21/191.74 [6365]~P110(x63651)+P1(f773(f773(f233(x63651),f773(f105(x63651),x63652)),f773(f105(x63651),x63653)))+~P1(f773(f773(f233(a1),x63652),x63653))
% 191.21/191.74 [6366]~P117(x63661)+P1(f773(f773(f233(x63661),f773(f102(x63661),x63662)),f773(f102(x63661),x63663)))+~P1(f773(f773(f233(a847),x63662),x63663))
% 191.21/191.74 [6367]~P117(x63671)+P1(f773(f773(f232(x63671),f773(f102(x63671),x63672)),f773(f102(x63671),x63673)))+~P1(f773(f773(f232(a847),x63672),x63673))
% 191.21/191.74 [6368]~P110(x63681)+P1(f773(f773(f232(x63681),f773(f105(x63681),x63682)),f773(f105(x63681),x63683)))+~P1(f773(f773(f232(a1),x63682),x63683))
% 191.21/191.74 [6374]~P100(x63741)+E(f773(f773(f103(f855(x63741,a841)),f773(f257(x63741),x63742)),f773(f294(x63741,x63742),x63743)),f773(f257(x63741),x63743))+~P1(f773(f773(f232(x63741),x63742),x63743))
% 191.21/191.74 [6405]~P77(x64051)+~P1(f773(f773(f233(x64051),x64053),x64052))+P1(f773(f773(f233(x64051),f773(f81(x64051),x64052)),f773(f81(x64051),x64053)))
% 191.21/191.74 [6407]~P77(x64071)+~P1(f773(f773(f232(x64071),x64073),x64072))+P1(f773(f773(f232(x64071),f773(f81(x64071),x64072)),f773(f81(x64071),x64073)))
% 191.21/191.74 [6409]~P90(x64091)+~P1(f773(f773(f232(x64091),x64093),x64092))+P1(f773(f773(f232(x64091),f773(f81(x64091),x64092)),f773(f81(x64091),x64093)))
% 191.21/191.74 [6444]~P100(x64441)+E(f773(f773(f103(f855(x64441,a841)),f773(f257(x64441),x64442)),f295(x64441,x64442,x64443)),f773(f293(x64441),x64443))+~P1(f773(f773(f232(x64441),x64442),x64443))
% 191.21/191.74 [6445]~P100(x64451)+E(f773(f773(f103(f855(x64451,a841)),f773(f293(x64451),x64452)),f297(x64451,x64452,x64453)),f773(f293(x64451),x64453))+~P1(f773(f773(f232(x64451),x64452),x64453))
% 191.21/191.74 [6446]~P100(x64461)+E(f773(f773(f103(f855(x64461,a841)),f773(f293(x64461),x64462)),f298(x64461,x64462,x64463)),f773(f257(x64461),x64463))+~P1(f773(f773(f233(x64461),x64462),x64463))
% 191.21/191.74 [6484]~P100(x64841)+E(f773(f773(f103(f855(x64841,a841)),f773(f294(x64841,x64842),x64843)),f773(f258(x64841),x64843)),f773(f258(x64841),x64842))+~P1(f773(f773(f232(x64841),x64842),x64843))
% 191.21/191.74 [6647]~P100(x66471)+E(f773(f773(f103(f855(x66471,a841)),f295(x66471,x66472,x66473)),f773(f296(x66471),x66473)),f773(f258(x66471),x66472))+~P1(f773(f773(f232(x66471),x66472),x66473))
% 191.21/191.74 [6648]~P100(x66481)+E(f773(f773(f103(f855(x66481,a841)),f297(x66481,x66482,x66483)),f773(f296(x66481),x66483)),f773(f296(x66481),x66482))+~P1(f773(f773(f232(x66481),x66482),x66483))
% 191.21/191.74 [6649]~P100(x66491)+E(f773(f773(f103(f855(x66491,a841)),f298(x66491,x66492,x66493)),f773(f258(x66491),x66493)),f773(f296(x66491),x66492))+~P1(f773(f773(f233(x66491),x66492),x66493))
% 191.21/191.74 [6666]P1(f773(x66661,x66662))+~P1(f773(f773(f232(a847),x66662),x66663))+P1(f773(f773(f334(a847),f797(x66661,x66663)),f295(a847,f2(a847),x66663)))
% 191.21/191.74 [6676]P1(f773(f773(f279(a1),x66761),f52(a1,x66762,x66763)))+~P1(f773(f773(f279(a1),x66761),x66762))+~P1(f773(f773(f279(a1),x66761),x66763))
% 191.21/191.74 [6702]E(x67021,x67022)+~E(f773(f773(f153(x67023),x67021),f730(x67023,x67022,x67021)),f773(f773(f153(x67023),x67022),f730(x67023,x67022,x67021)))+~E(f773(f181(f848(x67023)),x67021),f773(f181(f848(x67023)),x67022))
% 191.21/191.74 [6708]~E(x67083,f773(f773(f43(a847),x67081),x67082))+~P1(f773(f773(f233(a847),f2(a847)),x67082))+P1(f773(f773(f233(a847),x67081),f773(f773(f83(a847),x67082),f773(a114,x67083))))
% 191.21/191.74 [6723]~P1(f773(x67231,x67233))+~P1(f773(f773(f232(a847),x67233),x67232))+P1(f773(f773(f334(a847),f796(x67231,x67232)),f295(a847,f2(a847),x67232)))
% 191.21/191.74 [6766]~P1(f773(x67661,x67663))+P1(f773(x67661,f340(x67661,x67662)))+~P1(f773(f773(f334(a847),x67663),f295(a847,f2(a847),x67662)))
% 191.21/191.74 [6789]~P117(x67893)+~P1(f773(f773(f233(x67893),f773(f102(x67893),x67891)),f773(f102(x67893),x67892)))+P1(f773(f773(f233(a847),x67891),x67892))
% 191.21/191.74 [6790]~P110(x67903)+~P1(f773(f773(f233(x67903),f773(f105(x67903),x67901)),f773(f105(x67903),x67902)))+P1(f773(f773(f233(a1),x67901),x67902))
% 191.21/191.74 [6791]~P117(x67913)+~P1(f773(f773(f232(x67913),f773(f102(x67913),x67911)),f773(f102(x67913),x67912)))+P1(f773(f773(f232(a847),x67911),x67912))
% 191.21/191.74 [6792]~P110(x67923)+~P1(f773(f773(f232(x67923),f773(f105(x67923),x67921)),f773(f105(x67923),x67922)))+P1(f773(f773(f232(a1),x67921),x67922))
% 191.21/191.74 [6808]~P117(x68081)+~P1(f773(f773(f233(x68081),f80(x68081)),x68082))+P1(f773(f773(f233(x68081),f80(x68081)),f773(f773(f242(x68081),x68082),f773(a114,x68083))))
% 191.21/191.74 [6812]~P77(x68121)+~P1(f773(f773(f233(x68121),f773(f81(x68121),x68123)),f773(f81(x68121),x68122)))+P1(f773(f773(f233(x68121),x68122),x68123))
% 191.21/191.74 [6813]~P77(x68131)+~P1(f773(f773(f232(x68131),f773(f81(x68131),x68133)),f773(f81(x68131),x68132)))+P1(f773(f773(f232(x68131),x68132),x68133))
% 191.21/191.74 [6814]~P90(x68141)+~P1(f773(f773(f232(x68141),f773(f81(x68141),x68143)),f773(f81(x68141),x68142)))+P1(f773(f773(f232(x68141),x68142),x68143))
% 191.21/191.74 [6840]P1(f773(x68401,x68402))+~P1(f773(x68401,f836(x68401,x68403)))+~P1(f773(f773(f334(a847),x68402),f295(a847,f2(a847),x68403)))
% 191.21/191.74 [6861]~P62(x68611)+P1(f773(f773(f233(x68611),f799(x68613,x68612,x68611)),f80(x68611)))+P1(f773(f773(f232(x68611),x68612),x68613))
% 191.21/191.74 [6880]~E(f52(a847,x68803,x68802),f52(a847,x68801,x68802))+E(f773(f773(f82(a847),x68801),f773(f773(f83(a847),x68802),f808(x68801,x68802,x68803))),x68803)+~P1(f773(f773(f232(a847),x68801),x68803))
% 191.21/191.74 [6898]E(f773(x68981,f606(x68981,x68982,x68983)),f183(x68982))+~P1(f773(f63(x68983),f169(x68983,x68982,x68981)))+P1(f773(f63(x68983),f239(f855(x68983,a841))))
% 191.21/191.74 [6939]E(f773(f773(f8(x69391,a847),x69392),x69393),f2(a847))+~P1(f773(f63(x69391),x69393))+P1(f773(f773(f334(x69391),f405(x69392,x69393,x69391)),x69393))
% 191.21/191.74 [6940]E(f773(f773(f11(x69401,a847),x69402),x69403),f80(a847))+~P1(f773(f63(x69401),x69403))+P1(f773(f773(f334(x69401),f450(x69402,x69403,x69401)),x69403))
% 191.21/191.74 [6962]~P100(x69621)+~P1(f773(f773(f233(x69621),x69622),x69623))+P1(f773(f773(f233(f855(x69621,a841)),f773(f257(x69621),x69622)),f773(f257(x69621),x69623)))
% 191.21/191.74 [6963]~P100(x69631)+~P1(f773(f773(f232(x69631),x69632),x69633))+P1(f773(f773(f232(f855(x69631,a841)),f773(f257(x69631),x69632)),f773(f257(x69631),x69633)))
% 191.21/191.74 [6964]~P100(x69641)+~P1(f773(f773(f232(x69641),x69643),x69642))+P1(f773(f773(f232(f855(x69641,a841)),f773(f296(x69641),x69642)),f773(f296(x69641),x69643)))
% 191.21/191.74 [6965]~P99(x69651)+~P1(f773(f773(f232(x69651),x69652),x69653))+P1(f773(f773(f232(f855(x69651,a841)),f773(f293(x69651),x69652)),f773(f293(x69651),x69653)))
% 191.21/191.74 [6966]~P99(x69661)+~P1(f773(f773(f232(x69661),x69663),x69662))+P1(f773(f773(f232(f855(x69661,a841)),f773(f258(x69661),x69662)),f773(f258(x69661),x69663)))
% 191.21/191.74 [6971]~P9(x69711)+P1(f773(f773(f232(x69711),x69712),f45(x69711,x69713)))+P1(f773(f773(f334(x69711),f672(x69713,x69712,x69711)),x69713))
% 191.21/191.74 [6976]~P77(x69761)+P1(f773(f773(f233(x69761),f773(f773(f3(x69761),x69762),x69763)),f2(x69761)))+~P1(f773(f773(f233(x69761),x69762),x69763))
% 191.21/191.74 [6977]~P77(x69771)+P1(f773(f773(f232(x69771),f773(f773(f3(x69771),x69772),x69773)),f2(x69771)))+~P1(f773(f773(f232(x69771),x69772),x69773))
% 191.21/191.74 [7015]~P1(f773(f773(f279(a1),x70151),f52(a1,x70152,x70153)))+~P1(f773(f773(f279(a1),x70151),x70153))+P1(f773(f773(f279(a1),x70151),x70152))
% 191.21/191.74 [7022]P1(f773(x70221,x70222))+P1(f773(f773(f232(a847),f836(x70221,x70223)),x70223))+~P1(f773(f773(f334(a847),x70222),f295(a847,f2(a847),x70223)))
% 191.21/191.74 [7064]~E(f773(f773(f8(x70641,a847),x70642),x70643),f80(a847))+~P1(f773(f63(x70641),x70643))+P1(f773(f773(f334(x70641),f404(x70642,x70643,x70641)),x70643))
% 191.21/191.74 [7065]~P1(f773(x70651,x70653))+P1(f773(f773(f232(a847),f340(x70651,x70652)),x70652))+~P1(f773(f773(f334(a847),x70653),f295(a847,f2(a847),x70652)))
% 191.21/191.74 [7103]~P9(x71031)+P1(f773(f773(f334(x71031),f673(x71033,x71032,x71031)),x71032))+P1(f773(f773(f232(x71031),f44(x71031,x71032)),x71033))
% 191.21/191.74 [7133]~E(f773(f773(f8(x71331,a847),x71332),x71333),f773(a114,f2(a847)))+~P1(f773(f63(x71331),x71333))+P1(f773(f773(f334(x71331),f406(x71332,x71333,x71331)),x71333))
% 191.21/191.74 [7144]E(x71441,f2(a847))+P1(f773(x71442,f52(a847,x71443,x71441)))+P1(f773(f773(f233(a847),f801(x71441,x71443,x71442)),x71441))
% 191.21/191.74 [7268]~P1(f773(x72681,x72682))+P1(f773(x72681,f52(a847,x72682,x72683)))+P1(f773(f773(f233(a847),f801(x72683,x72682,x72681)),x72683))
% 191.21/191.74 [7395]E(x73951,f115(x73952))+~P1(f773(f773(f334(f848(x73952)),x73951),f149(x73952,x73953)))+P1(f773(f773(f334(x73952),f748(x73953,x73951,x73952)),x73953))
% 191.21/191.74 [7415]~P100(x74151)+E(f773(f773(f103(f855(x74151,a841)),f773(f773(f302(x74151),x74152),f180(f855(x74151,a841)))),f298(x74151,x74152,x74153)),f773(f294(x74151,x74152),x74153))+~P1(f773(f773(f233(x74151),x74152),x74153))
% 191.21/191.74 [7440]~P100(x74401)+E(f773(f773(f103(f855(x74401,a841)),f773(f773(f302(x74401),x74402),f180(f855(x74401,a841)))),f297(x74401,x74402,x74403)),f295(x74401,x74402,x74403))+~P1(f773(f773(f232(x74401),x74402),x74403))
% 191.21/191.74 [7552]~P100(x75521)+P1(f773(f773(f233(x75521),x75522),x75523))+~P1(f773(f773(f233(f855(x75521,a841)),f773(f257(x75521),x75522)),f773(f257(x75521),x75523)))
% 191.21/191.74 [7553]~P99(x75531)+P1(f773(f773(f232(x75531),x75532),x75533))+~P1(f773(f773(f232(f855(x75531,a841)),f773(f258(x75531),x75533)),f773(f258(x75531),x75532)))
% 191.21/191.74 [7554]~P100(x75541)+P1(f773(f773(f232(x75541),x75542),x75543))+~P1(f773(f773(f232(f855(x75541,a841)),f773(f296(x75541),x75543)),f773(f296(x75541),x75542)))
% 191.21/191.74 [7555]~P99(x75551)+P1(f773(f773(f232(x75551),x75552),x75553))+~P1(f773(f773(f232(f855(x75551,a841)),f773(f293(x75551),x75552)),f773(f293(x75551),x75553)))
% 191.21/191.74 [7556]~P100(x75561)+P1(f773(f773(f232(x75561),x75562),x75563))+~P1(f773(f773(f232(f855(x75561,a841)),f773(f257(x75561),x75562)),f773(f257(x75561),x75563)))
% 191.21/191.74 [7580]~P77(x75801)+~P1(f773(f773(f233(x75801),f773(f773(f3(x75801),x75802),x75803)),f2(x75801)))+P1(f773(f773(f233(x75801),x75802),x75803))
% 191.21/191.74 [7581]~P77(x75811)+~P1(f773(f773(f232(x75811),f773(f773(f3(x75811),x75812),x75813)),f2(x75811)))+P1(f773(f773(f232(x75811),x75812),x75813))
% 191.21/191.74 [7741]E(x77411,f2(a847))+~E(f773(f132(a847,a847,f82(a847),x77412),x77413),f2(a847))+~P1(f773(f773(f334(a847),x77411),f773(f158(a847),x77413)))
% 191.21/191.74 [7745]~P9(x77451)+~P1(f773(f773(f232(x77451),f673(x77453,x77452,x77451)),x77453))+P1(f773(f773(f232(x77451),f44(x77451,x77452)),x77453))
% 191.21/191.74 [7896]P1(f773(f773(f232(a1),f2(a1)),f792(x78961,x78962,x78963)))+P1(f773(f773(x78962,f773(f773(f43(a1),x78961),x78963)),f52(a1,x78961,x78963)))+~P1(f773(f773(f233(a1),f2(a1)),x78963))
% 191.21/191.74 [7989]E(x79891,x79892)+~E(f773(f181(f848(x79893)),x79891),f773(f181(f848(x79893)),x79892))+~P1(f773(f773(f251(x79893,x79893,a841),a330),f713(x79893,x79891,x79892)))
% 191.21/191.74 [8055]~P36(x80552,x80553)+E(x80551,f180(f855(x80552,a841)))+~P1(f773(f773(f232(f855(x80552,a841)),x80551),f773(f277(x80552,x80552,x80553),x80551)))
% 191.21/191.74 [8083]~P63(x80831)+~P1(f773(f773(f232(x80831),x80832),f773(f773(f82(x80831),x80833),f806(x80833,x80832,x80831))))+P1(f773(f773(f232(x80831),x80832),x80833))
% 191.21/191.74 [8119]P47(x81191,x81192,x81193)+P1(f773(f773(f334(x81191),f506(x81193,x81192,x81191)),x81192))+P1(f773(f773(f334(f854(x81191,x81191)),f507(x81193,x81192,x81191)),x81193))
% 191.21/191.74 [8142]P1(f773(f773(x81422,f773(f773(f43(a1),x81421),x81423)),f52(a1,x81421,x81423)))+~P1(f773(f773(f233(a1),f2(a1)),x81423))+P1(f773(f773(f233(a1),f792(x81421,x81422,x81423)),x81423))
% 191.21/191.74 [8166]E(f773(f303(a847,a847,f773(f773(f9(a847,a847,a847),f3(a847)),x81661)),f773(f294(a847,x81662),x81663)),f180(f855(a847,a841)))+P1(f773(f773(f233(a847),x81661),x81663))+P1(f773(f773(f233(a847),x81662),x81663))
% 191.21/191.74 [8268]E(f773(f303(a847,a847,f773(f773(f9(a847,a847,a847),f3(a847)),x82681)),f773(f294(a847,x82682),x82683)),f773(f773(f302(a847),f2(a847)),f180(f855(a847,a841))))+P1(f773(f773(f233(a847),x82681),x82683))+~P1(f773(f773(f233(a847),x82682),x82683))
% 191.21/191.74 [8283]~P100(x82831)+E(f139(x82831,x82831,f7(x82831),x82832,x82833),x82833)+~P1(f773(f773(f334(x82831),x82832),f773(f158(x82831),x82833)))
% 191.21/191.74 [8298]P29(x82981,x82981,x82982,x82983)+~P1(f773(f63(x82981),x82983))+~P1(f773(f773(f232(f855(x82981,a841)),x82983),f773(f303(x82981,x82981,x82982),x82983)))
% 191.21/191.74 [8325]E(f773(f773(f82(a1),f773(f773(f83(a1),x83251),f793(x83252,x83253,x83251))),f792(x83252,x83253,x83251)),x83252)+P1(f773(f773(x83253,f773(f773(f43(a1),x83252),x83251)),f52(a1,x83252,x83251)))+~P1(f773(f773(f233(a1),f2(a1)),x83251))
% 191.21/191.74 [8557]~P1(f773(f773(x85571,f793(x85572,x85571,x85573)),f792(x85572,x85571,x85573)))+P1(f773(f773(x85571,f773(f773(f43(a1),x85572),x85573)),f52(a1,x85572,x85573)))+~P1(f773(f773(f233(a1),f2(a1)),x85573))
% 191.21/191.74 [9347]~P1(f773(f63(x93471),x93472))+~P1(f773(f773(f334(x93471),x93473),x93472))+P1(f773(f773(f233(a847),f773(f42(x93471),f773(f773(f3(f855(x93471,a841)),x93472),f773(f773(f302(x93471),x93473),f180(f855(x93471,a841)))))),f773(f42(x93471),x93472)))
% 191.21/191.74 [9923]P47(x99231,x99232,x99233)+~P1(f773(f773(f251(x99231,x99231,a841),f773(f773(f9(x99231,f855(x99231,a841),f855(x99231,a841)),f773(f773(f10(f855(a841,a841),f855(f855(x99231,a841),f855(x99231,a841)),x99231),f10(a841,a841,x99231)),f773(f773(f10(a841,f855(a841,a841),x99231),a331),f773(f773(f9(x99231,f855(x99231,a841),a841),f334(x99231)),x99232)))),f773(f773(f9(x99231,f855(x99231,a841),a841),f334(x99231)),x99232))),f507(x99233,x99232,x99231)))+P1(f773(f773(f334(x99231),f506(x99233,x99232,x99231)),x99232))
% 191.21/191.74 [5355]~P113(x53552)+E(x53551,f2(x53552))+E(f773(f773(f283(x53552),x53553),f773(f81(x53552),x53551)),f773(f81(x53552),f773(f773(f283(x53552),x53553),x53551)))
% 191.21/191.74 [5486]~E(x54863,f180(f855(x54861,a841)))+~E(x54862,f180(f855(x54861,a841)))+E(f773(f773(f103(f855(x54861,a841)),x54862),x54863),f180(f855(x54861,a841)))
% 191.21/191.74 [5540]~E(x55403,f2(a847))+~P1(f773(x55401,f2(a847)))+P1(f773(x55401,f773(f773(f43(a847),x55402),x55403)))
% 191.21/191.74 [5688]~P63(x56882)+E(x56881,f2(x56882))+E(f773(f773(f283(x56882),f773(f77(x56882),x56883)),f773(f77(x56882),x56881)),f773(f77(x56882),f773(f773(f283(x56882),x56883),x56881)))
% 191.21/191.74 [5783]~P85(x57831)+~E(x57832,f80(x57831))+P1(f773(f773(f279(x57831),x57832),f773(f773(f242(x57831),x57832),x57833)))
% 191.21/191.74 [5800]~P7(x58001)+E(f773(f773(f83(x58001),x58002),f773(f773(f43(x58001),x58003),x58002)),x58003)+~P1(f773(f773(f279(x58001),x58002),x58003))
% 191.21/191.74 [5854]~P1(f773(f63(x58541),x58543))+E(f773(f42(x58541),f773(f773(f302(x58541),x58542),x58543)),f773(a114,f773(f42(x58541),x58543)))+P1(f773(f773(f334(x58541),x58542),x58543))
% 191.21/191.74 [5930]~E(x59302,f2(a847))+P1(f773(x59301,f2(a847)))+~P1(f773(x59301,f773(f773(f43(a847),x59303),x59302)))
% 191.21/191.74 [5948]~P1(f773(f63(x59481),x59483))+E(f773(f42(x59481),f773(f773(f302(x59481),x59482),x59483)),f773(f42(x59481),x59483))+~P1(f773(f773(f334(x59481),x59482),x59483))
% 191.21/191.74 [5982]~P1(f773(f63(x59821),x59823))+E(f773(f42(x59821),f773(f773(f302(x59821),x59822),x59823)),f773(f773(f82(a847),f80(a847)),f773(f42(x59821),x59823)))+P1(f773(f773(f334(x59821),x59822),x59823))
% 191.21/191.74 [5989]~P8(x59891)+E(f773(f773(f43(x59891),x59892),f773(f81(x59891),x59893)),f773(f81(x59891),f773(f773(f43(x59891),x59892),x59893)))+~P1(f773(f773(f279(x59891),x59893),x59892))
% 191.21/191.74 [6104]E(f773(f773(f82(a847),x61041),f798(x61041,x61042,x61043)),x61042)+~P1(f773(x61043,f2(a847)))+P1(f773(x61043,f773(f773(f3(a847),x61042),x61041)))
% 191.21/191.74 [6105]E(f773(f773(f82(a847),x61051),f805(x61051,x61052,x61053)),x61052)+~P1(f773(x61053,f2(a847)))+P1(f773(x61053,f773(f773(f3(a847),x61052),x61051)))
% 191.21/191.74 [6129]~P8(x61291)+E(f773(f773(f43(x61291),f773(f81(x61291),x61292)),x61293),f773(f81(x61291),f773(f773(f43(x61291),x61292),x61293)))+~P1(f773(f773(f279(x61291),x61293),x61292))
% 191.21/191.74 [6152]~P9(x61521)+~P1(f773(f63(x61521),x61523))+E(f773(f773(f66(x61521,x61521,f103(x61521)),x61522),x61523),f773(f773(f103(x61521),x61522),f44(x61521,x61523)))
% 191.21/191.74 [6153]~P9(x61531)+~P1(f773(f63(x61531),x61533))+E(f773(f773(f66(x61531,x61531,f104(x61531)),x61532),x61533),f773(f773(f104(x61531),x61532),f45(x61531,x61533)))
% 191.21/191.74 [6159]~P88(x61591)+~E(f773(f106(x61591),x61592),f773(f106(x61591),x61593))+P33(x61591,f773(f106(x61591),f773(f773(f82(a1),x61592),f773(f81(a1),x61593))))
% 191.21/191.74 [6166]~P133(x61661)+E(f773(f773(f3(x61661),f773(f102(x61661),x61662)),f773(f102(x61661),x61663)),f773(f102(x61661),f773(f773(f3(a847),x61662),x61663)))+~P1(f773(f773(f232(a847),x61663),x61662))
% 191.21/191.74 [6172]~P104(x61721)+~P1(f773(f773(f279(x61721),x61722),x61723))+P1(f773(f773(f279(x61721),f773(f81(x61721),x61722)),x61723))
% 191.21/191.74 [6173]~P110(x61731)+~P1(f773(f773(f279(x61731),x61732),x61733))+P1(f773(f773(f279(x61731),f773(f77(x61731),x61732)),x61733))
% 191.21/191.74 [6258]E(f773(f773(f82(a847),x62581),f798(x62581,x62582,x62583)),x62582)+P1(f773(f773(f233(a847),x62582),x62581))+P1(f773(x62583,f773(f773(f3(a847),x62582),x62581)))
% 191.21/191.74 [6259]E(f773(f773(f82(a847),x62591),f805(x62591,x62592,x62593)),x62592)+P1(f773(f773(f233(a847),x62592),x62591))+P1(f773(x62593,f773(f773(f3(a847),x62592),x62591)))
% 191.21/191.74 [6277]~P110(x62771)+E(f773(f773(f83(x62771),f773(f77(x62771),x62772)),x62773),f773(f77(x62771),f773(f773(f83(x62771),x62772),x62773)))+~P1(f773(f773(f232(x62771),f2(x62771)),x62773))
% 191.21/191.74 [6278]~P62(x62781)+E(f773(f773(f283(x62781),f773(f77(x62781),x62782)),x62783),f773(f77(x62781),f773(f773(f283(x62781),x62782),x62783)))+~P1(f773(f773(f233(x62781),f2(x62781)),x62783))
% 191.21/191.74 [6287]~P93(x62871)+~P1(f773(f63(x62871),x62873))+E(f773(f773(f66(x62871,x62871,f103(x62871)),x62872),x62873),f15(x62871,f773(f773(f302(x62871),x62872),x62873)))
% 191.21/191.74 [6288]~P100(x62881)+~P1(f773(f63(x62881),x62883))+E(f773(f773(f66(x62881,x62881,f179(x62881)),x62882),x62883),f16(x62881,f773(f773(f302(x62881),x62882),x62883)))
% 191.21/191.74 [6289]~P100(x62891)+~P1(f773(f63(x62891),x62893))+E(f773(f773(f66(x62891,x62891,f236(x62891)),x62892),x62893),f17(x62891,f773(f773(f302(x62891),x62892),x62893)))
% 191.21/191.74 [6290]~P93(x62901)+~P1(f773(f63(x62901),x62903))+E(f773(f773(f66(x62901,x62901,f104(x62901)),x62902),x62903),f12(x62901,f773(f773(f302(x62901),x62902),x62903)))
% 191.21/191.74 [6334]E(x63341,f115(x63342))+~E(f164(x63342,x63343),f115(f848(x63342)))+~P1(f773(f773(f334(f848(x63342)),x63341),f773(f158(f848(x63342)),x63343)))
% 191.21/191.74 [6353]~P85(x63531)+~P1(f773(f773(f233(a847),f2(a847)),x63533))+P1(f773(f773(f279(x63531),x63532),f773(f773(f242(x63531),x63532),x63533)))
% 191.21/191.74 [6384]~P1(f773(f127(x63841),x63843))+P1(f773(f773(f334(x63841),x63842),f773(f158(x63841),x63843)))+P1(f773(f127(x63841),f773(f773(f140(x63841),x63842),x63843)))
% 191.21/191.74 [6396]~P91(x63961)+~P1(f773(f63(x63961),x63963))+E(f773(f65(x63961,f83(x63961)),f773(f773(f302(x63961),x63962),x63963)),f773(f773(f66(x63961,x63961,f83(x63961)),x63962),x63963))
% 191.21/191.74 [6417]~P100(x64171)+~P1(f773(f63(x64171),x64173))+E(f13(x64171,f179(x64171),f773(f773(f302(x64171),x64172),x64173)),f773(f773(f66(x64171,x64171,f179(x64171)),x64172),x64173))
% 191.21/191.74 [6418]~P100(x64181)+~P1(f773(f63(x64181),x64183))+E(f14(x64181,f236(x64181),f773(f773(f302(x64181),x64182),x64183)),f773(f773(f66(x64181,x64181,f236(x64181)),x64182),x64183))
% 191.21/191.74 [6420]P1(f773(x64201,f2(a847)))+~P1(f773(f773(f233(a847),x64202),x64203))+~P1(f773(x64201,f773(f773(f3(a847),x64202),x64203)))
% 191.21/191.74 [6439]~P110(x64391)+P1(f773(f773(f233(x64391),x64392),x64393))+~P1(f773(f773(f233(x64391),f773(f77(x64391),x64392)),x64393))
% 191.21/191.74 [6441]~P79(x64411)+P1(f773(f773(f232(x64411),x64412),x64413))+~P1(f773(f773(f232(x64411),f773(f77(x64411),x64412)),x64413))
% 191.21/191.74 [6442]~P110(x64421)+P1(f773(f773(f279(x64421),x64422),x64423))+~P1(f773(f773(f279(x64421),f773(f77(x64421),x64422)),x64423))
% 191.21/191.74 [6443]~P104(x64431)+P1(f773(f773(f279(x64431),x64432),x64433))+~P1(f773(f773(f279(x64431),f773(f81(x64431),x64432)),x64433))
% 191.21/191.74 [6462]E(x64621,f115(x64622))+E(f773(f131(x64622),f773(f773(f128(x64622),x64623),x64621)),f773(f773(f153(x64622),x64621),x64623))+~P1(f773(f773(f233(a847),x64623),f773(f181(f848(x64622)),x64621)))
% 191.21/191.74 [6516]~P1(f773(x65161,x65163))+P1(f773(x65161,f343(x65161,x65162)))+~P1(f773(f773(f334(a847),x65163),f773(f294(a847,f2(a847)),x65162)))
% 191.21/191.74 [6539]P1(f773(x65391,x65392))+~P1(f773(f773(f233(a847),x65392),x65393))+P1(f773(f773(f334(a847),f342(x65391,x65393)),f773(f294(a847,f2(a847)),x65393)))
% 191.21/191.74 [6554]~P117(x65541)+~P1(f773(f773(f233(x65541),f2(x65541)),x65542))+P1(f773(f773(f233(x65541),f2(x65541)),f773(f773(f242(x65541),x65542),x65543)))
% 191.21/191.74 [6556]~P117(x65561)+~P1(f773(f773(f232(x65561),f2(x65561)),x65562))+P1(f773(f773(f232(x65561),f2(x65561)),f773(f773(f242(x65561),x65562),x65563)))
% 191.21/191.74 [6557]~P117(x65571)+~P1(f773(f773(f232(x65571),f80(x65571)),x65572))+P1(f773(f773(f232(x65571),f80(x65571)),f773(f773(f242(x65571),x65572),x65573)))
% 191.21/191.74 [6582]~P1(f773(x65821,x65823))+~P1(f773(f773(f233(a847),x65823),x65822))+P1(f773(f773(f334(a847),f339(x65821,x65822)),f773(f294(a847,f2(a847)),x65822)))
% 191.21/191.74 [6587]P1(f773(f63(x65871),x65872))+~P1(f773(f63(x65871),x65873))+~P1(f773(f773(f232(f855(x65871,a841)),x65872),x65873))
% 191.21/191.74 [6596]~P1(f773(f773(f279(a847),x65961),x65962))+~P1(f773(f773(f279(a847),x65961),x65963))+P1(f773(f773(f279(a847),x65961),f773(f773(f3(a847),x65962),x65963)))
% 191.21/191.74 [6597]P1(f773(x65971,x65972))+~P1(f773(x65971,f344(x65971,x65973)))+~P1(f773(f773(f334(a847),x65972),f773(f294(a847,f2(a847)),x65973)))
% 191.21/191.74 [6610]E(x66101,f2(a847))+P1(f773(x66102,f790(x66101,x66103,x66102)))+~P1(f773(x66102,f773(f773(f43(a847),x66103),x66101)))
% 191.21/191.74 [6619]~P119(x66192)+E(x66191,f2(x66192))+~E(f773(f773(f82(x66192),f773(f773(f83(x66192),x66193),x66193)),f773(f773(f83(x66192),x66191),x66191)),f2(x66192))
% 191.21/191.74 [6620]~P119(x66202)+E(x66201,f2(x66202))+~E(f773(f773(f82(x66202),f773(f773(f83(x66202),x66201),x66201)),f773(f773(f83(x66202),x66203),x66203)),f2(x66202))
% 191.21/191.74 [6667]E(x66671,f2(a847))+~P1(f773(x66672,f800(x66671,x66673,x66672)))+P1(f773(x66672,f773(f773(f43(a847),x66673),x66671)))
% 191.21/191.74 [6672]~P100(x66721)+~P18(x66721,x66723)+P18(x66721,f773(f773(f138(x66721,x66721,f7(x66721)),x66722),x66723))
% 191.21/191.74 [6716]P1(f773(x67161,f790(x67162,x67163,x67161)))+P1(f773(x67161,f2(a847)))+~P1(f773(x67161,f773(f773(f43(a847),x67163),x67162)))
% 191.21/191.74 [6722]~P88(x67221)+E(f773(f106(x67221),x67222),f773(f106(x67221),x67223))+~P33(x67221,f773(f106(x67221),f773(f773(f82(a1),x67222),f773(f81(a1),x67223))))
% 191.21/191.74 [6795]E(x67951,f2(a1))+E(x67952,f2(a1))+~P1(f773(f56(x67952,x67952),f773(f773(f241(a1,a1),x67953),x67951)))
% 191.21/191.74 [6796]E(x67961,f80(a1))+E(x67962,f2(a1))+~P1(f773(f56(x67962,x67962),f773(f773(f241(a1,a1),x67961),x67963)))
% 191.21/191.74 [6810]P1(f773(x68101,x68102))+P1(f773(f773(f233(a847),f344(x68101,x68103)),x68103))+~P1(f773(f773(f334(a847),x68102),f773(f294(a847,f2(a847)),x68103)))
% 191.21/191.74 [6835]~P1(f773(x68351,f800(x68353,x68352,x68351)))+~P1(f773(x68351,f2(a847)))+P1(f773(x68351,f773(f773(f43(a847),x68352),x68353)))
% 191.21/191.74 [6836]~P1(f773(x68361,f798(x68363,x68362,x68361)))+~P1(f773(x68361,f2(a847)))+P1(f773(x68361,f773(f773(f3(a847),x68362),x68363)))
% 191.21/191.74 [6837]~P1(f773(x68371,f805(x68373,x68372,x68371)))+~P1(f773(x68371,f2(a847)))+P1(f773(x68371,f773(f773(f3(a847),x68372),x68373)))
% 191.21/191.74 [6857]~P1(f773(x68571,x68573))+P1(f773(f773(f233(a847),f343(x68571,x68572)),x68572))+~P1(f773(f773(f334(a847),x68573),f773(f294(a847,f2(a847)),x68572)))
% 191.21/191.74 [6858]E(f773(f773(f3(a847),f773(f773(f3(a847),x68581),x68582)),f773(f773(f3(a847),x68583),x68582)),f773(f773(f3(a847),x68581),x68583))+~P1(f773(f773(f232(a847),x68582),x68581))+~P1(f773(f773(f232(a847),x68582),x68583))
% 191.21/191.74 [6892]~P77(x68921)+~P1(f773(f773(f233(x68921),f773(f81(x68921),x68923)),x68922))+P1(f773(f773(f233(x68921),f773(f81(x68921),x68922)),x68923))
% 191.21/191.74 [6893]~P110(x68931)+~P1(f773(f773(f233(x68931),f773(f77(x68931),x68932)),x68933))+P1(f773(f773(f233(x68931),f773(f81(x68931),x68932)),x68933))
% 191.21/191.74 [6895]~P77(x68951)+~P1(f773(f773(f232(x68951),f773(f81(x68951),x68953)),x68952))+P1(f773(f773(f232(x68951),f773(f81(x68951),x68952)),x68953))
% 191.21/191.74 [6897]~P79(x68971)+~P1(f773(f773(f232(x68971),f773(f77(x68971),x68972)),x68973))+P1(f773(f773(f232(x68971),f773(f81(x68971),x68972)),x68973))
% 191.21/191.74 [6900]~P1(f773(f773(f279(a1),x69001),x69003))+P1(f773(f773(f279(a1),x69001),x69002))+~P1(f773(f773(f279(a1),x69001),f773(f773(f3(a1),x69002),x69003)))
% 191.21/191.74 [6933]~P1(f773(x69333,f798(x69332,x69331,x69333)))+P1(f773(f773(f233(a847),x69331),x69332))+P1(f773(x69333,f773(f773(f3(a847),x69331),x69332)))
% 191.21/191.74 [6934]~P1(f773(x69343,f805(x69342,x69341,x69343)))+P1(f773(f773(f233(a847),x69341),x69342))+P1(f773(x69343,f773(f773(f3(a847),x69341),x69342)))
% 191.21/191.74 [6980]~E(f684(x69803,x69802,x69801),f679(x69803,x69802,x69801))+E(f773(f773(f104(f855(x69801,a841)),x69802),f44(f855(x69801,a841),x69803)),f180(f855(x69801,a841)))+P1(f773(f773(f334(f855(x69801,a841)),x69802),x69803))
% 191.21/191.74 [6989]~P1(f773(f63(x69891),x69893))+P1(f773(f63(x69891),f45(f855(x69891,a841),x69892)))+~P1(f773(f773(f334(f855(x69891,a841)),x69893),x69892))
% 191.21/191.74 [7050]~P100(x70501)+E(f773(f773(f103(f855(x70501,a841)),f773(f294(x70501,x70502),x70503)),f773(f773(f302(x70501),x70503),f180(f855(x70501,a841)))),f295(x70501,x70502,x70503))+~P1(f773(f773(f232(x70501),x70502),x70503))
% 191.21/191.74 [7053]E(x70531,f2(a847))+P1(f773(f773(f233(a847),f802(x70531,x70533,x70532)),x70531))+P1(f773(x70532,f773(f773(f43(a847),x70533),x70531)))
% 191.21/191.74 [7088]E(x70881,x70882)+~P1(f773(f773(f232(f855(x70883,a841)),x70881),x70882))+P1(f773(f773(f233(f855(x70883,a841)),x70881),x70882))
% 191.21/191.74 [7100]E(x71001,x71002)+~E(f773(f181(f848(x71003)),x71001),f773(f181(f848(x71003)),x71002))+P1(f773(f773(f233(a847),f730(x71003,x71001,x71002)),f773(f181(f848(x71003)),x71002)))
% 191.21/191.74 [7145]P12(x71451,x71452,x71453)+~E(f773(f261(x71451,x71451),x71453),x71452)+~E(f773(f773(f281(x71451,x71451,x71451),f773(f278(x71451,x71451),x71453)),x71453),x71453)
% 191.21/191.74 [7227]E(x72271,f2(a1))+~P1(f773(f773(f279(a1),x72272),x72273))+P1(f773(f773(f279(a1),f773(f773(f83(a1),x72271),x72272)),f773(f773(f83(a1),x72271),x72273)))
% 191.21/191.74 [7230]~P1(f773(x72301,f2(a847)))+P1(f773(f773(f233(a847),f802(x72303,x72302,x72301)),x72303))+P1(f773(x72301,f773(f773(f43(a847),x72302),x72303)))
% 191.21/191.74 [7243]~P100(x72431)+E(f773(f773(f103(f855(x72431,a841)),f298(x72431,x72432,x72433)),f773(f773(f302(x72431),x72433),f180(f855(x72431,a841)))),f297(x72431,x72432,x72433))+~P1(f773(f773(f233(x72431),x72432),x72433))
% 191.21/191.74 [7348]~P1(f773(f63(x73481),x73483))+P1(f773(f773(f233(a847),f773(f42(x73481),x73482)),f773(f42(x73481),x73483)))+~P1(f773(f773(f233(f855(x73481,a841)),x73482),x73483))
% 191.21/191.74 [7349]~P1(f773(f63(x73491),x73493))+P1(f773(f773(f232(a847),f773(f42(x73491),x73492)),f773(f42(x73491),x73493)))+~P1(f773(f773(f232(f855(x73491,a841)),x73492),x73493))
% 191.21/191.74 [7390]~P1(f773(x73903,x73902))+P1(f773(f773(f187(x73901),x73902),f415(x73902,x73901,x73903)))+~P1(f773(f773(f187(f35(x73903,x73901)),x73902),x73902))
% 191.21/191.74 [7488]E(x74881,x74882)+~P1(f773(f773(f232(f855(x74883,a841)),x74882),x74881))+~P1(f773(f773(f232(f855(x74883,a841)),x74881),x74882))
% 191.21/191.74 [7491]~P100(x74911)+P18(x74911,x74912)+~P18(x74911,f773(f773(f138(x74911,x74911,f7(x74911)),x74913),x74912))
% 191.21/191.74 [7560]~P1(f773(f773(f233(a847),x75603),x75602))+~P1(f773(f773(f233(a847),x75603),x75601))+P1(f773(f773(f233(a847),f773(f773(f3(a847),x75601),x75602)),f773(f773(f3(a847),x75601),x75603)))
% 191.21/191.74 [7561]~P1(f773(f773(f233(a847),x75611),x75613))+~P1(f773(f773(f232(a847),x75612),x75611))+P1(f773(f773(f233(a847),f773(f773(f3(a847),x75611),x75612)),f773(f773(f3(a847),x75613),x75612)))
% 191.21/191.74 [7578]~P1(f773(f773(f233(a1),x75782),f2(a1)))+~P1(f773(f773(f232(a1),x75783),x75781))+P1(f773(f773(f232(a1),f773(f773(f43(a1),x75781),x75782)),f773(f773(f43(a1),x75783),x75782)))
% 191.21/191.74 [7598]~P1(f773(f773(f233(a847),f2(a847)),x75982))+~P1(f773(f773(f233(a847),x75981),x75983))+P1(f773(f773(f233(a847),f773(f773(f83(a847),x75981),x75982)),f773(f773(f83(a847),x75983),x75982)))
% 191.21/191.74 [7599]~P1(f773(f773(f233(a847),f2(a847)),x75991))+~P1(f773(f773(f233(a847),x75992),x75993))+P1(f773(f773(f233(a847),f773(f773(f83(a847),x75991),x75992)),f773(f773(f83(a847),x75991),x75993)))
% 191.21/191.74 [7600]~P1(f773(f773(f233(a1),f2(a1)),x76001))+~P1(f773(f773(f233(a1),x76002),x76003))+P1(f773(f773(f233(a1),f773(f773(f83(a1),x76001),x76002)),f773(f773(f83(a1),x76001),x76003)))
% 191.21/191.74 [7602]~P1(f773(f773(f233(a847),f2(a847)),x76023))+~P1(f773(f773(f232(a847),x76023),x76022))+P1(f773(f773(f232(a847),f773(f773(f43(a847),x76021),x76022)),f773(f773(f43(a847),x76021),x76023)))
% 191.21/191.74 [7603]~P1(f773(f773(f233(a1),f2(a1)),x76032))+~P1(f773(f773(f232(a1),x76031),x76033))+P1(f773(f773(f232(a1),f773(f773(f43(a1),x76031),x76032)),f773(f773(f43(a1),x76033),x76032)))
% 191.21/191.74 [7652]E(x76521,f2(a847))+E(f773(f773(f82(a847),f773(f773(f83(a847),x76521),f800(x76521,x76522,x76523))),f802(x76521,x76522,x76523)),x76522)+P1(f773(x76523,f773(f773(f43(a847),x76522),x76521)))
% 191.21/191.74 [7710]E(f773(f773(f82(a847),f773(f773(f83(a847),x77101),f800(x77101,x77102,x77103))),f802(x77101,x77102,x77103)),x77102)+~P1(f773(x77103,f2(a847)))+P1(f773(x77103,f773(f773(f43(a847),x77102),x77101)))
% 191.21/191.74 [7726]~P1(f773(f63(x77261),x77263))+P1(f773(f773(f334(x77261),f460(x77262,x77263,x77261)),x77263))+P1(f773(f773(f233(a847),f2(a847)),f773(f773(f11(x77261,a847),x77262),x77263)))
% 191.21/191.74 [7727]~P1(f773(f63(x77271),x77273))+P1(f773(f773(f334(x77271),f572(x77272,x77273,x77271)),x77273))+P1(f773(f773(f233(a847),f2(a847)),f773(f773(f11(x77271,a847),x77272),x77273)))
% 191.21/191.74 [7832]E(x78321,f2(a847))+P1(f773(f773(f279(a847),x78322),x78323))+~P1(f773(f773(f279(a847),f773(f773(f83(a847),x78321),x78322)),f773(f773(f83(a847),x78321),x78323)))
% 191.21/191.74 [7834]E(x78341,f2(a1))+P1(f773(f773(f279(a1),x78342),x78343))+~P1(f773(f773(f279(a1),f773(f773(f83(a1),x78341),x78342)),f773(f773(f83(a1),x78341),x78343)))
% 191.21/191.74 [8020]E(x80201,f180(f855(x80202,a841)))+E(x80201,f773(f773(f302(x80202),x80203),f180(f855(x80202,a841))))+~P1(f773(f773(f232(f855(x80202,a841)),x80201),f773(f773(f302(x80202),x80203),f180(f855(x80202,a841)))))
% 191.21/191.74 [8057]~P1(f773(f773(f233(a847),f2(a847)),x80573))+P1(f773(f773(f233(a847),x80571),x80572))+~P1(f773(f773(f233(a847),f773(f773(f242(a847),x80573),x80571)),f773(f773(f242(a847),x80573),x80572)))
% 191.21/191.74 [8059]~P1(f773(f773(f233(a847),f2(a847)),x80593))+P1(f773(f773(f232(a847),x80591),x80592))+~P1(f773(f773(f232(a847),f773(f773(f83(a847),x80593),x80591)),f773(f773(f83(a847),x80593),x80592)))
% 191.21/191.74 [8060]~P1(f773(f773(f233(a847),f80(a847)),x80603))+P1(f773(f773(f232(a847),x80601),x80602))+~P1(f773(f773(f279(a847),f773(f773(f242(a847),x80603),x80601)),f773(f773(f242(a847),x80603),x80602)))
% 191.21/191.74 [8061]~P1(f773(f773(f233(a847),f2(a847)),x80613))+P1(f773(f773(f232(a847),x80611),x80612))+~P1(f773(f773(f232(a847),f773(f773(f83(a847),x80611),x80613)),f773(f773(f83(a847),x80612),x80613)))
% 191.21/191.74 [8063]~P1(f773(f773(f233(a847),f2(a847)),x80633))+P1(f773(f773(f279(a847),x80631),x80632))+~P1(f773(f773(f279(a847),f773(f773(f83(a847),x80633),x80631)),f773(f773(f83(a847),x80633),x80632)))
% 191.21/191.74 [8091]~P1(f773(x80911,x80913))+P1(f773(f773(f187(f35(x80911,x80912)),f415(x80913,x80912,x80911)),x80913))+~P1(f773(f773(f187(f35(x80911,x80912)),x80913),x80913))
% 191.21/191.74 [8099]~E(f773(f773(f104(f855(x80991,a841)),f679(x80993,x80992,x80991)),f684(x80993,x80992,x80991)),f180(f855(x80991,a841)))+E(f773(f773(f104(f855(x80991,a841)),x80992),f44(f855(x80991,a841),x80993)),f180(f855(x80991,a841)))+P1(f773(f773(f334(f855(x80991,a841)),x80992),x80993))
% 191.21/191.74 [8114]E(x81141,f115(x81142))+~E(f773(f132(f848(x81142),f848(x81142),f125(x81142),f115(x81142)),x81143),f115(x81142))+~P1(f773(f773(f334(f848(x81142)),x81141),f773(f158(f848(x81142)),x81143)))
% 191.21/191.74 [8171]E(x81711,f180(f855(f855(x81712,a841),a841)))+P1(f773(f773(f334(f855(x81712,a841)),f686(x81713,x81711,x81712)),x81711))+P1(f773(f773(f232(f855(x81712,a841)),f45(f855(x81712,a841),x81711)),x81713))
% 191.21/191.74 [8177]~P66(x81771)+~P70(x81771)+E(f773(f773(f8(a1,x81771),f773(f773(f10(a847,x81771,a1),x81772),a107)),f773(f303(a847,a1,f102(a1)),x81773)),f773(f773(f8(a847,x81771),x81772),x81773))
% 191.21/191.74 [8178]~P66(x81781)+~P70(x81781)+E(f773(f773(f11(a1,x81781),f773(f773(f10(a847,x81781,a1),x81782),a107)),f773(f303(a847,a1,f102(a1)),x81783)),f773(f773(f11(a847,x81781),x81782),x81783))
% 191.21/191.74 [8215]~P1(f773(f63(x82151),x82153))+~P1(f773(f773(f233(a847),f2(a847)),f773(x82152,f460(x82152,x82153,x82151))))+P1(f773(f773(f233(a847),f2(a847)),f773(f773(f11(x82151,a847),x82152),x82153)))
% 191.21/191.74 [8216]~P1(f773(f63(x82161),x82163))+~P1(f773(f773(f233(a847),f2(a847)),f773(x82162,f572(x82162,x82163,x82161))))+P1(f773(f773(f233(a847),f2(a847)),f773(f773(f11(x82161,a847),x82162),x82163)))
% 191.21/191.74 [8251]~P61(x82512)+E(x82511,f80(x82512))+E(f773(f773(f283(x82512),f773(f773(f3(x82512),f773(f773(f242(x82512),x82511),x82513)),f80(x82512))),f773(f773(f3(x82512),x82511),f80(x82512))),f773(f773(f8(a847,x82512),f773(f242(x82512),x82511)),f773(f294(a847,f2(a847)),x82513)))
% 191.21/191.74 [8310]E(x83101,f2(a847))+~P1(f773(x83103,f773(f773(f43(a847),x83102),x83101)))+P1(f773(f773(f233(a847),x83102),f773(f773(f83(a847),x83101),f773(a114,f790(x83101,x83102,x83103)))))
% 191.21/191.74 [8331]P1(f773(x83311,f2(a847)))+~P1(f773(x83311,f773(f773(f43(a847),x83312),x83313)))+P1(f773(f773(f233(a847),x83312),f773(f773(f83(a847),x83313),f773(a114,f790(x83313,x83312,x83311)))))
% 191.21/191.74 [8370]E(x83701,f2(a847))+~P1(f773(x83703,f773(f773(f43(a847),x83702),x83701)))+P1(f773(f773(f232(a847),f773(f773(f83(a847),x83701),f790(x83701,x83702,x83703))),x83702))
% 191.21/191.74 [8407]P1(f773(x84071,f2(a847)))+~P1(f773(x84071,f773(f773(f43(a847),x84073),x84072)))+P1(f773(f773(f232(a847),f773(f773(f83(a847),x84072),f790(x84072,x84073,x84071))),x84073))
% 191.21/191.74 [8410]~P100(x84101)+E(f773(f773(f138(x84101,x84101,f7(x84101)),x84102),x84103),f139(x84101,x84101,f7(x84101),x84102,x84103))+P1(f773(f773(f334(x84101),x84102),f773(f158(x84101),x84103)))
% 191.21/191.74 [8450]~E(f773(x84503,f609(x84502,x84503,x84501)),f773(x84503,f611(x84502,x84503,x84501)))+~P58(x84501,f773(x84503,f610(x84502,x84503,x84501)))+P58(x84501,f773(f773(f46(x84502,f855(x84501,f855(x84501,a841))),f239(f855(x84502,a841))),x84503))
% 191.21/191.74 [8458]E(x84581,f180(f855(f855(x84582,a841),a841)))+~P1(f773(f773(f232(f855(x84582,a841)),f686(x84583,x84581,x84582)),x84583))+P1(f773(f773(f232(f855(x84582,a841)),f45(f855(x84582,a841),x84581)),x84583))
% 191.21/191.74 [8517]~P63(x85171)+~P1(f773(f773(f233(x85171),x85172),x85173))+P1(f773(f773(f233(x85171),x85172),f773(f773(f283(x85171),f773(f773(f82(x85171),x85172),x85173)),f773(f773(f82(x85171),f80(x85171)),f80(x85171)))))
% 191.21/191.74 [8560]~P1(f773(f773(x85601,f822(x85601,x85603,x85602)),f823(x85601,x85603,x85602)))+P1(f773(f773(x85601,x85602),x85603))+~P1(f773(f321(f854(a1,a1),a59),f773(f773(f241(a1,a1),x85602),x85603)))
% 191.21/191.74 [8561]~P1(f773(f773(x85611,f824(x85611,x85613,x85612)),f825(x85611,x85613,x85612)))+P1(f773(f773(x85611,x85612),x85613))+~P1(f773(f321(f854(a1,a1),a62),f773(f773(f241(a1,a1),x85612),x85613)))
% 191.21/191.74 [8562]~P1(f773(f773(x85621,f826(x85621,x85623,x85622)),f829(x85621,x85623,x85622)))+P1(f773(f773(x85621,x85622),x85623))+~P1(f773(f321(f854(a1,a1),a216),f773(f773(f241(a1,a1),x85622),x85623)))
% 191.21/191.74 [8563]~P1(f773(f773(x85631,f830(x85631,x85633,x85632)),f832(x85631,x85633,x85632)))+P1(f773(f773(x85631,x85632),x85633))+~P1(f773(f321(f854(a847,a847),a214),f773(f773(f241(a847,a847),x85632),x85633)))
% 191.21/191.74 [8564]~P1(f773(f773(x85641,f394(x85641,x85643,x85642)),f395(x85641,x85643,x85642)))+P1(f773(f773(x85641,x85642),x85643))+~P1(f773(f321(f854(a1,a1),a168),f773(f773(f241(a1,a1),x85642),x85643)))
% 191.21/191.74 [8798]P1(f773(f773(x87981,x87982),x87983))+P1(f773(f321(f854(a847,a847),a214),f773(f773(f241(a847,a847),f830(x87981,x87983,x87982)),f832(x87981,x87983,x87982))))+~P1(f773(f321(f854(a847,a847),a214),f773(f773(f241(a847,a847),x87982),x87983)))
% 191.21/191.74 [8799]P1(f773(f773(x87991,x87992),x87993))+P1(f773(f321(f854(a1,a1),a59),f773(f773(f241(a1,a1),f822(x87991,x87993,x87992)),f823(x87991,x87993,x87992))))+~P1(f773(f321(f854(a1,a1),a59),f773(f773(f241(a1,a1),x87992),x87993)))
% 191.21/191.74 [8800]P1(f773(f773(x88001,x88002),x88003))+P1(f773(f321(f854(a1,a1),a62),f773(f773(f241(a1,a1),f824(x88001,x88003,x88002)),f825(x88001,x88003,x88002))))+~P1(f773(f321(f854(a1,a1),a62),f773(f773(f241(a1,a1),x88002),x88003)))
% 191.21/191.74 [8801]P1(f773(f773(x88011,x88012),x88013))+P1(f773(f321(f854(a1,a1),a216),f773(f773(f241(a1,a1),f826(x88011,x88013,x88012)),f829(x88011,x88013,x88012))))+~P1(f773(f321(f854(a1,a1),a216),f773(f773(f241(a1,a1),x88012),x88013)))
% 191.21/191.74 [8802]P1(f773(f773(x88021,x88022),x88023))+P1(f773(f321(f854(a1,a1),a168),f773(f773(f241(a1,a1),f394(x88021,x88023,x88022)),f395(x88021,x88023,x88022))))+~P1(f773(f321(f854(a1,a1),a168),f773(f773(f241(a1,a1),x88022),x88023)))
% 191.21/191.74 [9114]~P1(f773(f63(x91141),x91143))+P1(f773(f773(f334(f854(f855(x91141,a841),f855(x91141,a841))),f773(f773(f241(f855(x91141,a841),f855(x91141,a841)),x91142),x91143)),f299(x91141)))+~P1(f773(f773(f233(f855(x91141,a841)),x91142),x91143))
% 191.21/191.74 [9167]~P58(x91671,f773(x91673,f610(x91672,x91673,x91671)))+P58(x91671,f773(f773(f46(x91672,f855(x91671,f855(x91671,a841))),f239(f855(x91672,a841))),x91673))+~E(f773(f773(f104(f855(x91671,a841)),f246(x91671,x91671,f773(x91673,f609(x91672,x91673,x91671)))),f247(x91671,x91671,f773(x91673,f611(x91672,x91673,x91671)))),f180(f855(x91671,a841)))
% 191.21/191.74 [9360]P47(x93601,x93602,x93603)+P1(f773(f773(f334(f854(x93601,x93601)),f507(x93603,x93602,x93601)),x93603))+~P1(f773(f773(f334(f854(x93601,x93601)),f773(f773(f241(x93601,x93601),f506(x93603,x93602,x93601)),f506(x93603,x93602,x93601))),x93603))
% 191.21/191.74 [9925]P47(x99251,x99252,x99253)+~P1(f773(f773(f251(x99251,x99251,a841),f773(f773(f9(x99251,f855(x99251,a841),f855(x99251,a841)),f773(f773(f10(f855(a841,a841),f855(f855(x99251,a841),f855(x99251,a841)),x99251),f10(a841,a841,x99251)),f773(f773(f10(a841,f855(a841,a841),x99251),a331),f773(f773(f9(x99251,f855(x99251,a841),a841),f334(x99251)),x99252)))),f773(f773(f9(x99251,f855(x99251,a841),a841),f334(x99251)),x99252))),f507(x99253,x99252,x99251)))+~P1(f773(f773(f334(f854(x99251,x99251)),f773(f773(f241(x99251,x99251),f506(x99253,x99252,x99251)),f506(x99253,x99252,x99251))),x99253))
% 191.21/191.74 [5523]~P7(x55232)+E(x55231,f2(x55232))+E(f773(f773(f43(x55232),f773(f773(f83(x55232),x55233),x55231)),x55231),x55233)
% 191.21/191.74 [5524]~P7(x55242)+E(x55241,f2(x55242))+E(f773(f773(f43(x55242),f773(f773(f83(x55242),x55241),x55243)),x55241),x55243)
% 191.21/191.74 [6167]~P7(x61671)+E(f773(f773(f83(x61671),f773(f773(f43(x61671),x61672),x61673)),x61673),x61672)+~P1(f773(f773(f279(x61671),x61673),x61672))
% 191.21/191.74 [6333]~P66(x63331)+~E(f773(x63332,f2(a847)),f2(x63331))+E(f773(f773(f8(a847,x63331),x63332),f773(f294(a847,f773(a114,f2(a847))),x63333)),f773(f773(f8(a847,x63331),x63332),f773(f294(a847,f2(a847)),x63333)))
% 191.21/191.74 [6476]~P7(x64762)+E(x64761,f2(x64762))+E(f773(f773(f43(x64762),f773(f773(f82(x64762),x64763),x64761)),x64761),f773(f773(f82(x64762),f773(f773(f43(x64762),x64763),x64761)),f80(x64762)))
% 191.21/191.74 [6477]~P7(x64772)+E(x64771,f2(x64772))+E(f773(f773(f43(x64772),f773(f773(f82(x64772),x64771),x64773)),x64771),f773(f773(f82(x64772),f773(f773(f43(x64772),x64773),x64771)),f80(x64772)))
% 191.21/191.74 [6706]~P1(f773(x67063,f2(a1)))+P1(f773(f773(f232(a847),x67061),x67062))+P1(f773(x67063,f773(f102(a1),f773(f773(f3(a847),x67062),x67061))))
% 191.21/191.74 [6817]P1(f773(f773(f232(a847),x68172),x68171))+P1(f773(f773(f233(a847),x68171),x68172))+P1(f773(x68173,f773(f102(a1),f773(f773(f3(a847),x68171),x68172))))
% 191.21/191.74 [6890]E(f773(f773(f82(a847),f773(f106(a847),x68901)),f773(f773(f82(a847),f773(f106(a847),x68902)),x68903)),f773(f773(f82(a847),f773(f106(a847),x68901)),x68903))+P1(f773(a186,f773(f106(a1),x68901)))+~P1(f773(a186,f773(f106(a1),x68902)))
% 191.21/191.74 [6968]~E(x69682,f773(f773(f43(a847),x69683),x69681))+~P1(f773(f773(f233(a847),f2(a847)),x69681))+P1(f773(f773(f232(a847),f773(f773(f83(a847),x69681),x69682)),x69683))
% 191.21/191.74 [7086]~P1(f773(f63(x70861),x70863))+~P1(f773(f63(x70861),x70862))+P1(f773(f63(x70861),f773(f773(f103(f855(x70861,a841)),x70862),x70863)))
% 191.21/191.74 [7401]~P100(x74011)+~P1(f773(f63(x74011),x74012))+E(f130(x74011,f773(f773(f3(f855(x74011,a841)),x74012),f773(f773(f302(x74011),x74013),f180(f855(x74011,a841))))),f151(x74011,x74013,f130(x74011,x74012)))
% 191.21/191.74 [7467]P1(f773(x74671,f2(a1)))+~P1(f773(f773(f233(a847),x74672),x74673))+~P1(f773(x74671,f773(f102(a1),f773(f773(f3(a847),x74672),x74673))))
% 191.21/191.74 [7485]~P1(f773(f63(x74851),x74852))+E(f773(f42(x74851),f773(f773(f3(f855(x74851,a841)),x74852),f773(f773(f302(x74851),x74853),f180(f855(x74851,a841))))),f773(f42(x74851),x74852))+P1(f773(f773(f334(x74851),x74853),x74852))
% 191.21/191.74 [7619]~P117(x76191)+~P1(f773(f773(f233(x76191),f80(x76191)),x76192))+P1(f773(f773(f233(x76191),f80(x76191)),f773(f773(f83(x76191),x76192),f773(f773(f242(x76191),x76192),x76193))))
% 191.21/191.74 [7663]~P1(f773(f63(x76631),x76633))+E(f773(f773(f3(a847),f773(f42(x76631),x76632)),f773(f42(x76631),x76633)),f773(f42(x76631),f773(f773(f3(f855(x76631,a841)),x76632),x76633)))+~P1(f773(f773(f232(f855(x76631,a841)),x76633),x76632))
% 191.21/191.74 [7718]~P1(f773(f773(f232(a847),x77182),x77183))+~P1(f773(f773(f232(a847),x77181),f773(f773(f3(a847),x77183),x77182)))+P1(f773(f773(f232(a847),f773(f773(f82(a847),x77181),x77182)),x77183))
% 191.21/191.74 [7775]P1(f773(f63(x77751),x77752))+~P1(f773(f63(x77751),x77753))+~P1(f773(f63(x77751),f773(f773(f3(f855(x77751,a841)),x77752),x77753)))
% 191.21/191.74 [7782]~P1(f773(f63(x77821),x77822))+E(f773(f42(x77821),f773(f773(f3(f855(x77821,a841)),x77822),f773(f773(f302(x77821),x77823),f180(f855(x77821,a841))))),f773(f773(f3(a847),f773(f42(x77821),x77822)),f80(a847)))+~P1(f773(f773(f334(x77821),x77823),x77822))
% 191.21/191.74 [7857]P58(x78571,x78572)+~P58(x78571,x78573)+~P1(f773(f773(f232(f855(x78571,f855(x78571,a841))),x78572),x78573))
% 191.21/191.74 [7895]~P1(f773(f773(f232(a847),x78953),x78952))+P1(f773(f773(f232(a847),x78951),f773(f773(f3(a847),x78952),x78953)))+~P1(f773(f773(f232(a847),f773(f773(f82(a847),x78951),x78953)),x78952))
% 191.21/191.74 [7915]P36(x79151,x79152)+~P36(x79151,x79153)+~P1(f773(f773(f232(f855(f854(x79151,x79151),a841)),x79152),x79153))
% 191.21/191.74 [7916]P56(x79161,x79162)+~P56(x79161,x79163)+~P1(f773(f773(f232(f855(f854(x79161,x79161),a841)),x79162),x79163))
% 191.21/191.74 [8149]~P117(x81491)+~P1(f773(f773(f233(x81491),f80(x81491)),x81492))+P1(f773(f773(f233(x81491),f773(f773(f242(x81491),x81492),x81493)),f773(f773(f83(x81491),x81492),f773(f773(f242(x81491),x81492),x81493))))
% 191.21/191.74 [8235]~P1(f773(x82351,f2(a1)))+~P1(f773(x82351,f773(f773(f3(a1),f773(f102(a1),x82352)),f773(f102(a1),x82353))))+P1(f773(x82351,f773(f102(a1),f773(f773(f3(a847),x82352),x82353))))
% 191.21/191.74 [8248]~P1(f773(f773(f232(a847),x82483),x82482))+P1(f773(x82481,f773(f773(f3(a1),f773(f102(a1),x82482)),f773(f102(a1),x82483))))+~P1(f773(x82481,f773(f102(a1),f773(f773(f3(a847),x82482),x82483))))
% 191.21/191.74 [8265]P1(f773(f773(f233(a847),x82651),x82652))+~P1(f773(x82653,f773(f773(f3(a1),f773(f102(a1),x82651)),f773(f102(a1),x82652))))+P1(f773(x82653,f773(f102(a1),f773(f773(f3(a847),x82651),x82652))))
% 191.21/191.74 [8322]~P119(x83222)+E(x83221,f2(x83222))+P1(f773(f773(f233(x83222),f2(x83222)),f773(f773(f82(x83222),f773(f773(f83(x83222),x83223),x83223)),f773(f773(f83(x83222),x83221),x83221))))
% 191.21/191.74 [8323]~P119(x83232)+E(x83231,f2(x83232))+P1(f773(f773(f233(x83232),f2(x83232)),f773(f773(f82(x83232),f773(f773(f83(x83232),x83231),x83231)),f773(f773(f83(x83232),x83233),x83233))))
% 191.21/191.74 [8429]~P1(f773(f773(f233(a847),f2(a847)),x84291))+~P1(f773(f773(f233(a1),x84292),x84293))+P1(f773(f773(f233(a1),f773(f773(f83(a1),f773(f102(a1),x84291)),x84292)),f773(f773(f83(a1),f773(f102(a1),x84291)),x84293)))
% 191.21/191.74 [8489]E(f773(f773(f104(f855(x84891,a841)),x84892),f44(f855(x84891,a841),x84893)),f180(f855(x84891,a841)))+P1(f773(f773(f334(f855(x84891,a841)),x84892),x84893))+P1(f773(f773(f334(f855(x84891,a841)),f679(x84893,x84892,x84891)),f773(f773(f302(f855(x84891,a841)),x84892),x84893)))
% 191.21/191.74 [8490]E(f773(f773(f104(f855(x84901,a841)),x84902),f44(f855(x84901,a841),x84903)),f180(f855(x84901,a841)))+P1(f773(f773(f334(f855(x84901,a841)),x84902),x84903))+P1(f773(f773(f334(f855(x84901,a841)),f684(x84903,x84902,x84901)),f773(f773(f302(f855(x84901,a841)),x84902),x84903)))
% 191.21/191.75 [8516]E(x85161,x85162)+~E(f773(f181(f848(x85163)),x85161),f773(f181(f848(x85163)),x85162))+P1(f773(f773(f334(f854(x85163,x85163)),f713(x85163,x85161,x85162)),f773(f158(f854(x85163,x85163)),f773(f773(f167(x85163,x85163),x85162),x85161))))
% 191.21/191.75 [8726]E(f300(x87261,x87262),f300(x87261,x87263))+~P1(f773(f773(f232(f855(f854(x87261,x87261),a841)),x87263),f300(x87261,x87262)))+~P1(f773(f773(f232(f855(f854(x87261,x87261),a841)),x87262),x87263))
% 191.21/191.75 [8779]~P47(x87791,f239(f855(x87791,a841)),x87793)+P1(f773(f773(f232(f855(f854(f848(x87791),f848(x87791)),a841)),f146(x87791,x87792)),f147(x87791,x87793)))+~P1(f773(f773(f232(f855(f854(x87791,x87791),a841)),x87792),x87793))
% 191.21/191.75 [8958]P36(x89581,x89582)+~P1(f773(f773(f334(x89581),x89583),f682(x89582,x89581)))+P1(f773(f773(f334(f854(x89581,x89581)),f773(f773(f241(x89581,x89581),f697(x89582,x89581,x89583)),x89583)),x89582))
% 191.21/191.75 [8997]~P1(f773(f63(x89971),x89972))+P1(f773(f63(f855(x89971,a841)),f773(f773(f61(x89971),x89972),x89973)))+~P1(f773(f773(f232(f855(f854(x89971,x89971),a841)),x89973),f773(f773(f248(x89971,x89971),x89972),f773(f18(f855(x89971,a841),x89971),x89972))))
% 191.21/191.75 [9028]P47(x90281,x90282,x90283)+P1(f773(f773(f334(x90281),f550(x90283,x90282,x90281)),x90282))+~P1(f773(f773(f232(f855(f854(x90281,x90281),a841)),x90283),f773(f773(f248(x90281,x90281),x90282),f773(f18(f855(x90281,a841),x90281),x90282))))
% 191.21/191.75 [9029]P47(x90291,x90292,x90293)+P1(f773(f773(f334(x90291),f555(x90292,x90293,x90291)),x90292))+~P1(f773(f773(f232(f855(f854(x90291,x90291),a841)),x90293),f773(f773(f248(x90291,x90291),x90292),f773(f18(f855(x90291,a841),x90291),x90292))))
% 191.21/191.75 [9062]~P63(x90621)+~P1(f773(f773(f233(x90621),x90622),x90623))+P1(f773(f773(f233(x90621),f773(f773(f283(x90621),f773(f773(f82(x90621),x90622),x90623)),f773(f773(f82(x90621),f80(x90621)),f80(x90621)))),x90623))
% 191.21/191.75 [9089]~P62(x90891)+P1(f773(f773(f232(x90891),x90892),x90893))+~P1(f773(f773(f232(x90891),f773(f773(f83(x90891),f799(x90893,x90892,x90891)),x90892)),x90893))
% 191.21/191.75 [9199]E(f773(f181(f848(f848(x91991))),f773(f126(f848(x91991),f773(f773(f10(a847,a841,f848(x91991)),f773(f233(a847),x91992)),f181(f848(x91991)))),f164(x91991,x91993))),f773(f181(f848(x91991)),f773(f773(f153(f848(x91991)),x91993),x91992)))+~P18(a847,f773(f142(a847),f773(f773(f143(f848(x91991),a847),f181(f848(x91991))),x91993)))+~P1(f773(f773(f233(a847),x91992),f773(f181(f848(f848(x91991))),x91993)))
% 191.21/191.75 [9310]~P36(x93101,x93102)+P30(x93101,f773(f773(f241(f855(f854(x93101,x93101),a841),f855(f854(x93101,x93101),a841)),x93102),x93103))+~P1(f773(f773(f232(f855(f854(x93101,x93101),a841)),f773(f773(f281(x93101,x93101,x93101),x93102),x93103)),x93102))
% 191.21/191.75 [9317]E(f773(f773(f143(f848(x93171),x93171),f773(f773(f9(f848(x93171),a847,x93171),f153(x93171)),x93172)),f773(f126(f848(x93171),f773(f773(f10(a847,a841,f848(x93171)),f773(f233(a847),x93172)),f181(f848(x93171)))),f164(x93171,x93173))),f773(f773(f153(f848(x93171)),x93173),x93172))+~P18(a847,f773(f142(a847),f773(f773(f143(f848(x93171),a847),f181(f848(x93171))),x93173)))+~P1(f773(f773(f233(a847),x93172),f773(f181(f848(f848(x93171))),x93173)))
% 191.21/191.75 [9444]P47(x94441,x94442,x94443)+~P1(f773(f773(f334(f854(x94441,x94441)),f773(f773(f241(x94441,x94441),f550(x94443,x94442,x94441)),f550(x94443,x94442,x94441))),x94443))+~P1(f773(f773(f232(f855(f854(x94441,x94441),a841)),x94443),f773(f773(f248(x94441,x94441),x94442),f773(f18(f855(x94441,a841),x94441),x94442))))
% 191.21/191.75 [9445]P47(x94451,x94452,x94453)+~P1(f773(f773(f334(f854(x94451,x94451)),f773(f773(f241(x94451,x94451),f555(x94452,x94453,x94451)),f555(x94452,x94453,x94451))),x94453))+~P1(f773(f773(f232(f855(f854(x94451,x94451),a841)),x94453),f773(f773(f248(x94451,x94451),x94452),f773(f18(f855(x94451,a841),x94451),x94452))))
% 191.21/191.75 [9604]~P133(x96041)+~P116(x96041)+E(f773(f773(f283(x96041),f773(f105(x96041),f773(f773(f75(f854(a1,a1),a1,x96042,f240(a1,a1)),f207(x96042)),x96043))),f773(f105(x96041),f773(f773(f75(f854(a1,a1),a1,x96042,f250(a1,a1)),f207(x96042)),x96043))),f217(x96042,x96041,x96043))
% 191.21/191.75 [9800]~E(x98003,f2(a847))+~E(f773(f181(f848(x98001)),f773(f773(f153(f848(x98001)),x98002),f766(x98003,x98001,x98002))),x98003)+E(f773(f773(f143(a847,f848(x98001)),f773(f773(f9(a847,f848(a847),f848(x98001)),f773(f773(f10(f855(a847,x98001),f855(f848(a847),f848(x98001)),a847),f143(a847,x98001)),f773(f9(a847,a847,x98001),f773(f773(f10(f848(x98001),f855(a847,x98001),a847),f153(x98001)),f773(f153(f848(x98001)),x98002))))),f130(a847,f773(f294(a847,f2(a847)),f773(f181(f848(f848(x98001))),x98002))))),f130(a847,f773(f294(a847,f2(a847)),x98003))),f164(x98001,x98002))
% 191.21/191.75 [9801]E(x98011,f115(f848(x98012)))+~E(f773(f181(f848(x98012)),f773(f773(f153(f848(x98012)),x98011),f766(x98013,x98012,x98011))),x98013)+E(f773(f773(f143(a847,f848(x98012)),f773(f773(f9(a847,f848(a847),f848(x98012)),f773(f773(f10(f855(a847,x98012),f855(f848(a847),f848(x98012)),a847),f143(a847,x98012)),f773(f9(a847,a847,x98012),f773(f773(f10(f848(x98012),f855(a847,x98012),a847),f153(x98012)),f773(f153(f848(x98012)),x98011))))),f130(a847,f773(f294(a847,f2(a847)),f773(f181(f848(f848(x98012))),x98011))))),f130(a847,f773(f294(a847,f2(a847)),x98013))),f164(x98012,x98011))
% 191.21/191.75 [9802]~E(x98023,f2(a847))+E(f773(f773(f143(a847,f848(x98021)),f773(f773(f9(a847,f848(a847),f848(x98021)),f773(f773(f10(f855(a847,x98021),f855(f848(a847),f848(x98021)),a847),f143(a847,x98021)),f773(f9(a847,a847,x98021),f773(f773(f10(f848(x98021),f855(a847,x98021),a847),f153(x98021)),f773(f153(f848(x98021)),x98022))))),f130(a847,f773(f294(a847,f2(a847)),f773(f181(f848(f848(x98021))),x98022))))),f130(a847,f773(f294(a847,f2(a847)),x98023))),f164(x98021,x98022))+P1(f773(f773(f233(a847),f766(x98023,x98021,x98022)),f773(f181(f848(f848(x98021))),x98022)))
% 191.21/191.75 [9803]E(x98031,f115(f848(x98032)))+E(f773(f773(f143(a847,f848(x98032)),f773(f773(f9(a847,f848(a847),f848(x98032)),f773(f773(f10(f855(a847,x98032),f855(f848(a847),f848(x98032)),a847),f143(a847,x98032)),f773(f9(a847,a847,x98032),f773(f773(f10(f848(x98032),f855(a847,x98032),a847),f153(x98032)),f773(f153(f848(x98032)),x98031))))),f130(a847,f773(f294(a847,f2(a847)),f773(f181(f848(f848(x98032))),x98031))))),f130(a847,f773(f294(a847,f2(a847)),x98033))),f164(x98032,x98031))+P1(f773(f773(f233(a847),f766(x98033,x98032,x98031)),f773(f181(f848(f848(x98032))),x98031)))
% 191.21/191.75 [7660]E(f773(f773(f82(a847),f773(f106(a847),x76601)),f773(f773(f82(a847),f773(f106(a847),x76602)),x76603)),f773(f773(f82(a847),f773(f106(a847),f773(f773(f82(a1),x76601),x76602))),x76603))+P1(f773(a186,f773(f106(a1),x76601)))+P1(f773(a186,f773(f106(a1),x76602)))
% 191.21/191.75 [8420]~P1(f773(f63(x84201),x84202))+~P1(f773(f773(f334(x84201),x84203),x84202))+E(f773(a114,f773(f42(x84201),f773(f773(f3(f855(x84201,a841)),x84202),f773(f773(f302(x84201),x84203),f180(f855(x84201,a841)))))),f773(f42(x84201),x84202))
% 191.21/191.75 [8440]~P1(f773(f63(x84401),x84402))+~P1(f773(f773(f334(x84401),x84403),x84402))+E(f773(f773(f82(a847),f80(a847)),f773(f42(x84401),f773(f773(f3(f855(x84401,a841)),x84402),f773(f773(f302(x84401),x84403),f180(f855(x84401,a841)))))),f773(f42(x84401),x84402))
% 191.21/191.75 [8524]~P100(x85241)+~P1(f773(f63(x85241),x85243))+E(f773(f773(f138(x85241,x85241,f7(x85241)),x85242),f130(x85241,f773(f773(f3(f855(x85241,a841)),x85243),f773(f773(f302(x85241),x85242),f180(f855(x85241,a841)))))),f130(x85241,f773(f773(f302(x85241),x85242),x85243)))
% 191.21/191.75 [8662]~P1(f773(f63(x86621),x86623))+~P1(f773(f63(x86621),x86622))+E(f773(f773(f82(a847),f773(f42(x86621),f773(f773(f103(f855(x86621,a841)),x86622),x86623))),f773(f42(x86621),f773(f773(f104(f855(x86621,a841)),x86622),x86623))),f773(f773(f82(a847),f773(f42(x86621),x86622)),f773(f42(x86621),x86623)))
% 191.21/191.75 [9749]~P29(x97491,f855(f855(x97491,a841),a841),f773(f773(f9(x97491,f855(f854(x97491,x97491),a841),f855(f855(x97491,a841),a841)),f773(f773(f10(f855(x97491,a841),f855(f855(f854(x97491,x97491),a841),f855(f855(x97491,a841),a841)),x97491),f61(x97491)),f773(f773(f9(x97491,f855(x97491,a841),f855(x97491,a841)),f302(x97491)),f180(f855(x97491,a841))))),x97493),x97492)+~P1(f773(f63(x97491),x97492))+E(f773(f42(f855(x97491,a841)),f773(f773(f61(x97491),x97492),x97493)),f773(f42(x97491),x97492))
% 191.21/191.75 [7932]~P88(x79321)+P1(f773(f773(f232(a1),f2(a1)),f773(f106(a1),x79323)))+E(f773(f773(f242(x79321),x79322),f773(f106(a847),f773(f773(f3(a1),f773(f773(f82(a1),x79323),x79323)),a99))),f80(x79321))
% 191.21/191.75 [9293]~P88(x92931)+~P1(f773(f773(f232(a1),f2(a1)),f773(f106(a1),x92933)))+E(f773(f773(f242(x92931),x92932),f773(f106(a847),f773(f773(f3(a1),f773(f773(f82(a1),x92933),x92933)),a99))),f773(f773(f88(x92931,x92931),f773(f773(f242(x92931),x92932),f773(f106(a847),x92933))),f773(f773(f20(x92931,x92931,x92931),f773(f773(f10(x92931,f855(x92931,x92931),x92931),f83(x92931)),f773(f83(x92931),x92932))),f7(x92931))))
% 191.21/191.75 [9714]P1(f773(f773(f232(f855(f854(x97141,x97141),a841)),f300(x97141,x97142)),x97143))+~P1(f773(f773(f232(f855(f854(x97141,x97141),a841)),f300(x97141,f180(f855(f854(x97141,x97141),a841)))),x97143))+~P1(f773(f773(f232(f855(f854(x97141,x97141),a841)),f773(f773(f281(x97141,x97141,x97141),f773(f773(f104(f855(f854(x97141,x97141),a841)),f300(x97141,x97142)),x97143)),x97142)),x97143))
% 191.21/191.75 [9580]~P1(f773(f63(x95801),f773(f256(x95801),x95803)))+~P1(f773(f63(x95801),f773(f256(x95801),x95802)))+P1(f773(f63(x95801),f773(f256(x95801),f773(f773(f20(x95801,a841,a841),f773(f773(f10(a841,f855(a841,a841),x95801),a332),x95802)),x95803))))
% 191.21/191.75 [9868]P1(f773(f773(f232(f855(f854(x98681,x98681),a841)),f773(f773(f281(x98681,x98681,x98681),x98682),f300(x98681,x98682))),x98683))+~P1(f773(f773(f232(f855(f854(x98681,x98681),a841)),x98682),x98683))+~P1(f773(f773(f232(f855(f854(x98681,x98681),a841)),f773(f773(f281(x98681,x98681,x98681),f773(f773(f104(f855(f854(x98681,x98681),a841)),f773(f773(f281(x98681,x98681,x98681),x98682),f300(x98681,x98682))),x98683)),x98682)),x98683))
% 191.21/191.75 [9816]~P110(x98162)+E(x98161,f2(x98162))+~E(f773(f773(f82(x98162),f773(f773(f242(x98162),x98163),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))),f773(f773(f242(x98162),x98161),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))),f2(x98162))
% 191.21/191.75 [9817]~P110(x98172)+E(x98171,f2(x98172))+~E(f773(f773(f82(x98172),f773(f773(f242(x98172),x98171),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))),f773(f773(f242(x98172),x98173),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))),f2(x98172))
% 191.21/191.75 [9910]~P110(x99102)+E(x99101,f2(x99102))+P1(f773(f773(f233(x99102),f2(x99102)),f773(f773(f82(x99102),f773(f773(f242(x99102),x99103),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))),f773(f773(f242(x99102),x99101),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))))))
% 191.21/191.75 [9911]~P110(x99112)+E(x99111,f2(x99112))+P1(f773(f773(f233(x99112),f2(x99112)),f773(f773(f82(x99112),f773(f773(f242(x99112),x99111),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))),f773(f773(f242(x99112),x99113),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))))))
% 191.21/191.75 [9959]~P110(x99591)+P1(f773(f773(f232(x99591),f2(x99591)),x99592))+~P1(f773(f773(f232(x99591),f2(x99591)),f773(f773(f242(x99591),x99592),f773(a114,f773(f773(f83(a847),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),x99593)))))
% 191.21/191.75 [5368]~P28(x53681,x53684,x53683)+P28(x53681,x53682,x53683)+~P28(x53681,x53682,x53684)
% 191.21/191.75 [4845]~E(x48452,f92(x48453,x48451))+P1(f773(x48451,x48452))+~P1(f773(x48451,x48454))
% 191.21/191.75 [6611]~P36(x66112,x66114)+~P36(x66111,x66113)+P36(f854(x66111,x66112),f325(x66111,x66112,x66113,x66114))
% 191.21/191.75 [8003]~P39(f35(x80034,x80031),x80032,x80033,x80032)+P39(x80031,x80032,x80033,f795(x80033,x80032,x80031,x80034))+~P1(f773(x80034,x80032))
% 191.21/191.75 [8030]~P39(f35(x80301,x80302),x80304,x80303,x80304)+P39(f35(x80301,x80302),f795(x80303,x80304,x80302,x80301),x80303,x80304)+~P1(f773(x80301,x80304))
% 191.21/191.75 [5026]~P11(x50264,x50261)+~E(f773(x50261,x50262),f773(x50261,x50263))+P1(f773(f773(x50261,x50262),x50263))
% 191.21/191.75 [5187]~P11(x51874,x51871)+E(f773(x51871,x51872),f773(x51871,x51873))+~P1(f773(f773(x51871,x51872),x51873))
% 191.21/191.75 [5275]~P22(x52753,x52754,x52751)+E(f773(x52751,x52752),f773(f65(x52753,x52754),x52752))+~P1(f773(f63(x52753),x52752))
% 191.21/191.75 [5276]~P14(x52763,x52764,x52761)+E(f773(x52761,x52762),f773(f65(x52763,x52764),x52762))+~P1(f773(f63(x52763),x52762))
% 191.21/191.75 [5403]~P11(x54034,x54031)+~P1(f773(f773(x54031,x54033),x54032))+P1(f773(f773(x54031,x54032),x54033))
% 191.21/191.75 [5467]E(x54671,x54672)+~E(f773(f240(x54673,x54674),x54671),f773(f240(x54673,x54674),x54672))+~E(f773(f250(x54673,x54674),x54671),f773(f250(x54673,x54674),x54672))
% 191.21/191.75 [5493]E(x54931,x54932)+~P1(f773(f55(x54933,x54934),x54932))+~P1(f773(f55(x54933,x54934),x54931))
% 191.21/191.75 [5687]~P66(x56872)+E(f225(x56871,x56872,x56873,x56874),f2(x56872))+P1(f773(f63(x56871),x56874))
% 191.21/191.75 [5824]~P1(f773(f321(x58241,x58242),x58244))+P1(f773(f321(x58241,x58242),x58243))+~P1(f773(f773(x58242,x58243),x58244))
% 191.21/191.75 [8074]~P1(f773(f63(x80742),x80744))+~P1(f773(f63(x80741),x80743))+P1(f773(f63(f856(x80741,x80742)),f314(x80741,x80742,x80743,x80744)))
% 191.21/191.75 [8077]P1(f773(f773(f334(f848(x80771)),f773(f773(f125(x80771),x80772),x80773)),f149(x80771,x80774)))+~P1(f773(f773(f334(f848(x80771)),x80773),f149(x80771,x80774)))+~P1(f773(f773(f334(f848(x80771)),x80772),f149(x80771,x80774)))
% 191.21/191.75 [8652]~P1(f773(f773(f334(f854(x86521,x86521)),f773(f773(f241(x86521,x86521),x86522),x86524)),f300(x86521,x86523)))+P1(f773(f773(f334(x86521),x86522),f322(x86521,x86523)))+~P1(f773(f773(f334(x86521),x86524),f322(x86521,x86523)))
% 191.21/191.75 [5010]~P66(x50102)+E(f773(f773(f8(x50101,x50102),x50103),x50104),f2(x50102))+P1(f773(f63(x50101),x50104))
% 191.21/191.75 [5013]~P70(x50132)+E(f773(f773(f11(x50131,x50132),x50133),x50134),f80(x50132))+P1(f773(f63(x50131),x50134))
% 191.21/191.75 [5156]~P3(x51563)+E(x51561,x51562)+~E(f773(f773(f82(x51563),x51564),x51561),f773(f773(f82(x51563),x51564),x51562))
% 191.21/191.75 [5157]~P4(x51573)+E(x51571,x51572)+~E(f773(f773(f82(x51573),x51574),x51571),f773(f773(f82(x51573),x51574),x51572))
% 191.21/191.75 [5159]~P3(x51593)+E(x51591,x51592)+~E(f773(f773(f82(x51593),x51591),x51594),f773(f773(f82(x51593),x51592),x51594))
% 191.21/191.75 [5245]~P112(x52451)+~E(x52453,f773(f773(f83(x52451),x52452),x52454))+P1(f773(f773(f279(x52451),x52452),x52453))
% 191.21/191.75 [5270]~P9(x52703)+E(x52701,f180(f855(x52702,a841)))+E(f773(f773(f46(x52702,x52703),x52701),f773(f18(x52703,x52702),x52704)),x52704)
% 191.21/191.75 [5271]~P9(x52713)+E(x52711,f180(f855(x52712,a841)))+E(f773(f773(f47(x52712,x52713),x52711),f773(f18(x52713,x52712),x52714)),x52714)
% 191.21/191.75 [5481]~P99(x54813)+E(x54811,x54812)+~E(f295(x54813,x54814,x54811),f773(f773(f302(x54813),x54812),f180(f855(x54813,a841))))
% 191.21/191.75 [5482]~P99(x54823)+E(x54821,x54822)+~E(f295(x54823,x54821,x54822),f773(f773(f302(x54823),x54824),f180(f855(x54823,a841))))
% 191.21/191.75 [5786]P1(f773(x57861,x57862))+~P1(f773(f245(x57863,x57861),x57864))+~P1(f773(f773(f334(x57863),x57862),x57864))
% 191.21/191.75 [5815]E(x58151,x58152)+~P1(f773(f773(f187(x58153),x58154),x58152))+~P1(f773(f773(f187(x58153),x58154),x58151))
% 191.21/191.75 [5897]~P66(x58971)+E(f773(f773(f8(a847,x58971),x58972),f773(f294(a847,x58973),f773(a114,x58974))),f2(x58971))+~P1(f773(f773(f233(a847),x58974),x58973))
% 191.21/191.75 [5902]~P8(x59021)+~E(f52(x59021,x59022,x59023),f52(x59021,x59024,x59023))+E(f52(x59021,f773(f81(x59021),x59022),x59023),f52(x59021,f773(f81(x59021),x59024),x59023))
% 191.21/191.75 [5971]P1(f773(x59711,x59712))+~E(f773(f126(x59713,x59711),x59714),x59714)+~P1(f773(f773(f334(x59713),x59712),f773(f158(x59713),x59714)))
% 191.21/191.75 [5990]~E(f773(f773(f82(a847),x59903),x59902),f773(f773(f82(a847),x59901),x59904))+~P1(f773(f773(f233(a847),x59903),x59904))+P1(f773(f773(f233(a847),x59901),x59902))
% 191.21/191.75 [5997]~P7(x59971)+E(f52(x59971,f52(x59971,x59972,x59973),x59974),f52(x59971,x59972,x59974))+~P1(f773(f773(f279(x59971),x59974),x59973))
% 191.21/191.75 [6035]~E(f773(f126(x60351,x60352),x60353),f115(x60351))+~P1(f773(x60352,x60354))+~P1(f773(f773(f334(x60351),x60354),f773(f158(x60351),x60353)))
% 191.21/191.75 [6036]~E(f162(x60363,x60361,x60364),x60364)+P1(f773(x60361,x60362))+~P1(f773(f773(f334(x60363),x60362),f773(f158(x60363),x60364)))
% 191.21/191.75 [6071]~E(x60714,f180(f855(x60712,a841)))+~E(x60713,f180(f855(x60711,a841)))+E(f314(x60711,x60712,x60713,x60714),f180(f855(f856(x60711,x60712),a841)))
% 191.21/191.75 [6505]~P66(x65051)+E(f773(f773(f8(a847,x65051),x65052),f295(a847,x65053,f773(a114,x65054))),f2(x65051))+~P1(f773(f773(f233(a847),f773(a114,x65054)),x65053))
% 191.21/191.75 [6654]~P100(x66541)+E(f773(f773(f3(f855(x66541,a841)),f773(f294(x66541,x66542),x66543)),f773(f294(x66541,x66542),x66544)),f773(f294(x66541,x66544),x66543))+~P1(f773(f773(f232(x66541),x66542),x66544))
% 191.21/191.75 [7016]~P1(f773(f773(f334(f848(x70161)),x70164),f149(x70161,x70163)))+P1(f773(f773(f334(x70161),x70162),x70163))+~P1(f773(f773(f334(x70161),x70162),f773(f158(x70161),x70164)))
% 191.21/191.75 [7023]~P36(x70231,x70232)+P1(f773(f773(f334(x70231),f694(x70232,x70231,x70233)),x70233))+~P1(f773(f773(f334(x70231),x70234),x70233))
% 191.21/191.75 [7080]~P66(x70801)+E(f773(f773(f773(f67(x70801,x70802,f82(x70801)),x70803),f2(x70801)),x70804),f773(f773(f8(x70802,x70801),x70803),x70804))+~P1(f773(f63(x70802),x70804))
% 191.21/191.75 [7082]~P70(x70821)+E(f773(f773(f773(f67(x70821,x70822,f83(x70821)),x70823),f80(x70821)),x70824),f773(f773(f11(x70822,x70821),x70823),x70824))+~P1(f773(f63(x70822),x70824))
% 191.21/191.75 [7109]P29(x71091,x71092,x71093,x71094)+~E(f773(f42(x71092),f773(f303(x71091,x71092,x71093),x71094)),f773(f42(x71091),x71094))+~P1(f773(f63(x71091),x71094))
% 191.21/191.75 [7313]~P66(x73131)+E(f773(f773(f82(x73131),f773(x73132,x73133)),f773(f773(f8(a847,x73131),x73132),f297(a847,x73133,x73134))),f773(f773(f8(a847,x73131),x73132),f295(a847,x73133,x73134)))+~P1(f773(f773(f232(a847),x73133),x73134))
% 191.21/191.75 [7323]~P66(x73231)+~P29(x73232,x73231,x73233,x73234)+E(f773(f773(f8(x73231,x73231),f39(x73231)),f773(f303(x73232,x73231,x73233),x73234)),f773(f773(f8(x73232,x73231),x73233),x73234))
% 191.21/191.75 [7324]~P70(x73241)+~P29(x73242,x73241,x73243,x73244)+E(f773(f773(f11(x73241,x73241),f39(x73241)),f773(f303(x73242,x73241,x73243),x73244)),f773(f773(f11(x73242,x73241),x73243),x73244))
% 191.21/191.75 [7383]E(f773(f42(f856(x73831,x73832)),f314(x73831,x73832,x73833,x73834)),f773(f773(f82(a847),f773(f42(x73831),x73833)),f773(f42(x73832),x73834)))+~P1(f773(f63(x73832),x73834))+~P1(f773(f63(x73831),x73833))
% 191.21/191.75 [7468]E(x74681,x74682)+P1(f773(f773(f334(x74683),x74681),f773(f158(x74683),f151(x74683,x74682,x74684))))+~P1(f773(f773(f334(x74683),x74681),f773(f158(x74683),x74684)))
% 191.21/191.75 [7694]~P66(x76941)+E(f773(f773(f82(x76941),f773(f773(f8(a847,x76941),x76942),f773(f294(a847,x76943),x76944))),f773(x76942,x76944)),f773(f773(f8(a847,x76941),x76942),f773(f294(a847,x76943),f773(a114,x76944))))+P1(f773(f773(f233(a847),x76944),x76943))
% 191.21/191.75 [7751]~P29(x77511,x77512,x77513,f239(f855(x77511,a841)))+~P1(f773(f63(x77512),x77514))+P1(f773(f63(x77511),f773(f305(x77511,x77512,x77513),x77514)))
% 191.21/191.75 [7865]P1(f773(f773(f334(f848(x78651)),f773(f773(f140(x78651),x78652),x78653)),f149(x78651,x78654)))+~P1(f773(f773(f334(f848(x78651)),x78653),f149(x78651,x78654)))+~P1(f773(f773(f334(x78651),x78652),x78654))
% 191.21/191.75 [7956]~E(f773(f303(x79563,x79561,x79564),f239(f855(x79563,a841))),f239(f855(x79561,a841)))+P1(f773(f63(x79561),x79562))+~P1(f773(f63(x79563),f773(f305(x79563,x79561,x79564),x79562)))
% 191.21/191.75 [8046]~P29(x80461,x80463,x80464,x80462)+P1(f773(f63(x80461),x80462))+~P1(f773(f63(x80463),f773(f303(x80461,x80463,x80464),x80462)))
% 191.21/191.75 [8069]~E(x80692,x80693)+P1(f773(f773(f334(f854(x80691,x80691)),f773(f773(f241(x80691,x80691),x80692),x80693)),f260(x80691,x80694)))+~P1(f773(f773(f334(x80691),x80692),x80694))
% 191.21/191.75 [8100]~P66(x81001)+E(f773(f773(f82(x81001),f773(f773(f8(a847,x81001),x81002),f295(a847,x81003,x81004))),f773(x81002,f773(a114,x81004))),f773(f773(f8(a847,x81001),x81002),f295(a847,x81003,f773(a114,x81004))))+P1(f773(f773(f233(a847),f773(a114,x81004)),x81003))
% 191.21/191.75 [8163]P1(f773(x81631,x81632))+~P1(f773(x81631,f773(f773(f153(x81633),x81634),f725(x81631,x81634,x81633))))+~P1(f773(f773(f334(x81633),x81632),f773(f158(x81633),x81634)))
% 191.21/191.75 [8297]~P1(f773(f773(f334(x82971),x82972),f322(x82971,x82974)))+P1(f773(f773(f334(f848(x82971)),f773(f773(f140(x82971),x82972),x82973)),f322(f848(x82971),f146(x82971,x82974))))+~P1(f773(f773(f334(f848(x82971)),x82973),f322(f848(x82971),f146(x82971,x82974))))
% 191.21/191.75 [8313]~P29(x83132,x83133,x83134,f687(x83134,x83133,x83132,x83131))+P29(x83132,x83133,x83134,f45(f855(x83132,a841),x83131))+E(x83131,f180(f855(f855(x83132,a841),a841)))
% 191.21/191.75 [8574]E(x85741,x85742)+~P1(f773(f773(f334(f854(x85743,x85743)),f773(f773(f241(x85743,x85743),x85741),x85742)),f300(x85743,x85744)))+P1(f773(f773(f334(x85743),x85741),f773(f261(x85743,x85743),x85744)))
% 191.21/191.75 [8821]P29(x88212,x88213,x88214,f45(f855(x88212,a841),x88211))+E(x88211,f180(f855(f855(x88212,a841),a841)))+P1(f773(f773(f334(f855(x88212,a841)),f687(x88214,x88213,x88212,x88211)),x88211))
% 191.21/191.75 [8949]P1(f773(f63(x89491),x89492))+~P1(f773(f63(x89494),f773(f303(x89491,x89494,x89493),x89492)))+P1(f773(f773(f334(x89491),f599(x89493,x89494,x89492,x89491)),x89492))
% 191.21/191.75 [9041]~P9(x90412)+E(f773(f773(f66(x90411,x90412,f773(f773(f10(x90412,f855(x90412,x90412),x90411),f103(x90412)),x90413)),f180(x90412)),x90414),f773(f773(f46(x90411,x90412),x90414),x90413))+~P1(f773(f63(x90411),x90414))
% 191.21/191.75 [9042]~P9(x90422)+E(f773(f773(f66(x90421,x90422,f773(f773(f10(x90422,f855(x90422,x90422),x90421),f104(x90422)),x90423)),f239(x90422)),x90424),f773(f773(f47(x90421,x90422),x90424),x90423))+~P1(f773(f63(x90421),x90424))
% 191.21/191.75 [9068]~P1(f773(f773(f279(a847),x90683),x90684))+P1(f773(f773(f279(a847),x90681),x90682))+P1(f773(f773(f233(f855(a847,a841)),f282(a847,f279(a847),x90681,x90682)),f282(a847,f279(a847),x90683,x90684)))
% 191.21/191.75 [9079]~P1(f773(f773(f279(a847),x90792),x90794))+~P1(f773(f773(f279(a847),x90793),x90791))+P1(f773(f773(f232(f855(a847,a841)),f282(a847,f279(a847),x90791,x90792)),f282(a847,f279(a847),x90793,x90794)))
% 191.21/191.75 [9137]E(x91371,x91372)+~P1(f773(f773(f334(f854(x91373,x91373)),f773(f773(f241(x91373,x91373),x91371),x91372)),f300(x91373,x91374)))+P1(f773(f773(f334(f854(x91373,x91373)),f773(f773(f241(x91373,x91373),x91371),x91372)),f773(f773(f281(x91373,x91373,x91373),x91374),f300(x91373,x91374))))
% 191.21/191.75 [9168]~E(f773(f181(f848(x91681)),x91682),f773(f181(f848(x91681)),x91683))+~P1(f773(f773(f334(f854(f848(x91681),f848(x91681))),f773(f773(f241(f848(x91681),f848(x91681)),x91682),x91683)),f137(x91681,x91684)))+P1(f773(f773(f334(f854(f848(x91681),f848(x91681))),f773(f773(f241(f848(x91681),f848(x91681)),x91682),x91683)),f135(x91681,x91684)))
% 191.21/191.75 [9280]P1(f773(f773(f279(a847),x92801),x92802))+~P1(f773(f773(f279(a847),x92803),x92801))+~P1(f773(f773(f233(f855(a847,a841)),f282(a847,f279(a847),x92803,x92801)),f282(a847,f279(a847),x92804,x92802)))
% 191.21/191.75 [9281]P1(f773(f773(f279(a847),x92811),x92812))+~P1(f773(f773(f279(a847),x92813),x92811))+~P1(f773(f773(f232(f855(a847,a841)),f282(a847,f279(a847),x92813,x92811)),f282(a847,f279(a847),x92814,x92812)))
% 191.21/191.75 [9282]P1(f773(f773(f279(a847),x92821),x92822))+~P1(f773(f773(f279(a847),x92822),x92823))+~P1(f773(f773(f233(f855(a847,a841)),f282(a847,f279(a847),x92822,x92823)),f282(a847,f279(a847),x92821,x92824)))
% 191.21/191.75 [9283]P1(f773(f773(f279(a847),x92831),x92832))+~P1(f773(f773(f279(a847),x92832),x92833))+~P1(f773(f773(f232(f855(a847,a841)),f282(a847,f279(a847),x92832,x92833)),f282(a847,f279(a847),x92831,x92834)))
% 191.21/191.75 [9583]~P6(x95831)+E(f773(f773(f8(a847,x95831),f773(f773(f20(a847,x95831,x95831),f773(f773(f10(x95831,f855(x95831,x95831),a847),f3(x95831)),x95832)),f773(f773(f10(a847,x95831,a847),x95832),f773(f773(f9(a847,a847,a847),f82(a847)),f80(a847))))),f295(a847,x95833,x95834)),f2(x95831))+P1(f773(f773(f232(a847),x95833),x95834))
% 191.21/191.75 [9814]~P36(x98142,x98144)+~P29(x98142,x98141,x98143,f239(f855(x98142,a841)))+P36(x98141,f773(f303(f854(x98142,x98142),f854(x98141,x98141),f252(x98142,x98141,x98142,x98141,x98143,x98143)),x98144))
% 191.21/191.75 [9987]~E(f773(f181(f848(x99871)),x99873),f773(f181(f848(x99871)),x99872))+P1(f773(f773(f334(f854(f848(x99871),f848(x99871))),f773(f773(f241(f848(x99871),f848(x99871)),x99872),x99873)),f147(x99871,x99874)))+~P1(f773(f773(f251(x99871,x99871,a841),f773(f773(f9(x99871,f855(f854(x99871,x99871),a841),f855(x99871,a841)),f773(f773(f10(f855(x99871,f855(f855(f854(x99871,x99871),a841),a841)),f855(f855(f854(x99871,x99871),a841),f855(x99871,a841)),x99871),f9(x99871,f855(f854(x99871,x99871),a841),a841)),f773(f773(f10(f855(x99871,f854(x99871,x99871)),f855(x99871,f855(f855(f854(x99871,x99871),a841),a841)),x99871),f773(f10(f854(x99871,x99871),f855(f855(f854(x99871,x99871),a841),a841),x99871),f334(f854(x99871,x99871)))),f241(x99871,x99871)))),x99874)),f716(x99874,x99873,x99872,x99871)))
% 191.21/191.75 [5861]~E(x58614,x58612)+P1(f773(x58611,x58612))+P1(f773(f773(f187(f35(x58611,x58613)),x58612),x58614))
% 191.21/191.75 [5955]~P7(x59551)+~E(x59552,f2(x59551))+E(f773(f773(f43(x59551),f773(f773(f83(x59551),x59552),x59553)),f773(f773(f83(x59551),x59552),x59554)),f2(x59551))
% 191.21/191.75 [5994]E(x59941,f115(x59942))+E(x59943,f773(f773(f3(a847),f773(f181(f848(x59942)),x59941)),f80(a847)))+E(f134(x59942,f773(f773(f148(x59942,x59941),x59943),x59944)),f134(x59942,x59941))
% 191.21/191.75 [6026]E(x60261,x60262)+P1(f773(x60263,x60262))+~P1(f773(f773(f773(f302(x60264),x60261),x60263),x60262))
% 191.21/191.75 [6040]~P66(x60401)+~P1(f773(f127(x60402),x60404))+E(f773(f155(x60401),f773(f773(f143(x60402,x60401),x60403),x60404)),f773(f773(f8(x60402,x60401),x60403),f773(f158(x60402),x60404)))
% 191.21/191.75 [6064]~P70(x60642)+~P1(f773(f63(x60641),x60644))+E(f773(f773(f11(x60641,x60642),f773(f18(x60642,x60641),x60643)),x60644),f773(f773(f242(x60642),x60643),f773(f42(x60641),x60644)))
% 191.21/191.75 [6118]~P7(x61182)+E(x61181,f2(x61182))+E(f773(f773(f43(x61182),f773(f773(f83(x61182),x61183),x61181)),f773(f773(f83(x61182),x61184),x61181)),f773(f773(f43(x61182),x61183),x61184))
% 191.21/191.75 [6120]~P60(x61202)+E(x61201,f2(x61202))+E(f773(f773(f283(x61202),f773(f773(f83(x61202),x61203),x61201)),f773(f773(f83(x61202),x61204),x61201)),f773(f773(f283(x61202),x61203),x61204))
% 191.21/191.75 [6121]~P60(x61212)+E(x61211,f2(x61212))+E(f773(f773(f283(x61212),f773(f773(f83(x61212),x61211),x61213)),f773(f773(f83(x61212),x61211),x61214)),f773(f773(f283(x61212),x61213),x61214))
% 191.21/191.75 [6122]~P7(x61222)+E(x61221,f2(x61222))+E(f773(f773(f43(x61222),f773(f773(f83(x61222),x61221),x61223)),f773(f773(f83(x61222),x61221),x61224)),f773(f773(f43(x61222),x61223),x61224))
% 191.21/191.75 [6188]P1(f773(x61881,x61882))+~E(x61883,f773(f773(f82(a847),x61884),x61882))+~P1(f773(x61881,f773(f773(f3(a847),x61883),x61884)))
% 191.21/191.75 [6271]P32(x62711,x62712,x62713)+P31(x62711,f669(x62713,x62712,x62711),x62714)+~P1(f773(f773(f334(f846(x62711)),x62714),x62712))
% 191.21/191.75 [6317]E(x63171,f115(x63172))+~E(x63173,f773(f773(f3(a847),f773(f181(f848(x63172)),x63171)),f80(a847)))+E(f134(x63172,f773(f773(f148(x63172,x63171),x63173),x63174)),x63174)
% 191.21/191.75 [6340]~P100(x63401)+~P1(f773(f773(f233(x63401),x63402),x63404))+P1(f773(f773(f233(x63401),x63402),f773(f773(f179(x63401),x63403),x63404)))
% 191.21/191.75 [6342]~P100(x63421)+~P1(f773(f773(f233(x63421),x63422),x63423))+P1(f773(f773(f233(x63421),x63422),f773(f773(f179(x63421),x63423),x63424)))
% 191.21/191.75 [6343]~P92(x63431)+~P1(f773(f773(f233(x63431),x63432),x63434))+P1(f773(f773(f233(x63431),x63432),f773(f773(f103(x63431),x63433),x63434)))
% 191.21/191.75 [6344]~P92(x63441)+~P1(f773(f773(f233(x63441),x63442),x63443))+P1(f773(f773(f233(x63441),x63442),f773(f773(f103(x63441),x63443),x63444)))
% 191.21/191.75 [6346]~P100(x63461)+~P1(f773(f773(f232(x63461),x63462),x63464))+P1(f773(f773(f232(x63461),x63462),f773(f773(f179(x63461),x63463),x63464)))
% 191.21/191.75 [6348]~P100(x63481)+~P1(f773(f773(f232(x63481),x63482),x63483))+P1(f773(f773(f232(x63481),x63482),f773(f773(f179(x63481),x63483),x63484)))
% 191.21/191.75 [6349]~P92(x63491)+~P1(f773(f773(f232(x63491),x63492),x63494))+P1(f773(f773(f232(x63491),x63492),f773(f773(f103(x63491),x63493),x63494)))
% 191.21/191.75 [6350]~P92(x63501)+~P1(f773(f773(f232(x63501),x63502),x63503))+P1(f773(f773(f232(x63501),x63502),f773(f773(f103(x63501),x63503),x63504)))
% 191.21/191.75 [6351]~P85(x63511)+~P1(f773(f773(f279(x63511),x63512),x63514))+P1(f773(f773(f279(x63511),x63512),f773(f773(f83(x63511),x63513),x63514)))
% 191.21/191.75 [6352]~P85(x63521)+~P1(f773(f773(f279(x63521),x63522),x63523))+P1(f773(f773(f279(x63521),x63522),f773(f773(f83(x63521),x63523),x63524)))
% 191.21/191.75 [6447]~E(f773(f773(f153(x64471),x64472),x64473),x64474)+E(f773(f773(f148(x64471,x64472),x64473),x64474),x64472)+~P1(f773(f773(f233(a847),x64473),f773(f181(f848(x64471)),x64472)))
% 191.21/191.75 [6467]E(x64671,x64672)+P1(f773(x64673,x64671))+~P1(f773(f773(f187(f35(x64673,x64674)),x64671),x64672))
% 191.21/191.75 [6488]P1(f773(x64881,x64882))+~P1(f773(x64883,x64882))+~P1(f773(f773(f232(f855(x64884,a841)),x64883),x64881))
% 191.21/191.75 [6524]~E(f773(f773(f148(x65241,x65242),x65243),x65244),x65242)+E(f773(f773(f153(x65241),x65242),x65243),x65244)+~P1(f773(f773(f233(a847),x65243),f773(f181(f848(x65241)),x65242)))
% 191.21/191.75 [6642]P31(x66421,x66422,x66423)+~P31(x66421,f773(a114,x66422),f820(x66422,x66424,x66421))+~P1(f773(f773(f334(f846(x66421)),x66423),x66424))
% 191.21/191.75 [6651]E(x66511,f180(f855(x66512,a841)))+E(x66513,f180(f855(x66514,a841)))+~E(f773(f773(f248(x66514,x66512),x66513),f773(f18(f855(x66512,a841),x66514),x66511)),f180(f855(f854(x66514,x66512),a841)))
% 191.21/191.75 [6669]E(x66691,x66692)+P1(f773(f773(f334(x66693),x66691),x66694))+~P1(f773(f773(f334(x66693),x66691),f773(f773(f302(x66693),x66692),x66694)))
% 191.21/191.75 [6686]~P100(x66861)+P1(f773(f773(f233(x66861),x66862),x66863))+~P1(f773(f773(f233(x66861),x66862),f773(f773(f236(x66861),x66864),x66863)))
% 191.21/191.75 [6687]~P100(x66871)+P1(f773(f773(f233(x66871),x66872),x66873))+~P1(f773(f773(f233(x66871),x66872),f773(f773(f236(x66871),x66873),x66874)))
% 191.21/191.75 [6689]~P100(x66891)+P1(f773(f773(f232(x66891),x66892),x66893))+~P1(f773(f773(f232(x66891),x66892),f773(f773(f236(x66891),x66894),x66893)))
% 191.21/191.75 [6691]~P100(x66911)+P1(f773(f773(f232(x66911),x66912),x66913))+~P1(f773(f773(f232(x66911),x66912),f773(f773(f236(x66911),x66913),x66914)))
% 191.21/191.75 [6693]~P98(x66931)+P1(f773(f773(f232(x66931),x66932),x66933))+~P1(f773(f773(f232(x66931),x66932),f773(f773(f104(x66931),x66934),x66933)))
% 191.21/191.75 [6695]~P98(x66951)+P1(f773(f773(f232(x66951),x66952),x66953))+~P1(f773(f773(f232(x66951),x66952),f773(f773(f104(x66951),x66953),x66954)))
% 191.21/191.75 [6717]~E(f773(f773(f153(x67171),x67173),x67174),x67172)+P1(f773(f773(f334(x67171),x67172),f773(f158(x67171),x67173)))+~P1(f773(f773(f233(a847),x67174),f773(f181(f848(x67171)),x67173)))
% 191.21/191.75 [6729]~P100(x67291)+~P18(x67291,f773(f773(f140(x67291),x67292),f773(f773(f140(x67291),x67293),x67294)))+P1(f773(f773(f232(x67291),x67292),x67293))
% 191.21/191.75 [6899]E(x68991,f2(a1))+E(f773(f773(f43(a1),x68992),x68991),x68993)+~P1(f773(f56(x68992,x68991),f773(f773(f241(a1,a1),x68993),x68994)))
% 191.21/191.75 [6922]E(f52(a1,x69222,x69221),x69223)+E(x69221,f2(a1))+~P1(f773(f56(x69222,x69221),f773(f773(f241(a1,a1),x69224),x69223)))
% 191.21/191.75 [7037]P1(f773(f773(f334(x70371),x70372),x70373))+~P1(f773(f773(f334(x70371),x70372),x70374))+~P1(f773(f773(f233(f855(x70371,a841)),x70374),x70373))
% 191.21/191.75 [7041]P1(f773(f773(f334(x70411),x70412),x70413))+~P1(f773(f773(f334(x70411),x70412),x70414))+~P1(f773(f773(f232(f855(x70411,a841)),x70414),x70413))
% 191.21/191.75 [7051]~P111(x70511)+~E(x70513,f2(x70511))+P1(f773(f773(f279(x70511),f773(f773(f83(x70511),x70512),x70513)),f773(f773(f83(x70511),x70514),x70513)))
% 191.21/191.75 [7052]~P111(x70521)+~E(x70522,f2(x70521))+P1(f773(f773(f279(x70521),f773(f773(f83(x70521),x70522),x70523)),f773(f773(f83(x70521),x70522),x70524)))
% 191.21/191.75 [7277]~P102(x72772)+~P1(f773(f773(f233(f855(x72771,x72772)),x72773),x72774))+P1(f773(f773(f232(f855(x72771,x72772)),x72773),x72774))
% 191.21/191.75 [7372]~P28(x73721,x73722,x73724)+P28(x73721,x73722,f773(f773(f302(f846(x73721)),x73723),x73724))+~P28(x73721,x73722,f773(f773(f302(f846(x73721)),x73723),f180(f855(f846(x73721),a841))))
% 191.21/191.75 [7411]~P1(f773(f773(f334(x74111),x74112),x74114))+P1(f773(f773(f334(x74111),x74112),f44(f855(x74111,a841),x74113)))+~P1(f773(f773(f334(f855(x74111,a841)),x74114),x74113))
% 191.21/191.75 [7413]~P85(x74131)+~P1(f773(f773(f232(a847),x74133),x74134))+P1(f773(f773(f279(x74131),f773(f773(f242(x74131),x74132),x74133)),f773(f773(f242(x74131),x74132),x74134)))
% 191.21/191.75 [7424]P31(x74241,x74242,x74243)+P1(f773(f773(f334(f846(x74241)),f820(x74242,x74244,x74241)),x74244))+~P1(f773(f773(f334(f846(x74241)),x74243),x74244))
% 191.21/191.75 [7443]~P74(x74431)+~P1(f773(f773(f233(x74431),x74433),x74434))+P1(f773(f773(f233(x74431),f773(f773(f82(x74431),x74432),x74433)),f773(f773(f82(x74431),x74432),x74434)))
% 191.21/191.75 [7444]~P80(x74441)+~P1(f773(f773(f233(x74441),x74443),x74444))+P1(f773(f773(f233(x74441),f773(f773(f82(x74441),x74442),x74443)),f773(f773(f82(x74441),x74442),x74444)))
% 191.21/191.75 [7445]~P74(x74451)+~P1(f773(f773(f233(x74451),x74452),x74454))+P1(f773(f773(f233(x74451),f773(f773(f82(x74451),x74452),x74453)),f773(f773(f82(x74451),x74454),x74453)))
% 191.21/191.75 [7446]~P80(x74461)+~P1(f773(f773(f233(x74461),x74462),x74464))+P1(f773(f773(f233(x74461),f773(f773(f82(x74461),x74462),x74463)),f773(f773(f82(x74461),x74464),x74463)))
% 191.21/191.75 [7447]~P74(x74471)+~P1(f773(f773(f232(x74471),x74473),x74474))+P1(f773(f773(f232(x74471),f773(f773(f82(x74471),x74472),x74473)),f773(f773(f82(x74471),x74472),x74474)))
% 191.21/191.75 [7448]~P78(x74481)+~P1(f773(f773(f232(x74481),x74483),x74484))+P1(f773(f773(f232(x74481),f773(f773(f82(x74481),x74482),x74483)),f773(f773(f82(x74481),x74482),x74484)))
% 191.21/191.75 [7449]~P74(x74491)+~P1(f773(f773(f232(x74491),x74492),x74494))+P1(f773(f773(f232(x74491),f773(f773(f82(x74491),x74492),x74493)),f773(f773(f82(x74491),x74494),x74493)))
% 191.21/191.75 [7450]~P78(x74501)+~P1(f773(f773(f232(x74501),x74502),x74504))+P1(f773(f773(f232(x74501),f773(f773(f82(x74501),x74502),x74503)),f773(f773(f82(x74501),x74504),x74503)))
% 191.21/191.75 [7451]~P111(x74511)+~P1(f773(f773(f279(x74511),x74513),x74514))+P1(f773(f773(f279(x74511),f773(f773(f83(x74511),x74512),x74513)),f773(f773(f83(x74511),x74512),x74514)))
% 191.21/191.75 [7452]~P111(x74521)+~P1(f773(f773(f279(x74521),x74522),x74524))+P1(f773(f773(f279(x74521),f773(f773(f83(x74521),x74522),x74523)),f773(f773(f83(x74521),x74524),x74523)))
% 191.21/191.75 [7453]~P85(x74531)+~P1(f773(f773(f279(x74531),x74532),x74534))+P1(f773(f773(f279(x74531),f773(f773(f242(x74531),x74532),x74533)),f773(f773(f242(x74531),x74534),x74533)))
% 191.21/191.75 [7462]~P135(x74621)+~P89(x74621)+E(f773(f773(f82(x74621),f773(f773(f83(x74621),x74622),f773(f106(x74621),x74623))),f773(f773(f83(x74621),x74624),f773(f106(x74621),x74623))),f773(f773(f83(x74621),f773(f773(f82(x74621),x74622),x74624)),f773(f106(x74621),x74623)))
% 191.21/191.75 [7463]~P121(x74631)+~P89(x74631)+E(f773(f773(f3(x74631),f773(f773(f83(x74631),x74632),f773(f106(x74631),x74633))),f773(f773(f83(x74631),x74634),f773(f106(x74631),x74633))),f773(f773(f83(x74631),f773(f773(f3(x74631),x74632),x74634)),f773(f106(x74631),x74633)))
% 191.21/191.75 [7499]~P66(x74991)+E(f773(f773(f82(x74991),f773(x74992,x74993)),f773(f773(f8(a847,x74991),x74992),f295(a847,f773(a114,x74993),x74994))),f773(f773(f8(a847,x74991),x74992),f295(a847,x74993,x74994)))+~P1(f773(f773(f232(a847),x74993),x74994))
% 191.21/191.75 [7510]~P29(x75102,x75101,x75103,f773(f158(x75102),x75104))+~P1(f773(f127(x75102),x75104))+P1(f773(f127(x75101),f773(f773(f143(x75102,x75101),x75103),x75104)))
% 191.21/191.75 [7559]~P1(f773(f773(f233(a847),x75592),x75594))+~P1(f773(f773(f233(a847),x75591),x75593))+P1(f773(f773(f233(a847),f773(f773(f82(a847),x75591),x75592)),f773(f773(f82(a847),x75593),x75594)))
% 191.21/191.75 [7562]~P1(f773(f773(f233(a1),x75621),x75623))+~P1(f773(f773(f232(a1),x75622),x75624))+P1(f773(f773(f233(a1),f773(f773(f82(a1),x75621),x75622)),f773(f773(f82(a1),x75623),x75624)))
% 191.21/191.75 [7563]~P1(f773(f773(f232(a847),x75632),x75634))+~P1(f773(f773(f232(a847),x75631),x75633))+P1(f773(f773(f232(a847),f773(f773(f82(a847),x75631),x75632)),f773(f773(f82(a847),x75633),x75634)))
% 191.21/191.75 [7564]~P1(f773(f773(f232(a847),x75642),x75644))+~P1(f773(f773(f232(a847),x75641),x75643))+P1(f773(f773(f232(a847),f773(f773(f83(a847),x75641),x75642)),f773(f773(f83(a847),x75643),x75644)))
% 191.21/191.75 [7614]P1(f773(f773(f334(x76141),x76142),x76143))+~P1(f773(f773(f334(x76141),x76142),f45(f855(x76141,a841),x76144)))+~P1(f773(f773(f334(f855(x76141,a841)),x76143),x76144))
% 191.21/191.75 [7630]~P1(f773(x76301,f724(x76301,x76303,x76302)))+P1(f773(x76301,f773(f773(f153(x76302),x76303),x76304)))+~P1(f773(f773(f233(a847),x76304),f773(f181(f848(x76302)),x76303)))
% 191.21/191.75 [7634]P1(f773(x76341,x76342))+~P1(f773(f773(f334(x76344),x76342),f773(f158(x76344),x76343)))+P1(f773(f773(f233(a847),f725(x76341,x76343,x76344)),f773(f181(f848(x76344)),x76343)))
% 191.21/191.75 [7653]~P1(f773(f773(f187(x76532),x76533),x76534))+~P1(f773(f773(f187(f35(x76531,x76532)),x76534),x76533))+P1(f773(f773(f187(f35(x76531,x76532)),x76533),x76533))
% 191.21/191.75 [7681]~P102(x76811)+~P1(f773(f773(f232(f855(x76812,x76811)),x76814),x76813))+~P1(f773(f773(f233(f855(x76812,x76811)),x76813),x76814))
% 191.21/191.75 [7724]~P1(f773(x77244,x77242))+~P1(f773(f773(f334(x77241),x77242),x77243))+P1(f773(f773(f334(x77241),x77242),f773(f773(f104(f855(x77241,a841)),x77243),f773(f256(x77241),x77244))))
% 191.21/191.75 [7873]~P1(f773(f773(f334(x78731),x78733),x78734))+~P1(f773(f773(f233(f855(x78731,a841)),x78732),x78734))+P1(f773(f773(f233(f855(x78731,a841)),x78732),f773(f773(f302(x78731),x78733),x78734)))
% 191.21/191.75 [7875]E(f773(f773(f104(f855(x78751,a841)),x78752),x78753),f180(f855(x78751,a841)))+~E(f773(f773(f104(f855(x78751,a841)),f44(f855(x78751,a841),x78754)),x78753),f180(f855(x78751,a841)))+~P1(f773(f773(f334(f855(x78751,a841)),x78752),x78754))
% 191.21/191.75 [7952]P1(f773(f773(f334(x79521),x79522),x79523))+~P1(f773(f773(f232(f855(x79521,a841)),x79523),f773(f773(f302(x79521),x79522),x79524)))+P1(f773(f773(f232(f855(x79521,a841)),x79523),x79524))
% 191.21/191.75 [7972]P1(f773(f773(f334(x79722),f724(x79721,x79723,x79722)),f773(f158(x79722),x79723)))+P1(f773(x79721,f773(f773(f153(x79722),x79723),x79724)))+~P1(f773(f773(f233(a847),x79724),f773(f181(f848(x79722)),x79723)))
% 191.21/191.75 [7980]~P1(f773(f773(f233(f855(x79801,a841)),x79802),x79804))+P1(f773(f773(f233(f855(x79801,a841)),x79802),x79803))+~P1(f773(f773(f233(f855(x79801,a841)),x79804),x79803))
% 191.21/191.75 [7981]~P1(f773(f773(f232(f855(x79811,a841)),x79812),x79814))+P1(f773(f773(f233(f855(x79811,a841)),x79812),x79813))+~P1(f773(f773(f233(f855(x79811,a841)),x79814),x79813))
% 191.21/191.75 [7982]~P1(f773(f773(f232(f855(x79821,a841)),x79824),x79823))+~P1(f773(f773(f233(f855(x79821,a841)),x79822),x79824))+P1(f773(f773(f233(f855(x79821,a841)),x79822),x79823))
% 191.21/191.75 [7983]~P1(f773(f773(f232(f855(x79831,a841)),x79832),x79834))+P1(f773(f773(f232(f855(x79831,a841)),x79832),x79833))+~P1(f773(f773(f232(f855(x79831,a841)),x79834),x79833))
% 191.21/191.75 [8019]~P1(f773(f773(f334(x80191),x80194),x80193))+~P1(f773(f773(f233(f855(x80191,a841)),x80192),f773(f773(f302(x80191),x80194),x80193)))+P1(f773(f773(f233(f855(x80191,a841)),x80192),x80193))
% 191.21/191.75 [8032]~P74(x80321)+P1(f773(f773(f233(x80321),x80322),x80323))+~P1(f773(f773(f233(x80321),f773(f773(f82(x80321),x80324),x80322)),f773(f773(f82(x80321),x80324),x80323)))
% 191.21/191.75 [8034]~P74(x80341)+P1(f773(f773(f233(x80341),x80342),x80343))+~P1(f773(f773(f233(x80341),f773(f773(f82(x80341),x80342),x80344)),f773(f773(f82(x80341),x80343),x80344)))
% 191.21/191.75 [8036]~P74(x80361)+P1(f773(f773(f232(x80361),x80362),x80363))+~P1(f773(f773(f232(x80361),f773(f773(f82(x80361),x80364),x80362)),f773(f773(f82(x80361),x80364),x80363)))
% 191.21/191.75 [8038]~P74(x80381)+P1(f773(f773(f232(x80381),x80382),x80383))+~P1(f773(f773(f232(x80381),f773(f773(f82(x80381),x80382),x80384)),f773(f773(f82(x80381),x80383),x80384)))
% 191.21/191.75 [8202]P1(f773(x82021,x82022))+~P1(f773(f773(f334(x82023),x82022),f773(f158(x82023),x82024)))+P1(f773(f773(f233(a847),f773(f181(f848(x82023)),f773(f126(x82023,x82021),x82024))),f773(f181(f848(x82023)),x82024)))
% 191.21/191.75 [8332]E(x83321,x83322)+P1(f773(f773(f187(x83323),x83321),f422(x83322,x83321,x83323,x83324)))+~P1(f773(f773(f187(f35(x83324,x83323)),x83321),x83322))
% 191.21/191.75 [8333]E(x83331,x83332)+P1(f773(f773(f187(x83333),x83331),f528(x83332,x83331,x83333,x83334)))+~P1(f773(f773(f187(f35(x83334,x83333)),x83331),x83332))
% 191.21/191.75 [8360]~P1(f773(x83604,x83602))+P1(f773(f773(f187(x83601),x83602),f422(x83603,x83602,x83601,x83604)))+~P1(f773(f773(f187(f35(x83604,x83601)),x83602),x83603))
% 191.21/191.75 [8361]~P1(f773(x83614,x83612))+P1(f773(f773(f187(x83611),x83612),f528(x83613,x83612,x83611,x83614)))+~P1(f773(f773(f187(f35(x83614,x83611)),x83612),x83613))
% 191.21/191.75 [8685]~P29(x86854,x86853,x86851,f239(f855(x86854,a841)))+E(f773(x86851,f523(x86852,x86851,x86853,x86854)),x86852)+~P1(f773(f773(f334(x86853),x86852),f773(f303(x86854,x86853,x86851),f239(f855(x86854,a841)))))
% 191.21/191.75 [8823]~P1(f773(f63(x88231),x88234))+P1(f773(f773(f334(x88231),f561(x88232,x88233,x88234,x88231)),x88234))+P1(f773(f63(f854(x88231,x88233)),f773(f773(f248(x88231,x88233),x88234),x88232)))
% 191.21/191.75 [8867]E(x88671,x88672)+P1(f773(f773(f187(f35(x88673,x88674)),f422(x88671,x88672,x88674,x88673)),x88671))+~P1(f773(f773(f187(f35(x88673,x88674)),x88672),x88671))
% 191.21/191.75 [8868]E(x88681,x88682)+P1(f773(f773(f187(f35(x88683,x88684)),f528(x88681,x88682,x88684,x88683)),x88681))+~P1(f773(f773(f187(f35(x88683,x88684)),x88682),x88681))
% 191.21/191.75 [8888]~P1(f773(x88881,x88884))+P1(f773(f773(f187(f35(x88881,x88882)),f422(x88883,x88884,x88882,x88881)),x88883))+~P1(f773(f773(f187(f35(x88881,x88882)),x88884),x88883))
% 191.21/191.75 [8889]~P1(f773(x88891,x88894))+P1(f773(f773(f187(f35(x88891,x88892)),f528(x88893,x88894,x88892,x88891)),x88893))+~P1(f773(f773(f187(f35(x88891,x88892)),x88894),x88893))
% 191.21/191.75 [9128]~P1(f773(f63(x91281),x91283))+~P1(f773(f63(x91282),f773(x91284,f561(x91284,x91282,x91283,x91281))))+P1(f773(f63(f854(x91281,x91282)),f773(f773(f248(x91281,x91282),x91283),x91284)))
% 191.21/191.75 [9142]~E(f773(f181(f848(x91424)),x91422),f773(f181(f848(x91424)),x91423))+P1(f773(f773(f334(f854(f848(x91424),f848(x91424))),f773(f773(f241(f848(x91424),f848(x91424)),x91423),x91422)),f147(x91424,x91421)))+P1(f773(f773(f233(a847),f732(x91421,x91422,x91423,x91424)),f773(f181(f848(x91424)),x91423)))
% 191.21/191.75 [9255]E(f773(f773(f159(x92551),f739(x92552,x92553,x92554,x92551)),x92553),f773(f773(f159(x92551),f739(x92552,x92553,x92554,x92551)),x92554))+~P1(f773(f773(f334(f854(f848(x92551),f848(x92551))),f773(f773(f241(f848(x92551),f848(x92551)),x92554),x92553)),f137(x92551,x92552)))+P1(f773(f773(f233(a847),f773(f181(f848(x92551)),x92554)),f773(f181(f848(x92551)),x92553)))
% 191.21/191.75 [9313]~P1(f773(f773(f233(a847),f2(a847)),x93133))+~P1(f773(f773(f233(a847),x93134),x93131))+P1(f773(f773(f233(a847),f773(f773(f82(a847),f773(f773(f83(a847),x93131),f52(a847,x93132,x93133))),x93134)),f773(f773(f83(a847),x93131),x93133)))
% 191.21/191.75 [9495]~P102(x94952)+~P1(f773(f773(f232(x94952),f773(x94953,f704(x94954,x94953,x94951,x94952))),f773(x94954,f704(x94954,x94953,x94951,x94952))))+P1(f773(f773(f232(f855(x94951,x94952)),x94953),x94954))
% 191.21/191.75 [9586]~P6(x95861)+E(f773(f773(f8(a847,x95861),f773(f773(f20(a847,x95861,x95861),f773(f773(f10(x95861,f855(x95861,x95861),a847),f3(x95861)),x95862)),f773(f773(f10(a847,x95861,a847),x95862),f773(f773(f9(a847,a847,a847),f82(a847)),f80(a847))))),f295(a847,x95863,x95864)),f773(f773(f3(x95861),f773(x95862,x95863)),f773(x95862,f773(f773(f82(a847),x95864),f80(a847)))))+~P1(f773(f773(f232(a847),x95863),x95864))
% 191.21/191.75 [6631]~P7(x66311)+E(f773(f773(f43(x66311),f773(f773(f83(x66311),x66312),x66313)),x66314),f773(f773(f83(x66311),x66312),f773(f773(f43(x66311),x66313),x66314)))+~P1(f773(f773(f279(x66311),x66314),x66313))
% 191.21/191.75 [6721]E(f773(f773(f125(x67211),x67212),x67213),x67214)+~E(x67213,f773(f773(f128(x67211),f773(f181(f848(x67211)),x67212)),x67214))+~E(f773(f773(f159(x67211),f773(f181(f848(x67211)),x67212)),x67214),x67212)
% 191.21/191.75 [6782]~P61(x67822)+E(x67821,f2(x67822))+E(f773(f773(f283(x67822),f773(f773(f242(x67822),x67823),x67824)),f773(f773(f242(x67822),x67821),x67824)),f773(f773(f242(x67822),f773(f773(f283(x67822),x67823),x67821)),x67824))
% 191.21/191.75 [6932]~P7(x69321)+E(f773(f773(f43(x69321),f773(f773(f83(x69321),x69322),x69323)),x69324),f773(f773(f83(x69321),f773(f773(f43(x69321),x69322),x69324)),x69323))+~P1(f773(f773(f279(x69321),x69324),x69322))
% 191.21/191.75 [6942]~P100(x69421)+~P1(f773(f773(f233(x69421),x69423),x69424))+P1(f773(f773(f233(x69421),f773(f773(f236(x69421),x69422),x69423)),x69424))
% 191.21/191.75 [6944]~P100(x69441)+~P1(f773(f773(f233(x69441),x69442),x69444))+P1(f773(f773(f233(x69441),f773(f773(f236(x69441),x69442),x69443)),x69444))
% 191.21/191.75 [6945]~P98(x69451)+~P1(f773(f773(f233(x69451),x69453),x69454))+P1(f773(f773(f233(x69451),f773(f773(f104(x69451),x69452),x69453)),x69454))
% 191.21/191.75 [6946]~P98(x69461)+~P1(f773(f773(f233(x69461),x69462),x69464))+P1(f773(f773(f233(x69461),f773(f773(f104(x69461),x69462),x69463)),x69464))
% 191.21/191.75 [6948]~P100(x69481)+~P1(f773(f773(f232(x69481),x69483),x69484))+P1(f773(f773(f232(x69481),f773(f773(f236(x69481),x69482),x69483)),x69484))
% 191.21/191.75 [6950]~P100(x69501)+~P1(f773(f773(f232(x69501),x69502),x69504))+P1(f773(f773(f232(x69501),f773(f773(f236(x69501),x69502),x69503)),x69504))
% 191.21/191.75 [6951]~P98(x69511)+~P1(f773(f773(f232(x69511),x69513),x69514))+P1(f773(f773(f232(x69511),f773(f773(f104(x69511),x69512),x69513)),x69514))
% 191.21/191.75 [6952]~P98(x69521)+~P1(f773(f773(f232(x69521),x69522),x69524))+P1(f773(f773(f232(x69521),f773(f773(f104(x69521),x69522),x69523)),x69524))
% 191.21/191.75 [6969]~P1(f773(x69693,x69694))+~P1(f773(x69692,x69694))+P1(f773(f773(f773(f104(f855(x69691,a841)),x69692),x69693),x69694))
% 191.21/191.75 [7001]~E(f773(f181(f848(x70011)),x70013),f773(f181(f848(x70012)),x70014))+~P1(f773(f127(x70011),x70013))+E(f169(x70011,x70012,f166(x70011,x70012,f773(f773(f167(x70011,x70012),x70013),x70014))),f773(f158(x70011),x70013))
% 191.21/191.75 [7095]P28(x70951,x70952,x70953)+~P28(x70951,x70954,x70953)+~P1(f773(f773(f232(f855(f846(x70951),a841)),x70954),x70952))
% 191.21/191.75 [7096]P28(x70961,x70962,x70963)+~P28(x70961,x70962,x70964)+~P1(f773(f773(f232(f855(f846(x70961),a841)),x70963),x70964))
% 191.21/191.75 [7234]~P7(x72341)+E(f773(f773(f43(x72341),f773(f773(f242(x72341),x72342),x72343)),f773(f773(f242(x72341),x72344),x72343)),f773(f773(f242(x72341),f773(f773(f43(x72341),x72342),x72344)),x72343))+~P1(f773(f773(f279(x72341),x72344),x72342))
% 191.21/191.75 [7489]~P66(x74891)+E(f773(f773(f82(x74891),f773(x74892,x74893)),f773(f773(f8(a847,x74891),x74892),f773(f294(a847,f773(a114,x74893)),x74894))),f773(f773(f8(a847,x74891),x74892),f773(f294(a847,x74893),x74894)))+~P1(f773(f773(f233(a847),x74893),x74894))
% 191.21/191.75 [7517]~P100(x75171)+P1(f773(f773(f233(x75171),x75172),x75173))+~P1(f773(f773(f233(x75171),f773(f773(f179(x75171),x75174),x75172)),x75173))
% 191.21/191.75 [7518]~P100(x75181)+P1(f773(f773(f233(x75181),x75182),x75183))+~P1(f773(f773(f233(x75181),f773(f773(f179(x75181),x75182),x75184)),x75183))
% 191.21/191.75 [7520]~P100(x75201)+P1(f773(f773(f232(x75201),x75202),x75203))+~P1(f773(f773(f232(x75201),f773(f773(f179(x75201),x75204),x75202)),x75203))
% 191.21/191.75 [7522]~P100(x75221)+P1(f773(f773(f232(x75221),x75222),x75223))+~P1(f773(f773(f232(x75221),f773(f773(f179(x75221),x75222),x75224)),x75223))
% 191.21/191.75 [7524]~P92(x75241)+P1(f773(f773(f232(x75241),x75242),x75243))+~P1(f773(f773(f232(x75241),f773(f773(f103(x75241),x75244),x75242)),x75243))
% 191.21/191.75 [7526]~P92(x75261)+P1(f773(f773(f232(x75261),x75262),x75263))+~P1(f773(f773(f232(x75261),f773(f773(f103(x75261),x75262),x75264)),x75263))
% 191.21/191.75 [7527]~P85(x75271)+P1(f773(f773(f279(x75271),x75272),x75273))+~P1(f773(f773(f279(x75271),f773(f773(f83(x75271),x75274),x75272)),x75273))
% 191.21/191.75 [7528]~P85(x75281)+P1(f773(f773(f279(x75281),x75282),x75283))+~P1(f773(f773(f279(x75281),f773(f773(f83(x75281),x75282),x75284)),x75283))
% 191.21/191.75 [7606]~P1(f773(f773(f334(x76061),x76062),x76064))+P1(f773(f773(f334(x76061),x76062),x76063))+P1(f773(f773(f334(x76061),x76062),f773(f773(f3(f855(x76061,a841)),x76064),x76063)))
% 191.21/191.75 [7686]P1(f773(x76861,x76862))+P1(f773(x76863,x76862))+~P1(f773(f773(f773(f103(f855(x76864,a841)),x76863),x76861),x76862))
% 191.21/191.75 [7696]~P1(f773(f773(f334(x76961),x76962),x76964))+~P1(f773(f773(f334(x76961),x76962),x76963))+P1(f773(f773(f334(x76961),x76962),f773(f773(f104(f855(x76961,a841)),x76963),x76964)))
% 191.21/191.75 [7752]~P100(x77521)+~P1(f773(f63(x77521),x77524))+E(f773(f773(f66(x77521,x77521,f236(x77521)),x77522),f773(f773(f302(x77521),x77523),x77524)),f773(f773(f236(x77521),x77523),f773(f773(f66(x77521,x77521,f236(x77521)),x77522),x77524)))
% 191.21/191.75 [7753]~P100(x77531)+~P1(f773(f63(x77531),x77534))+E(f773(f773(f66(x77531,x77531,f179(x77531)),x77532),f773(f773(f302(x77531),x77533),x77534)),f773(f773(f179(x77531),x77533),f773(f773(f66(x77531,x77531,f179(x77531)),x77532),x77534)))
% 191.21/191.75 [7754]~P92(x77541)+~P1(f773(f63(x77541),x77544))+E(f773(f773(f66(x77541,x77541,f103(x77541)),x77542),f773(f773(f302(x77541),x77543),x77544)),f773(f773(f103(x77541),x77543),f773(f773(f66(x77541,x77541,f103(x77541)),x77542),x77544)))
% 191.21/191.75 [7755]~P98(x77551)+~P1(f773(f63(x77551),x77554))+E(f773(f773(f66(x77551,x77551,f104(x77551)),x77552),f773(f773(f302(x77551),x77553),x77554)),f773(f773(f104(x77551),x77553),f773(f773(f66(x77551,x77551,f104(x77551)),x77552),x77554)))
% 191.21/191.75 [7757]~P135(x77571)+~P89(x77571)+E(f773(f773(f82(x77571),f773(f773(f83(x77571),f773(f106(x77571),x77572)),x77573)),f773(f773(f83(x77571),f773(f106(x77571),x77572)),x77574)),f773(f773(f83(x77571),f773(f106(x77571),x77572)),f773(f773(f82(x77571),x77573),x77574)))
% 191.21/191.75 [7758]~P121(x77581)+~P89(x77581)+E(f773(f773(f3(x77581),f773(f773(f83(x77581),f773(f106(x77581),x77582)),x77583)),f773(f773(f83(x77581),f773(f106(x77581),x77582)),x77584)),f773(f773(f83(x77581),f773(f106(x77581),x77582)),f773(f773(f3(x77581),x77583),x77584)))
% 191.21/191.75 [7871]E(x78711,x78712)+P1(f773(f773(f334(x78713),x78711),f773(f158(x78713),x78714)))+~P1(f773(f773(f334(x78713),x78711),f773(f158(x78713),f773(f773(f140(x78713),x78712),x78714))))
% 191.21/191.75 [8042]P53(x80421,x80422,x80423)+~P53(x80421,x80422,x80424)+~P1(f773(f773(f232(f855(f854(x80421,x80422),a841)),x80423),x80424))
% 191.21/191.75 [8085]P1(f773(f773(f334(x80851),x80852),x80853))+P1(f773(f773(f334(x80851),x80852),x80854))+~P1(f773(f773(f334(x80851),x80852),f773(f773(f103(f855(x80851,a841)),x80854),x80853)))
% 191.21/191.75 [8096]~P47(x80961,x80964,x80963)+~P1(f773(f773(f334(x80961),x80962),x80964))+P1(f773(f773(f334(f854(x80961,x80961)),f773(f773(f241(x80961,x80961),x80962),x80962)),x80963))
% 191.21/191.75 [8108]~P1(f773(f63(x81082),x81084))+~P1(f773(f63(x81081),x81083))+P1(f773(f63(f854(x81081,x81082)),f773(f773(f248(x81081,x81082),x81083),f773(f18(f855(x81082,a841),x81081),x81084))))
% 191.21/191.75 [8109]~P1(f773(f773(f334(x81091),x81092),x81094))+~P1(f773(f773(f232(f855(x81091,a841)),x81093),x81094))+P1(f773(f773(f232(f855(x81091,a841)),f773(f773(f302(x81091),x81092),x81093)),x81094))
% 191.21/191.75 [8117]~P2(x81172)+~P70(x81172)+E(f773(f773(f11(x81171,x81172),f773(f773(f10(a847,x81172,x81171),f102(x81172)),x81173)),x81174),f773(f102(x81172),f773(f773(f11(x81171,a847),x81173),x81174)))
% 191.21/191.75 [8118]~P70(x81182)+~P133(x81182)+E(f773(f773(f11(x81181,x81182),f773(f773(f10(a1,x81182,x81181),f105(x81182)),x81183)),x81184),f773(f105(x81182),f773(f773(f11(x81181,a1),x81183),x81184)))
% 191.21/191.75 [8144]E(f773(f773(f3(f855(x81441,a841)),x81442),f773(f773(f3(f855(x81441,a841)),x81443),x81444)),x81444)+~P1(f773(f773(f232(f855(x81441,a841)),x81442),x81443))+~P1(f773(f773(f232(f855(x81441,a841)),x81444),x81442))
% 191.21/191.75 [8236]~P1(f773(f63(x82361),x82364))+E(f773(f773(f3(a847),f773(f773(f8(x82361,a847),x82362),x82363)),f773(f773(f8(x82361,a847),x82362),x82364)),f773(f773(f8(x82361,a847),x82362),f773(f773(f3(f855(x82361,a841)),x82363),x82364)))+~P1(f773(f773(f232(f855(x82361,a841)),x82364),x82363))
% 191.21/191.75 [8393]~P12(x83931,x83934,x83933)+~P1(f773(f773(f334(x83931),x83932),x83934))+P1(f773(f773(f334(x83931),x83932),f773(f277(x83931,x83931,x83933),f773(f773(f302(x83931),x83932),f180(f855(x83931,a841))))))
% 191.21/191.75 [8456]~P1(f773(f773(f232(f855(x84561,a841)),x84562),x84563))+~P1(f773(f773(f232(f855(x84561,a841)),x84562),x84564))+P1(f773(f773(f232(f855(x84561,a841)),x84562),f773(f773(f104(f855(x84561,a841)),x84563),x84564)))
% 191.21/191.75 [8548]E(x85481,f180(f855(x85482,a841)))+P1(f773(f63(x85483),x85484))+~P1(f773(f63(f854(x85483,x85482)),f773(f773(f248(x85483,x85482),x85484),f773(f18(f855(x85482,a841),x85483),x85481))))
% 191.21/191.75 [8549]E(x85491,f180(f855(x85492,a841)))+P1(f773(f63(x85493),x85494))+~P1(f773(f63(f854(x85492,x85493)),f773(f773(f248(x85492,x85493),x85491),f773(f18(f855(x85493,a841),x85492),x85494))))
% 191.21/191.75 [8607]P1(f773(f773(f334(x86071),x86072),f322(x86071,x86073)))+~P1(f773(f773(f334(x86071),x86074),f322(x86071,x86073)))+~P1(f773(f773(f334(f854(x86071,x86071)),f773(f773(f241(x86071,x86071),x86072),x86074)),x86073))
% 191.21/191.75 [8659]~P36(x86591,x86594)+P1(f773(f773(f334(f854(x86591,x86591)),f773(f773(f241(x86591,x86591),x86593),x86592)),f300(x86591,x86594)))+P36(x86591,f773(f773(f302(f854(x86591,x86591)),f773(f773(f241(x86591,x86591),x86592),x86593)),x86594))
% 191.21/191.75 [8660]~P56(x86601,x86604)+P1(f773(f773(f334(f854(x86601,x86601)),f773(f773(f241(x86601,x86601),x86603),x86602)),f300(x86601,x86604)))+P56(x86601,f773(f773(f302(f854(x86601,x86601)),f773(f773(f241(x86601,x86601),x86602),x86603)),x86604))
% 191.21/191.75 [8731]~E(x87312,x87313)+~P1(f773(f773(f334(x87311),x87312),f773(f158(x87311),x87314)))+P1(f773(f773(f334(f854(x87311,x87311)),f773(f773(f241(x87311,x87311),x87312),x87313)),f773(f158(f854(x87311,x87311)),f773(f773(f167(x87311,x87311),x87314),x87314))))
% 191.21/191.75 [8803]~E(x88033,x88034)+P1(f773(f773(f251(x88031,x88031,a841),a330),x88032))+~P1(f773(f773(f334(f854(x88031,x88031)),x88032),f773(f158(f854(x88031,x88031)),f773(f773(f167(x88031,x88031),x88033),x88034))))
% 191.21/191.75 [8839]P1(f773(f773(f334(f854(f848(x88391),f848(x88391))),f773(f773(f241(f848(x88391),f848(x88391)),x88392),x88393)),f137(x88391,x88394)))+~E(f773(f773(f159(x88391),f773(f181(f848(x88391)),x88392)),x88393),x88392)+~P1(f773(f773(f233(a847),f773(f181(f848(x88391)),x88392)),f773(f181(f848(x88391)),x88393)))
% 191.21/191.75 [8933]~P1(f773(f63(x89331),x89334))+P1(f773(f773(f334(x89331),f412(x89332,x89333,x89334,x89331)),x89334))+P1(f773(f63(x89333),f773(f773(f46(x89331,f855(x89333,a841)),x89334),x89332)))
% 191.21/191.75 [8934]~P1(f773(f63(x89341),x89344))+P1(f773(f773(f334(x89341),f608(x89342,x89343,x89344,x89341)),x89344))+P1(f773(f63(x89343),f773(f773(f46(x89341,f855(x89343,a841)),x89344),x89342)))
% 191.21/191.75 [9014]P1(f773(f773(f334(f854(x90141,x90141)),x90142),f773(f773(f281(x90141,x90141,x90141),x90143),f300(x90141,x90143))))+~P1(f773(f773(f233(a847),f2(a847)),x90144))+~P1(f773(f773(f334(f854(x90141,x90141)),x90142),f773(f773(f173(f854(x90141,x90141),a841),x90144),x90143)))
% 191.21/191.75 [9022]~P36(x90221,x90222)+~P1(f773(f773(f334(f854(x90221,x90221)),f773(f773(f241(x90221,x90221),x90224),x90223)),x90222))+~P1(f773(f773(f334(f854(x90221,x90221)),f773(f773(f241(x90221,x90221),x90223),x90224)),x90222))
% 191.21/191.75 [9138]~P1(f773(f63(x91381),x91384))+E(f773(f773(f8(x91381,a847),f773(f773(f10(f855(x91382,a841),a847,x91381),f42(x91382)),x91383)),x91384),f773(f42(f854(x91381,x91382)),f773(f773(f248(x91381,x91382),x91384),x91383)))+P1(f773(f773(f334(x91381),f562(x91383,x91382,x91384,x91381)),x91384))
% 191.21/191.75 [9140]~P1(f773(f127(x91401),x91402))+P1(f773(f127(x91401),f773(f773(f148(x91401,x91402),x91403),x91404)))+P1(f773(f773(f334(x91401),x91404),f773(f773(f3(f855(x91401,a841)),f773(f158(x91401),x91402)),f773(f773(f302(x91401),f773(f773(f153(x91401),x91402),x91403)),f180(f855(x91401,a841))))))
% 191.21/191.75 [9149]~P1(f773(f63(x91492),x91493))+~P1(f773(f63(x91491),f773(x91494,f412(x91494,x91491,x91493,x91492))))+P1(f773(f63(x91491),f773(f773(f46(x91492,f855(x91491,a841)),x91493),x91494)))
% 191.21/191.75 [9150]~P1(f773(f63(x91502),x91503))+~P1(f773(f63(x91501),f773(x91504,f608(x91504,x91501,x91503,x91502))))+P1(f773(f63(x91501),f773(f773(f46(x91502,f855(x91501,a841)),x91503),x91504)))
% 191.21/191.75 [9215]~P1(f773(f773(f334(f854(x92151,x92151)),x92152),f773(f773(f281(x92151,x92151,x92151),x92154),f300(x92151,x92154))))+P1(f773(f773(f334(f854(x92151,x92151)),x92152),f773(f773(f281(x92151,x92151,x92151),x92153),f300(x92151,x92153))))+~P1(f773(f773(f232(f855(f854(x92151,x92151),a841)),x92154),x92153))
% 191.21/191.75 [9223]E(f773(f773(f159(x92231),f739(x92234,x92233,x92232,x92231)),x92233),f773(f773(f159(x92231),f739(x92234,x92233,x92232,x92231)),x92232))+~P1(f773(f773(f334(f854(f848(x92231),f848(x92231))),f773(f773(f241(f848(x92231),f848(x92231)),x92232),x92233)),f137(x92231,x92234)))+E(f773(f773(f159(x92231),f773(f181(f848(x92231)),x92232)),x92233),x92232)
% 191.21/191.75 [9239]~P1(f773(f63(x92391),x92394))+E(f773(f773(f8(x92391,a847),f773(f773(f10(f855(x92392,a841),a847,x92391),f42(x92392)),x92393)),x92394),f773(f42(f854(x92391,x92392)),f773(f773(f248(x92391,x92392),x92394),x92393)))+~P1(f773(f63(x92392),f773(x92393,f562(x92393,x92392,x92394,x92391))))
% 191.21/191.75 [9244]~E(f773(f181(f848(x92441)),x92443),f773(f181(f848(x92441)),x92442))+P1(f773(f773(f334(f854(f848(x92441),f848(x92441))),f773(f773(f241(f848(x92441),f848(x92441)),x92442),x92443)),f147(x92441,x92444)))+P1(f773(f773(f334(f854(x92441,x92441)),f716(x92444,x92443,x92442,x92441)),f773(f158(f854(x92441,x92441)),f773(f773(f167(x92441,x92441),x92442),x92443))))
% 191.21/191.75 [9326]~P1(f773(f773(f334(f854(f848(x93261),f848(x93261))),f773(f773(f241(f848(x93261),f848(x93261)),x93262),x93263)),f137(x93261,x93264)))+E(f773(f773(f159(x93261),f773(f181(f848(x93261)),x93262)),x93263),x93262)+P1(f773(f773(f233(a847),f739(x93264,x93263,x93262,x93261)),f773(f773(f236(a847),f773(f181(f848(x93261)),x93262)),f773(f181(f848(x93261)),x93263))))
% 191.21/191.75 [9345]~P1(f773(f773(f334(f854(f848(x93451),f848(x93451))),f773(f773(f241(f848(x93451),f848(x93451)),x93452),x93453)),f137(x93451,x93454)))+P1(f773(f773(f233(a847),f773(f181(f848(x93451)),x93452)),f773(f181(f848(x93451)),x93453)))+P1(f773(f773(f233(a847),f739(x93454,x93453,x93452,x93451)),f773(f773(f236(a847),f773(f181(f848(x93451)),x93452)),f773(f181(f848(x93451)),x93453))))
% 191.21/191.75 [9621]~P1(f773(f773(f773(x96211,f707(x96211,x96214,x96213,x96212)),f710(x96211,x96214,x96213,x96212)),f711(x96211,x96214,x96213,x96212)))+P1(f773(f773(f773(x96211,x96212),x96213),x96214))+~P1(f773(f321(f854(f855(a1,f851(f848(a839))),f854(a1,a1)),a311),f773(f773(f241(f855(a1,f851(f848(a839))),f854(a1,a1)),x96212),f773(f773(f241(a1,a1),x96213),x96214))))
% 191.21/191.75 [9682]P1(f773(f773(f773(x96821,x96822),x96823),x96824))+P1(f773(f321(f854(f855(a1,f851(f848(a839))),f854(a1,a1)),a311),f773(f773(f241(f855(a1,f851(f848(a839))),f854(a1,a1)),f707(x96821,x96824,x96823,x96822)),f773(f773(f241(a1,a1),f710(x96821,x96824,x96823,x96822)),f711(x96821,x96824,x96823,x96822)))))+~P1(f773(f321(f854(f855(a1,f851(f848(a839))),f854(a1,a1)),a311),f773(f773(f241(f855(a1,f851(f848(a839))),f854(a1,a1)),x96822),f773(f773(f241(a1,a1),x96823),x96824))))
% 191.21/191.75 [9720]~P1(f773(f773(f334(f854(f848(x97201),f848(x97201))),f773(f773(f241(f848(x97201),f848(x97201)),x97202),x97203)),f137(x97201,x97204)))+E(f773(f773(f159(x97201),f773(f181(f848(x97201)),x97202)),x97203),x97202)+P1(f773(f773(f334(f854(x97201,x97201)),f773(f773(f241(x97201,x97201),f773(f773(f153(x97201),x97202),f739(x97204,x97203,x97202,x97201))),f773(f773(f153(x97201),x97203),f739(x97204,x97203,x97202,x97201)))),x97204))
% 191.21/191.75 [9723]~P1(f773(f773(f334(f854(f848(x97231),f848(x97231))),f773(f773(f241(f848(x97231),f848(x97231)),x97232),x97233)),f137(x97231,x97234)))+P1(f773(f773(f233(a847),f773(f181(f848(x97231)),x97232)),f773(f181(f848(x97231)),x97233)))+P1(f773(f773(f334(f854(x97231,x97231)),f773(f773(f241(x97231,x97231),f773(f773(f153(x97231),x97232),f739(x97234,x97233,x97232,x97231))),f773(f773(f153(x97231),x97233),f739(x97234,x97233,x97232,x97231)))),x97234))
% 191.21/191.75 [9793]~E(f773(f181(f848(x97931)),x97932),f773(f181(f848(x97931)),x97933))+P1(f773(f773(f334(f854(f848(x97931),f848(x97931))),f773(f773(f241(f848(x97931),f848(x97931)),x97932),x97933)),f147(x97931,x97934)))+~P1(f773(f773(f334(f854(x97931,x97931)),f773(f773(f241(x97931,x97931),f773(f773(f153(x97931),x97932),f732(x97934,x97933,x97932,x97931))),f773(f773(f153(x97931),x97933),f732(x97934,x97933,x97932,x97931)))),x97934))
% 191.21/191.75 [9933]~P66(x99331)+~P1(f773(f63(x99332),x99334))+E(f773(f155(x99331),f773(f773(f143(x99332,x99331),x99333),f92(f848(x99332),f773(f773(f20(f848(x99332),a841,a841),f773(f773(f10(a841,f855(a841,a841),f848(x99332)),a331),f773(f773(f9(f848(x99332),f855(x99332,a841),a841),f773(f773(f10(f855(x99332,a841),f855(f855(x99332,a841),a841),f848(x99332)),a330),f158(x99332))),x99334))),f127(x99332))))),f225(x99332,x99331,x99333,x99334))
% 191.21/191.75 [7325]~P60(x73252)+E(x73251,f2(x73252))+E(f773(f773(f283(x73252),f773(f773(f82(x73252),x73253),f773(f773(f83(x73252),x73254),x73251))),x73251),f773(f773(f82(x73252),x73254),f773(f773(f283(x73252),x73253),x73251)))
% 191.21/191.75 [7326]~P7(x73262)+E(x73261,f2(x73262))+E(f773(f773(f43(x73262),f773(f773(f82(x73262),x73263),f773(f773(f83(x73262),x73264),x73261))),x73261),f773(f773(f82(x73262),x73264),f773(f773(f43(x73262),x73263),x73261)))
% 191.21/191.75 [7327]~P7(x73272)+E(x73271,f2(x73272))+E(f773(f773(f43(x73272),f773(f773(f82(x73272),x73273),f773(f773(f83(x73272),x73271),x73274))),x73271),f773(f773(f82(x73272),x73274),f773(f773(f43(x73272),x73273),x73271)))
% 191.21/191.75 [7568]~P60(x75682)+E(x75681,f2(x75682))+E(f773(f773(f283(x75682),f773(f773(f82(x75682),x75683),f773(f773(f83(x75682),x75684),x75681))),x75681),f773(f773(f82(x75682),f773(f773(f283(x75682),x75683),x75681)),x75684))
% 191.21/191.75 [7569]~P61(x75692)+E(x75691,f2(x75692))+E(f773(f773(f283(x75692),f773(f773(f82(x75692),x75693),f773(f773(f83(x75692),x75691),x75694))),x75691),f773(f773(f82(x75692),f773(f773(f283(x75692),x75693),x75691)),x75694))
% 191.21/191.75 [7570]~P61(x75702)+E(x75701,f2(x75702))+E(f773(f773(f283(x75702),f773(f773(f3(x75702),x75703),f773(f773(f83(x75702),x75701),x75704))),x75701),f773(f773(f3(x75702),f773(f773(f283(x75702),x75703),x75701)),x75704))
% 191.21/191.75 [8621]~E(f773(f773(f281(x86211,x86211,x86211),x86212),x86214),f180(f855(f854(x86211,x86211),a841)))+~E(f773(f773(f281(x86211,x86211,x86211),x86212),x86213),f180(f855(f854(x86211,x86211),a841)))+E(f773(f773(f281(x86211,x86211,x86211),x86212),f773(f773(f103(f855(f854(x86211,x86211),a841)),x86213),x86214)),f180(f855(f854(x86211,x86211),a841)))
% 191.21/191.75 [8732]~P1(f773(f773(f232(f855(x87321,a841)),x87323),x87324))+~P1(f773(f773(f232(f855(x87321,a841)),x87322),x87324))+P1(f773(f773(f232(f855(x87321,a841)),f773(f773(f103(f855(x87321,a841)),x87322),x87323)),x87324))
% 191.21/191.75 [9072]~P1(f773(f63(x90721),x90724))+~P1(f773(f63(x90721),x90723))+E(f773(f773(f3(a847),f773(f773(f82(a847),f773(f773(f8(x90721,a847),x90722),x90723)),f773(f773(f8(x90721,a847),x90722),x90724))),f773(f773(f8(x90721,a847),x90722),f773(f773(f104(f855(x90721,a841)),x90723),x90724))),f773(f773(f8(x90721,a847),x90722),f773(f773(f103(f855(x90721,a841)),x90723),x90724)))
% 191.21/191.75 [9147]~P1(f773(f773(f334(x91471),x91473),x91472))+~P1(f773(f773(f232(f855(x91471,a841)),x91472),f773(f773(f302(x91471),x91473),x91474)))+P1(f773(f773(f232(f855(x91471,a841)),f773(f773(f3(f855(x91471,a841)),x91472),f773(f773(f302(x91471),x91473),f180(f855(x91471,a841))))),x91474))
% 191.21/191.75 [9298]~P1(f773(f773(f334(x92981),x92983),x92982))+P1(f773(f773(f232(f855(x92981,a841)),x92982),f773(f773(f302(x92981),x92983),x92984)))+~P1(f773(f773(f232(f855(x92981,a841)),f773(f773(f3(f855(x92981,a841)),x92982),f773(f773(f302(x92981),x92983),f180(f855(x92981,a841))))),x92984))
% 191.21/191.75 [9383]~P1(f773(f773(f233(a847),x93832),x93834))+~P1(f773(f773(f232(a847),x93831),x93833))+P1(f773(f773(f334(f854(f854(a847,a847),f854(a847,a847))),f773(f773(f241(f854(a847,a847),f854(a847,a847)),f773(f773(f241(a847,a847),x93831),x93832)),f773(f773(f241(a847,a847),x93833),x93834))),a40))
% 191.21/191.75 [9384]~P1(f773(f773(f232(a847),x93842),x93844))+~P1(f773(f773(f232(a847),x93841),x93843))+P1(f773(f773(f334(f854(f854(a847,a847),f854(a847,a847))),f773(f773(f241(f854(a847,a847),f854(a847,a847)),f773(f773(f241(a847,a847),x93841),x93842)),f773(f773(f241(a847,a847),x93843),x93844))),a72))
% 191.21/191.75 [9758]~P29(x97581,f855(f855(x97581,a841),a841),f773(f773(f9(x97581,f855(f854(x97581,x97581),a841),f855(f855(x97581,a841),a841)),f773(f773(f10(f855(x97581,a841),f855(f855(f854(x97581,x97581),a841),f855(f855(x97581,a841),a841)),x97581),f61(x97581)),f773(f773(f9(x97581,f855(x97581,a841),f855(x97581,a841)),f302(x97581)),f180(f855(x97581,a841))))),x97583),x97582)+~P1(f773(f773(f334(x97581),x97584),x97582))+E(f773(f773(f3(f855(f855(x97581,a841),a841)),f773(f773(f61(x97581),x97582),x97583)),f773(f773(f61(x97581),f773(f773(f302(x97581),x97584),f180(f855(x97581,a841)))),x97583)),f773(f773(f61(x97581),f773(f773(f3(f855(x97581,a841)),x97582),f773(f773(f302(x97581),x97584),f180(f855(x97581,a841))))),x97583))
% 191.21/191.75 [9897]~P47(x98971,x98972,x98974)+~P1(f773(f773(f334(f854(x98971,x98971)),x98973),x98974))+P1(f773(f773(f251(x98971,x98971,a841),f773(f773(f9(x98971,f855(x98971,a841),f855(x98971,a841)),f773(f773(f10(f855(a841,a841),f855(f855(x98971,a841),f855(x98971,a841)),x98971),f10(a841,a841,x98971)),f773(f773(f10(a841,f855(a841,a841),x98971),a331),f773(f773(f9(x98971,f855(x98971,a841),a841),f334(x98971)),x98972)))),f773(f773(f9(x98971,f855(x98971,a841),a841),f334(x98971)),x98972))),x98973))
% 191.21/191.75 [9907]P1(f773(f63(x99071),x99072))+~P1(f773(f63(x99073),f773(f303(x99071,x99073,x99074),x99072)))+~P1(f773(f63(x99071),f773(f256(x99071),f773(f773(f20(x99071,a841,a841),f773(f773(f10(a841,f855(a841,a841),x99071),a331),f773(f773(f9(x99071,f855(x99071,a841),a841),f334(x99071)),x99072))),f773(f773(f9(x99071,x99073,a841),f773(f773(f10(x99073,f855(x99073,a841),x99071),a330),x99074)),f773(x99074,f599(x99074,x99073,x99072,x99071)))))))
% 191.21/191.75 [8025]~P61(x80252)+E(x80251,f2(x80252))+E(f773(f773(f283(x80252),f773(f773(f82(x80252),f773(f773(f83(x80252),x80251),x80253)),x80254)),x80251),f773(f773(f82(x80252),x80253),f773(f773(f283(x80252),x80254),x80251)))
% 191.21/191.75 [8026]~P61(x80262)+E(x80261,f2(x80262))+E(f773(f773(f283(x80262),f773(f773(f3(x80262),f773(f773(f83(x80262),x80261),x80263)),x80264)),x80261),f773(f773(f3(x80262),x80263),f773(f773(f283(x80262),x80264),x80261)))
% 191.21/191.75 [8866]~E(f773(f773(f281(x88661,x88661,x88661),x88663),x88664),f180(f855(f854(x88661,x88661),a841)))+~E(f773(f773(f281(x88661,x88661,x88661),x88662),x88664),f180(f855(f854(x88661,x88661),a841)))+E(f773(f773(f281(x88661,x88661,x88661),f773(f773(f103(f855(f854(x88661,x88661),a841)),x88662),x88663)),x88664),f180(f855(f854(x88661,x88661),a841)))
% 191.21/191.75 [9841]~P139(x98411)+~P139(x98412)+E(f773(f773(f310(x98411),f773(f773(f9(x98411,a101,f851(f848(a839))),f773(f773(f10(f855(x98412,f851(f848(a839))),f855(a101,f851(f848(a839))),x98411),f310(x98412)),f773(f773(f10(f855(x98412,f854(x98411,x98412)),f855(x98412,f851(f848(a839))),x98411),f773(f10(f854(x98411,x98412),f851(f848(a839)),x98412),x98413)),f241(x98411,x98412)))),x98414)),x98414),f773(f773(f310(f854(x98411,x98412)),x98413),x98414))
% 191.21/191.75 [9833]P1(f773(x98331,f585(x98332,x98333,x98331,x98334)))+~P1(f773(f63(x98334),f773(f256(x98334),x98331)))+P1(f773(f63(x98333),f773(f256(x98333),f773(f773(f10(f855(x98334,a841),a841,x98333),f89(x98334)),f773(f773(f10(f855(x98334,a841),f855(x98334,a841),x98333),f773(f20(x98334,a841,a841),f773(f773(f10(a841,f855(a841,a841),x98334),a331),x98331))),x98332)))))
% 191.21/191.75 [9854]~P1(f773(f63(x98542),f773(f256(x98542),x98543)))+~P1(f773(f63(x98541),f773(f256(x98541),f773(f773(f9(x98541,x98542,a841),x98544),f585(x98544,x98541,x98543,x98542)))))+P1(f773(f63(x98541),f773(f256(x98541),f773(f773(f10(f855(x98542,a841),a841,x98541),f89(x98542)),f773(f773(f10(f855(x98542,a841),f855(x98542,a841),x98541),f773(f20(x98542,a841,a841),f773(f773(f10(a841,f855(a841,a841),x98542),a331),x98543))),x98544)))))
% 191.21/191.75 [5708]~E(x57085,x57082)+P39(f35(x57081,x57083),x57082,x57084,x57085)+P1(f773(x57081,x57082))
% 191.21/191.75 [6276]E(x62761,x62762)+~P39(f35(x62763,x62764),x62761,x62765,x62762)+P1(f773(x62763,x62761))
% 191.21/191.75 [7831]~P39(x78312,x78313,x78314,x78315)+~P39(f35(x78311,x78312),x78315,x78314,x78313)+P39(f35(x78311,x78312),x78313,x78314,x78313)
% 191.21/191.75 [8988]E(x89881,x89882)+~P39(f35(x89885,x89883),x89881,x89884,x89882)+P39(x89883,x89881,x89884,f810(x89882,x89884,x89881,x89883,x89885))
% 191.21/191.75 [8989]E(x89891,x89892)+~P39(f35(x89895,x89893),x89891,x89894,x89892)+P39(x89893,x89891,x89894,f359(x89892,x89894,x89891,x89893,x89895))
% 191.21/191.75 [8991]E(x89911,x89912)+P39(f35(x89913,x89914),f810(x89911,x89915,x89912,x89914,x89913),x89915,x89911)+~P39(f35(x89913,x89914),x89912,x89915,x89911)
% 191.21/191.75 [8992]E(x89921,x89922)+P39(f35(x89923,x89924),f359(x89921,x89925,x89922,x89924,x89923),x89925,x89921)+~P39(f35(x89923,x89924),x89922,x89925,x89921)
% 191.21/191.75 [8994]~P39(f35(x89945,x89941),x89942,x89943,x89944)+P39(x89941,x89942,x89943,f810(x89944,x89943,x89942,x89941,x89945))+~P1(f773(x89945,x89942))
% 191.21/191.75 [8995]~P39(f35(x89955,x89951),x89952,x89953,x89954)+P39(x89951,x89952,x89953,f359(x89954,x89953,x89952,x89951,x89955))+~P1(f773(x89955,x89952))
% 191.21/191.75 [8999]~P39(f35(x89991,x89992),x89995,x89994,x89993)+P39(f35(x89991,x89992),f810(x89993,x89994,x89995,x89992,x89991),x89994,x89993)+~P1(f773(x89991,x89995))
% 191.21/191.75 [9000]~P39(f35(x90001,x90002),x90005,x90004,x90003)+P39(f35(x90001,x90002),f359(x90003,x90004,x90005,x90002,x90001),x90004,x90003)+~P1(f773(x90001,x90005))
% 191.21/191.75 [6426]E(x64261,x64262)+~E(f773(x64263,x64261),f773(x64263,x64262))+~P29(x64264,x64265,x64263,f239(f855(x64264,a841)))
% 191.21/191.75 [6591]~E(f773(x65913,x65915),f183(x65912))+~E(f773(x65914,x65915),f183(x65912))+E(f773(f170(x65911,x65912,x65913,x65914),x65915),f183(x65912))
% 191.21/191.75 [7366]E(x73661,x73662)+~P29(x73663,x73664,x73665,f239(f855(x73663,a841)))+~E(f773(f303(x73663,x73664,x73665),x73661),f773(f303(x73663,x73664,x73665),x73662))
% 191.21/191.75 [7624]P29(x76242,x76243,f522(x76244,x76243,x76242,x76241),x76241)+~E(f773(f303(x76243,x76242,x76245),x76244),x76241)+E(x76241,f180(f855(x76242,a841)))
% 191.21/191.75 [8155]~P1(f773(f773(x81553,x81552),x81555))+~P1(f773(f773(x81553,x81554),x81552))+P1(f773(f773(f334(x81551),x81552),f282(x81551,x81553,x81554,x81555)))
% 191.21/191.75 [8156]~P1(f773(f773(x81563,x81562),x81565))+~P1(f773(f773(x81563,x81564),x81562))+P1(f773(f773(f334(x81561),x81562),f291(x81561,x81563,x81564,x81565)))
% 191.21/191.75 [8694]~P29(x86941,x86943,x86945,f239(f855(x86941,a841)))+~P29(x86943,x86942,x86944,f239(f855(x86943,a841)))+P29(x86941,x86942,f773(f75(x86943,x86942,x86941,x86944),x86945),f239(f855(x86941,a841)))
% 191.21/191.75 [9193]P1(f773(f773(f334(f854(x91931,x91931)),f773(f773(f241(x91931,x91931),x91932),x91933)),f300(x91931,x91934)))+~P1(f773(f773(f334(f854(x91931,x91931)),f773(f773(f241(x91931,x91931),x91932),x91935)),f300(x91931,x91934)))+~P1(f773(f773(f334(f854(x91931,x91931)),f773(f773(f241(x91931,x91931),x91935),x91933)),f300(x91931,x91934)))
% 191.21/191.75 [9230]~P100(x92302)+~P1(f773(f127(x92301),x92305))+P1(f773(f127(x92301),f139(x92301,x92302,x92303,x92304,x92305)))
% 191.21/191.75 [5240]~E(x52402,f115(x52401))+E(f773(f773(f125(x52401),x52402),x52403),f773(f773(f140(x52401),x52404),x52405))+~E(x52403,f773(f773(f140(x52401),x52404),x52405))
% 191.21/191.75 [5241]~E(x52412,f115(x52411))+E(f773(f773(f125(x52411),x52412),x52413),f773(f773(f140(x52411),x52414),x52415))+~E(f773(f773(f140(x52411),x52414),x52415),x52413)
% 191.21/191.75 [6382]~E(f773(f181(f848(x63821)),x63825),f773(f181(f848(x63822)),x63824))+E(f773(f773(f143(f854(x63821,x63822),x63822),f250(x63821,x63822)),x63823),x63824)+~E(f773(f773(f167(x63821,x63822),x63825),x63824),x63823)
% 191.21/191.75 [6383]~E(f773(f181(f848(x63831)),x63834),f773(f181(f848(x63832)),x63835))+E(f773(f773(f143(f854(x63831,x63832),x63831),f240(x63831,x63832)),x63833),x63834)+~E(f773(f773(f167(x63831,x63832),x63834),x63835),x63833)
% 191.21/191.75 [6881]~P100(x68811)+~P18(x68811,f773(f773(f143(x68812,x68811),x68813),x68815))+P18(x68811,f773(f773(f143(x68812,x68811),x68813),f773(f126(x68812,x68814),x68815)))
% 191.21/191.75 [6927]~P1(f773(x69273,x69275))+~P1(f773(f773(x69272,x69274),x69275))+P1(f773(f773(f94(x69271,x69272,x69273),x69274),x69275))
% 191.21/191.75 [7024]~P100(x70241)+P18(x70241,f773(f773(f143(x70242,x70241),x70243),f151(x70242,x70244,x70245)))+~P18(x70241,f773(f773(f143(x70242,x70241),x70243),x70245))
% 191.21/191.75 [7047]~P53(x70473,x70472,x70475)+~P53(x70471,x70473,x70474)+P53(x70471,x70472,f773(f773(f281(x70471,x70473,x70472),x70474),x70475))
% 191.21/191.75 [7138]E(x71381,x71382)+~P29(x71383,x71384,x71385,f239(f855(x71383,a841)))+~E(f773(f773(f143(x71383,x71384),x71385),x71381),f773(f773(f143(x71383,x71384),x71385),x71382))
% 191.21/191.75 [7221]P39(x72211,x72212,x72213,x72214)+~P39(x72211,x72212,x72215,x72214)+~P1(f773(f773(f232(a847),x72215),x72213))
% 191.21/191.75 [7311]~P1(f773(f773(f233(a847),x73111),f773(x73113,x73115)))+P1(f773(f773(f233(a847),x73111),f144(x73112,x73113,x73114)))+~P1(f773(f773(f334(x73112),x73115),f773(f158(x73112),x73114)))
% 191.21/191.75 [7312]~P1(f773(f773(f232(a847),x73121),f773(x73123,x73125)))+P1(f773(f773(f232(a847),x73121),f144(x73122,x73123,x73124)))+~P1(f773(f773(f334(x73122),x73125),f773(f158(x73122),x73124)))
% 191.21/191.75 [7723]~P99(x77231)+P1(f773(f773(f232(f855(x77231,a841)),f295(x77231,x77232,x77233)),f295(x77231,x77234,x77235)))+P1(f773(f773(f232(x77231),x77232),x77233))
% 191.21/191.75 [7750]~P9(x77501)+P1(f773(f773(f232(x77501),f773(f773(f47(x77502,x77501),x77503),x77504)),f773(x77504,x77505)))+~P1(f773(f773(f334(x77502),x77505),x77503))
% 191.21/191.75 [7818]~P29(x78181,x78182,x78184,x78183)+E(f773(f79(x78181,x78182,x78183,x78184),f773(x78184,x78185)),x78185)+~P1(f773(f773(f334(x78181),x78185),x78183))
% 191.21/191.75 [8014]~P1(f773(x80141,x80145))+P1(f773(x80141,f378(x80141,x80142,x80143,x80144)))+~P1(f773(f773(f334(x80144),x80145),x80143))
% 191.21/191.75 [8015]~P1(f773(x80151,x80155))+P1(f773(x80151,f378(x80151,x80152,x80153,x80154)))+~P1(f773(f773(f334(x80154),x80155),x80152))
% 191.21/191.75 [8106]P1(f773(f63(x81061),x81062))+~P1(f773(f63(x81063),x81064))+~P1(f773(f773(f232(f855(x81061,a841)),x81062),f773(f303(x81063,x81061,x81065),x81064)))
% 191.21/191.75 [8267]E(x82671,x82672)+~P29(x82673,x82674,x82675,f773(f773(f103(f855(x82673,a841)),f773(f158(x82673),x82671)),f773(f158(x82673),x82672)))+~E(f773(f773(f143(x82673,x82674),x82675),x82671),f773(f773(f143(x82673,x82674),x82675),x82672))
% 191.21/191.75 [8324]~P99(x83241)+~P1(f773(f773(f233(f855(x83241,a841)),f295(x83241,x83244,x83245)),f295(x83241,x83242,x83243)))+P1(f773(f773(f232(x83241),x83242),x83243))
% 191.21/191.75 [8392]~P29(x83921,x83924,x83925,f239(f855(x83921,a841)))+~P1(f773(f773(f334(x83924),f773(x83925,x83922)),f773(f303(x83921,x83924,x83925),x83923)))+P1(f773(f773(f334(x83921),x83922),x83923))
% 191.21/191.75 [8472]P1(f773(x84721,x84722))+~P1(f773(x84721,f382(x84721,x84723,x84724,x84725)))+~P1(f773(f773(f334(x84725),x84722),x84724))
% 191.21/191.75 [8473]P1(f773(x84731,x84732))+~P1(f773(x84731,f382(x84731,x84733,x84734,x84735)))+~P1(f773(f773(f334(x84735),x84732),x84733))
% 191.21/191.75 [8729]~P29(x87292,x87293,x87291,x87294)+E(f773(x87291,f773(f79(x87292,x87293,x87294,x87291),x87295)),x87295)+~P1(f773(f773(f334(x87293),x87295),f773(f303(x87292,x87293,x87291),x87294)))
% 191.21/191.75 [8813]E(x88131,f115(x88132))+E(f773(f773(f140(x88132),x88133),f731(x88134,x88133,x88135,x88131,x88132)),x88131)+~E(f773(f773(f125(x88132),x88131),x88135),f773(f773(f140(x88132),x88133),x88134))
% 191.21/191.75 [8814]E(x88141,f115(x88142))+E(f773(f773(f140(x88142),x88143),f733(x88144,x88141,x88145,x88143,x88142)),x88141)+~E(f773(f773(f125(x88142),x88141),x88144),f773(f773(f140(x88142),x88143),x88145))
% 191.21/191.75 [8829]E(f773(f773(f140(x88292),x88293),f731(x88294,x88293,x88291,x88295,x88292)),x88295)+~E(f773(f773(f125(x88292),x88295),x88291),f773(f773(f140(x88292),x88293),x88294))+E(x88291,f773(f773(f140(x88292),x88293),x88294))
% 191.21/191.75 [8830]E(f773(f773(f140(x88301),x88302),f733(x88304,x88305,x88303,x88302,x88301)),x88305)+~E(f773(f773(f125(x88301),x88305),x88304),f773(f773(f140(x88301),x88302),x88303))+E(f773(f773(f140(x88301),x88302),x88303),x88304)
% 191.21/191.75 [8906]~E(f773(f303(x89063,x89062,x89064),f239(f855(x89063,a841))),f239(f855(x89062,a841)))+~E(f773(f303(x89061,x89063,x89065),f239(f855(x89061,a841))),f239(f855(x89063,a841)))+E(f773(f303(x89061,x89062,f773(f75(x89063,x89062,x89061,x89064),x89065)),f239(f855(x89061,a841))),f239(f855(x89062,a841)))
% 191.21/191.75 [9236]E(x92361,f115(x92362))+~E(f773(f773(f125(x92362),x92361),x92363),f773(f773(f140(x92362),x92365),x92364))+E(f773(f773(f125(x92362),f733(x92363,x92361,x92364,x92365,x92362)),x92363),x92364)
% 191.21/191.75 [9237]E(x92371,f115(x92372))+~E(f773(f773(f125(x92372),x92371),x92375),f773(f773(f140(x92372),x92374),x92373))+E(f773(f773(f125(x92372),f731(x92373,x92374,x92375,x92371,x92372)),x92375),x92373)
% 191.21/191.75 [9245]E(f773(f773(f125(x92452),f731(x92454,x92453,x92451,x92455,x92452)),x92451),x92454)+~E(f773(f773(f125(x92452),x92455),x92451),f773(f773(f140(x92452),x92453),x92454))+E(x92451,f773(f773(f140(x92452),x92453),x92454))
% 191.21/191.75 [9246]~E(f773(f773(f125(x92461),x92465),x92464),f773(f773(f140(x92461),x92462),x92463))+E(f773(f773(f125(x92461),f733(x92464,x92465,x92463,x92462,x92461)),x92464),x92463)+E(f773(f773(f140(x92461),x92462),x92463),x92464)
% 191.21/191.75 [9247]E(f773(f773(f125(x92471),x92475),f735(x92473,x92472,x92474,x92475,x92471)),x92472)+E(f773(f773(f125(x92471),x92472),f734(x92473,x92472,x92474,x92475,x92471)),x92475)+~E(f773(f773(f125(x92471),x92475),x92474),f773(f773(f125(x92471),x92472),x92473))
% 191.21/191.75 [9278]~P100(x92781)+P18(x92781,f773(f773(f143(x92782,x92781),x92783),f139(x92782,x92781,x92783,x92784,x92785)))+~P18(x92781,f773(f773(f143(x92782,x92781),x92783),x92785))
% 191.21/191.75 [9294]~P57(x92945,x92941,x92944,x92943)+P1(f773(f773(x92941,x92942),f538(x92943,x92944,x92941,x92945,x92942)))+~P1(f773(f773(f334(x92945),x92942),x92944))
% 191.21/191.75 [9392]~P1(f773(f773(f334(f854(x93921,x93921)),f773(f773(f241(x93921,x93921),x93925),x93923)),f300(x93921,x93924)))+P1(f773(f773(f334(f854(x93921,x93921)),f773(f773(f241(x93921,x93921),x93922),x93923)),f773(f773(f281(x93921,x93921,x93921),x93924),f300(x93921,x93924))))+~P1(f773(f773(f334(f854(x93921,x93921)),f773(f773(f241(x93921,x93921),x93922),x93925)),f773(f773(f281(x93921,x93921,x93921),x93924),f300(x93921,x93924))))
% 191.21/191.75 [9393]~P1(f773(f773(f334(f854(x93931,x93931)),f773(f773(f241(x93931,x93931),x93932),x93935)),f300(x93931,x93934)))+P1(f773(f773(f334(f854(x93931,x93931)),f773(f773(f241(x93931,x93931),x93932),x93933)),f773(f773(f281(x93931,x93931,x93931),x93934),f300(x93931,x93934))))+~P1(f773(f773(f334(f854(x93931,x93931)),f773(f773(f241(x93931,x93931),x93935),x93933)),f773(f773(f281(x93931,x93931,x93931),x93934),f300(x93931,x93934))))
% 191.21/191.75 [9395]P1(f773(f773(f334(f854(f848(x93951),f848(x93951))),f773(f773(f241(f848(x93951),f848(x93951)),x93952),x93953)),f147(x93951,f300(x93951,x93954))))+~P1(f773(f773(f334(f854(f848(x93951),f848(x93951))),f773(f773(f241(f848(x93951),f848(x93951)),x93952),x93955)),f147(x93951,f300(x93951,x93954))))+~P1(f773(f773(f334(f854(f848(x93951),f848(x93951))),f773(f773(f241(f848(x93951),f848(x93951)),x93955),x93953)),f147(x93951,f300(x93951,x93954))))
% 191.21/191.75 [9399]E(f773(f773(f125(x93991),x93992),f734(x93993,x93992,x93994,x93995,x93991)),x93995)+E(f773(f773(f125(x93991),f735(x93993,x93992,x93994,x93995,x93991)),x93993),x93994)+~E(f773(f773(f125(x93991),x93992),x93993),f773(f773(f125(x93991),x93995),x93994))
% 191.21/191.75 [9400]E(f773(f773(f125(x94001),x94002),f735(x94003,x94004,x94005,x94002,x94001)),x94004)+E(f773(f773(f125(x94001),f734(x94003,x94004,x94005,x94002,x94001)),x94005),x94003)+~E(f773(f773(f125(x94001),x94002),x94005),f773(f773(f125(x94001),x94004),x94003))
% 191.21/191.75 [9457]P1(f773(f773(f334(f854(x94571,x94571)),f773(f773(f241(x94571,x94571),x94572),x94573)),f773(f773(f281(x94571,x94571,x94571),x94574),f300(x94571,x94574))))+~P1(f773(f773(f334(f854(x94571,x94571)),f773(f773(f241(x94571,x94571),x94572),x94575)),f773(f773(f281(x94571,x94571,x94571),x94574),f300(x94571,x94574))))+~P1(f773(f773(f334(f854(x94571,x94571)),f773(f773(f241(x94571,x94571),x94575),x94573)),f773(f773(f281(x94571,x94571,x94571),x94574),f300(x94571,x94574))))
% 191.21/191.75 [9490]E(f773(f773(f125(x94901),f734(x94902,x94903,x94904,x94905,x94901)),x94904),x94902)+~E(f773(f773(f125(x94901),x94903),x94902),f773(f773(f125(x94901),x94905),x94904))+E(f773(f773(f125(x94901),f735(x94902,x94903,x94904,x94905,x94901)),x94902),x94904)
% 191.21/191.75 [9505]~P57(x95051,x95054,x95053,x95052)+~P1(f773(f773(f334(x95051),x95055),x95053))+P1(f773(f773(f334(x95051),f538(x95052,x95053,x95054,x95051,x95055)),x95052))
% 191.21/191.75 [9613]~P1(f773(f773(f334(f854(f855(x96131,a841),f855(x96131,a841))),f773(f773(f241(f855(x96131,a841),f855(x96131,a841)),x96134),x96133)),f324(x96131,x96132)))+~P1(f773(f773(f334(x96131),x96135),x96134))+P1(f773(f773(f334(x96131),f624(x96132,x96133,x96134,x96131,x96135)),x96133))
% 191.21/191.75 [6458]~P21(x64582,x64585,x64581)+~P1(f773(f63(x64582),x64584))+E(f773(x64581,f773(f773(f302(x64582),x64583),x64584)),f773(f773(f66(x64582,x64582,x64585),x64583),x64584))
% 191.21/191.75 [6459]~E(x64593,x64594)+~E(x64592,x64595)+E(f773(f773(f302(x64591),x64592),f773(f773(f302(x64591),x64593),f180(f855(x64591,a841)))),f773(f773(f302(x64591),x64594),f773(f773(f302(x64591),x64595),f180(f855(x64591,a841)))))
% 191.21/191.75 [6471]P1(f773(x64712,x64715))+E(f162(x64711,x64712,f773(f773(f125(x64711),x64713),x64714)),f162(x64711,x64712,x64713))+~P1(f773(f773(f334(x64711),x64715),f773(f158(x64711),x64713)))
% 191.21/191.75 [6508]E(f773(x65081,x65082),f239(f855(x65083,a841)))+~E(f773(f773(f47(x65084,f855(x65083,a841)),x65085),x65081),f239(f855(x65083,a841)))+~P1(f773(f773(f334(x65084),x65082),x65085))
% 191.21/191.75 [6509]E(f773(x65091,x65092),f180(f855(x65093,a841)))+~E(f773(f773(f46(x65094,f855(x65093,a841)),x65095),x65091),f180(f855(x65093,a841)))+~P1(f773(f773(f334(x65094),x65092),x65095))
% 191.21/191.75 [6830]~P1(f773(f773(f187(x68301),x68303),x68305))+~P1(f773(f773(f187(x68302),x68305),x68304))+P1(f773(f773(f187(f36(x68301,x68302)),x68303),x68304))
% 191.21/191.75 [7034]~E(x70342,x70344)+~P137(x70341)+E(f773(f773(f82(x70341),f773(f773(f83(x70341),x70342),x70343)),f773(f773(f83(x70341),x70344),x70345)),f773(f773(f82(x70341),f773(f773(f83(x70341),x70342),x70345)),f773(f773(f83(x70341),x70344),x70343)))
% 191.21/191.75 [7094]~P9(x70941)+~P1(f773(f773(f334(x70944),x70943),x70945))+P1(f773(f773(f232(x70941),f773(x70942,x70943)),f773(f773(f46(x70944,x70941),x70945),x70942)))
% 191.21/191.75 [7143]~P102(x71431)+P1(f773(f773(f232(x71431),f773(x71432,x71433)),f773(x71434,x71433)))+~P1(f773(f773(f232(f855(x71435,x71431)),x71432),x71434))
% 191.21/191.75 [7279]E(x72791,x72792)+E(x72793,x72791)+~E(f773(f773(f302(x72794),x72791),f773(f773(f302(x72794),x72795),f180(f855(x72794,a841)))),f773(f773(f302(x72794),x72792),f773(f773(f302(x72794),x72793),f180(f855(x72794,a841)))))
% 191.21/191.75 [7280]E(x72801,x72802)+E(x72803,x72801)+~E(f773(f773(f302(x72804),x72803),f773(f773(f302(x72804),x72802),f180(f855(x72804,a841)))),f773(f773(f302(x72804),x72805),f773(f773(f302(x72804),x72801),f180(f855(x72804,a841)))))
% 191.21/191.75 [7281]E(x72811,x72812)+E(x72811,x72813)+~E(f773(f773(f302(x72814),x72813),f773(f773(f302(x72814),x72812),f180(f855(x72814,a841)))),f773(f773(f302(x72814),x72815),f773(f773(f302(x72814),x72811),f180(f855(x72814,a841)))))
% 191.21/191.75 [7282]E(x72821,x72822)+E(x72821,x72823)+~E(f773(f773(f302(x72824),x72821),f773(f773(f302(x72824),x72825),f180(f855(x72824,a841)))),f773(f773(f302(x72824),x72822),f773(f773(f302(x72824),x72823),f180(f855(x72824,a841)))))
% 191.21/191.75 [7828]P29(x78281,x78282,x78283,x78284)+~P29(x78281,x78282,x78283,x78285)+~P1(f773(f773(f232(f855(x78281,a841)),x78284),x78285))
% 191.21/191.75 [7931]P1(f773(x79311,x79312))+~P1(f773(f773(f187(x79314),x79312),x79315))+P1(f773(f773(f187(f33(x79311,x79313,x79314)),x79312),x79315))
% 191.21/191.75 [7959]~P1(f773(x79591,x79594))+~P1(f773(f773(f187(x79592),x79594),x79595))+P1(f773(f773(f187(f33(x79591,x79592,x79593)),x79594),x79595))
% 191.21/191.75 [8004]E(x80041,x80042)+~E(f773(f303(x80043,x80044,x80045),x80041),f773(f303(x80043,x80044,x80045),x80042))+~P29(x80043,x80044,x80045,f773(f773(f103(f855(x80043,a841)),x80041),x80042))
% 191.21/191.75 [8104]~P29(x81041,x81042,x81043,x81045)+~P29(x81041,x81042,x81043,x81044)+P29(x81041,x81042,x81043,f773(f773(f104(f855(x81041,a841)),x81044),x81045))
% 191.21/191.75 [8209]~P66(x82091)+E(f773(f773(f82(x82091),f773(x82092,x82093)),f773(f155(x82091),f773(f773(f143(x82094,x82091),x82092),f151(x82094,x82093,x82095)))),f773(f155(x82091),f773(f773(f143(x82094,x82091),x82092),x82095)))+~P1(f773(f773(f334(x82094),x82093),f773(f158(x82094),x82095)))
% 191.21/191.75 [8296]~P100(x82961)+~P18(x82961,f773(f773(f143(x82962,x82961),x82963),x82965))+P18(x82961,f773(f773(f143(x82962,x82961),x82963),f773(f773(f138(x82962,x82961,x82963),x82964),x82965)))
% 191.21/191.75 [8377]P1(f773(x83771,x83772))+P1(f773(f773(f187(x83773),x83772),x83774))+~P1(f773(f773(f187(f33(x83771,x83775,x83773)),x83772),x83774))
% 191.21/191.75 [8388]~P9(x83881)+P1(f773(f773(f232(x83881),f773(f773(f46(x83882,x83881),x83883),x83884)),f773(f773(f46(x83882,x83881),x83885),x83884)))+~P1(f773(f773(f232(f855(x83882,a841)),x83883),x83885))
% 191.21/191.75 [8389]~P9(x83891)+P1(f773(f773(f232(x83891),f773(f773(f47(x83892,x83891),x83893),x83894)),f773(f773(f47(x83892,x83891),x83895),x83894)))+~P1(f773(f773(f232(f855(x83892,a841)),x83895),x83893))
% 191.21/191.75 [8398]~P1(f773(x83984,x83982))+P1(f773(f773(f187(x83981),x83982),x83983))+~P1(f773(f773(f187(f33(x83984,x83981,x83985)),x83982),x83983))
% 191.21/191.75 [8422]~P100(x84223)+P1(f773(f127(x84221),x84222))+~P1(f773(f127(x84221),f773(f773(f138(x84221,x84223,x84224),x84225),x84222)))
% 191.21/191.75 [8432]P1(f773(f773(f187(x84321),x84322),x84323))+P1(f773(f773(f187(x84324),x84322),x84323))+~P1(f773(f773(f187(f33(x84325,x84321,x84324)),x84322),x84323))
% 191.21/191.75 [8556]~P100(x85561)+~P1(f773(f773(f334(x85562),x85563),f773(f158(x85562),x85564)))+~P1(f773(f127(x85562),f773(f773(f138(x85562,x85561,x85565),x85563),x85564)))
% 191.21/191.75 [8631]~P100(x86311)+P18(x86311,f773(f773(f143(x86312,x86311),x86313),x86314))+~P18(x86311,f773(f773(f143(x86312,x86311),x86313),f773(f773(f138(x86312,x86311,x86313),x86315),x86314)))
% 191.21/191.75 [8716]~P100(x87162)+E(f773(f773(f138(x87161,x87162,x87163),x87164),x87165),f139(x87161,x87162,x87163,x87164,x87165))+P1(f773(f773(f334(x87162),f773(x87163,x87164)),f773(f303(x87161,x87162,x87163),f773(f158(x87161),x87165))))
% 191.21/191.75 [8783]~P100(x87832)+E(f139(x87831,x87832,x87833,x87834,x87835),x87835)+~P1(f773(f773(f334(x87832),f773(x87833,x87834)),f773(f303(x87831,x87832,x87833),f773(f158(x87831),x87835))))
% 191.21/191.75 [8797]~P29(x87972,x87971,x87973,x87975)+P1(f773(f773(f233(f855(x87971,a841)),f773(f303(x87972,x87971,x87973),x87974)),f773(f303(x87972,x87971,x87973),x87975)))+~P1(f773(f773(f233(f855(x87972,a841)),x87974),x87975))
% 191.21/191.75 [8944]~P29(x89441,x89442,x89443,f239(f855(x89441,a841)))+~P1(f773(f773(f232(f855(x89442,a841)),x89444),f773(f303(x89441,x89442,x89443),x89445)))+P1(f773(f773(f232(f855(x89441,a841)),f773(f305(x89441,x89442,x89443),x89444)),x89445))
% 191.21/191.75 [8963]~E(f773(f303(x89633,x89631,x89634),f239(f855(x89633,a841))),f239(f855(x89631,a841)))+P1(f773(f773(f232(f855(x89631,a841)),x89632),f773(f303(x89633,x89631,x89634),x89635)))+~P1(f773(f773(f232(f855(x89633,a841)),f773(f305(x89633,x89631,x89634),x89632)),x89635))
% 191.21/191.75 [9001]~E(f773(f227(x90012),x90014),f773(f166(x90011,x90012,x90015),x90013))+~P1(f773(f127(x90011),f773(f773(f143(f854(x90011,x90012),x90011),f240(x90011,x90012)),x90015)))+P1(f773(f773(f334(f854(x90011,x90012)),f773(f773(f241(x90011,x90012),x90013),x90014)),f773(f158(f854(x90011,x90012)),x90015)))
% 191.21/191.75 [9065]~P29(x90651,x90654,x90655,f239(f855(x90651,a841)))+~P1(f773(f773(f232(f855(x90654,a841)),f773(f303(x90651,x90654,x90655),x90652)),f773(f303(x90651,x90654,x90655),x90653)))+P1(f773(f773(f232(f855(x90651,a841)),x90652),x90653))
% 191.21/191.75 [9131]E(f773(f227(x91311),x91312),f773(f166(x91313,x91311,x91314),x91315))+~P1(f773(f127(x91313),f773(f773(f143(f854(x91313,x91311),x91313),f240(x91313,x91311)),x91314)))+~P1(f773(f773(f334(f854(x91313,x91311)),f773(f773(f241(x91313,x91311),x91315),x91312)),f773(f158(f854(x91313,x91311)),x91314)))
% 191.21/191.75 [9133]E(f773(f166(x91331,x91332,x91333),x91334),f773(f227(x91332),x91335))+~P1(f773(f127(x91331),f773(f773(f143(f854(x91331,x91332),x91331),f240(x91331,x91332)),x91333)))+~P1(f773(f773(f334(f854(x91331,x91332)),f773(f773(f241(x91331,x91332),x91334),x91335)),f773(f158(f854(x91331,x91332)),x91333)))
% 191.21/191.75 [9340]~P20(x93401,x93402,x93403)+~P1(f773(f63(x93401),x93405))+P1(f773(f68(x93401,x93402,x93403,x93404,x93405),f773(f773(f66(x93401,x93402,x93403),x93404),x93405)))
% 191.21/191.75 [9414]P1(f773(x94141,f699(x94142,x94141,x94143,x94144,x94145)))+~P1(f773(f773(f232(f855(x94145,a841)),x94144),x94143))+P1(f773(f773(f232(f855(x94145,a841)),f773(f773(f104(f855(x94145,a841)),x94144),f773(f256(x94145),x94141))),f773(f773(f104(f855(x94145,a841)),x94143),f773(f256(x94145),x94142))))
% 191.21/191.75 [9503]~P9(x95035)+P1(f773(f773(f334(x95031),f664(x95032,x95033,x95031,x95034,x95035)),x95033))+P1(f773(f773(f232(x95035),x95034),f773(f773(f47(x95031,x95035),x95033),x95032)))
% 191.21/191.75 [9515]~P1(f773(x95155,f699(x95155,x95153,x95154,x95152,x95151)))+~P1(f773(f773(f232(f855(x95151,a841)),x95152),x95154))+P1(f773(f773(f232(f855(x95151,a841)),f773(f773(f104(f855(x95151,a841)),x95152),f773(f256(x95151),x95153))),f773(f773(f104(f855(x95151,a841)),x95154),f773(f256(x95151),x95155))))
% 191.21/191.75 [9578]P1(f773(f773(f334(x95781),f699(x95782,x95783,x95784,x95785,x95781)),x95785))+~P1(f773(f773(f232(f855(x95781,a841)),x95785),x95784))+P1(f773(f773(f232(f855(x95781,a841)),f773(f773(f104(f855(x95781,a841)),x95785),f773(f256(x95781),x95783))),f773(f773(f104(f855(x95781,a841)),x95784),f773(f256(x95781),x95782))))
% 191.21/191.75 [9624]~P9(x96241)+~P1(f773(f773(f232(x96241),x96242),f773(x96245,f664(x96245,x96244,x96243,x96242,x96241))))+P1(f773(f773(f232(x96241),x96242),f773(f773(f47(x96243,x96241),x96244),x96245)))
% 191.21/191.75 [9654]~P70(x96541)+~P1(f773(f63(x96542),x96545))+E(f773(f773(f773(f67(x96541,x96542,f83(x96541)),f773(f773(f20(x96542,x96541,x96541),f773(f773(f10(x96541,f855(x96541,x96541),x96542),f83(x96541)),x96543)),x96544)),f80(x96541)),x96545),f773(f773(f83(x96541),f773(f773(f773(f67(x96541,x96542,f83(x96541)),x96543),f80(x96541)),x96545)),f773(f773(f773(f67(x96541,x96542,f83(x96541)),x96544),f80(x96541)),x96545)))
% 191.21/191.75 [9703]~P1(f773(f773(f334(f854(f855(x97031,a841),f855(x97031,a841))),f773(f773(f241(f855(x97031,a841),f855(x97031,a841)),x97035),x97034)),f324(x97031,x97033)))+~P1(f773(f773(f334(x97031),x97032),x97035))+P1(f773(f773(f334(f854(x97031,x97031)),f773(f773(f241(x97031,x97031),x97032),f624(x97033,x97034,x97035,x97031,x97032))),x97033))
% 191.21/191.75 [9851]~P1(f773(f773(f334(f854(f848(x98511),f848(x98511))),f773(f773(f241(f848(x98511),f848(x98511)),f773(f773(f125(x98511),x98515),x98512)),f773(f773(f125(x98511),x98515),x98513))),f137(x98511,x98514)))+P1(f773(f773(f334(f854(f848(x98511),f848(x98511))),f773(f773(f241(f848(x98511),f848(x98511)),x98512),x98513)),f137(x98511,x98514)))+P1(f773(f773(f334(f854(x98511,x98511)),f773(f773(f241(x98511,x98511),f740(x98514,x98513,x98512,x98515,x98511)),f740(x98514,x98513,x98512,x98515,x98511))),x98514))
% 191.21/191.75 [7146]~E(x71463,x71465)+E(f773(f773(f153(x71461),f773(f773(f148(x71461,x71462),x71463),x71464)),x71465),x71464)+~P1(f773(f773(f233(a847),x71463),f773(f181(f848(x71461)),x71462)))
% 191.21/191.75 [7155]~E(f773(f181(f848(x71551)),x71553),f773(f181(f848(x71552)),x71554))+E(f773(f166(x71551,x71552,f773(f773(f167(x71551,x71552),x71553),x71554)),x71555),f183(x71552))+P1(f773(f773(f334(x71551),x71555),f773(f158(x71551),x71553)))
% 191.21/191.75 [7275]~E(f773(f773(f125(x72751),x72752),x72754),f773(f773(f125(x72751),x72753),x72755))+E(f773(f773(f159(x72751),f773(f181(f848(x72751)),x72752)),x72753),x72752)+P1(f773(f773(f232(a847),f773(f181(f848(x72751)),x72753)),f773(f181(f848(x72751)),x72752)))
% 191.21/191.75 [7789]~E(f773(f773(f125(x77891),x77892),x77894),f773(f773(f125(x77891),x77893),x77895))+E(f773(f773(f159(x77891),f773(f181(f848(x77891)),x77892)),x77893),x77892)+~P1(f773(f773(f232(a847),f773(f181(f848(x77891)),x77892)),f773(f181(f848(x77891)),x77893)))
% 191.21/191.75 [7813]~P1(f773(f63(x78131),f773(x78134,x78135)))+~P1(f773(f773(f334(x78132),x78135),x78133))+P1(f773(f63(x78131),f773(f773(f47(x78132,f855(x78131,a841)),x78133),x78134)))
% 191.21/191.75 [7925]~E(f773(f181(f848(x79251)),x79252),f773(f181(f848(x79253)),x79254))+~E(f773(f166(x79251,x79253,f773(f773(f167(x79251,x79253),x79252),x79254)),x79255),f183(x79253))+~P1(f773(f773(f334(x79251),x79255),f773(f158(x79251),x79252)))
% 191.21/191.75 [7991]~P47(x79911,x79913,x79915)+~P47(x79911,x79912,x79914)+P47(x79911,f773(f773(f103(f855(x79911,a841)),x79912),x79913),f773(f773(f103(f855(f854(x79911,x79911),a841)),x79914),x79915))
% 191.21/191.75 [7992]~P47(x79921,x79923,x79925)+~P47(x79921,x79922,x79924)+P47(x79921,f773(f773(f104(f855(x79921,a841)),x79922),x79923),f773(f773(f104(f855(f854(x79921,x79921),a841)),x79924),x79925))
% 191.21/191.75 [8340]E(f773(f773(f241(x83401,x83402),f773(f773(f153(x83401),x83403),x83404)),f773(f773(f153(x83402),x83405),x83404)),f773(f773(f153(f854(x83401,x83402)),f773(f773(f167(x83401,x83402),x83403),x83405)),x83404))+~P1(f773(f773(f233(a847),x83404),f773(f181(f848(x83401)),x83403)))+~P1(f773(f773(f233(a847),x83404),f773(f181(f848(x83402)),x83405)))
% 191.21/191.75 [8500]~P47(x85001,x85003,x85004)+P1(f773(f773(f334(x85001),x85002),x85003))+~P1(f773(f773(f334(f854(x85001,x85001)),f773(f773(f241(x85001,x85001),x85005),x85002)),x85004))
% 191.21/191.75 [8501]~P47(x85011,x85013,x85014)+P1(f773(f773(f334(x85011),x85012),x85013))+~P1(f773(f773(f334(f854(x85011,x85011)),f773(f773(f241(x85011,x85011),x85012),x85015)),x85014))
% 191.21/191.75 [8502]~P12(x85021,x85023,x85024)+P1(f773(f773(f334(x85021),x85022),x85023))+~P1(f773(f773(f334(f854(x85021,x85021)),f773(f773(f241(x85021,x85021),x85025),x85022)),x85024))
% 191.21/191.75 [8503]~P12(x85031,x85033,x85034)+P1(f773(f773(f334(x85031),x85032),x85033))+~P1(f773(f773(f334(f854(x85031,x85031)),f773(f773(f241(x85031,x85031),x85032),x85035)),x85034))
% 191.21/191.75 [8739]~P12(x87391,x87395,x87392)+E(f773(f277(x87391,x87391,x87392),f773(f773(f302(x87391),x87393),f180(f855(x87391,a841)))),f773(f277(x87391,x87391,x87392),f773(f773(f302(x87391),x87394),f180(f855(x87391,a841)))))+~P1(f773(f773(f334(f854(x87391,x87391)),f773(f773(f241(x87391,x87391),x87393),x87394)),x87392))
% 191.21/191.75 [8903]P1(f773(x89031,x89032))+~P1(f773(f773(f334(x89033),x89032),x89035))+P1(f773(f773(f334(x89033),f382(x89031,x89034,x89035,x89033)),f773(f773(f103(f855(x89033,a841)),x89035),x89034)))
% 191.21/191.75 [8904]P1(f773(x89041,x89042))+~P1(f773(f773(f334(x89043),x89042),x89044))+P1(f773(f773(f334(x89043),f382(x89041,x89044,x89045,x89043)),f773(f773(f103(f855(x89043,a841)),x89045),x89044)))
% 191.21/191.75 [8912]~P1(f773(x89122,x89125))+~P1(f773(f773(f334(x89121),x89125),x89124))+P1(f773(f773(f334(x89121),f378(x89122,x89123,x89124,x89121)),f773(f773(f103(f855(x89121,a841)),x89124),x89123)))
% 191.21/191.75 [8913]~P1(f773(x89132,x89135))+~P1(f773(f773(f334(x89131),x89135),x89133))+P1(f773(f773(f334(x89131),f378(x89132,x89133,x89134,x89131)),f773(f773(f103(f855(x89131,a841)),x89134),x89133)))
% 191.21/191.75 [8926]~P1(f773(f773(f232(f855(x89261,a841)),x89265),x89263))+~P1(f773(f773(f232(f855(x89261,a841)),x89262),x89264))+P1(f773(f773(f232(f855(x89261,a841)),f773(f773(f3(f855(x89261,a841)),x89262),x89263)),f773(f773(f3(f855(x89261,a841)),x89264),x89265)))
% 191.21/191.75 [8927]~P1(f773(f773(f232(f855(x89271,a841)),x89273),x89275))+~P1(f773(f773(f232(f855(x89271,a841)),x89272),x89274))+P1(f773(f773(f232(f855(x89271,a841)),f773(f773(f103(f855(x89271,a841)),x89272),x89273)),f773(f773(f103(f855(x89271,a841)),x89274),x89275)))
% 191.21/191.75 [8928]~P1(f773(f773(f232(f855(x89281,a841)),x89283),x89285))+~P1(f773(f773(f232(f855(x89281,a841)),x89282),x89284))+P1(f773(f773(f232(f855(x89281,a841)),f773(f773(f104(f855(x89281,a841)),x89282),x89283)),f773(f773(f104(f855(x89281,a841)),x89284),x89285)))
% 191.21/191.75 [9017]P1(f773(f773(f334(f854(x90171,x90171)),f773(f773(f241(x90171,x90171),x90172),x90173)),f327(x90171,x90174,x90175)))+~P1(f773(f773(f232(a847),f773(x90174,x90172)),f773(x90174,x90173)))+~P1(f773(f773(f334(f854(x90171,x90171)),f773(f773(f241(x90171,x90171),x90172),x90173)),x90175))
% 191.21/191.75 [9024]~E(f773(f181(f848(x90241)),x90243),f773(f181(f848(x90242)),x90244))+E(f773(f166(x90241,x90242,f773(f773(f167(x90241,x90242),x90243),x90244)),x90245),f773(f227(x90242),f715(x90245,x90244,x90242,x90243,x90241)))+~P1(f773(f773(f334(x90241),x90245),f773(f158(x90241),x90243)))
% 191.21/191.75 [9173]P1(f773(f773(f334(f854(x91731,x91731)),f773(f773(f241(x91731,x91731),x91732),x91733)),f300(x91731,x91734)))+~P1(f773(f773(f334(f854(x91731,x91731)),f773(f773(f241(x91731,x91731),x91732),x91735)),f300(x91731,x91734)))+~P1(f773(f773(f334(f854(x91731,x91731)),f773(f773(f241(x91731,x91731),x91735),x91733)),x91734))
% 191.21/191.75 [9174]P1(f773(f773(f334(f854(x91741,x91741)),f773(f773(f241(x91741,x91741),x91742),x91743)),f300(x91741,x91744)))+~P1(f773(f773(f334(f854(x91741,x91741)),f773(f773(f241(x91741,x91741),x91745),x91743)),f300(x91741,x91744)))+~P1(f773(f773(f334(f854(x91741,x91741)),f773(f773(f241(x91741,x91741),x91742),x91745)),x91744))
% 191.21/191.75 [9268]E(x92681,x92682)+E(f773(a114,f642(x92683,x92684,x92681,x92682,x92685)),x92684)+~P1(f773(f773(f334(f854(x92685,x92685)),f773(f773(f241(x92685,x92685),x92682),x92681)),f773(f773(f173(f854(x92685,x92685),a841),x92684),x92683)))
% 191.21/191.75 [9269]E(x92691,x92692)+E(f773(a114,f644(x92693,x92694,x92691,x92692,x92695)),x92694)+~P1(f773(f773(f334(f854(x92695,x92695)),f773(f773(f241(x92695,x92695),x92692),x92691)),f773(f773(f173(f854(x92695,x92695),a841),x92694),x92693)))
% 191.21/191.75 [9270]E(x92701,f2(a847))+E(f773(a114,f642(x92702,x92701,x92703,x92704,x92705)),x92701)+~P1(f773(f773(f334(f854(x92705,x92705)),f773(f773(f241(x92705,x92705),x92704),x92703)),f773(f773(f173(f854(x92705,x92705),a841),x92701),x92702)))
% 191.21/191.75 [9271]E(x92711,f2(a847))+E(f773(a114,f644(x92712,x92711,x92713,x92714,x92715)),x92711)+~P1(f773(f773(f334(f854(x92715,x92715)),f773(f773(f241(x92715,x92715),x92714),x92713)),f773(f773(f173(f854(x92715,x92715),a841),x92711),x92712)))
% 191.21/191.75 [9290]P1(f773(f773(f334(f854(x92901,x92901)),f773(f773(f241(x92901,x92901),x92902),x92903)),f773(f773(f281(x92901,x92901,x92901),x92904),f300(x92901,x92904))))+~P1(f773(f773(f334(f854(x92901,x92901)),f773(f773(f241(x92901,x92901),x92902),x92905)),x92904))+~P1(f773(f773(f334(f854(x92901,x92901)),f773(f773(f241(x92901,x92901),x92905),x92903)),x92904))
% 191.21/191.75 [9299]~P1(f773(f773(f334(f854(x92991,x92991)),f773(f773(f241(x92991,x92991),x92992),x92995)),f300(x92991,x92994)))+P1(f773(f773(f334(f854(x92991,x92991)),f773(f773(f241(x92991,x92991),x92992),x92993)),f773(f773(f281(x92991,x92991,x92991),x92994),f300(x92991,x92994))))+~P1(f773(f773(f334(f854(x92991,x92991)),f773(f773(f241(x92991,x92991),x92995),x92993)),x92994))
% 191.21/191.75 [9336]~P12(x93361,x93365,x93362)+~P1(f773(f773(f334(f854(x93361,x93361)),f773(f773(f241(x93361,x93361),x93363),x93364)),x93362))+P1(f773(f773(f232(f855(x93361,a841)),f773(f277(x93361,x93361,x93362),f773(f773(f302(x93361),x93363),f180(f855(x93361,a841))))),f773(f277(x93361,x93361,x93362),f773(f773(f302(x93361),x93364),f180(f855(x93361,a841))))))
% 191.21/191.75 [9388]P1(f773(f773(f334(f854(x93881,x93881)),f773(f773(f241(x93881,x93881),x93882),x93883)),f773(f773(f281(x93881,x93881,x93881),x93884),f300(x93881,x93884))))+~P1(f773(f773(f334(f854(x93881,x93881)),f773(f773(f241(x93881,x93881),x93882),x93885)),f773(f773(f281(x93881,x93881,x93881),x93884),f300(x93881,x93884))))+~P1(f773(f773(f334(f854(x93881,x93881)),f773(f773(f241(x93881,x93881),x93885),x93883)),x93884))
% 191.21/191.75 [9389]P1(f773(f773(f334(f854(x93891,x93891)),f773(f773(f241(x93891,x93891),x93892),x93893)),f773(f773(f281(x93891,x93891,x93891),x93894),f300(x93891,x93894))))+~P1(f773(f773(f334(f854(x93891,x93891)),f773(f773(f241(x93891,x93891),x93895),x93893)),f773(f773(f281(x93891,x93891,x93891),x93894),f300(x93891,x93894))))+~P1(f773(f773(f334(f854(x93891,x93891)),f773(f773(f241(x93891,x93891),x93892),x93895)),x93894))
% 191.21/191.75 [9436]~P1(f773(f68(x94361,x94361,x94364,x94362,x94363),x94365))+P1(f773(f773(f334(x94361),x94362),x94363))+P1(f773(f64(x94361,x94364,f773(f773(f302(x94361),x94362),x94363)),x94365))
% 191.21/191.75 [9479]~E(f773(f303(x94793,x94792,x94795),x94794),x94791)+E(x94791,f180(f855(x94792,a841)))+P1(f773(f773(f232(f855(x94793,a841)),f773(f303(x94792,x94793,f522(x94794,x94793,x94792,x94791)),x94791)),x94794))
% 191.21/191.75 [9518]~P9(x95185)+P1(f773(f773(f334(x95181),f391(x95182,x95183,x95184,x95181,x95185)),x95184))+P1(f773(f773(f232(x95185),f773(f773(f46(x95181,x95185),x95184),x95183)),x95182))
% 191.21/191.75 [9680]E(x96801,x96802)+P1(f773(f773(f334(f854(x96803,x96803)),f773(f773(f241(x96803,x96803),x96801),f643(x96804,x96805,x96802,x96801,x96803))),x96804))+~P1(f773(f773(f334(f854(x96803,x96803)),f773(f773(f241(x96803,x96803),x96801),x96802)),f773(f773(f173(f854(x96803,x96803),a841),x96805),x96804)))
% 191.21/191.75 [9681]E(x96811,f2(a847))+P1(f773(f773(f334(f854(x96812,x96812)),f773(f773(f241(x96812,x96812),x96813),f643(x96814,x96811,x96815,x96813,x96812))),x96814))+~P1(f773(f773(f334(f854(x96812,x96812)),f773(f773(f241(x96812,x96812),x96813),x96815)),f773(f773(f173(f854(x96812,x96812),a841),x96811),x96814)))
% 191.21/191.75 [9725]~P9(x97251)+~P1(f773(f773(f232(x97251),f773(x97254,f391(x97255,x97254,x97253,x97252,x97251))),x97255))+P1(f773(f773(f232(x97251),f773(f773(f46(x97252,x97251),x97253),x97254)),x97255))
% 191.21/191.75 [9780]E(x97801,x97802)+P1(f773(f773(f334(f854(x97803,x97803)),f773(f773(f241(x97803,x97803),f645(x97804,x97805,x97801,x97802,x97803)),x97801)),x97804))+~P1(f773(f773(f334(f854(x97803,x97803)),f773(f773(f241(x97803,x97803),x97802),x97801)),f773(f773(f173(f854(x97803,x97803),a841),x97805),x97804)))
% 191.21/191.75 [9781]E(x97811,f2(a847))+P1(f773(f773(f334(f854(x97812,x97812)),f773(f773(f241(x97812,x97812),f645(x97813,x97811,x97814,x97815,x97812)),x97814)),x97813))+~P1(f773(f773(f334(f854(x97812,x97812)),f773(f773(f241(x97812,x97812),x97815),x97814)),f773(f773(f173(f854(x97812,x97812),a841),x97811),x97813)))
% 191.21/191.75 [9785]E(x97851,x97852)+P1(f773(f773(f334(f854(x97853,x97853)),f773(f773(f241(x97853,x97853),x97851),f645(x97854,x97855,x97852,x97851,x97853))),f773(f773(f173(f854(x97853,x97853),a841),f644(x97854,x97855,x97852,x97851,x97853)),x97854)))+~P1(f773(f773(f334(f854(x97853,x97853)),f773(f773(f241(x97853,x97853),x97851),x97852)),f773(f773(f173(f854(x97853,x97853),a841),x97855),x97854)))
% 191.21/191.75 [9786]E(x97861,f2(a847))+P1(f773(f773(f334(f854(x97862,x97862)),f773(f773(f241(x97862,x97862),x97863),f645(x97864,x97861,x97865,x97863,x97862))),f773(f773(f173(f854(x97862,x97862),a841),f644(x97864,x97861,x97865,x97863,x97862)),x97864)))+~P1(f773(f773(f334(f854(x97862,x97862)),f773(f773(f241(x97862,x97862),x97863),x97865)),f773(f773(f173(f854(x97862,x97862),a841),x97861),x97864)))
% 191.21/191.75 [9842]E(x98421,x98422)+P1(f773(f773(f334(f854(x98423,x98423)),f773(f773(f241(x98423,x98423),f643(x98424,x98425,x98421,x98422,x98423)),x98421)),f773(f773(f173(f854(x98423,x98423),a841),f642(x98424,x98425,x98421,x98422,x98423)),x98424)))+~P1(f773(f773(f334(f854(x98423,x98423)),f773(f773(f241(x98423,x98423),x98422),x98421)),f773(f773(f173(f854(x98423,x98423),a841),x98425),x98424)))
% 191.21/191.75 [9843]E(x98431,f2(a847))+P1(f773(f773(f334(f854(x98432,x98432)),f773(f773(f241(x98432,x98432),f643(x98433,x98431,x98434,x98435,x98432)),x98434)),f773(f773(f173(f854(x98432,x98432),a841),f642(x98433,x98431,x98434,x98435,x98432)),x98433)))+~P1(f773(f773(f334(f854(x98432,x98432)),f773(f773(f241(x98432,x98432),x98435),x98434)),f773(f773(f173(f854(x98432,x98432),a841),x98431),x98433)))
% 191.21/191.75 [9876]~P66(x98762)+~P1(f773(f63(x98761),x98765))+E(f773(f773(f8(x98761,x98762),f773(f773(f9(x98761,x98762,x98762),f773(f773(f20(x98761,x98762,f855(x98762,x98762)),f773(f773(f10(a841,f855(x98762,f855(x98762,x98762)),x98761),f98(x98762)),f773(f773(f9(x98761,f855(x98761,a841),a841),f334(x98761)),x98763))),x98764)),f2(x98762))),x98765),f773(f773(f8(x98761,x98762),x98764),f773(f773(f104(f855(x98761,a841)),x98765),x98763)))
% 191.21/191.75 [8554]~P66(x85541)+~P1(f773(f63(x85544),x85545))+E(f773(f773(f82(x85541),f773(x85542,x85543)),f773(f773(f8(x85544,x85541),x85542),f773(f773(f3(f855(x85544,a841)),x85545),f773(f773(f302(x85544),x85543),f180(f855(x85544,a841)))))),f773(f773(f8(x85544,x85541),x85542),f773(f773(f302(x85544),x85543),x85545)))
% 191.21/191.75 [8555]~P70(x85551)+~P1(f773(f63(x85554),x85555))+E(f773(f773(f83(x85551),f773(x85552,x85553)),f773(f773(f11(x85554,x85551),x85552),f773(f773(f3(f855(x85554,a841)),x85555),f773(f773(f302(x85554),x85553),f180(f855(x85554,a841)))))),f773(f773(f11(x85554,x85551),x85552),f773(f773(f302(x85554),x85553),x85555)))
% 191.21/191.75 [8835]~P100(x88352)+~P18(x88352,f773(f142(x88352),f773(f773(f143(x88351,x88352),x88354),x88355)))+E(f773(f126(x88351,f773(f773(f10(x88352,a841,x88351),f773(f233(x88352),x88353)),x88354)),x88355),f162(x88351,f773(f773(f10(x88352,a841,x88351),f773(f233(x88352),x88353)),x88354),x88355))
% 191.21/191.75 [8856]~P66(x88561)+E(f773(f773(f82(x88561),f773(f773(f8(a847,x88561),x88562),f295(a847,x88563,x88564))),f773(f773(f8(a847,x88561),x88562),f295(a847,f773(f773(f82(a847),x88564),f80(a847)),f773(f773(f82(a847),x88564),x88565)))),f773(f773(f8(a847,x88561),x88562),f295(a847,x88563,f773(f773(f82(a847),x88564),x88565))))+~P1(f773(f773(f232(a847),x88563),f773(f773(f82(a847),x88564),f80(a847))))
% 191.21/191.75 [8857]~P1(f773(f773(f334(x88571),x88574),x88575))+~P1(f773(f773(f232(f855(x88571,a841)),f773(f158(x88571),x88572)),x88575))+P1(f773(f773(f232(f855(x88571,a841)),f773(f158(x88571),f773(f773(f148(x88571,x88572),x88573),x88574))),x88575))
% 191.21/191.75 [9074]~P9(x90742)+~P1(f773(f63(x90741),x90745))+E(f773(f773(f66(x90741,x90742,f773(f773(f10(x90742,f855(x90742,x90742),x90741),f103(x90742)),x90743)),x90744),x90745),f773(f773(f103(x90742),x90744),f773(f773(f46(x90741,x90742),x90745),x90743)))
% 191.21/191.75 [9075]~P9(x90752)+~P1(f773(f63(x90751),x90755))+E(f773(f773(f66(x90751,x90752,f773(f773(f10(x90752,f855(x90752,x90752),x90751),f104(x90752)),x90753)),x90754),x90755),f773(f773(f104(x90752),x90754),f773(f773(f47(x90751,x90752),x90755),x90753)))
% 191.21/191.75 [9160]~P29(x91601,x91602,x91603,x91605)+P29(x91601,x91602,x91603,f773(f773(f302(x91601),x91604),x91605))+P1(f773(f773(f334(x91602),f773(x91603,x91604)),f773(f303(x91601,x91602,x91603),f773(f773(f3(f855(x91601,a841)),x91605),f773(f773(f302(x91601),x91604),f180(f855(x91601,a841)))))))
% 191.21/191.75 [9362]~P1(f773(f773(f334(f854(f848(x93621),f848(x93621))),f773(f773(f241(f848(x93621),f848(x93621)),x93622),x93624)),f147(x93621,x93625)))+~P1(f773(f773(f233(a847),x93623),f773(f181(f848(x93621)),x93622)))+P1(f773(f773(f334(f854(x93621,x93621)),f773(f773(f241(x93621,x93621),f773(f773(f153(x93621),x93622),x93623)),f773(f773(f153(x93621),x93624),x93623))),x93625))
% 191.21/191.75 [9588]E(x95881,f2(a1))+~P1(f773(f56(x95883,x95881),f773(f773(f241(a1,a1),x95884),x95885)))+P1(f773(f56(f773(f773(f83(a1),x95882),x95883),x95881),f773(f773(f241(a1,a1),f773(f773(f82(a1),f773(f773(f83(a1),x95882),x95884)),f773(f773(f43(a1),f773(f773(f83(a1),x95882),x95885)),x95881))),f52(a1,f773(f773(f83(a1),x95882),x95885),x95881))))
% 191.21/191.75 [9593]~P1(f773(f773(f233(a847),f2(a847)),x95933))+~P1(f773(f55(x95932,x95933),f773(f773(f241(a847,a847),x95934),x95935)))+P1(f773(f55(f773(f773(f83(a847),x95931),x95932),x95933),f773(f773(f241(a847,a847),f773(f773(f82(a847),f773(f773(f83(a847),x95931),x95934)),f773(f773(f43(a847),f773(f773(f83(a847),x95931),x95935)),x95933))),f52(a847,f773(f773(f83(a847),x95931),x95935),x95933))))
% 191.21/191.75 [9898]~P66(x98982)+~P1(f773(f63(x98981),x98984))+E(f773(f773(f8(x98981,x98982),x98983),f773(f256(x98981),f773(f773(f20(x98981,a841,a841),f773(f773(f10(a841,f855(a841,a841),x98981),a331),f773(f773(f9(x98981,f855(x98981,a841),a841),f334(x98981)),x98984))),f773(f773(f9(x98981,f855(x98981,a841),a841),f334(x98981)),x98985)))),f773(f773(f8(x98981,x98982),f773(f773(f9(x98981,x98982,x98982),f773(f773(f20(x98981,x98982,f855(x98982,x98982)),f773(f773(f10(a841,f855(x98982,f855(x98982,x98982)),x98981),f98(x98982)),f773(f773(f9(x98981,f855(x98981,a841),a841),f334(x98981)),x98985))),x98983)),f2(x98982))),x98984))
% 191.21/191.75 [8192]~E(f773(f773(f125(x81921),x81922),x81925),f773(f773(f125(x81921),x81923),x81924))+E(f773(f773(f125(x81921),f773(f773(f128(x81921),f773(f181(f848(x81921)),x81922)),x81923)),x81924),x81925)+P1(f773(f773(f232(a847),f773(f181(f848(x81921)),x81923)),f773(f181(f848(x81921)),x81922)))
% 191.21/191.75 [8391]~E(f773(f773(f125(x83912),x83913),x83911),f773(f773(f125(x83912),x83914),x83915))+E(x83911,f773(f773(f125(x83912),f773(f773(f128(x83912),f773(f181(f848(x83912)),x83913)),x83914)),x83915))+~P1(f773(f773(f232(a847),f773(f181(f848(x83912)),x83913)),f773(f181(f848(x83912)),x83914)))
% 191.21/191.75 [8483]~E(f773(f773(f82(a847),f773(f773(f83(a847),x84833),x84834)),x84831),f773(f773(f82(a847),f773(f773(f83(a847),x84832),x84834)),x84835))+~P1(f773(f773(f232(a847),x84833),x84832))+E(x84831,f773(f773(f82(a847),f773(f773(f83(a847),f773(f773(f3(a847),x84832),x84833)),x84834)),x84835))
% 191.21/191.75 [8484]~E(f773(f773(f82(a847),f773(f773(f83(a847),x84841),x84843)),x84844),f773(f773(f82(a847),f773(f773(f83(a847),x84842),x84843)),x84845))+~P1(f773(f773(f232(a847),x84842),x84841))+E(f773(f773(f82(a847),f773(f773(f83(a847),f773(f773(f3(a847),x84841),x84842)),x84843)),x84844),x84845)
% 191.21/191.75 [8624]E(f773(f773(f82(a847),f773(f773(f83(a847),x86241),x86242)),x86243),f773(f773(f82(a847),f773(f773(f83(a847),x86244),x86242)),x86245))+~P1(f773(f773(f232(a847),x86244),x86241))+~E(x86245,f773(f773(f82(a847),f773(f773(f83(a847),f773(f773(f3(a847),x86241),x86244)),x86242)),x86243))
% 191.21/191.75 [8625]E(f773(f773(f82(a847),f773(f773(f83(a847),x86251),x86252)),x86253),f773(f773(f82(a847),f773(f773(f83(a847),x86254),x86252)),x86255))+~P1(f773(f773(f232(a847),x86254),x86251))+~E(f773(f773(f82(a847),f773(f773(f83(a847),f773(f773(f3(a847),x86251),x86254)),x86252)),x86253),x86255)
% 191.21/191.75 [8959]~P1(f773(f773(f279(a1),x89591),x89594))+~P1(f773(f773(f279(a1),x89591),f773(f773(f82(a1),x89592),x89595)))+P1(f773(f773(f279(a1),x89591),f773(f773(f82(a1),f773(f773(f82(a1),x89592),f773(f773(f83(a1),x89593),x89594))),x89595)))
% 191.21/191.75 [9161]~P1(f773(f773(f279(a1),x91611),x91614))+P1(f773(f773(f279(a1),x91611),f773(f773(f82(a1),x91612),x91613)))+~P1(f773(f773(f279(a1),x91611),f773(f773(f82(a1),f773(f773(f82(a1),x91612),f773(f773(f83(a1),x91615),x91614))),x91613)))
% 191.21/191.75 [9412]~P60(x94122)+~P1(f773(f63(x94121),x94125))+E(f773(f773(f11(x94121,x94122),f773(f773(f20(x94121,x94122,x94122),f773(f773(f10(x94122,f855(x94122,x94122),x94121),f283(x94122)),x94123)),x94124)),x94125),f773(f773(f283(x94122),f773(f773(f11(x94121,x94122),x94123),x94125)),f773(f773(f11(x94121,x94122),x94124),x94125)))
% 191.21/191.75 [9532]~E(f647(x95325,x95324,x95323,x95322,x95321),f648(x95325,x95324,x95323,x95322,x95321))+P1(f773(f773(f334(f854(x95321,x95321)),f773(f773(f241(x95321,x95321),x95322),x95323)),f300(x95321,x95324)))+~P1(f773(f773(f334(f854(x95321,x95321)),f773(f773(f241(x95321,x95321),x95322),x95323)),f300(x95321,f773(f773(f103(f855(f854(x95321,x95321),a841)),x95324),x95325))))
% 191.21/191.75 [9533]~E(f656(x95335,x95334,x95333,x95332,x95331),f657(x95335,x95334,x95333,x95332,x95331))+P1(f773(f773(f334(f854(x95331,x95331)),f773(f773(f241(x95331,x95331),x95332),x95333)),f300(x95331,x95334)))+~P1(f773(f773(f334(f854(x95331,x95331)),f773(f773(f241(x95331,x95331),x95332),x95333)),f300(x95331,f773(f773(f103(f855(f854(x95331,x95331),a841)),x95334),x95335))))
% 191.21/191.75 [9713]P1(f773(f773(f334(f854(x97131,x97131)),f773(f773(f241(x97131,x97131),x97132),f657(x97135,x97134,x97133,x97132,x97131))),f300(x97131,x97134)))+P1(f773(f773(f334(f854(x97131,x97131)),f773(f773(f241(x97131,x97131),x97132),x97133)),f300(x97131,x97134)))+~P1(f773(f773(f334(f854(x97131,x97131)),f773(f773(f241(x97131,x97131),x97132),x97133)),f300(x97131,f773(f773(f103(f855(f854(x97131,x97131),a841)),x97134),x97135))))
% 191.21/191.75 [9807]P1(f773(f773(f334(f854(x98071,x98071)),f773(f773(f241(x98071,x98071),f648(x98075,x98074,x98073,x98072,x98071)),x98073)),f300(x98071,x98074)))+P1(f773(f773(f334(f854(x98071,x98071)),f773(f773(f241(x98071,x98071),x98072),x98073)),f300(x98071,x98074)))+~P1(f773(f773(f334(f854(x98071,x98071)),f773(f773(f241(x98071,x98071),x98072),x98073)),f300(x98071,f773(f773(f103(f855(f854(x98071,x98071),a841)),x98074),x98075))))
% 191.21/191.75 [9849]P1(f773(f773(f334(f854(x98491,x98491)),f773(f773(f241(x98491,x98491),x98492),x98493)),f300(x98491,x98494)))+P1(f773(f773(f334(f854(x98491,x98491)),f773(f773(f241(x98491,x98491),f647(x98495,x98494,x98493,x98492,x98491)),f648(x98495,x98494,x98493,x98492,x98491))),x98495))+~P1(f773(f773(f334(f854(x98491,x98491)),f773(f773(f241(x98491,x98491),x98492),x98493)),f300(x98491,f773(f773(f103(f855(f854(x98491,x98491),a841)),x98494),x98495))))
% 191.21/191.75 [9850]P1(f773(f773(f334(f854(x98501,x98501)),f773(f773(f241(x98501,x98501),x98502),x98503)),f300(x98501,x98504)))+P1(f773(f773(f334(f854(x98501,x98501)),f773(f773(f241(x98501,x98501),f657(x98505,x98504,x98503,x98502,x98501)),f656(x98505,x98504,x98503,x98502,x98501))),x98505))+~P1(f773(f773(f334(f854(x98501,x98501)),f773(f773(f241(x98501,x98501),x98502),x98503)),f300(x98501,f773(f773(f103(f855(f854(x98501,x98501),a841)),x98504),x98505))))
% 191.21/191.75 [9975]~P1(f773(f773(f334(f854(f848(x99751),f848(x99751))),f773(f773(f241(f848(x99751),f848(x99751)),x99754),x99755)),f147(x99751,x99752)))+~P1(f773(f773(f334(f854(x99751,x99751)),x99753),f773(f158(f854(x99751,x99751)),f773(f773(f167(x99751,x99751),x99754),x99755))))+P1(f773(f773(f251(x99751,x99751,a841),f773(f773(f9(x99751,f855(f854(x99751,x99751),a841),f855(x99751,a841)),f773(f773(f10(f855(x99751,f855(f855(f854(x99751,x99751),a841),a841)),f855(f855(f854(x99751,x99751),a841),f855(x99751,a841)),x99751),f9(x99751,f855(f854(x99751,x99751),a841),a841)),f773(f773(f10(f855(x99751,f854(x99751,x99751)),f855(x99751,f855(f855(f854(x99751,x99751),a841),a841)),x99751),f773(f10(f854(x99751,x99751),f855(f855(f854(x99751,x99751),a841),a841),x99751),f334(f854(x99751,x99751)))),f241(x99751,x99751)))),x99752)),x99753))
% 191.21/191.75 [9440]~P1(f773(f773(f232(a847),x94403),x94402))+~P1(f773(f773(f233(a847),f773(f773(f82(a847),f773(f773(f83(a847),x94403),x94404)),x94401)),f773(f773(f82(a847),f773(f773(f83(a847),x94402),x94404)),x94405)))+P1(f773(f773(f233(a847),x94401),f773(f773(f82(a847),f773(f773(f83(a847),f773(f773(f3(a847),x94402),x94403)),x94404)),x94405)))
% 191.21/191.75 [9441]~P1(f773(f773(f232(a847),x94413),x94412))+~P1(f773(f773(f232(a847),f773(f773(f82(a847),f773(f773(f83(a847),x94413),x94414)),x94411)),f773(f773(f82(a847),f773(f773(f83(a847),x94412),x94414)),x94415)))+P1(f773(f773(f232(a847),x94411),f773(f773(f82(a847),f773(f773(f83(a847),f773(f773(f3(a847),x94412),x94413)),x94414)),x94415)))
% 191.21/191.75 [9461]~P1(f773(f773(f232(a847),x94611),x94614))+P1(f773(f773(f233(a847),f773(f773(f82(a847),f773(f773(f83(a847),x94611),x94612)),x94613)),f773(f773(f82(a847),f773(f773(f83(a847),x94614),x94612)),x94615)))+~P1(f773(f773(f233(a847),x94613),f773(f773(f82(a847),f773(f773(f83(a847),f773(f773(f3(a847),x94614),x94611)),x94612)),x94615)))
% 191.21/191.75 [9462]~P1(f773(f773(f232(a847),x94621),x94624))+P1(f773(f773(f232(a847),f773(f773(f82(a847),f773(f773(f83(a847),x94621),x94622)),x94623)),f773(f773(f82(a847),f773(f773(f83(a847),x94624),x94622)),x94625)))+~P1(f773(f773(f232(a847),x94623),f773(f773(f82(a847),f773(f773(f83(a847),f773(f773(f3(a847),x94624),x94621)),x94622)),x94625)))
% 191.21/191.75 [9568]~P1(f773(f773(f232(a847),x95682),x95681))+~P1(f773(f773(f233(a847),f773(f773(f82(a847),f773(f773(f83(a847),x95681),x95683)),x95684)),f773(f773(f82(a847),f773(f773(f83(a847),x95682),x95683)),x95685)))+P1(f773(f773(f233(a847),f773(f773(f82(a847),f773(f773(f83(a847),f773(f773(f3(a847),x95681),x95682)),x95683)),x95684)),x95685))
% 191.21/191.75 [9569]~P1(f773(f773(f232(a847),x95692),x95691))+~P1(f773(f773(f232(a847),f773(f773(f82(a847),f773(f773(f83(a847),x95691),x95693)),x95694)),f773(f773(f82(a847),f773(f773(f83(a847),x95692),x95693)),x95695)))+P1(f773(f773(f232(a847),f773(f773(f82(a847),f773(f773(f83(a847),f773(f773(f3(a847),x95691),x95692)),x95693)),x95694)),x95695))
% 191.21/191.75 [9610]~P1(f773(f773(f232(a847),x96104),x96101))+P1(f773(f773(f233(a847),f773(f773(f82(a847),f773(f773(f83(a847),x96101),x96102)),x96103)),f773(f773(f82(a847),f773(f773(f83(a847),x96104),x96102)),x96105)))+~P1(f773(f773(f233(a847),f773(f773(f82(a847),f773(f773(f83(a847),f773(f773(f3(a847),x96101),x96104)),x96102)),x96103)),x96105))
% 191.21/191.75 [9611]~P1(f773(f773(f232(a847),x96114),x96111))+P1(f773(f773(f232(a847),f773(f773(f82(a847),f773(f773(f83(a847),x96111),x96112)),x96113)),f773(f773(f82(a847),f773(f773(f83(a847),x96114),x96112)),x96115)))+~P1(f773(f773(f232(a847),f773(f773(f82(a847),f773(f773(f83(a847),f773(f773(f3(a847),x96111),x96114)),x96112)),x96113)),x96115))
% 191.21/191.75 [9834]~P16(x98341,x98342,x98345,x98343)+~P1(f773(f773(f334(f854(x98341,x98341)),x98344),x98345))+P1(f773(f773(f251(x98341,x98341,a841),f773(f773(f9(x98341,f855(x98341,x98342),f855(x98341,a841)),f773(f773(f10(f855(x98342,a841),f855(f855(x98341,x98342),f855(x98341,a841)),x98341),f10(x98342,a841,x98341)),f773(f773(f10(x98342,f855(x98342,a841),x98341),a330),x98343))),x98343)),x98344))
% 191.21/191.75 [7161]~P39(x71614,x71612,x71615,x71616)+P39(f33(x71611,x71613,x71614),x71612,x71615,x71616)+P1(f773(x71611,x71612))
% 191.21/191.75 [7241]~P39(x72412,x72414,x72415,x72416)+P39(f33(x72411,x72412,x72413),x72414,x72415,x72416)+~P1(f773(x72411,x72414))
% 191.21/191.75 [7332]P39(x73323,x73322,x73324,x73325)+~P39(f33(x73321,x73326,x73323),x73322,x73324,x73325)+P1(f773(x73321,x73322))
% 191.21/191.75 [7365]P39(x73651,x73652,x73653,x73654)+~P39(f33(x73655,x73651,x73656),x73652,x73653,x73654)+~P1(f773(x73655,x73652))
% 191.21/191.75 [7737]~P39(x77371,x77373,x77374,x77376)+~P39(x77372,x77376,x77374,x77375)+P39(f36(x77371,x77372),x77373,x77374,x77375)
% 191.21/191.75 [7740]P39(x77401,x77402,x77403,x77404)+P39(x77405,x77402,x77403,x77404)+~P39(f33(x77406,x77401,x77405),x77402,x77403,x77404)
% 191.21/191.75 [6711]~E(f773(x67114,x67115),f183(x67112))+E(f773(f170(x67111,x67112,x67113,x67114),x67115),f773(f227(x67112),x67116))+~E(f773(x67113,x67115),f773(f227(x67112),x67116))
% 191.21/191.75 [6818]~E(f773(x68183,x68186),f183(x68181))+E(f773(f229(f851(x68181),x68182,f183(x68181),x68183),f773(x68184,x68185)),f183(x68181))+~E(f773(x68184,x68185),f773(f227(x68182),x68186))
% 191.21/191.75 [7423]E(f773(x74231,x74232),f183(x74233))+~E(f773(f170(x74235,x74233,x74236,x74231),x74232),f773(f227(x74233),x74234))+E(f773(x74231,x74232),f773(f227(x74233),x74234))
% 191.21/191.75 [7461]~E(f773(f170(x74616,x74613,x74615,x74611),x74612),f773(f227(x74613),x74614))+E(f773(x74611,x74612),f773(f227(x74613),x74614))+E(f773(x74615,x74612),f773(f227(x74613),x74614))
% 191.21/191.75 [8352]~P23(x83526,x83521,x83522,x83524)+E(f773(f75(x83521,x83521,x83521,f773(x83522,x83523)),f773(x83524,x83525)),f773(f75(x83521,x83521,x83521,f773(x83524,x83525)),f773(x83522,x83523)))+~P1(f773(f63(x83526),x83525))
% 191.21/191.75 [8749]~P29(x87491,x87493,x87495,x87496)+~P29(x87493,x87492,x87494,f773(f303(x87491,x87493,x87495),x87496))+P29(x87491,x87492,f773(f75(x87493,x87492,x87491,x87494),x87495),x87496)
% 191.21/191.75 [9253]~P1(f773(f773(x92533,x92532),x92536))+~P1(f773(f773(x92534,x92535),x92532))+P1(f773(f773(f334(x92531),x92532),f292(x92531,x92533,x92534,x92535,x92536)))
% 191.21/191.75 [9254]~P1(f773(f773(x92544,x92542),x92546))+~P1(f773(f773(x92543,x92545),x92542))+P1(f773(f773(f334(x92541),x92542),f289(x92541,x92543,x92544,x92545,x92546)))
% 191.21/191.75 [9363]E(x93631,x93632)+E(x93633,x93634)+~P1(f773(f773(f334(f854(f848(x93635),f848(x93635))),f773(f773(f241(f848(x93635),f848(x93635)),f773(f773(f140(x93635),x93633),x93631)),f773(f773(f140(x93635),x93634),x93632))),f146(x93635,x93636)))
% 191.21/191.75 [9372]~E(x93722,x93724)+P1(f773(f773(f334(f854(f848(x93721),f848(x93721))),f773(f773(f241(f848(x93721),f848(x93721)),f773(f773(f140(x93721),x93722),x93723)),f773(f773(f140(x93721),x93724),x93725))),f135(x93721,x93726)))+~P1(f773(f773(f334(f854(f848(x93721),f848(x93721))),f773(f773(f241(f848(x93721),f848(x93721)),x93723),x93725)),f135(x93721,x93726)))
% 191.21/191.75 [9373]~E(x93732,x93734)+P1(f773(f773(f334(f854(f848(x93731),f848(x93731))),f773(f773(f241(f848(x93731),f848(x93731)),f773(f773(f140(x93731),x93732),x93733)),f773(f773(f140(x93731),x93734),x93735))),f137(x93731,x93736)))+~P1(f773(f773(f334(f854(f848(x93731),f848(x93731))),f773(f773(f241(f848(x93731),f848(x93731)),x93733),x93735)),f137(x93731,x93736)))
% 191.21/191.75 [9374]~E(x93742,x93744)+P1(f773(f773(f334(f854(f848(x93741),f848(x93741))),f773(f773(f241(f848(x93741),f848(x93741)),f773(f773(f140(x93741),x93742),x93743)),f773(f773(f140(x93741),x93744),x93745))),f146(x93741,x93746)))+~P1(f773(f773(f334(f854(f848(x93741),f848(x93741))),f773(f773(f241(f848(x93741),f848(x93741)),x93743),x93745)),f146(x93741,x93746)))
% 191.21/191.75 [9375]~E(x93752,x93754)+P1(f773(f773(f334(f854(f848(x93751),f848(x93751))),f773(f773(f241(f848(x93751),f848(x93751)),f773(f773(f125(x93751),x93752),x93753)),f773(f773(f125(x93751),x93754),x93755))),f146(x93751,x93756)))+~P1(f773(f773(f334(f854(f848(x93751),f848(x93751))),f773(f773(f241(f848(x93751),f848(x93751)),x93753),x93755)),f146(x93751,x93756)))
% 191.21/191.75 [9376]~E(x93763,x93765)+P1(f773(f773(f334(f854(f848(x93761),f848(x93761))),f773(f773(f241(f848(x93761),f848(x93761)),f773(f773(f125(x93761),x93762),x93763)),f773(f773(f125(x93761),x93764),x93765))),f146(x93761,x93766)))+~P1(f773(f773(f334(f854(f848(x93761),f848(x93761))),f773(f773(f241(f848(x93761),f848(x93761)),x93762),x93764)),f146(x93761,x93766)))
% 191.21/191.75 [9429]E(x94291,x94292)+P1(f773(f773(f334(f854(f848(x94293),f848(x94293))),f773(f773(f241(f848(x94293),f848(x94293)),x94291),x94292)),f146(x94293,x94294)))+~P1(f773(f773(f334(f854(f848(x94293),f848(x94293))),f773(f773(f241(f848(x94293),f848(x94293)),f773(f773(f140(x94293),x94295),x94291)),f773(f773(f140(x94293),x94296),x94292))),f146(x94293,x94294)))
% 191.21/191.75 [9570]~E(x95703,x95705)+P1(f773(f773(f334(f854(f848(x95701),f848(x95701))),f773(f773(f241(f848(x95701),f848(x95701)),f773(f773(f125(x95701),x95702),f773(f773(f140(x95701),x95703),f115(x95701)))),f773(f773(f125(x95701),x95704),f773(f773(f140(x95701),x95705),f115(x95701))))),f146(x95701,x95706)))+~P1(f773(f773(f334(f854(f848(x95701),f848(x95701))),f773(f773(f241(f848(x95701),f848(x95701)),x95702),x95704)),f146(x95701,x95706)))
% 191.21/191.75 [9581]E(f773(x95811,x95812),f183(x95813))+~E(f773(f229(f851(x95816),x95813,f183(x95816),x95814),f773(x95811,x95812)),f183(x95816))+E(f773(x95814,f706(x95812,x95811,x95814,x95815,x95816,x95813)),f183(x95816))
% 191.21/191.75 [9582]E(f773(x95821,x95822),f183(x95823))+~E(f773(f229(f851(x95826),x95823,f183(x95826),x95824),f773(x95821,x95822)),f183(x95826))+E(f773(f227(x95823),f706(x95822,x95821,x95824,x95825,x95826,x95823)),f773(x95821,x95822))
% 191.21/191.75 [9614]E(x96141,x96142)+E(x96143,x96144)+~P1(f773(f773(f334(f854(f848(x96145),f848(x96145))),f773(f773(f241(f848(x96145),f848(x96145)),f773(f773(f125(x96145),x96143),f773(f773(f140(x96145),x96141),f115(x96145)))),f773(f773(f125(x96145),x96144),f773(f773(f140(x96145),x96142),f115(x96145))))),f146(x96145,x96146)))
% 191.21/191.75 [9636]E(x96361,x96362)+~P1(f773(f773(f334(f854(f848(x96363),f848(x96363))),f773(f773(f241(f848(x96363),f848(x96363)),f773(f773(f125(x96363),x96361),f773(f773(f140(x96363),x96365),f115(x96363)))),f773(f773(f125(x96363),x96362),f773(f773(f140(x96363),x96366),f115(x96363))))),f146(x96363,x96364)))+P1(f773(f773(f334(f854(f848(x96363),f848(x96363))),f773(f773(f241(f848(x96363),f848(x96363)),x96361),x96362)),f146(x96363,x96364)))
% 191.21/191.75 [9665]~P1(f773(f773(f334(f854(f855(x96651,a841),f855(x96651,a841))),f773(f773(f241(f855(x96651,a841),f855(x96651,a841)),x96652),x96654)),f324(x96651,x96656)))+~P1(f773(f773(f334(f854(f855(x96651,a841),f855(x96651,a841))),f773(f773(f241(f855(x96651,a841),f855(x96651,a841)),x96653),x96655)),f324(x96651,x96656)))+P1(f773(f773(f334(f854(f855(x96651,a841),f855(x96651,a841))),f773(f773(f241(f855(x96651,a841),f855(x96651,a841)),f773(f773(f103(f855(x96651,a841)),x96652),x96653)),f773(f773(f103(f855(x96651,a841)),x96654),x96655))),f324(x96651,x96656)))
% 191.21/191.75 [5133]~E(f773(x51333,x51336),x51335)+~E(x51334,f773(f227(x51331),x51336))+E(f773(f773(f196(x51331,x51332),x51333),x51334),f773(f227(x51332),x51335))
% 191.21/191.75 [5531]~E(f773(f773(f125(x55311),x55316),x55313),x55315)+E(f773(f773(f125(x55311),x55312),x55313),f773(f773(f140(x55311),x55314),x55315))+~E(x55312,f773(f773(f140(x55311),x55314),x55316))
% 191.21/191.75 [5532]~E(f773(f773(f125(x55321),x55326),x55323),x55325)+E(f773(f773(f125(x55321),x55322),x55323),f773(f773(f125(x55321),x55324),x55325))+~E(x55322,f773(f773(f125(x55321),x55324),x55326))
% 191.21/191.75 [5534]E(f773(f773(f125(x55341),x55342),x55343),f773(f773(f140(x55341),x55344),x55345))+~E(f773(f773(f140(x55341),x55344),x55346),x55342)+~E(x55345,f773(f773(f125(x55341),x55346),x55343))
% 191.21/191.75 [5536]~E(f773(f773(f125(x55361),x55362),x55366),x55364)+E(f773(f773(f125(x55361),x55362),x55363),f773(f773(f125(x55361),x55364),x55365))+~E(x55363,f773(f773(f125(x55361),x55366),x55365))
% 191.21/191.75 [6704]E(f773(x67041,x67042),f773(x67043,x67042))+~E(f773(f773(f143(x67044,x67045),x67041),x67046),f773(f773(f143(x67044,x67045),x67043),x67046))+~P1(f773(f773(f334(x67044),x67042),f773(f158(x67044),x67046)))
% 191.21/191.75 [7097]~P23(x70974,x70975,x70976,x70971)+E(f773(f773(x70971,x70972),x70973),f773(f773(f66(x70974,x70975,x70976),x70973),x70972))+~P1(f773(f63(x70974),x70972))
% 191.21/191.75 [7166]~E(x71662,f773(x71664,x71666))+~P1(f773(f773(f334(x71663),x71666),x71665))+P1(f773(f773(f334(x71661),x71662),f773(f303(x71663,x71661,x71664),x71665)))
% 191.21/191.75 [7167]~E(f773(x71674,x71672),x71676)+~P1(f773(f773(f334(x71673),x71676),x71675))+P1(f773(f773(f334(x71671),x71672),f773(f305(x71671,x71673,x71674),x71675)))
% 191.21/191.75 [7643]~P34(x76431,x76432,x76434,x76436)+P34(x76431,x76432,f773(f773(f140(x76431),x76433),x76434),f773(f773(f140(x76431),x76435),x76436))+~P1(f773(f773(x76432,x76433),x76435))
% 191.21/191.75 [8632]~P55(x86324,x86325,x86321,x86322,x86326)+E(f773(x86321,f773(x86322,x86323)),x86323)+~P1(f773(f773(f334(x86325),x86323),x86326))
% 191.21/191.75 [9365]E(x93651,x93652)+E(f773(f181(f848(x93653)),x93654),f773(f181(f848(x93653)),x93655))+~P1(f773(f773(f334(f854(f848(x93653),f848(x93653))),f773(f773(f241(f848(x93653),f848(x93653)),f773(f773(f140(x93653),x93651),x93654)),f773(f773(f140(x93653),x93652),x93655))),f135(x93653,x93656)))
% 191.21/191.75 [9426]~P20(x94261,x94262,x94263)+E(f773(f773(f66(x94261,x94262,x94263),x94264),x94265),x94266)+~P1(f773(f68(x94261,x94262,x94263,x94264,x94265),x94266))
% 191.21/191.75 [9432]E(f773(f181(f848(x94321)),x94322),f773(f181(f848(x94321)),x94323))+P1(f773(f773(f334(f854(f848(x94321),f848(x94321))),f773(f773(f241(f848(x94321),f848(x94321)),x94322),x94323)),f135(x94321,x94324)))+~P1(f773(f773(f334(f854(f848(x94321),f848(x94321))),f773(f773(f241(f848(x94321),f848(x94321)),f773(f773(f140(x94321),x94325),x94322)),f773(f773(f140(x94321),x94326),x94323))),f135(x94321,x94324)))
% 191.21/191.75 [9453]~P1(f773(f773(f334(f854(x94531,x94531)),f773(f773(f241(x94531,x94531),x94532),x94534)),f300(x94531,x94536)))+P1(f773(f773(f334(f854(f848(x94531),f848(x94531))),f773(f773(f241(f848(x94531),f848(x94531)),f773(f773(f140(x94531),x94532),x94533)),f773(f773(f140(x94531),x94534),x94535))),f300(f848(x94531),f146(x94531,x94536))))+~P1(f773(f773(f334(f854(f848(x94531),f848(x94531))),f773(f773(f241(f848(x94531),f848(x94531)),x94533),x94535)),f300(f848(x94531),f146(x94531,x94536))))
% 191.21/191.75 [9926]~P66(x99262)+E(f773(f773(f8(x99261,x99262),f773(f773(f10(f855(x99263,a841),x99262,x99261),f773(f8(x99263,x99262),x99264)),f773(f773(f10(f855(x99263,a841),f855(x99263,a841),x99261),f256(x99263)),f773(f773(f10(f855(x99263,a841),f855(x99263,a841),x99261),f773(f20(x99263,a841,a841),f773(f773(f10(a841,f855(a841,a841),x99263),a331),f773(f773(f9(x99263,f855(x99263,a841),a841),f334(x99263)),x99265)))),f773(f9(x99263,x99261,a841),f773(f773(f10(x99261,f855(x99261,a841),x99263),a330),x99266)))))),f773(f303(x99263,x99261,x99266),x99265)),f773(f773(f8(x99263,x99262),x99264),x99265))+~P1(f773(f63(x99263),x99265))
% 191.21/191.75 [6765]~P100(x67653)+P1(f773(x67652,x67655))+E(f773(f126(x67651,x67652),f773(f773(f138(x67651,x67653,x67654),x67655),x67656)),f773(f126(x67651,x67652),x67656))
% 191.21/191.75 [6767]P1(f773(x67671,x67672))+~E(f156(x67673,x67671,x67674),f773(f773(f241(f848(x67673),f848(x67673)),x67675),x67676))+~P1(f773(f773(f334(x67673),x67672),f773(f158(x67673),x67675)))
% 191.21/191.75 [6815]~P1(f773(x68152,x68156))+~E(f156(x68151,x68152,x68153),f773(f773(f241(f848(x68151),f848(x68151)),x68154),x68155))+~P1(f773(f773(f334(x68151),x68156),f773(f158(x68151),x68155)))
% 191.21/191.75 [7506]~P19(x75061,x75062,x75063)+~P1(f773(f63(x75061),x75066))+E(f773(f773(f66(x75061,x75062,x75063),x75064),f773(f773(f302(x75061),x75065),x75066)),f773(f773(f66(x75061,x75062,x75063),f773(f773(x75063,x75065),x75064)),x75066))
% 191.21/191.75 [7558]~P100(x75582)+~P1(f773(f773(f232(x75582),f773(x75583,x75584)),f773(x75583,x75585)))+E(f773(f773(f138(x75581,x75582,x75583),x75584),f773(f773(f140(x75581),x75585),x75586)),f773(f773(f140(x75581),x75584),f773(f773(f140(x75581),x75585),x75586)))
% 191.21/191.75 [7674]E(x76741,x76742)+~E(f773(f773(f248(x76743,x76744),x76741),f773(f18(f855(x76744,a841),x76743),x76745)),f773(f773(f248(x76743,x76744),x76742),f773(f18(f855(x76744,a841),x76743),x76745)))+~P1(f773(f773(f334(x76744),x76746),x76745))
% 191.21/191.75 [7742]~P19(x77421,x77422,x77423)+~P1(f773(f63(x77421),x77426))+E(f773(f773(f66(x77421,x77422,x77423),x77424),f773(f773(f302(x77421),x77425),x77426)),f773(f773(x77423,x77425),f773(f773(f66(x77421,x77422,x77423),x77424),x77426)))
% 191.21/191.75 [7858]~P20(x78581,x78582,x78583)+~P1(f773(f63(x78581),x78586))+E(f773(f773(f66(x78581,x78582,x78583),f773(f773(x78583,x78584),x78585)),x78586),f773(f773(x78583,x78584),f773(f773(f66(x78581,x78582,x78583),x78585),x78586)))
% 191.21/191.75 [7926]~P24(x79262,x79265,x79266,x79261)+~P1(f773(f63(x79262),x79264))+E(f773(x79261,f773(f773(f302(x79262),x79263),x79264)),f773(f75(x79265,x79265,x79265,f773(x79261,x79264)),f773(x79266,x79263)))
% 191.21/191.75 [7964]~P100(x79642)+P1(f773(f773(f232(x79642),f773(x79643,x79644)),f773(x79643,x79645)))+E(f773(f773(f138(x79641,x79642,x79643),x79644),f773(f773(f140(x79641),x79645),x79646)),f773(f773(f140(x79641),x79645),f773(f773(f138(x79641,x79642,x79643),x79644),x79646)))
% 191.21/191.75 [8097]~E(f773(f181(f848(x80971)),x80975),f773(f181(f848(x80972)),x80976))+~E(f773(f181(f848(x80971)),x80973),f773(f181(f848(x80972)),x80974))+E(f773(f773(f125(f854(x80971,x80972)),f773(f773(f167(x80971,x80972),x80973),x80974)),f773(f773(f167(x80971,x80972),x80975),x80976)),f773(f773(f167(x80971,x80972),f773(f773(f125(x80971),x80973),x80975)),f773(f773(f125(x80972),x80974),x80976)))
% 191.21/191.75 [8206]~E(x82062,f773(f303(x82063,x82061,x82064),x82066))+P1(f773(f773(f232(f855(x82061,a841)),x82062),f773(f303(x82063,x82061,x82064),x82065)))+~P1(f773(f773(f232(f855(x82063,a841)),x82066),x82065))
% 191.21/191.75 [8308]~P100(x83085)+E(f773(x83081,x83082),f773(x83081,x83083))+E(f773(f773(f138(x83084,x83085,x83081),x83082),f773(f773(f138(x83084,x83085,x83081),x83083),x83086)),f773(f773(f138(x83084,x83085,x83081),x83083),f773(f773(f138(x83084,x83085,x83081),x83082),x83086)))
% 191.21/191.75 [8345]~P29(x83453,x83451,x83454,x83455)+P29(x83453,x83451,f773(f773(f773(f74(x83453,x83451),x83454),x83456),x83452),x83455)+P1(f773(f773(f334(x83451),x83452),f773(f303(x83453,x83451,x83454),x83455)))
% 191.21/191.75 [8492]~P1(f773(f773(f334(x84922),x84924),f773(x84926,x84923)))+~P1(f773(f773(f334(x84921),x84923),x84925))+P1(f773(f773(f334(f854(x84921,x84922)),f773(f773(f241(x84921,x84922),x84923),x84924)),f773(f773(f248(x84921,x84922),x84925),x84926)))
% 191.21/191.75 [8901]~P66(x89012)+~P29(x89014,x89011,x89015,x89016)+E(f773(f773(f8(x89011,x89012),x89013),f773(f303(x89014,x89011,x89015),x89016)),f773(f773(f8(x89014,x89012),f773(f75(x89011,x89012,x89014,x89013),x89015)),x89016))
% 191.21/191.75 [8902]~P70(x89022)+~P29(x89024,x89021,x89025,x89026)+E(f773(f773(f11(x89021,x89022),x89023),f773(f303(x89024,x89021,x89025),x89026)),f773(f773(f11(x89024,x89022),f773(f75(x89021,x89022,x89024,x89023),x89025)),x89026))
% 191.21/191.75 [9141]~P23(x91413,x91411,x91416,x91412)+~P1(f773(f63(x91413),x91414))+E(f773(f75(x91411,x91411,x91411,f773(x91412,f773(f773(f3(f855(x91413,a841)),x91414),f773(f773(f302(x91413),x91415),f180(f855(x91413,a841)))))),f773(x91416,x91415)),f773(x91412,f773(f773(f302(x91413),x91415),x91414)))
% 191.21/191.75 [9694]~E(f773(f303(x96942,x96944,x96946),f239(f855(x96942,a841))),f239(f855(x96944,a841)))+~E(f773(f303(x96941,x96943,x96945),f239(f855(x96941,a841))),f239(f855(x96943,a841)))+E(f773(f303(f854(x96941,x96942),f854(x96943,x96944),f252(x96941,x96943,x96942,x96944,x96945,x96946)),f239(f855(f854(x96941,x96942),a841))),f239(f855(f854(x96943,x96944),a841)))
% 191.21/191.75 [9756]~P29(x97563,x97564,x97565,f773(x97566,f690(x97566,x97565,x97564,x97563,x97562,x97561)))+P29(x97563,x97564,x97565,f773(f773(f47(x97562,f855(x97563,a841)),x97561),x97566))+E(x97561,f180(f855(x97562,a841)))
% 191.21/191.75 [9813]P29(x98136,x98135,x98134,f773(f773(f47(x98132,f855(x98136,a841)),x98131),x98133))+E(x98131,f180(f855(x98132,a841)))+P1(f773(f773(f334(x98132),f690(x98133,x98134,x98135,x98136,x98132,x98131)),x98131))
% 191.21/191.75 [9820]P1(f773(f773(f334(x98201),f620(x98202,x98203,x98204,x98205,x98206,x98201)),x98206))+P1(f773(f773(f232(f855(f854(x98201,x98204),a841)),f773(f773(f248(x98201,x98204),x98206),x98203)),f773(f773(f248(x98201,x98204),x98205),x98202)))+~P1(f773(f773(f232(f855(x98201,a841)),x98206),x98205))
% 191.21/191.75 [9863]P28(x98636,x98635,f773(f773(f302(f846(x98636)),f773(f773(f773(f93(x98636),x98634),x98633),x98632)),f180(f855(f846(x98636),a841))))+~P28(x98636,x98635,f773(f773(f302(f846(x98636)),f773(f773(f773(f93(x98636),x98634),x98633),x98631)),f180(f855(f846(x98636),a841))))+P1(f773(f773(x98631,f541(x98632,x98631,x98633,x98634,x98635,x98636)),f542(x98632,x98631,x98633,x98634,x98635,x98636)))
% 191.21/191.75 [9864]P28(x98646,x98645,f773(f773(f302(f846(x98646)),f773(f773(f773(f93(x98646),x98641),x98643),x98642)),f180(f855(f846(x98646),a841))))+~P28(x98646,x98645,f773(f773(f302(f846(x98646)),f773(f773(f773(f93(x98646),x98644),x98643),x98642)),f180(f855(f846(x98646),a841))))+P1(f773(f773(x98641,f543(x98641,x98642,x98643,x98644,x98645,x98646)),f544(x98641,x98642,x98643,x98644,x98645,x98646)))
% 191.21/191.75 [9901]~P28(x99011,x99012,f773(f773(f302(f846(x99011)),f773(f773(f773(f93(x99011),x99013),x99014),x99016)),f180(f855(f846(x99011),a841))))+P28(x99011,x99012,f773(f773(f302(f846(x99011)),f773(f773(f773(f93(x99011),x99013),x99014),x99015)),f180(f855(f846(x99011),a841))))+~P1(f773(f773(x99015,f541(x99015,x99016,x99014,x99013,x99012,x99011)),f542(x99015,x99016,x99014,x99013,x99012,x99011)))
% 191.21/191.75 [9902]~P28(x99021,x99022,f773(f773(f302(f846(x99021)),f773(f773(f773(f93(x99021),x99026),x99024),x99025)),f180(f855(f846(x99021),a841))))+P28(x99021,x99022,f773(f773(f302(f846(x99021)),f773(f773(f773(f93(x99021),x99023),x99024),x99025)),f180(f855(f846(x99021),a841))))+~P1(f773(f773(x99026,f543(x99023,x99025,x99024,x99026,x99022,x99021)),f544(x99023,x99025,x99024,x99026,x99022,x99021)))
% 191.21/191.75 [9943]~P1(f773(f773(f232(f855(x99432,a841)),f773(x99434,f620(x99436,x99434,x99432,x99435,x99433,x99431))),f773(x99436,f620(x99436,x99434,x99432,x99435,x99433,x99431))))+~P1(f773(f773(f232(f855(x99431,a841)),x99433),x99435))+P1(f773(f773(f232(f855(f854(x99431,x99432),a841)),f773(f773(f248(x99431,x99432),x99433),x99434)),f773(f773(f248(x99431,x99432),x99435),x99436)))
% 191.21/191.75 [7691]~P1(f773(x76911,x76915))+~P1(f773(x76916,x76914))+P1(f773(x76911,f773(f250(x76912,x76913),f773(f773(f241(x76912,x76913),x76914),x76915))))
% 191.21/191.75 [7692]~P1(f773(x76921,x76924))+~P1(f773(x76926,x76925))+P1(f773(x76921,f773(f240(x76922,x76923),f773(f773(f241(x76922,x76923),x76924),x76925))))
% 191.21/191.75 [7747]~P1(f773(f773(x77474,x77476),x77475))+~P1(f773(f773(f334(x77471),x77476),x77473))+P1(f773(f773(f773(f46(x77471,f855(x77472,a841)),x77473),x77474),x77475))
% 191.21/191.75 [7780]~E(f773(f181(f848(x77801)),x77803),f773(f181(f848(x77804)),x77805))+~E(f773(f166(x77801,x77804,f773(f773(f167(x77801,x77804),x77803),x77805)),x77802),f773(f227(x77804),x77806))+P1(f773(f773(f334(x77801),x77802),f773(f158(x77801),x77803)))
% 191.21/191.75 [8050]~P1(f773(f773(f334(x80501),x80502),f773(x80505,x80506)))+~P1(f773(f773(f334(x80503),x80506),x80504))+P1(f773(f773(f334(x80501),x80502),f773(f773(f46(x80503,f855(x80501,a841)),x80504),x80505)))
% 191.21/191.75 [8090]P1(f773(f773(x80901,x80902),x80903))+~P1(f773(f773(x80904,x80902),x80903))+~P1(f773(f773(f232(f855(x80905,f855(x80906,a841))),x80904),x80901))
% 191.21/191.75 [8230]P1(f773(f773(x82301,x82302),x82303))+~P1(f773(f773(f334(x82304),x82302),x82305))+~P1(f773(f773(f773(f47(x82304,f855(x82306,a841)),x82305),x82301),x82303))
% 191.21/191.75 [8368]P1(f773(f773(f334(x83681),x83682),f773(x83683,x83684)))+~P1(f773(f773(f334(x83685),x83684),x83686))+~P1(f773(f773(f334(x83681),x83682),f773(f773(f47(x83685,f855(x83681,a841)),x83686),x83683)))
% 191.21/191.75 [8614]~P16(x86144,x86145,x86146,x86141)+E(f773(x86141,x86142),f773(x86141,x86143))+~P1(f773(f773(f334(f854(x86144,x86144)),f773(f773(f241(x86144,x86144),x86142),x86143)),x86146))
% 191.21/191.75 [8645]P1(f773(f773(f232(f855(x86451,a841)),x86452),f773(x86453,x86454)))+~P1(f773(f773(f334(x86455),x86454),x86456))+~P1(f773(f773(f232(f855(x86451,a841)),x86452),f773(f773(f47(x86455,f855(x86451,a841)),x86456),x86453)))
% 191.21/191.75 [8670]~P53(x86703,x86704,f773(f278(x86704,x86703),x86705))+E(x86701,f180(f855(x86702,a841)))+E(f773(f773(f47(x86702,f855(x86703,a841)),x86701),f773(f773(f10(f855(x86704,a841),f855(x86703,a841),x86702),f277(x86704,x86703,x86705)),x86706)),f773(f277(x86704,x86703,x86705),f773(f773(f47(x86702,f855(x86704,a841)),x86701),x86706)))
% 191.21/191.75 [8742]P1(f773(f773(f334(x87421),x87422),f773(f277(x87423,x87421,x87424),x87425)))+~P1(f773(f773(f334(x87423),x87426),x87425))+~P1(f773(f773(f334(f854(x87423,x87421)),f773(f773(f241(x87423,x87421),x87426),x87422)),x87424))
% 191.21/191.75 [9019]P1(f773(f773(f232(f855(x90191,a841)),f773(f277(x90192,x90191,x90193),x90194)),f773(f277(x90192,x90191,x90195),x90196)))+~P1(f773(f773(f232(f855(x90192,a841)),x90194),x90196))+~P1(f773(f773(f232(f855(f854(x90192,x90191),a841)),x90193),x90195))
% 191.21/191.75 [9175]~P1(f773(f773(f334(x91752),x91756),x91754))+~P1(f773(f773(f232(f855(x91751,a841)),x91753),x91755))+P1(f773(f773(f232(f855(f854(x91751,x91752),a841)),f773(f773(f248(x91751,x91752),x91753),f773(f18(f855(x91752,a841),x91751),x91754))),f773(f773(f248(x91751,x91752),x91755),f773(f18(f855(x91752,a841),x91751),x91754))))
% 191.21/191.75 [9323]~E(x93233,x93235)+P1(f773(f773(f334(f854(f848(x93231),f848(x93231))),f773(f773(f241(f848(x93231),f848(x93231)),f773(f773(f140(x93231),x93232),x93233)),f773(f773(f140(x93231),x93234),x93235))),f146(x93231,x93236)))+~P1(f773(f773(f334(f854(x93231,x93231)),f773(f773(f241(x93231,x93231),x93232),x93234)),x93236))
% 191.21/191.75 [9329]~E(f773(f181(f848(x93291)),x93293),f773(f181(f848(x93291)),x93295))+P1(f773(f773(f334(f854(f848(x93291),f848(x93291))),f773(f773(f241(f848(x93291),f848(x93291)),f773(f773(f140(x93291),x93292),x93293)),f773(f773(f140(x93291),x93294),x93295))),f135(x93291,x93296)))+~P1(f773(f773(f334(f854(x93291,x93291)),f773(f773(f241(x93291,x93291),x93292),x93294)),x93296))
% 191.21/191.75 [9357]P1(f773(f773(f334(f854(x93571,x93571)),f773(f773(f241(x93571,x93571),x93572),x93573)),f773(f773(f173(f854(x93571,x93571),a841),f773(a114,x93574)),x93575)))+~P1(f773(f773(f334(f854(x93571,x93571)),f773(f773(f241(x93571,x93571),x93576),x93573)),x93575))+~P1(f773(f773(f334(f854(x93571,x93571)),f773(f773(f241(x93571,x93571),x93572),x93576)),f773(f773(f173(f854(x93571,x93571),a841),x93574),x93575)))
% 191.21/191.75 [9358]P1(f773(f773(f334(f854(x93581,x93581)),f773(f773(f241(x93581,x93581),x93582),x93583)),f773(f773(f173(f854(x93581,x93581),a841),f773(a114,x93584)),x93585)))+~P1(f773(f773(f334(f854(x93581,x93581)),f773(f773(f241(x93581,x93581),x93582),x93586)),x93585))+~P1(f773(f773(f334(f854(x93581,x93581)),f773(f773(f241(x93581,x93581),x93586),x93583)),f773(f773(f173(f854(x93581,x93581),a841),x93584),x93585)))
% 191.21/191.75 [9361]~P1(f773(f773(f334(x93614),x93615),x93616))+P1(f773(f773(f232(f855(x93611,a841)),x93612),x93613))+~P1(f773(f773(f232(f855(f854(x93611,x93614),a841)),f773(f773(f248(x93611,x93614),x93612),f773(f18(f855(x93614,a841),x93611),x93616))),f773(f773(f248(x93611,x93614),x93613),f773(f18(f855(x93614,a841),x93611),x93616))))
% 191.21/191.75 [9401]E(x94011,x94012)+~P1(f773(f773(f334(f854(f848(x94013),f848(x94013))),f773(f773(f241(f848(x94013),f848(x94013)),f773(f773(f140(x94013),x94011),x94015)),f773(f773(f140(x94013),x94012),x94016))),f135(x94013,x94014)))+P1(f773(f773(f334(f854(x94013,x94013)),f773(f773(f241(x94013,x94013),x94011),x94012)),x94014))
% 191.21/191.75 [9402]E(x94021,x94022)+~P1(f773(f773(f334(f854(f848(x94023),f848(x94023))),f773(f773(f241(f848(x94023),f848(x94023)),f773(f773(f140(x94023),x94021),x94025)),f773(f773(f140(x94023),x94022),x94026))),f137(x94023,x94024)))+P1(f773(f773(f334(f854(x94023,x94023)),f773(f773(f241(x94023,x94023),x94021),x94022)),x94024))
% 191.21/191.75 [9403]E(x94031,x94032)+~P1(f773(f773(f334(f854(f848(x94033),f848(x94033))),f773(f773(f241(f848(x94033),f848(x94033)),f773(f773(f140(x94033),x94031),x94035)),f773(f773(f140(x94033),x94032),x94036))),f146(x94033,x94034)))+P1(f773(f773(f334(f854(x94033,x94033)),f773(f773(f241(x94033,x94033),x94031),x94032)),x94034))
% 191.21/191.75 [9439]P1(f773(f773(f334(f854(f848(x94391),f848(x94391))),f773(f773(f241(f848(x94391),f848(x94391)),f773(f773(f140(x94391),x94392),x94393)),f773(f773(f140(x94391),x94394),x94395))),f147(x94391,x94396)))+~P1(f773(f773(f334(f854(f848(x94391),f848(x94391))),f773(f773(f241(f848(x94391),f848(x94391)),x94393),x94395)),f147(x94391,x94396)))+~P1(f773(f773(f334(f854(x94391,x94391)),f773(f773(f241(x94391,x94391),x94392),x94394)),x94396))
% 191.21/191.75 [9459]P1(f773(x94591,x94592))+~P1(f773(x94591,f388(x94591,x94593,x94594,x94595,x94596)))+~P1(f773(f773(f334(x94596),x94592),f773(f773(f46(x94595,f855(x94596,a841)),x94594),x94593)))
% 191.21/191.75 [9464]~P1(f773(f773(f334(f854(f848(x94641),f848(x94641))),f773(f773(f241(f848(x94641),f848(x94641)),f773(f773(f140(x94641),x94642),x94645)),f773(f773(f140(x94641),x94643),x94646))),f135(x94641,x94644)))+P1(f773(f773(f334(f854(f848(x94641),f848(x94641))),f773(f773(f241(f848(x94641),f848(x94641)),x94645),x94646)),f135(x94641,x94644)))+P1(f773(f773(f334(f854(x94641,x94641)),f773(f773(f241(x94641,x94641),x94642),x94643)),x94644))
% 191.21/191.75 [9465]~P1(f773(f773(f334(f854(f848(x94651),f848(x94651))),f773(f773(f241(f848(x94651),f848(x94651)),f773(f773(f140(x94651),x94652),x94655)),f773(f773(f140(x94651),x94653),x94656))),f137(x94651,x94654)))+P1(f773(f773(f334(f854(f848(x94651),f848(x94651))),f773(f773(f241(f848(x94651),f848(x94651)),x94655),x94656)),f137(x94651,x94654)))+P1(f773(f773(f334(f854(x94651,x94651)),f773(f773(f241(x94651,x94651),x94652),x94653)),x94654))
% 191.21/191.75 [9466]~P1(f773(f773(f334(f854(f848(x94661),f848(x94661))),f773(f773(f241(f848(x94661),f848(x94661)),f773(f773(f140(x94661),x94662),x94665)),f773(f773(f140(x94661),x94663),x94666))),f146(x94661,x94664)))+P1(f773(f773(f334(f854(f848(x94661),f848(x94661))),f773(f773(f241(f848(x94661),f848(x94661)),x94665),x94666)),f146(x94661,x94664)))+P1(f773(f773(f334(f854(x94661,x94661)),f773(f773(f241(x94661,x94661),x94662),x94663)),x94664))
% 191.21/191.75 [9542]P1(f773(x95421,x95422))+P1(f773(f773(f334(x95423),f389(x95421,x95424,x95425,x95423,x95426)),x95425))+~P1(f773(f773(f334(x95426),x95422),f773(f773(f46(x95423,f855(x95426,a841)),x95425),x95424)))
% 191.21/191.75 [9548]~E(x95482,x95484)+P1(f773(f773(f334(f854(f848(x95481),f848(x95481))),f773(f773(f241(f848(x95481),f848(x95481)),f773(f773(f125(x95481),x95482),f773(f773(f140(x95481),x95483),f115(x95481)))),f773(f773(f125(x95481),x95484),f773(f773(f140(x95481),x95485),f115(x95481))))),f146(x95481,x95486)))+~P1(f773(f773(f334(f854(x95481,x95481)),f773(f773(f241(x95481,x95481),x95483),x95485)),x95486))
% 191.21/191.75 [9628]E(x96281,x96282)+~P1(f773(f773(f334(f854(f848(x96283),f848(x96283))),f773(f773(f241(f848(x96283),f848(x96283)),f773(f773(f125(x96283),x96285),f773(f773(f140(x96283),x96281),f115(x96283)))),f773(f773(f125(x96283),x96286),f773(f773(f140(x96283),x96282),f115(x96283))))),f146(x96283,x96284)))+P1(f773(f773(f334(f854(x96283,x96283)),f773(f773(f241(x96283,x96283),x96281),x96282)),x96284))
% 191.21/191.75 [9653]~P1(f773(f773(f334(f854(f848(x96531),f848(x96531))),f773(f773(f241(f848(x96531),f848(x96531)),f773(f773(f125(x96531),x96535),f773(f773(f140(x96531),x96532),f115(x96531)))),f773(f773(f125(x96531),x96536),f773(f773(f140(x96531),x96533),f115(x96531))))),f146(x96531,x96534)))+P1(f773(f773(f334(f854(f848(x96531),f848(x96531))),f773(f773(f241(f848(x96531),f848(x96531)),x96535),x96536)),f146(x96531,x96534)))+P1(f773(f773(f334(f854(x96531,x96531)),f773(f773(f241(x96531,x96531),x96532),x96533)),x96534))
% 191.21/191.75 [9666]P1(f773(x96661,x96662))+P1(f773(f773(f334(x96663),f388(x96661,x96664,x96665,x96666,x96663)),f773(x96664,f389(x96661,x96664,x96665,x96666,x96663))))+~P1(f773(f773(f334(x96663),x96662),f773(f773(f46(x96666,f855(x96663,a841)),x96665),x96664)))
% 191.21/191.75 [8755]~P20(x87553,x87554,x87551)+~P1(f773(f63(x87553),x87556))+E(f773(f773(x87551,x87552),f773(f773(f66(x87553,x87554,x87551),x87555),f773(f773(f3(f855(x87553,a841)),x87556),f773(f773(f302(x87553),x87552),f180(f855(x87553,a841)))))),f773(f773(f66(x87553,x87554,x87551),x87555),f773(f773(f302(x87553),x87552),x87556)))
% 191.21/191.75 [8852]~E(f773(f166(x88521,x88522,x88524),x88525),f773(f227(x88522),x88526))+~P1(f773(f773(x88523,x88525),x88526))+E(f773(f166(x88521,x88522,f773(f126(f854(x88521,x88522),f773(f251(x88521,x88522,a841),x88523)),x88524)),x88525),f773(f227(x88522),x88526))
% 191.21/191.75 [9025]~P1(f773(f773(f334(x90255),x90253),x90256))+P1(f773(f773(f232(f855(x90251,a841)),f773(x90252,x90253)),x90254))+~P1(f773(f773(f232(f855(x90251,a841)),f773(f773(f46(x90255,f855(x90251,a841)),x90256),x90252)),x90254))
% 191.21/191.75 [9603]~P12(x96031,x96035,x96034)+P1(f773(f773(f334(f854(x96031,x96031)),f773(f773(f241(x96031,x96031),x96032),x96033)),x96034))+~P1(f773(f773(f334(x96031),x96036),f773(f773(f104(f855(x96031,a841)),f773(f277(x96031,x96031,x96034),f773(f773(f302(x96031),x96032),f180(f855(x96031,a841))))),f773(f277(x96031,x96031,x96034),f773(f773(f302(x96031),x96033),f180(f855(x96031,a841)))))))
% 191.21/191.75 [8525]~P121(x85252)+~E(f773(f773(f82(x85252),f773(f773(f83(x85252),x85254),x85255)),x85251),f773(f773(f82(x85252),f773(f773(f83(x85252),x85253),x85255)),x85256))+E(x85251,f773(f773(f82(x85252),f773(f773(f83(x85252),f773(f773(f3(x85252),x85253),x85254)),x85255)),x85256))
% 191.21/191.75 [8526]~P121(x85261)+~E(f773(f773(f82(x85261),f773(f773(f83(x85261),x85262),x85264)),x85265),f773(f773(f82(x85261),f773(f773(f83(x85261),x85263),x85264)),x85266))+E(f773(f773(f82(x85261),f773(f773(f83(x85261),f773(f773(f3(x85261),x85262),x85263)),x85264)),x85265),x85266)
% 191.21/191.75 [8673]~P121(x86731)+E(f773(f773(f82(x86731),f773(f773(f83(x86731),x86732),x86733)),x86734),f773(f773(f82(x86731),f773(f773(f83(x86731),x86735),x86733)),x86736))+~E(x86736,f773(f773(f82(x86731),f773(f773(f83(x86731),f773(f773(f3(x86731),x86732),x86735)),x86733)),x86734))
% 191.21/191.75 [8674]~P121(x86741)+E(f773(f773(f82(x86741),f773(f773(f83(x86741),x86742),x86743)),x86744),f773(f773(f82(x86741),f773(f773(f83(x86741),x86745),x86743)),x86746))+~E(f773(f773(f82(x86741),f773(f773(f83(x86741),f773(f773(f3(x86741),x86742),x86745)),x86743)),x86744),x86746)
% 191.21/191.75 [8965]~P1(f773(f773(x89654,x89655),x89656))+~P1(f773(f773(x89653,x89655),x89656))+P1(f773(f773(f773(f773(f104(f855(x89651,f855(x89652,a841))),x89653),x89654),x89655),x89656))
% 191.21/191.75 [9194]P1(f773(f773(x91941,x91942),x91943))+P1(f773(f773(x91944,x91942),x91943))+~P1(f773(f773(f773(f773(f103(f855(x91945,f855(x91946,a841))),x91944),x91941),x91942),x91943))
% 191.21/191.75 [9353]~E(f773(f181(f848(x93531)),x93535),f773(f181(f848(x93532)),x93536))+E(f170(x93531,x93532,f172(x93531,x93532,x93533,f773(f773(f3(f855(x93531,a841)),x93534),f773(f158(x93531),x93535))),f166(x93531,x93532,f773(f142(f854(x93531,x93532)),f773(f773(f167(x93531,x93532),x93535),x93536)))),f172(x93531,x93532,f170(x93531,x93532,x93533,f166(x93531,x93532,f773(f142(f854(x93531,x93532)),f773(f773(f167(x93531,x93532),x93535),x93536)))),x93534))+~P1(f773(f773(f232(f855(x93531,a841)),f773(f158(x93531),x93535)),x93534))
% 191.21/191.75 [9481]~P129(x94811)+~P1(f773(f773(f233(x94811),f773(f773(f82(x94811),f773(f773(f83(x94811),x94814),x94815)),x94812)),f773(f773(f82(x94811),f773(f773(f83(x94811),x94813),x94815)),x94816)))+P1(f773(f773(f233(x94811),x94812),f773(f773(f82(x94811),f773(f773(f83(x94811),f773(f773(f3(x94811),x94813),x94814)),x94815)),x94816)))
% 191.21/191.75 [9482]~P129(x94821)+~P1(f773(f773(f232(x94821),f773(f773(f82(x94821),f773(f773(f83(x94821),x94824),x94825)),x94822)),f773(f773(f82(x94821),f773(f773(f83(x94821),x94823),x94825)),x94826)))+P1(f773(f773(f232(x94821),x94822),f773(f773(f82(x94821),f773(f773(f83(x94821),f773(f773(f3(x94821),x94823),x94824)),x94825)),x94826)))
% 191.21/191.75 [9499]~P129(x94991)+P1(f773(f773(f233(x94991),f773(f773(f82(x94991),f773(f773(f83(x94991),x94992),x94993)),x94994)),f773(f773(f82(x94991),f773(f773(f83(x94991),x94995),x94993)),x94996)))+~P1(f773(f773(f233(x94991),x94994),f773(f773(f82(x94991),f773(f773(f83(x94991),f773(f773(f3(x94991),x94995),x94992)),x94993)),x94996)))
% 191.21/191.75 [9500]~P129(x95001)+P1(f773(f773(f232(x95001),f773(f773(f82(x95001),f773(f773(f83(x95001),x95002),x95003)),x95004)),f773(f773(f82(x95001),f773(f773(f83(x95001),x95005),x95003)),x95006)))+~P1(f773(f773(f232(x95001),x95004),f773(f773(f82(x95001),f773(f773(f83(x95001),f773(f773(f3(x95001),x95005),x95002)),x95003)),x95006)))
% 191.21/191.75 [9596]~P129(x95961)+~P1(f773(f773(f233(x95961),f773(f773(f82(x95961),f773(f773(f83(x95961),x95962),x95964)),x95965)),f773(f773(f82(x95961),f773(f773(f83(x95961),x95963),x95964)),x95966)))+P1(f773(f773(f233(x95961),f773(f773(f82(x95961),f773(f773(f83(x95961),f773(f773(f3(x95961),x95962),x95963)),x95964)),x95965)),x95966))
% 191.21/191.75 [9597]~P129(x95971)+~P1(f773(f773(f232(x95971),f773(f773(f82(x95971),f773(f773(f83(x95971),x95972),x95974)),x95975)),f773(f773(f82(x95971),f773(f773(f83(x95971),x95973),x95974)),x95976)))+P1(f773(f773(f232(x95971),f773(f773(f82(x95971),f773(f773(f83(x95971),f773(f773(f3(x95971),x95972),x95973)),x95974)),x95975)),x95976))
% 191.21/191.75 [9638]~P129(x96381)+P1(f773(f773(f233(x96381),f773(f773(f82(x96381),f773(f773(f83(x96381),x96382),x96383)),x96384)),f773(f773(f82(x96381),f773(f773(f83(x96381),x96385),x96383)),x96386)))+~P1(f773(f773(f233(x96381),f773(f773(f82(x96381),f773(f773(f83(x96381),f773(f773(f3(x96381),x96382),x96385)),x96383)),x96384)),x96386))
% 191.21/191.75 [9639]~P129(x96391)+P1(f773(f773(f232(x96391),f773(f773(f82(x96391),f773(f773(f83(x96391),x96392),x96393)),x96394)),f773(f773(f82(x96391),f773(f773(f83(x96391),x96395),x96393)),x96396)))+~P1(f773(f773(f232(x96391),f773(f773(f82(x96391),f773(f773(f83(x96391),f773(f773(f3(x96391),x96392),x96395)),x96393)),x96394)),x96396))
% 191.21/191.75 [9808]~P66(x98082)+~P1(f773(f63(x98081),x98086))+E(f773(f773(f8(x98081,x98082),f773(f773(f20(x98081,x98082,x98082),f773(f773(f20(x98081,x98082,f855(x98082,x98082)),f773(f773(f10(a841,f855(x98082,f855(x98082,x98082)),x98081),f98(x98082)),x98083)),x98084)),x98085)),x98086),f773(f773(f82(x98082),f773(f773(f8(x98081,x98082),x98084),f773(f773(f104(f855(x98081,a841)),x98086),f773(f256(x98081),x98083)))),f773(f773(f8(x98081,x98082),x98085),f773(f773(f104(f855(x98081,a841)),x98086),f773(f81(f855(x98081,a841)),f773(f256(x98081),x98083))))))
% 191.21/191.75 [9872]P1(f773(f773(f334(x98722),x98724),x98726))+P1(f773(f773(f334(x98722),x98725),x98726))+E(f773(f305(x98721,x98722,f773(f773(f9(x98721,x98722,x98722),f773(f773(f9(x98721,x98722,f855(x98722,x98722)),f773(f773(f10(a841,f855(x98722,f855(x98722,x98722)),x98721),f98(x98722)),f773(f773(f9(x98721,f855(x98721,a841),a841),f334(x98721)),x98723))),x98724)),x98725)),x98726),f180(f855(x98721,a841)))
% 191.21/191.75 [9873]P1(f773(f773(f334(x98732),x98735),x98736))+~P1(f773(f773(f334(x98732),x98734),x98736))+E(f773(f305(x98731,x98732,f773(f773(f9(x98731,x98732,x98732),f773(f773(f9(x98731,x98732,f855(x98732,x98732)),f773(f773(f10(a841,f855(x98732,f855(x98732,x98732)),x98731),f98(x98732)),f773(f773(f9(x98731,f855(x98731,a841),a841),f334(x98731)),x98733))),x98734)),x98735)),x98736),x98733)
% 191.21/191.75 [9874]P1(f773(f773(f334(x98742),x98744),x98746))+~P1(f773(f773(f334(x98742),x98745),x98746))+E(f773(f305(x98741,x98742,f773(f773(f9(x98741,x98742,x98742),f773(f773(f9(x98741,x98742,f855(x98742,x98742)),f773(f773(f10(a841,f855(x98742,f855(x98742,x98742)),x98741),f98(x98742)),f773(f773(f9(x98741,f855(x98741,a841),a841),f334(x98741)),x98743))),x98744)),x98745)),x98746),f773(f81(f855(x98741,a841)),x98743))
% 191.21/191.75 [9875]~P1(f773(f773(f334(x98752),x98754),x98756))+~P1(f773(f773(f334(x98752),x98755),x98756))+E(f773(f305(x98751,x98752,f773(f773(f9(x98751,x98752,x98752),f773(f773(f9(x98751,x98752,f855(x98752,x98752)),f773(f773(f10(a841,f855(x98752,f855(x98752,x98752)),x98751),f98(x98752)),f773(f773(f9(x98751,f855(x98751,a841),a841),f334(x98751)),x98753))),x98754)),x98755)),x98756),f239(f855(x98751,a841)))
% 191.21/191.75 [10007]P28(x100071,x100072,f773(f773(f302(f846(x100071)),f773(f773(f773(f93(x100071),f773(x100073,x100074)),f773(a27,x100074)),f773(x100075,x100074))),f180(f855(f846(x100071),a841))))+~P1(f773(f773(f334(a843),x100074),x100076))+~P28(x100071,f773(f773(f103(f855(f846(x100071),a841)),x100072),f773(f303(a843,f846(x100071),f773(f773(f20(a843,f855(x100071,f855(a844,a841)),f846(x100071)),f773(f773(f20(a843,a842,f855(f855(x100071,f855(a844,a841)),f846(x100071))),f773(f773(f10(f855(x100071,f855(a844,a841)),f855(a842,f855(f855(x100071,f855(a844,a841)),f846(x100071))),a843),f93(x100071)),x100073)),a27)),x100075)),x100076)),f773(f303(a843,f846(x100071),f773(f773(f20(a843,f855(x100071,f855(a844,a841)),f846(x100071)),f773(f773(f20(a843,a842,f855(f855(x100071,f855(a844,a841)),f846(x100071))),f773(f773(f10(f855(x100071,f855(a844,a841)),f855(a842,f855(f855(x100071,f855(a844,a841)),f846(x100071))),a843),f93(x100071)),x100073)),f773(f773(f10(f851(a842),a842,a843),f231(a842)),a30))),x100075)),x100076))
% 191.21/191.75 [8550]E(x85501,x85502)+~P55(x85504,x85505,x85503,x85506,x85507)+~E(f773(x85503,x85501),f773(x85503,x85502))
% 191.21/191.75 [6925]E(f773(f229(f851(x69251),x69252,f183(x69251),x69253),f773(x69254,x69255)),f773(f227(x69251),x69256))+~E(f773(x69254,x69255),f773(f227(x69252),x69257))+~E(f773(x69253,x69257),f773(f227(x69251),x69256))
% 191.21/191.75 [8572]~P15(x85726,x85725,x85727,x85724,x85721)+E(f773(f773(x85721,x85722),x85723),x85724)+P1(f773(f63(x85725),x85723))
% 191.21/191.75 [9348]P41(x93481,x93482,x93483,x93484,x93485,f773(f773(x93483,x93486),x93487))+~E(f773(f773(x93483,x93486),x93487),x93484)+~E(x93485,f180(f855(x93481,a841)))
% 191.21/191.75 [9519]~P1(f773(x95196,x95193))+~P1(f773(f773(f334(f854(x95192,x95192)),f773(f773(f241(x95192,x95192),x95194),x95195)),f773(x95197,x95193)))+P1(f773(f773(f334(f854(f854(x95191,x95192),f854(x95191,x95192))),f773(f773(f241(f854(x95191,x95192),f854(x95191,x95192)),f773(f773(f241(x95191,x95192),x95193),x95194)),f773(f773(f241(x95191,x95192),x95193),x95195))),f275(x95191,x95192,x95196,x95197)))
% 191.21/191.75 [9692]~P29(x96923,x96921,x96924,f239(f855(x96923,a841)))+E(f773(f166(x96921,x96922,f773(f773(f143(f854(x96923,x96922),f854(x96921,x96922)),f773(f251(x96923,x96922,f854(x96921,x96922)),f773(f773(f10(x96921,f855(x96922,f854(x96921,x96922)),x96923),f241(x96921,x96922)),x96924))),x96925)),f773(x96924,x96926)),f773(f227(x96922),x96927))+~E(f773(f166(x96923,x96922,x96925),x96926),f773(f227(x96922),x96927))
% 191.21/191.75 [9928]~P41(x99282,x99287,x99283,x99286,x99281,f773(f773(x99283,x99285),x99284))+E(f773(f773(x99283,f453(x99284,x99285,x99281,x99286,x99283,x99287,x99282)),f454(x99284,x99285,x99281,x99286,x99283,x99287,x99282)),f773(f773(x99283,x99285),x99284))+E(x99281,f180(f855(x99282,a841)))
% 191.21/191.75 [9929]~P41(x99297,x99296,x99291,x99294,x99295,f773(f773(x99291,x99292),x99293))+E(f773(f773(x99291,f453(x99293,x99292,x99295,x99294,x99291,x99296,x99297)),f454(x99293,x99292,x99295,x99294,x99291,x99296,x99297)),f773(f773(x99291,x99292),x99293))+E(f773(f773(x99291,x99292),x99293),x99294)
% 191.21/191.75 [9584]~P1(f773(f68(x95841,x95844,x95845,x95846,x95843),x95847))+P1(f773(f68(x95841,x95844,x95845,x95846,f773(f773(f302(x95841),x95842),x95843)),f773(f773(x95845,x95842),x95847)))+P1(f773(f773(f334(x95841),x95842),x95843))
% 191.21/191.75 [9953]~P41(x99532,x99537,x99536,x99535,x99531,f773(f773(x99536,x99534),x99533))+E(x99531,f180(f855(x99532,a841)))+P1(f773(f773(f334(x99532),f453(x99533,x99534,x99531,x99535,x99536,x99537,x99532)),x99531))
% 191.21/191.75 [9954]~P41(x99545,x99547,x99541,x99544,x99546,f773(f773(x99541,x99542),x99543))+E(f773(f773(x99541,x99542),x99543),x99544)+P1(f773(f773(f334(x99545),f453(x99543,x99542,x99546,x99544,x99541,x99547,x99545)),x99546))
% 191.21/191.75 [6703]~E(x67035,x67037)+~E(x67036,x67034)+E(f773(f773(f773(f773(f74(x67031,f851(x67032)),x67033),x67034),f773(f227(x67032),x67035)),x67036),f773(f227(x67032),x67037))
% 191.21/191.75 [6839]E(x68391,x68392)+~E(f773(x68395,x68391),f773(f227(x68394),x68397))+E(f773(f773(f773(f773(f74(x68393,f851(x68394)),x68395),x68392),f773(f227(x68394),x68396)),x68391),f773(f227(x68394),x68397))
% 191.21/191.75 [7584]E(x75841,x75842)+~E(x75843,x75844)+~E(f773(f773(f773(f773(f74(x75845,f851(x75846)),x75847),x75844),f773(f227(x75846),x75841)),x75843),f773(f227(x75846),x75842))
% 191.21/191.75 [7649]E(x76491,x76492)+E(f773(x76493,x76494),f773(f227(x76495),x76491))+~E(f773(f773(f773(f773(f74(x76496,f851(x76495)),x76493),x76497),f773(f227(x76495),x76492)),x76494),f773(f227(x76495),x76491))
% 191.21/191.75 [7650]E(x76501,x76502)+E(f773(x76503,x76501),f773(f227(x76504),x76505))+~E(f773(f773(f773(f773(f74(x76506,f851(x76504)),x76503),x76502),f773(f227(x76504),x76507)),x76501),f773(f227(x76504),x76505))
% 191.21/191.75 [8776]~P25(x87764,x87765,x87766,x87767,x87761)+~P1(f773(f63(x87765),x87763))+E(f773(f773(x87761,x87762),x87763),f773(f773(f773(f67(x87764,x87765,x87766),x87762),x87767),x87763))
% 191.21/191.75 [8777]~P15(x87774,x87775,x87776,x87777,x87771)+~P1(f773(f63(x87775),x87773))+E(f773(f773(x87771,x87772),x87773),f773(f773(f773(f67(x87774,x87775,x87776),x87772),x87777),x87773))
% 191.21/191.75 [9316]~P28(x93161,x93162,f773(f773(f302(f846(x93161)),f773(f773(f773(f93(x93161),x93163),x93164),x93167)),f180(f855(f846(x93161),a841))))+P28(x93161,x93162,f773(f773(f302(f846(x93161)),f773(f773(f773(f93(x93161),x93163),f36(x93164,x93165)),x93166)),f180(f855(f846(x93161),a841))))+~P28(x93161,x93162,f773(f773(f302(f846(x93161)),f773(f773(f773(f93(x93161),x93167),x93165),x93166)),f180(f855(f846(x93161),a841))))
% 191.21/191.75 [9494]~P27(x94943,x94944,x94945,x94947,x94946,x94941)+~P1(f773(f63(x94944),x94942))+E(f773(x94941,x94942),f773(f773(f773(f67(x94943,x94944,x94945),x94946),x94947),x94942))
% 191.21/191.75 [9633]P41(x96331,x96332,x96333,x96334,x96335,f773(f773(x96333,x96336),x96337))+~P41(x96331,x96332,x96333,x96334,f773(f773(f3(f855(x96331,a841)),x96335),f773(f773(f302(x96331),x96336),f180(f855(x96331,a841)))),x96337)+~P1(f773(f773(f334(x96331),x96336),x96335))
% 191.21/191.75 [9903]~P28(x99031,x99032,f773(f773(f302(f846(x99031)),f773(f773(f773(f93(x99031),f94(x99031,x99033,x99034)),x99035),x99037)),f180(f855(f846(x99031),a841))))+P28(x99031,x99032,f773(f773(f302(f846(x99031)),f773(f773(f773(f93(x99031),x99033),f33(x99034,x99035,x99036)),x99037)),f180(f855(f846(x99031),a841))))+~P28(x99031,x99032,f773(f773(f302(f846(x99031)),f773(f773(f773(f93(x99031),f94(x99031,x99033,f773(f75(a841,a841,a844,a328),x99034))),x99036),x99037)),f180(f855(f846(x99031),a841))))
% 191.21/191.75 [9971]P1(f773(f773(x99717,f833(x99714,x99715,x99711,x99716,x99713,x99712,x99717)),f834(x99714,x99715,x99711,x99716,x99713,x99712,x99717)))+~P1(f773(f773(x99717,f773(f250(x99712,x99713),x99716)),f773(f240(x99712,x99713),x99716)))+P1(f773(x99711,f773(f773(f251(x99712,x99713,x99714),x99715),x99716)))
% 191.21/191.75 [9980]~P41(x99802,x99803,x99804,x99805,x99801,f773(f773(x99804,x99807),x99806))+P41(x99802,x99803,x99804,x99805,f773(f773(f3(f855(x99802,a841)),x99801),f773(f773(f302(x99802),f453(x99806,x99807,x99801,x99805,x99804,x99803,x99802)),f180(f855(x99802,a841)))),f454(x99806,x99807,x99801,x99805,x99804,x99803,x99802))+E(x99801,f180(f855(x99802,a841)))
% 191.21/191.75 [9981]~P41(x99815,x99816,x99811,x99814,x99817,f773(f773(x99811,x99812),x99813))+P41(x99815,x99816,x99811,x99814,f773(f773(f3(f855(x99815,a841)),x99817),f773(f773(f302(x99815),f453(x99813,x99812,x99817,x99814,x99811,x99816,x99815)),f180(f855(x99815,a841)))),f454(x99813,x99812,x99817,x99814,x99811,x99816,x99815))+E(f773(f773(x99811,x99812),x99813),x99814)
% 191.21/191.75 [10001]~P1(f773(x100011,f773(f773(x100015,f834(x100014,x100015,x100011,x100016,x100013,x100012,x100017)),f833(x100014,x100015,x100011,x100016,x100013,x100012,x100017))))+~P1(f773(f773(x100017,f773(f250(x100012,x100013),x100016)),f773(f240(x100012,x100013),x100016)))+P1(f773(x100011,f773(f773(f251(x100012,x100013,x100014),x100015),x100016)))
% 191.21/191.75 [9337]P1(f773(f773(f232(f855(f854(x93371,x93372),a841)),f773(f773(f281(x93371,x93373,x93372),x93374),x93375)),f773(f773(f281(x93371,x93373,x93372),x93376),x93377)))+~P1(f773(f773(f232(f855(f854(x93373,x93372),a841)),x93375),x93377))+~P1(f773(f773(f232(f855(f854(x93371,x93373),a841)),x93374),x93376))
% 191.21/191.75 [9644]~P1(f773(f773(f334(x96441),x96446),x96445))+P1(f773(f68(x96441,x96442,x96443,x96444,x96445),f773(f773(x96443,x96446),x96447)))+~P1(f773(f68(x96441,x96442,x96443,x96444,f773(f773(f3(f855(x96441,a841)),x96445),f773(f773(f302(x96441),x96446),f180(f855(x96441,a841))))),x96447))
% 191.21/191.75 [9243]E(f170(x92431,x92432,x92433,f166(x92431,x92432,f773(f142(f854(x92431,x92432)),f773(f773(f167(x92431,x92432),x92434),f773(f773(f148(x92432,x92435),x92436),x92437))))),f170(x92431,x92432,x92433,f166(x92431,x92432,f773(f142(f854(x92431,x92432)),f773(f773(f167(x92431,x92432),x92434),x92435)))))+~P1(f773(f773(f233(a847),x92436),f773(f181(f848(x92432)),x92435)))+~P1(f773(f773(f232(a847),f773(f181(f848(x92431)),x92434)),x92436))
% 191.21/191.75 [10031]~P136(x100311)+~P29(f854(x100312,x100313),x100311,f773(f251(x100312,x100313,x100311),f773(f773(f9(x100312,f855(x100313,x100311),f855(x100313,x100311)),f773(f773(f10(f855(x100311,x100311),f855(f855(x100313,x100311),f855(x100313,x100311)),x100312),f10(x100311,x100311,x100313)),f773(f773(f10(x100311,f855(x100311,x100311),x100312),f83(x100311)),x100314))),x100315)),f773(f773(f248(x100312,x100313),x100316),f773(f18(f855(x100313,a841),x100312),x100317)))+E(f773(f773(f8(x100311,x100311),f39(x100311)),f773(f256(x100311),f773(f773(f10(f855(x100312,a841),a841,x100311),f89(x100312)),f773(f773(f10(f855(x100312,f855(x100313,a841)),f855(x100312,a841),x100311),f773(f10(f855(x100313,a841),a841,x100312),f89(x100313))),f773(f773(f9(x100311,f855(x100312,f855(x100313,a841)),f855(x100312,f855(x100313,a841))),f773(f773(f10(f855(x100312,f855(f855(x100313,a841),f855(x100313,a841))),f855(f855(x100312,f855(x100313,a841)),f855(x100312,f855(x100313,a841))),x100311),f20(x100312,f855(x100313,a841),f855(x100313,a841))),f773(f773(f10(f855(x100312,f855(x100313,f855(a841,a841))),f855(x100312,f855(f855(x100313,a841),f855(x100313,a841))),x100311),f773(f10(f855(x100313,f855(a841,a841)),f855(f855(x100313,a841),f855(x100313,a841)),x100312),f20(x100313,a841,a841))),f773(f773(f10(f855(x100312,f855(x100313,a841)),f855(x100312,f855(x100313,f855(a841,a841))),x100311),f773(f10(f855(x100313,a841),f855(x100313,f855(a841,a841)),x100312),f773(f10(a841,f855(a841,a841),x100313),a331))),f773(f773(f9(x100311,f855(x100312,f855(x100313,x100311)),f855(x100312,f855(x100313,a841))),f773(f773(f10(f855(f855(x100313,x100311),f855(x100313,a841)),f855(f855(x100312,f855(x100313,x100311)),f855(x100312,f855(x100313,a841))),x100311),f10(f855(x100313,x100311),f855(x100313,a841),x100312)),f773(f773(f10(f855(x100311,a841),f855(f855(x100313,x100311),f855(x100313,a841)),x100311),f10(x100311,a841,x100313)),a330))),f773(f773(f9(x100312,f855(x100313,x100311),f855(x100313,x100311)),f773(f773(f10(f855(x100311,x100311),f855(f855(x100313,x100311),f855(x100313,x100311)),x100312),f10(x100311,x100311,x100313)),f773(f773(f10(x100311,f855(x100311,x100311),x100312),f83(x100311)),x100314))),x100315)))))),f773(f773(f9(x100312,f855(x100313,a841),f855(x100313,a841)),f773(f773(f10(f855(a841,a841),f855(f855(x100313,a841),f855(x100313,a841)),x100312),f10(a841,a841,x100313)),f773(f773(f10(a841,f855(a841,a841),x100312),a331),f773(f773(f9(x100312,f855(x100312,a841),a841),f334(x100312)),x100316)))),f773(f773(f9(x100313,f855(x100313,a841),a841),f334(x100313)),x100317))))))),f773(f773(f83(x100311),f773(f773(f8(x100312,x100311),x100314),x100316)),f773(f773(f8(x100313,x100311),x100315),x100317)))
% 191.21/191.75 [9722]P51(x97221,x97222,x97223,x97224,x97225,x97226,x97227)+~P1(f773(f773(x97224,x97226),x97228))+~P1(f773(f773(x97225,x97228),x97227))
% 191.21/191.75 [9123]~P23(x91238,x91231,x91233,x91235)+~P1(f773(f63(x91238),x91236))+E(f773(f75(x91231,x91231,x91232,f773(x91233,x91234)),f773(f75(x91231,x91231,x91232,f773(x91235,x91236)),x91237)),f773(f75(x91231,x91231,x91232,f773(x91235,x91236)),f773(f75(x91231,x91231,x91232,f773(x91233,x91234)),x91237)))
% 191.21/191.75 [9486]~P26(x94867,x94862,x94865,x94868,x94866,x94861)+~P1(f773(f63(x94862),x94864))+E(f773(x94861,f773(f773(f302(x94862),x94863),x94864)),f773(f773(x94865,f773(x94866,x94863)),f773(x94861,x94864)))
% 191.21/191.75 [9594]~P29(x95942,x95944,x95946,x95948)+~P29(x95941,x95943,x95945,x95947)+P29(f854(x95941,x95942),f854(x95943,x95944),f252(x95941,x95943,x95942,x95944,x95945,x95946),f773(f773(f248(x95941,x95942),x95947),f773(f18(f855(x95942,a841),x95941),x95948)))
% 191.21/191.75 [9279]P1(f773(f773(f334(f854(x92791,x92792)),f773(f773(f241(x92791,x92792),x92793),x92794)),f773(f773(f281(x92791,x92795,x92792),x92796),x92797)))+~P1(f773(f773(f334(f854(x92791,x92795)),f773(f773(f241(x92791,x92795),x92793),x92798)),x92796))+~P1(f773(f773(f334(f854(x92795,x92792)),f773(f773(f241(x92795,x92792),x92798),x92794)),x92797))
% 191.21/191.75 [9469]~P1(f773(f773(f232(f855(f854(x94693,x94692),a841)),x94695),f773(f773(f248(x94693,x94692),x94698),f773(f18(f855(x94692,a841),x94693),x94697))))+~P1(f773(f773(f232(f855(f854(x94691,x94693),a841)),x94694),f773(f773(f248(x94691,x94693),x94696),f773(f18(f855(x94693,a841),x94691),x94698))))+P1(f773(f773(f232(f855(f854(x94691,x94692),a841)),f773(f773(f281(x94691,x94693,x94692),x94694),x94695)),f773(f773(f248(x94691,x94692),x94696),f773(f18(f855(x94692,a841),x94691),x94697))))
% 191.21/191.75 [9514]~E(x95143,x95145)+P1(f773(f773(f334(f854(f854(x95141,x95142),f854(x95141,x95142))),f773(f773(f241(f854(x95141,x95142),f854(x95141,x95142)),f773(f773(f241(x95141,x95142),x95143),x95144)),f773(f773(f241(x95141,x95142),x95145),x95146))),f325(x95141,x95142,x95147,x95148)))+~P1(f773(f773(f334(f854(x95142,x95142)),f773(f773(f241(x95142,x95142),x95144),x95146)),x95148))
% 191.21/191.75 [9612]E(x96121,x96122)+~P1(f773(f773(f334(f854(f854(x96123,x96125),f854(x96123,x96125))),f773(f773(f241(f854(x96123,x96125),f854(x96123,x96125)),f773(f773(f241(x96123,x96125),x96121),x96126)),f773(f773(f241(x96123,x96125),x96122),x96127))),f325(x96123,x96125,x96124,x96128)))+P1(f773(f773(f334(f854(x96123,x96123)),f773(f773(f241(x96123,x96123),x96121),x96122)),x96124))
% 191.21/191.75 [9627]~P1(f773(f773(f334(f854(f854(x96271,x96275),f854(x96271,x96275))),f773(f773(f241(f854(x96271,x96275),f854(x96271,x96275)),f773(f773(f241(x96271,x96275),x96272),x96276)),f773(f773(f241(x96271,x96275),x96273),x96277))),f325(x96271,x96275,x96274,x96278)))+P1(f773(f773(f334(f854(x96271,x96271)),f773(f773(f241(x96271,x96271),x96272),x96273)),x96274))+P1(f773(f773(f334(f854(x96275,x96275)),f773(f773(f241(x96275,x96275),x96276),x96277)),x96278))
% 191.21/191.75 [9543]~P27(x95437,x95435,x95431,x95438,x95432,x95434)+~P1(f773(f63(x95435),x95436))+E(f773(f773(x95431,f773(x95432,x95433)),f773(x95434,f773(f773(f3(f855(x95435,a841)),x95436),f773(f773(f302(x95435),x95433),f180(f855(x95435,a841)))))),f773(x95434,f773(f773(f302(x95435),x95433),x95436)))
% 191.21/191.75 [9082]~P1(f773(f773(f773(x90825,x90828),x90826),x90827))+~P1(f773(f773(f334(x90821),x90828),x90824))+P1(f773(f773(f773(f773(f46(x90821,f855(x90822,f855(x90823,a841))),x90824),x90825),x90826),x90827))
% 191.21/191.75 [9267]P1(f773(f773(f773(x92671,x92672),x92673),x92674))+~P1(f773(f773(f334(x92675),x92672),x92676))+~P1(f773(f773(f773(f773(f47(x92675,f855(x92677,f855(x92678,a841))),x92676),x92671),x92673),x92674))
% 191.21/191.75 [9460]~P25(x94603,x94602,x94604,x94608,x94601)+~P1(f773(f63(x94602),x94607))+E(f773(f773(x94601,f773(f773(f20(x94602,x94603,x94603),f773(f773(f10(x94603,f855(x94603,x94603),x94602),x94604),x94605)),x94606)),x94607),f773(f773(x94604,f773(f773(x94601,x94605),x94607)),f773(f773(x94601,x94606),x94607)))
% 191.21/191.75 [9700]~E(f773(f303(x97002,x97004,x97006),x97008),x970010)+~E(f773(f303(x97001,x97003,x97005),x97007),x97009)+E(f773(f303(f854(x97001,x97002),f854(x97003,x97004),f252(x97001,x97003,x97002,x97004,x97005,x97006)),f773(f773(f248(x97001,x97002),x97007),f773(f18(f855(x97002,a841),x97001),x97008))),f773(f773(f248(x97003,x97004),x97009),f773(f18(f855(x97004,a841),x97003),x970010)))
% 191.21/191.75 [4732]~P100(x47322)+~P18(x47322,x47321)+P18(x47322,f116(x47322,x47321))+E(x47321,f115(x47322))
% 191.21/191.75 [4965]~P9(x49652)+E(f12(x49652,x49651),f45(x49652,x49651))+E(x49651,f180(f855(x49652,a841)))+~P1(f773(f63(x49652),x49651))
% 191.21/191.75 [4966]~P9(x49662)+E(f15(x49662,x49661),f44(x49662,x49661))+E(x49661,f180(f855(x49662,a841)))+~P1(f773(f63(x49662),x49661))
% 191.21/191.75 [5906]~P93(x59062)+E(x59061,f180(f855(x59062,a841)))+P1(f773(f773(f232(x59062),f12(x59062,x59061)),f15(x59062,x59061)))+~P1(f773(f63(x59062),x59061))
% 191.21/191.75 [5920]~P38(x59202)+~P38(x59201)+E(x59201,x59202)+~E(f773(f303(a1,a847,a107),x59201),f773(f303(a1,a847,a107),x59202))
% 191.21/191.75 [8945]~P110(x89451)+~P1(f773(f773(f334(x89451),x89452),f112(x89451)))+P1(f773(f773(f233(x89451),f773(f773(f82(x89451),f773(f773(f82(x89451),f80(x89451)),x89452)),x89452)),f2(x89451)))+~P1(f773(f773(f233(x89451),x89452),f2(x89451)))
% 191.21/191.75 [9164]~P110(x91641)+~P1(f773(f773(f334(x91641),x91642),f112(x91641)))+~P1(f773(f773(f233(x91641),f773(f773(f82(x91641),f773(f773(f82(x91641),f80(x91641)),x91642)),x91642)),f2(x91641)))+P1(f773(f773(f233(x91641),x91642),f2(x91641)))
% 191.21/191.75 [4785]~P105(x47852)+~P136(x47852)+E(x47851,f2(a847))+E(f773(f773(f242(x47852),f2(x47852)),x47851),f2(x47852))
% 191.21/191.75 [4789]~P105(x47891)+~P136(x47891)+~E(x47892,f2(a847))+E(f773(f773(f242(x47891),f2(x47891)),x47892),f80(x47891))
% 191.21/191.75 [4952]~P120(x49522)+E(x49521,f80(x49522))+E(x49521,f773(f81(x49522),f80(x49522)))+~E(f773(f773(f83(x49522),x49521),x49521),f80(x49522))
% 191.21/191.75 [5196]~P82(x51962)+E(x51961,f2(x51962))+E(f84(x51962,x51961),f773(f81(x51962),f80(x51962)))+P1(f773(f773(f233(x51962),f2(x51962)),x51961))
% 191.21/191.75 [5428]~P82(x54282)+E(f84(x54282,x54281),f80(x54282))+E(x54281,f2(x54282))+~P1(f773(f773(f233(x54282),f2(x54282)),x54281))
% 191.21/191.75 [5437]E(x54371,x54372)+~E(f773(f106(a847),x54371),f773(f106(a847),x54372))+P1(f773(a186,f773(f106(a1),x54372)))+P1(f773(a186,f773(f106(a1),x54371)))
% 191.21/191.75 [5484]~P87(x54841)+~E(x54842,f2(x54841))+E(f773(f773(f82(x54841),x54842),x54842),f2(x54841))+~P1(f773(f773(f334(x54841),x54842),f112(x54841)))
% 191.21/191.75 [5520]E(x55201,f2(a1))+~E(f773(f773(f43(a1),x55202),x55201),f2(a1))+P1(f773(f773(f233(a1),x55201),x55202))+P1(f773(f773(f233(a1),x55202),x55201))
% 191.21/191.75 [5549]E(x55491,f2(a1))+~E(f773(f773(f43(a1),x55492),x55491),f2(a1))+P1(f773(f773(f232(a1),x55492),f2(a1)))+P1(f773(f773(f233(a1),x55492),x55491))
% 191.21/191.75 [5581]E(x55811,f2(a1))+~E(f773(f773(f43(a1),x55812),x55811),f2(a1))+P1(f773(f773(f232(a1),f2(a1)),x55812))+P1(f773(f773(f233(a1),x55811),x55812))
% 191.21/191.75 [5618]~P87(x56182)+E(x56181,f2(x56182))+~E(f773(f773(f82(x56182),x56181),x56181),f2(x56182))+~P1(f773(f773(f334(x56182),x56181),f112(x56182)))
% 191.21/191.75 [5685]E(f773(f106(a847),x56851),f773(f106(a847),x56852))+~E(f773(f106(a1),x56852),f2(a1))+P1(f773(a186,f773(f106(a1),x56852)))+~P1(f773(a186,f773(f106(a1),x56851)))
% 191.21/191.75 [5714]~E(f773(f106(a847),x57142),f773(f106(a847),x57141))+E(f773(f106(a1),x57141),f2(a1))+P1(f773(a186,f773(f106(a1),x57141)))+~P1(f773(a186,f773(f106(a1),x57142)))
% 191.21/191.75 [5723]~P100(x57232)+E(x57231,f180(f855(x57232,a841)))+~P1(f773(f63(x57232),x57231))+P1(f773(f773(f334(x57232),f16(x57232,x57231)),x57231))
% 191.21/191.75 [5724]~P100(x57242)+E(x57241,f180(f855(x57242,a841)))+~P1(f773(f63(x57242),x57241))+P1(f773(f773(f334(x57242),f17(x57242,x57241)),x57241))
% 191.21/191.75 [5886]~P110(x58861)+~P88(x58861)+P1(f773(f773(f233(x58861),f2(x58861)),f773(f106(x58861),x58862)))+~P1(f773(f773(f233(a1),a85),x58862))
% 191.21/191.75 [5887]~P110(x58871)+~P88(x58871)+P1(f773(f773(f232(x58871),f2(x58871)),f773(f106(x58871),x58872)))+~P1(f773(f773(f232(a1),a85),x58872))
% 191.21/191.75 [5905]~P110(x59051)+~P88(x59051)+E(f773(f77(x59051),f773(f106(x59051),x59052)),f773(f106(x59051),x59052))+P1(f773(f773(f233(x59051),f773(f106(x59051),x59052)),f2(x59051)))
% 191.21/191.75 [5947]E(x59471,x59472)+~E(f773(a107,x59471),f773(a107,x59472))+~P1(f773(f773(f232(a1),f2(a1)),x59472))+~P1(f773(f773(f232(a1),f2(a1)),x59471))
% 191.21/191.75 [6144]~P88(x61442)+~P110(x61442)+~P1(f773(f773(f233(x61442),f2(x61442)),f773(f106(x61442),x61441)))+P1(f773(f773(f233(a1),a85),x61441))
% 191.21/191.75 [6145]~P88(x61452)+~P110(x61452)+~P1(f773(f773(f232(x61452),f2(x61452)),f773(f106(x61452),x61451)))+P1(f773(f773(f232(a1),a85),x61451))
% 191.21/191.75 [6150]~P110(x61501)+~P88(x61501)+P1(f773(f773(f233(x61501),f773(f106(x61501),x61502)),f2(x61501)))+~P1(f773(f773(f233(a1),x61502),a85))
% 191.21/191.75 [6151]~P110(x61511)+~P88(x61511)+P1(f773(f773(f232(x61511),f773(f106(x61511),x61512)),f2(x61511)))+~P1(f773(f773(f232(a1),x61512),a85))
% 191.21/191.75 [6482]~P88(x64822)+~P110(x64822)+~P1(f773(f773(f233(x64822),f773(f106(x64822),x64821)),f2(x64822)))+P1(f773(f773(f233(a1),x64821),a85))
% 191.21/191.75 [6483]~P88(x64832)+~P110(x64832)+~P1(f773(f773(f232(x64832),f773(f106(x64832),x64831)),f2(x64832)))+P1(f773(f773(f232(a1),x64831),a85))
% 191.21/191.75 [6574]~P110(x65741)+~P88(x65741)+E(f773(f77(x65741),f773(f106(x65741),x65742)),f773(f81(x65741),f773(f106(x65741),x65742)))+~P1(f773(f773(f233(x65741),f773(f106(x65741),x65742)),f2(x65741)))
% 191.21/191.75 [6592]E(f773(f106(a847),x65921),f773(f106(a847),x65922))+~E(f773(f106(a1),x65922),f2(a1))+~P1(f773(f773(f232(a1),f773(f106(a1),x65921)),f2(a1)))+~P1(f773(a186,f773(f106(a1),x65921)))
% 191.21/191.75 [7005]P1(f773(f773(f279(a847),f773(a107,x70051)),f773(a107,x70052)))+~P1(f773(f773(f232(a1),f2(a1)),x70052))+~P1(f773(f773(f232(a1),f2(a1)),x70051))+~P1(f773(f773(f279(a1),x70051),x70052))
% 191.21/191.75 [7248]~P1(f773(f773(f279(a847),f773(a107,x72481)),f773(a107,x72482)))+~P1(f773(f773(f232(a1),f2(a1)),x72482))+~P1(f773(f773(f232(a1),f2(a1)),x72481))+P1(f773(f773(f279(a1),x72481),x72482))
% 191.21/191.75 [7512]~P100(x75122)+E(x75121,f180(f855(x75122,a841)))+~P1(f773(f63(x75122),x75121))+P1(f773(f773(f232(x75122),f14(x75122,f236(x75122),x75121)),f13(x75122,f179(x75122),x75121)))
% 191.21/191.75 [7837]~P10(x78371)+~P38(x78372)+P1(f773(f773(f334(a1),x78371),x78372))+~P1(f773(f773(f334(a847),f773(a107,x78371)),f773(f303(a1,a847,a107),x78372)))
% 191.21/191.75 [5720]~P133(x57202)+E(x57201,f2(a1))+E(f773(f81(x57202),f773(f105(x57202),f773(f81(a1),x57201))),f773(f105(x57202),x57201))+~P1(f773(f773(f233(a1),x57201),f2(a1)))
% 191.21/191.75 [5796]~P87(x57961)+~P88(x57961)+~P33(x57961,f773(f106(x57961),x57962))+P33(x57961,f773(f106(x57961),f773(f773(f82(a1),x57962),x57962)))
% 191.21/191.75 [6134]~P68(x61342)+E(x61341,f180(f855(x61342,a841)))+E(f17(x61342,f773(f303(x61342,x61342,f81(x61342)),x61341)),f773(f81(x61342),f16(x61342,x61341)))+~P1(f773(f63(x61342),x61341))
% 191.21/191.75 [6135]~P68(x61352)+E(x61351,f180(f855(x61352,a841)))+E(f16(x61352,f773(f303(x61352,x61352,f81(x61352)),x61351)),f773(f81(x61352),f17(x61352,x61351)))+~P1(f773(f63(x61352),x61351))
% 191.21/191.75 [6165]~P87(x61651)+~P88(x61651)+P33(x61651,f773(f106(x61651),x61652))+~P33(x61651,f773(f106(x61651),f773(f773(f82(a1),x61652),x61652)))
% 191.21/191.75 [6260]E(x62601,f2(a1))+E(f773(a58,f57(f773(f81(a1),x62601),f773(f81(a1),x62602))),f53(x62601,x62602))+P1(f773(f773(f232(a1),f2(a1)),x62602))+~P1(f773(f773(f232(a1),f2(a1)),x62601))
% 191.21/191.75 [8594]~P38(x85942)+~P38(x85941)+P1(f773(f773(f233(f855(a847,a841)),f773(f303(a1,a847,a107),x85941)),f773(f303(a1,a847,a107),x85942)))+~P1(f773(f773(f233(f855(a1,a841)),x85941),x85942))
% 191.21/191.75 [8869]~P38(x88692)+~P38(x88691)+~P1(f773(f773(f233(f855(a847,a841)),f773(f303(a1,a847,a107),x88691)),f773(f303(a1,a847,a107),x88692)))+P1(f773(f773(f233(f855(a1,a841)),x88691),x88692))
% 191.21/191.75 [8870]~P38(x88702)+~P38(x88701)+~P1(f773(f773(f232(f855(a847,a841)),f773(f303(a1,a847,a107),x88701)),f773(f303(a1,a847,a107),x88702)))+P1(f773(f773(f232(f855(a1,a841)),x88701),x88702))
% 191.21/191.75 [9308]E(x93081,f2(a1))+E(x93082,f2(a1))+E(f773(f773(f88(a1,f854(a1,a1)),f773(f773(a212,x93082),x93081)),f773(f773(f20(a1,a1,f854(a1,a1)),f773(f773(f10(a1,f855(a1,f854(a1,a1)),a1),f241(a1,a1)),f773(f43(a1),x93082))),f773(f43(a1),x93081))),f210(x93082,x93081))+P1(f773(f773(f233(a1),x93081),f2(a1)))
% 191.21/191.75 [8159]~P88(x81592)+~P110(x81592)+~P1(f773(f773(f233(x81592),f773(f106(x81592),x81591)),f80(x81592)))+P1(f773(f773(f233(a1),x81591),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))
% 191.21/191.75 [8160]~P88(x81602)+~P110(x81602)+~P1(f773(f773(f232(x81602),f773(f106(x81602),x81601)),f80(x81602)))+P1(f773(f773(f232(a1),x81601),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))
% 191.21/191.75 [8434]~P110(x84341)+~P88(x84341)+P1(f773(f773(f233(x84341),f773(f106(x84341),x84342)),f80(x84341)))+~P1(f773(f773(f233(a1),x84342),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))
% 191.21/191.75 [8435]~P110(x84351)+~P88(x84351)+P1(f773(f773(f232(x84351),f773(f106(x84351),x84352)),f80(x84351)))+~P1(f773(f773(f232(a1),x84352),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))
% 191.21/191.75 [8619]~P88(x86192)+~P110(x86192)+~P1(f773(f773(f233(x86192),f80(x86192)),f773(f106(x86192),x86191)))+P1(f773(f773(f233(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),x86191))
% 191.21/191.75 [8620]~P88(x86202)+~P110(x86202)+~P1(f773(f773(f232(x86202),f80(x86202)),f773(f106(x86202),x86201)))+P1(f773(f773(f232(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),x86201))
% 191.21/191.75 [8952]~P110(x89521)+~P88(x89521)+P1(f773(f773(f233(x89521),f80(x89521)),f773(f106(x89521),x89522)))+~P1(f773(f773(f233(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),x89522))
% 191.21/191.75 [8953]~P110(x89531)+~P88(x89531)+P1(f773(f773(f232(x89531),f80(x89531)),f773(f106(x89531),x89532)))+~P1(f773(f773(f232(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),x89532))
% 191.21/191.75 [9431]~P120(x94312)+E(x94311,f80(x94312))+E(x94311,f773(f81(x94312),f80(x94312)))+~E(f773(f773(f242(x94312),x94311),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),f80(x94312))
% 191.21/191.75 [9676]~P62(x96761)+~P88(x96761)+~P1(f773(f773(f233(x96761),f2(x96761)),x96762))+P1(f773(f773(f233(x96761),f2(x96761)),f773(f773(f283(x96761),x96762),f773(f106(x96761),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))))
% 191.21/191.75 [9731]~P62(x97311)+~P88(x97311)+P1(f773(f773(f233(x97311),f2(x97311)),x97312))+~P1(f773(f773(f233(x97311),f2(x97311)),f773(f773(f283(x97311),x97312),f773(f106(x97311),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))))
% 191.21/191.75 [10006]~P133(x100062)+E(x100061,f2(a1))+P1(f773(f773(f233(a1),x100061),f2(a1)))+E(f773(f773(f251(a1,a1,x100062),f773(f773(f9(a1,f855(a1,f855(x100062,x100062)),f855(a1,x100062)),f773(f773(f10(f855(f855(x100062,x100062),x100062),f855(f855(a1,f855(x100062,x100062)),f855(a1,x100062)),a1),f10(f855(x100062,x100062),x100062,a1)),f773(f773(f10(x100062,f855(f855(x100062,x100062),x100062),a1),f88(x100062,x100062)),f105(x100062)))),f773(f773(f9(a1,f855(x100062,x100062),f855(x100062,x100062)),f773(f773(f10(f855(x100062,f855(x100062,x100062)),f855(f855(x100062,x100062),f855(x100062,x100062)),a1),f20(x100062,x100062,x100062)),f773(f773(f9(a1,f855(x100062,x100062),f855(x100062,f855(x100062,x100062))),f773(f773(f10(f855(x100062,f855(x100062,x100062)),f855(f855(x100062,x100062),f855(x100062,f855(x100062,x100062))),a1),f10(x100062,f855(x100062,x100062),x100062)),f773(f773(f10(a841,f855(x100062,f855(x100062,x100062)),a1),f98(x100062)),f773(f773(f9(a1,a1,a841),a330),f2(a1))))),f773(f773(f20(x100062,x100062,x100062),f82(x100062)),f7(x100062))))),f773(f773(f9(x100062,x100062,x100062),f773(f773(f10(x100062,f855(x100062,x100062),x100062),f82(x100062)),f773(f773(f20(x100062,x100062,x100062),f82(x100062)),f7(x100062)))),f80(x100062))))),f53(x100061,f773(f106(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))),f773(f105(x100062),x100061))
% 191.21/191.75 [4758]~P87(x47583)+~P88(x47583)+E(x47581,x47582)+~E(f773(f106(x47583),x47581),f773(f106(x47583),x47582))
% 191.21/191.75 [5895]~P1(f773(x58951,x58952))+~P1(f773(x58951,x58953))+~P1(f773(f773(f232(a847),x58953),f789(x58952,x58951)))+P1(f773(x58951,f2(a847)))
% 191.21/191.75 [6327]P140(x63272,x63271,x63273)+E(x63271,f2(a1))+P1(f773(f773(f232(a1),f2(a1)),f777(x63273,x63271,x63272)))+P1(f773(f773(f233(a1),x63271),f2(a1)))
% 191.21/191.75 [6328]P141(x63282,x63281,x63283)+E(x63281,f2(a1))+P1(f773(f773(f232(a1),f2(a1)),f783(x63283,x63281,x63282)))+P1(f773(f773(f233(a1),x63281),f2(a1)))
% 191.21/191.75 [6460]P140(x64601,x64602,x64603)+~P1(f773(x64601,x64603))+P1(f773(f773(f232(a1),f2(a1)),f777(x64603,x64602,x64601)))+P1(f773(f773(f233(a1),x64602),f2(a1)))
% 191.21/191.75 [6485]P141(x64851,x64852,x64853)+P1(f773(f773(f232(a1),f2(a1)),f783(x64853,x64852,x64851)))+~P1(f773(x64851,f2(a1)))+P1(f773(f773(f233(a1),x64852),f2(a1)))
% 191.21/191.75 [6517]P140(x65172,x65171,x65173)+E(x65171,f2(a1))+~P1(f773(x65172,f777(x65173,x65171,x65172)))+P1(f773(f773(f233(a1),x65171),f2(a1)))
% 191.21/191.75 [6518]P141(x65182,x65181,x65183)+E(x65181,f2(a1))+~P1(f773(x65182,f784(x65183,x65181,x65182)))+P1(f773(f773(f233(a1),x65181),f2(a1)))
% 191.21/191.75 [6622]~P100(x66221)+~P9(x66221)+~P1(f773(f773(f233(x66221),x66222),f44(x66221,x66223)))+P1(f773(f773(f233(x66221),x66222),f671(x66223,x66222,x66221)))
% 191.21/191.75 [6632]P140(x66321,x66322,x66323)+~P1(f773(x66321,x66323))+~P1(f773(x66321,f777(x66323,x66322,x66321)))+P1(f773(f773(f233(a1),x66322),f2(a1)))
% 191.21/191.75 [6665]P141(x66651,x66652,x66653)+~P1(f773(x66651,f784(x66653,x66652,x66651)))+~P1(f773(x66651,f2(a1)))+P1(f773(f773(f233(a1),x66652),f2(a1)))
% 191.21/191.75 [6928]P140(x69282,x69281,x69283)+E(x69281,f2(a1))+P1(f773(f773(f232(a1),f2(a1)),f777(x69283,x69281,x69282)))+P1(f773(f773(f233(a1),x69281),f780(x69283,x69281,x69282)))
% 191.21/191.75 [6929]P141(x69292,x69291,x69293)+E(x69291,f2(a1))+P1(f773(f773(f232(a1),f2(a1)),f783(x69293,x69291,x69292)))+P1(f773(f773(f233(a1),x69291),f782(x69293,x69291,x69292)))
% 191.21/191.75 [7046]P140(x70461,x70462,x70463)+~P1(f773(x70461,x70463))+P1(f773(f773(f232(a1),f2(a1)),f777(x70463,x70462,x70461)))+P1(f773(f773(f233(a1),x70462),f780(x70463,x70462,x70461)))
% 191.21/191.75 [7067]P141(x70671,x70672,x70673)+P1(f773(f773(f232(a1),f2(a1)),f783(x70673,x70672,x70671)))+P1(f773(f773(f233(a1),x70672),f782(x70673,x70672,x70671)))+~P1(f773(x70671,f2(a1)))
% 191.21/191.75 [7098]P140(x70982,x70981,x70983)+E(x70981,f2(a1))+~P1(f773(x70982,f777(x70983,x70981,x70982)))+P1(f773(f773(f233(a1),x70981),f780(x70983,x70981,x70982)))
% 191.21/191.75 [7099]P141(x70992,x70991,x70993)+E(x70991,f2(a1))+~P1(f773(x70992,f784(x70993,x70991,x70992)))+P1(f773(f773(f233(a1),x70991),f782(x70993,x70991,x70992)))
% 191.21/191.75 [7139]P140(x71392,x71391,x71393)+E(x71391,f2(a1))+P1(f773(f773(f232(a1),f2(a1)),f777(x71393,x71391,x71392)))+~P1(f773(x71392,f780(x71393,x71391,x71392)))
% 191.21/191.75 [7140]P141(x71402,x71401,x71403)+E(x71401,f2(a1))+P1(f773(f773(f232(a1),f2(a1)),f783(x71403,x71401,x71402)))+~P1(f773(x71402,f785(x71403,x71401,x71402)))
% 191.21/191.75 [7245]P140(x72451,x72452,x72453)+~P1(f773(x72451,x72453))+~P1(f773(x72451,f777(x72453,x72452,x72451)))+P1(f773(f773(f233(a1),x72452),f780(x72453,x72452,x72451)))
% 191.21/191.75 [7261]P141(x72611,x72612,x72613)+~P1(f773(x72611,f784(x72613,x72612,x72611)))+P1(f773(f773(f233(a1),x72612),f782(x72613,x72612,x72611)))+~P1(f773(x72611,f2(a1)))
% 191.21/191.75 [7267]P140(x72671,x72672,x72673)+~P1(f773(x72671,x72673))+P1(f773(f773(f232(a1),f2(a1)),f777(x72673,x72672,x72671)))+~P1(f773(x72671,f780(x72673,x72672,x72671)))
% 191.21/191.75 [7285]P141(x72851,x72852,x72853)+P1(f773(f773(f232(a1),f2(a1)),f783(x72853,x72852,x72851)))+~P1(f773(x72851,f785(x72853,x72852,x72851)))+~P1(f773(x72851,f2(a1)))
% 191.21/191.75 [7309]P140(x73092,x73091,x73093)+E(x73091,f2(a1))+~P1(f773(x73092,f777(x73093,x73091,x73092)))+~P1(f773(x73092,f780(x73093,x73091,x73092)))
% 191.21/191.75 [7310]P141(x73102,x73101,x73103)+E(x73101,f2(a1))+~P1(f773(x73102,f784(x73103,x73101,x73102)))+~P1(f773(x73102,f785(x73103,x73101,x73102)))
% 191.21/191.75 [7406]P140(x74061,x74062,x74063)+~P1(f773(x74061,x74063))+~P1(f773(x74061,f777(x74063,x74062,x74061)))+~P1(f773(x74061,f780(x74063,x74062,x74061)))
% 191.21/191.75 [7421]P141(x74211,x74212,x74213)+~P1(f773(x74211,f784(x74213,x74212,x74211)))+~P1(f773(x74211,f785(x74213,x74212,x74211)))+~P1(f773(x74211,f2(a1)))
% 191.21/191.75 [7472]P140(x74722,x74721,x74723)+E(x74721,f2(a1))+P1(f773(f773(f232(a1),f2(a1)),f777(x74723,x74721,x74722)))+P1(f773(f773(f232(a1),f780(x74723,x74721,x74722)),f2(a1)))
% 191.21/191.75 [7473]P141(x74732,x74731,x74733)+E(x74731,f2(a1))+P1(f773(f773(f232(a1),f2(a1)),f783(x74733,x74731,x74732)))+P1(f773(f773(f232(a1),f782(x74733,x74731,x74732)),f2(a1)))
% 191.21/191.75 [7474]~P2(x74741)+~P1(f773(f773(f334(x74741),x74743),f176(x74741)))+~P1(f773(f773(f334(x74741),x74742),f176(x74741)))+P1(f773(f773(f334(x74741),f773(f773(f82(x74741),x74742),x74743)),f176(x74741)))
% 191.21/191.75 [7475]~P133(x74751)+~P1(f773(f773(f334(x74751),x74753),f112(x74751)))+~P1(f773(f773(f334(x74751),x74752),f112(x74751)))+P1(f773(f773(f334(x74751),f773(f773(f82(x74751),x74752),x74753)),f112(x74751)))
% 191.21/191.75 [7476]~P2(x74761)+~P1(f773(f773(f334(x74761),x74763),f176(x74761)))+~P1(f773(f773(f334(x74761),x74762),f176(x74761)))+P1(f773(f773(f334(x74761),f773(f773(f83(x74761),x74762),x74763)),f176(x74761)))
% 191.21/191.75 [7477]~P133(x74771)+~P1(f773(f773(f334(x74771),x74773),f112(x74771)))+~P1(f773(f773(f334(x74771),x74772),f112(x74771)))+P1(f773(f773(f334(x74771),f773(f773(f83(x74771),x74772),x74773)),f112(x74771)))
% 191.21/191.75 [7478]~P133(x74781)+~P1(f773(f773(f334(x74781),x74783),f112(x74781)))+~P1(f773(f773(f334(x74781),x74782),f112(x74781)))+P1(f773(f773(f334(x74781),f773(f773(f3(x74781),x74782),x74783)),f112(x74781)))
% 191.21/191.75 [7479]~P81(x74791)+~P1(f773(f773(f233(x74791),x74793),f2(x74791)))+~P1(f773(f773(f233(x74791),x74792),f2(x74791)))+P1(f773(f773(f233(x74791),f773(f773(f82(x74791),x74792),x74793)),f2(x74791)))
% 191.21/191.75 [7480]~P81(x74801)+~P1(f773(f773(f232(x74801),x74802),f2(x74801)))+~P1(f773(f773(f233(x74801),x74803),f2(x74801)))+P1(f773(f773(f233(x74801),f773(f773(f82(x74801),x74802),x74803)),f2(x74801)))
% 191.21/191.75 [7481]~P81(x74811)+~P1(f773(f773(f232(x74811),x74813),f2(x74811)))+~P1(f773(f773(f233(x74811),x74812),f2(x74811)))+P1(f773(f773(f233(x74811),f773(f773(f82(x74811),x74812),x74813)),f2(x74811)))
% 191.21/191.75 [7482]~P81(x74821)+~P1(f773(f773(f232(x74821),x74823),f2(x74821)))+~P1(f773(f773(f232(x74821),x74822),f2(x74821)))+P1(f773(f773(f232(x74821),f773(f773(f82(x74821),x74822),x74823)),f2(x74821)))
% 191.21/191.75 [7508]P140(x75083,x75081,x75082)+E(x75081,f2(a1))+E(f773(f773(f82(a1),f773(f773(f83(a1),x75081),f778(x75082,x75081,x75083))),f777(x75082,x75081,x75083)),x75082)+P1(f773(f773(f233(a1),x75081),f2(a1)))
% 191.21/191.75 [7509]P141(x75093,x75091,x75092)+E(x75091,f2(a1))+E(f773(f773(f82(a1),f773(f773(f83(a1),x75091),f784(x75092,x75091,x75093))),f783(x75092,x75091,x75093)),x75092)+P1(f773(f773(f233(a1),x75091),f2(a1)))
% 191.21/191.75 [7594]P140(x75941,x75942,x75943)+~P1(f773(x75941,x75943))+P1(f773(f773(f232(a1),f2(a1)),f777(x75943,x75942,x75941)))+P1(f773(f773(f232(a1),f780(x75943,x75942,x75941)),f2(a1)))
% 191.21/191.75 [7625]P141(x76251,x76252,x76253)+P1(f773(f773(f232(a1),f2(a1)),f783(x76253,x76252,x76251)))+~P1(f773(x76251,f2(a1)))+P1(f773(f773(f232(a1),f782(x76253,x76252,x76251)),f2(a1)))
% 191.21/191.75 [7633]P140(x76333,x76331,x76332)+~P1(f773(x76333,x76332))+E(f773(f773(f82(a1),f773(f773(f83(a1),x76331),f778(x76332,x76331,x76333))),f777(x76332,x76331,x76333)),x76332)+P1(f773(f773(f233(a1),x76331),f2(a1)))
% 191.21/191.75 [7638]P140(x76382,x76381,x76383)+E(x76381,f2(a1))+~P1(f773(x76382,f777(x76383,x76381,x76382)))+P1(f773(f773(f232(a1),f780(x76383,x76381,x76382)),f2(a1)))
% 191.21/191.75 [7639]P141(x76392,x76391,x76393)+E(x76391,f2(a1))+~P1(f773(x76392,f784(x76393,x76391,x76392)))+P1(f773(f773(f232(a1),f782(x76393,x76391,x76392)),f2(a1)))
% 191.21/191.75 [7644]P141(x76443,x76441,x76442)+E(f773(f773(f82(a1),f773(f773(f83(a1),x76441),f784(x76442,x76441,x76443))),f783(x76442,x76441,x76443)),x76442)+~P1(f773(x76443,f2(a1)))+P1(f773(f773(f233(a1),x76441),f2(a1)))
% 191.21/191.75 [7697]P140(x76971,x76972,x76973)+~P1(f773(x76971,x76973))+~P1(f773(x76971,f777(x76973,x76972,x76971)))+P1(f773(f773(f232(a1),f780(x76973,x76972,x76971)),f2(a1)))
% 191.21/191.75 [7702]P141(x77021,x77022,x77023)+~P1(f773(x77021,f784(x77023,x77022,x77021)))+~P1(f773(x77021,f2(a1)))+P1(f773(f773(f232(a1),f782(x77023,x77022,x77021)),f2(a1)))
% 191.21/191.75 [7776]~P62(x77761)+~P1(f773(f773(f233(x77761),f773(f773(f283(x77761),x77763),x77762)),f2(x77761)))+P1(f773(f773(f233(x77761),x77762),f2(x77761)))+P1(f773(f773(f233(x77761),x77763),f2(x77761)))
% 191.21/191.75 [7777]~P119(x77771)+~P1(f773(f773(f232(x77771),f773(f773(f83(x77771),x77773),x77772)),f2(x77771)))+P1(f773(f773(f232(x77771),x77772),f2(x77771)))+P1(f773(f773(f232(x77771),x77773),f2(x77771)))
% 191.21/191.75 [7778]~P62(x77781)+~P1(f773(f773(f232(x77781),f773(f773(f283(x77781),x77783),x77782)),f2(x77781)))+P1(f773(f773(f232(x77781),x77782),f2(x77781)))+P1(f773(f773(f232(x77781),x77783),f2(x77781)))
% 191.21/191.75 [7890]P140(x78903,x78901,x78902)+E(x78901,f2(a1))+E(f773(f773(f82(a1),f773(f773(f83(a1),x78901),f778(x78902,x78901,x78903))),f777(x78902,x78901,x78903)),x78902)+P1(f773(f773(f233(a1),x78901),f780(x78902,x78901,x78903)))
% 191.21/191.75 [7891]P141(x78913,x78911,x78912)+E(x78911,f2(a1))+E(f773(f773(f82(a1),f773(f773(f83(a1),x78911),f784(x78912,x78911,x78913))),f783(x78912,x78911,x78913)),x78912)+P1(f773(f773(f233(a1),x78911),f782(x78912,x78911,x78913)))
% 191.21/191.75 [7902]P140(x79023,x79021,x79022)+E(x79021,f2(a1))+E(f773(f773(f82(a1),f773(f773(f83(a1),x79021),f779(x79022,x79021,x79023))),f780(x79022,x79021,x79023)),x79022)+P1(f773(f773(f232(a1),f2(a1)),f777(x79022,x79021,x79023)))
% 191.21/191.75 [7903]P141(x79033,x79031,x79032)+E(x79031,f2(a1))+E(f773(f773(f82(a1),f773(f773(f83(a1),x79031),f785(x79032,x79031,x79033))),f782(x79032,x79031,x79033)),x79032)+P1(f773(f773(f232(a1),f2(a1)),f783(x79032,x79031,x79033)))
% 191.21/191.75 [7950]P140(x79503,x79501,x79502)+~P1(f773(x79503,x79502))+E(f773(f773(f82(a1),f773(f773(f83(a1),x79501),f778(x79502,x79501,x79503))),f777(x79502,x79501,x79503)),x79502)+P1(f773(f773(f233(a1),x79501),f780(x79502,x79501,x79503)))
% 191.21/191.75 [7961]P141(x79613,x79611,x79612)+E(f773(f773(f82(a1),f773(f773(f83(a1),x79611),f784(x79612,x79611,x79613))),f783(x79612,x79611,x79613)),x79612)+P1(f773(f773(f233(a1),x79611),f782(x79612,x79611,x79613)))+~P1(f773(x79613,f2(a1)))
% 191.21/191.75 [7967]P140(x79673,x79671,x79672)+~P1(f773(x79673,x79672))+E(f773(f773(f82(a1),f773(f773(f83(a1),x79671),f779(x79672,x79671,x79673))),f780(x79672,x79671,x79673)),x79672)+P1(f773(f773(f232(a1),f2(a1)),f777(x79672,x79671,x79673)))
% 191.21/191.75 [7974]P141(x79743,x79741,x79742)+E(f773(f773(f82(a1),f773(f773(f83(a1),x79741),f785(x79742,x79741,x79743))),f782(x79742,x79741,x79743)),x79742)+P1(f773(f773(f232(a1),f2(a1)),f783(x79742,x79741,x79743)))+~P1(f773(x79743,f2(a1)))
% 191.21/191.75 [7984]P140(x79843,x79841,x79842)+E(x79841,f2(a1))+E(f773(f773(f82(a1),f773(f773(f83(a1),x79841),f778(x79842,x79841,x79843))),f777(x79842,x79841,x79843)),x79842)+~P1(f773(x79843,f780(x79842,x79841,x79843)))
% 191.21/191.75 [7985]P141(x79853,x79851,x79852)+E(x79851,f2(a1))+E(f773(f773(f82(a1),f773(f773(f83(a1),x79851),f784(x79852,x79851,x79853))),f783(x79852,x79851,x79853)),x79852)+~P1(f773(x79853,f785(x79852,x79851,x79853)))
% 191.21/191.75 [7986]P140(x79863,x79861,x79862)+E(x79861,f2(a1))+E(f773(f773(f82(a1),f773(f773(f83(a1),x79861),f779(x79862,x79861,x79863))),f780(x79862,x79861,x79863)),x79862)+~P1(f773(x79863,f777(x79862,x79861,x79863)))
% 191.21/191.75 [7987]P141(x79873,x79871,x79872)+E(x79871,f2(a1))+E(f773(f773(f82(a1),f773(f773(f83(a1),x79871),f785(x79872,x79871,x79873))),f782(x79872,x79871,x79873)),x79872)+~P1(f773(x79873,f784(x79872,x79871,x79873)))
% 191.21/191.75 [8040]P140(x80403,x80401,x80402)+~P1(f773(x80403,x80402))+E(f773(f773(f82(a1),f773(f773(f83(a1),x80401),f778(x80402,x80401,x80403))),f777(x80402,x80401,x80403)),x80402)+~P1(f773(x80403,f780(x80402,x80401,x80403)))
% 191.21/191.75 [8041]P140(x80413,x80411,x80412)+~P1(f773(x80413,x80412))+E(f773(f773(f82(a1),f773(f773(f83(a1),x80411),f779(x80412,x80411,x80413))),f780(x80412,x80411,x80413)),x80412)+~P1(f773(x80413,f777(x80412,x80411,x80413)))
% 191.21/191.75 [8053]P141(x80533,x80531,x80532)+E(f773(f773(f82(a1),f773(f773(f83(a1),x80531),f784(x80532,x80531,x80533))),f783(x80532,x80531,x80533)),x80532)+~P1(f773(x80533,f785(x80532,x80531,x80533)))+~P1(f773(x80533,f2(a1)))
% 191.21/191.75 [8054]P141(x80543,x80541,x80542)+E(f773(f773(f82(a1),f773(f773(f83(a1),x80541),f785(x80542,x80541,x80543))),f782(x80542,x80541,x80543)),x80542)+~P1(f773(x80543,f784(x80542,x80541,x80543)))+~P1(f773(x80543,f2(a1)))
% 191.21/191.75 [8152]P140(x81523,x81521,x81522)+E(x81521,f2(a1))+E(f773(f773(f82(a1),f773(f773(f83(a1),x81521),f778(x81522,x81521,x81523))),f777(x81522,x81521,x81523)),x81522)+P1(f773(f773(f232(a1),f780(x81522,x81521,x81523)),f2(a1)))
% 191.21/191.75 [8153]P141(x81533,x81531,x81532)+E(x81531,f2(a1))+E(f773(f773(f82(a1),f773(f773(f83(a1),x81531),f784(x81532,x81531,x81533))),f783(x81532,x81531,x81533)),x81532)+P1(f773(f773(f232(a1),f782(x81532,x81531,x81533)),f2(a1)))
% 191.21/191.75 [8191]P140(x81913,x81911,x81912)+~P1(f773(x81913,x81912))+E(f773(f773(f82(a1),f773(f773(f83(a1),x81911),f778(x81912,x81911,x81913))),f777(x81912,x81911,x81913)),x81912)+P1(f773(f773(f232(a1),f780(x81912,x81911,x81913)),f2(a1)))
% 191.21/191.75 [8196]P141(x81963,x81961,x81962)+E(f773(f773(f82(a1),f773(f773(f83(a1),x81961),f784(x81962,x81961,x81963))),f783(x81962,x81961,x81963)),x81962)+~P1(f773(x81963,f2(a1)))+P1(f773(f773(f232(a1),f782(x81962,x81961,x81963)),f2(a1)))
% 191.21/191.75 [8327]P140(x83273,x83271,x83272)+E(x83271,f2(a1))+E(f773(f773(f82(a1),f773(f773(f83(a1),x83271),f779(x83272,x83271,x83273))),f780(x83272,x83271,x83273)),x83272)+E(f773(f773(f82(a1),f773(f773(f83(a1),x83271),f778(x83272,x83271,x83273))),f777(x83272,x83271,x83273)),x83272)
% 191.21/191.75 [8328]P141(x83283,x83281,x83282)+E(x83281,f2(a1))+E(f773(f773(f82(a1),f773(f773(f83(a1),x83281),f785(x83282,x83281,x83283))),f782(x83282,x83281,x83283)),x83282)+E(f773(f773(f82(a1),f773(f773(f83(a1),x83281),f784(x83282,x83281,x83283))),f783(x83282,x83281,x83283)),x83282)
% 191.21/191.75 [8351]P140(x83513,x83511,x83512)+~P1(f773(x83513,x83512))+E(f773(f773(f82(a1),f773(f773(f83(a1),x83511),f779(x83512,x83511,x83513))),f780(x83512,x83511,x83513)),x83512)+E(f773(f773(f82(a1),f773(f773(f83(a1),x83511),f778(x83512,x83511,x83513))),f777(x83512,x83511,x83513)),x83512)
% 191.21/191.75 [8363]P141(x83633,x83631,x83632)+E(f773(f773(f82(a1),f773(f773(f83(a1),x83631),f785(x83632,x83631,x83633))),f782(x83632,x83631,x83633)),x83632)+E(f773(f773(f82(a1),f773(f773(f83(a1),x83631),f784(x83632,x83631,x83633))),f783(x83632,x83631,x83633)),x83632)+~P1(f773(x83633,f2(a1)))
% 191.21/191.75 [8957]~P119(x89571)+~E(x89573,f2(x89571))+~E(x89572,f2(x89571))+P1(f773(f773(f232(x89571),f773(f773(f82(x89571),f773(f773(f83(x89571),x89572),x89572)),f773(f773(f83(x89571),x89573),x89573))),f2(x89571)))
% 191.21/191.75 [9956]~P110(x99561)+~E(x99563,f2(x99561))+~E(x99562,f2(x99561))+P1(f773(f773(f232(x99561),f773(f773(f82(x99561),f773(f773(f242(x99561),x99562),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))),f773(f773(f242(x99561),x99563),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))))),f2(x99561)))
% 191.21/191.75 [4708]~E(x47083,x47081)+~P113(x47082)+E(x47081,f2(x47082))+E(f773(f773(f283(x47082),x47083),x47081),f80(x47082))
% 191.21/191.75 [4759]~P95(x47591)+~E(x47593,f180(x47591))+~E(x47592,f180(x47591))+E(f773(f773(f103(x47591),x47592),x47593),f180(x47591))
% 191.21/191.75 [4760]~P94(x47601)+~E(x47603,f239(x47601))+~E(x47602,f239(x47601))+E(f773(f773(f104(x47601),x47602),x47603),f239(x47601))
% 191.21/191.75 [4846]~P113(x48463)+E(x48461,x48462)+E(x48462,f2(x48463))+~E(f773(f773(f283(x48463),x48461),x48462),f80(x48463))
% 191.21/191.75 [4862]~P134(x48622)+E(x48621,f2(x48622))+E(x48623,f2(x48622))+~E(f773(f773(f83(x48622),x48623),x48621),f2(x48622))
% 191.21/191.75 [4864]~P127(x48642)+E(x48641,f2(x48642))+E(x48643,f2(x48642))+~E(f773(f773(f83(x48642),x48643),x48641),f2(x48642))
% 191.21/191.75 [5233]~P111(x52333)+E(x52331,x52332)+E(x52331,f773(f81(x52333),x52332))+~E(f773(f773(f83(x52333),x52331),x52331),f773(f773(f83(x52333),x52332),x52332))
% 191.21/191.75 [5269]~P90(x52691)+E(f773(f81(x52691),x52692),x52693)+~E(f773(f773(f103(x52691),x52692),x52693),f239(x52691))+~E(f773(f773(f104(x52691),x52692),x52693),f180(x52691))
% 191.21/191.75 [5344]~P110(x53443)+E(x53441,x53442)+P1(f773(f773(f233(x53443),x53442),x53441))+P1(f773(f773(f233(x53443),x53441),x53442))
% 191.21/191.75 [5350]~P100(x53503)+E(x53501,x53502)+P1(f773(f773(f233(x53503),x53502),x53501))+P1(f773(f773(f233(x53503),x53501),x53502))
% 191.21/191.75 [5351]~E(x53512,x53513)+~P100(x53511)+P1(f773(f773(f232(x53511),x53512),x53513))+P1(f773(f773(f233(x53511),x53512),x53513))
% 191.21/191.75 [5597]~P99(x55973)+E(x55971,x55972)+~P1(f773(f773(f232(x55973),x55972),x55971))+P1(f773(f773(f233(x55973),x55972),x55971))
% 191.21/191.75 [5603]~P99(x56033)+E(x56031,x56032)+~P1(f773(f773(f232(x56033),x56031),x56032))+P1(f773(f773(f233(x56033),x56031),x56032))
% 191.21/191.75 [5605]~P100(x56053)+E(x56051,x56052)+~P1(f773(f773(f232(x56053),x56051),x56052))+P1(f773(f773(f233(x56053),x56051),x56052))
% 191.21/191.75 [5717]P140(x57171,x57172,x57173)+~P1(f773(x57171,x57173))+P1(f773(f773(f233(a1),x57172),f2(a1)))+P1(f773(f773(f233(a1),f2(a1)),x57172))
% 191.21/191.75 [5768]P141(x57681,x57682,x57683)+~P1(f773(x57681,f2(a1)))+P1(f773(f773(f233(a1),x57682),f2(a1)))+P1(f773(f773(f233(a1),f2(a1)),x57682))
% 191.21/191.75 [5772]~P93(x57721)+E(f773(f773(f103(x57721),x57722),f12(x57721,x57723)),x57722)+~P1(f773(f63(x57721),x57723))+~P1(f773(f773(f334(x57721),x57722),x57723))
% 191.21/191.75 [5773]~P93(x57731)+E(f773(f773(f104(x57731),x57732),f15(x57731,x57733)),x57732)+~P1(f773(f63(x57731),x57733))+~P1(f773(f773(f334(x57731),x57732),x57733))
% 191.21/191.75 [5806]~P100(x58061)+E(f773(f773(f236(x58061),x58062),f17(x58061,x58063)),f17(x58061,x58063))+~P1(f773(f63(x58061),x58063))+~P1(f773(f773(f334(x58061),x58062),x58063))
% 191.21/191.75 [5807]~P100(x58071)+E(f773(f773(f179(x58071),x58072),f16(x58071,x58073)),f16(x58071,x58073))+~P1(f773(f63(x58071),x58073))+~P1(f773(f773(f334(x58071),x58072),x58073))
% 191.21/191.75 [5808]~P93(x58081)+E(f773(f773(f103(x58081),x58082),f15(x58081,x58083)),f15(x58081,x58083))+~P1(f773(f63(x58081),x58083))+~P1(f773(f773(f334(x58081),x58082),x58083))
% 191.21/191.75 [5809]~P93(x58091)+E(f773(f773(f104(x58091),x58092),f12(x58091,x58093)),f12(x58091,x58093))+~P1(f773(f63(x58091),x58093))+~P1(f773(f773(f334(x58091),x58092),x58093))
% 191.21/191.75 [5849]E(x58491,x58492)+~P99(x58493)+~P1(f773(f773(f232(x58493),x58492),x58491))+~P1(f773(f773(f232(x58493),x58491),x58492))
% 191.21/191.75 [5991]~P103(x59911)+P1(f773(f773(f232(x59911),x59913),x59912))+~P1(f773(f773(f232(x59911),x59912),x59913))+P1(f773(f773(f233(x59911),x59912),x59913))
% 191.21/191.75 [6015]~P100(x60151)+~P1(f773(f63(x60151),x60153))+P1(f773(f773(f232(x60151),x60152),f16(x60151,x60153)))+~P1(f773(f773(f334(x60151),x60152),x60153))
% 191.21/191.75 [6069]~P100(x60691)+E(f773(f773(f236(x60691),x60692),f13(x60691,f179(x60691),x60693)),x60692)+~P1(f773(f63(x60691),x60693))+~P1(f773(f773(f334(x60691),x60692),x60693))
% 191.21/191.75 [6070]~P100(x60701)+E(f773(f773(f179(x60701),x60702),f14(x60701,f236(x60701),x60703)),x60702)+~P1(f773(f63(x60701),x60703))+~P1(f773(f773(f334(x60701),x60702),x60703))
% 191.21/191.75 [6211]E(x62111,x62112)+~E(f773(f773(f3(a847),x62111),x62113),f773(f773(f3(a847),x62112),x62113))+~P1(f773(f773(f232(a847),x62113),x62111))+~P1(f773(f773(f232(a847),x62113),x62112))
% 191.21/191.75 [6239]~P100(x62391)+~P1(f773(f63(x62391),x62392))+~P1(f773(f773(f334(x62391),x62393),x62392))+P1(f773(f773(f232(x62391),f17(x62391,x62392)),x62393))
% 191.21/191.75 [6306]P140(x63062,x63061,x63063)+E(x63061,f2(a1))+P1(f773(f773(f233(a1),x63061),f780(x63063,x63061,x63062)))+P1(f773(f773(f233(a1),f2(a1)),x63061))
% 191.21/191.75 [6307]P141(x63072,x63071,x63073)+E(x63071,f2(a1))+P1(f773(f773(f233(a1),x63071),f782(x63073,x63071,x63072)))+P1(f773(f773(f233(a1),f2(a1)),x63071))
% 191.21/191.75 [6308]~P100(x63081)+E(f773(f773(f236(x63081),x63082),f14(x63081,f236(x63081),x63083)),f14(x63081,f236(x63081),x63083))+~P1(f773(f63(x63081),x63083))+~P1(f773(f773(f334(x63081),x63082),x63083))
% 191.21/191.75 [6309]~P100(x63091)+E(f773(f773(f179(x63091),x63092),f13(x63091,f179(x63091),x63093)),f13(x63091,f179(x63091),x63093))+~P1(f773(f63(x63091),x63093))+~P1(f773(f773(f334(x63091),x63092),x63093))
% 191.21/191.75 [6316]~P1(f773(x63161,x63162))+P1(f773(x63161,f807(x63162,x63161,x63163)))+P1(f773(x63161,f2(a847)))+~P1(f773(f773(f233(a847),x63162),x63163))
% 191.21/191.75 [6375]~P1(f773(x63751,x63752))+~P1(f773(f63(x63753),x63752))+P1(f773(x63751,f482(x63751,x63752,x63753)))+P1(f773(x63751,f180(f855(x63753,a841))))
% 191.21/191.75 [6390]~P110(x63901)+~P88(x63901)+P1(f773(f773(f233(x63901),f773(f106(x63901),x63902)),f773(f106(x63901),x63903)))+~P1(f773(f773(f233(a1),x63902),x63903))
% 191.21/191.75 [6391]~P110(x63911)+~P88(x63911)+P1(f773(f773(f232(x63911),f773(f106(x63911),x63912)),f773(f106(x63911),x63913)))+~P1(f773(f773(f232(a1),x63912),x63913))
% 191.21/191.75 [6394]~P1(f773(x63941,x63943))+~P1(f773(f63(x63942),x63943))+P1(f773(f63(x63942),f482(x63941,x63943,x63942)))+P1(f773(x63941,f180(f855(x63942,a841))))
% 191.21/191.75 [6428]P140(x64281,x64282,x64283)+~P1(f773(x64281,x64283))+P1(f773(f773(f233(a1),x64282),f780(x64283,x64282,x64281)))+P1(f773(f773(f233(a1),f2(a1)),x64282))
% 191.21/191.75 [6468]P141(x64681,x64682,x64683)+P1(f773(f773(f233(a1),x64682),f782(x64683,x64682,x64681)))+~P1(f773(x64681,f2(a1)))+P1(f773(f773(f233(a1),f2(a1)),x64682))
% 191.21/191.75 [6496]~P102(x64961)+~P89(x64961)+E(f773(f773(f236(x64961),f773(f106(x64961),x64962)),f773(f106(x64961),x64963)),f773(f106(x64961),x64963))+P1(f773(f773(f232(x64961),f773(f106(x64961),x64962)),f773(f106(x64961),x64963)))
% 191.21/191.75 [6497]~P102(x64971)+~P89(x64971)+E(f773(f773(f179(x64971),f773(f106(x64971),x64972)),f773(f106(x64971),x64973)),f773(f106(x64971),x64972))+P1(f773(f773(f232(x64971),f773(f106(x64971),x64972)),f773(f106(x64971),x64973)))
% 191.21/191.75 [6559]P140(x65592,x65591,x65593)+E(x65591,f2(a1))+~P1(f773(x65592,f780(x65593,x65591,x65592)))+P1(f773(f773(f233(a1),f2(a1)),x65591))
% 191.21/191.75 [6560]P141(x65602,x65601,x65603)+E(x65601,f2(a1))+~P1(f773(x65602,f785(x65603,x65601,x65602)))+P1(f773(f773(f233(a1),f2(a1)),x65601))
% 191.21/191.75 [6655]P140(x66551,x66552,x66553)+~P1(f773(x66551,x66553))+~P1(f773(x66551,f780(x66553,x66552,x66551)))+P1(f773(f773(f233(a1),f2(a1)),x66552))
% 191.21/191.75 [6685]P141(x66851,x66852,x66853)+~P1(f773(x66851,f785(x66853,x66852,x66851)))+~P1(f773(x66851,f2(a1)))+P1(f773(f773(f233(a1),f2(a1)),x66852))
% 191.21/191.75 [6802]~P88(x68023)+~P110(x68023)+~P1(f773(f773(f233(x68023),f773(f106(x68023),x68021)),f773(f106(x68023),x68022)))+P1(f773(f773(f233(a1),x68021),x68022))
% 191.21/191.75 [6803]~P88(x68033)+~P110(x68033)+~P1(f773(f773(f232(x68033),f773(f106(x68033),x68031)),f773(f106(x68033),x68032)))+P1(f773(f773(f232(a1),x68031),x68032))
% 191.21/191.75 [6832]~P100(x68321)+~P18(x68321,x68323)+P18(x68321,f773(f773(f140(x68321),x68322),x68323))+~P1(f773(f773(f232(x68321),x68322),f762(x68323,x68322,x68321)))
% 191.21/191.75 [6833]~P100(x68331)+~P18(x68331,x68333)+P18(x68331,f773(f773(f140(x68331),x68332),x68333))+~P1(f773(f773(f232(x68331),x68332),f763(x68333,x68332,x68331)))
% 191.21/191.75 [6920]P140(x69202,x69201,x69203)+E(x69201,f2(a1))+P1(f773(f773(f233(a1),x69201),f2(a1)))+P1(f773(f773(f233(a1),f777(x69203,x69201,x69202)),x69201))
% 191.21/191.75 [6921]P141(x69212,x69211,x69213)+E(x69211,f2(a1))+P1(f773(f773(f233(a1),x69211),f2(a1)))+P1(f773(f773(f233(a1),f783(x69213,x69211,x69212)),x69211))
% 191.21/191.75 [6960]P140(x69602,x69601,x69603)+E(x69601,f2(a1))+P1(f773(f773(f232(a1),f780(x69603,x69601,x69602)),f2(a1)))+P1(f773(f773(f233(a1),f2(a1)),x69601))
% 191.21/191.75 [6961]P141(x69612,x69611,x69613)+E(x69611,f2(a1))+P1(f773(f773(f232(a1),f782(x69613,x69611,x69612)),f2(a1)))+P1(f773(f773(f233(a1),f2(a1)),x69611))
% 191.21/191.75 [6979]~P100(x69791)+~P18(x69791,x69793)+E(f773(f773(f138(x69791,x69791,f7(x69791)),x69792),f151(x69791,x69792,x69793)),x69793)+~P1(f773(f773(f334(x69791),x69792),f773(f158(x69791),x69793)))
% 191.21/191.75 [7029]P140(x70291,x70292,x70293)+~P1(f773(x70291,x70293))+P1(f773(f773(f233(a1),x70292),f2(a1)))+P1(f773(f773(f233(a1),f777(x70293,x70292,x70291)),x70292))
% 191.21/191.75 [7035]~P102(x70351)+~P89(x70351)+E(f773(f773(f236(x70351),f773(f106(x70351),x70352)),f773(f106(x70351),x70353)),f773(f106(x70351),x70352))+~P1(f773(f773(f232(x70351),f773(f106(x70351),x70352)),f773(f106(x70351),x70353)))
% 191.21/191.75 [7036]~P102(x70361)+~P89(x70361)+E(f773(f773(f179(x70361),f773(f106(x70361),x70362)),f773(f106(x70361),x70363)),f773(f106(x70361),x70363))+~P1(f773(f773(f232(x70361),f773(f106(x70361),x70362)),f773(f106(x70361),x70363)))
% 191.21/191.75 [7049]P141(x70491,x70492,x70493)+~P1(f773(x70491,f2(a1)))+P1(f773(f773(f233(a1),x70492),f2(a1)))+P1(f773(f773(f233(a1),f783(x70493,x70492,x70491)),x70492))
% 191.21/191.75 [7059]P140(x70591,x70592,x70593)+~P1(f773(x70591,x70593))+P1(f773(f773(f232(a1),f780(x70593,x70592,x70591)),f2(a1)))+P1(f773(f773(f233(a1),f2(a1)),x70592))
% 191.21/191.75 [7083]P141(x70831,x70832,x70833)+~P1(f773(x70831,f2(a1)))+P1(f773(f773(f232(a1),f782(x70833,x70832,x70831)),f2(a1)))+P1(f773(f773(f233(a1),f2(a1)),x70832))
% 191.21/191.75 [7110]~P1(f773(x71101,x71102))+P1(f773(x71101,f2(a847)))+~P1(f773(f773(f233(a847),x71102),x71103))+P1(f773(f773(f233(a847),f807(x71102,x71101,x71103)),x71103))
% 191.21/191.75 [7127]~P100(x71271)+~P18(x71271,x71273)+P18(x71271,f773(f773(f140(x71271),x71272),x71273))+P1(f773(f773(f334(x71271),f762(x71273,x71272,x71271)),f773(f158(x71271),x71273)))
% 191.21/191.75 [7128]~P100(x71281)+~P18(x71281,x71283)+P18(x71281,f773(f773(f140(x71281),x71282),x71283))+P1(f773(f773(f334(x71281),f763(x71283,x71282,x71281)),f773(f158(x71281),x71283)))
% 191.21/191.75 [7250]~P100(x72501)+~P9(x72501)+~P1(f773(f773(f233(x72501),x72503),f44(x72501,x72502)))+P1(f773(f773(f334(x72501),f671(x72502,x72503,x72501)),x72502))
% 191.21/191.75 [7419]~P100(x74191)+~P9(x74191)+~P1(f773(f773(f233(x74191),f45(x74191,x74193)),x74192))+P1(f773(f773(f334(x74191),f674(x74192,x74193,x74191)),x74193))
% 191.21/191.75 [7420]~P100(x74201)+~P9(x74201)+~P1(f773(f773(f233(x74201),f45(x74201,x74203)),x74202))+P1(f773(f773(f233(x74201),f674(x74202,x74203,x74201)),x74202))
% 191.21/191.75 [7434]P140(x74342,x74341,x74343)+E(x74341,f2(a1))+P1(f773(f773(f233(a1),x74341),f780(x74343,x74341,x74342)))+P1(f773(f773(f233(a1),f777(x74343,x74341,x74342)),x74341))
% 191.21/191.75 [7435]P141(x74352,x74351,x74353)+E(x74351,f2(a1))+P1(f773(f773(f233(a1),x74351),f782(x74353,x74351,x74352)))+P1(f773(f773(f233(a1),f783(x74353,x74351,x74352)),x74351))
% 191.21/191.75 [7531]P140(x75313,x75311,x75312)+E(x75311,f2(a1))+E(f773(f773(f82(a1),f773(f773(f83(a1),x75311),f779(x75312,x75311,x75313))),f780(x75312,x75311,x75313)),x75312)+P1(f773(f773(f233(a1),f2(a1)),x75311))
% 191.21/191.75 [7532]P141(x75323,x75321,x75322)+E(x75321,f2(a1))+E(f773(f773(f82(a1),f773(f773(f83(a1),x75321),f785(x75322,x75321,x75323))),f782(x75322,x75321,x75323)),x75322)+P1(f773(f773(f233(a1),f2(a1)),x75321))
% 191.21/191.75 [7534]~P123(x75341)+~P1(f773(f773(f233(x75341),x75343),f2(x75341)))+P1(f773(f773(f233(x75341),f773(f773(f83(x75341),x75342),x75343)),f2(x75341)))+~P1(f773(f773(f233(x75341),f2(x75341)),x75342))
% 191.21/191.75 [7535]~P123(x75351)+~P1(f773(f773(f233(x75351),x75352),f2(x75351)))+P1(f773(f773(f233(x75351),f773(f773(f83(x75351),x75352),x75353)),f2(x75351)))+~P1(f773(f773(f233(x75351),f2(x75351)),x75353))
% 191.21/191.75 [7536]~P62(x75361)+~P1(f773(f773(f233(x75361),x75363),f2(x75361)))+P1(f773(f773(f233(x75361),f773(f773(f283(x75361),x75362),x75363)),f2(x75361)))+~P1(f773(f773(f233(x75361),f2(x75361)),x75362))
% 191.21/191.75 [7537]~P62(x75371)+~P1(f773(f773(f233(x75371),x75372),f2(x75371)))+P1(f773(f773(f233(x75371),f773(f773(f283(x75371),x75372),x75373)),f2(x75371)))+~P1(f773(f773(f233(x75371),f2(x75371)),x75373))
% 191.21/191.75 [7538]~P63(x75381)+~P1(f773(f773(f233(x75381),x75383),f2(x75381)))+P1(f773(f773(f233(x75381),f773(f773(f283(x75381),x75382),x75383)),f2(x75381)))+~P1(f773(f773(f233(x75381),f2(x75381)),x75382))
% 191.21/191.75 [7539]~P63(x75391)+~P1(f773(f773(f233(x75391),x75392),f2(x75391)))+P1(f773(f773(f233(x75391),f773(f773(f283(x75391),x75392),x75393)),f2(x75391)))+~P1(f773(f773(f233(x75391),f2(x75391)),x75393))
% 191.21/191.75 [7541]~P119(x75411)+~P1(f773(f773(f232(x75411),x75413),f2(x75411)))+P1(f773(f773(f232(x75411),f773(f773(f83(x75411),x75412),x75413)),f2(x75411)))+~P1(f773(f773(f232(x75411),f2(x75411)),x75412))
% 191.21/191.75 [7542]~P119(x75421)+~P1(f773(f773(f232(x75421),x75422),f2(x75421)))+P1(f773(f773(f232(x75421),f773(f773(f83(x75421),x75422),x75423)),f2(x75421)))+~P1(f773(f773(f232(x75421),f2(x75421)),x75423))
% 191.21/191.75 [7544]~P128(x75441)+~P1(f773(f773(f232(x75441),x75443),f2(x75441)))+P1(f773(f773(f232(x75441),f773(f773(f83(x75441),x75442),x75443)),f2(x75441)))+~P1(f773(f773(f232(x75441),f2(x75441)),x75442))
% 191.21/191.75 [7546]~P128(x75461)+~P1(f773(f773(f232(x75461),x75462),f2(x75461)))+P1(f773(f773(f232(x75461),f773(f773(f83(x75461),x75462),x75463)),f2(x75461)))+~P1(f773(f773(f232(x75461),f2(x75461)),x75463))
% 191.21/191.75 [7547]~P62(x75471)+~P1(f773(f773(f232(x75471),x75473),f2(x75471)))+P1(f773(f773(f232(x75471),f773(f773(f283(x75471),x75472),x75473)),f2(x75471)))+~P1(f773(f773(f232(x75471),f2(x75471)),x75472))
% 191.21/191.75 [7548]~P62(x75481)+~P1(f773(f773(f232(x75481),x75482),f2(x75481)))+P1(f773(f773(f232(x75481),f773(f773(f283(x75481),x75482),x75483)),f2(x75481)))+~P1(f773(f773(f232(x75481),f2(x75481)),x75483))
% 191.21/191.75 [7549]~P63(x75491)+~P1(f773(f773(f233(x75491),x75493),f2(x75491)))+P1(f773(f773(f232(x75491),f773(f773(f283(x75491),x75492),x75493)),f2(x75491)))+~P1(f773(f773(f232(x75491),f2(x75491)),x75492))
% 191.21/191.75 [7550]~P63(x75501)+~P1(f773(f773(f232(x75501),x75502),f2(x75501)))+P1(f773(f773(f232(x75501),f773(f773(f283(x75501),x75502),x75503)),f2(x75501)))+~P1(f773(f773(f233(x75501),f2(x75501)),x75503))
% 191.21/191.75 [7566]P140(x75661,x75662,x75663)+~P1(f773(x75661,x75663))+P1(f773(f773(f233(a1),x75662),f780(x75663,x75662,x75661)))+P1(f773(f773(f233(a1),f777(x75663,x75662,x75661)),x75662))
% 191.21/191.75 [7579]P141(x75791,x75792,x75793)+P1(f773(f773(f233(a1),x75792),f782(x75793,x75792,x75791)))+~P1(f773(x75791,f2(a1)))+P1(f773(f773(f233(a1),f783(x75793,x75792,x75791)),x75792))
% 191.21/191.75 [7631]P140(x76312,x76311,x76313)+E(x76311,f2(a1))+~P1(f773(x76312,f780(x76313,x76311,x76312)))+P1(f773(f773(f233(a1),f777(x76313,x76311,x76312)),x76311))
% 191.21/191.75 [7632]P141(x76322,x76321,x76323)+E(x76321,f2(a1))+~P1(f773(x76322,f785(x76323,x76321,x76322)))+P1(f773(f773(f233(a1),f783(x76323,x76321,x76322)),x76321))
% 191.21/191.75 [7641]P140(x76413,x76411,x76412)+~P1(f773(x76413,x76412))+E(f773(f773(f82(a1),f773(f773(f83(a1),x76411),f779(x76412,x76411,x76413))),f780(x76412,x76411,x76413)),x76412)+P1(f773(f773(f233(a1),f2(a1)),x76411))
% 191.21/191.75 [7659]P141(x76593,x76591,x76592)+E(f773(f773(f82(a1),f773(f773(f83(a1),x76591),f785(x76592,x76591,x76593))),f782(x76592,x76591,x76593)),x76592)+~P1(f773(x76593,f2(a1)))+P1(f773(f773(f233(a1),f2(a1)),x76591))
% 191.21/191.75 [7683]~P1(f773(x76831,x76833))+~P1(f773(f63(x76832),x76833))+P1(f773(f773(f334(x76832),f483(x76831,x76833,x76832)),f482(x76831,x76833,x76832)))+P1(f773(x76831,f180(f855(x76832,a841))))
% 191.21/191.75 [7693]P140(x76931,x76932,x76933)+~P1(f773(x76931,x76933))+~P1(f773(x76931,f780(x76933,x76932,x76931)))+P1(f773(f773(f233(a1),f777(x76933,x76932,x76931)),x76932))
% 191.21/191.75 [7699]P141(x76991,x76992,x76993)+~P1(f773(x76991,f785(x76993,x76992,x76991)))+~P1(f773(x76991,f2(a1)))+P1(f773(f773(f233(a1),f783(x76993,x76992,x76991)),x76992))
% 191.21/191.75 [7807]~P62(x78071)+~P1(f773(f773(f233(x78071),f773(f773(f283(x78071),x78073),x78072)),f2(x78071)))+P1(f773(f773(f233(x78071),x78072),f2(x78071)))+P1(f773(f773(f233(x78071),f2(x78071)),x78072))
% 191.21/191.75 [7808]~P62(x78081)+~P1(f773(f773(f233(x78081),f773(f773(f283(x78081),x78082),x78083)),f2(x78081)))+P1(f773(f773(f233(x78081),x78082),f2(x78081)))+P1(f773(f773(f233(x78081),f2(x78081)),x78082))
% 191.21/191.75 [7809]~P119(x78091)+~P1(f773(f773(f232(x78091),f773(f773(f83(x78091),x78093),x78092)),f2(x78091)))+P1(f773(f773(f232(x78091),x78092),f2(x78091)))+P1(f773(f773(f232(x78091),f2(x78091)),x78092))
% 191.21/191.75 [7810]~P119(x78101)+~P1(f773(f773(f232(x78101),f773(f773(f83(x78101),x78102),x78103)),f2(x78101)))+P1(f773(f773(f232(x78101),x78102),f2(x78101)))+P1(f773(f773(f232(x78101),f2(x78101)),x78102))
% 191.21/191.75 [7811]~P62(x78111)+~P1(f773(f773(f232(x78111),f773(f773(f283(x78111),x78113),x78112)),f2(x78111)))+P1(f773(f773(f232(x78111),x78112),f2(x78111)))+P1(f773(f773(f232(x78111),f2(x78111)),x78112))
% 191.21/191.75 [7812]~P62(x78121)+~P1(f773(f773(f232(x78121),f773(f773(f283(x78121),x78122),x78123)),f2(x78121)))+P1(f773(f773(f232(x78121),x78122),f2(x78121)))+P1(f773(f773(f232(x78121),f2(x78121)),x78122))
% 191.21/191.75 [7838]~P62(x78381)+~P1(f773(f773(f233(x78381),f773(f773(f283(x78381),x78382),x78383)),f2(x78381)))+P1(f773(f773(f233(x78381),f2(x78381)),x78382))+P1(f773(f773(f233(x78381),f2(x78381)),x78383))
% 191.21/191.75 [7839]~P119(x78391)+~P1(f773(f773(f232(x78391),f773(f773(f83(x78391),x78392),x78393)),f2(x78391)))+P1(f773(f773(f232(x78391),f2(x78391)),x78392))+P1(f773(f773(f232(x78391),f2(x78391)),x78393))
% 191.21/191.75 [7840]~P62(x78401)+~P1(f773(f773(f232(x78401),f773(f773(f283(x78401),x78402),x78403)),f2(x78401)))+P1(f773(f773(f232(x78401),f2(x78401)),x78402))+P1(f773(f773(f232(x78401),f2(x78401)),x78403))
% 191.21/191.75 [7859]P140(x78592,x78591,x78593)+E(x78591,f2(a1))+P1(f773(f773(f232(a1),f780(x78593,x78591,x78592)),f2(a1)))+P1(f773(f773(f233(a1),f777(x78593,x78591,x78592)),x78591))
% 191.21/191.75 [7860]P141(x78602,x78601,x78603)+E(x78601,f2(a1))+P1(f773(f773(f232(a1),f782(x78603,x78601,x78602)),f2(a1)))+P1(f773(f773(f233(a1),f783(x78603,x78601,x78602)),x78601))
% 191.21/191.75 [7866]~P117(x78661)+~P1(f773(f773(f233(x78661),x78662),f80(x78661)))+P1(f773(f773(f233(x78661),f773(f773(f242(x78661),x78662),f773(a114,x78663))),f80(x78661)))+~P1(f773(f773(f233(x78661),f2(x78661)),x78662))
% 191.21/191.75 [7920]~P100(x79201)+~E(x79203,f115(x79201))+~P18(x79201,f773(f142(x79201),x79203))+E(f773(f132(x79201,x79201,f773(f9(x79201,x79201,x79201),f179(x79201)),x79202),f773(f142(x79201),x79203)),x79202)
% 191.21/191.75 [7922]P140(x79221,x79222,x79223)+~P1(f773(x79221,x79223))+P1(f773(f773(f232(a1),f780(x79223,x79222,x79221)),f2(a1)))+P1(f773(f773(f233(a1),f777(x79223,x79222,x79221)),x79222))
% 191.21/191.75 [7934]P141(x79341,x79342,x79343)+~P1(f773(x79341,f2(a1)))+P1(f773(f773(f232(a1),f782(x79343,x79342,x79341)),f2(a1)))+P1(f773(f773(f233(a1),f783(x79343,x79342,x79341)),x79342))
% 191.21/191.75 [8147]P140(x81473,x81471,x81472)+E(x81471,f2(a1))+E(f773(f773(f82(a1),f773(f773(f83(a1),x81471),f779(x81472,x81471,x81473))),f780(x81472,x81471,x81473)),x81472)+P1(f773(f773(f233(a1),f777(x81472,x81471,x81473)),x81471))
% 191.21/191.75 [8148]P141(x81483,x81481,x81482)+E(x81481,f2(a1))+E(f773(f773(f82(a1),f773(f773(f83(a1),x81481),f785(x81482,x81481,x81483))),f782(x81482,x81481,x81483)),x81482)+P1(f773(f773(f233(a1),f783(x81482,x81481,x81483)),x81481))
% 191.21/191.75 [8183]P140(x81833,x81831,x81832)+~P1(f773(x81833,x81832))+E(f773(f773(f82(a1),f773(f773(f83(a1),x81831),f779(x81832,x81831,x81833))),f780(x81832,x81831,x81833)),x81832)+P1(f773(f773(f233(a1),f777(x81832,x81831,x81833)),x81831))
% 191.21/191.75 [8184]~P66(x81841)+~P70(x81841)+~P38(x81843)+E(f773(f773(f8(a847,x81841),f773(f773(f10(a1,x81841,a847),x81842),f102(a1))),f773(f303(a1,a847,a107),x81843)),f773(f773(f8(a1,x81841),x81842),x81843))
% 191.21/191.75 [8185]~P66(x81851)+~P70(x81851)+~P38(x81853)+E(f773(f773(f11(a847,x81851),f773(f773(f10(a1,x81851,a847),x81852),f102(a1))),f773(f303(a1,a847,a107),x81853)),f773(f773(f11(a1,x81851),x81852),x81853))
% 191.21/191.75 [8193]P141(x81933,x81931,x81932)+E(f773(f773(f82(a1),f773(f773(f83(a1),x81931),f785(x81932,x81931,x81933))),f782(x81932,x81931,x81933)),x81932)+~P1(f773(x81933,f2(a1)))+P1(f773(f773(f233(a1),f783(x81932,x81931,x81933)),x81931))
% 191.21/191.75 [8211]~E(x82112,f2(a847))+~E(f773(f240(a847,a847),x82113),f2(a847))+~E(x82111,f773(f773(f82(a847),f773(f773(f83(a847),f773(f240(a847,a847),x82113)),x82112)),f773(f250(a847,a847),x82113)))+P1(f773(f55(x82111,x82112),x82113))
% 191.21/191.75 [9059]P1(f773(f773(f232(a1),x90591),f2(a1)))+~P1(f773(f773(f233(a1),f773(f773(f82(a1),f773(f773(f83(a1),x90592),x90591)),x90593)),f2(a1)))+~P1(f773(f773(f233(a1),f2(a1)),x90592))+~P1(f773(f773(f232(a1),f2(a1)),x90593))
% 191.21/191.75 [5666]~P93(x56662)+E(x56661,f180(f855(x56662,a841)))+~P1(f773(f63(x56662),x56661))+E(f15(x56662,f773(f773(f302(x56662),x56663),x56661)),f773(f773(f103(x56662),x56663),f15(x56662,x56661)))
% 191.21/191.75 [5667]~P100(x56672)+E(x56671,f180(f855(x56672,a841)))+~P1(f773(f63(x56672),x56671))+E(f16(x56672,f773(f773(f302(x56672),x56673),x56671)),f773(f773(f179(x56672),x56673),f16(x56672,x56671)))
% 191.21/191.75 [5668]~P100(x56682)+E(x56681,f180(f855(x56682,a841)))+~P1(f773(f63(x56682),x56681))+E(f17(x56682,f773(f773(f302(x56682),x56683),x56681)),f773(f773(f236(x56682),x56683),f17(x56682,x56681)))
% 191.21/191.75 [5669]~P93(x56692)+E(x56691,f180(f855(x56692,a841)))+~P1(f773(f63(x56692),x56691))+E(f12(x56692,f773(f773(f302(x56692),x56693),x56691)),f773(f773(f104(x56692),x56693),f12(x56692,x56691)))
% 191.21/191.75 [5988]~P119(x59881)+~E(x59883,f2(x59881))+~E(x59882,f2(x59881))+E(f773(f773(f82(x59881),f773(f773(f83(x59881),x59882),x59882)),f773(f773(f83(x59881),x59883),x59883)),f2(x59881))
% 191.21/191.75 [6063]~P91(x60632)+E(x60631,f180(f855(x60632,a841)))+~P1(f773(f63(x60632),x60631))+E(f773(f65(x60632,f83(x60632)),f773(f773(f302(x60632),x60633),x60631)),f773(f773(f83(x60632),x60633),f773(f65(x60632,f83(x60632)),x60631)))
% 191.21/191.75 [6189]~P100(x61892)+E(x61891,f180(f855(x61892,a841)))+~P1(f773(f63(x61892),x61891))+E(f13(x61892,f179(x61892),f773(f773(f302(x61892),x61893),x61891)),f773(f773(f179(x61892),x61893),f13(x61892,f179(x61892),x61891)))
% 191.21/191.75 [6190]~P100(x61902)+E(x61901,f180(f855(x61902,a841)))+~P1(f773(f63(x61902),x61901))+E(f14(x61902,f236(x61902),f773(f773(f302(x61902),x61903),x61901)),f773(f773(f236(x61902),x61903),f14(x61902,f236(x61902),x61901)))
% 191.21/191.75 [6720]~P64(x67201)+~P1(f773(f63(x67201),x67203))+E(f773(f65(x67201,f83(x67201)),f773(f773(f302(x67201),x67202),x67203)),f773(f773(f66(x67201,x67201,f83(x67201)),x67202),x67203))+P1(f773(f773(f334(x67201),x67202),x67203))
% 191.21/191.75 [6807]~E(f773(f773(f82(a1),x68072),f773(f773(f83(a1),x68073),x68071)),x68073)+~P1(f773(f773(f233(a1),f2(a1)),x68073))+P1(f773(f773(f232(a1),f80(a1)),x68071))+~P1(f773(f773(f233(a1),x68072),x68073))
% 191.21/191.75 [6838]~E(f773(f773(f82(a1),x68382),f773(f773(f83(a1),x68383),x68381)),x68383)+P1(f773(f773(f232(a1),x68381),f80(a1)))+~P1(f773(f773(f233(a1),f2(a1)),x68383))+~P1(f773(f773(f232(a1),f2(a1)),x68382))
% 191.21/191.75 [6856]E(x68561,f2(a847))+~P1(f773(f55(x68563,x68561),x68562))+~P1(f773(f773(f233(a847),f2(a847)),x68561))+P1(f773(f773(f233(a847),f773(f250(a847,a847),x68562)),x68561))
% 191.21/191.75 [6885]~P132(x68851)+~P1(f773(f773(f232(x68851),x68852),f2(x68851)))+~P1(f773(f773(f232(x68851),x68853),f2(x68851)))+E(f773(f773(f83(x68851),f773(f77(x68851),x68852)),f773(f77(x68851),x68853)),f773(f77(x68851),f773(f773(f83(x68851),x68852),x68853)))
% 191.21/191.75 [6937]~P132(x69371)+~P1(f773(f773(f232(x69371),x69372),f2(x69371)))+E(f773(f773(f83(x69371),f773(f77(x69371),x69372)),f773(f77(x69371),x69373)),f773(f77(x69371),f773(f773(f83(x69371),x69372),x69373)))+~P1(f773(f773(f232(x69371),f2(x69371)),x69373))
% 191.21/191.75 [6938]~P132(x69381)+~P1(f773(f773(f232(x69381),x69383),f2(x69381)))+E(f773(f773(f83(x69381),f773(f77(x69381),x69382)),f773(f77(x69381),x69383)),f773(f77(x69381),f773(f773(f83(x69381),x69382),x69383)))+~P1(f773(f773(f232(x69381),f2(x69381)),x69382))
% 191.21/191.75 [6988]~P132(x69881)+E(f773(f773(f83(x69881),f773(f77(x69881),x69882)),f773(f77(x69881),x69883)),f773(f77(x69881),f773(f773(f83(x69881),x69882),x69883)))+~P1(f773(f773(f232(x69881),f2(x69881)),x69882))+~P1(f773(f773(f232(x69881),f2(x69881)),x69883))
% 191.21/191.75 [7006]~P119(x70061)+~P1(f773(f773(f233(x70061),x70063),f2(x70061)))+~P1(f773(f773(f233(x70061),x70062),f2(x70061)))+P1(f773(f773(f233(x70061),f2(x70061)),f773(f773(f83(x70061),x70062),x70063)))
% 191.21/191.75 [7007]~P62(x70071)+~P1(f773(f773(f233(x70071),x70073),f2(x70071)))+~P1(f773(f773(f233(x70071),x70072),f2(x70071)))+P1(f773(f773(f233(x70071),f2(x70071)),f773(f773(f283(x70071),x70072),x70073)))
% 191.21/191.75 [7008]~P63(x70081)+~P1(f773(f773(f233(x70081),x70083),f2(x70081)))+~P1(f773(f773(f233(x70081),x70082),f2(x70081)))+P1(f773(f773(f233(x70081),f2(x70081)),f773(f773(f283(x70081),x70082),x70083)))
% 191.21/191.75 [7009]~P119(x70091)+~P1(f773(f773(f232(x70091),x70093),f2(x70091)))+~P1(f773(f773(f232(x70091),x70092),f2(x70091)))+P1(f773(f773(f232(x70091),f2(x70091)),f773(f773(f83(x70091),x70092),x70093)))
% 191.21/191.75 [7011]~P129(x70111)+~P1(f773(f773(f232(x70111),x70113),f2(x70111)))+~P1(f773(f773(f232(x70111),x70112),f2(x70111)))+P1(f773(f773(f232(x70111),f2(x70111)),f773(f773(f83(x70111),x70112),x70113)))
% 191.21/191.75 [7012]~P62(x70121)+~P1(f773(f773(f232(x70121),x70123),f2(x70121)))+~P1(f773(f773(f232(x70121),x70122),f2(x70121)))+P1(f773(f773(f232(x70121),f2(x70121)),f773(f773(f283(x70121),x70122),x70123)))
% 191.21/191.75 [7013]~P63(x70131)+~P1(f773(f773(f233(x70131),x70133),f2(x70131)))+~P1(f773(f773(f232(x70131),x70132),f2(x70131)))+P1(f773(f773(f232(x70131),f2(x70131)),f773(f773(f283(x70131),x70132),x70133)))
% 191.21/191.75 [7014]~P117(x70141)+~P1(f773(f773(f233(a847),f2(a847)),x70143))+~P1(f773(f773(f233(x70141),f80(x70141)),x70142))+P1(f773(f773(f233(x70141),f80(x70141)),f773(f773(f242(x70141),x70142),x70143)))
% 191.21/191.75 [7111]~P81(x71111)+~P1(f773(f773(f233(x71111),f2(x71111)),x71113))+~P1(f773(f773(f233(x71111),f2(x71111)),x71112))+P1(f773(f773(f233(x71111),f2(x71111)),f773(f773(f82(x71111),x71112),x71113)))
% 191.21/191.75 [7114]~P123(x71141)+~P1(f773(f773(f233(x71141),f2(x71141)),x71143))+~P1(f773(f773(f233(x71141),f2(x71141)),x71142))+P1(f773(f773(f233(x71141),f2(x71141)),f773(f773(f83(x71141),x71142),x71143)))
% 191.21/191.75 [7115]~P62(x71151)+~P1(f773(f773(f233(x71151),f2(x71151)),x71153))+~P1(f773(f773(f233(x71151),f2(x71151)),x71152))+P1(f773(f773(f233(x71151),f2(x71151)),f773(f773(f283(x71151),x71152),x71153)))
% 191.21/191.75 [7116]~P63(x71161)+~P1(f773(f773(f233(x71161),f2(x71161)),x71163))+~P1(f773(f773(f233(x71161),f2(x71161)),x71162))+P1(f773(f773(f233(x71161),f2(x71161)),f773(f773(f283(x71161),x71162),x71163)))
% 191.21/191.75 [7117]~P117(x71171)+~P1(f773(f773(f233(x71171),f80(x71171)),x71173))+~P1(f773(f773(f233(x71171),f80(x71171)),x71172))+P1(f773(f773(f233(x71171),f80(x71171)),f773(f773(f83(x71171),x71172),x71173)))
% 191.21/191.75 [7119]~P119(x71191)+~P1(f773(f773(f232(x71191),f2(x71191)),x71193))+~P1(f773(f773(f232(x71191),f2(x71191)),x71192))+P1(f773(f773(f232(x71191),f2(x71191)),f773(f773(f83(x71191),x71192),x71193)))
% 191.21/191.75 [7120]~P128(x71201)+~P1(f773(f773(f232(x71201),f2(x71201)),x71203))+~P1(f773(f773(f232(x71201),f2(x71201)),x71202))+P1(f773(f773(f232(x71201),f2(x71201)),f773(f773(f83(x71201),x71202),x71203)))
% 191.21/191.75 [7121]~P129(x71211)+~P1(f773(f773(f232(x71211),f2(x71211)),x71213))+~P1(f773(f773(f232(x71211),f2(x71211)),x71212))+P1(f773(f773(f232(x71211),f2(x71211)),f773(f773(f83(x71211),x71212),x71213)))
% 191.21/191.75 [7122]~P62(x71221)+~P1(f773(f773(f232(x71221),f2(x71221)),x71223))+~P1(f773(f773(f232(x71221),f2(x71221)),x71222))+P1(f773(f773(f232(x71221),f2(x71221)),f773(f773(f283(x71221),x71222),x71223)))
% 191.21/191.75 [7123]~P63(x71231)+~P1(f773(f773(f233(x71231),f2(x71231)),x71233))+~P1(f773(f773(f232(x71231),f2(x71231)),x71232))+P1(f773(f773(f232(x71231),f2(x71231)),f773(f773(f283(x71231),x71232),x71233)))
% 191.21/191.75 [7201]~P93(x72011)+~P1(f773(f63(x72011),x72013))+E(f15(x72011,f773(f773(f302(x72011),x72012),x72013)),x72012)+~E(f773(f773(f3(f855(x72011,a841)),x72013),f773(f773(f302(x72011),x72012),f180(f855(x72011,a841)))),f180(f855(x72011,a841)))
% 191.21/191.75 [7202]~P100(x72021)+~P1(f773(f63(x72021),x72023))+E(f16(x72021,f773(f773(f302(x72021),x72022),x72023)),x72022)+~E(f773(f773(f3(f855(x72021,a841)),x72023),f773(f773(f302(x72021),x72022),f180(f855(x72021,a841)))),f180(f855(x72021,a841)))
% 191.21/191.75 [7203]~P100(x72031)+~P1(f773(f63(x72031),x72033))+E(f17(x72031,f773(f773(f302(x72031),x72032),x72033)),x72032)+~E(f773(f773(f3(f855(x72031,a841)),x72033),f773(f773(f302(x72031),x72032),f180(f855(x72031,a841)))),f180(f855(x72031,a841)))
% 191.21/191.75 [7204]~P93(x72041)+~P1(f773(f63(x72041),x72043))+E(f12(x72041,f773(f773(f302(x72041),x72042),x72043)),x72042)+~E(f773(f773(f3(f855(x72041,a841)),x72043),f773(f773(f302(x72041),x72042),f180(f855(x72041,a841)))),f180(f855(x72041,a841)))
% 191.21/191.75 [7205]~P62(x72051)+P1(f773(f773(f233(x72051),x72052),f2(x72051)))+P1(f773(f773(f233(x72051),f2(x72051)),x72053))+~P1(f773(f773(f233(x72051),f2(x72051)),f773(f773(f283(x72051),x72053),x72052)))
% 191.21/191.75 [7206]~P62(x72061)+P1(f773(f773(f233(x72061),x72062),f2(x72061)))+P1(f773(f773(f233(x72061),f2(x72061)),x72063))+~P1(f773(f773(f233(x72061),f2(x72061)),f773(f773(f283(x72061),x72062),x72063)))
% 191.21/191.75 [7207]~P62(x72071)+P1(f773(f773(f233(x72071),x72072),f2(x72071)))+P1(f773(f773(f233(x72071),f2(x72071)),x72072))+~P1(f773(f773(f233(x72071),f2(x72071)),f773(f773(f283(x72071),x72073),x72072)))
% 191.21/191.75 [7208]~P62(x72081)+P1(f773(f773(f233(x72081),x72082),f2(x72081)))+P1(f773(f773(f233(x72081),f2(x72081)),x72082))+~P1(f773(f773(f233(x72081),f2(x72081)),f773(f773(f283(x72081),x72082),x72083)))
% 191.21/191.75 [7209]~P119(x72091)+P1(f773(f773(f232(x72091),x72092),f2(x72091)))+P1(f773(f773(f232(x72091),f2(x72091)),x72093))+~P1(f773(f773(f232(x72091),f2(x72091)),f773(f773(f83(x72091),x72093),x72092)))
% 191.21/191.75 [7210]~P119(x72101)+P1(f773(f773(f232(x72101),x72102),f2(x72101)))+P1(f773(f773(f232(x72101),f2(x72101)),x72103))+~P1(f773(f773(f232(x72101),f2(x72101)),f773(f773(f83(x72101),x72102),x72103)))
% 191.21/191.75 [7211]~P62(x72111)+P1(f773(f773(f232(x72111),x72112),f2(x72111)))+P1(f773(f773(f232(x72111),f2(x72111)),x72113))+~P1(f773(f773(f232(x72111),f2(x72111)),f773(f773(f283(x72111),x72113),x72112)))
% 191.21/191.75 [7212]~P62(x72121)+P1(f773(f773(f232(x72121),x72122),f2(x72121)))+P1(f773(f773(f232(x72121),f2(x72121)),x72123))+~P1(f773(f773(f232(x72121),f2(x72121)),f773(f773(f283(x72121),x72122),x72123)))
% 191.21/191.75 [7213]~P119(x72131)+P1(f773(f773(f232(x72131),x72132),f2(x72131)))+P1(f773(f773(f232(x72131),f2(x72131)),x72132))+~P1(f773(f773(f232(x72131),f2(x72131)),f773(f773(f83(x72131),x72133),x72132)))
% 191.21/191.75 [7214]~P119(x72141)+P1(f773(f773(f232(x72141),x72142),f2(x72141)))+P1(f773(f773(f232(x72141),f2(x72141)),x72142))+~P1(f773(f773(f232(x72141),f2(x72141)),f773(f773(f83(x72141),x72142),x72143)))
% 191.21/191.75 [7215]~P62(x72151)+P1(f773(f773(f232(x72151),x72152),f2(x72151)))+P1(f773(f773(f232(x72151),f2(x72151)),x72152))+~P1(f773(f773(f232(x72151),f2(x72151)),f773(f773(f283(x72151),x72153),x72152)))
% 191.21/191.75 [7216]~P62(x72161)+P1(f773(f773(f232(x72161),x72162),f2(x72161)))+P1(f773(f773(f232(x72161),f2(x72161)),x72162))+~P1(f773(f773(f232(x72161),f2(x72161)),f773(f773(f283(x72161),x72162),x72163)))
% 191.21/191.75 [7301]~P1(f773(f773(f279(a847),x73011),x73013))+P1(f773(f773(f279(a847),x73011),x73012))+~P1(f773(f773(f232(a847),x73012),x73013))+~P1(f773(f773(f279(a847),x73011),f773(f773(f3(a847),x73013),x73012)))
% 191.21/191.75 [7302]~P1(f773(f773(f279(a847),x73021),x73023))+P1(f773(f773(f279(a847),x73021),x73022))+~P1(f773(f773(f232(a847),x73023),x73022))+~P1(f773(f773(f279(a847),x73021),f773(f773(f3(a847),x73022),x73023)))
% 191.21/191.75 [7317]~E(f773(f773(f104(f855(x73171,a841)),f773(f158(x73171),x73172)),f773(f158(x73171),x73173)),f180(f855(x73171,a841)))+~P1(f773(f127(x73171),x73173))+~P1(f773(f127(x73171),x73172))+P1(f773(f127(x73171),f773(f773(f125(x73171),x73172),x73173)))
% 191.21/191.75 [7318]~P100(x73181)+~P1(f773(f63(x73181),x73183))+E(f13(x73181,f179(x73181),f773(f773(f302(x73181),x73182),x73183)),x73182)+~E(f773(f773(f3(f855(x73181,a841)),x73183),f773(f773(f302(x73181),x73182),f180(f855(x73181,a841)))),f180(f855(x73181,a841)))
% 191.21/191.75 [7319]~P100(x73191)+~P1(f773(f63(x73191),x73193))+E(f14(x73191,f236(x73191),f773(f773(f302(x73191),x73192),x73193)),x73192)+~E(f773(f773(f3(f855(x73191,a841)),x73193),f773(f773(f302(x73191),x73192),f180(f855(x73191,a841)))),f180(f855(x73191,a841)))
% 191.21/191.75 [7337]~P110(x73371)+~P1(f773(f773(f233(x73371),x73372),x73373))+~P1(f773(f773(f233(x73371),f773(f81(x73371),x73372)),x73373))+P1(f773(f773(f233(x73371),f773(f77(x73371),x73372)),x73373))
% 191.21/191.75 [7339]~P79(x73391)+~P1(f773(f773(f232(x73391),x73392),x73393))+~P1(f773(f773(f232(x73391),f773(f81(x73391),x73392)),x73393))+P1(f773(f773(f232(x73391),f773(f77(x73391),x73392)),x73393))
% 191.21/191.75 [7408]~P123(x74081)+P1(f773(f773(f233(x74081),f2(x74081)),x74082))+~P1(f773(f773(f233(x74081),f2(x74081)),x74083))+~P1(f773(f773(f233(x74081),f2(x74081)),f773(f773(f83(x74081),x74083),x74082)))
% 191.21/191.75 [7409]~P123(x74091)+P1(f773(f773(f233(x74091),f2(x74091)),x74092))+~P1(f773(f773(f233(x74091),f2(x74091)),x74093))+~P1(f773(f773(f233(x74091),f2(x74091)),f773(f773(f83(x74091),x74092),x74093)))
% 191.21/191.75 [7716]E(x77161,x77162)+~P1(f773(f63(x77163),x77161))+~P1(f773(f773(f232(a847),f773(f42(x77163),x77161)),f773(f42(x77163),x77162)))+~P1(f773(f773(f232(f855(x77163,a841)),x77162),x77161))
% 191.21/191.75 [7863]~P1(f773(f773(f233(a1),x78631),f2(a1)))+~P1(f773(f773(f233(a1),f2(a1)),x78632))+~P1(f773(f773(f232(a1),x78632),x78633))+P1(f773(f773(f232(a1),f773(f773(f43(a1),x78631),x78632)),f773(f773(f43(a1),x78631),x78633)))
% 191.21/191.75 [7874]~P1(f773(f773(f233(a1),f2(a1)),x78743))+~P1(f773(f773(f232(a1),f2(a1)),x78741))+~P1(f773(f773(f232(a1),x78743),x78742))+P1(f773(f773(f232(a1),f773(f773(f43(a1),x78741),x78742)),f773(f773(f43(a1),x78741),x78743)))
% 191.21/191.75 [8009]E(f773(x80091,f811(x80092,x80091,x80093)),x80092)+~P1(f773(f773(f232(a1),x80092),f773(x80091,x80093)))+P1(f773(f773(f233(a847),f812(x80092,x80091,x80093)),x80093))+~P1(f773(f773(f232(a1),f773(x80091,f2(a847))),x80092))
% 191.21/191.75 [8010]E(f773(x80101,f813(x80102,x80101,x80103)),x80102)+~P1(f773(f773(f232(a1),x80102),f773(x80101,x80103)))+P1(f773(f773(f233(a847),f814(x80102,x80101,x80103)),x80103))+~P1(f773(f773(f232(a1),f773(x80101,f2(a847))),x80102))
% 191.21/191.75 [8107]~P1(f773(f63(x81071),x81073))+~P1(f773(f773(f233(a847),f773(f42(x81071),x81072)),f773(f42(x81071),x81073)))+~P1(f773(f773(f232(f855(x81071,a841)),x81072),x81073))+P1(f773(f773(f233(f855(x81071,a841)),x81072),x81073))
% 191.21/191.75 [8136]E(f773(f773(f3(a1),f418(x81363,x81361,x81362)),f419(x81363,x81361,x81362)),x81361)+E(f773(f773(f82(a1),x81361),x81362),x81361)+~P1(f773(f773(f233(a1),f2(a1)),x81362))+~P1(f773(f773(f334(a1),f773(f773(f82(a1),x81361),f80(a1))),x81363))
% 191.21/191.75 [8137]E(f773(f773(f82(a1),f420(x81373,x81371,x81372)),f421(x81373,x81371,x81372)),x81371)+E(f773(f773(f3(a1),x81371),x81372),x81371)+~P1(f773(f773(f233(a1),f2(a1)),x81372))+~P1(f773(f773(f334(a1),f773(f773(f3(a1),x81371),f80(a1))),x81373))
% 191.21/191.75 [8189]~P1(f773(f773(f232(a847),x81893),x81891))+P1(f773(f773(f233(a847),x81891),x81892))+~P1(f773(f773(f232(a847),x81893),x81892))+~P1(f773(f773(f233(a847),f773(f773(f3(a847),x81891),x81893)),f773(f773(f3(a847),x81892),x81893)))
% 191.21/191.75 [8190]~P1(f773(f773(f232(a847),x81903),x81901))+P1(f773(f773(f232(a847),x81901),x81902))+~P1(f773(f773(f232(a847),x81903),x81902))+~P1(f773(f773(f232(a847),f773(f773(f3(a847),x81901),x81903)),f773(f773(f3(a847),x81902),x81903)))
% 191.21/191.75 [8204]~P100(x82042)+E(x82041,f115(x82042))+~P18(x82042,f773(f142(x82042),x82041))+E(f773(f132(x82042,x82042,f773(f9(x82042,x82042,x82042),f179(x82042)),x82043),f773(f142(x82042),x82041)),f773(f773(f179(x82042),f773(f773(f153(x82042),x82041),f2(a847))),x82043))
% 191.21/191.75 [8269]E(f773(f773(f82(a1),x82691),x82692),x82691)+~P1(f773(f773(f233(a1),f2(a1)),x82692))+P1(f773(f773(f334(a1),f418(x82693,x82691,x82692)),x82693))+~P1(f773(f773(f334(a1),f773(f773(f82(a1),x82691),f80(a1))),x82693))
% 191.21/191.75 [8270]E(f773(f773(f3(a1),x82701),x82702),x82701)+~P1(f773(f773(f233(a1),f2(a1)),x82702))+P1(f773(f773(f334(a1),f420(x82703,x82701,x82702)),x82703))+~P1(f773(f773(f334(a1),f773(f773(f3(a1),x82701),f80(a1))),x82703))
% 191.21/191.75 [8349]~P1(f773(f773(f232(a1),x83491),f773(x83492,x83493)))+P1(f773(f773(f232(a847),f811(x83491,x83492,x83493)),x83493))+P1(f773(f773(f233(a847),f812(x83491,x83492,x83493)),x83493))+~P1(f773(f773(f232(a1),f773(x83492,f2(a847))),x83491))
% 191.21/191.75 [8350]~P1(f773(f773(f232(a1),x83501),f773(x83502,x83503)))+P1(f773(f773(f232(a847),f813(x83501,x83502,x83503)),x83503))+P1(f773(f773(f233(a847),f814(x83501,x83502,x83503)),x83503))+~P1(f773(f773(f232(a1),f773(x83502,f2(a847))),x83501))
% 191.21/191.75 [8425]E(f773(f773(f82(a1),x84251),x84252),x84251)+~P1(f773(f773(f233(a1),f2(a1)),x84252))+P1(f773(f773(f334(a1),f419(x84253,x84251,x84252)),f295(a1,f80(a1),x84252)))+~P1(f773(f773(f334(a1),f773(f773(f82(a1),x84251),f80(a1))),x84253))
% 191.21/191.75 [8426]E(f773(f773(f3(a1),x84261),x84262),x84261)+~P1(f773(f773(f233(a1),f2(a1)),x84262))+P1(f773(f773(f334(a1),f421(x84263,x84261,x84262)),f295(a1,f80(a1),x84262)))+~P1(f773(f773(f334(a1),f773(f773(f3(a1),x84261),f80(a1))),x84263))
% 191.21/191.75 [8551]~P117(x85511)+~P1(f773(f773(f233(x85511),x85512),f80(x85511)))+~P1(f773(f773(f233(x85511),f2(x85511)),x85512))+P1(f773(f773(f233(x85511),f773(f773(f83(x85511),x85512),f773(f773(f242(x85511),x85512),x85513))),f773(f773(f242(x85511),x85512),x85513)))
% 191.21/191.75 [8626]~P1(f773(x86261,x86262))+P1(f773(x86261,f2(a847)))+~P1(f773(f773(f233(a847),x86262),x86263))+~P1(f773(x86261,f52(a847,f773(a114,f807(x86262,x86261,x86263)),x86263)))
% 191.21/191.75 [8756]E(f832(x87561,x87562,x87563),f2(a847))+P1(f773(f773(x87561,x87563),x87562))+P1(f773(f773(x87561,f832(x87561,x87562,x87563)),f52(a847,f830(x87561,x87562,x87563),f832(x87561,x87562,x87563))))+~P1(f773(f321(f854(a847,a847),a214),f773(f773(f241(a847,a847),x87563),x87562)))
% 191.21/191.75 [8788]~P29(x87881,x87881,x87882,x87883)+E(f773(f303(x87881,x87881,x87882),x87883),x87883)+~P1(f773(f63(x87881),x87883))+~P1(f773(f773(f232(f855(x87881,a841)),f773(f303(x87881,x87881,x87882),x87883)),x87883))
% 191.21/191.75 [9008]P1(f773(f773(x90081,x90082),x90083))+~P1(f773(f773(f233(a1),f829(x90081,x90083,x90082)),f2(a1)))+P1(f773(f773(x90081,f773(f81(a1),f826(x90081,x90083,x90082))),f773(f81(a1),f829(x90081,x90083,x90082))))+~P1(f773(f321(f854(a1,a1),a216),f773(f773(f241(a1,a1),x90082),x90083)))
% 191.21/191.75 [9166]P1(f773(f773(x91661,x91662),x91663))+P1(f773(f773(x91661,f773(f773(f82(a1),f394(x91661,x91663,x91662)),f80(a1))),f395(x91661,x91663,x91662)))+~P1(f773(f773(f232(a1),f394(x91661,x91663,x91662)),f395(x91661,x91663,x91662)))+~P1(f773(f321(f854(a1,a1),a168),f773(f773(f241(a1,a1),x91662),x91663)))
% 191.21/191.75 [9839]E(f773(x98391,f811(x98392,x98391,x98393)),x98392)+~P1(f773(f773(f232(a1),x98392),f773(x98391,x98393)))+~P1(f773(f773(f232(a1),f773(f77(a1),f773(f773(f3(a1),f773(x98391,f773(f773(f82(a847),f812(x98392,x98391,x98393)),f80(a847)))),f773(x98391,f812(x98392,x98391,x98393))))),f80(a1)))+~P1(f773(f773(f232(a1),f773(x98391,f2(a847))),x98392))
% 191.21/191.75 [9840]E(f773(x98401,f813(x98402,x98401,x98403)),x98402)+~P1(f773(f773(f232(a1),x98402),f773(x98401,x98403)))+~P1(f773(f773(f232(a1),f773(f77(a1),f773(f773(f3(a1),f773(x98401,f773(f773(f82(a847),f814(x98402,x98401,x98403)),f80(a847)))),f773(x98401,f814(x98402,x98401,x98403))))),f80(a1)))+~P1(f773(f773(f232(a1),f773(x98401,f2(a847))),x98402))
% 191.21/191.75 [9844]~P1(f773(f773(f232(a1),x98441),f773(x98442,x98443)))+~P1(f773(f773(f232(a1),f773(f77(a1),f773(f773(f3(a1),f773(x98442,f773(f773(f82(a847),f812(x98441,x98442,x98443)),f80(a847)))),f773(x98442,f812(x98441,x98442,x98443))))),f80(a1)))+P1(f773(f773(f232(a847),f811(x98441,x98442,x98443)),x98443))+~P1(f773(f773(f232(a1),f773(x98442,f2(a847))),x98441))
% 191.21/191.75 [9845]~P1(f773(f773(f232(a1),x98451),f773(x98452,x98453)))+~P1(f773(f773(f232(a1),f773(f77(a1),f773(f773(f3(a1),f773(x98452,f773(f773(f82(a847),f814(x98451,x98452,x98453)),f80(a847)))),f773(x98452,f814(x98451,x98452,x98453))))),f80(a1)))+P1(f773(f773(f232(a847),f813(x98451,x98452,x98453)),x98453))+~P1(f773(f773(f232(a1),f773(x98452,f2(a847))),x98451))
% 191.21/191.75 [9899]E(x98991,x98992)+~E(f773(f132(f848(x98993),f848(x98993),f125(x98993),f115(x98993)),x98991),f773(f132(f848(x98993),f848(x98993),f125(x98993),f115(x98993)),x98992))+~E(f773(f181(f848(f848(x98993))),x98991),f773(f181(f848(f848(x98993))),x98992))+~P1(f773(f773(f251(f848(x98993),f848(x98993),a841),f773(f773(f9(f848(x98993),f855(f848(x98993),a847),f855(f848(x98993),a841)),f773(f773(f10(f855(a847,a841),f855(f855(f848(x98993),a847),f855(f848(x98993),a841)),f848(x98993)),f10(a847,a841,f848(x98993))),f773(f773(f10(a847,f855(a847,a841),f848(x98993)),a330),f181(f848(x98993))))),f181(f848(x98993)))),f770(x98991,x98992,x98993)))
% 191.21/191.75 [9900]E(x99001,x99002)+~E(f773(f132(f848(x99003),f848(x99003),f125(x99003),f115(x99003)),x99001),f773(f132(f848(x99003),f848(x99003),f125(x99003),f115(x99003)),x99002))+~E(f773(f181(f848(f848(x99003))),x99001),f773(f181(f848(f848(x99003))),x99002))+~P1(f773(f773(f251(f848(x99003),f848(x99003),a841),f773(f773(f9(f848(x99003),f855(f848(x99003),a847),f855(f848(x99003),a841)),f773(f773(f10(f855(a847,a841),f855(f855(f848(x99003),a847),f855(f848(x99003),a841)),f848(x99003)),f10(a847,a841,f848(x99003))),f773(f773(f10(a847,f855(a847,a841),f848(x99003)),a330),f181(f848(x99003))))),f181(f848(x99003)))),f771(x99002,x99001,x99003)))
% 191.21/191.75 [6709]~E(f80(a847),f2(a847))+~P1(f773(f63(x67091),x67093))+~P1(f773(f63(x67091),x67092))+E(f773(f773(f82(a847),f773(f42(x67091),x67092)),f773(f42(x67091),x67093)),f773(f42(x67091),f773(f773(f103(f855(x67091,a841)),x67092),x67093)))
% 191.21/191.75 [7129]~P100(x71291)+~P1(f773(f63(x71291),x71292))+~P1(f773(f773(f334(x71291),x71293),x71292))+P1(f773(f773(f232(x71291),f773(f65(x71291,f236(x71291)),x71292)),x71293))
% 191.21/191.75 [7130]~P98(x71301)+~P1(f773(f63(x71301),x71302))+~P1(f773(f773(f334(x71301),x71303),x71302))+P1(f773(f773(f232(x71301),f773(f65(x71301,f104(x71301)),x71302)),x71303))
% 191.21/191.75 [7405]~P1(f773(f63(x74051),x74053))+~P1(f773(f63(x74051),x74052))+~E(f773(f773(f104(f855(x74051,a841)),x74052),x74053),f180(f855(x74051,a841)))+E(f773(f773(f82(a847),f773(f42(x74051),x74052)),f773(f42(x74051),x74053)),f773(f42(x74051),f773(f773(f103(f855(x74051,a841)),x74052),x74053)))
% 191.21/191.75 [8194]~P36(x81941,x81943)+~P36(x81941,x81942)+~E(f773(f773(f104(f855(x81941,a841)),f773(f261(x81941,x81941),x81942)),f773(f259(x81941,x81941),x81943)),f180(f855(x81941,a841)))+P36(x81941,f773(f773(f103(f855(f854(x81941,x81941),a841)),x81942),x81943))
% 191.21/191.75 [8282]E(x82821,f773(f773(f43(a847),x82822),x82823))+~P1(f773(f773(f233(a847),f2(a847)),x82823))+~P1(f773(f773(f233(a847),x82822),f773(f773(f83(a847),x82823),f773(a114,x82821))))+~P1(f773(f773(f232(a847),f773(f773(f83(a847),x82823),x82821)),x82822))
% 191.21/191.75 [8423]~P1(f773(f63(x84231),x84232))+~P1(f773(f63(x84231),x84233))+E(f773(f773(f82(a847),f773(f42(x84231),x84232)),f773(f42(x84231),x84233)),f773(f42(x84231),f773(f773(f103(f855(x84231,a841)),x84232),x84233)))+P1(f773(f773(f334(x84231),f508(x84233,x84232,x84231)),f773(f773(f104(f855(x84231,a841)),x84232),x84233)))
% 191.21/191.75 [8767]~P119(x87672)+~E(x87671,f2(x87672))+~E(x87673,f2(x87672))+~P1(f773(f773(f233(x87672),f2(x87672)),f773(f773(f82(x87672),f773(f773(f83(x87672),x87673),x87673)),f773(f773(f83(x87672),x87671),x87671))))
% 191.21/191.75 [9238]~P36(x92381,x92383)+~P36(x92381,x92382)+P36(x92381,f773(f773(f103(f855(f854(x92381,x92381),a841)),x92382),x92383))+~P1(f773(f773(f232(f855(f854(x92381,x92381),a841)),f773(f773(f281(x92381,x92381,x92381),x92382),x92383)),x92382))
% 191.21/191.75 [9364]~P1(f773(x93641,x93643))+~P1(f773(f63(x93642),x93643))+P1(f773(x93641,f180(f855(x93642,a841))))+~P1(f773(x93641,f773(f773(f3(f855(x93642,a841)),f482(x93641,x93643,x93642)),f773(f773(f302(x93642),f483(x93641,x93643,x93642)),f180(f855(x93642,a841))))))
% 191.21/191.75 [8580]~P1(f773(f773(f233(a1),f2(a1)),x85803))+P1(f773(f773(f232(a1),f2(a1)),x85801))+~P1(f773(f773(f233(a1),x85802),x85803))+~P1(f773(f773(f232(a1),f2(a1)),f773(f773(f82(a1),f773(f773(f83(a1),x85803),x85801)),x85802)))
% 191.21/191.75 [8600]~P93(x86001)+~P1(f773(f63(x86001),x86002))+E(f773(f773(f3(f855(x86001,a841)),x86002),f773(f773(f302(x86001),x86003),f180(f855(x86001,a841)))),f180(f855(x86001,a841)))+E(f773(f773(f103(x86001),x86003),f15(x86001,f773(f773(f3(f855(x86001,a841)),x86002),f773(f773(f302(x86001),x86003),f180(f855(x86001,a841)))))),f15(x86001,f773(f773(f302(x86001),x86003),x86002)))
% 191.21/191.75 [8601]~P100(x86011)+~P1(f773(f63(x86011),x86012))+E(f773(f773(f3(f855(x86011,a841)),x86012),f773(f773(f302(x86011),x86013),f180(f855(x86011,a841)))),f180(f855(x86011,a841)))+E(f773(f773(f179(x86011),x86013),f16(x86011,f773(f773(f3(f855(x86011,a841)),x86012),f773(f773(f302(x86011),x86013),f180(f855(x86011,a841)))))),f16(x86011,f773(f773(f302(x86011),x86013),x86012)))
% 191.21/191.75 [8602]~P100(x86021)+~P1(f773(f63(x86021),x86022))+E(f773(f773(f3(f855(x86021,a841)),x86022),f773(f773(f302(x86021),x86023),f180(f855(x86021,a841)))),f180(f855(x86021,a841)))+E(f773(f773(f236(x86021),x86023),f17(x86021,f773(f773(f3(f855(x86021,a841)),x86022),f773(f773(f302(x86021),x86023),f180(f855(x86021,a841)))))),f17(x86021,f773(f773(f302(x86021),x86023),x86022)))
% 191.21/191.75 [8603]~P93(x86031)+~P1(f773(f63(x86031),x86032))+E(f773(f773(f3(f855(x86031,a841)),x86032),f773(f773(f302(x86031),x86033),f180(f855(x86031,a841)))),f180(f855(x86031,a841)))+E(f773(f773(f104(x86031),x86033),f12(x86031,f773(f773(f3(f855(x86031,a841)),x86032),f773(f773(f302(x86031),x86033),f180(f855(x86031,a841)))))),f12(x86031,f773(f773(f302(x86031),x86033),x86032)))
% 191.21/191.75 [8665]~P100(x86651)+~P1(f773(f63(x86651),x86652))+E(f773(f773(f3(f855(x86651,a841)),x86652),f773(f773(f302(x86651),x86653),f180(f855(x86651,a841)))),f180(f855(x86651,a841)))+E(f773(f773(f179(x86651),x86653),f13(x86651,f179(x86651),f773(f773(f3(f855(x86651,a841)),x86652),f773(f773(f302(x86651),x86653),f180(f855(x86651,a841)))))),f13(x86651,f179(x86651),f773(f773(f302(x86651),x86653),x86652)))
% 191.21/191.75 [8666]~P100(x86661)+~P1(f773(f63(x86661),x86662))+E(f773(f773(f3(f855(x86661,a841)),x86662),f773(f773(f302(x86661),x86663),f180(f855(x86661,a841)))),f180(f855(x86661,a841)))+E(f773(f773(f236(x86661),x86663),f14(x86661,f236(x86661),f773(f773(f3(f855(x86661,a841)),x86662),f773(f773(f302(x86661),x86663),f180(f855(x86661,a841)))))),f14(x86661,f236(x86661),f773(f773(f302(x86661),x86663),x86662)))
% 191.21/191.75 [9180]E(x91801,x91802)+~E(f773(f132(f848(x91803),f848(x91803),f125(x91803),f115(x91803)),x91801),f773(f132(f848(x91803),f848(x91803),f125(x91803),f115(x91803)),x91802))+~E(f773(f181(f848(f848(x91803))),x91801),f773(f181(f848(f848(x91803))),x91802))+P1(f773(f773(f334(f854(f848(x91803),f848(x91803))),f770(x91801,x91802,x91803)),f773(f158(f854(f848(x91803),f848(x91803))),f773(f773(f167(f848(x91803),f848(x91803)),x91802),x91801))))
% 191.21/191.75 [9181]E(x91811,x91812)+~E(f773(f132(f848(x91813),f848(x91813),f125(x91813),f115(x91813)),x91811),f773(f132(f848(x91813),f848(x91813),f125(x91813),f115(x91813)),x91812))+~E(f773(f181(f848(f848(x91813))),x91811),f773(f181(f848(f848(x91813))),x91812))+P1(f773(f773(f334(f854(f848(x91813),f848(x91813))),f771(x91812,x91811,x91813)),f773(f158(f854(f848(x91813),f848(x91813))),f773(f773(f167(f848(x91813),f848(x91813)),x91811),x91812))))
% 191.21/191.75 [9990]~P72(x99902)+E(x99901,f180(f855(x99902,a841)))+~P1(f773(f63(x99902),x99901))+E(f16(x99902,f773(f256(x99902),f773(f773(f10(f855(x99902,a841),a841,x99902),f89(x99902)),f773(f773(f9(x99902,f855(x99902,a841),f855(x99902,a841)),f773(f773(f10(f855(x99902,f855(a841,a841)),f855(f855(x99902,a841),f855(x99902,a841)),x99902),f20(x99902,a841,a841)),f773(f773(f10(f855(x99902,a841),f855(x99902,f855(a841,a841)),x99902),f773(f10(a841,f855(a841,a841),x99902),a331)),f773(f773(f9(x99902,f855(x99902,x99902),f855(x99902,a841)),f773(f773(f10(f855(x99902,a841),f855(f855(x99902,x99902),f855(x99902,a841)),x99902),f10(x99902,a841,x99902)),a330)),f773(f82(x99902),x99903))))),f773(f773(f9(x99902,f855(x99902,a841),a841),f334(x99902)),x99901))))),f773(f773(f82(x99902),x99903),f16(x99902,x99901)))
% 191.21/191.75 [9991]~P72(x99912)+E(x99911,f180(f855(x99912,a841)))+~P1(f773(f63(x99912),x99911))+E(f17(x99912,f773(f256(x99912),f773(f773(f10(f855(x99912,a841),a841,x99912),f89(x99912)),f773(f773(f9(x99912,f855(x99912,a841),f855(x99912,a841)),f773(f773(f10(f855(x99912,f855(a841,a841)),f855(f855(x99912,a841),f855(x99912,a841)),x99912),f20(x99912,a841,a841)),f773(f773(f10(f855(x99912,a841),f855(x99912,f855(a841,a841)),x99912),f773(f10(a841,f855(a841,a841),x99912),a331)),f773(f773(f9(x99912,f855(x99912,x99912),f855(x99912,a841)),f773(f773(f10(f855(x99912,a841),f855(f855(x99912,x99912),f855(x99912,a841)),x99912),f10(x99912,a841,x99912)),a330)),f773(f82(x99912),x99913))))),f773(f773(f9(x99912,f855(x99912,a841),a841),f334(x99912)),x99911))))),f773(f773(f82(x99912),x99913),f17(x99912,x99911)))
% 191.21/191.75 [9992]~P97(x99922)+E(x99921,f180(f855(x99922,a841)))+~P1(f773(f63(x99922),x99921))+E(f12(x99922,f773(f256(x99922),f773(f773(f10(f855(x99922,a841),a841,x99922),f89(x99922)),f773(f773(f9(x99922,f855(x99922,a841),f855(x99922,a841)),f773(f773(f10(f855(x99922,f855(a841,a841)),f855(f855(x99922,a841),f855(x99922,a841)),x99922),f20(x99922,a841,a841)),f773(f773(f10(f855(x99922,a841),f855(x99922,f855(a841,a841)),x99922),f773(f10(a841,f855(a841,a841),x99922),a331)),f773(f773(f9(x99922,f855(x99922,x99922),f855(x99922,a841)),f773(f773(f10(f855(x99922,a841),f855(f855(x99922,x99922),f855(x99922,a841)),x99922),f10(x99922,a841,x99922)),a330)),f773(f103(x99922),x99923))))),f773(f773(f9(x99922,f855(x99922,a841),a841),f334(x99922)),x99921))))),f773(f773(f103(x99922),x99923),f12(x99922,x99921)))
% 191.21/191.75 [9993]~P97(x99932)+E(x99931,f180(f855(x99932,a841)))+~P1(f773(f63(x99932),x99931))+E(f15(x99932,f773(f256(x99932),f773(f773(f10(f855(x99932,a841),a841,x99932),f89(x99932)),f773(f773(f9(x99932,f855(x99932,a841),f855(x99932,a841)),f773(f773(f10(f855(x99932,f855(a841,a841)),f855(f855(x99932,a841),f855(x99932,a841)),x99932),f20(x99932,a841,a841)),f773(f773(f10(f855(x99932,a841),f855(x99932,f855(a841,a841)),x99932),f773(f10(a841,f855(a841,a841),x99932),a331)),f773(f773(f9(x99932,f855(x99932,x99932),f855(x99932,a841)),f773(f773(f10(f855(x99932,a841),f855(f855(x99932,x99932),f855(x99932,a841)),x99932),f10(x99932,a841,x99932)),a330)),f773(f104(x99932),x99933))))),f773(f773(f9(x99932,f855(x99932,a841),a841),f334(x99932)),x99931))))),f773(f773(f104(x99932),x99933),f15(x99932,x99931)))
% 191.21/191.75 [9994]~P100(x99942)+E(x99941,f180(f855(x99942,a841)))+~P1(f773(f63(x99942),x99941))+E(f13(x99942,f179(x99942),f773(f256(x99942),f773(f773(f10(f855(x99942,a841),a841,x99942),f89(x99942)),f773(f773(f9(x99942,f855(x99942,a841),f855(x99942,a841)),f773(f773(f10(f855(x99942,f855(a841,a841)),f855(f855(x99942,a841),f855(x99942,a841)),x99942),f20(x99942,a841,a841)),f773(f773(f10(f855(x99942,a841),f855(x99942,f855(a841,a841)),x99942),f773(f10(a841,f855(a841,a841),x99942),a331)),f773(f773(f9(x99942,f855(x99942,x99942),f855(x99942,a841)),f773(f773(f10(f855(x99942,a841),f855(f855(x99942,x99942),f855(x99942,a841)),x99942),f10(x99942,a841,x99942)),a330)),f773(f236(x99942),x99943))))),f773(f773(f9(x99942,f855(x99942,a841),a841),f334(x99942)),x99941))))),f773(f773(f236(x99942),x99943),f13(x99942,f179(x99942),x99941)))
% 191.21/191.75 [9995]~P100(x99952)+E(x99951,f180(f855(x99952,a841)))+~P1(f773(f63(x99952),x99951))+E(f14(x99952,f236(x99952),f773(f256(x99952),f773(f773(f10(f855(x99952,a841),a841,x99952),f89(x99952)),f773(f773(f9(x99952,f855(x99952,a841),f855(x99952,a841)),f773(f773(f10(f855(x99952,f855(a841,a841)),f855(f855(x99952,a841),f855(x99952,a841)),x99952),f20(x99952,a841,a841)),f773(f773(f10(f855(x99952,a841),f855(x99952,f855(a841,a841)),x99952),f773(f10(a841,f855(a841,a841),x99952),a331)),f773(f773(f9(x99952,f855(x99952,x99952),f855(x99952,a841)),f773(f773(f10(f855(x99952,a841),f855(f855(x99952,x99952),f855(x99952,a841)),x99952),f10(x99952,a841,x99952)),a330)),f773(f179(x99952),x99953))))),f773(f773(f9(x99952,f855(x99952,a841),a841),f334(x99952)),x99951))))),f773(f773(f179(x99952),x99953),f14(x99952,f236(x99952),x99951)))
% 191.21/191.75 [9724]~P110(x97241)+~E(x97243,f2(x97241))+~E(x97242,f2(x97241))+E(f773(f773(f82(x97241),f773(f773(f242(x97241),x97242),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))),f773(f773(f242(x97241),x97243),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))),f2(x97241))
% 191.21/191.75 [9884]~P117(x98841)+~P1(f773(f773(f232(x98841),f2(x98841)),x98843))+P1(f773(f773(f232(x98841),x98842),x98843))+~P1(f773(f773(f232(x98841),f773(f773(f242(x98841),x98842),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))),f773(f773(f242(x98841),x98843),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))))
% 191.21/191.75 [9930]~P110(x99302)+~E(x99301,f2(x99302))+~E(x99303,f2(x99302))+~P1(f773(f773(f233(x99302),f2(x99302)),f773(f773(f82(x99302),f773(f773(f242(x99302),x99303),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99))))),f773(f773(f242(x99302),x99301),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))))))
% 191.21/191.75 [9154]E(x91541,x91542)+~E(f751(x91541,x91542,x91544,x91543),f753(x91541,x91542,x91544,x91543))+P1(f773(f773(f334(f854(f848(x91543),f848(x91543))),f773(f773(f241(f848(x91543),f848(x91543)),x91542),x91541)),f137(x91543,x91544)))+P1(f773(f773(f334(f854(f848(x91543),f848(x91543))),f773(f773(f241(f848(x91543),f848(x91543)),x91541),x91542)),f137(x91543,x91544)))
% 191.21/191.75 [4745]~P60(x47452)+~E(x47454,f2(x47452))+~E(x47451,f2(x47452))+E(x47451,f773(f773(f283(x47452),x47453),x47454))
% 191.21/191.75 [4746]~P60(x47461)+~E(x47463,f2(x47461))+~E(x47464,f2(x47461))+E(f773(f773(f283(x47461),x47462),x47463),x47464)
% 191.21/191.75 [4853]~P60(x48532)+E(x48531,f2(x48532))+~E(x48533,f2(x48532))+~E(x48531,f773(f773(f283(x48532),x48534),x48533))
% 191.21/191.75 [4854]~P60(x48542)+E(x48541,f2(x48542))+~E(x48543,f2(x48542))+~E(f773(f773(f283(x48542),x48544),x48543),x48541)
% 191.21/191.75 [5033]~P113(x50332)+E(x50331,f2(x50332))+~E(f773(f773(f283(x50332),x50333),x50331),x50334)+E(x50333,f773(f773(f83(x50332),x50334),x50331))
% 191.21/191.75 [5035]~P113(x50352)+E(x50351,f2(x50352))+~E(f773(f773(f83(x50352),x50353),x50351),x50354)+E(x50353,f773(f773(f283(x50352),x50354),x50351))
% 191.21/191.75 [5036]~P60(x50362)+E(x50361,f2(x50362))+~E(f773(f773(f283(x50362),x50363),x50361),x50364)+E(x50363,f773(f773(f83(x50362),x50364),x50361))
% 191.21/191.75 [5037]~P60(x50372)+E(x50371,f2(x50372))+~E(f773(f773(f83(x50372),x50373),x50371),x50374)+E(x50373,f773(f773(f283(x50372),x50374),x50371))
% 191.21/191.75 [5038]~P113(x50382)+E(x50381,f2(x50382))+~E(x50383,f773(f773(f283(x50382),x50384),x50381))+E(f773(f773(f83(x50382),x50383),x50381),x50384)
% 191.21/191.75 [5040]~P113(x50402)+E(x50401,f2(x50402))+~E(x50403,f773(f773(f83(x50402),x50404),x50401))+E(f773(f773(f283(x50402),x50403),x50401),x50404)
% 191.21/191.75 [5041]~P60(x50412)+E(x50411,f2(x50412))+~E(x50413,f773(f773(f283(x50412),x50414),x50411))+E(f773(f773(f83(x50412),x50413),x50411),x50414)
% 191.21/191.75 [5042]~P60(x50422)+E(x50421,f2(x50422))+~E(x50423,f773(f773(f83(x50422),x50424),x50421))+E(f773(f773(f283(x50422),x50423),x50421),x50424)
% 191.21/191.75 [5075]~P60(x50752)+~E(x50751,f2(x50752))+~E(f773(f773(f83(x50752),x50751),x50754),x50753)+E(x50751,f773(f773(f283(x50752),x50753),x50754))
% 191.21/191.75 [5076]~P60(x50761)+~E(x50764,f2(x50761))+~E(x50762,f773(f773(f83(x50761),x50764),x50763))+E(f773(f773(f283(x50761),x50762),x50763),x50764)
% 191.21/191.75 [5143]~E(x51433,x51434)+~E(x51432,x51433)+~P99(x51431)+E(f295(x51431,x51432,x51433),f773(f773(f302(x51431),x51434),f180(f855(x51431,a841))))
% 191.21/191.75 [5338]~E(f134(x53382,x53381),x53384)+~E(f116(x53382,x53381),x53383)+E(x53381,f115(x53382))+E(f773(f773(f125(x53382),x53383),f773(f773(f140(x53382),x53384),f115(x53382))),x53381)
% 191.21/191.75 [5956]~P117(x59563)+E(x59561,x59562)+~E(f773(f773(f242(x59563),x59564),x59561),f773(f773(f242(x59563),x59564),x59562))+~P1(f773(f773(f233(x59563),f80(x59563)),x59564))
% 191.21/191.75 [5957]E(x59571,x59572)+~E(f773(f773(f302(x59573),x59574),x59571),f773(f773(f302(x59573),x59574),x59572))+P1(f773(f773(f334(x59573),x59574),x59572))+P1(f773(f773(f334(x59573),x59574),x59571))
% 191.21/191.75 [5995]E(f773(x59951,x59952),f2(a847))+~E(f773(f773(f8(x59953,a847),x59951),x59954),f2(a847))+~P1(f773(f63(x59953),x59954))+~P1(f773(f773(f334(x59953),x59952),x59954))
% 191.21/191.75 [5996]E(f773(x59961,x59962),f80(a847))+~E(f773(f773(f11(x59963,a847),x59961),x59964),f80(a847))+~P1(f773(f63(x59963),x59964))+~P1(f773(f773(f334(x59963),x59962),x59964))
% 191.21/191.75 [6221]~P99(x62211)+~P1(f773(f773(f233(x62211),x62214),x62213))+P1(f773(f773(f233(x62211),x62212),x62213))+~P1(f773(f773(f233(x62211),x62212),x62214))
% 191.21/191.75 [6222]~P99(x62221)+~P1(f773(f773(f232(x62221),x62224),x62223))+P1(f773(f773(f233(x62221),x62222),x62223))+~P1(f773(f773(f233(x62221),x62222),x62224))
% 191.21/191.75 [6223]~P99(x62231)+~P1(f773(f773(f232(x62231),x62232),x62234))+P1(f773(f773(f233(x62231),x62232),x62233))+~P1(f773(f773(f233(x62231),x62234),x62233))
% 191.21/191.75 [6224]~P103(x62241)+~P1(f773(f773(f233(x62241),x62242),x62244))+P1(f773(f773(f233(x62241),x62242),x62243))+~P1(f773(f773(f233(x62241),x62244),x62243))
% 191.21/191.75 [6225]~P103(x62251)+~P1(f773(f773(f232(x62251),x62252),x62254))+P1(f773(f773(f233(x62251),x62252),x62253))+~P1(f773(f773(f233(x62251),x62254),x62253))
% 191.21/191.75 [6226]~P103(x62261)+~P1(f773(f773(f232(x62261),x62264),x62263))+P1(f773(f773(f233(x62261),x62262),x62263))+~P1(f773(f773(f233(x62261),x62262),x62264))
% 191.21/191.75 [6227]~P99(x62271)+~P1(f773(f773(f232(x62271),x62274),x62273))+P1(f773(f773(f232(x62271),x62272),x62273))+~P1(f773(f773(f232(x62271),x62272),x62274))
% 191.21/191.75 [6228]~P103(x62281)+~P1(f773(f773(f232(x62281),x62282),x62284))+P1(f773(f773(f232(x62281),x62282),x62283))+~P1(f773(f773(f232(x62281),x62284),x62283))
% 191.21/191.75 [6229]~P85(x62291)+~P1(f773(f773(f279(x62291),x62292),x62294))+P1(f773(f773(f279(x62291),x62292),x62293))+~P1(f773(f773(f279(x62291),x62294),x62293))
% 191.21/191.75 [6474]~P9(x64741)+~P1(f773(f773(f232(x64741),x64742),f45(x64741,x64744)))+P1(f773(f773(f232(x64741),x64742),x64743))+~P1(f773(f773(f334(x64741),x64743),x64744))
% 191.21/191.75 [6625]~P100(x66251)+~P18(x66251,f773(f773(f140(x66251),x66252),x66254))+~P1(f773(f773(f334(x66251),x66253),f773(f158(x66251),x66254)))+P1(f773(f773(f232(x66251),x66252),x66253))
% 191.21/191.75 [6718]~P9(x67181)+~P1(f773(f773(f232(x67181),f44(x67181,x67184)),x67183))+P1(f773(f773(f232(x67181),x67182),x67183))+~P1(f773(f773(f334(x67181),x67182),x67184))
% 191.21/191.75 [6871]~P7(x68711)+P1(f773(f773(f279(x68711),x68712),f52(x68711,x68713,x68714)))+~P1(f773(f773(f279(x68711),x68712),x68714))+~P1(f773(f773(f279(x68711),x68712),x68713))
% 191.21/191.75 [7132]~P100(x71321)+E(f773(f773(f103(f855(x71321,a841)),f773(f294(x71321,x71322),x71323)),f773(f294(x71321,x71323),x71324)),f773(f294(x71321,x71322),x71324))+~P1(f773(f773(f232(x71321),x71323),x71324))+~P1(f773(f773(f232(x71321),x71322),x71323))
% 191.21/191.75 [7219]~P7(x72191)+~P1(f773(f773(f279(x72191),x72192),f52(x72191,x72193,x72194)))+P1(f773(f773(f279(x72191),x72192),x72193))+~P1(f773(f773(f279(x72191),x72192),x72194))
% 191.21/191.75 [7260]~P100(x72601)+E(f773(f773(f103(f855(x72601,a841)),f773(f294(x72601,x72602),x72603)),f295(x72601,x72603,x72604)),f295(x72601,x72602,x72604))+~P1(f773(f773(f232(x72601),x72603),x72604))+~P1(f773(f773(f232(x72601),x72602),x72603))
% 191.21/191.75 [7274]~P99(x72741)+~P50(a847,x72741,f279(a847),x72742)+P1(f773(f773(f232(x72741),f773(x72742,x72743)),f773(x72742,x72744)))+~P1(f773(f773(f279(a847),x72743),x72744))
% 191.21/191.75 [7328]~P100(x73281)+E(f773(f773(f103(f855(x73281,a841)),f298(x73281,x73282,x73283)),f773(f294(x73281,x73283),x73284)),f298(x73281,x73282,x73284))+~P1(f773(f773(f233(x73281),x73282),x73283))+~P1(f773(f773(f232(x73281),x73283),x73284))
% 191.21/191.75 [7351]~P100(x73511)+E(f773(f773(f103(f855(x73511,a841)),f295(x73511,x73512,x73513)),f298(x73511,x73513,x73514)),f773(f294(x73511,x73512),x73514))+~P1(f773(f773(f233(x73511),x73513),x73514))+~P1(f773(f773(f232(x73511),x73512),x73513))
% 191.21/191.75 [7386]~P100(x73861)+E(f773(f773(f103(f855(x73861,a841)),f295(x73861,x73862,x73863)),f297(x73861,x73863,x73864)),f295(x73861,x73862,x73864))+~P1(f773(f773(f232(x73861),x73863),x73864))+~P1(f773(f773(f232(x73861),x73862),x73863))
% 191.21/191.75 [7387]~P100(x73871)+E(f773(f773(f103(f855(x73871,a841)),f297(x73871,x73872,x73873)),f297(x73871,x73873,x73874)),f297(x73871,x73872,x73874))+~P1(f773(f773(f232(x73871),x73873),x73874))+~P1(f773(f773(f232(x73871),x73872),x73873))
% 191.21/191.75 [7388]~P100(x73881)+E(f773(f773(f103(f855(x73881,a841)),f297(x73881,x73882,x73883)),f298(x73881,x73883,x73884)),f298(x73881,x73882,x73884))+~P1(f773(f773(f233(x73881),x73883),x73884))+~P1(f773(f773(f232(x73881),x73882),x73883))
% 191.21/191.75 [7389]~P100(x73891)+E(f773(f773(f103(f855(x73891,a841)),f298(x73891,x73892,x73893)),f295(x73891,x73893,x73894)),f297(x73891,x73892,x73894))+~P1(f773(f773(f233(x73891),x73892),x73893))+~P1(f773(f773(f232(x73891),x73893),x73894))
% 191.21/191.75 [8179]P29(x81791,x81792,f527(x81793,x81792,x81794,x81791),x81794)+~P1(f773(f63(x81792),x81793))+~P1(f773(f63(x81791),x81794))+~P1(f773(f773(f232(a847),f773(f42(x81791),x81794)),f773(f42(x81792),x81793)))
% 191.21/191.75 [8249]~P70(x82491)+~E(f773(x82493,f622(x82493,x82494,x82492,x82491)),f80(x82491))+E(f773(f773(f773(f67(x82491,x82492,f83(x82491)),x82493),f80(x82491)),x82494),f80(x82491))+~P1(f773(f63(x82492),x82494))
% 191.21/191.75 [8523]~P117(x85231)+~P1(f773(f773(f232(x85231),f2(x85231)),x85233))+P1(f773(f773(f232(x85231),x85232),x85233))+~P1(f773(f773(f232(x85231),f773(f773(f242(x85231),x85232),f773(a114,x85234))),f773(f773(f242(x85231),x85233),f773(a114,x85234))))
% 191.21/191.75 [8853]~P70(x88531)+E(f773(f773(f773(f67(x88531,x88532,f83(x88531)),x88533),f80(x88531)),x88534),f80(x88531))+~P1(f773(f63(x88532),x88534))+P1(f773(f773(f334(x88532),f622(x88533,x88534,x88532,x88531)),x88534))
% 191.21/191.75 [9105]~P12(x91052,x91053,x91054)+~P1(f773(f63(x91052),x91053))+~P1(f773(f773(f279(a847),x91051),f773(f42(x91052),f517(x91051,x91054,x91053,x91052))))+P1(f773(f773(f279(a847),x91051),f773(f42(x91052),x91053)))
% 191.21/191.75 [9303]~P1(f773(f773(f279(a847),x93031),x93033))+~P1(f773(f773(f279(a847),x93031),x93032))+~P1(f773(f773(f279(a847),x93034),x93033))+~P1(f773(f773(f233(f855(a847,a841)),f282(a847,f279(a847),x93031,x93033)),f282(a847,f279(a847),x93032,x93034)))
% 191.21/191.75 [9309]~P1(f773(f773(f232(a1),x93094),f2(a1)))+P1(f773(f773(f232(a1),f773(f773(f82(a1),f773(f773(f83(a1),x93091),f52(a1,x93092,x93093))),x93094)),f2(a1)))+~P1(f773(f773(f233(a1),f2(a1)),x93093))+~P1(f773(f773(f233(a1),x93091),x93094))
% 191.21/191.75 [9715]~P1(f773(f63(x97151),x97152))+~P1(f773(f773(f334(x97151),x97154),x97152))+~P1(f773(f773(f334(x97151),x97153),x97152))+P1(f773(f773(f233(a847),f773(f42(x97151),f773(f773(f3(f855(x97151,a841)),f773(f773(f3(f855(x97151,a841)),x97152),f773(f773(f302(x97151),x97153),f180(f855(x97151,a841))))),f773(f773(f302(x97151),x97154),f180(f855(x97151,a841)))))),f773(f42(x97151),x97152)))
% 191.21/191.75 [6781]~P136(x67813)+~P112(x67813)+P1(f773(x67811,f835(x67812,x67811,x67813)))+~P1(f773(x67811,f773(f773(f83(x67813),x67812),x67814)))
% 191.21/191.75 [6841]~P100(x68411)+~P1(f773(f773(f233(x68411),x68412),x68414))+~P1(f773(f773(f233(x68411),x68412),x68413))+P1(f773(f773(f233(x68411),x68412),f773(f773(f236(x68411),x68413),x68414)))
% 191.21/191.75 [6844]~P100(x68441)+~P1(f773(f773(f232(x68441),x68442),x68444))+~P1(f773(f773(f232(x68441),x68442),x68443))+P1(f773(f773(f232(x68441),x68442),f773(f773(f236(x68441),x68443),x68444)))
% 191.21/191.75 [6847]~P98(x68471)+~P1(f773(f773(f232(x68471),x68472),x68474))+~P1(f773(f773(f232(x68471),x68472),x68473))+P1(f773(f773(f232(x68471),x68472),f773(f773(f104(x68471),x68473),x68474)))
% 191.21/191.75 [6848]~P85(x68481)+~P1(f773(f773(f279(x68481),x68482),x68484))+~P1(f773(f773(f279(x68481),x68482),x68483))+P1(f773(f773(f279(x68481),x68482),f773(f773(f82(x68481),x68483),x68484)))
% 191.21/191.75 [6849]~P104(x68491)+~P1(f773(f773(f279(x68491),x68492),x68494))+~P1(f773(f773(f279(x68491),x68492),x68493))+P1(f773(f773(f279(x68491),x68492),f773(f773(f3(x68491),x68493),x68494)))
% 191.21/191.75 [6869]~P61(x68692)+E(x68691,f2(x68692))+E(f773(f773(f283(x68692),f773(f773(f242(x68692),x68691),x68693)),f773(f773(f242(x68692),x68691),x68694)),f773(f773(f242(x68692),x68691),f773(f773(f3(a847),x68693),x68694)))+~P1(f773(f773(f232(a847),x68694),x68693))
% 191.21/191.75 [6914]~P100(x69141)+~P18(x69141,f773(f773(f140(x69141),x69143),x69144))+P18(x69141,f773(f773(f140(x69141),x69142),f773(f773(f140(x69141),x69143),x69144)))+~P1(f773(f773(f232(x69141),x69142),x69143))
% 191.21/191.75 [6954]~P81(x69541)+~P1(f773(f773(f232(x69541),f2(x69541)),x69543))+~P1(f773(f773(f233(x69541),x69542),x69544))+P1(f773(f773(f233(x69541),x69542),f773(f773(f82(x69541),x69543),x69544)))
% 191.21/191.75 [6955]~P81(x69551)+~P1(f773(f773(f232(x69551),x69552),x69554))+~P1(f773(f773(f233(x69551),f2(x69551)),x69553))+P1(f773(f773(f233(x69551),x69552),f773(f773(f82(x69551),x69553),x69554)))
% 191.21/191.75 [6956]~P117(x69561)+~P1(f773(f773(f233(x69561),f2(x69561)),x69563))+~P1(f773(f773(f233(x69561),x69562),x69564))+P1(f773(f773(f233(x69561),x69562),f773(f773(f82(x69561),x69563),x69564)))
% 191.21/191.75 [6957]~P81(x69571)+~P1(f773(f773(f232(x69571),f2(x69571)),x69574))+~P1(f773(f773(f232(x69571),x69572),x69573))+P1(f773(f773(f232(x69571),x69572),f773(f773(f82(x69571),x69573),x69574)))
% 191.21/191.75 [6958]~P81(x69581)+~P1(f773(f773(f232(x69581),f2(x69581)),x69583))+~P1(f773(f773(f232(x69581),x69582),x69584))+P1(f773(f773(f232(x69581),x69582),f773(f773(f82(x69581),x69583),x69584)))
% 191.21/191.75 [6992]~P100(x69921)+P1(f773(f773(f233(x69921),x69922),x69923))+P1(f773(f773(f233(x69921),x69922),x69924))+~P1(f773(f773(f233(x69921),x69922),f773(f773(f179(x69921),x69924),x69923)))
% 191.21/191.75 [6993]~P100(x69931)+P1(f773(f773(f232(x69931),x69932),x69933))+P1(f773(f773(f232(x69931),x69932),x69934))+~P1(f773(f773(f232(x69931),x69932),f773(f773(f179(x69931),x69934),x69933)))
% 191.21/191.75 [7677]~P63(x76771)+~P1(f773(f773(f233(x76771),x76774),f2(x76771)))+~P1(f773(f773(f233(x76771),x76773),f773(f773(f283(x76771),x76772),x76774)))+P1(f773(f773(f233(x76771),x76772),f773(f773(f83(x76771),x76773),x76774)))
% 191.21/191.75 [7678]~P63(x76781)+~P1(f773(f773(f233(x76781),x76784),f2(x76781)))+~P1(f773(f773(f233(x76781),x76783),f773(f773(f83(x76781),x76782),x76784)))+P1(f773(f773(f233(x76781),x76782),f773(f773(f283(x76781),x76783),x76784)))
% 191.21/191.75 [7679]~P63(x76791)+~P1(f773(f773(f233(x76791),x76794),f2(x76791)))+~P1(f773(f773(f232(x76791),x76793),f773(f773(f283(x76791),x76792),x76794)))+P1(f773(f773(f232(x76791),x76792),f773(f773(f83(x76791),x76793),x76794)))
% 191.21/191.75 [7680]~P63(x76801)+~P1(f773(f773(f233(x76801),x76804),f2(x76801)))+~P1(f773(f773(f232(x76801),x76803),f773(f773(f83(x76801),x76802),x76804)))+P1(f773(f773(f232(x76801),x76802),f773(f773(f283(x76801),x76803),x76804)))
% 191.21/191.75 [7793]~P119(x77931)+~P1(f773(f773(f233(x77931),x77933),f2(x77931)))+~P1(f773(f773(f233(x77931),x77934),x77932))+P1(f773(f773(f233(x77931),f773(f773(f83(x77931),x77932),x77933)),f773(f773(f83(x77931),x77934),x77933)))
% 191.21/191.75 [7794]~P119(x77941)+~P1(f773(f773(f233(x77941),x77942),f2(x77941)))+~P1(f773(f773(f233(x77941),x77944),x77943))+P1(f773(f773(f233(x77941),f773(f773(f83(x77941),x77942),x77943)),f773(f773(f83(x77941),x77942),x77944)))
% 191.21/191.75 [7795]~P63(x77951)+~P1(f773(f773(f233(x77951),x77953),f2(x77951)))+~P1(f773(f773(f233(x77951),x77954),x77952))+P1(f773(f773(f233(x77951),f773(f773(f283(x77951),x77952),x77953)),f773(f773(f283(x77951),x77954),x77953)))
% 191.21/191.75 [7796]~P119(x77961)+~P1(f773(f773(f233(x77961),x77962),f2(x77961)))+~P1(f773(f773(f232(x77961),x77964),x77963))+P1(f773(f773(f232(x77961),f773(f773(f83(x77961),x77962),x77963)),f773(f773(f83(x77961),x77962),x77964)))
% 191.21/191.75 [7797]~P129(x77971)+~P1(f773(f773(f232(x77971),x77972),f2(x77971)))+~P1(f773(f773(f232(x77971),x77974),x77973))+P1(f773(f773(f232(x77971),f773(f773(f83(x77971),x77972),x77973)),f773(f773(f83(x77971),x77972),x77974)))
% 191.21/191.75 [7798]~P129(x77981)+~P1(f773(f773(f232(x77981),x77983),f2(x77981)))+~P1(f773(f773(f232(x77981),x77984),x77982))+P1(f773(f773(f232(x77981),f773(f773(f83(x77981),x77982),x77983)),f773(f773(f83(x77981),x77984),x77983)))
% 191.21/191.75 [7799]~P62(x77991)+~P1(f773(f773(f232(x77991),x77993),f2(x77991)))+~P1(f773(f773(f232(x77991),x77994),x77992))+P1(f773(f773(f232(x77991),f773(f773(f283(x77991),x77992),x77993)),f773(f773(f283(x77991),x77994),x77993)))
% 191.21/191.75 [7801]~P117(x78011)+~P1(f773(f773(f233(x78011),f80(x78011)),x78012))+~P1(f773(f773(f233(a847),x78013),x78014))+P1(f773(f773(f233(x78011),f773(f773(f242(x78011),x78012),x78013)),f773(f773(f242(x78011),x78012),x78014)))
% 191.21/191.75 [7802]~P117(x78021)+~P1(f773(f773(f233(x78021),f80(x78021)),x78022))+~P1(f773(f773(f232(a847),x78023),x78024))+P1(f773(f773(f232(x78021),f773(f773(f242(x78021),x78022),x78023)),f773(f773(f242(x78021),x78022),x78024)))
% 191.21/191.75 [7803]~P117(x78031)+~P1(f773(f773(f232(x78031),f80(x78031)),x78032))+~P1(f773(f773(f232(a847),x78033),x78034))+P1(f773(f773(f232(x78031),f773(f773(f242(x78031),x78032),x78033)),f773(f773(f242(x78031),x78032),x78034)))
% 191.21/191.75 [7830]P1(f773(f773(f233(a847),f2(a847)),f773(x78301,x78302)))+~P1(f773(f63(x78303),x78304))+~P1(f773(f773(f334(x78303),x78302),x78304))+~P1(f773(f773(f233(a847),f2(a847)),f773(f773(f11(x78303,a847),x78301),x78304)))
% 191.21/191.75 [7842]~P123(x78421)+~P1(f773(f773(f233(x78421),x78423),x78424))+~P1(f773(f773(f233(x78421),f2(x78421)),x78422))+P1(f773(f773(f233(x78421),f773(f773(f83(x78421),x78422),x78423)),f773(f773(f83(x78421),x78422),x78424)))
% 191.21/191.75 [7843]~P115(x78431)+~P1(f773(f773(f233(x78431),x78433),x78434))+~P1(f773(f773(f233(x78431),f2(x78431)),x78432))+P1(f773(f773(f233(x78431),f773(f773(f83(x78431),x78432),x78433)),f773(f773(f83(x78431),x78432),x78434)))
% 191.21/191.75 [7844]~P119(x78441)+~P1(f773(f773(f233(x78441),x78442),x78444))+~P1(f773(f773(f233(x78441),f2(x78441)),x78443))+P1(f773(f773(f233(x78441),f773(f773(f83(x78441),x78442),x78443)),f773(f773(f83(x78441),x78444),x78443)))
% 191.21/191.75 [7845]~P123(x78451)+~P1(f773(f773(f233(x78451),x78452),x78454))+~P1(f773(f773(f233(x78451),f2(x78451)),x78453))+P1(f773(f773(f233(x78451),f773(f773(f83(x78451),x78452),x78453)),f773(f773(f83(x78451),x78454),x78453)))
% 191.21/191.75 [7846]~P119(x78461)+~P1(f773(f773(f233(x78461),x78463),x78464))+~P1(f773(f773(f233(x78461),f2(x78461)),x78462))+P1(f773(f773(f233(x78461),f773(f773(f83(x78461),x78462),x78463)),f773(f773(f83(x78461),x78462),x78464)))
% 191.21/191.75 [7847]~P63(x78471)+~P1(f773(f773(f233(x78471),x78472),x78474))+~P1(f773(f773(f233(x78471),f2(x78471)),x78473))+P1(f773(f773(f233(x78471),f773(f773(f283(x78471),x78472),x78473)),f773(f773(f283(x78471),x78474),x78473)))
% 191.21/191.75 [7848]~P119(x78481)+~P1(f773(f773(f233(x78481),f2(x78481)),x78482))+~P1(f773(f773(f232(x78481),x78483),x78484))+P1(f773(f773(f232(x78481),f773(f773(f83(x78481),x78482),x78483)),f773(f773(f83(x78481),x78482),x78484)))
% 191.21/191.75 [7849]~P131(x78491)+~P1(f773(f773(f232(x78491),x78493),x78494))+~P1(f773(f773(f232(x78491),f2(x78491)),x78492))+P1(f773(f773(f232(x78491),f773(f773(f83(x78491),x78492),x78493)),f773(f773(f83(x78491),x78492),x78494)))
% 191.21/191.75 [7850]~P130(x78501)+~P1(f773(f773(f232(x78501),x78503),x78504))+~P1(f773(f773(f232(x78501),f2(x78501)),x78502))+P1(f773(f773(f232(x78501),f773(f773(f83(x78501),x78502),x78503)),f773(f773(f83(x78501),x78502),x78504)))
% 191.21/191.75 [7851]~P131(x78511)+~P1(f773(f773(f232(x78511),x78512),x78514))+~P1(f773(f773(f232(x78511),f2(x78511)),x78513))+P1(f773(f773(f232(x78511),f773(f773(f83(x78511),x78512),x78513)),f773(f773(f83(x78511),x78514),x78513)))
% 191.21/191.75 [7852]~P117(x78521)+~P1(f773(f773(f232(x78521),x78522),x78524))+~P1(f773(f773(f232(x78521),f2(x78521)),x78522))+P1(f773(f773(f232(x78521),f773(f773(f242(x78521),x78522),x78523)),f773(f773(f242(x78521),x78524),x78523)))
% 191.21/191.75 [7853]~P62(x78531)+~P1(f773(f773(f232(x78531),x78532),x78534))+~P1(f773(f773(f232(x78531),f2(x78531)),x78533))+P1(f773(f773(f232(x78531),f773(f773(f283(x78531),x78532),x78533)),f773(f773(f283(x78531),x78534),x78533)))
% 191.21/191.75 [7892]~P102(x78922)+P1(f773(f773(f232(f855(x78921,x78922)),x78924),x78923))+~P1(f773(f773(f232(f855(x78921,x78922)),x78923),x78924))+P1(f773(f773(f233(f855(x78921,x78922)),x78923),x78924))
% 191.21/191.75 [7936]P1(f773(f773(f334(x79361),x79362),x79363))+P1(f773(f773(f334(x79361),x79362),x79364))+~P1(f773(f773(f232(f855(x79361,a841)),x79364),x79363))+P1(f773(f773(f233(f855(x79361,a841)),x79364),f773(f773(f302(x79361),x79362),x79363)))
% 191.21/191.75 [8043]~P111(x80432)+E(x80431,f2(x80432))+P1(f773(f773(f279(x80432),x80433),x80434))+~P1(f773(f773(f279(x80432),f773(f773(f83(x80432),x80433),x80431)),f773(f773(f83(x80432),x80434),x80431)))
% 191.21/191.75 [8044]~P111(x80442)+E(x80441,f2(x80442))+P1(f773(f773(f279(x80442),x80443),x80444))+~P1(f773(f773(f279(x80442),f773(f773(f83(x80442),x80441),x80443)),f773(f773(f83(x80442),x80441),x80444)))
% 191.21/191.75 [8088]P1(f773(f773(f334(x80881),x80882),x80883))+P1(f773(f773(f334(x80881),x80882),x80884))+~P1(f773(f773(f233(f855(x80881,a841)),x80884),f773(f773(f302(x80881),x80882),x80883)))+P1(f773(f773(f232(f855(x80881,a841)),x80884),x80883))
% 191.21/191.75 [8157]~P119(x81571)+P1(f773(f773(f233(x81571),x81573),x81572))+P1(f773(f773(f233(x81571),x81572),x81573))+~P1(f773(f773(f233(x81571),f773(f773(f83(x81571),x81574),x81572)),f773(f773(f83(x81571),x81574),x81573)))
% 191.21/191.75 [8158]~P119(x81581)+P1(f773(f773(f233(x81581),x81583),x81582))+P1(f773(f773(f233(x81581),x81582),x81583))+~P1(f773(f773(f233(x81581),f773(f773(f83(x81581),x81582),x81584)),f773(f773(f83(x81581),x81583),x81584)))
% 191.21/191.75 [8169]~P119(x81691)+P1(f773(f773(f233(x81691),x81694),f2(x81691)))+P1(f773(f773(f233(x81691),x81692),x81693))+~P1(f773(f773(f233(x81691),f773(f773(f83(x81691),x81692),x81694)),f773(f773(f83(x81691),x81693),x81694)))
% 191.21/191.75 [8170]~P119(x81701)+P1(f773(f773(f233(x81701),x81704),f2(x81701)))+P1(f773(f773(f233(x81701),x81702),x81703))+~P1(f773(f773(f233(x81701),f773(f773(f83(x81701),x81704),x81702)),f773(f773(f83(x81701),x81704),x81703)))
% 191.21/191.75 [8173]~P119(x81731)+P1(f773(f773(f233(x81731),x81732),x81733))+P1(f773(f773(f233(x81731),f2(x81731)),x81734))+~P1(f773(f773(f233(x81731),f773(f773(f83(x81731),x81734),x81733)),f773(f773(f83(x81731),x81734),x81732)))
% 191.21/191.75 [8174]~P119(x81741)+P1(f773(f773(f233(x81741),x81742),x81743))+P1(f773(f773(f233(x81741),f2(x81741)),x81744))+~P1(f773(f773(f233(x81741),f773(f773(f83(x81741),x81743),x81744)),f773(f773(f83(x81741),x81742),x81744)))
% 191.21/191.75 [8187]~P119(x81871)+P1(f773(f773(f233(x81871),x81872),f2(x81871)))+P1(f773(f773(f233(x81871),f2(x81871)),x81872))+~P1(f773(f773(f233(x81871),f773(f773(f83(x81871),x81873),x81872)),f773(f773(f83(x81871),x81874),x81872)))
% 191.21/191.75 [8188]~P119(x81881)+P1(f773(f773(f233(x81881),x81882),f2(x81881)))+P1(f773(f773(f233(x81881),f2(x81881)),x81882))+~P1(f773(f773(f233(x81881),f773(f773(f83(x81881),x81882),x81883)),f773(f773(f83(x81881),x81882),x81884)))
% 191.21/191.75 [8212]~P119(x82121)+~P1(f773(f773(f233(x82121),x82124),f2(x82121)))+P1(f773(f773(f233(x82121),x82122),x82123))+~P1(f773(f773(f233(x82121),f773(f773(f83(x82121),x82124),x82123)),f773(f773(f83(x82121),x82124),x82122)))
% 191.21/191.75 [8213]~P119(x82131)+~P1(f773(f773(f233(x82131),x82134),f2(x82131)))+P1(f773(f773(f232(x82131),x82132),x82133))+~P1(f773(f773(f232(x82131),f773(f773(f83(x82131),x82134),x82133)),f773(f773(f83(x82131),x82134),x82132)))
% 191.21/191.75 [8225]~P117(x82253)+~P1(f773(f773(f233(x82253),f80(x82253)),x82254))+P1(f773(f773(f233(a847),x82251),x82252))+~P1(f773(f773(f233(x82253),f773(f773(f242(x82253),x82254),x82251)),f773(f773(f242(x82253),x82254),x82252)))
% 191.21/191.75 [8227]~P117(x82273)+~P1(f773(f773(f233(x82273),f80(x82273)),x82274))+P1(f773(f773(f232(a847),x82271),x82272))+~P1(f773(f773(f232(x82273),f773(f773(f242(x82273),x82274),x82271)),f773(f773(f242(x82273),x82274),x82272)))
% 191.21/191.75 [8237]~P119(x82371)+P1(f773(f773(f233(x82371),x82372),x82373))+~P1(f773(f773(f233(x82371),f2(x82371)),x82374))+~P1(f773(f773(f233(x82371),f773(f773(f83(x82371),x82374),x82372)),f773(f773(f83(x82371),x82374),x82373)))
% 191.21/191.75 [8238]~P123(x82381)+P1(f773(f773(f233(x82381),x82382),x82383))+~P1(f773(f773(f232(x82381),f2(x82381)),x82384))+~P1(f773(f773(f233(x82381),f773(f773(f83(x82381),x82384),x82382)),f773(f773(f83(x82381),x82384),x82383)))
% 191.21/191.75 [8239]~P125(x82391)+P1(f773(f773(f233(x82391),x82392),x82393))+~P1(f773(f773(f232(x82391),f2(x82391)),x82394))+~P1(f773(f773(f233(x82391),f773(f773(f83(x82391),x82394),x82392)),f773(f773(f83(x82391),x82394),x82393)))
% 191.21/191.75 [8240]~P117(x82401)+~P1(f773(f773(f232(x82401),f2(x82401)),x82403))+P1(f773(f773(f233(x82401),x82402),x82403))+~P1(f773(f773(f233(x82401),f773(f773(f242(x82401),x82402),x82404)),f773(f773(f242(x82401),x82403),x82404)))
% 191.21/191.75 [8241]~P123(x82411)+P1(f773(f773(f233(x82411),x82412),x82413))+~P1(f773(f773(f232(x82411),f2(x82411)),x82414))+~P1(f773(f773(f233(x82411),f773(f773(f83(x82411),x82412),x82414)),f773(f773(f83(x82411),x82413),x82414)))
% 191.21/191.75 [8242]~P125(x82421)+P1(f773(f773(f233(x82421),x82422),x82423))+~P1(f773(f773(f232(x82421),f2(x82421)),x82424))+~P1(f773(f773(f233(x82421),f773(f773(f83(x82421),x82422),x82424)),f773(f773(f83(x82421),x82423),x82424)))
% 191.21/191.75 [8243]~P119(x82431)+P1(f773(f773(f232(x82431),x82432),x82433))+~P1(f773(f773(f233(x82431),f2(x82431)),x82434))+~P1(f773(f773(f232(x82431),f773(f773(f83(x82431),x82434),x82432)),f773(f773(f83(x82431),x82434),x82433)))
% 191.21/191.75 [8244]~P123(x82441)+P1(f773(f773(f232(x82441),x82442),x82443))+~P1(f773(f773(f233(x82441),f2(x82441)),x82444))+~P1(f773(f773(f232(x82441),f773(f773(f83(x82441),x82444),x82442)),f773(f773(f83(x82441),x82444),x82443)))
% 191.21/191.75 [8245]~P123(x82451)+P1(f773(f773(f232(x82451),x82452),x82453))+~P1(f773(f773(f233(x82451),f2(x82451)),x82454))+~P1(f773(f773(f232(x82451),f773(f773(f83(x82451),x82452),x82454)),f773(f773(f83(x82451),x82453),x82454)))
% 191.21/191.75 [8285]P1(f773(f773(f334(x82851),x82852),x82853))+~P1(f773(f773(f232(f855(x82851,a841)),x82853),x82854))+~P1(f773(f773(f233(f855(x82851,a841)),x82853),x82854))+P1(f773(f773(f233(f855(x82851,a841)),x82853),f773(f773(f302(x82851),x82852),x82854)))
% 191.21/191.75 [8320]~P136(x83201)+~P112(x83201)+P1(f773(f773(f279(x83201),x83202),f773(f773(f82(x83201),f835(x83202,x83203,x83201)),f2(x83201))))+~P1(f773(x83203,f773(f773(f83(x83201),x83202),x83204)))
% 191.21/191.75 [8646]E(f773(f773(f3(a1),f346(x86461,x86462,x86463,x86464)),f347(x86461,x86462,x86463,x86464)),x86464)+~P1(f773(f773(f233(a1),f2(a1)),x86463))+~P1(f773(f773(f232(a1),x86461),x86464))+P1(f773(f773(f232(a1),x86461),f773(f773(f82(a1),x86464),x86463)))
% 191.21/191.75 [8647]E(f773(f773(f3(a1),f354(x86471,x86472,x86473,x86474)),f355(x86471,x86472,x86473,x86474)),x86474)+~P1(f773(f773(f233(a1),f2(a1)),x86473))+~P1(f773(f773(f233(a1),x86471),x86474))+P1(f773(f773(f233(a1),x86471),f773(f773(f82(a1),x86474),x86473)))
% 191.21/191.75 [8773]~E(f773(f773(f153(x87731),x87733),f756(x87734,x87733,x87731,x87732)),f773(f773(f153(x87731),x87734),f756(x87734,x87733,x87731,x87732)))+E(f773(f773(f159(x87731),x87732),x87733),f773(f773(f159(x87731),x87732),x87734))+~P1(f773(f773(f232(a847),x87732),f773(f181(f848(x87731)),x87733)))+~P1(f773(f773(f232(a847),x87732),f773(f181(f848(x87731)),x87734)))
% 191.21/191.75 [8824]~P1(f773(f773(f233(a1),f2(a1)),x88243))+~P1(f773(f773(f232(a1),x88241),x88244))+P1(f773(f773(f334(a1),f346(x88241,x88242,x88243,x88244)),x88242))+P1(f773(f773(f232(a1),x88241),f773(f773(f82(a1),x88244),x88243)))
% 191.21/191.75 [8825]~P1(f773(f773(f233(a1),f2(a1)),x88253))+~P1(f773(f773(f233(a1),x88251),x88254))+P1(f773(f773(f334(a1),f354(x88251,x88252,x88253,x88254)),x88252))+P1(f773(f773(f233(a1),x88251),f773(f773(f82(a1),x88254),x88253)))
% 191.21/191.75 [8862]~P100(x88621)+~P1(f773(f63(x88621),x88623))+~P1(f773(f773(f334(x88621),x88624),x88623))+P1(f773(f773(f232(x88621),f773(f773(f66(x88621,x88621,f236(x88621)),x88622),x88623)),f773(f773(f236(x88621),x88624),x88622)))
% 191.21/191.75 [8863]~P98(x88631)+~P1(f773(f63(x88631),x88633))+~P1(f773(f773(f334(x88631),x88634),x88633))+P1(f773(f773(f232(x88631),f773(f773(f66(x88631,x88631,f104(x88631)),x88632),x88633)),f773(f773(f104(x88631),x88634),x88632)))
% 191.21/191.75 [8872]~P12(x88722,x88723,x88724)+~P1(f773(f63(x88722),x88723))+P1(f773(f773(f279(a847),x88721),f773(f42(x88722),x88723)))+P1(f773(f773(f334(f855(x88722,a841)),f517(x88721,x88724,x88723,x88722)),f773(f773(f61(x88722),x88723),x88724)))
% 191.21/191.75 [8911]E(f773(f773(f159(x89111),x89112),x89113),f773(f773(f159(x89111),x89112),x89114))+P1(f773(f773(f233(a847),f756(x89113,x89114,x89111,x89112)),x89112))+~P1(f773(f773(f232(a847),x89112),f773(f181(f848(x89111)),x89113)))+~P1(f773(f773(f232(a847),x89112),f773(f181(f848(x89111)),x89114)))
% 191.21/191.75 [8916]~P1(f773(f773(f233(a1),f2(a1)),x89163))+~P1(f773(f773(f233(a1),x89161),x89162))+P1(f773(f773(f334(a1),f355(x89161,x89164,x89163,x89162)),f295(a1,f80(a1),x89163)))+P1(f773(f773(f233(a1),x89161),f773(f773(f82(a1),x89162),x89163)))
% 191.21/191.75 [8917]~P1(f773(f773(f233(a1),f2(a1)),x89173))+~P1(f773(f773(f232(a1),x89171),x89172))+P1(f773(f773(f334(a1),f347(x89171,x89174,x89173,x89172)),f295(a1,f80(a1),x89173)))+P1(f773(f773(f232(a1),x89171),f773(f773(f82(a1),x89172),x89173)))
% 191.21/191.75 [9080]~E(f166(x90801,x90802,x90803),f166(x90801,x90802,x90804))+E(f773(f158(f854(x90801,x90802)),x90803),f773(f158(f854(x90801,x90802)),x90804))+~P1(f773(f127(x90801),f773(f773(f143(f854(x90801,x90802),x90801),f240(x90801,x90802)),x90804)))+~P1(f773(f127(x90801),f773(f773(f143(f854(x90801,x90802),x90801),f240(x90801,x90802)),x90803)))
% 191.21/191.75 [9083]E(f166(x90831,x90832,x90833),f166(x90831,x90832,x90834))+~E(f773(f158(f854(x90831,x90832)),x90833),f773(f158(f854(x90831,x90832)),x90834))+~P1(f773(f127(x90831),f773(f773(f143(f854(x90831,x90832),x90831),f240(x90831,x90832)),x90834)))+~P1(f773(f127(x90831),f773(f773(f143(f854(x90831,x90832),x90831),f240(x90831,x90832)),x90833)))
% 191.21/191.75 [9200]~P100(x92001)+~P1(f773(f63(x92001),x92004))+P1(f773(f773(f334(x92001),f689(x92002,x92003,x92004,x92001)),x92004))+P1(f773(f773(f232(x92001),f773(f773(f66(x92001,x92001,f179(x92001)),x92002),x92004)),f773(f773(f179(x92001),x92003),x92002)))
% 191.21/191.75 [9201]~P92(x92011)+~P1(f773(f63(x92011),x92014))+P1(f773(f773(f334(x92011),f693(x92012,x92013,x92014,x92011)),x92014))+P1(f773(f773(f232(x92011),f773(f773(f66(x92011,x92011,f103(x92011)),x92012),x92014)),f773(f773(f103(x92011),x92013),x92012)))
% 191.21/191.75 [9327]~P100(x93271)+~P1(f773(f63(x93271),x93273))+~P1(f773(f773(f232(x93271),f689(x93272,x93274,x93273,x93271)),x93274))+P1(f773(f773(f232(x93271),f773(f773(f66(x93271,x93271,f179(x93271)),x93272),x93273)),f773(f773(f179(x93271),x93274),x93272)))
% 191.21/191.75 [9328]~P92(x93281)+~P1(f773(f63(x93281),x93283))+~P1(f773(f773(f232(x93281),f693(x93282,x93284,x93283,x93281)),x93284))+P1(f773(f773(f232(x93281),f773(f773(f66(x93281,x93281,f103(x93281)),x93282),x93283)),f773(f773(f103(x93281),x93284),x93282)))
% 191.21/191.75 [9330]~P1(f773(f773(f233(a1),f2(a1)),x93303))+~P1(f773(f773(f232(a1),f2(a1)),x93304))+~P1(f773(f773(f233(a1),x93304),x93301))+P1(f773(f773(f233(a1),f773(f773(f82(a1),f773(f773(f83(a1),x93301),f52(a1,x93302,x93303))),x93304)),f773(f773(f83(a1),x93301),x93303)))
% 191.21/191.75 [9590]~P99(x95901)+P1(f773(f773(f233(x95901),f773(x95902,x95903)),f773(x95902,x95904)))+~P1(f773(f773(f233(a847),x95903),x95904))+~P1(f773(f773(f233(x95901),f773(x95902,f649(x95904,x95903,x95902,x95901))),f773(x95902,f773(a114,f649(x95904,x95903,x95902,x95901)))))
% 191.21/191.75 [9591]~P99(x95911)+P1(f773(f773(f233(x95911),f773(x95912,x95913)),f773(x95912,x95914)))+~P1(f773(f773(f233(a847),x95913),x95914))+~P1(f773(f773(f233(x95911),f773(x95912,f662(x95914,x95913,x95912,x95911))),f773(x95912,f773(a114,f662(x95914,x95913,x95912,x95911)))))
% 191.21/191.75 [9592]~P99(x95923)+~P1(f773(f773(f233(x95923),f773(x95924,x95921)),f773(x95924,x95922)))+P1(f773(f773(f233(a847),x95921),x95922))+~P1(f773(f773(f233(x95923),f773(x95924,f649(x95922,x95921,x95924,x95923))),f773(x95924,f773(a114,f649(x95922,x95921,x95924,x95923)))))
% 191.21/191.75 [9685]E(x96851,x96852)+P1(f773(f773(f334(f854(f848(x96853),f848(x96853))),f773(f773(f241(f848(x96853),f848(x96853)),x96852),x96851)),f137(x96853,x96854)))+P1(f773(f773(f334(f854(f848(x96853),f848(x96853))),f773(f773(f241(f848(x96853),f848(x96853)),x96851),x96852)),f137(x96853,x96854)))+~P1(f773(f773(f334(f854(x96853,x96853)),f773(f773(f241(x96853,x96853),f751(x96851,x96852,x96854,x96853)),f753(x96851,x96852,x96854,x96853))),x96854))
% 191.21/191.75 [9686]E(x96861,x96862)+P1(f773(f773(f334(f854(f848(x96863),f848(x96863))),f773(f773(f241(f848(x96863),f848(x96863)),x96862),x96861)),f137(x96863,x96864)))+P1(f773(f773(f334(f854(f848(x96863),f848(x96863))),f773(f773(f241(f848(x96863),f848(x96863)),x96861),x96862)),f137(x96863,x96864)))+~P1(f773(f773(f334(f854(x96863,x96863)),f773(f773(f241(x96863,x96863),f753(x96861,x96862,x96864,x96863)),f751(x96861,x96862,x96864,x96863))),x96864))
% 191.21/191.75 [7375]~P100(x73751)+~P1(f773(f773(f233(x73751),x73753),x73754))+~P1(f773(f773(f233(x73751),x73752),x73754))+P1(f773(f773(f233(x73751),f773(f773(f179(x73751),x73752),x73753)),x73754))
% 191.21/191.75 [7378]~P100(x73781)+~P1(f773(f773(f232(x73781),x73783),x73784))+~P1(f773(f773(f232(x73781),x73782),x73784))+P1(f773(f773(f232(x73781),f773(f773(f179(x73781),x73782),x73783)),x73784))
% 191.21/191.75 [7381]~P92(x73811)+~P1(f773(f773(f232(x73811),x73813),x73814))+~P1(f773(f773(f232(x73811),x73812),x73814))+P1(f773(f773(f232(x73811),f773(f773(f103(x73811),x73812),x73813)),x73814))
% 191.21/191.75 [7622]~P7(x76221)+E(f773(f773(f82(x76221),f773(f773(f43(x76221),x76222),x76223)),f773(f773(f43(x76221),x76224),x76223)),f773(f773(f43(x76221),f773(f773(f82(x76221),x76222),x76224)),x76223))+~P1(f773(f773(f279(x76221),x76223),x76224))+~P1(f773(f773(f279(x76221),x76223),x76222))
% 191.21/191.75 [7700]~E(x77001,x77003)+E(f130(a847,f773(f294(a847,x77001),x77002)),f773(f773(f140(a847),x77003),x77004))+~E(f130(a847,f773(f294(a847,f773(f773(f82(a847),x77001),f80(a847))),x77002)),x77004)+~P1(f773(f773(f233(a847),x77001),x77002))
% 191.21/191.75 [7711]~P100(x77111)+P1(f773(f773(f233(x77111),x77112),x77113))+P1(f773(f773(f233(x77111),x77114),x77113))+~P1(f773(f773(f233(x77111),f773(f773(f236(x77111),x77114),x77112)),x77113))
% 191.21/191.75 [7712]~P100(x77121)+P1(f773(f773(f232(x77121),x77122),x77123))+P1(f773(f773(f232(x77121),x77124),x77123))+~P1(f773(f773(f232(x77121),f773(f773(f236(x77121),x77124),x77122)),x77123))
% 191.21/191.75 [7993]~P62(x79931)+~P1(f773(f773(f233(x79931),f2(x79931)),x79933))+~P1(f773(f773(f233(x79931),x79932),f773(f773(f283(x79931),x79934),x79933)))+P1(f773(f773(f233(x79931),f773(f773(f83(x79931),x79932),x79933)),x79934))
% 191.21/191.75 [7994]~P63(x79941)+~P1(f773(f773(f233(x79941),f2(x79941)),x79943))+~P1(f773(f773(f233(x79941),x79942),f773(f773(f283(x79941),x79944),x79943)))+P1(f773(f773(f233(x79941),f773(f773(f83(x79941),x79942),x79943)),x79944))
% 191.21/191.75 [7995]~P62(x79951)+~P1(f773(f773(f233(x79951),f2(x79951)),x79953))+~P1(f773(f773(f233(x79951),x79952),f773(f773(f83(x79951),x79954),x79953)))+P1(f773(f773(f233(x79951),f773(f773(f283(x79951),x79952),x79953)),x79954))
% 191.21/191.75 [7997]~P63(x79971)+~P1(f773(f773(f233(x79971),f2(x79971)),x79973))+~P1(f773(f773(f233(x79971),x79972),f773(f773(f83(x79971),x79974),x79973)))+P1(f773(f773(f233(x79971),f773(f773(f283(x79971),x79972),x79973)),x79974))
% 191.21/191.75 [7998]~P62(x79981)+~P1(f773(f773(f233(x79981),f2(x79981)),x79983))+~P1(f773(f773(f232(x79981),x79982),f773(f773(f283(x79981),x79984),x79983)))+P1(f773(f773(f232(x79981),f773(f773(f83(x79981),x79982),x79983)),x79984))
% 191.21/191.75 [7999]~P63(x79991)+~P1(f773(f773(f233(x79991),f2(x79991)),x79993))+~P1(f773(f773(f232(x79991),x79992),f773(f773(f283(x79991),x79994),x79993)))+P1(f773(f773(f232(x79991),f773(f773(f83(x79991),x79992),x79993)),x79994))
% 191.21/191.75 [8000]~P62(x80001)+~P1(f773(f773(f233(x80001),f2(x80001)),x80003))+~P1(f773(f773(f232(x80001),x80002),f773(f773(f83(x80001),x80004),x80003)))+P1(f773(f773(f232(x80001),f773(f773(f283(x80001),x80002),x80003)),x80004))
% 191.21/191.75 [8002]~P63(x80021)+~P1(f773(f773(f233(x80021),f2(x80021)),x80023))+~P1(f773(f773(f232(x80021),x80022),f773(f773(f83(x80021),x80024),x80023)))+P1(f773(f773(f232(x80021),f773(f773(f283(x80021),x80022),x80023)),x80024))
% 191.21/191.75 [8126]~P62(x81261)+~P1(f773(f773(f233(x81261),f2(x81261)),x81264))+P1(f773(f773(f233(x81261),x81262),f773(f773(f83(x81261),x81263),x81264)))+~P1(f773(f773(f233(x81261),f773(f773(f283(x81261),x81262),x81264)),x81263))
% 191.21/191.75 [8127]~P62(x81271)+~P1(f773(f773(f233(x81271),f2(x81271)),x81274))+P1(f773(f773(f233(x81271),x81272),f773(f773(f283(x81271),x81273),x81274)))+~P1(f773(f773(f233(x81271),f773(f773(f83(x81271),x81272),x81274)),x81273))
% 191.21/191.75 [8129]~P63(x81291)+~P1(f773(f773(f233(x81291),f2(x81291)),x81294))+P1(f773(f773(f233(x81291),x81292),f773(f773(f83(x81291),x81293),x81294)))+~P1(f773(f773(f233(x81291),f773(f773(f283(x81291),x81292),x81294)),x81293))
% 191.21/191.75 [8130]~P63(x81301)+~P1(f773(f773(f233(x81301),f2(x81301)),x81304))+P1(f773(f773(f233(x81301),x81302),f773(f773(f283(x81301),x81303),x81304)))+~P1(f773(f773(f233(x81301),f773(f773(f83(x81301),x81302),x81304)),x81303))
% 191.21/191.75 [8131]~P62(x81311)+~P1(f773(f773(f233(x81311),f2(x81311)),x81314))+P1(f773(f773(f232(x81311),x81312),f773(f773(f83(x81311),x81313),x81314)))+~P1(f773(f773(f232(x81311),f773(f773(f283(x81311),x81312),x81314)),x81313))
% 191.21/191.75 [8132]~P62(x81321)+~P1(f773(f773(f233(x81321),f2(x81321)),x81324))+P1(f773(f773(f232(x81321),x81322),f773(f773(f283(x81321),x81323),x81324)))+~P1(f773(f773(f232(x81321),f773(f773(f83(x81321),x81322),x81324)),x81323))
% 191.21/191.75 [8134]~P63(x81341)+~P1(f773(f773(f233(x81341),f2(x81341)),x81344))+P1(f773(f773(f232(x81341),x81342),f773(f773(f83(x81341),x81343),x81344)))+~P1(f773(f773(f232(x81341),f773(f773(f283(x81341),x81342),x81344)),x81343))
% 191.21/191.75 [8135]~P63(x81351)+~P1(f773(f773(f233(x81351),f2(x81351)),x81354))+P1(f773(f773(f232(x81351),x81352),f773(f773(f283(x81351),x81353),x81354)))+~P1(f773(f773(f232(x81351),f773(f773(f83(x81351),x81352),x81354)),x81353))
% 191.21/191.75 [8290]~P63(x82901)+~P1(f773(f773(f233(x82901),x82903),f2(x82901)))+~P1(f773(f773(f233(x82901),f773(f773(f283(x82901),x82904),x82903)),x82902))+P1(f773(f773(f233(x82901),f773(f773(f83(x82901),x82902),x82903)),x82904))
% 191.21/191.75 [8291]~P63(x82911)+~P1(f773(f773(f233(x82911),x82913),f2(x82911)))+~P1(f773(f773(f233(x82911),f773(f773(f83(x82911),x82914),x82913)),x82912))+P1(f773(f773(f233(x82911),f773(f773(f283(x82911),x82912),x82913)),x82914))
% 191.21/191.75 [8292]~P63(x82921)+~P1(f773(f773(f233(x82921),x82923),f2(x82921)))+~P1(f773(f773(f232(x82921),f773(f773(f283(x82921),x82924),x82923)),x82922))+P1(f773(f773(f232(x82921),f773(f773(f83(x82921),x82922),x82923)),x82924))
% 191.21/191.75 [8293]~P63(x82931)+~P1(f773(f773(f233(x82931),x82933),f2(x82931)))+~P1(f773(f773(f232(x82931),f773(f773(f83(x82931),x82934),x82933)),x82932))+P1(f773(f773(f232(x82931),f773(f773(f283(x82931),x82932),x82933)),x82934))
% 191.21/191.75 [8306]~P1(f773(x83061,x83064))+~P1(f773(f773(f233(a847),x83062),f773(f773(f83(a847),x83063),f773(a114,x83064))))+P1(f773(x83061,f773(f773(f43(a847),x83062),x83063)))+~P1(f773(f773(f232(a847),f773(f773(f83(a847),x83063),x83064)),x83062))
% 191.21/191.75 [8521]~P100(x85211)+~P1(f773(f63(x85211),x85214))+~P1(f773(f773(f334(x85211),x85212),x85214))+P1(f773(f773(f232(x85211),f773(f773(f179(x85211),x85212),x85213)),f773(f773(f66(x85211,x85211,f179(x85211)),x85213),x85214)))
% 191.21/191.75 [8522]~P92(x85221)+~P1(f773(f63(x85221),x85224))+~P1(f773(f773(f334(x85221),x85222),x85224))+P1(f773(f773(f232(x85221),f773(f773(f103(x85221),x85222),x85223)),f773(f773(f66(x85221,x85221,f103(x85221)),x85223),x85224)))
% 191.21/191.75 [8648]~P1(f773(f63(x86481),x86482))+E(f773(f42(x86481),f773(f773(f3(f855(x86481,a841)),x86482),f773(f773(f302(x86481),x86483),x86484))),f773(f773(f3(a847),f773(f42(x86481),f773(f773(f3(f855(x86481,a841)),x86482),x86484))),f80(a847)))+P1(f773(f773(f334(x86481),x86483),x86484))+~P1(f773(f773(f334(x86481),x86483),x86482))
% 191.21/191.75 [8712]E(f773(f773(f82(a1),f348(x87121,x87122,x87123,x87124)),f349(x87121,x87122,x87123,x87124)),x87124)+~P1(f773(f773(f233(a1),f2(a1)),x87123))+~P1(f773(f773(f232(a1),x87124),x87121))+P1(f773(f773(f232(a1),f773(f773(f3(a1),x87124),x87123)),x87121))
% 191.21/191.75 [8713]E(f773(f773(f82(a1),f357(x87131,x87132,x87133,x87134)),f358(x87131,x87132,x87133,x87134)),x87134)+~P1(f773(f773(f233(a1),f2(a1)),x87133))+~P1(f773(f773(f233(a1),x87134),x87131))+P1(f773(f773(f233(a1),f773(f773(f3(a1),x87134),x87133)),x87131))
% 191.21/191.75 [8896]~P1(f773(f773(f233(a1),f2(a1)),x88963))+~P1(f773(f773(f232(a1),x88964),x88961))+P1(f773(f773(f334(a1),f348(x88961,x88962,x88963,x88964)),x88962))+P1(f773(f773(f232(a1),f773(f773(f3(a1),x88964),x88963)),x88961))
% 191.21/191.75 [8897]~P1(f773(f773(f233(a1),f2(a1)),x88973))+~P1(f773(f773(f233(a1),x88974),x88971))+P1(f773(f773(f334(a1),f357(x88971,x88972,x88973,x88974)),x88972))+P1(f773(f773(f233(a1),f773(f773(f3(a1),x88974),x88973)),x88971))
% 191.21/191.75 [8976]~P1(f773(f773(f233(a1),f2(a1)),x89762))+~P1(f773(f773(f233(a1),x89761),x89763))+P1(f773(f773(f334(a1),f358(x89763,x89764,x89762,x89761)),f295(a1,f80(a1),x89762)))+P1(f773(f773(f233(a1),f773(f773(f3(a1),x89761),x89762)),x89763))
% 191.21/191.75 [8977]~P1(f773(f773(f233(a1),f2(a1)),x89772))+~P1(f773(f773(f232(a1),x89771),x89773))+P1(f773(f773(f334(a1),f349(x89773,x89774,x89772,x89771)),f295(a1,f80(a1),x89772)))+P1(f773(f773(f232(a1),f773(f773(f3(a1),x89771),x89772)),x89773))
% 191.21/191.75 [8998]~P1(f773(f773(f233(a1),f2(a1)),x89983))+~P1(f773(f773(f232(a1),f2(a1)),x89984))+~P1(f773(f773(f233(a1),x89984),x89981))+P1(f773(f773(f232(a1),f2(a1)),f773(f773(f82(a1),f773(f773(f83(a1),x89981),f52(a1,x89982,x89983))),x89984)))
% 191.21/191.75 [9056]~P100(x90561)+~P1(f773(f63(x90561),x90564))+~P1(f773(f773(f232(x90561),x90562),f688(x90563,x90562,x90564,x90561)))+P1(f773(f773(f232(x90561),f773(f773(f236(x90561),x90562),x90563)),f773(f773(f66(x90561,x90561,f236(x90561)),x90563),x90564)))
% 191.21/191.75 [9057]~P98(x90571)+~P1(f773(f63(x90571),x90574))+~P1(f773(f773(f232(x90571),x90572),f692(x90573,x90572,x90574,x90571)))+P1(f773(f773(f232(x90571),f773(f773(f104(x90571),x90572),x90573)),f773(f773(f66(x90571,x90571,f104(x90571)),x90573),x90574)))
% 191.21/191.75 [9070]~P1(f773(f773(f232(a1),x90704),f2(a1)))+~P1(f773(f773(f233(a1),f2(a1)),x90702))+~P1(f773(f773(f233(a1),x90701),x90704))+P1(f773(f773(f233(a1),f773(f773(f83(a1),x90701),x90702)),f773(f773(f82(a1),f773(f773(f83(a1),x90701),f52(a1,x90703,x90702))),x90704)))
% 191.21/191.75 [9092]P1(f773(f63(x90921),x90922))+~P1(f773(f63(x90921),x90923))+~P1(f773(f773(f334(f855(x90921,a841)),x90922),f773(f773(f61(x90921),x90923),x90924)))+~P1(f773(f773(f232(f855(f854(x90921,x90921),a841)),x90924),f773(f773(f248(x90921,x90921),x90923),f773(f18(f855(x90921,a841),x90921),x90923))))
% 191.21/191.75 [9115]~P100(x91151)+~P1(f773(f63(x91151),x91154))+P1(f773(f773(f334(x91151),f688(x91152,x91153,x91154,x91151)),x91154))+P1(f773(f773(f232(x91151),f773(f773(f236(x91151),x91153),x91152)),f773(f773(f66(x91151,x91151,f236(x91151)),x91152),x91154)))
% 191.21/191.75 [9116]~P98(x91161)+~P1(f773(f63(x91161),x91164))+P1(f773(f773(f334(x91161),f692(x91162,x91163,x91164,x91161)),x91164))+P1(f773(f773(f232(x91161),f773(f773(f104(x91161),x91163),x91162)),f773(f773(f66(x91161,x91161,f104(x91161)),x91162),x91164)))
% 191.21/191.75 [9488]~P1(f773(f63(x94882),x94884))+~P1(f773(f63(x94881),x94883))+~P1(f773(f773(f232(a847),f773(f42(x94882),x94884)),f773(f42(x94881),x94883)))+P1(f773(f773(f232(f855(x94881,a841)),f773(f303(x94882,x94881,f527(x94883,x94881,x94884,x94882)),x94884)),x94883))
% 191.21/191.75 [9153]~P1(f773(f773(f334(x91531),x91532),x91534))+P1(f773(f773(f334(x91531),x91532),x91533))+~P1(f773(f773(f233(f855(x91531,a841)),x91534),f773(f773(f302(x91531),x91532),x91533)))+P1(f773(f773(f233(f855(x91531,a841)),f773(f773(f3(f855(x91531,a841)),x91534),f773(f773(f302(x91531),x91532),f180(f855(x91531,a841))))),x91533))
% 191.21/191.75 [9305]~P1(f773(f773(f334(x93051),x93052),x93054))+P1(f773(f773(f334(x93051),x93052),x93053))+P1(f773(f773(f233(f855(x93051,a841)),x93054),f773(f773(f302(x93051),x93052),x93053)))+~P1(f773(f773(f233(f855(x93051,a841)),f773(f773(f3(f855(x93051,a841)),x93054),f773(f773(f302(x93051),x93052),f180(f855(x93051,a841))))),x93053))
% 191.21/191.75 [9333]P1(f773(f773(f334(x93331),x93332),x93333))+~P1(f773(f773(f232(f855(x93331,a841)),x93334),x93333))+P1(f773(f773(f233(f855(x93331,a841)),x93334),f773(f773(f302(x93331),x93332),x93333)))+~P1(f773(f773(f233(f855(x93331,a841)),f773(f773(f3(f855(x93331,a841)),x93334),f773(f773(f302(x93331),x93332),f180(f855(x93331,a841))))),x93333))
% 191.21/191.75 [9338]~P1(f773(f773(f334(x93381),x93383),x93382))+~P1(f773(f773(f233(f855(x93381,a841)),x93382),x93384))+P1(f773(f773(f233(f855(x93381,a841)),x93382),f773(f773(f302(x93381),x93383),x93384)))+~P1(f773(f773(f233(f855(x93381,a841)),f773(f773(f3(f855(x93381,a841)),x93382),f773(f773(f302(x93381),x93383),f180(f855(x93381,a841))))),x93384))
% 191.21/191.75 [9350]~P1(f773(f773(f232(f855(x93501,a841)),x93502),x93504))+~P1(f773(f773(f233(f855(x93501,a841)),x93502),x93504))+P1(f773(f773(f233(f855(x93501,a841)),x93502),f773(f773(f302(x93501),x93503),x93504)))+~P1(f773(f773(f233(f855(x93501,a841)),f773(f773(f3(f855(x93501,a841)),x93502),f773(f773(f302(x93501),x93503),f180(f855(x93501,a841))))),x93504))
% 191.21/191.75 [9677]E(f773(f773(f153(x96771),f773(f773(f153(f848(x96771)),f164(x96771,x96772)),x96773)),x96774),f773(f773(f153(x96771),f773(f773(f153(f848(x96771)),x96772),x96774)),x96773))+~P1(f773(f773(f233(a847),x96773),f773(f181(f848(f848(x96771))),f164(x96771,x96772))))+~P18(a847,f773(f142(a847),f773(f773(f143(f848(x96771),a847),f181(f848(x96771))),x96772)))+~P1(f773(f773(f233(a847),x96774),f773(f181(f848(f848(x96771))),f773(f126(f848(x96771),f773(f773(f10(a847,a841,f848(x96771)),f773(f233(a847),x96773)),f181(f848(x96771)))),x96772))))
% 191.21/191.75 [9698]~P1(f773(f773(f334(f854(a847,a847)),x96984),x96981))+~P1(f773(f773(f334(f854(f854(a847,a847),f854(a847,a847))),f773(f773(f241(f854(a847,a847),f854(a847,a847)),x96984),x96982)),a40))+~P1(f773(f773(f334(f854(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841))),f773(f773(f241(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841)),x96981),x96983)),a70))+P1(f773(f773(f334(f854(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841))),f773(f773(f241(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841)),x96981),f773(f773(f302(f854(a847,a847)),x96982),x96983))),a70))
% 191.21/191.75 [9699]~P1(f773(f773(f334(f854(a847,a847)),x96994),x96991))+~P1(f773(f773(f334(f854(f854(a847,a847),f854(a847,a847))),f773(f773(f241(f854(a847,a847),f854(a847,a847)),x96994),x96992)),a72))+~P1(f773(f773(f334(f854(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841))),f773(f773(f241(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841)),x96991),x96993)),a73))+P1(f773(f773(f334(f854(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841))),f773(f773(f241(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841)),x96991),f773(f773(f302(f854(a847,a847)),x96992),x96993))),a73))
% 191.21/191.75 [9711]~P1(f773(f773(f334(f854(a847,a847)),x97114),x97113))+~P1(f773(f773(f334(f854(f854(a847,a847),f854(a847,a847))),f773(f773(f241(f854(a847,a847),f854(a847,a847)),x97111),x97114)),a40))+~P1(f773(f773(f334(f854(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841))),f773(f773(f241(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841)),x97112),x97113)),a41))+P1(f773(f773(f334(f854(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841))),f773(f773(f241(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841)),f773(f773(f302(f854(a847,a847)),x97111),x97112)),x97113)),a41))
% 191.21/191.75 [9712]~P1(f773(f773(f334(f854(a847,a847)),x97124),x97123))+~P1(f773(f773(f334(f854(f854(a847,a847),f854(a847,a847))),f773(f773(f241(f854(a847,a847),f854(a847,a847)),x97121),x97124)),a72))+~P1(f773(f773(f334(f854(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841))),f773(f773(f241(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841)),x97122),x97123)),a71))+P1(f773(f773(f334(f854(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841))),f773(f773(f241(f855(f854(a847,a847),a841),f855(f854(a847,a847),a841)),f773(f773(f302(f854(a847,a847)),x97121),x97122)),x97123)),a71))
% 191.21/191.75 [5904]~P11(x59044,x59041)+~P1(f773(f773(x59041,x59042),x59045))+P1(f773(f773(x59041,x59042),x59043))+~P1(f773(f773(x59041,x59045),x59043))
% 191.21/191.75 [5171]~P6(x51715)+E(x51711,x51712)+~E(x51713,x51714)+~E(f773(f773(f3(x51715),x51713),x51714),f773(f773(f3(x51715),x51711),x51712))
% 191.21/191.75 [6016]~P21(x60165,x60161,x60163)+E(f773(f773(x60161,x60162),f773(x60163,x60164)),f773(x60163,x60164))+~P1(f773(f63(x60165),x60164))+~P1(f773(f773(f334(x60165),x60162),x60164))
% 191.21/191.75 [6213]~P77(x62131)+~E(f773(f773(f3(x62131),x62134),x62135),f773(f773(f3(x62131),x62132),x62133))+~P1(f773(f773(f233(x62131),x62134),x62135))+P1(f773(f773(f233(x62131),x62132),x62133))
% 191.21/191.75 [6215]~P77(x62151)+~E(f773(f773(f3(x62151),x62154),x62155),f773(f773(f3(x62151),x62152),x62153))+~P1(f773(f773(f232(x62151),x62154),x62155))+P1(f773(f773(f232(x62151),x62152),x62153))
% 191.21/191.75 [7220]~E(x72202,f773(f773(f140(x72201),x72204),x72205))+P1(f773(f773(f334(f848(x72201)),x72202),f149(x72201,x72203)))+~P1(f773(f773(f334(f848(x72201)),x72205),f149(x72201,x72203)))+~P1(f773(f773(f334(x72201),x72204),x72203))
% 191.21/191.75 [7654]~E(f773(f181(f848(x76541)),x76543),f773(f181(f848(x76542)),x76544))+~E(f773(f773(f143(f854(x76541,x76542),x76542),f250(x76541,x76542)),x76545),x76544)+~E(f773(f773(f143(f854(x76541,x76542),x76541),f240(x76541,x76542)),x76545),x76543)+E(f773(f773(f167(x76541,x76542),x76543),x76544),x76545)
% 191.21/191.75 [7990]~P99(x79901)+P1(f773(f773(f233(f855(x79901,a841)),f295(x79901,x79902,x79903)),f295(x79901,x79904,x79905)))+~P1(f773(f773(f232(x79901),x79904),x79905))+P1(f773(f773(f232(x79901),x79902),x79903))
% 191.21/191.75 [8082]~P99(x80821)+P1(f773(f773(f232(f855(x80821,a841)),f295(x80821,x80822,x80823)),f295(x80821,x80824,x80825)))+~P1(f773(f773(f232(x80821),x80823),x80825))+~P1(f773(f773(f232(x80821),x80824),x80822))
% 191.21/191.75 [8200]~P100(x82001)+P1(f773(f773(f232(x82001),x82002),x82003))+P1(f773(f773(f232(x82001),x82004),x82003))+~P1(f773(f773(f232(f855(x82001,a841)),f773(f294(x82001,x82003),x82002)),f773(f294(x82001,x82004),x82005)))
% 191.21/191.75 [8201]~P100(x82011)+P1(f773(f773(f232(x82011),x82012),x82013))+P1(f773(f773(f232(x82011),x82012),x82014))+~P1(f773(f773(f232(f855(x82011,a841)),f773(f294(x82011,x82013),x82012)),f773(f294(x82011,x82015),x82014)))
% 191.21/191.75 [8441]~P99(x84411)+~P1(f773(f773(f233(f855(x84411,a841)),f295(x84411,x84414,x84412)),f295(x84411,x84415,x84413)))+P1(f773(f773(f232(x84411),x84412),x84413))+~P1(f773(f773(f232(x84411),x84414),x84412))
% 191.21/191.75 [8442]~P99(x84421)+~P1(f773(f773(f232(f855(x84421,a841)),f295(x84421,x84424,x84422)),f295(x84421,x84425,x84423)))+P1(f773(f773(f232(x84421),x84422),x84423))+~P1(f773(f773(f232(x84421),x84424),x84422))
% 191.21/191.75 [8443]~P99(x84431)+~P1(f773(f773(f233(f855(x84431,a841)),f295(x84431,x84433,x84434)),f295(x84431,x84432,x84435)))+P1(f773(f773(f232(x84431),x84432),x84433))+~P1(f773(f773(f232(x84431),x84433),x84434))
% 191.21/191.75 [8444]~P99(x84441)+~P1(f773(f773(f232(f855(x84441,a841)),f295(x84441,x84443,x84444)),f295(x84441,x84442,x84445)))+P1(f773(f773(f232(x84441),x84442),x84443))+~P1(f773(f773(f232(x84441),x84443),x84444))
% 191.21/191.75 [5903]~P21(x59032,x59035,x59033)+E(x59031,f180(f855(x59032,a841)))+~P1(f773(f63(x59032),x59031))+E(f773(x59033,f773(f773(f302(x59032),x59034),x59031)),f773(f773(x59035,x59034),f773(x59033,x59031)))
% 191.21/191.75 [6707]~E(x67071,x67072)+~E(f773(f773(f104(f855(x67073,a841)),x67074),x67075),f180(f855(x67073,a841)))+~P1(f773(f773(f334(x67073),x67072),x67075))+~P1(f773(f773(f334(x67073),x67071),x67074))
% 191.21/191.75 [6794]~P22(x67942,x67945,x67941)+~P1(f773(f63(x67942),x67944))+E(f773(x67941,f773(f773(f302(x67942),x67943),x67944)),f773(f773(f66(x67942,x67942,x67945),x67943),x67944))+P1(f773(f773(f334(x67942),x67943),x67944))
% 191.21/191.75 [6865]~P66(x68652)+~P1(f773(f63(x68651),x68655))+E(f773(f773(f8(x68651,x68652),x68653),f773(f773(f302(x68651),x68654),x68655)),f773(f773(f82(x68652),f773(x68653,x68654)),f773(f773(f8(x68651,x68652),x68653),x68655)))+P1(f773(f773(f334(x68651),x68654),x68655))
% 191.21/191.75 [6867]~P70(x68672)+~P1(f773(f63(x68671),x68675))+E(f773(f773(f11(x68671,x68672),x68673),f773(f773(f302(x68671),x68674),x68675)),f773(f773(f83(x68672),f773(x68673,x68674)),f773(f773(f11(x68671,x68672),x68673),x68675)))+P1(f773(f773(f334(x68671),x68674),x68675))
% 191.21/191.75 [7278]~P85(x72781)+~P1(f773(f63(x72784),x72785))+~P1(f773(f773(f334(x72784),x72783),x72785))+P1(f773(f773(f279(x72781),f773(x72782,x72783)),f773(f773(f11(x72784,x72781),x72782),x72785)))
% 191.21/191.75 [7391]~P22(x73912,x73915,x73911)+~P1(f773(f63(x73912),x73914))+E(f773(x73911,f773(f773(f302(x73912),x73913),x73914)),x73913)+~E(f773(f773(f3(f855(x73912,a841)),x73914),f773(f773(f302(x73912),x73913),f180(f855(x73912,a841)))),f180(f855(x73912,a841)))
% 191.21/191.75 [7704]~P1(f773(x77041,x77043))+~P1(f773(f773(f187(x77042),x77043),x77045))+~P1(f773(f773(f187(f35(x77041,x77042)),x77045),x77044))+P1(f773(f773(f187(f35(x77041,x77042)),x77043),x77044))
% 191.21/191.75 [7722]~P85(x77221)+~P1(f773(f773(f279(x77221),x77222),x77224))+~P1(f773(f773(f232(a847),x77223),x77225))+P1(f773(f773(f279(x77221),f773(f773(f242(x77221),x77222),x77223)),f773(f773(f242(x77221),x77224),x77225)))
% 191.21/191.75 [7756]~P7(x77561)+E(f773(f773(f43(x77561),f773(f773(f83(x77561),x77562),x77563)),f773(f773(f83(x77561),x77564),x77565)),f773(f773(f83(x77561),f773(f773(f43(x77561),x77562),x77564)),f773(f773(f43(x77561),x77563),x77565)))+~P1(f773(f773(f279(x77561),x77565),x77563))+~P1(f773(f773(f279(x77561),x77564),x77562))
% 191.21/191.75 [7760]~P80(x77601)+~P1(f773(f773(f233(x77601),x77603),x77605))+~P1(f773(f773(f233(x77601),x77602),x77604))+P1(f773(f773(f233(x77601),f773(f773(f82(x77601),x77602),x77603)),f773(f773(f82(x77601),x77604),x77605)))
% 191.21/191.75 [7761]~P80(x77611)+~P1(f773(f773(f232(x77611),x77612),x77614))+~P1(f773(f773(f233(x77611),x77613),x77615))+P1(f773(f773(f233(x77611),f773(f773(f82(x77611),x77612),x77613)),f773(f773(f82(x77611),x77614),x77615)))
% 191.21/191.75 [7762]~P80(x77621)+~P1(f773(f773(f232(x77621),x77623),x77625))+~P1(f773(f773(f233(x77621),x77622),x77624))+P1(f773(f773(f233(x77621),f773(f773(f82(x77621),x77622),x77623)),f773(f773(f82(x77621),x77624),x77625)))
% 191.21/191.75 [7763]~P78(x77631)+~P1(f773(f773(f232(x77631),x77633),x77635))+~P1(f773(f773(f232(x77631),x77632),x77634))+P1(f773(f773(f232(x77631),f773(f773(f82(x77631),x77632),x77633)),f773(f773(f82(x77631),x77634),x77635)))
% 191.21/191.75 [7764]~P100(x77641)+~P1(f773(f773(f232(x77641),x77643),x77645))+~P1(f773(f773(f232(x77641),x77642),x77644))+P1(f773(f773(f232(x77641),f773(f773(f236(x77641),x77642),x77643)),f773(f773(f236(x77641),x77644),x77645)))
% 191.21/191.75 [7765]~P100(x77651)+~P1(f773(f773(f232(x77651),x77653),x77655))+~P1(f773(f773(f232(x77651),x77652),x77654))+P1(f773(f773(f232(x77651),f773(f773(f179(x77651),x77652),x77653)),f773(f773(f179(x77651),x77654),x77655)))
% 191.21/191.75 [7766]~P92(x77661)+~P1(f773(f773(f232(x77661),x77663),x77665))+~P1(f773(f773(f232(x77661),x77662),x77664))+P1(f773(f773(f232(x77661),f773(f773(f103(x77661),x77662),x77663)),f773(f773(f103(x77661),x77664),x77665)))
% 191.21/191.75 [7767]~P98(x77671)+~P1(f773(f773(f232(x77671),x77673),x77675))+~P1(f773(f773(f232(x77671),x77672),x77674))+P1(f773(f773(f232(x77671),f773(f773(f104(x77671),x77672),x77673)),f773(f773(f104(x77671),x77674),x77675)))
% 191.21/191.75 [7768]~P85(x77681)+~P1(f773(f773(f279(x77681),x77683),x77685))+~P1(f773(f773(f279(x77681),x77682),x77684))+P1(f773(f773(f279(x77681),f773(f773(f83(x77681),x77682),x77683)),f773(f773(f83(x77681),x77684),x77685)))
% 191.21/191.75 [7901]~P137(x79015)+E(x79011,x79012)+E(x79013,x79014)+~E(f773(f773(f82(x79015),f773(f773(f83(x79015),x79013),x79011)),f773(f773(f83(x79015),x79014),x79012)),f773(f773(f82(x79015),f773(f773(f83(x79015),x79013),x79012)),f773(f773(f83(x79015),x79014),x79011)))
% 191.21/191.75 [8039]P31(x80391,x80392,x80393)+~P32(x80391,x80394,x80395)+~P31(x80391,x80392,f560(x80395,x80394,x80391,x80392))+~P1(f773(f773(f334(f846(x80391)),x80393),x80395))
% 191.21/191.75 [8102]~P100(x81024)+~P1(f773(f127(x81021),x81023))+P1(f773(f773(f334(x81021),x81022),f773(f158(x81021),x81023)))+P1(f773(f127(x81021),f773(f773(f138(x81021,x81024,x81025),x81022),x81023)))
% 191.21/191.75 [8246]~P66(x82461)+E(f773(f773(f82(x82461),f773(f773(f8(a847,x82461),x82462),f773(f294(a847,x82463),x82464))),f773(f773(f8(a847,x82461),x82462),f773(f294(a847,x82464),x82465))),f773(f773(f8(a847,x82461),x82462),f773(f294(a847,x82463),x82465)))+~P1(f773(f773(f232(a847),x82464),x82465))+~P1(f773(f773(f232(a847),x82463),x82464))
% 191.21/191.75 [8247]~P6(x82471)+E(f773(f773(f3(x82471),f773(f773(f8(a847,x82471),x82472),f773(f294(a847,x82473),x82474))),f773(f773(f8(a847,x82471),x82472),f773(f294(a847,x82473),x82475))),f773(f773(f8(a847,x82471),x82472),f773(f294(a847,x82475),x82474)))+~P1(f773(f773(f232(a847),x82475),x82474))+~P1(f773(f773(f232(a847),x82473),x82475))
% 191.21/191.75 [8566]~P61(x85662)+E(x85661,f2(x85662))+E(x85663,f2(x85662))+E(f773(f773(f283(x85662),f773(f773(f82(x85662),f773(f773(f83(x85662),x85664),x85661)),f773(f773(f83(x85662),x85665),x85663))),f773(f773(f83(x85662),x85663),x85661)),f773(f773(f82(x85662),f773(f773(f283(x85662),x85664),x85663)),f773(f773(f283(x85662),x85665),x85661)))
% 191.21/191.75 [8567]~P61(x85672)+E(x85671,f2(x85672))+E(x85673,f2(x85672))+E(f773(f773(f283(x85672),f773(f773(f3(x85672),f773(f773(f83(x85672),x85674),x85671)),f773(f773(f83(x85672),x85675),x85673))),f773(f773(f83(x85672),x85673),x85671)),f773(f773(f3(x85672),f773(f773(f283(x85672),x85674),x85673)),f773(f773(f283(x85672),x85675),x85671)))
% 191.21/191.75 [8576]~E(x85762,f773(x85763,x85761))+E(x85761,f523(x85762,x85763,x85764,x85765))+~P29(x85765,x85764,x85763,f239(f855(x85765,a841)))+~P1(f773(f773(f334(x85764),x85762),f773(f303(x85765,x85764,x85763),f239(f855(x85765,a841)))))
% 191.21/191.75 [8760]~P110(x87601)+~P1(f773(f773(f233(x87601),f773(f77(x87601),x87602)),x87604))+P1(f773(f773(f233(x87601),f773(f773(f83(x87601),f773(f77(x87601),x87602)),f773(f77(x87601),x87603))),f773(f773(f83(x87601),x87604),x87605)))+~P1(f773(f773(f233(x87601),f773(f77(x87601),x87603)),x87605))
% 191.21/191.75 [8774]~P32(x87741,x87745,x87744)+P31(x87741,x87742,x87743)+P1(f773(f773(f334(f846(x87741)),f560(x87744,x87745,x87741,x87742)),x87745))+~P1(f773(f773(f334(f846(x87741)),x87743),x87744))
% 191.21/191.75 [8854]~P29(x88541,x88543,x88545,x88542)+~P1(f773(f63(x88543),x88544))+P1(f773(f773(f232(a847),f773(f42(x88541),x88542)),f773(f42(x88543),x88544)))+~P1(f773(f773(f232(f855(x88543,a841)),f773(f303(x88541,x88543,x88545),x88542)),x88544))
% 191.21/191.75 [8923]~P66(x89232)+~P29(x89231,x89231,x89234,x89235)+~P1(f773(f63(x89231),x89235))+E(f773(f773(f8(x89231,x89232),f773(f75(x89231,x89232,x89231,x89233),x89234)),x89235),f773(f773(f8(x89231,x89232),x89233),f773(f303(x89231,x89231,x89234),x89235)))
% 191.21/191.75 [8924]~P70(x89242)+~P29(x89241,x89241,x89244,x89245)+~P1(f773(f63(x89241),x89245))+E(f773(f773(f11(x89241,x89242),f773(f75(x89241,x89242,x89241,x89243),x89244)),x89245),f773(f773(f11(x89241,x89242),x89243),f773(f303(x89241,x89241,x89244),x89245)))
% 191.21/191.75 [9036]~P36(x90361,x90362)+~P1(f773(f773(f334(x90361),x90363),x90364))+~P1(f773(f773(f334(x90361),x90365),x90364))+~P1(f773(f773(f334(f854(x90361,x90361)),f773(f773(f241(x90361,x90361),x90365),f694(x90362,x90361,x90364))),x90362))
% 191.21/191.75 [9069]~P29(x90692,x90693,x90695,x90691)+E(x90691,f180(f855(x90692,a841)))+E(f773(f303(x90693,x90692,f525(x90694,x90693,x90692,x90691)),x90694),x90691)+~P1(f773(f773(f232(f855(x90693,a841)),f773(f303(x90692,x90693,x90695),x90691)),x90694))
% 191.21/191.75 [9511]~P100(x95115)+~P9(x95115)+P1(f773(f773(f334(x95111),f390(x95112,x95113,x95111,x95114,x95115)),x95113))+~P1(f773(f773(f233(x95115),x95114),f773(f773(f46(x95111,x95115),x95113),x95112)))
% 191.21/191.75 [9516]~P100(x95161)+~P9(x95161)+P1(f773(f773(f233(x95161),x95162),f773(x95163,f390(x95163,x95164,x95165,x95162,x95161))))+~P1(f773(f773(f233(x95161),x95162),f773(f773(f46(x95165,x95161),x95164),x95163)))
% 191.21/191.75 [9585]~P64(x95851)+~P1(f773(f68(x95851,x95851,f83(x95851),x95852,x95853),x95855))+P1(f773(f773(f334(x95851),x95852),x95853))+P1(f773(f68(x95851,x95851,f83(x95851),x95854,f773(f773(f302(x95851),x95852),x95853)),f773(f773(f83(x95851),x95854),x95855)))
% 191.21/191.75 [9794]~P66(x97942)+~P1(f773(f63(x97941),x97945))+E(f773(f773(f8(x97941,x97942),f773(f773(f9(x97941,x97942,x97942),f773(f773(f20(x97941,x97942,f855(x97942,x97942)),f773(f773(f10(a841,f855(x97942,f855(x97942,x97942)),x97941),f98(x97942)),f773(a330,x97943))),x97944)),f2(x97942))),x97945),f2(x97942))+P1(f773(f773(f334(x97941),x97943),x97945))
% 191.21/191.75 [9795]~P70(x97952)+~P1(f773(f63(x97951),x97955))+E(f773(f773(f11(x97951,x97952),f773(f773(f9(x97951,x97952,x97952),f773(f773(f20(x97951,x97952,f855(x97952,x97952)),f773(f773(f10(a841,f855(x97952,f855(x97952,x97952)),x97951),f98(x97952)),f773(a330,x97953))),x97954)),f80(x97952))),x97955),f80(x97952))+P1(f773(f773(f334(x97951),x97953),x97955))
% 191.21/191.75 [9796]~P66(x97962)+~P1(f773(f63(x97961),x97965))+E(f773(f773(f8(x97961,x97962),f773(f773(f9(x97961,x97962,x97962),f773(f773(f20(x97961,x97962,f855(x97962,x97962)),f773(f773(f10(a841,f855(x97962,f855(x97962,x97962)),x97961),f98(x97962)),f773(a330,x97963))),x97964)),f2(x97962))),x97965),f773(x97964,x97963))+~P1(f773(f773(f334(x97961),x97963),x97965))
% 191.21/191.75 [9797]~P70(x97972)+~P1(f773(f63(x97971),x97975))+E(f773(f773(f11(x97971,x97972),f773(f773(f9(x97971,x97972,x97972),f773(f773(f20(x97971,x97972,f855(x97972,x97972)),f773(f773(f10(a841,f855(x97972,f855(x97972,x97972)),x97971),f98(x97972)),f773(a330,x97973))),x97974)),f80(x97972))),x97975),f773(x97974,x97973))+~P1(f773(f773(f334(x97971),x97973),x97975))
% 191.21/191.75 [9858]~P66(x98582)+~P1(f773(f63(x98581),x98585))+E(f773(f773(f8(x98581,x98582),f773(f773(f9(x98581,x98582,x98582),f773(f773(f20(x98581,x98582,f855(x98582,x98582)),f773(f773(f10(a841,f855(x98582,f855(x98582,x98582)),x98581),f98(x98582)),f773(f773(f9(x98581,x98581,a841),a330),x98583))),x98584)),f2(x98582))),x98585),f2(x98582))+P1(f773(f773(f334(x98581),x98583),x98585))
% 191.21/191.75 [9859]~P70(x98592)+~P1(f773(f63(x98591),x98595))+E(f773(f773(f11(x98591,x98592),f773(f773(f9(x98591,x98592,x98592),f773(f773(f20(x98591,x98592,f855(x98592,x98592)),f773(f773(f10(a841,f855(x98592,f855(x98592,x98592)),x98591),f98(x98592)),f773(f773(f9(x98591,x98591,a841),a330),x98593))),x98594)),f80(x98592))),x98595),f80(x98592))+P1(f773(f773(f334(x98591),x98593),x98595))
% 191.21/191.75 [9861]~P66(x98612)+~P1(f773(f63(x98611),x98615))+E(f773(f773(f8(x98611,x98612),f773(f773(f9(x98611,x98612,x98612),f773(f773(f20(x98611,x98612,f855(x98612,x98612)),f773(f773(f10(a841,f855(x98612,f855(x98612,x98612)),x98611),f98(x98612)),f773(f773(f9(x98611,x98611,a841),a330),x98613))),x98614)),f2(x98612))),x98615),f773(x98614,x98613))+~P1(f773(f773(f334(x98611),x98613),x98615))
% 191.21/191.75 [9862]~P70(x98622)+~P1(f773(f63(x98621),x98625))+E(f773(f773(f11(x98621,x98622),f773(f773(f9(x98621,x98622,x98622),f773(f773(f20(x98621,x98622,f855(x98622,x98622)),f773(f773(f10(a841,f855(x98622,f855(x98622,x98622)),x98621),f98(x98622)),f773(f773(f9(x98621,x98621,a841),a330),x98623))),x98624)),f80(x98622))),x98625),f773(x98624,x98623))+~P1(f773(f773(f334(x98621),x98623),x98625))
% 191.21/191.75 [7759]~P6(x77592)+~P1(f773(f63(x77591),x77594))+E(f773(f773(f8(x77591,x77592),x77593),f773(f773(f3(f855(x77591,a841)),x77594),f773(f773(f302(x77591),x77595),f180(f855(x77591,a841))))),f773(f773(f8(x77591,x77592),x77593),x77594))+P1(f773(f773(f334(x77591),x77595),x77594))
% 191.21/191.75 [8252]~P121(x82522)+~P1(f773(f63(x82521),x82524))+E(f773(f773(f8(x82521,x82522),x82523),f773(f773(f3(f855(x82521,a841)),x82524),f773(f773(f302(x82521),x82525),f180(f855(x82521,a841))))),f773(f773(f3(x82522),f773(f773(f8(x82521,x82522),x82523),x82524)),f773(x82523,x82525)))+~P1(f773(f773(f334(x82521),x82525),x82524))
% 191.21/191.75 [8253]~P6(x82532)+~P1(f773(f63(x82531),x82534))+E(f773(f773(f8(x82531,x82532),x82533),f773(f773(f3(f855(x82531,a841)),x82534),f773(f773(f302(x82531),x82535),f180(f855(x82531,a841))))),f773(f773(f3(x82532),f773(f773(f8(x82531,x82532),x82533),x82534)),f773(x82533,x82535)))+~P1(f773(f773(f334(x82531),x82535),x82534))
% 191.21/191.75 [8264]~P85(x82641)+~P1(f773(f773(f232(a847),x82643),x82645))+~P1(f773(f773(f279(x82641),f773(f773(f242(x82641),x82642),x82645)),x82644))+P1(f773(f773(f279(x82641),f773(f773(f242(x82641),x82642),x82643)),x82644))
% 191.21/191.75 [8281]~P6(x82811)+~P1(f773(f63(x82812),x82814))+E(f773(f773(f3(x82811),f773(f773(f8(x82812,x82811),x82813),x82814)),f773(f773(f8(x82812,x82811),x82813),x82815)),f773(f773(f8(x82812,x82811),x82813),f773(f773(f3(f855(x82812,a841)),x82814),x82815)))+~P1(f773(f773(f232(f855(x82812,a841)),x82815),x82814))
% 191.21/191.75 [8302]P1(f773(f63(x83021),f773(x83022,x83023)))+~P1(f773(f63(x83024),x83025))+~P1(f773(f773(f334(x83024),x83023),x83025))+~P1(f773(f63(x83021),f773(f773(f46(x83024,f855(x83021,a841)),x83025),x83022)))
% 191.21/191.75 [8725]~P12(x87251,x87255,x87254)+~E(f773(f277(x87251,x87251,x87254),f773(f773(f302(x87251),x87252),f180(f855(x87251,a841)))),f773(f277(x87251,x87251,x87254),f773(f773(f302(x87251),x87253),f180(f855(x87251,a841)))))+~P1(f773(f773(f334(x87251),x87253),x87255))+P1(f773(f773(f334(f854(x87251,x87251)),f773(f773(f241(x87251,x87251),x87252),x87253)),x87254))
% 191.21/191.75 [8996]~P1(f773(x89961,x89965))+P1(f773(x89961,f381(x89961,x89962,x89963,x89964)))+P1(f773(x89961,f379(x89961,x89962,x89963,x89964)))+~P1(f773(f773(f334(x89964),x89965),f773(f773(f103(f855(x89964,a841)),x89963),x89962)))
% 191.21/191.75 [9157]~P1(f773(x91571,x91575))+P1(f773(x91571,f379(x91571,x91572,x91573,x91574)))+P1(f773(f773(f334(x91574),f381(x91571,x91572,x91573,x91574)),x91572))+~P1(f773(f773(f334(x91574),x91575),f773(f773(f103(f855(x91574,a841)),x91573),x91572)))
% 191.21/191.75 [9158]~P1(f773(x91581,x91585))+P1(f773(x91581,f381(x91581,x91582,x91583,x91584)))+P1(f773(f773(f334(x91584),f379(x91581,x91582,x91583,x91584)),x91583))+~P1(f773(f773(f334(x91584),x91585),f773(f773(f103(f855(x91584,a841)),x91583),x91582)))
% 191.21/191.75 [9162]P1(f773(x91621,x91622))+~P1(f773(x91621,f385(x91621,x91623,x91624,x91625)))+~P1(f773(x91621,f384(x91621,x91623,x91624,x91625)))+~P1(f773(f773(f334(x91625),x91622),f773(f773(f103(f855(x91625,a841)),x91624),x91623)))
% 191.21/191.75 [9195]E(x91951,x91952)+~P1(f773(f773(f334(f854(x91953,x91953)),f773(f773(f241(x91953,x91953),x91951),x91952)),f300(x91953,x91955)))+P1(f773(f773(f334(x91953),x91951),x91954))+~P1(f773(f773(f232(f855(f854(x91953,x91953),a841)),x91955),f773(f773(f248(x91953,x91953),x91954),f773(f18(f855(x91953,a841),x91953),x91954))))
% 191.21/191.75 [9212]P1(f773(x92121,x92122))+~P1(f773(x92121,f384(x92121,x92124,x92125,x92123)))+P1(f773(f773(f334(x92123),f385(x92121,x92124,x92125,x92123)),x92124))+~P1(f773(f773(f334(x92123),x92122),f773(f773(f103(f855(x92123,a841)),x92125),x92124)))
% 191.21/191.75 [9213]P1(f773(x92131,x92132))+~P1(f773(x92131,f385(x92131,x92134,x92135,x92133)))+P1(f773(f773(f334(x92133),f384(x92131,x92134,x92135,x92133)),x92135))+~P1(f773(f773(f334(x92133),x92132),f773(f773(f103(f855(x92133,a841)),x92135),x92134)))
% 191.21/191.75 [9275]P1(f773(x92751,x92752))+P1(f773(f773(f334(x92753),f385(x92751,x92754,x92755,x92753)),x92754))+P1(f773(f773(f334(x92753),f384(x92751,x92754,x92755,x92753)),x92755))+~P1(f773(f773(f334(x92753),x92752),f773(f773(f103(f855(x92753,a841)),x92755),x92754)))
% 191.21/191.75 [9277]~P1(f773(x92772,x92775))+P1(f773(f773(f334(x92771),f381(x92772,x92773,x92774,x92771)),x92773))+P1(f773(f773(f334(x92771),f379(x92772,x92773,x92774,x92771)),x92774))+~P1(f773(f773(f334(x92771),x92775),f773(f773(f103(f855(x92771,a841)),x92774),x92773)))
% 191.21/191.75 [9424]~P12(x94241,x94245,x94244)+~P1(f773(f773(f334(x94241),x94243),x94245))+P1(f773(f773(f334(f854(x94241,x94241)),f773(f773(f241(x94241,x94241),x94242),x94243)),x94244))+~P1(f773(f773(f232(f855(x94241,a841)),f773(f277(x94241,x94241,x94244),f773(f773(f302(x94241),x94243),f180(f855(x94241,a841))))),f773(f277(x94241,x94241,x94244),f773(f773(f302(x94241),x94242),f180(f855(x94241,a841))))))
% 191.21/191.75 [9540]~P100(x95405)+~P9(x95405)+P1(f773(f773(f334(x95401),f661(x95402,x95403,x95404,x95401,x95405)),x95404))+~P1(f773(f773(f233(x95405),f773(f773(f47(x95401,x95405),x95404),x95403)),x95402))
% 191.21/191.75 [9572]~P67(x95725)+~P78(x95725)+P1(f773(f773(f334(x95721),f752(x95722,x95723,x95724,x95721,x95725)),f773(f158(x95721),x95724)))+P1(f773(f773(f232(x95725),f773(f155(x95725),f773(f773(f143(x95721,x95725),x95723),x95724))),f773(f155(x95725),f773(f773(f143(x95721,x95725),x95722),x95724))))
% 191.21/191.75 [9667]~P100(x96671)+~P9(x96671)+P1(f773(f773(f233(x96671),f773(x96672,f661(x96673,x96672,x96674,x96675,x96671))),x96673))+~P1(f773(f773(f233(x96671),f773(f773(f47(x96675,x96671),x96674),x96672)),x96673))
% 191.21/191.75 [9811]~P67(x98111)+~P78(x98111)+~P1(f773(f773(f232(x98111),f773(x98113,f752(x98115,x98113,x98114,x98112,x98111))),f773(x98115,f752(x98115,x98113,x98114,x98112,x98111))))+P1(f773(f773(f232(x98111),f773(f155(x98111),f773(f773(f143(x98112,x98111),x98113),x98114))),f773(f155(x98111),f773(f773(f143(x98112,x98111),x98115),x98114))))
% 191.21/191.75 [8584]~P66(x85841)+~P1(f773(f63(x85844),x85845))+~P1(f773(f773(f334(x85844),x85843),x85845))+E(f773(f773(f82(x85841),f773(x85842,x85843)),f773(f773(f8(x85844,x85841),x85842),f773(f773(f3(f855(x85844,a841)),x85845),f773(f773(f302(x85844),x85843),f180(f855(x85844,a841)))))),f773(f773(f8(x85844,x85841),x85842),x85845))
% 191.21/191.75 [8585]~P70(x85851)+~P1(f773(f63(x85854),x85855))+~P1(f773(f773(f334(x85854),x85853),x85855))+E(f773(f773(f83(x85851),f773(x85852,x85853)),f773(f773(f11(x85854,x85851),x85852),f773(f773(f3(f855(x85854,a841)),x85855),f773(f773(f302(x85854),x85853),f180(f855(x85854,a841)))))),f773(f773(f11(x85854,x85851),x85852),x85855))
% 191.21/191.75 [8638]~P22(x86381,x86384,x86385)+~P1(f773(f63(x86381),x86382))+E(f773(f773(f3(f855(x86381,a841)),x86382),f773(f773(f302(x86381),x86383),f180(f855(x86381,a841)))),f180(f855(x86381,a841)))+E(f773(f773(x86384,x86383),f773(x86385,f773(f773(f3(f855(x86381,a841)),x86382),f773(f773(f302(x86381),x86383),f180(f855(x86381,a841)))))),f773(x86385,f773(f773(f302(x86381),x86383),x86382)))
% 191.21/191.75 [8971]~P66(x89711)+~P1(f773(f63(x89712),x89715))+~P1(f773(f63(x89712),x89714))+E(f773(f773(f82(x89711),f773(f773(f8(x89712,x89711),x89713),f773(f773(f103(f855(x89712,a841)),x89714),x89715))),f773(f773(f8(x89712,x89711),x89713),f773(f773(f104(f855(x89712,a841)),x89714),x89715))),f773(f773(f82(x89711),f773(f773(f8(x89712,x89711),x89713),x89714)),f773(f773(f8(x89712,x89711),x89713),x89715)))
% 191.21/191.75 [8973]~P70(x89731)+~P1(f773(f63(x89732),x89735))+~P1(f773(f63(x89732),x89734))+E(f773(f773(f83(x89731),f773(f773(f11(x89732,x89731),x89733),f773(f773(f103(f855(x89732,a841)),x89734),x89735))),f773(f773(f11(x89732,x89731),x89733),f773(f773(f104(f855(x89732,a841)),x89734),x89735))),f773(f773(f83(x89731),f773(f773(f11(x89732,x89731),x89733),x89734)),f773(f773(f11(x89732,x89731),x89733),x89735)))
% 191.21/191.75 [9107]~P6(x91071)+~P1(f773(f63(x91072),x91075))+~P1(f773(f63(x91072),x91074))+E(f773(f773(f3(x91071),f773(f773(f82(x91071),f773(f773(f8(x91072,x91071),x91073),x91074)),f773(f773(f8(x91072,x91071),x91073),x91075))),f773(f773(f8(x91072,x91071),x91073),f773(f773(f104(f855(x91072,a841)),x91074),x91075))),f773(f773(f8(x91072,x91071),x91073),f773(f773(f103(f855(x91072,a841)),x91074),x91075)))
% 191.21/191.75 [9289]~P29(x92891,x92892,x92893,x92895)+~P29(x92891,x92892,x92893,x92894)+P29(x92891,x92892,x92893,f773(f773(f103(f855(x92891,a841)),x92894),x92895))+~E(f773(f773(f104(f855(x92892,a841)),f773(f303(x92891,x92892,x92893),f773(f773(f3(f855(x92891,a841)),x92894),x92895))),f773(f303(x92891,x92892,x92893),f773(f773(f3(f855(x92891,a841)),x92895),x92894))),f180(f855(x92892,a841)))
% 191.21/191.75 [9396]E(x93961,f2(a1))+~P1(f773(f773(f233(a1),f2(a1)),x93963))+~P1(f773(f56(x93962,x93961),f773(f773(f241(a1,a1),x93964),x93965)))+P1(f773(f56(x93962,f773(f773(f83(a1),x93961),x93963)),f773(f773(f241(a1,a1),f773(f773(f43(a1),x93964),x93963)),f773(f773(f82(a1),f773(f773(f83(a1),x93961),f52(a1,x93964,x93963))),x93965))))
% 191.21/191.75 [9404]~P1(f773(f773(f233(a847),f2(a847)),x94043))+~P1(f773(f773(f233(a847),f2(a847)),x94042))+~P1(f773(f55(x94041,x94042),f773(f773(f241(a847,a847),x94044),x94045)))+P1(f773(f55(x94041,f773(f773(f83(a847),x94042),x94043)),f773(f773(f241(a847,a847),f773(f773(f43(a847),x94044),x94043)),f773(f773(f82(a847),f773(f773(f83(a847),x94042),f52(a847,x94044,x94043))),x94045))))
% 191.21/191.75 [9454]E(f773(f773(f82(a1),f363(x94541,x94542,x94543,x94544,x94545)),f364(x94541,x94542,x94543,x94544,x94545)),x94545)+~P1(f773(f773(f279(a1),x94544),x94543))+~P1(f773(f773(f279(a1),x94544),f773(f773(f82(a1),x94545),x94541)))+P1(f773(f773(f279(a1),x94544),f773(f773(f82(a1),f773(f773(f3(a1),x94545),x94543)),x94541)))
% 191.21/191.75 [9455]E(f773(f773(f3(a1),f365(x94551,x94552,x94553,x94554,x94555)),f366(x94551,x94552,x94553,x94554,x94555)),x94555)+~P1(f773(f773(f279(a1),x94554),x94553))+~P1(f773(f773(f279(a1),x94554),f773(f773(f82(a1),x94555),x94551)))+P1(f773(f773(f279(a1),x94554),f773(f773(f82(a1),f773(f773(f82(a1),x94555),x94553)),x94551)))
% 191.21/191.75 [9456]~P70(x94561)+~P1(f773(f63(x94562),x94565))+~P1(f773(f63(x94562),x94564))+E(f773(f773(f83(x94561),f773(f773(f773(f67(x94561,x94562,f83(x94561)),x94563),f80(x94561)),f773(f773(f103(f855(x94562,a841)),x94564),x94565))),f773(f773(f773(f67(x94561,x94562,f83(x94561)),x94563),f80(x94561)),f773(f773(f104(f855(x94562,a841)),x94564),x94565))),f773(f773(f83(x94561),f773(f773(f773(f67(x94561,x94562,f83(x94561)),x94563),f80(x94561)),x94564)),f773(f773(f773(f67(x94561,x94562,f83(x94561)),x94563),f80(x94561)),x94565)))
% 191.21/191.75 [9458]~E(f773(f773(f159(x94581),x94585),x94582),f773(f773(f159(x94581),x94585),x94583))+P1(f773(f773(f334(f854(f848(x94581),f848(x94581))),f773(f773(f241(f848(x94581),f848(x94581)),x94582),x94583)),f137(x94581,x94584)))+~P1(f773(f773(f233(a847),x94585),f773(f773(f236(a847),f773(f181(f848(x94581)),x94582)),f773(f181(f848(x94581)),x94583))))+~P1(f773(f773(f334(f854(x94581,x94581)),f773(f773(f241(x94581,x94581),f773(f773(f153(x94581),x94582),x94585)),f773(f773(f153(x94581),x94583),x94585))),x94584))
% 191.21/191.75 [9467]E(f773(f773(f82(a1),f367(x94671,x94672,x94673,x94674,x94675)),f368(x94671,x94672,x94673,x94674,x94675)),x94675)+~P1(f773(f773(f279(a1),x94674),x94673))+P1(f773(f773(f279(a1),x94674),f773(f773(f82(a1),x94675),x94671)))+~P1(f773(f773(f279(a1),x94674),f773(f773(f82(a1),f773(f773(f3(a1),x94675),x94673)),x94671)))
% 191.21/191.75 [9468]E(f773(f773(f3(a1),f360(x94681,x94682,x94683,x94684,x94685)),f361(x94681,x94682,x94683,x94684,x94685)),x94685)+~P1(f773(f773(f279(a1),x94684),x94683))+P1(f773(f773(f279(a1),x94684),f773(f773(f82(a1),x94685),x94681)))+~P1(f773(f773(f279(a1),x94684),f773(f773(f82(a1),f773(f773(f82(a1),x94685),x94683)),x94681)))
% 191.21/191.75 [9549]~P1(f773(f773(f279(a1),x95494),x95493))+P1(f773(f773(f334(a1),f365(x95491,x95492,x95493,x95494,x95495)),x95492))+~P1(f773(f773(f279(a1),x95494),f773(f773(f82(a1),x95495),x95491)))+P1(f773(f773(f279(a1),x95494),f773(f773(f82(a1),f773(f773(f82(a1),x95495),x95493)),x95491)))
% 191.21/191.75 [9550]~P1(f773(f773(f279(a1),x95504),x95503))+P1(f773(f773(f334(a1),f363(x95501,x95502,x95503,x95504,x95505)),x95502))+~P1(f773(f773(f279(a1),x95504),f773(f773(f82(a1),x95505),x95501)))+P1(f773(f773(f279(a1),x95504),f773(f773(f82(a1),f773(f773(f3(a1),x95505),x95503)),x95501)))
% 191.21/191.75 [9557]~P1(f773(f773(f279(a1),x95574),x95573))+P1(f773(f773(f334(a1),f366(x95571,x95572,x95573,x95574,x95575)),f295(a1,f80(a1),x95573)))+~P1(f773(f773(f279(a1),x95574),f773(f773(f82(a1),x95575),x95571)))+P1(f773(f773(f279(a1),x95574),f773(f773(f82(a1),f773(f773(f82(a1),x95575),x95573)),x95571)))
% 191.21/191.75 [9558]~P1(f773(f773(f279(a1),x95584),x95583))+P1(f773(f773(f334(a1),f364(x95581,x95582,x95583,x95584,x95585)),f295(a1,f80(a1),x95583)))+~P1(f773(f773(f279(a1),x95584),f773(f773(f82(a1),x95585),x95581)))+P1(f773(f773(f279(a1),x95584),f773(f773(f82(a1),f773(f773(f3(a1),x95585),x95583)),x95581)))
% 191.21/191.75 [9559]~P2(x95595)+~P78(x95595)+P1(f773(f773(f334(x95591),f440(x95592,x95593,x95594,x95591,x95595)),x95594))+P1(f773(f773(f232(x95595),f773(f773(f8(x95591,x95595),x95593),x95594)),f773(f773(f83(x95595),f773(f102(x95595),f773(f42(x95591),x95594))),x95592)))
% 191.21/191.75 [9560]~P1(f773(f773(f279(a1),x95604),x95603))+P1(f773(f773(f334(a1),f360(x95601,x95602,x95603,x95604,x95605)),x95602))+P1(f773(f773(f279(a1),x95604),f773(f773(f82(a1),x95605),x95601)))+~P1(f773(f773(f279(a1),x95604),f773(f773(f82(a1),f773(f773(f82(a1),x95605),x95603)),x95601)))
% 191.21/191.75 [9561]~P1(f773(f773(f279(a1),x95614),x95613))+P1(f773(f773(f334(a1),f367(x95611,x95612,x95613,x95614,x95615)),x95612))+P1(f773(f773(f279(a1),x95614),f773(f773(f82(a1),x95615),x95611)))+~P1(f773(f773(f279(a1),x95614),f773(f773(f82(a1),f773(f773(f3(a1),x95615),x95613)),x95611)))
% 191.21/191.75 [9562]~P1(f773(f773(f279(a1),x95621),x95625))+P1(f773(f773(f334(a1),f361(x95623,x95624,x95625,x95621,x95622)),f295(a1,f80(a1),x95625)))+P1(f773(f773(f279(a1),x95621),f773(f773(f82(a1),x95622),x95623)))+~P1(f773(f773(f279(a1),x95621),f773(f773(f82(a1),f773(f773(f82(a1),x95622),x95625)),x95623)))
% 191.21/191.75 [9563]~P1(f773(f773(f279(a1),x95631),x95635))+P1(f773(f773(f334(a1),f368(x95633,x95634,x95635,x95631,x95632)),f295(a1,f80(a1),x95635)))+P1(f773(f773(f279(a1),x95631),f773(f773(f82(a1),x95632),x95633)))+~P1(f773(f773(f279(a1),x95631),f773(f773(f82(a1),f773(f773(f3(a1),x95632),x95635)),x95633)))
% 191.21/191.75 [9727]~P2(x97271)+~P78(x97271)+~P1(f773(f773(f232(x97271),f773(x97273,f440(x97275,x97273,x97274,x97272,x97271))),x97275))+P1(f773(f773(f232(x97271),f773(f773(f8(x97272,x97271),x97273),x97274)),f773(f773(f83(x97271),f773(f102(x97271),f773(f42(x97272),x97274))),x97275)))
% 191.21/191.75 [8610]E(f773(f773(f125(x86101),x86102),x86103),f773(f773(f125(x86101),x86104),x86105))+~E(f773(f773(f159(x86101),f773(f181(f848(x86101)),x86102)),x86104),x86102)+~E(f773(f773(f125(x86101),f773(f773(f128(x86101),f773(f181(f848(x86101)),x86102)),x86104)),x86105),x86103)+P1(f773(f773(f232(a847),f773(f181(f848(x86101)),x86104)),f773(f181(f848(x86101)),x86102)))
% 191.21/191.75 [8723]E(f773(f773(f125(x87231),x87232),x87233),f773(f773(f125(x87231),x87234),x87235))+~E(f773(f773(f159(x87231),f773(f181(f848(x87231)),x87232)),x87234),x87232)+~E(x87233,f773(f773(f125(x87231),f773(f773(f128(x87231),f773(f181(f848(x87231)),x87232)),x87234)),x87235))+~P1(f773(f773(f232(a847),f773(f181(f848(x87231)),x87232)),f773(f181(f848(x87231)),x87234)))
% 191.21/191.75 [9879]~P1(f773(x98795,x98794))+~P1(f773(f63(x98792),f773(f256(x98792),x98795)))+P1(f773(f63(x98791),f773(f256(x98791),f773(f773(f9(x98791,x98792,a841),x98793),x98794))))+~P1(f773(f63(x98791),f773(f256(x98791),f773(f773(f10(f855(x98792,a841),a841,x98791),f89(x98792)),f773(f773(f10(f855(x98792,a841),f855(x98792,a841),x98791),f773(f20(x98792,a841,a841),f773(f773(f10(a841,f855(a841,a841),x98792),a331),x98795))),x98793)))))
% 191.21/191.75 [7905]~P39(x79052,x79053,x79054,x79056)+~P39(f35(x79051,x79052),x79056,x79054,x79055)+P39(f35(x79051,x79052),x79053,x79054,x79055)+~P1(f773(x79051,x79053))
% 191.21/191.75 [8417]~P23(x84175,x84171,x84176,x84172)+E(f773(f75(x84171,x84171,x84171,f773(x84172,x84173)),f773(x84172,x84174)),f773(f75(x84171,x84171,x84171,f773(x84172,x84174)),f773(x84172,x84173)))+~P1(f773(f63(x84175),x84174))+~P1(f773(f63(x84175),x84173))
% 191.21/191.75 [7815]~P29(x78151,x78152,x78154,x78153)+~E(f773(x78154,x78156),x78155)+E(f773(f79(x78151,x78152,x78153,x78154),x78155),x78156)+~P1(f773(f773(f334(x78151),x78156),x78153))
% 191.21/191.75 [8008]~P24(x80086,x80081,x80084,x80082)+E(f773(f75(x80081,x80081,x80081,f773(x80082,x80083)),f773(x80084,x80085)),f773(x80082,x80083))+~P1(f773(f63(x80086),x80083))+~P1(f773(f773(f334(x80086),x80085),x80083))
% 191.21/191.75 [9145]~P23(x91453,x91451,x91456,x91452)+E(f773(f75(x91451,x91451,x91451,f773(x91452,f773(f773(f3(f855(x91453,a841)),x91454),f773(f773(f302(x91453),x91455),f180(f855(x91453,a841)))))),f773(x91456,x91455)),f773(x91452,x91454))+~P1(f773(f63(x91453),x91454))+~P1(f773(f773(f334(x91453),x91455),x91454))
% 191.21/191.75 [6872]~P7(x68721)+~E(f52(x68721,x68723,x68724),f52(x68721,x68726,x68724))+~E(f52(x68721,x68722,x68724),f52(x68721,x68725,x68724))+E(f52(x68721,f773(f773(f82(x68721),x68722),x68723),x68724),f52(x68721,f773(f773(f82(x68721),x68725),x68726),x68724))
% 191.21/191.75 [6873]~P7(x68731)+~E(f52(x68731,x68733,x68734),f52(x68731,x68736,x68734))+~E(f52(x68731,x68732,x68734),f52(x68731,x68735,x68734))+E(f52(x68731,f773(f773(f83(x68731),x68732),x68733),x68734),f52(x68731,f773(f773(f83(x68731),x68735),x68736),x68734))
% 191.21/191.75 [6874]~P8(x68741)+~E(f52(x68741,x68743,x68744),f52(x68741,x68746,x68744))+~E(f52(x68741,x68742,x68744),f52(x68741,x68745,x68744))+E(f52(x68741,f773(f773(f3(x68741),x68742),x68743),x68744),f52(x68741,f773(f773(f3(x68741),x68745),x68746),x68744))
% 191.21/191.75 [7706]~P20(x77061,x77062,x77063)+~P1(f773(f63(x77061),x77066))+E(f773(f773(f66(x77061,x77062,x77063),x77064),f773(f773(f302(x77061),x77065),x77066)),f773(f773(f66(x77061,x77062,x77063),f773(f773(x77063,x77065),x77064)),x77066))+P1(f773(f773(f334(x77061),x77065),x77066))
% 191.21/191.75 [7773]~P9(x77731)+P1(f773(f773(f232(x77731),x77732),f773(x77733,x77734)))+~P1(f773(f773(f334(x77735),x77734),x77736))+~P1(f773(f773(f232(x77731),x77732),f773(f773(f47(x77735,x77731),x77736),x77733)))
% 191.21/191.75 [7933]~P20(x79331,x79332,x79333)+~P1(f773(f63(x79331),x79336))+E(f773(f773(f66(x79331,x79332,x79333),x79334),f773(f773(f302(x79331),x79335),x79336)),f773(f773(x79333,x79335),f773(f773(f66(x79331,x79332,x79333),x79334),x79336)))+P1(f773(f773(f334(x79331),x79335),x79336))
% 191.21/191.75 [8024]~P100(x80243)+~P1(f773(x80242,x80245))+~P18(x80243,f773(f773(f143(x80241,x80243),x80244),x80246))+E(f773(f126(x80241,x80242),f773(f773(f138(x80241,x80243,x80244),x80245),x80246)),f773(f773(f138(x80241,x80243,x80244),x80245),f773(f126(x80241,x80242),x80246)))
% 191.21/191.75 [8047]E(x80471,x80472)+E(x80473,f2(a1))+~P1(f773(f56(x80474,x80473),f773(f773(f241(a1,a1),x80475),x80472)))+~P1(f773(f56(x80474,x80473),f773(f773(f241(a1,a1),x80476),x80471)))
% 191.21/191.75 [8048]E(x80481,x80482)+E(x80483,f2(a1))+~P1(f773(f56(x80484,x80483),f773(f773(f241(a1,a1),x80482),x80485)))+~P1(f773(f56(x80484,x80483),f773(f773(f241(a1,a1),x80481),x80486)))
% 191.21/191.75 [8070]~P23(x80702,x80705,x80706,x80701)+~P1(f773(f63(x80702),x80704))+E(f773(x80701,f773(f773(f302(x80702),x80703),x80704)),f773(f75(x80705,x80705,x80705,f773(x80701,x80704)),f773(x80706,x80703)))+P1(f773(f773(f334(x80702),x80703),x80704))
% 191.21/191.75 [8284]~P24(x82845,x82841,x82846,x82842)+E(f773(f75(x82841,x82841,x82841,f773(x82842,x82843)),f773(x82842,x82844)),f773(x82842,x82843))+~P1(f773(f63(x82845),x82843))+~P1(f773(f773(f232(f855(x82845,a841)),x82844),x82843))
% 191.21/191.75 [9335]~P29(x93351,x93352,x93354,x93353)+~P1(f773(f773(f334(x93352),x93355),f773(f303(x93351,x93352,x93354),x93353)))+P1(f773(f773(f334(x93351),f773(f79(x93351,x93352,x93353,x93354),x93355)),x93356))+~P1(f773(f773(f232(f855(x93351,a841)),x93353),x93356))
% 191.21/191.75 [9678]~P66(x96782)+~E(f495(x96781,x96783,x96785,x96786,x96784,x96782),f496(x96781,x96783,x96785,x96786,x96784,x96782))+~P1(f773(f63(x96784),x96786))+E(f773(f773(f8(x96781,x96782),x96783),f773(f303(x96784,x96781,x96785),x96786)),f773(f773(f8(x96784,x96782),f773(f75(x96781,x96782,x96784,x96783),x96785)),x96786))
% 191.21/191.75 [9707]~P66(x97076)+E(f773(x97071,f495(x97072,x97073,x97071,x97074,x97075,x97076)),f773(x97071,f496(x97072,x97073,x97071,x97074,x97075,x97076)))+E(f773(f773(f8(x97072,x97076),x97073),f773(f303(x97075,x97072,x97071),x97074)),f773(f773(f8(x97075,x97076),f773(f75(x97072,x97076,x97075,x97073),x97071)),x97074))+~P1(f773(f63(x97075),x97074))
% 191.21/191.75 [9761]~P66(x97612)+~E(f773(x97613,f773(x97615,f496(x97611,x97613,x97615,x97616,x97614,x97612))),f2(x97612))+~P1(f773(f63(x97614),x97616))+E(f773(f773(f8(x97611,x97612),x97613),f773(f303(x97614,x97611,x97615),x97616)),f773(f773(f8(x97614,x97612),f773(f75(x97611,x97612,x97614,x97613),x97615)),x97616))
% 191.21/191.75 [9821]~P66(x98212)+~P1(f773(f63(x98214),x98216))+E(f773(f773(f8(x98211,x98212),x98213),f773(f303(x98214,x98211,x98215),x98216)),f773(f773(f8(x98214,x98212),f773(f75(x98211,x98212,x98214,x98213),x98215)),x98216))+P1(f773(f773(f334(x98214),f496(x98211,x98213,x98215,x98216,x98214,x98212)),x98216))
% 191.21/191.75 [9822]~P66(x98222)+~P1(f773(f63(x98224),x98226))+E(f773(f773(f8(x98221,x98222),x98223),f773(f303(x98224,x98221,x98225),x98226)),f773(f773(f8(x98224,x98222),f773(f75(x98221,x98222,x98224,x98223),x98225)),x98226))+P1(f773(f773(f334(x98224),f495(x98221,x98223,x98225,x98226,x98224,x98222)),x98226))
% 191.21/191.75 [9944]~P70(x99441)+~P1(f773(f63(x99442),x99446))+E(f773(f773(f773(f67(x99441,x99442,f83(x99441)),f773(f773(f20(x99442,f855(x99443,a841),x99441),f773(f773(f9(x99442,x99441,f855(f855(x99443,a841),x99441)),f773(f773(f10(f855(x99443,x99441),f855(x99441,f855(f855(x99443,a841),x99441)),x99442),f67(x99441,x99443,f83(x99441))),x99444)),f80(x99441))),x99445)),f80(x99441)),x99446),f773(f773(f773(f67(x99441,f854(x99442,x99443),f83(x99441)),f773(f251(x99442,x99443,x99441),x99444)),f80(x99441)),f773(f773(f248(x99442,x99443),x99446),x99445)))+P1(f773(f773(f334(x99442),f564(x99444,x99445,x99443,x99446,x99442,x99441)),x99446))
% 191.21/191.75 [9960]~P70(x99601)+~P1(f773(f63(x99602),x99606))+E(f773(f773(f773(f67(x99601,x99602,f83(x99601)),f773(f773(f20(x99602,f855(x99603,a841),x99601),f773(f773(f9(x99602,x99601,f855(f855(x99603,a841),x99601)),f773(f773(f10(f855(x99603,x99601),f855(x99601,f855(f855(x99603,a841),x99601)),x99602),f67(x99601,x99603,f83(x99601))),x99604)),f80(x99601))),x99605)),f80(x99601)),x99606),f773(f773(f773(f67(x99601,f854(x99602,x99603),f83(x99601)),f773(f251(x99602,x99603,x99601),x99604)),f80(x99601)),f773(f773(f248(x99602,x99603),x99606),x99605)))+~P1(f773(f63(x99603),f773(x99605,f564(x99604,x99605,x99603,x99606,x99602,x99601))))
% 191.21/191.75 [8199]~P24(x81992,x81995,x81996,x81991)+~P1(f773(f63(x81992),x81994))+~P1(f773(f63(x81992),x81993))+E(f773(x81991,f773(f773(f103(f855(x81992,a841)),x81993),x81994)),f773(f75(x81995,x81995,x81995,f773(x81991,x81993)),f773(x81991,x81994)))
% 191.21/191.75 [8419]~P9(x84191)+P1(f773(f773(f232(x84191),f773(x84192,x84193)),x84194))+~P1(f773(f773(f334(x84195),x84193),x84196))+~P1(f773(f773(f232(x84191),f773(f773(f46(x84195,x84191),x84196),x84192)),x84194))
% 191.21/191.75 [8793]~P29(x87932,x87931,x87933,x87936)+E(f773(f773(f3(f855(x87931,a841)),f773(f303(x87932,x87931,x87933),x87934)),f773(f303(x87932,x87931,x87933),x87935)),f773(f303(x87932,x87931,x87933),f773(f773(f3(f855(x87932,a841)),x87934),x87935)))+~P1(f773(f773(f232(f855(x87932,a841)),x87935),x87936))+~P1(f773(f773(f232(f855(x87932,a841)),x87934),x87936))
% 191.21/191.75 [8794]~P29(x87942,x87941,x87943,x87946)+E(f773(f773(f104(f855(x87941,a841)),f773(f303(x87942,x87941,x87943),x87944)),f773(f303(x87942,x87941,x87943),x87945)),f773(f303(x87942,x87941,x87943),f773(f773(f104(f855(x87942,a841)),x87944),x87945)))+~P1(f773(f773(f232(f855(x87942,a841)),x87945),x87946))+~P1(f773(f773(f232(f855(x87942,a841)),x87944),x87946))
% 191.21/191.75 [9038]E(x90381,x90382)+~P53(x90383,x90384,x90385)+~P1(f773(f773(f334(f854(x90383,x90384)),f773(f773(f241(x90383,x90384),x90386),x90382)),x90385))+~P1(f773(f773(f334(f854(x90383,x90384)),f773(f773(f241(x90383,x90384),x90386),x90381)),x90385))
% 191.21/191.75 [9618]~P66(x96181)+~P1(f773(f63(x96183),x96186))+~P1(f773(f63(x96182),x96185))+E(f773(f773(f82(x96181),f773(f773(f8(x96182,x96181),f773(f75(f856(x96182,x96183),x96181,x96182,x96184),f304(x96182,x96183))),x96185)),f773(f773(f8(x96183,x96181),f773(f75(f856(x96182,x96183),x96181,x96183,x96184),f313(x96183,x96182))),x96186)),f773(f773(f8(f856(x96182,x96183),x96181),x96184),f314(x96182,x96183,x96185,x96186)))
% 191.21/191.75 [9757]~P64(x97571)+~E(f773(x97573,f630(x97574,x97576,x97573,x97575,x97572,x97571)),f773(x97576,f630(x97574,x97576,x97573,x97575,x97572,x97571)))+~P1(f773(f63(x97572),x97575))+E(f773(f773(f773(f67(x97571,x97572,f83(x97571)),x97573),x97574),x97575),f773(f773(f773(f67(x97571,x97572,f83(x97571)),x97576),x97574),x97575))
% 191.21/191.75 [9818]~P64(x98181)+~P1(f773(f63(x98182),x98185))+E(f773(f773(f773(f67(x98181,x98182,f83(x98181)),x98183),x98184),x98185),f773(f773(f773(f67(x98181,x98182,f83(x98181)),x98186),x98184),x98185))+P1(f773(f773(f334(x98182),f630(x98184,x98183,x98186,x98185,x98182,x98181)),x98185))
% 191.21/191.75 [8623]~P64(x86231)+~P1(f773(f63(x86232),x86236))+P1(f773(f773(f334(x86232),x86235),x86236))+E(f773(f773(f773(f67(x86231,x86232,f83(x86231)),x86233),x86234),f773(f773(f302(x86232),x86235),x86236)),f773(f773(f83(x86231),f773(x86233,x86235)),f773(f773(f773(f67(x86231,x86232,f83(x86231)),x86233),x86234),x86236)))
% 191.21/191.75 [8667]~P12(x86671,x86676,x86673)+~P16(x86671,f855(x86672,a841),x86673,x86675)+~P1(f773(f773(f334(x86671),x86674),x86676))+E(f773(f773(f46(x86671,f855(x86672,a841)),f773(f277(x86671,x86671,x86673),f773(f773(f302(x86671),x86674),f180(f855(x86671,a841))))),x86675),f773(x86675,x86674))
% 191.21/191.75 [8775]~P20(x87753,x87754,x87751)+~P1(f773(f63(x87753),x87756))+~P1(f773(f773(f334(x87753),x87752),x87756))+E(f773(f773(x87751,x87752),f773(f773(f66(x87753,x87754,x87751),x87755),f773(f773(f3(f855(x87753,a841)),x87756),f773(f773(f302(x87753),x87752),f180(f855(x87753,a841)))))),f773(f773(f66(x87753,x87754,x87751),x87755),x87756))
% 191.21/191.75 [9048]~P23(x90483,x90481,x90486,x90482)+~P1(f773(f63(x90483),x90485))+~P1(f773(f63(x90483),x90484))+E(f773(f75(x90481,x90481,x90481,f773(x90482,f773(f773(f103(f855(x90483,a841)),x90484),x90485))),f773(x90482,f773(f773(f104(f855(x90483,a841)),x90484),x90485))),f773(f75(x90481,x90481,x90481,f773(x90482,x90484)),f773(x90482,x90485)))
% 191.21/191.75 [9355]~E(x93553,f773(f773(f148(x93551,x93552),x93555),x93556))+P1(f773(f773(f334(f854(f848(x93551),f848(x93551))),f773(f773(f241(f848(x93551),f848(x93551)),x93552),x93553)),f146(x93551,x93554)))+~P1(f773(f773(f233(a847),x93555),f773(f181(f848(x93551)),x93552)))+~P1(f773(f773(f334(f854(x93551,x93551)),f773(f773(f241(x93551,x93551),f773(f773(f153(x93551),x93552),x93555)),x93556)),x93554))
% 191.21/191.75 [9837]~P66(x98372)+~P1(f773(f63(x98371),x98376))+P1(f773(f773(f334(x98371),f563(x98374,x98375,x98373,x98376,x98371,x98372)),x98376))+E(f773(f773(f8(x98371,x98372),f773(f773(f20(x98371,f855(x98373,a841),x98372),f773(f773(f10(f855(x98373,x98372),f855(f855(x98373,a841),x98372),x98371),f8(x98373,x98372)),x98374)),x98375)),x98376),f773(f773(f8(f854(x98371,x98373),x98372),f773(f251(x98371,x98373,x98372),x98374)),f773(f773(f248(x98371,x98373),x98376),x98375)))
% 191.21/191.75 [9838]~P70(x98382)+~P1(f773(f63(x98381),x98386))+P1(f773(f773(f334(x98381),f556(x98384,x98385,x98383,x98386,x98381,x98382)),x98386))+E(f773(f773(f11(x98381,x98382),f773(f773(f20(x98381,f855(x98383,a841),x98382),f773(f773(f10(f855(x98383,x98382),f855(f855(x98383,a841),x98382),x98381),f11(x98383,x98382)),x98384)),x98385)),x98386),f773(f773(f11(f854(x98381,x98383),x98382),f773(f251(x98381,x98383,x98382),x98384)),f773(f773(f248(x98381,x98383),x98386),x98385)))
% 191.21/191.75 [9877]~P66(x98772)+~P1(f773(f63(x98771),x98776))+~P1(f773(f63(x98773),f773(x98775,f563(x98774,x98775,x98773,x98776,x98771,x98772))))+E(f773(f773(f8(x98771,x98772),f773(f773(f20(x98771,f855(x98773,a841),x98772),f773(f773(f10(f855(x98773,x98772),f855(f855(x98773,a841),x98772),x98771),f8(x98773,x98772)),x98774)),x98775)),x98776),f773(f773(f8(f854(x98771,x98773),x98772),f773(f251(x98771,x98773,x98772),x98774)),f773(f773(f248(x98771,x98773),x98776),x98775)))
% 191.21/191.75 [9878]~P70(x98782)+~P1(f773(f63(x98781),x98786))+~P1(f773(f63(x98783),f773(x98785,f556(x98784,x98785,x98783,x98786,x98781,x98782))))+E(f773(f773(f11(x98781,x98782),f773(f773(f20(x98781,f855(x98783,a841),x98782),f773(f773(f10(f855(x98783,x98782),f855(f855(x98783,a841),x98782),x98781),f11(x98783,x98782)),x98784)),x98785)),x98786),f773(f773(f11(f854(x98781,x98783),x98782),f773(f251(x98781,x98783,x98782),x98784)),f773(f773(f248(x98781,x98783),x98786),x98785)))
% 191.21/191.75 [9860]~P70(x98602)+~P1(f773(f63(x98601),x98606))+P1(f773(f773(f334(x98601),x98603),x98606))+E(f773(f773(f11(x98601,x98602),f773(f773(f9(x98601,x98602,x98602),f773(f773(f20(x98601,x98602,f855(x98602,x98602)),f773(f773(f10(a841,f855(x98602,f855(x98602,x98602)),x98601),f98(x98602)),f773(f773(f9(x98601,x98601,a841),a330),x98603))),x98604)),x98605)),x98606),f773(f773(f242(x98602),x98605),f773(f42(x98601),x98606)))
% 191.21/191.75 [9865]~P70(x98652)+~P1(f773(f63(x98651),x98656))+~P1(f773(f773(f334(x98651),x98653),x98656))+E(f773(f773(f11(x98651,x98652),f773(f773(f9(x98651,x98652,x98652),f773(f773(f20(x98651,x98652,f855(x98652,x98652)),f773(f773(f10(a841,f855(x98652,f855(x98652,x98652)),x98651),f98(x98652)),f773(f773(f9(x98651,x98651,a841),a330),x98653))),x98654)),x98655)),x98656),f773(f773(f83(x98652),f773(x98654,x98653)),f773(f773(f242(x98652),x98655),f773(f773(f3(a847),f773(f42(x98651),x98656)),f80(a847)))))
% 191.21/191.75 [9931]~P1(f773(f63(x99311),x99315))+~P1(f773(f63(x99312),x99313))+P1(f773(f773(f334(x99312),f586(x99316,x99314,x99313,x99312,x99315,x99311)),x99313))+E(f773(f773(f8(x99311,a847),f773(f773(f10(f855(x99312,a841),a847,x99311),f42(x99312)),f773(f773(f10(f855(x99312,a841),f855(x99312,a841),x99311),f256(x99312)),f773(f773(f10(f855(x99312,a841),f855(x99312,a841),x99311),f773(f20(x99312,a841,a841),f773(f773(f10(a841,f855(a841,a841),x99312),a331),f773(f773(f9(x99312,f855(x99312,a841),a841),f334(x99312)),x99313)))),x99314)))),x99315),f773(f773(f83(a847),x99316),f773(f42(x99312),x99313)))
% 191.21/191.75 [9932]~P1(f773(f63(x99321),x99325))+~P1(f773(f63(x99322),x99323))+P1(f773(f773(f334(x99322),f587(x99326,x99324,x99323,x99322,x99325,x99321)),x99323))+E(f773(f773(f8(x99321,a847),f773(f773(f10(f855(x99322,a841),a847,x99321),f42(x99322)),f773(f773(f10(f855(x99322,a841),f855(x99322,a841),x99321),f256(x99322)),f773(f773(f10(f855(x99322,a841),f855(x99322,a841),x99321),f773(f20(x99322,a841,a841),f773(f773(f10(a841,f855(a841,a841),x99322),a331),f773(f773(f9(x99322,f855(x99322,a841),a841),f334(x99322)),x99323)))),x99324)))),x99325),f773(f773(f8(x99322,a847),x99326),x99323))
% 191.21/191.75 [9966]~P1(f773(f63(x99662),x99663))+~P1(f773(f63(x99661),x99665))+~E(f773(f42(x99661),f773(f256(x99661),f773(f773(f20(x99661,a841,a841),f773(f773(f10(a841,f855(a841,a841),x99661),a331),f773(f773(f9(x99661,f855(x99661,a841),a841),f334(x99661)),x99665))),f773(f773(f9(x99661,x99662,a841),x99664),f586(x99666,x99664,x99663,x99662,x99665,x99661))))),x99666)+E(f773(f773(f8(x99661,a847),f773(f773(f10(f855(x99662,a841),a847,x99661),f42(x99662)),f773(f773(f10(f855(x99662,a841),f855(x99662,a841),x99661),f256(x99662)),f773(f773(f10(f855(x99662,a841),f855(x99662,a841),x99661),f773(f20(x99662,a841,a841),f773(f773(f10(a841,f855(a841,a841),x99662),a331),f773(f773(f9(x99662,f855(x99662,a841),a841),f334(x99662)),x99663)))),x99664)))),x99665),f773(f773(f83(a847),x99666),f773(f42(x99662),x99663)))
% 191.21/191.75 [9968]~P1(f773(f63(x99682),x99683))+~P1(f773(f63(x99681),x99685))+~E(f773(f42(x99681),f773(f256(x99681),f773(f773(f20(x99681,a841,a841),f773(f773(f10(a841,f855(a841,a841),x99681),a331),f773(f773(f9(x99681,f855(x99681,a841),a841),f334(x99681)),x99685))),f773(f773(f9(x99681,x99682,a841),x99684),f587(x99686,x99684,x99683,x99682,x99685,x99681))))),f773(x99686,f587(x99686,x99684,x99683,x99682,x99685,x99681)))+E(f773(f773(f8(x99681,a847),f773(f773(f10(f855(x99682,a841),a847,x99681),f42(x99682)),f773(f773(f10(f855(x99682,a841),f855(x99682,a841),x99681),f256(x99682)),f773(f773(f10(f855(x99682,a841),f855(x99682,a841),x99681),f773(f20(x99682,a841,a841),f773(f773(f10(a841,f855(a841,a841),x99682),a331),f773(f773(f9(x99682,f855(x99682,a841),a841),f334(x99682)),x99683)))),x99684)))),x99685),f773(f773(f8(x99682,a847),x99686),x99683))
% 191.21/191.75 [9617]E(x96171,x96172)+~P20(x96173,x96174,x96175)+~P1(f773(f68(x96173,x96174,x96175,x96176,x96177),x96172))+~P1(f773(f68(x96173,x96174,x96175,x96176,x96177),x96171))
% 191.21/191.75 [9427]P1(f773(x94271,x94272))+~P1(f773(f773(f334(x94277),x94272),f773(x94276,x94274)))+~P1(f773(x94271,f387(x94271,x94276,x94275,x94273,x94277)))+~P1(f773(f773(f334(x94273),x94274),x94275))
% 191.21/191.75 [9852]~P20(x98527,x98526,x98521)+E(f773(f773(x98521,x98522),f663(x98522,x98523,x98524,x98525,x98521,x98526,x98527)),x98523)+~P1(f773(f68(x98527,x98526,x98521,x98525,x98524),x98523))+~P1(f773(f773(f334(x98527),x98522),x98524))
% 191.21/191.75 [9916]~P20(x99161,x99162,x99163)+~P1(f773(f68(x99161,x99162,x99163,x99164,x99165),x99167))+P1(f773(f68(x99161,x99162,x99163,x99164,f773(f773(f3(f855(x99161,a841)),x99165),f773(f773(f302(x99161),x99166),f180(f855(x99161,a841))))),f663(x99166,x99167,x99165,x99164,x99163,x99162,x99161)))+~P1(f773(f773(f334(x99161),x99166),x99165))
% 191.21/191.75 [9331]~P64(x93311)+~P29(x93315,x93312,x93316,x93317)+~P1(f773(f63(x93315),x93317))+E(f773(f773(f773(f67(x93311,x93312,f83(x93311)),x93313),x93314),f773(f303(x93315,x93312,x93316),x93317)),f773(f773(f773(f67(x93311,x93315,f83(x93311)),f773(f75(x93312,x93311,x93315,x93313),x93316)),x93314),x93317))
% 191.21/191.75 [9449]~E(f773(f773(f302(x94491),x94495),x94496),f773(f773(f302(x94491),x94492),x94493))+~P1(f773(f68(x94491,x94491,x94494,x94492,x94493),x94497))+P1(f773(f773(f334(x94491),x94492),x94493))+P1(f773(f64(x94491,x94494,f773(f773(f302(x94491),x94495),x94496)),x94497))
% 191.21/191.75 [9528]P1(f773(x95281,x95282))+~P1(f773(f773(f334(x95283),x95282),f773(x95284,x95287)))+~P1(f773(f773(f334(x95286),x95287),x95285))+P1(f773(f773(f334(x95283),f387(x95281,x95284,x95285,x95286,x95283)),f773(f773(f46(x95286,f855(x95283,a841)),x95285),x95284)))
% 191.21/191.75 [9541]~P29(x95412,x95411,x95415,x95414)+~P29(x95411,x95413,x95416,f773(f303(x95412,x95411,x95415),x95414))+E(f773(f773(f75(x95411,x95412,x95413,f79(x95412,x95411,x95414,x95415)),f79(x95411,x95413,f773(f303(x95412,x95411,x95415),x95414),x95416)),x95417),f773(f79(x95412,x95413,x95414,f773(f75(x95411,x95413,x95412,x95416),x95415)),x95417))+~P1(f773(f773(f334(x95413),x95417),f773(f303(x95411,x95413,x95416),f773(f303(x95412,x95411,x95415),x95414))))
% 191.21/191.75 [9853]~P20(x98537,x98536,x98531)+E(f773(f773(x98531,x98532),f691(x98533,x98534,x98532,x98535,x98531,x98536,x98537)),x98533)+P1(f773(f773(f334(x98537),x98532),x98534))+~P1(f773(f68(x98537,x98536,x98531,x98535,f773(f773(f302(x98537),x98532),x98534)),x98533))
% 191.21/191.75 [9915]~P20(x99151,x99154,x99155)+P1(f773(f68(x99151,x99154,x99155,x99156,x99153),f691(x99157,x99153,x99152,x99156,x99155,x99154,x99151)))+P1(f773(f773(f334(x99151),x99152),x99153))+~P1(f773(f68(x99151,x99154,x99155,x99156,f773(f773(f302(x99151),x99152),x99153)),x99157))
% 191.21/191.75 [9600]E(x96001,f2(a1))+~P1(f773(f56(x96003,x96001),f773(f773(f241(a1,a1),x96005),x96007)))+~P1(f773(f56(x96002,x96001),f773(f773(f241(a1,a1),x96004),x96006)))+P1(f773(f56(f773(f773(f82(a1),x96002),x96003),x96001),f773(f773(f241(a1,a1),f773(f773(f82(a1),f773(f773(f82(a1),x96004),x96005)),f773(f773(f43(a1),f773(f773(f82(a1),x96006),x96007)),x96001))),f52(a1,f773(f773(f82(a1),x96006),x96007),x96001))))
% 191.21/191.75 [9602]~P1(f773(f773(f233(a847),f2(a847)),x96023))+~P1(f773(f55(x96022,x96023),f773(f773(f241(a847,a847),x96025),x96027)))+~P1(f773(f55(x96021,x96023),f773(f773(f241(a847,a847),x96024),x96026)))+P1(f773(f55(f773(f773(f82(a847),x96021),x96022),x96023),f773(f773(f241(a847,a847),f773(f773(f82(a847),f773(f773(f82(a847),x96024),x96025)),f773(f773(f43(a847),f773(f773(f82(a847),x96026),x96027)),x96023))),f52(a847,f773(f773(f82(a847),x96026),x96027),x96023))))
% 191.21/191.75 [9965]~P66(x99652)+~P1(f773(f63(x99653),x99655))+~P1(f773(f63(x99651),x99657))+E(f773(f773(f8(x99651,x99652),f773(f773(f20(x99651,f855(x99653,a841),x99652),f773(f773(f10(f855(x99653,x99652),f855(f855(x99653,a841),x99652),x99651),f8(x99653,x99652)),x99654)),f773(f773(f10(f855(x99653,a841),f855(x99653,a841),x99651),f256(x99653)),f773(f773(f10(f855(x99653,a841),f855(x99653,a841),x99651),f773(f20(x99653,a841,a841),f773(f773(f10(a841,f855(a841,a841),x99653),a331),f773(f773(f9(x99653,f855(x99653,a841),a841),f334(x99653)),x99655)))),x99656)))),x99657),f773(f773(f8(x99653,x99652),f773(f773(f20(x99653,f855(x99651,a841),x99652),f773(f773(f10(f855(x99651,x99652),f855(f855(x99651,a841),x99652),x99653),f8(x99651,x99652)),f773(f9(x99651,x99653,x99652),x99654))),f773(f773(f10(f855(x99651,a841),f855(x99651,a841),x99653),f256(x99651)),f773(f773(f10(f855(x99651,a841),f855(x99651,a841),x99653),f773(f20(x99651,a841,a841),f773(f773(f10(a841,f855(a841,a841),x99651),a331),f773(f773(f9(x99651,f855(x99651,a841),a841),f334(x99651)),x99657)))),f773(f9(x99651,x99653,a841),x99656))))),x99655))
% 191.21/191.75 [9487]~P26(x94877,x94876,x94871,x94878,x94872,x94874)+E(f773(f773(x94871,f773(x94872,x94873)),f773(x94874,x94875)),f773(x94874,x94875))+~P1(f773(f63(x94876),x94875))+~P1(f773(f773(f334(x94876),x94873),x94875))
% 191.21/191.75 [9491]~P17(x94916,x94911,x94912,x94918,x94913,x94914)+~P12(x94916,x94917,x94918)+P16(x94911,x94912,x94913,f773(x94914,x94915))+~P1(f773(f773(f334(x94916),x94915),x94917))
% 191.21/191.75 [7733]~P39(x77334,x77335,x77336,x77333)+~P31(x77338,x77336,f773(f773(f773(f93(x77338),x77337),x77334),x77331))+P1(f773(f773(x77331,x77332),x77333))+~P1(f773(f773(x77337,x77332),x77335))
% 191.21/191.75 [9135]~P23(x91357,x91351,x91358,x91353)+~P1(f773(f63(x91357),x91355))+~P1(f773(f63(x91357),x91354))+E(f773(f75(x91351,x91351,x91352,f773(x91353,x91354)),f773(f75(x91351,x91351,x91352,f773(x91353,x91355)),x91356)),f773(f75(x91351,x91351,x91352,f773(x91353,x91355)),f773(f75(x91351,x91351,x91352,f773(x91353,x91354)),x91356)))
% 191.21/191.75 [9202]~P29(x92022,x92022,x92025,x92026)+~P25(x92023,x92022,x92027,x92028,x92021)+~P1(f773(f63(x92022),x92026))+E(f773(f773(x92021,f773(f75(x92022,x92023,x92022,x92024),x92025)),x92026),f773(f773(x92021,x92024),f773(f303(x92022,x92022,x92025),x92026)))
% 191.21/191.75 [9489]~P27(x94897,x94892,x94895,x94898,x94896,x94891)+~P1(f773(f63(x94892),x94894))+E(f773(x94891,f773(f773(f302(x94892),x94893),x94894)),f773(f773(x94895,f773(x94896,x94893)),f773(x94891,x94894)))+P1(f773(f773(f334(x94892),x94893),x94894))
% 191.21/191.75 [9496]~P26(x94966,x94965,x94961,x94967,x94968,x94962)+E(f773(f773(x94961,f773(x94962,x94963)),f773(x94962,x94964)),f773(x94962,x94964))+~P1(f773(f63(x94965),x94964))+~P1(f773(f773(f232(f855(x94965,a841)),x94963),x94964))
% 191.21/191.75 [9122]P1(f773(f773(f334(f854(f848(x91221),f848(x91221))),f773(f773(f241(f848(x91221),f848(x91221)),x91222),x91223)),f146(x91221,x91224)))+~E(x91223,f773(f773(f125(x91221),x91225),f773(f773(f140(x91221),x91226),x91227)))+~E(x91222,f773(f773(f125(x91221),x91225),f773(f773(f140(x91221),x91228),x91227)))+~P1(f773(f773(f334(f854(x91221,x91221)),f773(f773(f241(x91221,x91221),x91228),x91226)),x91224))
% 191.21/191.75 [9492]~P26(x94926,x94922,x94925,x94927,x94928,x94921)+~P1(f773(f63(x94922),x94924))+~P1(f773(f63(x94922),x94923))+E(f773(x94921,f773(f773(f103(f855(x94922,a841)),x94923),x94924)),f773(f773(x94925,f773(x94921,x94923)),f773(x94921,x94924)))
% 191.21/191.75 [10005]~P29(x100054,x100052,x100055,x100058)+E(f773(f773(f47(x100051,f855(x100052,a841)),x100053),f773(f773(f10(f855(x100054,a841),f855(x100052,a841),x100051),f303(x100054,x100052,x100055)),x100056)),f773(f303(x100054,x100052,x100055),f773(f773(f47(x100051,f855(x100054,a841)),x100053),x100056)))+~P1(f773(f773(f334(x100051),x100057),x100053))+P1(f773(f773(f334(x100051),f678(x100057,x100056,x100053,x100051,x100058,x100055,x100052,x100054)),x100053))
% 191.21/191.75 [10023]~P29(x100234,x100232,x100235,x100237)+E(f773(f773(f47(x100231,f855(x100232,a841)),x100233),f773(f773(f10(f855(x100234,a841),f855(x100232,a841),x100231),f303(x100234,x100232,x100235)),x100236)),f773(f303(x100234,x100232,x100235),f773(f773(f47(x100231,f855(x100234,a841)),x100233),x100236)))+~P1(f773(f773(f334(x100231),x100238),x100233))+~P1(f773(f773(f232(f855(x100234,a841)),f773(x100236,f678(x100238,x100236,x100233,x100231,x100237,x100235,x100232,x100234))),x100237))
% 191.21/191.75 [9546]~P27(x95467,x95465,x95461,x95468,x95462,x95464)+~P1(f773(f63(x95465),x95466))+~P1(f773(f773(f334(x95465),x95463),x95466))+E(f773(f773(x95461,f773(x95462,x95463)),f773(x95464,f773(f773(f3(f855(x95465,a841)),x95466),f773(f773(f302(x95465),x95463),f180(f855(x95465,a841)))))),f773(x95464,x95466))
% 191.21/191.75 [9555]~P27(x95556,x95553,x95551,x95557,x95558,x95552)+~P1(f773(f63(x95553),x95555))+~P1(f773(f63(x95553),x95554))+E(f773(f773(x95551,f773(x95552,f773(f773(f103(f855(x95553,a841)),x95554),x95555))),f773(x95552,f773(f773(f104(f855(x95553,a841)),x95554),x95555))),f773(f773(x95551,f773(x95552,x95554)),f773(x95552,x95555)))
% 191.21/191.75 [9637]P41(x96371,x96372,x96373,x96374,x96375,f773(f773(x96373,x96376),x96377))+~P41(x96371,x96372,x96373,x96374,f773(f773(f3(f855(x96371,a841)),x96375),f773(f773(f302(x96371),x96378),f180(f855(x96371,a841)))),x96379)+~E(f773(f773(x96373,x96376),x96377),f773(f773(x96373,x96378),x96379))+~P1(f773(f773(f334(x96371),x96378),x96375))
% 191.21/191.75 [10034]P28(x100341,x100342,f773(f773(f302(f846(x100341)),f773(f773(f773(f93(x100341),f773(x100343,f426(x100344,x100345,x100346,x100347,x100343,x100342,x100341,x100348,x100349))),f773(x100347,f426(x100344,x100345,x100346,x100347,x100343,x100342,x100341,x100348,x100349))),f773(x100346,f426(x100344,x100345,x100346,x100347,x100343,x100342,x100341,x100348,x100349)))),f180(f855(f846(x100341),a841))))+~P1(f773(f63(x100349),x100348))+~P28(x100341,x100342,f773(f303(x100349,f846(x100341),f773(f773(f20(x100349,f855(x100341,f855(a844,a841)),f846(x100341)),f773(f773(f20(x100349,a842,f855(f855(x100341,f855(a844,a841)),f846(x100341))),f773(f773(f10(f855(x100341,f855(a844,a841)),f855(a842,f855(f855(x100341,f855(a844,a841)),f846(x100341))),x100349),f93(x100341)),x100343)),x100347)),x100346)),x100348))+P28(x100341,x100342,f773(f303(x100349,f846(x100341),f773(f773(f20(x100349,f855(x100341,f855(a844,a841)),f846(x100341)),f773(f773(f20(x100349,a842,f855(f855(x100341,f855(a844,a841)),f846(x100341))),f773(f773(f10(f855(x100341,f855(a844,a841)),f855(a842,f855(f855(x100341,f855(a844,a841)),f846(x100341))),x100349),f93(x100341)),x100345)),x100347)),x100344)),x100348))
% 191.21/191.75 [10035]~P28(x100351,x100352,f773(f773(f302(f846(x100351)),f773(f773(f773(f93(x100351),f773(x100354,f426(x100356,x100354,x100358,x100355,x100359,x100352,x100351,x100357,x100353))),f773(x100355,f426(x100356,x100354,x100358,x100355,x100359,x100352,x100351,x100357,x100353))),f773(x100356,f426(x100356,x100354,x100358,x100355,x100359,x100352,x100351,x100357,x100353)))),f180(f855(f846(x100351),a841))))+~P1(f773(f63(x100353),x100357))+~P28(x100351,x100352,f773(f303(x100353,f846(x100351),f773(f773(f20(x100353,f855(x100351,f855(a844,a841)),f846(x100351)),f773(f773(f20(x100353,a842,f855(f855(x100351,f855(a844,a841)),f846(x100351))),f773(f773(f10(f855(x100351,f855(a844,a841)),f855(a842,f855(f855(x100351,f855(a844,a841)),f846(x100351))),x100353),f93(x100351)),x100359)),x100355)),x100358)),x100357))+P28(x100351,x100352,f773(f303(x100353,f846(x100351),f773(f773(f20(x100353,f855(x100351,f855(a844,a841)),f846(x100351)),f773(f773(f20(x100353,a842,f855(f855(x100351,f855(a844,a841)),f846(x100351))),f773(f773(f10(f855(x100351,f855(a844,a841)),f855(a842,f855(f855(x100351,f855(a844,a841)),f846(x100351))),x100353),f93(x100351)),x100354)),x100355)),x100356)),x100357))
% 191.21/191.75 [9579]~P17(x95796,x95797,x95798,x95799,x957910,x95791)+E(f773(f773(x95791,x95792),x95793),f773(f773(x95791,x95794),x95795))+~P1(f773(f773(f334(f854(x95797,x95797)),f773(f773(f241(x95797,x95797),x95793),x95795)),x957910))+~P1(f773(f773(f334(f854(x95796,x95796)),f773(f773(f241(x95796,x95796),x95792),x95794)),x95799))
% 191.21/191.75 [6801]E(x68011,x68012)+~P1(f773(f773(f232(a1),f2(a1)),x68012))+~P1(f773(f773(f232(a1),f2(a1)),x68011))+~P1(f773(f773(f279(a1),x68012),x68011))+~P1(f773(f773(f279(a1),x68011),x68012))
% 191.21/191.75 [9204]~P93(x92042)+E(x92041,f180(f855(x92042,a841)))+~P1(f773(f63(x92042),x92041))+P1(f773(f773(f334(x92042),f15(x92042,x92041)),x92041))+~P1(f773(f773(f334(x92042),f773(f773(f103(x92042),f443(x92041,x92042)),f444(x92041,x92042))),f773(f773(f302(x92042),f443(x92041,x92042)),f773(f773(f302(x92042),f444(x92041,x92042)),f180(f855(x92042,a841))))))
% 191.21/191.75 [9207]~P93(x92072)+E(x92071,f180(f855(x92072,a841)))+~P1(f773(f63(x92072),x92071))+P1(f773(f773(f334(x92072),f12(x92072,x92071)),x92071))+~P1(f773(f773(f334(x92072),f773(f773(f104(x92072),f516(x92071,x92072)),f518(x92071,x92072))),f773(f773(f302(x92072),f516(x92071,x92072)),f773(f773(f302(x92072),f518(x92071,x92072)),f180(f855(x92072,a841))))))
% 191.21/191.75 [9235]~P64(x92352)+E(x92351,f180(f855(x92352,a841)))+~P1(f773(f63(x92352),x92351))+P1(f773(f773(f334(x92352),f773(f65(x92352,f83(x92352)),x92351)),x92351))+~P1(f773(f773(f334(x92352),f773(f773(f83(x92352),f565(x92351,x92352)),f566(x92351,x92352))),f773(f773(f302(x92352),f565(x92351,x92352)),f773(f773(f302(x92352),f566(x92351,x92352)),f180(f855(x92352,a841))))))
% 191.21/191.75 [9241]~P100(x92412)+E(x92411,f180(f855(x92412,a841)))+~P1(f773(f63(x92412),x92411))+P1(f773(f773(f334(x92412),f13(x92412,f179(x92412),x92411)),x92411))+~P1(f773(f773(f334(x92412),f773(f773(f179(x92412),f452(x92411,x92412)),f455(x92411,x92412))),f773(f773(f302(x92412),f452(x92411,x92412)),f773(f773(f302(x92412),f455(x92411,x92412)),f180(f855(x92412,a841))))))
% 191.21/191.75 [9242]~P100(x92422)+E(x92421,f180(f855(x92422,a841)))+~P1(f773(f63(x92422),x92421))+P1(f773(f773(f334(x92422),f14(x92422,f236(x92422),x92421)),x92421))+~P1(f773(f773(f334(x92422),f773(f773(f236(x92422),f456(x92421,x92422)),f457(x92421,x92422))),f773(f773(f302(x92422),f456(x92421,x92422)),f773(f773(f302(x92422),f457(x92421,x92422)),f180(f855(x92422,a841))))))
% 191.21/191.75 [6413]~P81(x64132)+E(x64131,f2(x64132))+~E(f773(f773(f82(x64132),x64133),x64131),f2(x64132))+~P1(f773(f773(f232(x64132),f2(x64132)),x64133))+~P1(f773(f773(f232(x64132),f2(x64132)),x64131))
% 191.21/191.75 [6414]~P81(x64142)+E(x64141,f2(x64142))+~E(f773(f773(f82(x64142),x64141),x64143),f2(x64142))+~P1(f773(f773(f232(x64142),f2(x64142)),x64143))+~P1(f773(f773(f232(x64142),f2(x64142)),x64141))
% 191.21/191.75 [7134]~P100(x71341)+E(f17(x71341,x71342),x71343)+~P1(f773(f63(x71341),x71342))+~P1(f773(f773(f232(x71341),x71343),f629(x71343,x71342,x71341)))+~P1(f773(f773(f334(x71341),x71343),x71342))
% 191.21/191.75 [7169]~P100(x71691)+~P18(x71691,x71692)+~P18(x71691,x71693)+P18(x71691,f773(f773(f125(x71691),x71692),x71693))+P1(f773(f773(f334(x71691),f764(x71693,x71692,x71691)),f773(f158(x71691),x71692)))
% 191.21/191.75 [7170]~P100(x71701)+~P18(x71701,x71702)+~P18(x71701,x71703)+P18(x71701,f773(f773(f125(x71701),x71702),x71703))+P1(f773(f773(f334(x71701),f765(x71703,x71702,x71701)),f773(f158(x71701),x71703)))
% 191.21/191.75 [7236]~P100(x72361)+E(f16(x72361,x72362),x72363)+~P1(f773(f63(x72361),x72362))+P1(f773(f773(f334(x72361),f632(x72363,x72362,x72361)),x72362))+~P1(f773(f773(f334(x72361),x72363),x72362))
% 191.21/191.75 [7237]~P100(x72371)+E(f17(x72371,x72372),x72373)+~P1(f773(f63(x72371),x72372))+P1(f773(f773(f334(x72371),f629(x72373,x72372,x72371)),x72372))+~P1(f773(f773(f334(x72371),x72373),x72372))
% 191.21/191.75 [7836]~P100(x78361)+E(f16(x78361,x78362),x78363)+~P1(f773(f63(x78361),x78362))+~P1(f773(f773(f334(x78361),x78363),x78362))+~P1(f773(f773(f232(x78361),f632(x78363,x78362,x78361)),x78363))
% 191.21/191.75 [8150]~P100(x81501)+~P18(x81501,x81502)+~P18(x81501,x81503)+P18(x81501,f773(f773(f125(x81501),x81502),x81503))+~P1(f773(f773(f232(x81501),f764(x81503,x81502,x81501)),f765(x81503,x81502,x81501)))
% 191.21/191.75 [8879]~P93(x88792)+E(x88791,f180(f855(x88792,a841)))+~E(f773(f773(f103(x88792),f773(x88793,f474(x88791,x88793,x88792))),f773(x88793,f477(x88791,x88793,x88792))),f773(x88793,f773(f773(f103(x88792),f474(x88791,x88793,x88792)),f477(x88791,x88793,x88792))))+E(f15(x88792,f773(f303(x88792,x88792,x88793),x88791)),f773(x88793,f15(x88792,x88791)))+~P1(f773(f63(x88792),x88791))
% 191.21/191.75 [8880]~P100(x88802)+E(x88801,f180(f855(x88802,a841)))+~E(f773(f773(f179(x88802),f773(x88803,f465(x88801,x88803,x88802))),f773(x88803,f470(x88801,x88803,x88802))),f773(x88803,f773(f773(f179(x88802),f465(x88801,x88803,x88802)),f470(x88801,x88803,x88802))))+E(f16(x88802,f773(f303(x88802,x88802,x88803),x88801)),f773(x88803,f16(x88802,x88801)))+~P1(f773(f63(x88802),x88801))
% 191.21/191.75 [8881]~P100(x88812)+E(x88811,f180(f855(x88812,a841)))+~E(f773(f773(f236(x88812),f773(x88813,f475(x88811,x88813,x88812))),f773(x88813,f476(x88811,x88813,x88812))),f773(x88813,f773(f773(f236(x88812),f475(x88811,x88813,x88812)),f476(x88811,x88813,x88812))))+E(f17(x88812,f773(f303(x88812,x88812,x88813),x88811)),f773(x88813,f17(x88812,x88811)))+~P1(f773(f63(x88812),x88811))
% 191.21/191.75 [8882]~P93(x88822)+E(x88821,f180(f855(x88822,a841)))+~E(f773(f773(f104(x88822),f773(x88823,f530(x88821,x88823,x88822))),f773(x88823,f532(x88821,x88823,x88822))),f773(x88823,f773(f773(f104(x88822),f530(x88821,x88823,x88822)),f532(x88821,x88823,x88822))))+E(f12(x88822,f773(f303(x88822,x88822,x88823),x88821)),f773(x88823,f12(x88822,x88821)))+~P1(f773(f63(x88822),x88821))
% 191.21/191.75 [8946]~P100(x89462)+E(x89461,f180(f855(x89462,a841)))+~E(f773(f773(f179(x89462),f773(x89463,f466(x89461,x89463,x89462))),f773(x89463,f467(x89461,x89463,x89462))),f773(x89463,f773(f773(f179(x89462),f466(x89461,x89463,x89462)),f467(x89461,x89463,x89462))))+E(f13(x89462,f179(x89462),f773(f303(x89462,x89462,x89463),x89461)),f773(x89463,f13(x89462,f179(x89462),x89461)))+~P1(f773(f63(x89462),x89461))
% 191.21/191.75 [8947]~P100(x89472)+E(x89471,f180(f855(x89472,a841)))+~E(f773(f773(f236(x89472),f773(x89473,f468(x89471,x89473,x89472))),f773(x89473,f469(x89471,x89473,x89472))),f773(x89473,f773(f773(f236(x89472),f468(x89471,x89473,x89472)),f469(x89471,x89473,x89472))))+E(f14(x89472,f236(x89472),f773(f303(x89472,x89472,x89473),x89471)),f773(x89473,f14(x89472,f236(x89472),x89471)))+~P1(f773(f63(x89472),x89471))
% 191.21/191.75 [6430]~P64(x64302)+E(x64301,f180(f855(x64302,a841)))+~P1(f773(f63(x64302),x64301))+E(f773(f65(x64302,f83(x64302)),f773(f773(f302(x64302),x64303),x64301)),f773(f773(f83(x64302),x64303),f773(f65(x64302,f83(x64302)),x64301)))+P1(f773(f773(f334(x64302),x64303),x64301))
% 191.21/191.75 [6972]~P100(x69722)+E(f773(f773(f236(x69722),f17(x69722,x69721)),f17(x69722,x69723)),f17(x69722,x69723))+E(x69721,f180(f855(x69722,a841)))+~P1(f773(f63(x69722),x69723))+~P1(f773(f773(f232(f855(x69722,a841)),x69721),x69723))
% 191.21/191.75 [6973]~P100(x69732)+E(f773(f773(f179(x69732),f16(x69732,x69731)),f16(x69732,x69733)),f16(x69732,x69733))+E(x69731,f180(f855(x69732,a841)))+~P1(f773(f63(x69732),x69733))+~P1(f773(f773(f232(f855(x69732,a841)),x69731),x69733))
% 191.21/191.75 [6974]~P93(x69742)+E(f773(f773(f103(x69742),f15(x69742,x69741)),f15(x69742,x69743)),f15(x69742,x69743))+E(x69741,f180(f855(x69742,a841)))+~P1(f773(f63(x69742),x69743))+~P1(f773(f773(f232(f855(x69742,a841)),x69741),x69743))
% 191.21/191.75 [6975]~P93(x69752)+E(f773(f773(f104(x69752),f12(x69752,x69751)),f12(x69752,x69753)),f12(x69752,x69753))+E(x69751,f180(f855(x69752,a841)))+~P1(f773(f63(x69752),x69753))+~P1(f773(f773(f232(f855(x69752,a841)),x69751),x69753))
% 191.21/191.75 [7292]~P100(x72922)+E(x72921,f180(f855(x72922,a841)))+~P1(f773(f63(x72922),x72923))+P1(f773(f773(f232(x72922),f16(x72922,x72921)),f16(x72922,x72923)))+~P1(f773(f773(f232(f855(x72922,a841)),x72921),x72923))
% 191.21/191.75 [7293]~P100(x72932)+E(x72931,f180(f855(x72932,a841)))+~P1(f773(f63(x72932),x72933))+P1(f773(f773(f232(x72932),f17(x72932,x72933)),f17(x72932,x72931)))+~P1(f773(f773(f232(f855(x72932,a841)),x72931),x72933))
% 191.21/191.75 [7355]~P93(x73551)+E(f15(x73551,x73552),x73553)+~P1(f773(f63(x73551),x73552))+~E(f773(f773(f3(f855(x73551,a841)),x73552),f773(f773(f302(x73551),x73553),f180(f855(x73551,a841)))),f180(f855(x73551,a841)))+~P1(f773(f773(f334(x73551),x73553),x73552))
% 191.21/191.75 [7356]~P100(x73561)+E(f16(x73561,x73562),x73563)+~P1(f773(f63(x73561),x73562))+~E(f773(f773(f3(f855(x73561,a841)),x73562),f773(f773(f302(x73561),x73563),f180(f855(x73561,a841)))),f180(f855(x73561,a841)))+~P1(f773(f773(f334(x73561),x73563),x73562))
% 191.21/191.75 [7357]~P100(x73571)+E(f17(x73571,x73572),x73573)+~P1(f773(f63(x73571),x73572))+~E(f773(f773(f3(f855(x73571,a841)),x73572),f773(f773(f302(x73571),x73573),f180(f855(x73571,a841)))),f180(f855(x73571,a841)))+~P1(f773(f773(f334(x73571),x73573),x73572))
% 191.21/191.75 [7358]~P93(x73581)+E(f12(x73581,x73582),x73583)+~P1(f773(f63(x73581),x73582))+~E(f773(f773(f3(f855(x73581,a841)),x73582),f773(f773(f302(x73581),x73583),f180(f855(x73581,a841)))),f180(f855(x73581,a841)))+~P1(f773(f773(f334(x73581),x73583),x73582))
% 191.21/191.75 [7458]~P100(x74581)+E(f13(x74581,f179(x74581),x74582),x74583)+~P1(f773(f63(x74581),x74582))+~E(f773(f773(f3(f855(x74581,a841)),x74582),f773(f773(f302(x74581),x74583),f180(f855(x74581,a841)))),f180(f855(x74581,a841)))+~P1(f773(f773(f334(x74581),x74583),x74582))
% 191.21/191.75 [7459]~P100(x74591)+E(f14(x74591,f236(x74591),x74592),x74593)+~P1(f773(f63(x74591),x74592))+~E(f773(f773(f3(f855(x74591,a841)),x74592),f773(f773(f302(x74591),x74593),f180(f855(x74591,a841)))),f180(f855(x74591,a841)))+~P1(f773(f773(f334(x74591),x74593),x74592))
% 191.21/191.75 [7496]~P100(x74962)+E(x74961,f180(f855(x74962,a841)))+~P1(f773(f63(x74962),x74961))+~P1(f773(f773(f233(x74962),x74963),f547(x74963,x74961,x74962)))+P1(f773(f773(f233(x74962),x74963),f773(f65(x74962,f236(x74962)),x74961)))
% 191.21/191.75 [7497]~P100(x74972)+E(x74971,f180(f855(x74972,a841)))+~P1(f773(f63(x74972),x74971))+~P1(f773(f773(f232(x74972),x74973),f548(x74973,x74971,x74972)))+P1(f773(f773(f232(x74972),x74973),f773(f65(x74972,f236(x74972)),x74971)))
% 191.21/191.75 [7498]~P98(x74982)+E(x74981,f180(f855(x74982,a841)))+~P1(f773(f63(x74982),x74981))+~P1(f773(f773(f232(x74982),x74983),f549(x74983,x74981,x74982)))+P1(f773(f773(f232(x74982),x74983),f773(f65(x74982,f104(x74982)),x74981)))
% 191.21/191.75 [7586]~P98(x75862)+E(x75861,f180(f855(x75862,a841)))+~P1(f773(f63(x75862),x75861))+P1(f773(f773(f334(x75862),f549(x75863,x75861,x75862)),x75861))+P1(f773(f773(f232(x75862),x75863),f773(f65(x75862,f104(x75862)),x75861)))
% 191.21/191.75 [7587]~P100(x75872)+E(x75871,f180(f855(x75872,a841)))+~P1(f773(f63(x75872),x75871))+P1(f773(f773(f334(x75872),f548(x75873,x75871,x75872)),x75871))+P1(f773(f773(f232(x75872),x75873),f773(f65(x75872,f236(x75872)),x75871)))
% 191.21/191.75 [7588]~P100(x75882)+E(x75881,f180(f855(x75882,a841)))+~P1(f773(f63(x75882),x75881))+P1(f773(f773(f334(x75882),f547(x75883,x75881,x75882)),x75881))+P1(f773(f773(f233(x75882),x75883),f773(f65(x75882,f236(x75882)),x75881)))
% 191.21/191.75 [7708]~P100(x77082)+E(x77081,f180(f855(x77082,a841)))+E(f773(f773(f236(x77082),f14(x77082,f236(x77082),x77081)),f14(x77082,f236(x77082),x77083)),f14(x77082,f236(x77082),x77083))+~P1(f773(f63(x77082),x77083))+~P1(f773(f773(f232(f855(x77082,a841)),x77081),x77083))
% 191.21/191.75 [7709]~P100(x77092)+E(x77091,f180(f855(x77092,a841)))+E(f773(f773(f179(x77092),f13(x77092,f179(x77092),x77091)),f13(x77092,f179(x77092),x77093)),f13(x77092,f179(x77092),x77093))+~P1(f773(f63(x77092),x77093))+~P1(f773(f773(f232(f855(x77092,a841)),x77091),x77093))
% 191.21/191.75 [7911]~E(f675(x79111,x79113,x79112),f676(x79111,x79113,x79112))+~E(f773(f42(x79112),f677(x79111,x79113,x79112)),x79111)+E(f773(f773(f83(a847),x79111),f773(f42(f855(x79112,a841)),x79113)),f773(f42(x79112),f44(f855(x79112,a841),x79113)))+~P1(f773(f63(x79112),f44(f855(x79112,a841),x79113)))+~P1(f773(f63(f855(x79112,a841)),x79113))
% 191.21/191.75 [8086]~P100(x80862)+E(x80861,f180(f855(x80862,a841)))+~P1(f773(f63(x80862),x80863))+P1(f773(f773(f232(x80862),f773(f65(x80862,f236(x80862)),x80863)),f773(f65(x80862,f236(x80862)),x80861)))+~P1(f773(f773(f232(f855(x80862,a841)),x80861),x80863))
% 191.21/191.75 [8390]~E(f675(x83901,x83903,x83902),f676(x83901,x83903,x83902))+E(f773(f773(f83(a847),x83901),f773(f42(f855(x83902,a841)),x83903)),f773(f42(x83902),f44(f855(x83902,a841),x83903)))+P1(f773(f773(f334(f855(x83902,a841)),f677(x83901,x83903,x83902)),x83903))+~P1(f773(f63(x83902),f44(f855(x83902,a841),x83903)))+~P1(f773(f63(f855(x83902,a841)),x83903))
% 191.21/191.75 [8414]~E(f773(f42(x84142),f677(x84141,x84143,x84142)),x84141)+E(f773(f773(f83(a847),x84141),f773(f42(f855(x84142,a841)),x84143)),f773(f42(x84142),f44(f855(x84142,a841),x84143)))+P1(f773(f773(f334(f855(x84142,a841)),f676(x84141,x84143,x84142)),x84143))+~P1(f773(f63(x84142),f44(f855(x84142,a841),x84143)))+~P1(f773(f63(f855(x84142,a841)),x84143))
% 191.21/191.75 [8415]~E(f773(f42(x84152),f677(x84151,x84153,x84152)),x84151)+E(f773(f773(f83(a847),x84151),f773(f42(f855(x84152,a841)),x84153)),f773(f42(x84152),f44(f855(x84152,a841),x84153)))+P1(f773(f773(f334(f855(x84152,a841)),f675(x84151,x84153,x84152)),x84153))+~P1(f773(f63(x84152),f44(f855(x84152,a841),x84153)))+~P1(f773(f63(f855(x84152,a841)),x84153))
% 191.21/191.75 [8445]~E(f773(f42(x84452),f677(x84451,x84453,x84452)),x84451)+~E(f773(f773(f104(f855(x84452,a841)),f676(x84451,x84453,x84452)),f675(x84451,x84453,x84452)),f180(f855(x84452,a841)))+E(f773(f773(f83(a847),x84451),f773(f42(f855(x84452,a841)),x84453)),f773(f42(x84452),f44(f855(x84452,a841),x84453)))+~P1(f773(f63(f855(x84452,a841)),x84453))+~P1(f773(f63(x84452),f44(f855(x84452,a841),x84453)))
% 191.21/191.75 [8671]E(f773(f773(f83(a847),x86711),f773(f42(f855(x86712,a841)),x86713)),f773(f42(x86712),f44(f855(x86712,a841),x86713)))+P1(f773(f773(f334(f855(x86712,a841)),f677(x86711,x86713,x86712)),x86713))+P1(f773(f773(f334(f855(x86712,a841)),f676(x86711,x86713,x86712)),x86713))+~P1(f773(f63(f855(x86712,a841)),x86713))+~P1(f773(f63(x86712),f44(f855(x86712,a841),x86713)))
% 191.21/191.75 [8672]E(f773(f773(f83(a847),x86721),f773(f42(f855(x86722,a841)),x86723)),f773(f42(x86722),f44(f855(x86722,a841),x86723)))+P1(f773(f773(f334(f855(x86722,a841)),f677(x86721,x86723,x86722)),x86723))+P1(f773(f773(f334(f855(x86722,a841)),f675(x86721,x86723,x86722)),x86723))+~P1(f773(f63(f855(x86722,a841)),x86723))+~P1(f773(f63(x86722),f44(f855(x86722,a841),x86723)))
% 191.21/191.75 [8697]~E(f773(f773(f104(f855(x86972,a841)),f676(x86971,x86973,x86972)),f675(x86971,x86973,x86972)),f180(f855(x86972,a841)))+E(f773(f773(f83(a847),x86971),f773(f42(f855(x86972,a841)),x86973)),f773(f42(x86972),f44(f855(x86972,a841),x86973)))+~P1(f773(f63(f855(x86972,a841)),x86973))+P1(f773(f773(f334(f855(x86972,a841)),f677(x86971,x86973,x86972)),x86973))+~P1(f773(f63(x86972),f44(f855(x86972,a841),x86973)))
% 191.21/191.75 [8925]~P91(x89252)+E(x89251,f180(f855(x89252,a841)))+~E(f773(f773(f83(x89252),f773(x89253,f567(x89251,x89253,x89252))),f773(x89253,f568(x89251,x89253,x89252))),f773(x89253,f773(f773(f83(x89252),f567(x89251,x89253,x89252)),f568(x89251,x89253,x89252))))+~P1(f773(f63(x89252),x89251))+E(f773(f65(x89252,f83(x89252)),f773(f303(x89252,x89252,x89253),x89251)),f773(x89253,f773(f65(x89252,f83(x89252)),x89251)))
% 191.21/191.75 [9792]P1(f773(f773(x97921,x97922),x97923))+P1(f773(f773(f233(a1),f824(x97921,x97923,x97922)),f825(x97921,x97923,x97922)))+P1(f773(f773(f232(a1),f825(x97921,x97923,x97922)),f2(a1)))+P1(f773(f773(x97921,f824(x97921,x97923,x97922)),f773(f773(f83(a1),f773(f106(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),f825(x97921,x97923,x97922))))+~P1(f773(f321(f854(a1,a1),a62),f773(f773(f241(a1,a1),x97922),x97923)))
% 191.21/191.75 [9798]P1(f773(f773(x97981,x97982),x97983))+P1(f773(f773(f232(a1),f823(x97981,x97983,x97982)),f2(a1)))+P1(f773(f773(x97981,f822(x97981,x97983,x97982)),f773(f773(f83(a1),f773(f106(a1),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),f823(x97981,x97983,x97982))))+P1(f773(f773(f232(a1),f2(a1)),f773(f773(f82(a1),f822(x97981,x97983,x97982)),f823(x97981,x97983,x97982))))+~P1(f773(f321(f854(a1,a1),a59),f773(f773(f241(a1,a1),x97982),x97983)))
% 191.21/191.75 [7881]~P110(x78811)+~P1(f773(f773(f232(x78811),x78812),f80(x78811)))+~P1(f773(f773(f232(x78811),f2(x78811)),x78812))+~P1(f773(f773(f232(x78811),f2(x78811)),x78813))+P1(f773(f773(f232(x78811),f773(f773(f83(x78811),x78812),x78813)),x78813))
% 191.21/191.75 [7882]~P110(x78821)+~P1(f773(f773(f232(x78821),x78823),f80(x78821)))+~P1(f773(f773(f232(x78821),f2(x78821)),x78823))+~P1(f773(f773(f232(x78821),f2(x78821)),x78822))+P1(f773(f773(f232(x78821),f773(f773(f83(x78821),x78822),x78823)),x78822))
% 191.21/191.75 [8231]~P100(x82312)+E(x82311,f180(f855(x82312,a841)))+~P1(f773(f63(x82312),x82311))+P1(f773(f773(f334(x82312),f552(x82313,x82311,x82312)),x82311))+~P1(f773(f773(f232(x82312),f773(f65(x82312,f236(x82312)),x82311)),x82313))
% 191.21/191.75 [8232]~P100(x82322)+E(x82321,f180(f855(x82322,a841)))+~P1(f773(f63(x82322),x82321))+P1(f773(f773(f334(x82322),f553(x82323,x82321,x82322)),x82321))+~P1(f773(f773(f233(x82322),f773(f65(x82322,f236(x82322)),x82321)),x82323))
% 191.21/191.75 [8233]~P100(x82332)+E(x82331,f180(f855(x82332,a841)))+~P1(f773(f63(x82332),x82331))+P1(f773(f773(f233(x82332),f553(x82333,x82331,x82332)),x82333))+~P1(f773(f773(f233(x82332),f773(f65(x82332,f236(x82332)),x82331)),x82333))
% 191.21/191.75 [8234]~P100(x82342)+E(x82341,f180(f855(x82342,a841)))+~P1(f773(f63(x82342),x82341))+P1(f773(f773(f232(x82342),f552(x82343,x82341,x82342)),x82343))+~P1(f773(f773(f232(x82342),f773(f65(x82342,f236(x82342)),x82341)),x82343))
% 191.21/191.75 [8319]~P1(f773(x83191,x83193))+P1(f773(x83191,f351(x83191,x83192)))+P1(f773(x83191,f350(x83191,x83192)))+~P1(f773(f773(f233(a1),f2(a1)),x83192))+P1(f773(x83191,f773(f773(f3(a1),f350(x83191,x83192)),f773(f773(f83(a1),f352(x83191,x83192)),x83192))))
% 191.21/191.75 [8537]~P1(f773(x85371,x85373))+P1(f773(x85371,f350(x85371,x85372)))+~P1(f773(f773(f233(a1),f2(a1)),x85372))+P1(f773(f773(f334(a1),f351(x85371,x85372)),f295(a1,f80(a1),x85372)))+P1(f773(x85371,f773(f773(f3(a1),f350(x85371,x85372)),f773(f773(f83(a1),f352(x85371,x85372)),x85372))))
% 191.21/191.75 [8715]~P1(f773(x87151,x87153))+~P1(f773(x87151,f350(x87151,x87152)))+P1(f773(x87151,f351(x87151,x87152)))+~P1(f773(f773(f233(a1),f2(a1)),x87152))+~P1(f773(x87151,f773(f773(f3(a1),f350(x87151,x87152)),f773(f773(f83(a1),f352(x87151,x87152)),x87152))))
% 191.21/191.75 [8818]~P1(f773(x88181,x88183))+~P1(f773(x88181,f350(x88181,x88182)))+~P1(f773(f773(f233(a1),f2(a1)),x88182))+P1(f773(f773(f334(a1),f351(x88181,x88182)),f295(a1,f80(a1),x88182)))+~P1(f773(x88181,f773(f773(f3(a1),f350(x88181,x88182)),f773(f773(f83(a1),f352(x88181,x88182)),x88182))))
% 191.21/191.75 [8634]~P93(x86341)+~P1(f773(f63(x86341),x86342))+E(f773(f773(f3(f855(x86341,a841)),x86342),f773(f773(f302(x86341),x86343),f180(f855(x86341,a841)))),f180(f855(x86341,a841)))+~P1(f773(f773(f334(x86341),x86343),x86342))+E(f773(f773(f103(x86341),x86343),f15(x86341,f773(f773(f3(f855(x86341,a841)),x86342),f773(f773(f302(x86341),x86343),f180(f855(x86341,a841)))))),f15(x86341,x86342))
% 191.21/191.75 [8635]~P100(x86351)+~P1(f773(f63(x86351),x86352))+E(f773(f773(f3(f855(x86351,a841)),x86352),f773(f773(f302(x86351),x86353),f180(f855(x86351,a841)))),f180(f855(x86351,a841)))+~P1(f773(f773(f334(x86351),x86353),x86352))+E(f773(f773(f179(x86351),x86353),f16(x86351,f773(f773(f3(f855(x86351,a841)),x86352),f773(f773(f302(x86351),x86353),f180(f855(x86351,a841)))))),f16(x86351,x86352))
% 191.21/191.75 [8636]~P100(x86361)+~P1(f773(f63(x86361),x86362))+E(f773(f773(f3(f855(x86361,a841)),x86362),f773(f773(f302(x86361),x86363),f180(f855(x86361,a841)))),f180(f855(x86361,a841)))+~P1(f773(f773(f334(x86361),x86363),x86362))+E(f773(f773(f236(x86361),x86363),f17(x86361,f773(f773(f3(f855(x86361,a841)),x86362),f773(f773(f302(x86361),x86363),f180(f855(x86361,a841)))))),f17(x86361,x86362))
% 191.21/191.75 [8637]~P93(x86371)+~P1(f773(f63(x86371),x86372))+E(f773(f773(f3(f855(x86371,a841)),x86372),f773(f773(f302(x86371),x86373),f180(f855(x86371,a841)))),f180(f855(x86371,a841)))+~P1(f773(f773(f334(x86371),x86373),x86372))+E(f773(f773(f104(x86371),x86373),f12(x86371,f773(f773(f3(f855(x86371,a841)),x86372),f773(f773(f302(x86371),x86373),f180(f855(x86371,a841)))))),f12(x86371,x86372))
% 191.21/191.75 [8692]~P100(x86921)+~P1(f773(f63(x86921),x86922))+E(f773(f773(f3(f855(x86921,a841)),x86922),f773(f773(f302(x86921),x86923),f180(f855(x86921,a841)))),f180(f855(x86921,a841)))+~P1(f773(f773(f334(x86921),x86923),x86922))+E(f773(f773(f179(x86921),x86923),f13(x86921,f179(x86921),f773(f773(f3(f855(x86921,a841)),x86922),f773(f773(f302(x86921),x86923),f180(f855(x86921,a841)))))),f13(x86921,f179(x86921),x86922))
% 191.21/191.75 [8693]~P100(x86931)+~P1(f773(f63(x86931),x86932))+E(f773(f773(f3(f855(x86931,a841)),x86932),f773(f773(f302(x86931),x86933),f180(f855(x86931,a841)))),f180(f855(x86931,a841)))+~P1(f773(f773(f334(x86931),x86933),x86932))+E(f773(f773(f236(x86931),x86933),f14(x86931,f236(x86931),f773(f773(f3(f855(x86931,a841)),x86932),f773(f773(f302(x86931),x86933),f180(f855(x86931,a841)))))),f14(x86931,f236(x86931),x86932))
% 191.21/191.75 [8703]~P100(x87031)+~P1(f773(f63(x87031),x87033))+~P1(f773(f63(x87031),x87032))+E(f773(f773(f104(f855(x87031,a841)),x87032),x87033),f180(f855(x87031,a841)))+E(f773(f773(f236(x87031),f17(x87031,f773(f773(f103(f855(x87031,a841)),x87032),x87033))),f17(x87031,f773(f773(f104(f855(x87031,a841)),x87032),x87033))),f773(f773(f236(x87031),f17(x87031,x87032)),f17(x87031,x87033)))
% 191.21/191.75 [8704]~P100(x87041)+~P1(f773(f63(x87041),x87043))+~P1(f773(f63(x87041),x87042))+E(f773(f773(f104(f855(x87041,a841)),x87042),x87043),f180(f855(x87041,a841)))+E(f773(f773(f179(x87041),f16(x87041,f773(f773(f103(f855(x87041,a841)),x87042),x87043))),f16(x87041,f773(f773(f104(f855(x87041,a841)),x87042),x87043))),f773(f773(f179(x87041),f16(x87041,x87042)),f16(x87041,x87043)))
% 191.21/191.75 [8705]~P93(x87051)+~P1(f773(f63(x87051),x87053))+~P1(f773(f63(x87051),x87052))+E(f773(f773(f104(f855(x87051,a841)),x87052),x87053),f180(f855(x87051,a841)))+E(f773(f773(f103(x87051),f15(x87051,f773(f773(f103(f855(x87051,a841)),x87052),x87053))),f15(x87051,f773(f773(f104(f855(x87051,a841)),x87052),x87053))),f773(f773(f103(x87051),f15(x87051,x87052)),f15(x87051,x87053)))
% 191.21/191.75 [8706]~P93(x87061)+~P1(f773(f63(x87061),x87063))+~P1(f773(f63(x87061),x87062))+E(f773(f773(f104(f855(x87061,a841)),x87062),x87063),f180(f855(x87061,a841)))+E(f773(f773(f104(x87061),f12(x87061,f773(f773(f103(f855(x87061,a841)),x87062),x87063))),f12(x87061,f773(f773(f104(f855(x87061,a841)),x87062),x87063))),f773(f773(f104(x87061),f12(x87061,x87062)),f12(x87061,x87063)))
% 191.21/191.75 [8899]~P100(x88991)+~P1(f773(f63(x88991),x88993))+~P1(f773(f63(x88991),x88992))+E(f773(f773(f104(f855(x88991,a841)),x88992),x88993),f180(f855(x88991,a841)))+E(f773(f773(f236(x88991),f14(x88991,f236(x88991),f773(f773(f103(f855(x88991,a841)),x88992),x88993))),f14(x88991,f236(x88991),f773(f773(f104(f855(x88991,a841)),x88992),x88993))),f773(f773(f236(x88991),f14(x88991,f236(x88991),x88992)),f14(x88991,f236(x88991),x88993)))
% 191.21/191.75 [8900]~P100(x89001)+~P1(f773(f63(x89001),x89003))+~P1(f773(f63(x89001),x89002))+E(f773(f773(f104(f855(x89001,a841)),x89002),x89003),f180(f855(x89001,a841)))+E(f773(f773(f179(x89001),f13(x89001,f179(x89001),f773(f773(f103(f855(x89001,a841)),x89002),x89003))),f13(x89001,f179(x89001),f773(f773(f104(f855(x89001,a841)),x89002),x89003))),f773(f773(f179(x89001),f13(x89001,f179(x89001),x89002)),f13(x89001,f179(x89001),x89003)))
% 191.21/191.75 [9634]~P117(x96343)+E(x96341,x96342)+~P1(f773(f773(f232(x96343),f2(x96343)),x96342))+~P1(f773(f773(f232(x96343),f2(x96343)),x96341))+~E(f773(f773(f242(x96343),x96341),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))),f773(f773(f242(x96343),x96342),f773(f106(a847),f773(f773(f82(a1),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)),f773(f773(f3(a1),f773(f773(f82(a1),a85),a85)),a99)))))
% 191.21/191.75 [6578]P142(x65781,x65782)+~P142(x65781,x65783)+~P39(a858,x65783,x65784,x65782)+~P31(a840,x65784,f772(x65784))+~P1(f773(a853,x65783))
% 191.21/191.75 [5752]~P7(x57522)+E(x57521,f2(x57522))+~E(f773(f773(f43(x57522),x57523),x57521),x57524)+E(x57523,f773(f773(f83(x57522),x57524),x57521))+~P1(f773(f773(f279(x57522),x57521),x57523))
% 191.21/191.75 [5753]~P7(x57532)+E(x57531,f2(x57532))+~E(x57533,f773(f773(f83(x57532),x57534),x57531))+E(f773(f773(f43(x57532),x57533),x57531),x57534)+~P1(f773(f773(f279(x57532),x57531),x57533))
% 191.21/191.75 [6217]E(f404(x62171,x62172,x62173),x62174)+E(f773(x62171,x62174),f2(a847))+~E(f773(f773(f8(x62173,a847),x62171),x62172),f80(a847))+~P1(f773(f63(x62173),x62172))+~P1(f773(f773(f334(x62173),x62174),x62172))
% 191.21/191.75 [6285]E(f406(x62851,x62852,x62853),x62854)+E(f773(x62851,x62854),f2(a847))+~E(f773(f773(f8(x62853,a847),x62851),x62852),f773(a114,f2(a847)))+~P1(f773(f63(x62853),x62852))+~P1(f773(f773(f334(x62853),x62854),x62852))
% 191.21/191.75 [6399]~P100(x63991)+~P9(x63991)+P1(f773(f773(f233(x63991),x63992),f44(x63991,x63993)))+~P1(f773(f773(f233(x63991),x63992),x63994))+~P1(f773(f773(f334(x63991),x63994),x63993))
% 191.21/191.75 [6577]~P100(x65771)+~P9(x65771)+~P1(f773(f773(f233(x65771),x65774),x65773))+P1(f773(f773(f233(x65771),f45(x65771,x65772)),x65773))+~P1(f773(f773(f334(x65771),x65774),x65772))
% 191.21/191.75 [6735]P142(x67351,x67352)+~P142(x67351,x67354)+~P39(a858,x67354,x67353,x67352)+~P1(f773(a853,x67354))+P1(f773(f773(f334(f846(a840)),f772(x67353)),a857))
% 191.21/191.75 [6855]~P117(x68553)+E(x68551,x68552)+~E(f773(f773(f242(x68553),x68551),f773(a114,x68554)),f773(f773(f242(x68553),x68552),f773(a114,x68554)))+~P1(f773(f773(f232(x68553),f2(x68553)),x68552))+~P1(f773(f773(f232(x68553),f2(x68553)),x68551))
% 191.21/191.75 [7066]~E(f409(x70662,x70663,x70661,x70664),x70664)+~E(f773(x70662,x70664),f80(a847))+E(f773(f773(f8(x70661,a847),x70662),x70663),f80(a847))+~P1(f773(f63(x70661),x70663))+~P1(f773(f773(f334(x70661),x70664),x70663))
% 191.21/191.75 [7073]~P85(x70734)+~P127(x70734)+E(f773(x70731,f451(x70731,x70732,x70733,x70734)),f2(x70734))+~E(f773(f773(f11(x70733,x70734),x70731),x70732),f2(x70734))+~P1(f773(f63(x70733),x70732))
% 191.21/191.75 [7156]~E(f408(x71562,x71563,x71561,x71564),x71564)+~E(f773(x71562,x71564),f773(a114,f2(a847)))+E(f773(f773(f8(x71561,a847),x71562),x71563),f773(a114,f2(a847)))+~P1(f773(f63(x71561),x71563))+~P1(f773(f773(f334(x71561),x71564),x71563))
% 191.21/191.75 [7921]~E(f773(x79212,x79214),f80(a847))+~E(f773(x79212,f409(x79212,x79213,x79211,x79214)),f2(a847))+E(f773(f773(f8(x79211,a847),x79212),x79213),f80(a847))+~P1(f773(f63(x79211),x79213))+~P1(f773(f773(f334(x79211),x79214),x79213))
% 191.21/191.75 [7966]~E(f773(x79662,x79664),f773(a114,f2(a847)))+~E(f773(x79662,f408(x79662,x79663,x79661,x79664)),f2(a847))+E(f773(f773(f8(x79661,a847),x79662),x79663),f773(a114,f2(a847)))+~P1(f773(f63(x79661),x79663))+~P1(f773(f773(f334(x79661),x79664),x79663))
% 191.21/191.75 [8045]~P136(x80452)+~P112(x80452)+~P1(f773(x80451,x80454))+~P1(f773(f773(f279(x80452),x80453),f773(f773(f82(x80452),x80454),f2(x80452))))+P1(f773(x80451,f773(f773(f83(x80452),x80453),f837(x80453,x80451,x80452))))
% 191.21/191.75 [8540]E(x85401,x85402)+E(f773(f773(f82(a1),f433(x85403,x85402,x85404,x85401)),f434(x85403,x85402,x85404,x85401)),x85401)+~E(f773(f773(f3(a1),x85401),x85404),x85402)+~P1(f773(f773(f233(a1),f2(a1)),x85404))+~P1(f773(f773(f334(a1),x85402),x85403))
% 191.21/191.75 [8541]E(x85411,x85412)+E(f773(f773(f3(a1),f423(x85413,x85412,x85414,x85411)),f424(x85413,x85412,x85414,x85411)),x85411)+~E(f773(f773(f82(a1),x85411),x85414),x85412)+~P1(f773(f773(f233(a1),f2(a1)),x85414))+~P1(f773(f773(f334(a1),x85412),x85413))
% 191.21/191.75 [8702]E(f773(x87021,f815(x87022,x87021,x87023,x87024)),x87022)+P1(f773(f773(f232(a847),x87024),f816(x87022,x87021,x87023,x87024)))+~P1(f773(f773(f232(a1),x87022),f773(x87021,x87023)))+~P1(f773(f773(f233(a847),x87024),x87023))+~P1(f773(f773(f232(a1),f773(x87021,x87024)),x87022))
% 191.21/191.75 [8719]~P85(x87194)+~P127(x87194)+~E(f773(f773(f11(x87191,x87194),x87192),x87193),f2(x87194))+~P1(f773(f63(x87191),x87193))+P1(f773(f773(f334(x87191),f451(x87192,x87193,x87191,x87194)),x87193))
% 191.21/191.75 [8752]~E(f773(x87522,x87524),f80(a847))+E(f773(f773(f8(x87521,a847),x87522),x87523),f80(a847))+~P1(f773(f63(x87521),x87523))+~P1(f773(f773(f334(x87521),x87524),x87523))+P1(f773(f773(f334(x87521),f409(x87522,x87523,x87521,x87524)),x87523))
% 191.21/191.75 [8761]E(x87611,x87612)+~E(f773(f773(f82(a1),x87612),x87614),x87611)+~P1(f773(f773(f233(a1),f2(a1)),x87614))+~P1(f773(f773(f334(a1),x87611),x87613))+P1(f773(f773(f334(a1),f423(x87613,x87611,x87614,x87612)),x87613))
% 191.21/191.75 [8762]E(x87621,x87622)+~E(f773(f773(f3(a1),x87622),x87624),x87621)+~P1(f773(f773(f233(a1),f2(a1)),x87624))+~P1(f773(f773(f334(a1),x87621),x87623))+P1(f773(f773(f334(a1),f433(x87623,x87621,x87624,x87622)),x87623))
% 191.21/191.75 [8764]~E(f773(x87642,x87644),f773(a114,f2(a847)))+E(f773(f773(f8(x87641,a847),x87642),x87643),f773(a114,f2(a847)))+~P1(f773(f63(x87641),x87643))+~P1(f773(f773(f334(x87641),x87644),x87643))+P1(f773(f773(f334(x87641),f408(x87642,x87643,x87641,x87644)),x87643))
% 191.21/191.75 [8768]P57(x87682,x87683,x87684,x87681)+E(x87681,f180(f855(x87682,a841)))+~P1(f773(f63(x87682),x87684))+~P1(f773(f63(x87682),x87681))+P1(f773(f773(f334(x87682),f537(x87681,x87684,x87683,x87682)),x87684))
% 191.21/191.75 [8831]E(x88311,x88312)+~E(f773(f773(f82(a1),x88312),x88314),x88311)+~P1(f773(f773(f233(a1),f2(a1)),x88314))+~P1(f773(f773(f334(a1),x88311),x88313))+P1(f773(f773(f334(a1),f424(x88313,x88311,x88314,x88312)),f295(a1,f80(a1),x88314)))
% 191.21/191.75 [8832]E(x88321,x88322)+~E(f773(f773(f3(a1),x88322),x88324),x88321)+~P1(f773(f773(f233(a1),f2(a1)),x88324))+~P1(f773(f773(f334(a1),x88321),x88323))+P1(f773(f773(f334(a1),f434(x88323,x88321,x88324,x88322)),f295(a1,f80(a1),x88324)))
% 191.21/191.75 [8905]P1(f773(f773(f232(a847),x89051),f815(x89052,x89053,x89054,x89051)))+~P1(f773(f773(f232(a1),x89052),f773(x89053,x89054)))+P1(f773(f773(f232(a847),x89051),f816(x89052,x89053,x89054,x89051)))+~P1(f773(f773(f233(a847),x89051),x89054))+~P1(f773(f773(f232(a1),f773(x89053,x89051)),x89052))
% 191.21/191.75 [9012]E(f773(x90121,f815(x90122,x90121,x90123,x90124)),x90122)+~P1(f773(f773(f232(a1),x90122),f773(x90121,x90123)))+P1(f773(f773(f233(a847),f816(x90122,x90121,x90123,x90124)),x90123))+~P1(f773(f773(f233(a847),x90124),x90123))+~P1(f773(f773(f232(a1),f773(x90121,x90124)),x90122))
% 191.21/191.75 [9117]~P1(f773(f773(f279(a847),x91174),x91171))+~P1(f773(f773(f279(a847),x91174),x91173))+~P1(f773(f773(f279(a847),x91172),x91171))+P1(f773(f773(f279(a847),x91171),x91172))+P1(f773(f773(f233(f855(a847,a841)),f282(a847,f279(a847),x91173,x91172)),f282(a847,f279(a847),x91174,x91171)))
% 191.21/191.75 [9118]~P1(f773(f773(f279(a847),x91182),x91181))+~P1(f773(f773(f279(a847),x91183),x91184))+~P1(f773(f773(f279(a847),x91182),x91184))+P1(f773(f773(f279(a847),x91181),x91182))+P1(f773(f773(f233(f855(a847,a841)),f282(a847,f279(a847),x91181,x91183)),f282(a847,f279(a847),x91182,x91184)))
% 191.21/191.75 [9129]~P1(f773(f773(f232(a1),x91292),f773(x91293,x91294)))+P1(f773(f773(f232(a847),x91291),f816(x91292,x91293,x91294,x91291)))+P1(f773(f773(f232(a847),f815(x91292,x91293,x91294,x91291)),x91294))+~P1(f773(f773(f233(a847),x91291),x91294))+~P1(f773(f773(f232(a1),f773(x91293,x91291)),x91292))
% 191.21/191.75 [9130]~P1(f773(f773(f232(a1),x91302),f773(x91303,x91304)))+P1(f773(f773(f232(a847),x91301),f815(x91302,x91303,x91304,x91301)))+P1(f773(f773(f233(a847),f816(x91302,x91303,x91304,x91301)),x91304))+~P1(f773(f773(f233(a847),x91301),x91304))+~P1(f773(f773(f232(a1),f773(x91303,x91301)),x91302))
% 191.21/191.75 [9217]~P1(f773(f773(f232(a1),x92171),f773(x92172,x92173)))+P1(f773(f773(f232(a847),f815(x92171,x92172,x92173,x92174)),x92173))+~P1(f773(f773(f233(a847),x92174),x92173))+~P1(f773(f773(f232(a1),f773(x92172,x92174)),x92171))+P1(f773(f773(f233(a847),f816(x92171,x92172,x92173,x92174)),x92173))
% 191.21/191.75 [9301]E(x93011,f180(f855(x93012,a841)))+~P1(f773(f63(x93012),x93014))+~P1(f773(f63(x93012),x93011))+P1(f773(f773(f334(f854(f855(x93012,a841),f855(x93012,a841))),f773(f773(f241(f855(x93012,a841),f855(x93012,a841)),x93014),x93011)),f324(x93012,x93013)))+P1(f773(f773(f334(x93012),f539(x93013,x93011,x93014,x93012)),x93014))
% 191.21/191.75 [9302]E(x93021,f180(f855(x93022,a841)))+~P1(f773(f63(x93022),x93024))+~P1(f773(f63(x93022),x93021))+P1(f773(f773(f334(f854(f855(x93022,a841),f855(x93022,a841))),f773(f773(f241(f855(x93022,a841),f855(x93022,a841)),x93024),x93021)),f324(x93022,x93023)))+P1(f773(f773(f334(x93022),f623(x93023,x93021,x93024,x93022)),x93024))
% 191.21/191.75 [9945]E(f773(x99451,f815(x99452,x99451,x99453,x99454)),x99452)+~P1(f773(f773(f232(a1),x99452),f773(x99451,x99453)))+~P1(f773(f773(f232(a1),f773(f77(a1),f773(f773(f3(a1),f773(x99451,f773(f773(f82(a847),f816(x99452,x99451,x99453,x99454)),f80(a847)))),f773(x99451,f816(x99452,x99451,x99453,x99454))))),f80(a1)))+~P1(f773(f773(f233(a847),x99454),x99453))+~P1(f773(f773(f232(a1),f773(x99451,x99454)),x99452))
% 191.21/191.75 [9946]~P1(f773(f773(f232(a1),x99462),f773(x99463,x99464)))+P1(f773(f773(f232(a847),x99461),f815(x99462,x99463,x99464,x99461)))+~P1(f773(f773(f232(a1),f773(f77(a1),f773(f773(f3(a1),f773(x99463,f773(f773(f82(a847),f816(x99462,x99463,x99464,x99461)),f80(a847)))),f773(x99463,f816(x99462,x99463,x99464,x99461))))),f80(a1)))+~P1(f773(f773(f233(a847),x99461),x99464))+~P1(f773(f773(f232(a1),f773(x99463,x99461)),x99462))
% 191.21/191.75 [9947]~P1(f773(f773(f232(a1),x99471),f773(x99472,x99473)))+~P1(f773(f773(f232(a1),f773(f77(a1),f773(f773(f3(a1),f773(x99472,f773(f773(f82(a847),f816(x99471,x99472,x99473,x99474)),f80(a847)))),f773(x99472,f816(x99471,x99472,x99473,x99474))))),f80(a1)))+~P1(f773(f773(f233(a847),x99474),x99473))+~P1(f773(f773(f232(a1),f773(x99472,x99474)),x99471))+P1(f773(f773(f232(a847),f815(x99471,x99472,x99473,x99474)),x99473))
% 191.21/191.75 [7124]~P62(x71241)+P1(f773(f773(f233(x71241),x71242),f2(x71241)))+~P1(f773(f773(f233(x71241),x71243),f2(x71241)))+P1(f773(f773(f233(x71241),f2(x71241)),x71242))+P1(f773(f773(f233(x71241),x71243),f773(f773(f283(x71241),x71244),x71242)))
% 191.21/191.75 [7125]~P62(x71251)+P1(f773(f773(f233(x71251),x71252),f2(x71251)))+~P1(f773(f773(f232(x71251),x71253),f2(x71251)))+P1(f773(f773(f233(x71251),f2(x71251)),x71252))+P1(f773(f773(f232(x71251),x71253),f773(f773(f283(x71251),x71254),x71252)))
% 191.21/191.75 [7396]~P62(x73961)+P1(f773(f773(f233(x73961),x73962),f2(x73961)))+P1(f773(f773(f233(x73961),x73963),f2(x73961)))+P1(f773(f773(f233(x73961),f2(x73961)),x73963))+~P1(f773(f773(f233(x73961),x73962),f773(f773(f283(x73961),x73964),x73963)))
% 191.21/191.75 [7397]~P62(x73971)+P1(f773(f773(f233(x73971),x73972),f2(x73971)))+P1(f773(f773(f232(x73971),x73973),f2(x73971)))+P1(f773(f773(f233(x73971),f2(x73971)),x73972))+~P1(f773(f773(f232(x73971),x73973),f773(f773(f283(x73971),x73974),x73972)))
% 191.21/191.75 [7516]E(x75161,x75162)+~E(f773(f773(f153(x75163),x75164),x75161),f773(f773(f153(x75163),x75164),x75162))+~P1(f773(f127(x75163),x75164))+~P1(f773(f773(f233(a847),x75162),f773(f181(f848(x75163)),x75164)))+~P1(f773(f773(f233(a847),x75161),f773(f181(f848(x75163)),x75164)))
% 191.21/191.75 [7883]~P62(x78831)+~P1(f773(f773(f233(x78831),x78833),f2(x78831)))+P1(f773(f773(f233(x78831),f2(x78831)),x78832))+~P1(f773(f773(f233(x78831),x78834),f773(f773(f83(x78831),x78833),x78832)))+P1(f773(f773(f233(x78831),x78833),f773(f773(f283(x78831),x78834),x78832)))
% 191.21/191.75 [7884]~P62(x78841)+~P1(f773(f773(f232(x78841),x78843),f2(x78841)))+P1(f773(f773(f233(x78841),f2(x78841)),x78842))+~P1(f773(f773(f232(x78841),x78844),f773(f773(f83(x78841),x78843),x78842)))+P1(f773(f773(f232(x78841),x78843),f773(f773(f283(x78841),x78844),x78842)))
% 191.21/191.75 [7885]~P62(x78851)+~P1(f773(f773(f233(x78851),x78852),f2(x78851)))+P1(f773(f773(f233(x78851),f2(x78851)),x78852))+~P1(f773(f773(f233(x78851),x78854),f773(f773(f83(x78851),x78853),x78852)))+P1(f773(f773(f233(x78851),x78853),f773(f773(f283(x78851),x78854),x78852)))
% 191.21/191.75 [7886]~P62(x78861)+~P1(f773(f773(f233(x78861),x78862),f2(x78861)))+P1(f773(f773(f233(x78861),f2(x78861)),x78862))+~P1(f773(f773(f233(x78861),x78864),f773(f773(f283(x78861),x78863),x78862)))+P1(f773(f773(f233(x78861),x78863),f773(f773(f83(x78861),x78864),x78862)))
% 191.21/191.75 [7887]~P62(x78871)+~P1(f773(f773(f233(x78871),x78872),f2(x78871)))+P1(f773(f773(f233(x78871),f2(x78871)),x78872))+~P1(f773(f773(f232(x78871),x78874),f773(f773(f83(x78871),x78873),x78872)))+P1(f773(f773(f232(x78871),x78873),f773(f773(f283(x78871),x78874),x78872)))
% 191.21/191.75 [7888]~P62(x78881)+~P1(f773(f773(f233(x78881),x78882),f2(x78881)))+P1(f773(f773(f233(x78881),f2(x78881)),x78882))+~P1(f773(f773(f232(x78881),x78884),f773(f773(f283(x78881),x78883),x78882)))+P1(f773(f773(f232(x78881),x78883),f773(f773(f83(x78881),x78884),x78882)))
% 191.21/191.75 [8013]~P7(x80131)+~P1(f773(f773(f279(x80131),x80133),x80134))+~P1(f773(f773(f279(x80131),x80133),x80132))+~P1(f773(f773(f279(x80131),x80132),x80134))+P1(f773(f773(f279(x80131),f773(f773(f43(x80131),x80132),x80133)),f773(f773(f43(x80131),x80134),x80133)))
% 191.21/191.75 [8028]~P100(x80281)+~P18(x80281,x80282)+~P1(f773(f773(f232(a847),x80283),x80284))+P1(f773(f773(f232(x80281),f773(f773(f153(x80281),x80282),x80283)),f773(f773(f153(x80281),x80282),x80284)))+~P1(f773(f773(f233(a847),x80284),f773(f181(f848(x80281)),x80282)))
% 191.21/191.75 [8078]~P117(x80781)+~P1(f773(f773(f233(x80781),x80782),f80(x80781)))+~P1(f773(f773(f233(x80781),f2(x80781)),x80782))+~P1(f773(f773(f233(a847),x80784),x80783))+P1(f773(f773(f233(x80781),f773(f773(f242(x80781),x80782),x80783)),f773(f773(f242(x80781),x80782),x80784)))
% 191.21/191.75 [8079]~P117(x80791)+~P1(f773(f773(f232(x80791),x80792),f80(x80791)))+~P1(f773(f773(f232(x80791),f2(x80791)),x80792))+~P1(f773(f773(f232(a847),x80794),x80793))+P1(f773(f773(f232(x80791),f773(f773(f242(x80791),x80792),x80793)),f773(f773(f242(x80791),x80792),x80794)))
% 191.21/191.75 [8080]~P117(x80801)+~P1(f773(f773(f232(x80801),f2(x80801)),x80802))+~P1(f773(f773(f233(a847),f2(a847)),x80803))+~P1(f773(f773(f233(x80801),x80802),x80804))+P1(f773(f773(f233(x80801),f773(f773(f242(x80801),x80802),x80803)),f773(f773(f242(x80801),x80804),x80803)))
% 191.21/191.75 [8098]~P100(x80981)+~P18(x80981,f773(f142(x80981),x80982))+~P1(f773(f773(f232(a847),x80984),x80983))+P1(f773(f773(f232(x80981),f773(f773(f153(x80981),x80982),x80983)),f773(f773(f153(x80981),x80982),x80984)))+~P1(f773(f773(f233(a847),x80983),f773(f181(f848(x80981)),x80982)))
% 191.21/191.75 [8326]~P7(x83261)+P1(f773(f773(f279(x83261),x83262),x83263))+~P1(f773(f773(f279(x83261),x83264),x83263))+~P1(f773(f773(f279(x83261),x83264),x83262))+~P1(f773(f773(f279(x83261),f773(f773(f43(x83261),x83262),x83264)),f773(f773(f43(x83261),x83263),x83264)))
% 191.21/191.75 [8343]~P63(x83431)+~P1(f773(f773(f233(x83431),x83432),f2(x83431)))+~P1(f773(f773(f233(x83431),x83433),x83434))+~P1(f773(f773(f233(x83431),f2(x83431)),f773(f773(f83(x83431),x83433),x83434)))+P1(f773(f773(f233(x83431),f773(f773(f283(x83431),x83432),x83433)),f773(f773(f283(x83431),x83432),x83434)))
% 191.21/191.75 [8344]~P62(x83441)+~P1(f773(f773(f232(x83441),x83442),f2(x83441)))+~P1(f773(f773(f232(x83441),x83443),x83444))+~P1(f773(f773(f233(x83441),f2(x83441)),f773(f773(f83(x83441),x83443),x83444)))+P1(f773(f773(f232(x83441),f773(f773(f283(x83441),x83442),x83443)),f773(f773(f283(x83441),x83442),x83444)))
% 191.21/191.75 [8354]~P63(x83541)+~P1(f773(f773(f233(x83541),x83544),x83543))+~P1(f773(f773(f233(x83541),f2(x83541)),x83542))+~P1(f773(f773(f233(x83541),f2(x83541)),f773(f773(f83(x83541),x83543),x83544)))+P1(f773(f773(f233(x83541),f773(f773(f283(x83541),x83542),x83543)),f773(f773(f283(x83541),x83542),x83544)))
% 191.21/191.75 [8355]~P63(x83551)+~P1(f773(f773(f232(x83551),x83554),x83553))+~P1(f773(f773(f232(x83551),f2(x83551)),x83552))+~P1(f773(f773(f233(x83551),f2(x83551)),f773(f773(f83(x83551),x83553),x83554)))+P1(f773(f773(f232(x83551),f773(f773(f283(x83551),x83552),x83553)),f773(f773(f283(x83551),x83552),x83554)))
% 191.21/191.75 [8463]P1(f773(x84631,x84632))+~P1(f773(f63(x84634),x84632))+P1(f773(x84631,f486(x84631,x84633,x84632,x84634)))+~P1(f773(x84631,f180(f855(x84634,a841))))+~P1(f773(f773(f232(f855(x84634,a841)),x84632),x84633))
% 191.21/191.75 [8471]P1(f773(x84711,x84712))+P1(f773(f63(x84713),f486(x84711,x84714,x84712,x84713)))+~P1(f773(f63(x84713),x84712))+~P1(f773(x84711,f180(f855(x84713,a841))))+~P1(f773(f773(f232(f855(x84713,a841)),x84712),x84714))
% 191.21/191.75 [8699]E(f773(f773(f82(a1),f436(x86991,x86992,x86993,x86994)),f437(x86991,x86992,x86993,x86994)),x86994)+~P1(f773(f773(f233(a1),f2(a1)),x86993))+~P1(f773(f773(f233(a1),x86992),x86994))+~P1(f773(f773(f334(a1),x86992),x86991))+P1(f773(f773(f233(a1),x86992),f773(f773(f3(a1),x86994),x86993)))
% 191.21/191.75 [8885]~P1(f773(f773(f233(a1),f2(a1)),x88853))+~P1(f773(f773(f233(a1),x88852),x88854))+~P1(f773(f773(f334(a1),x88852),x88851))+P1(f773(f773(f334(a1),f436(x88851,x88852,x88853,x88854)),x88851))+P1(f773(f773(f233(a1),x88852),f773(f773(f3(a1),x88854),x88853)))
% 191.21/191.75 [8898]P1(f773(x88981,x88982))+~P1(f773(f63(x88983),x88982))+P1(f773(f773(f334(x88983),f487(x88981,x88984,x88982,x88983)),x88984))+~P1(f773(x88981,f180(f855(x88983,a841))))+~P1(f773(f773(f232(f855(x88983,a841)),x88982),x88984))
% 191.21/191.75 [8915]E(f773(f773(f82(a1),f428(x89151,x89152,x89153,x89154)),f429(x89151,x89152,x89153,x89154)),x89154)+~P1(f773(f773(f233(a1),f2(a1)),x89153))+~P1(f773(f773(f232(a1),x89152),x89154))+P1(f773(f773(f232(a1),x89152),f773(f773(f3(a1),x89154),x89153)))+~P1(f773(f773(f334(a1),f773(f773(f3(a1),x89152),f80(a1))),x89151))
% 191.21/191.75 [8962]~P1(f773(f773(f233(a1),f2(a1)),x89623))+~P1(f773(f773(f233(a1),x89621),x89622))+~P1(f773(f773(f334(a1),x89621),x89624))+P1(f773(f773(f334(a1),f437(x89624,x89621,x89623,x89622)),f295(a1,f80(a1),x89623)))+P1(f773(f773(f233(a1),x89621),f773(f773(f3(a1),x89622),x89623)))
% 191.21/191.75 [9055]~P1(f773(f773(f233(a1),f2(a1)),x90553))+~P1(f773(f773(f232(a1),x90552),x90554))+P1(f773(f773(f334(a1),f428(x90551,x90552,x90553,x90554)),x90551))+P1(f773(f773(f232(a1),x90552),f773(f773(f3(a1),x90554),x90553)))+~P1(f773(f773(f334(a1),f773(f773(f3(a1),x90552),f80(a1))),x90551))
% 191.21/191.75 [9093]~P1(f773(f773(f233(a1),f2(a1)),x90933))+~P1(f773(f773(f232(a1),x90931),x90932))+P1(f773(f773(f334(a1),f429(x90934,x90931,x90933,x90932)),f295(a1,f80(a1),x90933)))+P1(f773(f773(f232(a1),x90931),f773(f773(f3(a1),x90932),x90933)))+~P1(f773(f773(f334(a1),f773(f773(f3(a1),x90931),f80(a1))),x90934))
% 191.21/191.75 [9304]P1(f773(x93041,x93042))+~P1(f773(f773(f334(x93043),f487(x93041,x93044,x93042,x93043)),f486(x93041,x93044,x93042,x93043)))+~P1(f773(f63(x93043),x93042))+~P1(f773(x93041,f180(f855(x93043,a841))))+~P1(f773(f773(f232(f855(x93043,a841)),x93042),x93044))
% 191.21/191.75 [9508]P1(f773(x95081,x95082))+~P1(f773(f63(x95083),x95082))+~P1(f773(x95081,f773(f773(f302(x95083),f487(x95081,x95084,x95082,x95083)),f486(x95081,x95084,x95082,x95083))))+~P1(f773(x95081,f180(f855(x95083,a841))))+~P1(f773(f773(f232(f855(x95083,a841)),x95082),x95084))
% 191.21/191.75 [9827]~P99(x98273)+~P52(a847,x98273,f773(f773(f20(a847,f855(a847,a841),f855(a847,a841)),f773(f773(f10(f855(a847,f855(a841,a841)),f855(f855(a847,a841),f855(a847,a841)),a847),f20(a847,a841,a841)),f773(f773(f10(f855(a847,a841),f855(a847,f855(a841,a841)),a847),f773(f10(a841,f855(a841,a841),a847),a331)),f279(a847)))),f773(f773(f10(f855(a847,a841),f855(a847,a841),a847),f773(f10(a841,a841,a847),a328)),f773(f9(a847,a847,a841),f279(a847)))),x98274)+P1(f773(f773(f233(x98273),f773(x98274,x98272)),f773(x98274,x98271)))+~P1(f773(f773(f279(a847),x98272),x98271))+P1(f773(f773(f279(a847),x98271),x98272))
% 191.21/191.75 [7655]~P62(x76551)+P1(f773(f773(f233(x76551),x76552),f2(x76551)))+P1(f773(f773(f233(x76551),f2(x76551)),x76552))+~P1(f773(f773(f233(x76551),f2(x76551)),x76554))+P1(f773(f773(f233(x76551),f773(f773(f283(x76551),x76553),x76552)),x76554))
% 191.21/191.75 [7656]~P62(x76561)+P1(f773(f773(f233(x76561),x76562),f2(x76561)))+~P1(f773(f773(f232(x76561),f2(x76561)),x76564))+P1(f773(f773(f233(x76561),f2(x76561)),x76562))+P1(f773(f773(f232(x76561),f773(f773(f283(x76561),x76563),x76562)),x76564))
% 191.21/191.75 [7939]~P1(f773(f773(f232(a1),x79394),f2(a1)))+~E(x79392,f773(f773(f82(a1),f773(f773(f83(a1),x79391),x79393)),x79394))+P1(f773(f773(f233(a1),f2(a1)),x79391))+~P1(f773(f773(f233(a1),x79391),x79394))+P1(f773(f56(x79392,x79391),f773(f773(f241(a1,a1),x79393),x79394)))
% 191.21/191.75 [7976]~P1(f773(x79761,x79764))+P1(f773(x79761,f804(x79762,x79761,x79763)))+~P1(f773(f773(f233(a1),f2(a1)),x79763))+~P1(f773(f773(f232(a1),f2(a1)),x79762))+P1(f773(x79761,f773(f773(f82(a1),x79764),f773(f773(f83(a1),x79762),x79763))))
% 191.21/191.75 [7977]~P1(f773(x79771,x79774))+P1(f773(x79771,f809(x79772,x79771,x79773)))+~P1(f773(f773(f233(a1),f2(a1)),x79773))+~P1(f773(f773(f232(a1),f2(a1)),x79772))+P1(f773(x79771,f773(f773(f3(a1),x79774),f773(f773(f83(a1),x79772),x79773))))
% 191.21/191.75 [7978]~P62(x79781)+P1(f773(f773(f233(x79781),x79782),f2(x79781)))+P1(f773(f773(f233(x79781),f2(x79781)),x79782))+P1(f773(f773(f233(x79781),f2(x79781)),x79783))+~P1(f773(f773(f233(x79781),f773(f773(f283(x79781),x79784),x79782)),x79783))
% 191.21/191.75 [7979]~P62(x79791)+P1(f773(f773(f233(x79791),x79792),f2(x79791)))+P1(f773(f773(f233(x79791),f2(x79791)),x79792))+P1(f773(f773(f232(x79791),f2(x79791)),x79793))+~P1(f773(f773(f232(x79791),f773(f773(f283(x79791),x79794),x79792)),x79793))
% 191.21/191.75 [8023]~E(x80231,f773(f773(f82(a1),f773(f773(f83(a1),x80232),x80233)),x80234))+~P1(f773(f773(f233(a1),f2(a1)),x80232))+~P1(f773(f773(f232(a1),f2(a1)),x80234))+~P1(f773(f773(f233(a1),x80234),x80232))+P1(f773(f56(x80231,x80232),f773(f773(f241(a1,a1),x80233),x80234)))
% 191.21/191.75 [8140]~P62(x81401)+P1(f773(f773(f233(x81401),x81402),f2(x81401)))+~P1(f773(f773(f233(x81401),f2(x81401)),x81404))+~P1(f773(f773(f233(x81401),x81403),f773(f773(f83(x81401),x81404),x81402)))+P1(f773(f773(f233(x81401),f773(f773(f283(x81401),x81403),x81402)),x81404))
% 191.21/191.75 [8141]~P62(x81411)+P1(f773(f773(f233(x81411),x81412),f2(x81411)))+~P1(f773(f773(f232(x81411),f2(x81411)),x81414))+~P1(f773(f773(f232(x81411),x81413),f773(f773(f83(x81411),x81414),x81412)))+P1(f773(f773(f232(x81411),f773(f773(f283(x81411),x81413),x81412)),x81414))
% 191.21/191.75 [8219]~P62(x82191)+P1(f773(f773(f233(x82191),x82192),f2(x82191)))+~P1(f773(f773(f233(x82191),x82193),f2(x82191)))+P1(f773(f773(f233(x82191),x82193),f773(f773(f283(x82191),x82194),x82192)))+~P1(f773(f773(f233(x82191),f773(f773(f83(x82191),x82193),x82192)),x82194))
% 191.21/191.75 [8220]~P62(x82201)+P1(f773(f773(f233(x82201),x82202),f2(x82201)))+~P1(f773(f773(f232(x82201),x82203),f2(x82201)))+P1(f773(f773(f232(x82201),x82203),f773(f773(f283(x82201),x82204),x82202)))+~P1(f773(f773(f232(x82201),f773(f773(f83(x82201),x82203),x82202)),x82204))
% 191.21/191.75 [8379]~P62(x83791)+~P1(f773(f773(f233(x83791),x83792),f2(x83791)))+P1(f773(f773(f233(x83791),f2(x83791)),x83792))+~P1(f773(f773(f233(x83791),f773(f773(f283(x83791),x83794),x83792)),x83793))+P1(f773(f773(f233(x83791),f773(f773(f83(x83791),x83793),x83792)),x83794))
% 191.21/191.75 [8380]~P62(x83801)+~P1(f773(f773(f233(x83801),x83802),f2(x83801)))+P1(f773(f773(f233(x83801),f2(x83801)),x83802))+~P1(f773(f773(f233(x83801),f773(f773(f83(x83801),x83804),x83802)),x83803))+P1(f773(f773(f233(x83801),f773(f773(f283(x83801),x83803),x83802)),x83804))
% 191.21/191.75 [8381]~P62(x83811)+~P1(f773(f773(f233(x83811),x83812),f2(x83811)))+P1(f773(f773(f233(x83811),f2(x83811)),x83812))+~P1(f773(f773(f232(x83811),f773(f773(f283(x83811),x83814),x83812)),x83813))+P1(f773(f773(f232(x83811),f773(f773(f83(x83811),x83813),x83812)),x83814))
% 191.21/191.75 [8382]~P62(x83821)+~P1(f773(f773(f233(x83821),x83822),f2(x83821)))+P1(f773(f773(f233(x83821),f2(x83821)),x83822))+~P1(f773(f773(f232(x83821),f773(f773(f83(x83821),x83824),x83822)),x83823))+P1(f773(f773(f232(x83821),f773(f773(f283(x83821),x83823),x83822)),x83824))
% 191.21/191.75 [8401]~P62(x84011)+~P1(f773(f773(f233(x84011),f2(x84011)),x84014))+P1(f773(f773(f233(x84011),f2(x84011)),x84012))+~P1(f773(f773(f233(x84011),f773(f773(f83(x84011),x84014),x84012)),x84013))+P1(f773(f773(f233(x84011),f773(f773(f283(x84011),x84013),x84012)),x84014))
% 191.21/191.75 [8402]~P62(x84021)+~P1(f773(f773(f232(x84021),f2(x84021)),x84024))+P1(f773(f773(f233(x84021),f2(x84021)),x84022))+~P1(f773(f773(f232(x84021),f773(f773(f83(x84021),x84024),x84022)),x84023))+P1(f773(f773(f232(x84021),f773(f773(f283(x84021),x84023),x84022)),x84024))
% 191.21/191.75 [8479]~P62(x84791)+~P1(f773(f773(f233(x84791),x84794),f2(x84791)))+~P1(f773(f773(f233(x84791),x84793),f773(f773(f83(x84791),x84792),x84794)))+P1(f773(f773(f233(x84791),x84792),f773(f773(f283(x84791),x84793),x84794)))+~P1(f773(f773(f233(x84791),f773(f773(f83(x84791),x84792),x84794)),x84793))
% 191.21/191.75 [8480]~P62(x84801)+~P1(f773(f773(f233(x84801),x84802),f2(x84801)))+~P1(f773(f773(f233(x84801),x84803),f773(f773(f83(x84801),x84802),x84804)))+P1(f773(f773(f233(x84801),x84802),f773(f773(f283(x84801),x84803),x84804)))+~P1(f773(f773(f233(x84801),f773(f773(f83(x84801),x84802),x84804)),x84803))
% 191.21/191.75 [8481]~P62(x84811)+~P1(f773(f773(f233(x84811),x84814),f2(x84811)))+~P1(f773(f773(f232(x84811),x84813),f773(f773(f83(x84811),x84812),x84814)))+P1(f773(f773(f232(x84811),x84812),f773(f773(f283(x84811),x84813),x84814)))+~P1(f773(f773(f232(x84811),f773(f773(f83(x84811),x84812),x84814)),x84813))
% 191.21/191.75 [8482]~P62(x84821)+~P1(f773(f773(f232(x84821),x84822),f2(x84821)))+~P1(f773(f773(f232(x84821),x84823),f773(f773(f83(x84821),x84822),x84824)))+P1(f773(f773(f232(x84821),x84822),f773(f773(f283(x84821),x84823),x84824)))+~P1(f773(f773(f232(x84821),f773(f773(f83(x84821),x84822),x84824)),x84823))
% 191.21/191.75 [8581]~P62(x85811)+~P1(f773(f773(f233(x85811),x85813),f2(x85811)))+~P1(f773(f773(f233(x85811),x85812),f773(f773(f83(x85811),x85814),x85813)))+~P1(f773(f773(f233(x85811),f773(f773(f83(x85811),x85814),x85813)),x85812))+P1(f773(f773(f233(x85811),f773(f773(f283(x85811),x85812),x85813)),x85814))
% 191.21/191.75 [8582]~P62(x85821)+~P1(f773(f773(f233(x85821),x85823),f2(x85821)))+~P1(f773(f773(f232(x85821),x85822),f773(f773(f83(x85821),x85824),x85823)))+~P1(f773(f773(f232(x85821),f773(f773(f83(x85821),x85824),x85823)),x85822))+P1(f773(f773(f232(x85821),f773(f773(f283(x85821),x85822),x85823)),x85824))
% 191.21/191.75 [8596]~P62(x85961)+~P1(f773(f773(f233(x85961),f2(x85961)),x85964))+~P1(f773(f773(f233(x85961),x85962),f773(f773(f83(x85961),x85964),x85963)))+~P1(f773(f773(f233(x85961),f773(f773(f83(x85961),x85964),x85963)),x85962))+P1(f773(f773(f233(x85961),f773(f773(f283(x85961),x85962),x85963)),x85964))
% 191.21/191.75 [8597]~P62(x85971)+~P1(f773(f773(f232(x85971),f2(x85971)),x85974))+~P1(f773(f773(f232(x85971),x85972),f773(f773(f83(x85971),x85974),x85973)))+~P1(f773(f773(f232(x85971),f773(f773(f83(x85971),x85974),x85973)),x85972))+P1(f773(f773(f232(x85971),f773(f773(f283(x85971),x85972),x85973)),x85974))
% 191.21/191.75 [8754]E(f773(f773(f3(a1),f438(x87541,x87542,x87543,x87544)),f439(x87541,x87542,x87543,x87544)),x87544)+~P1(f773(f773(f233(a1),f2(a1)),x87543))+~P1(f773(f773(f334(a1),x87542),x87541))+~P1(f773(f773(f233(a1),x87544),x87542))+P1(f773(f773(f233(a1),f773(f773(f82(a1),x87544),x87543)),x87542))
% 191.21/191.75 [8815]~P1(f773(x88151,x88152))+~P1(f773(f773(f233(a1),f2(a1)),x88154))+~P1(f773(f773(f232(a1),f2(a1)),x88153))+~P1(f773(x88151,f773(f773(f82(a1),f804(x88153,x88151,x88154)),x88154)))+P1(f773(x88151,f773(f773(f82(a1),x88152),f773(f773(f83(a1),x88153),x88154))))
% 191.21/191.75 [8816]~P1(f773(x88161,x88162))+~P1(f773(f773(f233(a1),f2(a1)),x88164))+~P1(f773(f773(f232(a1),f2(a1)),x88163))+~P1(f773(x88161,f773(f773(f3(a1),f809(x88163,x88161,x88164)),x88164)))+P1(f773(x88161,f773(f773(f3(a1),x88162),f773(f773(f83(a1),x88163),x88164))))
% 191.21/191.75 [8955]~P1(f773(f773(f233(a1),f2(a1)),x89553))+~P1(f773(f773(f334(a1),x89552),x89551))+~P1(f773(f773(f233(a1),x89554),x89552))+P1(f773(f773(f334(a1),f438(x89551,x89552,x89553,x89554)),x89551))+P1(f773(f773(f233(a1),f773(f773(f82(a1),x89554),x89553)),x89552))
% 191.21/191.75 [8975]E(f773(f773(f3(a1),f431(x89751,x89752,x89753,x89754)),f432(x89751,x89752,x89753,x89754)),x89754)+~P1(f773(f773(f233(a1),f2(a1)),x89753))+~P1(f773(f773(f232(a1),x89754),x89752))+~P1(f773(f773(f334(a1),f773(f773(f82(a1),x89752),f80(a1))),x89751))+P1(f773(f773(f232(a1),f773(f773(f82(a1),x89754),x89753)),x89752))
% 191.21/191.75 [9007]~P1(f773(f773(f233(a1),f2(a1)),x90072))+~P1(f773(f773(f334(a1),x90073),x90074))+~P1(f773(f773(f233(a1),x90071),x90073))+P1(f773(f773(f334(a1),f439(x90074,x90073,x90072,x90071)),f295(a1,f80(a1),x90072)))+P1(f773(f773(f233(a1),f773(f773(f82(a1),x90071),x90072)),x90073))
% 191.21/191.75 [9086]~P1(f773(f773(f233(a1),f2(a1)),x90863))+~P1(f773(f773(f232(a1),x90864),x90862))+P1(f773(f773(f334(a1),f431(x90861,x90862,x90863,x90864)),x90861))+~P1(f773(f773(f334(a1),f773(f773(f82(a1),x90862),f80(a1))),x90861))+P1(f773(f773(f232(a1),f773(f773(f82(a1),x90864),x90863)),x90862))
% 191.21/191.75 [9125]~P1(f773(f773(f233(a1),f2(a1)),x91252))+~P1(f773(f773(f232(a1),x91251),x91253))+P1(f773(f773(f334(a1),f432(x91254,x91253,x91252,x91251)),f295(a1,f80(a1),x91252)))+~P1(f773(f773(f334(a1),f773(f773(f82(a1),x91253),f80(a1))),x91254))+P1(f773(f773(f232(a1),f773(f773(f82(a1),x91251),x91252)),x91253))
% 191.21/191.75 [9391]~P36(x93911,x93913)+~P30(x93911,x93914)+P36(x93911,f773(f773(f103(f855(f854(x93911,x93911),a841)),x93912),x93913))+~P1(f773(f773(f232(f855(f854(x93911,x93911),a841)),x93912),f773(f240(f855(f854(x93911,x93911),a841),f855(f854(x93911,x93911),a841)),x93914)))+~P1(f773(f773(f232(f855(f854(x93911,x93911),a841)),x93913),f773(f250(f855(f854(x93911,x93911),a841),f855(f854(x93911,x93911),a841)),x93914)))
% 191.21/191.75 [9659]~E(f773(f707(x96591,x96594,x96593,x96592),f711(x96591,x96594,x96593,x96592)),f183(f848(a839)))+P1(f773(f773(f233(a1),f710(x96591,x96594,x96593,x96592)),f711(x96591,x96594,x96593,x96592)))+P1(f773(f773(f773(x96591,x96592),x96593),x96594))+P1(f773(f773(f773(x96591,f707(x96591,x96594,x96593,x96592)),f710(x96591,x96594,x96593,x96592)),f773(f773(f82(a1),f711(x96591,x96594,x96593,x96592)),f80(a1))))+~P1(f773(f321(f854(f855(a1,f851(f848(a839))),f854(a1,a1)),a311),f773(f773(f241(f855(a1,f851(f848(a839))),f854(a1,a1)),x96592),f773(f773(f241(a1,a1),x96593),x96594))))
% 191.21/191.75 [9760]~P22(x97602,x97604,x97603)+E(x97601,f180(f855(x97602,a841)))+~P1(f773(f63(x97602),x97601))+P1(f773(f773(f334(x97602),f773(x97603,x97601)),x97601))+~P1(f773(f773(f334(x97602),f773(f773(x97604,f458(x97601,x97603,x97604,x97602)),f459(x97601,x97603,x97604,x97602))),f773(f773(f302(x97602),f458(x97601,x97603,x97604,x97602)),f773(f773(f302(x97602),f459(x97601,x97603,x97604,x97602)),f180(f855(x97602,a841))))))
% 191.21/191.75 [9311]~P53(x93111,x93111,x93114)+P1(f773(f773(f334(f854(x93111,x93111)),f773(f773(f241(x93111,x93111),x93112),x93113)),f300(x93111,x93114)))+P1(f773(f773(f334(f854(x93111,x93111)),f773(f773(f241(x93111,x93111),x93113),x93112)),f300(x93111,x93114)))+~P1(f773(f773(f334(f854(x93111,x93111)),f773(f773(f241(x93111,x93111),x93115),x93112)),f300(x93111,x93114)))+~P1(f773(f773(f334(f854(x93111,x93111)),f773(f773(f241(x93111,x93111),x93115),x93113)),f300(x93111,x93114)))
% 191.21/191.75 [5491]E(x54911,f2(a847))+~E(f773(f42(x54912),x54915),x54911)+E(f773(f42(x54912),x54913),f773(a114,x54911))+~E(x54913,f773(f773(f302(x54912),x54914),x54915))+P1(f773(f773(f334(x54912),x54914),x54915))
% 191.21/191.75 [5612]~P61(x56122)+E(x56121,f2(x56122))+E(x56123,f2(x56122))+~E(f773(f773(f283(x56122),x56124),x56123),f773(f773(f283(x56122),x56125),x56121))+E(f773(f773(f83(x56122),x56124),x56121),f773(f773(f83(x56122),x56125),x56123))
% 191.21/191.75 [5613]~P61(x56132)+E(x56131,f2(x56132))+E(x56133,f2(x56132))+~E(f773(f773(f83(x56132),x56134),x56133),f773(f773(f83(x56132),x56135),x56131))+E(f773(f773(f283(x56132),x56134),x56131),f773(f773(f283(x56132),x56135),x56133))
% 191.21/191.75 [5686]~E(f773(f42(x56861),x56865),x56863)+~E(x56865,f180(f855(x56861,a841)))+E(f773(f42(x56861),x56862),f773(a114,x56863))+~E(x56862,f773(f773(f302(x56861),x56864),x56865))+P1(f773(f773(f334(x56861),x56864),x56865))
% 191.21/191.75 [5913]~P85(x59132)+~E(f773(x59133,x59135),f2(x59132))+E(f773(f773(f11(x59131,x59132),x59133),x59134),f2(x59132))+~P1(f773(f63(x59131),x59134))+~P1(f773(f773(f334(x59131),x59135),x59134))
% 191.21/191.75 [6298]~P100(x62983)+E(x62981,x62982)+~E(f773(f294(x62983,x62984),x62981),f773(f294(x62983,x62985),x62982))+~P1(f773(f773(f233(x62983),x62985),x62982))+~P1(f773(f773(f233(x62983),x62984),x62981))
% 191.21/191.75 [6299]~P100(x62993)+E(x62991,x62992)+~E(f773(f294(x62993,x62991),x62994),f773(f294(x62993,x62992),x62995))+~P1(f773(f773(f233(x62993),x62992),x62995))+~P1(f773(f773(f233(x62993),x62991),x62994))
% 191.21/191.75 [7410]~P100(x74101)+~P18(x74101,f773(f773(f125(x74101),x74104),x74105))+~P1(f773(f773(f334(x74101),x74103),f773(f158(x74101),x74105)))+~P1(f773(f773(f334(x74101),x74102),f773(f158(x74101),x74104)))+P1(f773(f773(f232(x74101),x74102),x74103))
% 191.21/191.75 [8513]~P99(x85131)+~P1(f773(f773(f233(f855(x85131,a841)),f295(x85131,x85135,x85132)),f295(x85131,x85134,x85133)))+~P1(f773(f773(f232(x85131),x85135),x85132))+P1(f773(f773(f233(x85131),x85132),x85133))+P1(f773(f773(f233(x85131),x85134),x85135))
% 191.21/191.75 [9804]~P21(x98042,x98045,x98043)+E(x98041,f180(f855(x98042,a841)))+~E(f773(f773(x98045,f773(x98044,f576(x98041,x98044,x98043,x98045,x98042))),f773(x98044,f577(x98041,x98044,x98043,x98045,x98042))),f773(x98044,f773(f773(x98045,f576(x98041,x98044,x98043,x98045,x98042)),f577(x98041,x98044,x98043,x98045,x98042))))+E(f773(x98043,f773(f303(x98042,x98042,x98044),x98041)),f773(x98044,f773(x98043,x98041)))+~P1(f773(f63(x98042),x98041))
% 191.21/191.75 [6295]~P22(x62952,x62955,x62953)+E(x62951,f180(f855(x62952,a841)))+~P1(f773(f63(x62952),x62951))+E(f773(x62953,f773(f773(f302(x62952),x62954),x62951)),f773(f773(x62955,x62954),f773(x62953,x62951)))+P1(f773(f773(f334(x62952),x62954),x62951))
% 191.21/191.75 [7147]~P21(x71472,x71473,x71474)+E(f773(f773(x71473,f773(x71474,x71471)),f773(x71474,x71475)),f773(x71474,x71475))+E(x71471,f180(f855(x71472,a841)))+~P1(f773(f63(x71472),x71475))+~P1(f773(f773(f232(f855(x71472,a841)),x71471),x71475))
% 191.21/191.75 [7551]~P22(x75514,x75515,x75511)+E(f773(x75511,x75512),x75513)+~P1(f773(f63(x75514),x75512))+~E(f773(f773(f3(f855(x75514,a841)),x75512),f773(f773(f302(x75514),x75513),f180(f855(x75514,a841)))),f180(f855(x75514,a841)))+~P1(f773(f773(f334(x75514),x75513),x75512))
% 191.21/191.75 [7698]E(x76981,x76982)+~E(f773(f181(f848(x76983)),x76982),f773(f181(f848(x76984)),x76985))+~E(f773(f181(f848(x76983)),x76981),f773(f181(f848(x76984)),x76985))+~E(f166(x76984,x76983,f773(f773(f167(x76984,x76983),x76985),x76981)),f166(x76984,x76983,f773(f773(f167(x76984,x76983),x76985),x76982)))+~P1(f773(f127(x76984),x76985))
% 191.21/191.75 [8436]~P70(x84361)+~P112(x84361)+~P1(f773(f63(x84362),x84365))+P1(f773(f773(f279(x84361),f773(f773(f11(x84362,x84361),x84363),x84364)),f773(f773(f11(x84362,x84361),x84363),x84365)))+~P1(f773(f773(f232(f855(x84362,a841)),x84364),x84365))
% 191.21/191.75 [8486]E(x84861,x84862)+~P12(x84863,x84864,x84865)+E(f773(f773(f104(f855(x84863,a841)),x84861),x84862),f180(f855(x84863,a841)))+~P1(f773(f773(f334(f855(x84863,a841)),x84862),f773(f773(f61(x84863),x84864),x84865)))+~P1(f773(f773(f334(f855(x84863,a841)),x84861),f773(f773(f61(x84863),x84864),x84865)))
% 191.21/191.75 [9189]~P66(x91892)+~E(f773(x91893,f478(x91893,x91894,x91895,x91891,x91892)),f2(x91892))+E(f773(f773(f8(x91891,x91892),x91893),x91894),f773(f773(f8(x91891,x91892),x91893),x91895))+~P1(f773(f63(x91891),x91895))+~P1(f773(f773(f232(f855(x91891,a841)),x91894),x91895))
% 191.21/191.75 [9190]~P66(x91902)+~E(f773(x91903,f481(x91903,x91904,x91905,x91901,x91902)),f2(x91902))+E(f773(f773(f8(x91901,x91902),x91903),x91904),f773(f773(f8(x91901,x91902),x91903),x91905))+~P1(f773(f63(x91901),x91905))+~P1(f773(f773(f232(f855(x91901,a841)),x91904),x91905))
% 191.21/191.75 [9191]~P70(x91912)+~E(f773(x91913,f479(x91913,x91914,x91915,x91911,x91912)),f80(x91912))+E(f773(f773(f11(x91911,x91912),x91913),x91914),f773(f773(f11(x91911,x91912),x91913),x91915))+~P1(f773(f63(x91911),x91915))+~P1(f773(f773(f232(f855(x91911,a841)),x91914),x91915))
% 191.21/191.75 [9192]~P70(x91922)+~E(f773(x91923,f480(x91923,x91924,x91925,x91921,x91922)),f80(x91922))+E(f773(f773(f11(x91921,x91922),x91923),x91924),f773(f773(f11(x91921,x91922),x91923),x91925))+~P1(f773(f63(x91921),x91925))+~P1(f773(f773(f232(f855(x91921,a841)),x91924),x91925))
% 191.21/191.75 [9642]~P81(x96421)+~P1(f773(f63(x96422),x96425))+~P1(f773(f773(f232(x96421),f2(x96421)),f773(x96423,f441(x96423,x96424,x96425,x96422,x96421))))+P1(f773(f773(f232(x96421),f773(f773(f8(x96422,x96421),x96423),x96424)),f773(f773(f8(x96422,x96421),x96423),x96425)))+~P1(f773(f773(f232(f855(x96422,a841)),x96424),x96425))
% 191.21/191.75 [7407]E(x74071,f2(a847))+P1(f773(x74072,x74073))+~E(x74074,f773(f773(f82(a847),f773(f773(f83(a847),x74071),x74073)),x74075))+~P1(f773(f773(f233(a847),x74075),x74071))+~P1(f773(x74072,f773(f773(f43(a847),x74074),x74071)))
% 191.21/191.75 [7490]E(x74901,f2(a847))+P1(f773(x74902,x74903))+~P1(f773(x74902,f52(a847,x74904,x74901)))+~E(x74904,f773(f773(f82(a847),f773(f773(f83(a847),x74901),x74905)),x74903))+~P1(f773(f773(f233(a847),x74903),x74901))
% 191.21/191.75 [7786]~P61(x77863)+E(f773(x77861,x77862),f2(x77863))+~P1(f773(f63(x77864),x77865))+E(f773(f773(f11(x77864,x77863),x77861),f773(f773(f3(f855(x77864,a841)),x77865),f773(f773(f302(x77864),x77862),f180(f855(x77864,a841))))),f773(f773(f11(x77864,x77863),x77861),x77865))+P1(f773(f773(f334(x77864),x77862),x77865))
% 191.21/191.75 [8180]~P66(x81801)+~P1(f773(f63(x81802),x81805))+~P1(f773(f63(x81802),x81804))+~E(f773(f773(f104(f855(x81802,a841)),x81804),x81805),f180(f855(x81802,a841)))+E(f773(f773(f82(x81801),f773(f773(f8(x81802,x81801),x81803),x81804)),f773(f773(f8(x81802,x81801),x81803),x81805)),f773(f773(f8(x81802,x81801),x81803),f773(f773(f103(f855(x81802,a841)),x81804),x81805)))
% 191.21/191.75 [8182]~P70(x81821)+~P1(f773(f63(x81822),x81825))+~P1(f773(f63(x81822),x81824))+~E(f773(f773(f104(f855(x81822,a841)),x81824),x81825),f180(f855(x81822,a841)))+E(f773(f773(f83(x81821),f773(f773(f11(x81822,x81821),x81823),x81824)),f773(f773(f11(x81822,x81821),x81823),x81825)),f773(f773(f11(x81822,x81821),x81823),f773(f773(f103(f855(x81822,a841)),x81824),x81825)))
% 191.21/191.75 [8272]~P61(x82723)+E(f773(x82721,x82722),f2(x82723))+~P1(f773(f63(x82724),x82725))+E(f773(f773(f11(x82724,x82723),x82721),f773(f773(f3(f855(x82724,a841)),x82725),f773(f773(f302(x82724),x82722),f180(f855(x82724,a841))))),f773(f773(f283(x82723),f773(f773(f11(x82724,x82723),x82721),x82725)),f773(x82721,x82722)))+~P1(f773(f773(f334(x82724),x82722),x82725))
% 191.21/191.75 [8937]~P12(x89371,x89375,x89374)+~E(f773(f773(f61(x89371),f773(f773(f302(x89371),x89372),f180(f855(x89371,a841)))),x89374),f773(f773(f61(x89371),f773(f773(f302(x89371),x89373),f180(f855(x89371,a841)))),x89374))+~P1(f773(f773(f334(x89371),x89373),x89375))+~P1(f773(f773(f334(x89371),x89372),x89375))+P1(f773(f773(f334(f854(x89371,x89371)),f773(f773(f241(x89371,x89371),x89372),x89373)),x89374))
% 191.21/191.75 [8954]~P12(x89541,x89545,x89543)+E(f773(f773(f61(x89541),f773(f773(f302(x89541),x89542),f180(f855(x89541,a841)))),x89543),f773(f773(f61(x89541),f773(f773(f302(x89541),x89544),f180(f855(x89541,a841)))),x89543))+~P1(f773(f773(f334(x89541),x89544),x89545))+~P1(f773(f773(f334(x89541),x89542),x89545))+~P1(f773(f773(f334(f854(x89541,x89541)),f773(f773(f241(x89541,x89541),x89542),x89544)),x89543))
% 191.21/191.75 [9216]~P70(x92161)+~P1(f773(f63(x92162),x92165))+~P1(f773(f63(x92162),x92164))+~E(f773(f773(f104(f855(x92162,a841)),x92164),x92165),f180(f855(x92162,a841)))+E(f773(f773(f83(x92161),f773(f773(f773(f67(x92161,x92162,f83(x92161)),x92163),f80(x92161)),x92164)),f773(f773(f773(f67(x92161,x92162,f83(x92161)),x92163),f80(x92161)),x92165)),f773(f773(f773(f67(x92161,x92162,f83(x92161)),x92163),f80(x92161)),f773(f773(f103(f855(x92162,a841)),x92164),x92165)))
% 191.21/191.75 [9226]~P66(x92261)+~E(f773(x92263,f510(x92263,x92265,x92264,x92262,x92261)),f2(x92261))+~P1(f773(f63(x92262),x92264))+~P1(f773(f63(x92262),x92265))+E(f773(f773(f82(x92261),f773(f773(f8(x92262,x92261),x92263),x92264)),f773(f773(f8(x92262,x92261),x92263),x92265)),f773(f773(f8(x92262,x92261),x92263),f773(f773(f103(f855(x92262,a841)),x92264),x92265)))
% 191.21/191.75 [9227]~P66(x92271)+~E(f773(x92273,f514(x92273,x92275,x92274,x92272,x92271)),f2(x92271))+~P1(f773(f63(x92272),x92274))+~P1(f773(f63(x92272),x92275))+E(f773(f773(f82(x92271),f773(f773(f8(x92272,x92271),x92273),x92274)),f773(f773(f8(x92272,x92271),x92273),x92275)),f773(f773(f8(x92272,x92271),x92273),f773(f773(f103(f855(x92272,a841)),x92274),x92275)))
% 191.21/191.75 [9228]~P70(x92281)+~E(f773(x92283,f511(x92283,x92285,x92284,x92282,x92281)),f80(x92281))+~P1(f773(f63(x92282),x92284))+~P1(f773(f63(x92282),x92285))+E(f773(f773(f83(x92281),f773(f773(f11(x92282,x92281),x92283),x92284)),f773(f773(f11(x92282,x92281),x92283),x92285)),f773(f773(f11(x92282,x92281),x92283),f773(f773(f103(f855(x92282,a841)),x92284),x92285)))
% 191.21/191.75 [9229]~P70(x92291)+~E(f773(x92293,f513(x92293,x92295,x92294,x92292,x92291)),f80(x92291))+~P1(f773(f63(x92292),x92294))+~P1(f773(f63(x92292),x92295))+E(f773(f773(f83(x92291),f773(f773(f11(x92292,x92291),x92293),x92294)),f773(f773(f11(x92292,x92291),x92293),x92295)),f773(f773(f11(x92292,x92291),x92293),f773(f773(f103(f855(x92292,a841)),x92294),x92295)))
% 191.21/191.75 [9433]~P70(x94331)+~E(f773(x94333,f531(x94333,x94335,x94334,x94332,x94331)),f80(x94331))+~P1(f773(f63(x94332),x94334))+~P1(f773(f63(x94332),x94335))+E(f773(f773(f83(x94331),f773(f773(f773(f67(x94331,x94332,f83(x94331)),x94333),f80(x94331)),x94334)),f773(f773(f773(f67(x94331,x94332,f83(x94331)),x94333),f80(x94331)),x94335)),f773(f773(f773(f67(x94331,x94332,f83(x94331)),x94333),f80(x94331)),f773(f773(f103(f855(x94332,a841)),x94334),x94335)))
% 191.21/191.75 [9534]~P66(x95342)+E(f773(f773(f8(x95341,x95342),x95343),x95344),f773(f773(f8(x95341,x95342),x95343),x95345))+~P1(f773(f63(x95341),x95345))+~P1(f773(f773(f232(f855(x95341,a841)),x95344),x95345))+P1(f773(f773(f334(x95341),f478(x95343,x95344,x95345,x95341,x95342)),f773(f773(f3(f855(x95341,a841)),x95345),x95344)))
% 191.21/191.75 [9535]~P66(x95352)+E(f773(f773(f8(x95351,x95352),x95353),x95354),f773(f773(f8(x95351,x95352),x95353),x95355))+~P1(f773(f63(x95351),x95355))+~P1(f773(f773(f232(f855(x95351,a841)),x95354),x95355))+P1(f773(f773(f334(x95351),f481(x95353,x95354,x95355,x95351,x95352)),f773(f773(f3(f855(x95351,a841)),x95355),x95354)))
% 191.21/191.75 [9536]~P70(x95362)+E(f773(f773(f11(x95361,x95362),x95363),x95364),f773(f773(f11(x95361,x95362),x95363),x95365))+~P1(f773(f63(x95361),x95365))+~P1(f773(f773(f232(f855(x95361,a841)),x95364),x95365))+P1(f773(f773(f334(x95361),f479(x95363,x95364,x95365,x95361,x95362)),f773(f773(f3(f855(x95361,a841)),x95365),x95364)))
% 191.21/191.75 [9537]~P70(x95372)+E(f773(f773(f11(x95371,x95372),x95373),x95374),f773(f773(f11(x95371,x95372),x95373),x95375))+~P1(f773(f63(x95371),x95375))+~P1(f773(f773(f232(f855(x95371,a841)),x95374),x95375))+P1(f773(f773(f334(x95371),f480(x95373,x95374,x95375,x95371,x95372)),f773(f773(f3(f855(x95371,a841)),x95375),x95374)))
% 191.21/191.75 [9551]~P66(x95511)+~P1(f773(f63(x95512),x95514))+~P1(f773(f63(x95512),x95515))+E(f773(f773(f82(x95511),f773(f773(f8(x95512,x95511),x95513),x95514)),f773(f773(f8(x95512,x95511),x95513),x95515)),f773(f773(f8(x95512,x95511),x95513),f773(f773(f103(f855(x95512,a841)),x95514),x95515)))+P1(f773(f773(f334(x95512),f510(x95513,x95515,x95514,x95512,x95511)),f773(f773(f104(f855(x95512,a841)),x95514),x95515)))
% 191.21/191.75 [9552]~P66(x95521)+~P1(f773(f63(x95522),x95524))+~P1(f773(f63(x95522),x95525))+E(f773(f773(f82(x95521),f773(f773(f8(x95522,x95521),x95523),x95524)),f773(f773(f8(x95522,x95521),x95523),x95525)),f773(f773(f8(x95522,x95521),x95523),f773(f773(f103(f855(x95522,a841)),x95524),x95525)))+P1(f773(f773(f334(x95522),f514(x95523,x95525,x95524,x95522,x95521)),f773(f773(f104(f855(x95522,a841)),x95524),x95525)))
% 191.21/191.75 [9553]~P70(x95531)+~P1(f773(f63(x95532),x95534))+~P1(f773(f63(x95532),x95535))+E(f773(f773(f83(x95531),f773(f773(f11(x95532,x95531),x95533),x95534)),f773(f773(f11(x95532,x95531),x95533),x95535)),f773(f773(f11(x95532,x95531),x95533),f773(f773(f103(f855(x95532,a841)),x95534),x95535)))+P1(f773(f773(f334(x95532),f511(x95533,x95535,x95534,x95532,x95531)),f773(f773(f104(f855(x95532,a841)),x95534),x95535)))
% 191.21/191.75 [9554]~P70(x95541)+~P1(f773(f63(x95542),x95544))+~P1(f773(f63(x95542),x95545))+E(f773(f773(f83(x95541),f773(f773(f11(x95542,x95541),x95543),x95544)),f773(f773(f11(x95542,x95541),x95543),x95545)),f773(f773(f11(x95542,x95541),x95543),f773(f773(f103(f855(x95542,a841)),x95544),x95545)))+P1(f773(f773(f334(x95542),f513(x95543,x95545,x95544,x95542,x95541)),f773(f773(f104(f855(x95542,a841)),x95544),x95545)))
% 191.21/191.75 [9566]~P81(x95665)+~P1(f773(f63(x95661),x95664))+P1(f773(f773(f232(x95665),f773(f773(f8(x95661,x95665),x95662),x95663)),f773(f773(f8(x95661,x95665),x95662),x95664)))+~P1(f773(f773(f232(f855(x95661,a841)),x95663),x95664))+P1(f773(f773(f334(x95661),f441(x95662,x95663,x95664,x95661,x95665)),f773(f773(f3(f855(x95661,a841)),x95664),x95663)))
% 191.21/191.75 [9608]~P70(x96081)+~P1(f773(f63(x96082),x96084))+~P1(f773(f63(x96082),x96085))+E(f773(f773(f83(x96081),f773(f773(f773(f67(x96081,x96082,f83(x96081)),x96083),f80(x96081)),x96084)),f773(f773(f773(f67(x96081,x96082,f83(x96081)),x96083),f80(x96081)),x96085)),f773(f773(f773(f67(x96081,x96082,f83(x96081)),x96083),f80(x96081)),f773(f773(f103(f855(x96082,a841)),x96084),x96085)))+P1(f773(f773(f334(x96082),f531(x96083,x96085,x96084,x96082,x96081)),f773(f773(f104(f855(x96082,a841)),x96084),x96085)))
% 191.21/191.75 [8663]~P22(x86631,x86634,x86635)+~P1(f773(f63(x86631),x86632))+E(f773(f773(f3(f855(x86631,a841)),x86632),f773(f773(f302(x86631),x86633),f180(f855(x86631,a841)))),f180(f855(x86631,a841)))+~P1(f773(f773(f334(x86631),x86633),x86632))+E(f773(f773(x86634,x86633),f773(x86635,f773(f773(f3(f855(x86631,a841)),x86632),f773(f773(f302(x86631),x86633),f180(f855(x86631,a841)))))),f773(x86635,x86632))
% 191.21/191.75 [8730]~P22(x87301,x87304,x87305)+~P1(f773(f63(x87301),x87303))+~P1(f773(f63(x87301),x87302))+E(f773(f773(f104(f855(x87301,a841)),x87302),x87303),f180(f855(x87301,a841)))+E(f773(f773(x87304,f773(x87305,f773(f773(f103(f855(x87301,a841)),x87302),x87303))),f773(x87305,f773(f773(f104(f855(x87301,a841)),x87302),x87303))),f773(f773(x87304,f773(x87305,x87302)),f773(x87305,x87303)))
% 191.21/191.75 [9231]~P1(f773(f773(f232(a1),x92314),f2(a1)))+~P1(f773(f773(f233(a1),x92313),x92315))+P1(f773(f773(f232(a1),x92311),x92312))+~P1(f773(f773(f233(a1),x92313),x92314))+~P1(f773(f773(f232(a1),f773(f773(f82(a1),f773(f773(f83(a1),x92313),x92312)),x92315)),f773(f773(f82(a1),f773(f773(f83(a1),x92313),x92311)),x92314)))
% 191.21/191.75 [9233]~P1(f773(f773(f232(a1),f2(a1)),x92335))+P1(f773(f773(f232(a1),x92331),x92332))+~P1(f773(f773(f233(a1),x92333),x92334))+~P1(f773(f773(f233(a1),x92335),x92334))+~P1(f773(f773(f232(a1),f773(f773(f82(a1),f773(f773(f83(a1),x92334),x92331)),x92335)),f773(f773(f82(a1),f773(f773(f83(a1),x92334),x92332)),x92333)))
% 191.21/191.75 [9346]~P61(x93465)+E(f773(x93461,f512(x93461,x93462,x93463,x93464,x93465)),f2(x93465))+~P1(f773(f63(x93464),x93463))+~P1(f773(f63(x93464),x93462))+E(f773(f773(f283(x93465),f773(f773(f83(x93465),f773(f773(f11(x93464,x93465),x93461),x93463)),f773(f773(f11(x93464,x93465),x93461),x93462))),f773(f773(f11(x93464,x93465),x93461),f773(f773(f104(f855(x93464,a841)),x93463),x93462))),f773(f773(f11(x93464,x93465),x93461),f773(f773(f103(f855(x93464,a841)),x93463),x93462)))
% 191.21/191.75 [9601]~P61(x96011)+~P1(f773(f63(x96012),x96014))+~P1(f773(f63(x96012),x96015))+E(f773(f773(f283(x96011),f773(f773(f83(x96011),f773(f773(f11(x96012,x96011),x96013),x96014)),f773(f773(f11(x96012,x96011),x96013),x96015))),f773(f773(f11(x96012,x96011),x96013),f773(f773(f104(f855(x96012,a841)),x96014),x96015))),f773(f773(f11(x96012,x96011),x96013),f773(f773(f103(f855(x96012,a841)),x96014),x96015)))+P1(f773(f773(f334(x96012),f512(x96013,x96015,x96014,x96012,x96011)),f773(f773(f104(f855(x96012,a841)),x96014),x96015)))
% 191.21/191.75 [8974]E(f773(f773(f125(x89741),x89742),x89743),f773(f773(f125(x89741),x89744),x89745))+~E(f773(f773(f159(x89741),f773(f181(f848(x89741)),x89744)),x89742),x89744)+~E(f773(f773(f159(x89741),f773(f181(f848(x89741)),x89742)),x89744),x89742)+~E(x89745,f773(f773(f125(x89741),f773(f773(f128(x89741),f773(f181(f848(x89741)),x89744)),x89742)),x89743))+~E(f773(f773(f125(x89741),f773(f773(f128(x89741),f773(f181(f848(x89741)),x89742)),x89744)),x89745),x89743)
% 191.21/191.75 [9344]~P100(x93442)+E(f773(f773(f138(x93441,x93442,x93443),x93444),f151(x93441,x93444,x93445)),x93445)+~P18(x93442,f773(f773(f143(x93441,x93442),x93443),x93445))+~P1(f773(f773(f334(x93441),x93444),f773(f158(x93441),x93445)))+~E(f773(f131(x93441),f773(f126(x93441,f773(f773(f10(x93442,a841,x93441),f773(a330,f773(x93443,x93444))),x93443)),x93445)),x93444)
% 191.21/191.75 [9656]~P64(x96561)+~P1(f773(f68(x96561,x96561,f83(x96561),x96562,x96563),x96565))+~P1(f773(f773(f334(x96561),x96564),x96563))+P1(f773(f773(f334(x96561),x96562),x96563))+P1(f773(f68(x96561,x96561,f83(x96561),x96564,f773(f773(f302(x96561),x96562),f773(f773(f3(f855(x96561,a841)),x96563),f773(f773(f302(x96561),x96564),f180(f855(x96561,a841)))))),x96565))
% 191.21/191.75 [7154]E(x71541,x71542)+~P29(x71544,x71545,x71543,x71546)+~E(f773(x71543,x71541),f773(x71543,x71542))+~P1(f773(f773(f334(x71544),x71542),x71546))+~P1(f773(f773(f334(x71544),x71541),x71546))
% 191.21/191.75 [6393]~P137(x63934)+E(x63931,x63932)+~E(x63935,x63936)+E(x63933,f2(x63934))+~E(f773(f773(f82(x63934),x63935),f773(f773(f83(x63934),x63933),x63931)),f773(f773(f82(x63934),x63936),f773(f773(f83(x63934),x63933),x63932)))
% 191.21/191.75 [7470]~P100(x74701)+~P9(x74701)+~P1(f773(f773(f233(x74701),x74702),f773(x74705,x74706)))+~P1(f773(f773(f334(x74703),x74706),x74704))+P1(f773(f773(f233(x74701),x74702),f773(f773(f46(x74703,x74701),x74704),x74705)))
% 191.21/191.75 [9819]~P85(x98196)+~P1(f773(f63(x98191),x98195))+P1(f773(f773(f334(x98191),f631(x98192,x98193,x98194,x98195,x98191,x98196)),x98194))+P1(f773(f773(f279(x98196),f773(f773(f11(x98191,x98196),x98193),x98194)),f773(f773(f11(x98191,x98196),x98192),x98195)))+~P1(f773(f773(f232(f855(x98191,a841)),x98194),x98195))
% 191.21/191.75 [9942]~P85(x99421)+~P1(f773(f63(x99422),x99426))+~P1(f773(f773(f279(x99421),f773(x99423,f631(x99425,x99423,x99424,x99426,x99422,x99421))),f773(x99425,f631(x99425,x99423,x99424,x99426,x99422,x99421))))+P1(f773(f773(f279(x99421),f773(f773(f11(x99422,x99421),x99423),x99424)),f773(f773(f11(x99422,x99421),x99425),x99426)))+~P1(f773(f773(f232(f855(x99422,a841)),x99424),x99426))
% 191.21/191.75 [8151]~P100(x81511)+~P9(x81511)+~P1(f773(f773(f233(x81511),f773(x81514,x81516)),x81515))+~P1(f773(f773(f334(x81512),x81516),x81513))+P1(f773(f773(f233(x81511),f773(f773(f47(x81512,x81511),x81513),x81514)),x81515))
% 191.21/191.75 [8408]~P23(x84082,x84085,x84086,x84081)+~P1(f773(f63(x84082),x84084))+~P1(f773(f63(x84082),x84083))+~E(f773(f773(f104(f855(x84082,a841)),x84083),x84084),f180(f855(x84082,a841)))+E(f773(x84081,f773(f773(f103(f855(x84082,a841)),x84083),x84084)),f773(f75(x84085,x84085,x84085,f773(x84081,x84083)),f773(x84081,x84084)))
% 191.21/191.75 [9061]~P112(x90611)+~P108(x90611)+~P1(f773(f773(f279(x90611),x90612),x90615))+~P1(f773(f773(f279(x90611),x90612),f773(f773(f82(x90611),x90613),x90616)))+P1(f773(f773(f279(x90611),x90612),f773(f773(f82(x90611),f773(f773(f3(x90611),x90613),f773(f773(f83(x90611),x90614),x90615))),x90616)))
% 191.21/191.75 [9221]~P112(x92211)+~P108(x92211)+~P1(f773(f773(f279(x92211),x92212),x92215))+P1(f773(f773(f279(x92211),x92212),f773(f773(f82(x92211),x92213),x92214)))+~P1(f773(f773(f279(x92211),x92212),f773(f773(f82(x92211),f773(f773(f3(x92211),x92213),f773(f773(f83(x92211),x92216),x92215))),x92214)))
% 191.21/191.75 [8701]E(x87011,x87012)+~P55(x87014,x87015,x87016,x87013,x87017)+~E(f773(x87013,x87011),f773(x87013,x87012))+~P1(f773(f773(f334(x87015),x87012),x87017))+~P1(f773(f773(f334(x87015),x87011),x87017))
% 191.21/191.75 [9950]~P12(x99501,x99507,x99506)+~P16(x99501,f855(x99505,a841),x99506,x99504)+P1(f773(f773(f334(x99501),f509(x99502,x99503,x99504,x99505,x99506,x99507,x99501)),x99507))+~P1(f773(f773(f334(f855(x99501,a841)),x99503),f773(f773(f61(x99501),x99507),x99506)))+P1(f773(f773(f334(f855(x99505,a841)),f773(f773(f46(x99501,f855(x99505,a841)),x99503),x99504)),x99502))
% 191.21/191.75 [9997]~P12(x99972,x99976,x99977)+~P16(x99972,f855(x99971,a841),x99977,x99974)+~P1(f773(f773(f334(f855(x99972,a841)),x99973),f773(f773(f61(x99972),x99976),x99977)))+~P1(f773(f773(f334(f855(x99971,a841)),f773(x99974,f509(x99975,x99973,x99974,x99971,x99977,x99976,x99972))),x99975))+P1(f773(f773(f334(f855(x99971,a841)),f773(f773(f46(x99972,f855(x99971,a841)),x99973),x99974)),x99975))
% 191.21/191.75 [8318]~P70(x83182)+~P29(x83181,x83185,x83188,x83184)+~E(x83183,f773(f75(x83185,x83182,x83181,x83186),x83188))+~E(x83187,f773(f303(x83181,x83185,x83188),x83184))+E(f773(f773(f11(x83181,x83182),x83183),x83184),f773(f773(f11(x83185,x83182),x83186),x83187))
% 191.21/191.75 [10000]~P70(x100002)+~P29(x100005,x100001,x100008,x100007)+~E(f773(x100006,f535(x100003,x100006,x100004,x100007,x100008,x100001,x100005,x100002)),f773(f773(f75(x100001,x100002,x100005,x100003),x100008),f535(x100003,x100006,x100004,x100007,x100008,x100001,x100005,x100002)))+~E(x100004,f773(f303(x100005,x100001,x100008),x100007))+E(f773(f773(f11(x100001,x100002),x100003),x100004),f773(f773(f11(x100005,x100002),x100006),x100007))
% 191.21/191.75 [10003]~P66(x100032)+~P29(x100031,x100035,x100038,x100034)+~E(x100037,f773(f303(x100031,x100035,x100038),x100034))+E(f773(f773(f8(x100031,x100032),x100033),x100034),f773(f773(f8(x100035,x100032),x100036),x100037))+P1(f773(f773(f334(x100031),f636(x100036,x100033,x100037,x100034,x100038,x100035,x100031,x100032)),x100034))
% 191.21/191.75 [10004]~P70(x100042)+~P29(x100041,x100045,x100048,x100044)+~E(x100047,f773(f303(x100041,x100045,x100048),x100044))+E(f773(f773(f11(x100041,x100042),x100043),x100044),f773(f773(f11(x100045,x100042),x100046),x100047))+P1(f773(f773(f334(x100041),f535(x100046,x100043,x100047,x100044,x100048,x100045,x100041,x100042)),x100044))
% 191.21/191.75 [10008]~P66(x100082)+~P29(x100085,x100081,x100088,x100087)+~E(x100084,f773(f303(x100085,x100081,x100088),x100087))+~E(f773(x100086,f636(x100083,x100086,x100084,x100087,x100088,x100081,x100085,x100082)),f773(x100083,f773(x100088,f636(x100083,x100086,x100084,x100087,x100088,x100081,x100085,x100082))))+E(f773(f773(f8(x100081,x100082),x100083),x100084),f773(f773(f8(x100085,x100082),x100086),x100087))
% 191.21/191.75 [9409]~E(f773(f181(f848(x94092)),x94095),f773(f181(f848(x94091)),x94093))+~E(f773(f181(f848(x94092)),x94094),f773(f181(f848(x94091)),x94093))+~E(f773(f773(f773(f74(x94091,f851(x94092)),f166(x94091,x94092,f773(f773(f167(x94091,x94092),x94093),x94094))),x94096),f773(f227(x94092),x94097)),f773(f773(f773(f74(x94091,f851(x94092)),f166(x94091,x94092,f773(f773(f167(x94091,x94092),x94093),x94095))),x94096),f773(f227(x94092),x94098)))+E(f166(x94091,x94092,f773(f773(f167(x94091,x94092),x94093),x94094)),f166(x94091,x94092,f773(f773(f167(x94091,x94092),x94093),x94095)))+P1(f773(f773(f334(x94091),x94096),f773(f158(x94091),x94093)))
% 191.21/191.75 [9504]~P27(x95046,x95042,x95045,x95047,x95048,x95041)+~P1(f773(f63(x95042),x95044))+~P1(f773(f63(x95042),x95043))+~E(f773(f773(f104(f855(x95042,a841)),x95043),x95044),f180(f855(x95042,a841)))+E(f773(x95041,f773(f773(f103(f855(x95042,a841)),x95043),x95044)),f773(f773(x95045,f773(x95041,x95043)),f773(x95041,x95044)))
% 191.21/191.75 [9894]~P27(x98948,x98942,x98945,x98947,x98946,x98941)+~E(f773(x98946,f578(x98944,x98943,x98941,x98946,x98947,x98945,x98942)),x98947)+~P1(f773(f63(x98942),x98943))+~P1(f773(f63(x98942),x98944))+E(f773(x98941,f773(f773(f103(f855(x98942,a841)),x98943),x98944)),f773(f773(x98945,f773(x98941,x98943)),f773(x98941,x98944)))
% 191.21/191.75 [9955]~P27(x99558,x99552,x99555,x99557,x99556,x99551)+~P1(f773(f63(x99552),x99553))+~P1(f773(f63(x99552),x99554))+E(f773(x99551,f773(f773(f103(f855(x99552,a841)),x99553),x99554)),f773(f773(x99555,f773(x99551,x99553)),f773(x99551,x99554)))+P1(f773(f773(f334(x99552),f578(x99554,x99553,x99551,x99556,x99557,x99555,x99552)),f773(f773(f104(f855(x99552,a841)),x99553),x99554)))
% 191.21/191.75 [9647]~P12(x96474,x96478,x96475)+~P12(x96471,x96479,x96473)+~P17(x96471,x96474,f855(x96472,a841),x96473,x96475,x96477)+P16(x96471,f855(x96472,a841),x96473,f773(f773(f10(f855(x96474,f855(x96472,a841)),f855(x96472,a841),x96471),f773(f46(x96474,f855(x96472,a841)),f773(f277(x96474,x96474,x96475),f773(f773(f302(x96474),x96476),f180(f855(x96474,a841)))))),x96477))+~P1(f773(f773(f334(x96474),x96476),x96478))
% 191.21/191.75 [4932]~P122(x49322)+~P127(x49322)+~P138(x49322)+~P105(x49322)+E(x49321,f2(x49322))+~E(f773(f773(f242(x49322),x49321),x49323),f2(x49322))
% 191.21/191.75 [4933]~P122(x49332)+~P127(x49332)+~P138(x49332)+~P105(x49332)+~E(x49331,f2(a847))+~E(f773(f773(f242(x49332),x49333),x49331),f2(x49332))
% 191.21/191.75 [6373]~P81(x63731)+~E(x63733,f2(x63731))+~E(x63732,f2(x63731))+E(f773(f773(f82(x63731),x63732),x63733),f2(x63731))+~P1(f773(f773(f232(x63731),f2(x63731)),x63733))+~P1(f773(f773(f232(x63731),f2(x63731)),x63732))
% 191.21/191.75 [8759]~E(f773(f240(a847,a847),x87593),f2(a847))+~E(x87591,f773(f773(f82(a847),f773(f773(f83(a847),f773(f240(a847,a847),x87593)),x87592)),f773(f250(a847,a847),x87593)))+P1(f773(f55(x87591,x87592),x87593))+~P1(f773(f773(f232(a847),f773(f250(a847,a847),x87593)),f2(a847)))+P1(f773(f773(f233(a847),f2(a847)),x87592))+~P1(f773(f773(f233(a847),x87592),f773(f250(a847,a847),x87593)))
% 191.21/191.75 [8766]E(x87661,f2(a847))+~E(x87662,f773(f773(f82(a847),f773(f773(f83(a847),f773(f240(a847,a847),x87663)),x87661)),f773(f250(a847,a847),x87663)))+P1(f773(f55(x87662,x87661),x87663))+~P1(f773(f773(f233(a847),f2(a847)),x87661))+~P1(f773(f773(f232(a847),f2(a847)),f773(f250(a847,a847),x87663)))+~P1(f773(f773(f233(a847),f773(f250(a847,a847),x87663)),x87661))
% 191.21/191.75 [8780]~E(f773(f240(a847,a847),x87803),f2(a847))+~E(x87801,f773(f773(f82(a847),f773(f773(f83(a847),f773(f240(a847,a847),x87803)),x87802)),f773(f250(a847,a847),x87803)))+P1(f773(f55(x87801,x87802),x87803))+~P1(f773(f773(f233(a847),f2(a847)),x87802))+~P1(f773(f773(f232(a847),f2(a847)),f773(f250(a847,a847),x87803)))+~P1(f773(f773(f233(a847),f773(f250(a847,a847),x87803)),x87802))
% 191.21/191.75 [6775]~P93(x67752)+E(x67751,f180(f855(x67752,a841)))+E(x67753,f180(f855(x67752,a841)))+~P1(f773(f63(x67752),x67751))+~P1(f773(f63(x67752),x67753))+E(f15(x67752,f773(f773(f103(f855(x67752,a841)),x67753),x67751)),f773(f773(f103(x67752),f15(x67752,x67753)),f15(x67752,x67751)))
% 191.21/191.75 [6776]~P100(x67762)+E(x67761,f180(f855(x67762,a841)))+E(x67763,f180(f855(x67762,a841)))+~P1(f773(f63(x67762),x67761))+~P1(f773(f63(x67762),x67763))+E(f16(x67762,f773(f773(f103(f855(x67762,a841)),x67763),x67761)),f773(f773(f179(x67762),f16(x67762,x67763)),f16(x67762,x67761)))
% 191.21/191.75 [6777]~P100(x67772)+E(x67771,f180(f855(x67772,a841)))+E(x67773,f180(f855(x67772,a841)))+~P1(f773(f63(x67772),x67771))+~P1(f773(f63(x67772),x67773))+E(f17(x67772,f773(f773(f103(f855(x67772,a841)),x67773),x67771)),f773(f773(f236(x67772),f17(x67772,x67773)),f17(x67772,x67771)))
% 191.21/191.75 [6778]~P93(x67782)+E(x67781,f180(f855(x67782,a841)))+E(x67783,f180(f855(x67782,a841)))+~P1(f773(f63(x67782),x67781))+~P1(f773(f63(x67782),x67783))+E(f12(x67782,f773(f773(f103(f855(x67782,a841)),x67783),x67781)),f773(f773(f104(x67782),f12(x67782,x67783)),f12(x67782,x67781)))
% 191.21/191.75 [7442]~P91(x74422)+E(x74421,f180(f855(x74422,a841)))+E(x74423,f180(f855(x74422,a841)))+~P1(f773(f63(x74422),x74421))+~P1(f773(f63(x74422),x74423))+E(f773(f773(f83(x74422),f773(f65(x74422,f83(x74422)),x74423)),f773(f65(x74422,f83(x74422)),x74421)),f773(f65(x74422,f83(x74422)),f773(f773(f103(f855(x74422,a841)),x74423),x74421)))
% 191.21/191.75 [7607]~P100(x76072)+E(x76071,f180(f855(x76072,a841)))+E(x76073,f180(f855(x76072,a841)))+~P1(f773(f63(x76072),x76071))+~P1(f773(f63(x76072),x76073))+E(f773(f773(f179(x76072),f13(x76072,f179(x76072),x76073)),f13(x76072,f179(x76072),x76071)),f13(x76072,f179(x76072),f773(f773(f103(f855(x76072,a841)),x76073),x76071)))
% 191.21/191.75 [7608]~P100(x76082)+E(x76081,f180(f855(x76082,a841)))+E(x76083,f180(f855(x76082,a841)))+~P1(f773(f63(x76082),x76081))+~P1(f773(f63(x76082),x76083))+E(f773(f773(f236(x76082),f14(x76082,f236(x76082),x76083)),f14(x76082,f236(x76082),x76081)),f14(x76082,f236(x76082),f773(f773(f103(f855(x76082,a841)),x76083),x76081)))
% 191.21/191.75 [8616]~P1(f773(x86161,x86163))+P1(f773(x86161,f353(x86161,x86162)))+P1(f773(x86161,f350(x86161,x86162)))+~P1(f773(f773(f233(a1),f2(a1)),x86162))+~P1(f773(f773(f334(a1),x86163),f295(a1,f80(a1),x86162)))+P1(f773(x86161,f773(f773(f3(a1),f350(x86161,x86162)),f773(f773(f83(a1),f352(x86161,x86162)),x86162))))
% 191.21/191.75 [8878]~P1(f773(x88781,x88783))+~P1(f773(x88781,f350(x88781,x88782)))+P1(f773(x88781,f353(x88781,x88782)))+~P1(f773(f773(f233(a1),f2(a1)),x88782))+~P1(f773(f773(f334(a1),x88783),f295(a1,f80(a1),x88782)))+~P1(f773(x88781,f773(f773(f3(a1),f350(x88781,x88782)),f773(f773(f83(a1),f352(x88781,x88782)),x88782))))
% 191.21/191.75 [10027]~P97(x100272)+E(x100271,f180(f855(x100272,a841)))+E(x100273,f180(f855(x100272,a841)))+~P1(f773(f63(x100272),x100271))+~P1(f773(f63(x100272),x100273))+E(f12(x100272,f773(f256(x100272),f773(f773(f10(f855(x100272,a841),a841,x100272),f89(x100272)),f773(f773(f10(f855(x100272,f855(x100272,a841)),f855(x100272,a841),x100272),f773(f10(f855(x100272,a841),a841,x100272),f89(x100272))),f773(f773(f9(x100272,f855(x100272,f855(x100272,a841)),f855(x100272,f855(x100272,a841))),f773(f773(f10(f855(x100272,f855(f855(x100272,a841),f855(x100272,a841))),f855(f855(x100272,f855(x100272,a841)),f855(x100272,f855(x100272,a841))),x100272),f20(x100272,f855(x100272,a841),f855(x100272,a841))),f773(f773(f10(f855(x100272,f855(x100272,f855(a841,a841))),f855(x100272,f855(f855(x100272,a841),f855(x100272,a841))),x100272),f773(f10(f855(x100272,f855(a841,a841)),f855(f855(x100272,a841),f855(x100272,a841)),x100272),f20(x100272,a841,a841))),f773(f773(f10(f855(x100272,f855(x100272,a841)),f855(x100272,f855(x100272,f855(a841,a841))),x100272),f773(f10(f855(x100272,a841),f855(x100272,f855(a841,a841)),x100272),f773(f10(a841,f855(a841,a841),x100272),a331))),f773(f773(f9(x100272,f855(x100272,f855(x100272,x100272)),f855(x100272,f855(x100272,a841))),f773(f773(f10(f855(f855(x100272,x100272),f855(x100272,a841)),f855(f855(x100272,f855(x100272,x100272)),f855(x100272,f855(x100272,a841))),x100272),f10(f855(x100272,x100272),f855(x100272,a841),x100272)),f773(f773(f10(f855(x100272,a841),f855(f855(x100272,x100272),f855(x100272,a841)),x100272),f10(x100272,a841,x100272)),a330))),f103(x100272)))))),f773(f773(f9(x100272,f855(x100272,a841),f855(x100272,a841)),f773(f773(f10(f855(a841,a841),f855(f855(x100272,a841),f855(x100272,a841)),x100272),f10(a841,a841,x100272)),f773(f773(f10(a841,f855(a841,a841),x100272),a331),f773(f773(f9(x100272,f855(x100272,a841),a841),f334(x100272)),x100273)))),f773(f773(f9(x100272,f855(x100272,a841),a841),f334(x100272)),x100271))))))),f773(f773(f103(x100272),f12(x100272,x100273)),f12(x100272,x100271)))
% 191.21/191.75 [10028]~P97(x100282)+E(x100281,f180(f855(x100282,a841)))+E(x100283,f180(f855(x100282,a841)))+~P1(f773(f63(x100282),x100281))+~P1(f773(f63(x100282),x100283))+E(f15(x100282,f773(f256(x100282),f773(f773(f10(f855(x100282,a841),a841,x100282),f89(x100282)),f773(f773(f10(f855(x100282,f855(x100282,a841)),f855(x100282,a841),x100282),f773(f10(f855(x100282,a841),a841,x100282),f89(x100282))),f773(f773(f9(x100282,f855(x100282,f855(x100282,a841)),f855(x100282,f855(x100282,a841))),f773(f773(f10(f855(x100282,f855(f855(x100282,a841),f855(x100282,a841))),f855(f855(x100282,f855(x100282,a841)),f855(x100282,f855(x100282,a841))),x100282),f20(x100282,f855(x100282,a841),f855(x100282,a841))),f773(f773(f10(f855(x100282,f855(x100282,f855(a841,a841))),f855(x100282,f855(f855(x100282,a841),f855(x100282,a841))),x100282),f773(f10(f855(x100282,f855(a841,a841)),f855(f855(x100282,a841),f855(x100282,a841)),x100282),f20(x100282,a841,a841))),f773(f773(f10(f855(x100282,f855(x100282,a841)),f855(x100282,f855(x100282,f855(a841,a841))),x100282),f773(f10(f855(x100282,a841),f855(x100282,f855(a841,a841)),x100282),f773(f10(a841,f855(a841,a841),x100282),a331))),f773(f773(f9(x100282,f855(x100282,f855(x100282,x100282)),f855(x100282,f855(x100282,a841))),f773(f773(f10(f855(f855(x100282,x100282),f855(x100282,a841)),f855(f855(x100282,f855(x100282,x100282)),f855(x100282,f855(x100282,a841))),x100282),f10(f855(x100282,x100282),f855(x100282,a841),x100282)),f773(f773(f10(f855(x100282,a841),f855(f855(x100282,x100282),f855(x100282,a841)),x100282),f10(x100282,a841,x100282)),a330))),f104(x100282)))))),f773(f773(f9(x100282,f855(x100282,a841),f855(x100282,a841)),f773(f773(f10(f855(a841,a841),f855(f855(x100282,a841),f855(x100282,a841)),x100282),f10(a841,a841,x100282)),f773(f773(f10(a841,f855(a841,a841),x100282),a331),f773(f773(f9(x100282,f855(x100282,a841),a841),f334(x100282)),x100283)))),f773(f773(f9(x100282,f855(x100282,a841),a841),f334(x100282)),x100281))))))),f773(f773(f104(x100282),f15(x100282,x100283)),f15(x100282,x100281)))
% 191.21/191.75 [10029]~P100(x100292)+E(x100291,f180(f855(x100292,a841)))+E(x100293,f180(f855(x100292,a841)))+~P1(f773(f63(x100292),x100291))+~P1(f773(f63(x100292),x100293))+E(f13(x100292,f179(x100292),f773(f256(x100292),f773(f773(f10(f855(x100292,a841),a841,x100292),f89(x100292)),f773(f773(f10(f855(x100292,f855(x100292,a841)),f855(x100292,a841),x100292),f773(f10(f855(x100292,a841),a841,x100292),f89(x100292))),f773(f773(f9(x100292,f855(x100292,f855(x100292,a841)),f855(x100292,f855(x100292,a841))),f773(f773(f10(f855(x100292,f855(f855(x100292,a841),f855(x100292,a841))),f855(f855(x100292,f855(x100292,a841)),f855(x100292,f855(x100292,a841))),x100292),f20(x100292,f855(x100292,a841),f855(x100292,a841))),f773(f773(f10(f855(x100292,f855(x100292,f855(a841,a841))),f855(x100292,f855(f855(x100292,a841),f855(x100292,a841))),x100292),f773(f10(f855(x100292,f855(a841,a841)),f855(f855(x100292,a841),f855(x100292,a841)),x100292),f20(x100292,a841,a841))),f773(f773(f10(f855(x100292,f855(x100292,a841)),f855(x100292,f855(x100292,f855(a841,a841))),x100292),f773(f10(f855(x100292,a841),f855(x100292,f855(a841,a841)),x100292),f773(f10(a841,f855(a841,a841),x100292),a331))),f773(f773(f9(x100292,f855(x100292,f855(x100292,x100292)),f855(x100292,f855(x100292,a841))),f773(f773(f10(f855(f855(x100292,x100292),f855(x100292,a841)),f855(f855(x100292,f855(x100292,x100292)),f855(x100292,f855(x100292,a841))),x100292),f10(f855(x100292,x100292),f855(x100292,a841),x100292)),f773(f773(f10(f855(x100292,a841),f855(f855(x100292,x100292),f855(x100292,a841)),x100292),f10(x100292,a841,x100292)),a330))),f236(x100292)))))),f773(f773(f9(x100292,f855(x100292,a841),f855(x100292,a841)),f773(f773(f10(f855(a841,a841),f855(f855(x100292,a841),f855(x100292,a841)),x100292),f10(a841,a841,x100292)),f773(f773(f10(a841,f855(a841,a841),x100292),a331),f773(f773(f9(x100292,f855(x100292,a841),a841),f334(x100292)),x100293)))),f773(f773(f9(x100292,f855(x100292,a841),a841),f334(x100292)),x100291))))))),f773(f773(f236(x100292),f13(x100292,f179(x100292),x100293)),f13(x100292,f179(x100292),x100291)))
% 191.21/191.75 [10030]~P100(x100302)+E(x100301,f180(f855(x100302,a841)))+E(x100303,f180(f855(x100302,a841)))+~P1(f773(f63(x100302),x100301))+~P1(f773(f63(x100302),x100303))+E(f14(x100302,f236(x100302),f773(f256(x100302),f773(f773(f10(f855(x100302,a841),a841,x100302),f89(x100302)),f773(f773(f10(f855(x100302,f855(x100302,a841)),f855(x100302,a841),x100302),f773(f10(f855(x100302,a841),a841,x100302),f89(x100302))),f773(f773(f9(x100302,f855(x100302,f855(x100302,a841)),f855(x100302,f855(x100302,a841))),f773(f773(f10(f855(x100302,f855(f855(x100302,a841),f855(x100302,a841))),f855(f855(x100302,f855(x100302,a841)),f855(x100302,f855(x100302,a841))),x100302),f20(x100302,f855(x100302,a841),f855(x100302,a841))),f773(f773(f10(f855(x100302,f855(x100302,f855(a841,a841))),f855(x100302,f855(f855(x100302,a841),f855(x100302,a841))),x100302),f773(f10(f855(x100302,f855(a841,a841)),f855(f855(x100302,a841),f855(x100302,a841)),x100302),f20(x100302,a841,a841))),f773(f773(f10(f855(x100302,f855(x100302,a841)),f855(x100302,f855(x100302,f855(a841,a841))),x100302),f773(f10(f855(x100302,a841),f855(x100302,f855(a841,a841)),x100302),f773(f10(a841,f855(a841,a841),x100302),a331))),f773(f773(f9(x100302,f855(x100302,f855(x100302,x100302)),f855(x100302,f855(x100302,a841))),f773(f773(f10(f855(f855(x100302,x100302),f855(x100302,a841)),f855(f855(x100302,f855(x100302,x100302)),f855(x100302,f855(x100302,a841))),x100302),f10(f855(x100302,x100302),f855(x100302,a841),x100302)),f773(f773(f10(f855(x100302,a841),f855(f855(x100302,x100302),f855(x100302,a841)),x100302),f10(x100302,a841,x100302)),a330))),f179(x100302)))))),f773(f773(f9(x100302,f855(x100302,a841),f855(x100302,a841)),f773(f773(f10(f855(a841,a841),f855(f855(x100302,a841),f855(x100302,a841)),x100302),f10(a841,a841,x100302)),f773(f773(f10(a841,f855(a841,a841),x100302),a331),f773(f773(f9(x100302,f855(x100302,a841),a841),f334(x100302)),x100303)))),f773(f773(f9(x100302,f855(x100302,a841),a841),f334(x100302)),x100301))))))),f773(f773(f179(x100302),f14(x100302,f236(x100302),x100303)),f14(x100302,f236(x100302),x100301)))
% 191.21/191.75 [7107]~P117(x71073)+E(x71071,x71072)+~E(f773(f773(f242(x71073),x71071),x71074),f773(f773(f242(x71073),x71072),x71074))+~P1(f773(f773(f232(x71073),f2(x71073)),x71072))+~P1(f773(f773(f232(x71073),f2(x71073)),x71071))+~P1(f773(f773(f233(a847),f2(a847)),x71074))
% 191.21/191.75 [7402]~P100(x74022)+E(x74021,f180(f855(x74022,a841)))+~P1(f773(f63(x74022),x74021))+~P1(f773(f773(f334(x74022),x74024),x74021))+P1(f773(f773(f233(x74022),x74023),x74024))+~P1(f773(f773(f233(x74022),x74023),f773(f65(x74022,f236(x74022)),x74021)))
% 191.21/191.75 [7403]~P100(x74032)+E(x74031,f180(f855(x74032,a841)))+~P1(f773(f63(x74032),x74031))+~P1(f773(f773(f334(x74032),x74034),x74031))+P1(f773(f773(f232(x74032),x74033),x74034))+~P1(f773(f773(f232(x74032),x74033),f773(f65(x74032,f236(x74032)),x74031)))
% 191.21/191.75 [7404]~P98(x74042)+E(x74041,f180(f855(x74042,a841)))+~P1(f773(f63(x74042),x74041))+~P1(f773(f773(f334(x74042),x74044),x74041))+P1(f773(f773(f232(x74042),x74043),x74044))+~P1(f773(f773(f232(x74042),x74043),f773(f65(x74042,f104(x74042)),x74041)))
% 191.21/191.75 [7298]E(x72981,f2(a1))+E(f773(f773(f43(a1),x72982),x72981),x72983)+~P1(f773(f773(f232(a1),x72984),f2(a1)))+~E(x72982,f773(f773(f82(a1),f773(f773(f83(a1),x72981),x72983)),x72984))+P1(f773(f773(f233(a1),f2(a1)),x72981))+~P1(f773(f773(f233(a1),x72981),x72984))
% 191.21/191.75 [7314]E(f52(a1,x73142,x73141),x73143)+E(x73141,f2(a1))+~P1(f773(f773(f232(a1),x73143),f2(a1)))+~E(x73142,f773(f773(f82(a1),f773(f773(f83(a1),x73141),x73144)),x73143))+P1(f773(f773(f233(a1),f2(a1)),x73141))+~P1(f773(f773(f233(a1),x73141),x73143))
% 191.21/191.75 [7441]E(x74411,f2(a1))+E(f773(f773(f43(a1),x74412),x74411),x74413)+~E(x74412,f773(f773(f82(a1),f773(f773(f83(a1),x74411),x74413)),x74414))+~P1(f773(f773(f233(a1),f2(a1)),x74411))+~P1(f773(f773(f232(a1),f2(a1)),x74414))+~P1(f773(f773(f233(a1),x74414),x74411))
% 191.21/191.75 [7466]E(f52(a1,x74662,x74661),x74663)+E(x74661,f2(a1))+~E(x74662,f773(f773(f82(a1),f773(f773(f83(a1),x74661),x74664)),x74663))+~P1(f773(f773(f233(a1),f2(a1)),x74661))+~P1(f773(f773(f232(a1),f2(a1)),x74663))+~P1(f773(f773(f233(a1),x74663),x74661))
% 191.21/191.75 [7611]~P100(x76112)+E(x76111,f180(f855(x76112,a841)))+~P1(f773(f63(x76112),x76111))+~P1(f773(f773(f233(x76112),x76114),x76113))+~P1(f773(f773(f334(x76112),x76114),x76111))+P1(f773(f773(f233(x76112),f773(f65(x76112,f236(x76112)),x76111)),x76113))
% 191.21/191.75 [7612]~P100(x76122)+E(x76121,f180(f855(x76122,a841)))+~P1(f773(f63(x76122),x76121))+~P1(f773(f773(f232(x76122),x76124),x76123))+~P1(f773(f773(f334(x76122),x76124),x76121))+P1(f773(f773(f232(x76122),f773(f65(x76122,f236(x76122)),x76121)),x76123))
% 191.21/191.75 [8175]~P1(f773(f773(f232(a1),x81754),f2(a1)))+~E(x81751,f773(f773(f82(a1),f773(f773(f83(a1),x81752),x81753)),x81754))+~P1(f773(f773(f232(a1),f2(a1)),x81754))+~P1(f773(f773(f233(a1),x81754),x81752))+~P1(f773(f773(f233(a1),x81752),x81754))+P1(f773(f56(x81751,x81752),f773(f773(f241(a1,a1),x81753),x81754)))
% 191.21/191.75 [8341]~P99(x83411)+P1(f773(f773(f233(f855(x83411,a841)),f295(x83411,x83412,x83413)),f295(x83411,x83414,x83415)))+~P1(f773(f773(f233(x83411),x83413),x83415))+~P1(f773(f773(f232(x83411),x83414),x83412))+~P1(f773(f773(f232(x83411),x83414),x83415))+~P1(f773(f773(f232(x83411),x83413),x83415))
% 191.21/191.75 [8342]~P99(x83421)+P1(f773(f773(f233(f855(x83421,a841)),f295(x83421,x83422,x83423)),f295(x83421,x83424,x83425)))+~P1(f773(f773(f233(x83421),x83424),x83422))+~P1(f773(f773(f232(x83421),x83423),x83425))+~P1(f773(f773(f232(x83421),x83424),x83425))+~P1(f773(f773(f232(x83421),x83424),x83422))
% 191.21/191.75 [9124]P57(x91242,x91243,x91244,x91241)+E(x91241,f180(f855(x91242,a841)))+~P1(f773(f63(x91242),x91244))+~P1(f773(f63(x91242),x91241))+~P1(f773(f773(x91243,f537(x91241,x91244,x91243,x91242)),x91245))+~P1(f773(f773(f334(x91242),x91245),x91241))
% 191.21/191.75 [9250]~E(x92503,x92505)+~P66(x92501)+~P70(x92501)+~P38(x92503)+E(f773(f773(f8(a1,x92501),x92502),x92503),f773(f773(f8(a1,x92501),x92504),x92505))+P1(f773(f773(f232(a1),f2(a1)),f380(x92502,x92504,x92503,x92505,x92501)))
% 191.21/191.75 [9251]~E(x92513,x92515)+~P66(x92511)+~P70(x92511)+~P38(x92513)+E(f773(f773(f11(a1,x92511),x92512),x92513),f773(f773(f11(a1,x92511),x92514),x92515))+P1(f773(f773(f232(a1),f2(a1)),f533(x92512,x92514,x92513,x92515,x92511)))
% 191.21/191.75 [9416]~E(x94165,x94163)+~P66(x94161)+~P70(x94161)+~P38(x94165)+~E(f773(x94162,f380(x94164,x94162,x94165,x94163,x94161)),f773(x94164,f380(x94164,x94162,x94165,x94163,x94161)))+E(f773(f773(f8(a1,x94161),x94162),x94163),f773(f773(f8(a1,x94161),x94164),x94165))
% 191.21/191.75 [9417]~E(x94175,x94173)+~P66(x94171)+~P70(x94171)+~P38(x94175)+~E(f773(x94172,f533(x94174,x94172,x94175,x94173,x94171)),f773(x94174,f533(x94174,x94172,x94175,x94173,x94171)))+E(f773(f773(f11(a1,x94171),x94172),x94173),f773(f773(f11(a1,x94171),x94174),x94175))
% 191.21/191.75 [9501]~P77(x95013)+E(f773(x95011,x95012),f2(x95013))+~E(f773(f773(f8(x95014,x95013),x95011),x95015),f2(x95013))+~P1(f773(f63(x95014),x95015))+P1(f773(f773(f334(x95014),f463(x95012,x95011,x95015,x95014,x95013)),x95015))+~P1(f773(f773(f334(x95014),x95012),x95015))
% 191.21/191.75 [9623]~P77(x96233)+E(f773(x96231,x96232),f2(x96233))+~E(f773(f773(f8(x96234,x96233),x96231),x96235),f2(x96233))+~P1(f773(f63(x96234),x96235))+~P1(f773(f773(f334(x96234),x96232),x96235))+~P1(f773(f773(f232(x96233),f2(x96233)),f773(x96231,f463(x96232,x96231,x96235,x96234,x96233))))
% 191.21/191.75 [8254]~P123(x82541)+~P1(f773(f773(f232(x82541),f2(x82541)),x82543))+~P1(f773(f773(f233(x82541),x82543),x82545))+~P1(f773(f773(f233(x82541),x82542),x82544))+~P1(f773(f773(f233(x82541),f2(x82541)),x82544))+P1(f773(f773(f233(x82541),f773(f773(f83(x82541),x82542),x82543)),f773(f773(f83(x82541),x82544),x82545)))
% 191.21/191.75 [8255]~P123(x82551)+~P1(f773(f773(f232(x82551),f2(x82551)),x82553))+~P1(f773(f773(f232(x82551),f2(x82551)),x82552))+~P1(f773(f773(f233(x82551),x82553),x82555))+~P1(f773(f773(f233(x82551),x82552),x82554))+P1(f773(f773(f233(x82551),f773(f773(f83(x82551),x82552),x82553)),f773(f773(f83(x82551),x82554),x82555)))
% 191.21/191.75 [8256]~P123(x82561)+~P1(f773(f773(f232(x82561),x82562),x82564))+~P1(f773(f773(f232(x82561),f2(x82561)),x82563))+~P1(f773(f773(f233(x82561),x82563),x82565))+~P1(f773(f773(f233(x82561),f2(x82561)),x82562))+P1(f773(f773(f233(x82561),f773(f773(f83(x82561),x82562),x82563)),f773(f773(f83(x82561),x82564),x82565)))
% 191.21/191.75 [8257]~P123(x82571)+~P1(f773(f773(f232(x82571),x82573),x82575))+~P1(f773(f773(f232(x82571),f2(x82571)),x82572))+~P1(f773(f773(f233(x82571),x82572),x82574))+~P1(f773(f773(f233(x82571),f2(x82571)),x82573))+P1(f773(f773(f233(x82571),f773(f773(f83(x82571),x82572),x82573)),f773(f773(f83(x82571),x82574),x82575)))
% 191.21/191.75 [8258]~P63(x82581)+~P1(f773(f773(f232(x82581),x82582),x82584))+~P1(f773(f773(f233(x82581),x82585),x82583))+~P1(f773(f773(f233(x82581),f2(x82581)),x82585))+~P1(f773(f773(f233(x82581),f2(x82581)),x82582))+P1(f773(f773(f233(x82581),f773(f773(f283(x82581),x82582),x82583)),f773(f773(f283(x82581),x82584),x82585)))
% 191.21/191.75 [8259]~P63(x82591)+~P1(f773(f773(f232(x82591),x82595),x82593))+~P1(f773(f773(f232(x82591),f2(x82591)),x82592))+~P1(f773(f773(f233(x82591),x82592),x82594))+~P1(f773(f773(f233(x82591),f2(x82591)),x82595))+P1(f773(f773(f233(x82591),f773(f773(f283(x82591),x82592),x82593)),f773(f773(f283(x82591),x82594),x82595)))
% 191.21/191.75 [8260]~P131(x82601)+~P1(f773(f773(f232(x82601),x82603),x82605))+~P1(f773(f773(f232(x82601),x82602),x82604))+~P1(f773(f773(f232(x82601),f2(x82601)),x82603))+~P1(f773(f773(f232(x82601),f2(x82601)),x82604))+P1(f773(f773(f232(x82601),f773(f773(f83(x82601),x82602),x82603)),f773(f773(f83(x82601),x82604),x82605)))
% 191.21/191.75 [8261]~P131(x82611)+~P1(f773(f773(f232(x82611),x82613),x82615))+~P1(f773(f773(f232(x82611),x82612),x82614))+~P1(f773(f773(f232(x82611),f2(x82611)),x82613))+~P1(f773(f773(f232(x82611),f2(x82611)),x82612))+P1(f773(f773(f232(x82611),f773(f773(f83(x82611),x82612),x82613)),f773(f773(f83(x82611),x82614),x82615)))
% 191.21/191.75 [8262]~P63(x82621)+~P1(f773(f773(f233(x82621),f2(x82621)),x82625))+~P1(f773(f773(f232(x82621),x82625),x82623))+~P1(f773(f773(f232(x82621),x82622),x82624))+~P1(f773(f773(f232(x82621),f2(x82621)),x82622))+P1(f773(f773(f232(x82621),f773(f773(f283(x82621),x82622),x82623)),f773(f773(f283(x82621),x82624),x82625)))
% 191.21/191.75 [9538]~P66(x95385)+~P80(x95385)+E(x95381,f180(f855(x95382,a841)))+~P1(f773(f63(x95382),x95381))+P1(f773(f773(f334(x95382),f489(x95383,x95384,x95381,x95382,x95385)),x95381))+P1(f773(f773(f233(x95385),f773(f773(f8(x95382,x95385),x95384),x95381)),f773(f773(f8(x95382,x95385),x95383),x95381)))
% 191.21/191.75 [9643]~P66(x96431)+~P78(x96431)+~P1(f773(f63(x96432),x96435))+~P1(f773(f773(f232(x96431),f2(x96431)),f773(x96433,f413(x96433,x96434,x96435,x96432,x96431))))+P1(f773(f773(f232(x96431),f773(f773(f8(x96432,x96431),x96433),x96434)),f773(f773(f8(x96432,x96431),x96433),x96435)))+~P1(f773(f773(f232(f855(x96432,a841)),x96434),x96435))
% 191.21/191.75 [9809]~P66(x98093)+~P80(x98093)+E(x98091,f180(f855(x98092,a841)))+~P1(f773(f63(x98092),x98091))+~P1(f773(f773(f233(x98093),f773(x98094,f489(x98095,x98094,x98091,x98092,x98093))),f773(x98095,f489(x98095,x98094,x98091,x98092,x98093))))+P1(f773(f773(f233(x98093),f773(f773(f8(x98092,x98093),x98094),x98091)),f773(f773(f8(x98092,x98093),x98095),x98091)))
% 191.21/191.75 [6967]~P21(x69672,x69675,x69674)+E(x69671,f180(f855(x69672,a841)))+E(x69673,f180(f855(x69672,a841)))+~P1(f773(f63(x69672),x69671))+~P1(f773(f63(x69672),x69673))+E(f773(x69674,f773(f773(f103(f855(x69672,a841)),x69673),x69671)),f773(f773(x69675,f773(x69674,x69673)),f773(x69674,x69671)))
% 191.21/191.75 [7576]~P141(x75761,x75764,x75763)+P1(f773(x75761,x75762))+~P1(f773(f773(f233(a1),x75764),f2(a1)))+~P1(f773(f773(f232(a1),x75765),f2(a1)))+~E(x75763,f773(f773(f82(a1),f773(f773(f83(a1),x75764),x75762)),x75765))+~P1(f773(f773(f233(a1),x75764),x75765))
% 191.21/191.75 [7577]~P140(x75771,x75774,x75773)+P1(f773(x75771,x75772))+~P1(f773(f773(f233(a1),x75774),f2(a1)))+~P1(f773(f773(f232(a1),x75772),f2(a1)))+~E(x75773,f773(f773(f82(a1),f773(f773(f83(a1),x75774),x75775)),x75772))+~P1(f773(f773(f233(a1),x75774),x75772))
% 191.21/191.75 [7620]~P141(x76201,x76204,x76203)+P1(f773(x76201,x76202))+~E(x76203,f773(f773(f82(a1),f773(f773(f83(a1),x76204),x76202)),x76205))+~P1(f773(f773(f233(a1),f2(a1)),x76204))+~P1(f773(f773(f232(a1),f2(a1)),x76205))+~P1(f773(f773(f233(a1),x76205),x76204))
% 191.21/191.75 [7621]~P140(x76211,x76214,x76213)+P1(f773(x76211,x76212))+~E(x76213,f773(f773(f82(a1),f773(f773(f83(a1),x76214),x76215)),x76212))+~P1(f773(f773(f233(a1),f2(a1)),x76214))+~P1(f773(f773(f232(a1),f2(a1)),x76212))+~P1(f773(f773(f233(a1),x76212),x76214))
% 191.21/191.75 [8546]P1(f773(f773(x85461,x85462),x85463))+~P1(f773(f773(x85461,f773(f773(f43(a1),x85464),x85465)),f52(a1,x85464,x85465)))+~P1(f773(f773(f233(a1),x85465),f2(a1)))+~P1(f773(f773(f232(a1),x85463),f2(a1)))+~E(x85464,f773(f773(f82(a1),f773(f773(f83(a1),x85465),x85462)),x85463))+~P1(f773(f773(f233(a1),x85465),x85463))
% 191.21/191.75 [8553]P1(f773(f773(x85531,x85532),x85533))+~P1(f773(f773(x85531,f773(f773(f43(a1),x85534),x85535)),f52(a1,x85534,x85535)))+~E(x85534,f773(f773(f82(a1),f773(f773(f83(a1),x85535),x85532)),x85533))+~P1(f773(f773(f233(a1),f2(a1)),x85535))+~P1(f773(f773(f232(a1),f2(a1)),x85533))+~P1(f773(f773(f233(a1),x85533),x85535))
% 191.21/191.75 [8772]E(x87721,x87722)+~P54(x87723,x87725,x87724)+~P1(f773(f773(f334(x87723),x87722),x87725))+~P1(f773(f773(f334(x87723),x87721),x87725))+P1(f773(f773(f334(f854(x87723,x87723)),f773(f773(f241(x87723,x87723),x87721),x87722)),x87724))+P1(f773(f773(f334(f854(x87723,x87723)),f773(f773(f241(x87723,x87723),x87722),x87721)),x87724))
% 191.21/191.75 [9567]~P66(x95675)+~P78(x95675)+~P1(f773(f63(x95671),x95674))+P1(f773(f773(f232(x95675),f773(f773(f8(x95671,x95675),x95672),x95673)),f773(f773(f8(x95671,x95675),x95672),x95674)))+~P1(f773(f773(f232(f855(x95671,a841)),x95673),x95674))+P1(f773(f773(f334(x95671),f413(x95672,x95673,x95674,x95671,x95675)),f773(f773(f3(f855(x95671,a841)),x95674),x95673)))
% 191.21/191.75 [9650]E(x96501,f180(f855(x96502,a841)))+~P1(f773(f63(x96502),x96503))+~P1(f773(f63(x96502),x96501))+P1(f773(f773(f334(f854(f855(x96502,a841),f855(x96502,a841))),f773(f773(f241(f855(x96502,a841),f855(x96502,a841)),x96503),x96501)),f324(x96502,x96504)))+~P1(f773(f773(f334(x96502),x96505),x96501))+~P1(f773(f773(f334(f854(x96502,x96502)),f773(f773(f241(x96502,x96502),f539(x96504,x96501,x96503,x96502)),x96505)),x96504))
% 191.21/191.75 [9651]E(x96511,f180(f855(x96512,a841)))+~P1(f773(f63(x96512),x96513))+~P1(f773(f63(x96512),x96511))+P1(f773(f773(f334(f854(f855(x96512,a841),f855(x96512,a841))),f773(f773(f241(f855(x96512,a841),f855(x96512,a841)),x96513),x96511)),f324(x96512,x96514)))+~P1(f773(f773(f334(x96512),x96515),x96511))+~P1(f773(f773(f334(f854(x96512,x96512)),f773(f773(f241(x96512,x96512),f623(x96514,x96511,x96513,x96512)),x96515)),x96514))
% 191.21/191.75 [9812]~P77(x98121)+~E(f773(f773(f8(x98125,x98121),x98122),x98126),x98124)+~P1(f773(f63(x98125),x98126))+P1(f773(f773(f334(x98125),f464(x98123,x98124,x98122,x98126,x98125,x98121)),x98126))+P1(f773(f773(f232(x98121),f773(x98122,x98123)),x98124))+~P1(f773(f773(f334(x98125),x98123),x98126))
% 191.21/191.75 [9866]~P77(x98661)+~E(f773(f773(f8(x98665,x98661),x98662),x98666),x98664)+~P1(f773(f63(x98665),x98666))+~P1(f773(f773(f334(x98665),x98663),x98666))+~P1(f773(f773(f232(x98661),f2(x98661)),f773(x98662,f464(x98663,x98664,x98662,x98666,x98665,x98661))))+P1(f773(f773(f232(x98661),f773(x98662,x98663)),x98664))
% 191.21/191.75 [9983]~E(x99835,x99838)+~E(x99834,x99837)+~P66(x99832)+~P102(x99831)+E(f773(f773(f8(x99831,x99832),x99833),f773(f294(x99831,x99834),x99835)),f773(f773(f8(x99831,x99832),x99836),f773(f294(x99831,x99837),x99838)))+P1(f773(f773(f232(x99831),x99834),f372(x99833,x99836,x99835,x99838,x99834,x99837,x99831,x99832)))
% 191.21/191.75 [9999]~E(x99997,x99994)+~E(x99998,x99995)+~P66(x99992)+~P102(x99991)+~E(f773(x99993,f372(x99996,x99993,x99998,x99995,x99997,x99994,x99991,x99992)),f773(x99996,f372(x99996,x99993,x99998,x99995,x99997,x99994,x99991,x99992)))+E(f773(f773(f8(x99991,x99992),x99993),f773(f294(x99991,x99994),x99995)),f773(f773(f8(x99991,x99992),x99996),f773(f294(x99991,x99997),x99998)))
% 191.21/191.75 [10002]~E(x100024,x100027)+~E(x100025,x100028)+~P66(x100022)+~P102(x100021)+E(f773(f773(f8(x100021,x100022),x100023),f773(f294(x100021,x100024),x100025)),f773(f773(f8(x100021,x100022),x100026),f773(f294(x100021,x100027),x100028)))+P1(f773(f773(f233(x100021),f372(x100023,x100026,x100025,x100028,x100024,x100027,x100021,x100022)),x100025))
% 191.21/191.75 [9655]~P12(x96555,x96559,x96556)+~P12(x96551,x965510,x96553)+~P17(x96551,x96555,f855(x96552,a841),x96553,x96556,x96558)+~P1(f773(f773(f334(x96555),x96557),x96559))+~P1(f773(f773(f334(x96551),x96554),x965510))+E(f773(f773(f46(x96551,f855(x96552,a841)),f773(f277(x96551,x96551,x96553),f773(f773(f302(x96551),x96554),f180(f855(x96551,a841))))),f773(f773(f10(f855(x96555,f855(x96552,a841)),f855(x96552,a841),x96551),f773(f46(x96555,f855(x96552,a841)),f773(f277(x96555,x96555,x96556),f773(f773(f302(x96555),x96557),f180(f855(x96555,a841)))))),x96558)),f773(f773(x96558,x96554),x96557))
% 191.21/191.75 [5462]~P100(x54623)+~P18(x54623,x54622)+~P18(x54623,x54621)+E(x54621,x54622)+~E(f773(f158(x54623),x54621),f773(f158(x54623),x54622))+~P1(f773(f127(x54623),x54622))+~P1(f773(f127(x54623),x54621))
% 191.21/191.75 [4816]~P122(x48162)+~P127(x48162)+~P138(x48162)+~P105(x48162)+~E(x48163,f2(x48162))+E(x48161,f2(a847))+E(f773(f773(f242(x48162),x48163),x48161),f2(x48162))
% 191.21/191.75 [9010]E(x90101,f2(a847))+~E(x90102,f773(f773(f82(a847),f773(f773(f83(a847),f773(f240(a847,a847),x90103)),x90101)),f773(f250(a847,a847),x90103)))+P1(f773(f55(x90102,x90101),x90103))+~P1(f773(f773(f232(a847),f773(f250(a847,a847),x90103)),f2(a847)))+~P1(f773(f773(f232(a847),f2(a847)),f773(f250(a847,a847),x90103)))+~P1(f773(f773(f233(a847),x90101),f773(f250(a847,a847),x90103)))+~P1(f773(f773(f233(a847),f773(f250(a847,a847),x90103)),x90101))
% 191.21/191.75 [9018]~E(f773(f240(a847,a847),x90183),f2(a847))+~E(x90181,f773(f773(f82(a847),f773(f773(f83(a847),f773(f240(a847,a847),x90183)),x90182)),f773(f250(a847,a847),x90183)))+P1(f773(f55(x90181,x90182),x90183))+~P1(f773(f773(f232(a847),f773(f250(a847,a847),x90183)),f2(a847)))+~P1(f773(f773(f232(a847),f2(a847)),f773(f250(a847,a847),x90183)))+~P1(f773(f773(f233(a847),x90182),f773(f250(a847,a847),x90183)))+~P1(f773(f773(f233(a847),f773(f250(a847,a847),x90183)),x90182))
% 191.21/191.75 [7935]~P64(x79352)+E(x79351,f180(f855(x79352,a841)))+E(x79353,f180(f855(x79352,a841)))+~P1(f773(f63(x79352),x79351))+~P1(f773(f63(x79352),x79353))+~E(f773(f773(f104(f855(x79352,a841)),x79353),x79351),f180(f855(x79352,a841)))+E(f773(f773(f83(x79352),f773(f65(x79352,f83(x79352)),x79353)),f773(f65(x79352,f83(x79352)),x79351)),f773(f65(x79352,f83(x79352)),f773(f773(f103(f855(x79352,a841)),x79353),x79351)))
% 191.21/191.75 [7714]E(x77141,f2(a1))+E(f773(f773(f43(a1),x77142),x77141),x77143)+~P1(f773(f773(f232(a1),x77144),f2(a1)))+~E(x77142,f773(f773(f82(a1),f773(f773(f83(a1),x77141),x77143)),x77144))+~P1(f773(f773(f232(a1),f2(a1)),x77144))+~P1(f773(f773(f233(a1),x77144),x77141))+~P1(f773(f773(f233(a1),x77141),x77144))
% 191.21/191.75 [7720]E(f52(a1,x77202,x77201),x77203)+E(x77201,f2(a1))+~P1(f773(f773(f232(a1),x77203),f2(a1)))+~E(x77202,f773(f773(f82(a1),f773(f773(f83(a1),x77201),x77204)),x77203))+~P1(f773(f773(f232(a1),f2(a1)),x77203))+~P1(f773(f773(f233(a1),x77203),x77201))+~P1(f773(f773(f233(a1),x77201),x77203))
% 191.21/191.75 [6741]~P7(x67412)+E(x67411,f2(x67412))+E(x67413,f2(x67412))+~E(f773(f773(f43(x67412),x67414),x67413),f773(f773(f43(x67412),x67415),x67411))+E(f773(f773(f83(x67412),x67414),x67411),f773(f773(f83(x67412),x67413),x67415))+~P1(f773(f773(f279(x67412),x67411),x67415))+~P1(f773(f773(f279(x67412),x67413),x67414))
% 191.21/191.75 [6742]~P7(x67422)+E(x67421,f2(x67422))+E(x67423,f2(x67422))+~E(f773(f773(f83(x67422),x67424),x67423),f773(f773(f83(x67422),x67421),x67425))+E(f773(f773(f43(x67422),x67424),x67421),f773(f773(f43(x67422),x67425),x67423))+~P1(f773(f773(f279(x67422),x67421),x67424))+~P1(f773(f773(f279(x67422),x67423),x67425))
% 191.21/191.75 [7629]~P22(x76292,x76295,x76294)+E(x76291,f180(f855(x76292,a841)))+E(x76293,f180(f855(x76292,a841)))+~P1(f773(f63(x76292),x76291))+~P1(f773(f63(x76292),x76293))+~E(f773(f773(f104(f855(x76292,a841)),x76293),x76291),f180(f855(x76292,a841)))+E(f773(x76294,f773(f773(f103(f855(x76292,a841)),x76293),x76291)),f773(f773(x76295,f773(x76294,x76293)),f773(x76294,x76291)))
% 191.21/191.75 [9222]~P29(x92223,x92221,x92225,x92224)+~P29(x92221,x92223,x92226,x92222)+E(f773(f42(x92221),x92222),f773(f42(x92223),x92224))+~P1(f773(f63(x92223),x92224))+~P1(f773(f63(x92221),x92222))+~P1(f773(f773(f232(f855(x92223,a841)),f773(f303(x92221,x92223,x92226),x92222)),x92224))+~P1(f773(f773(f232(f855(x92221,a841)),f773(f303(x92223,x92221,x92225),x92224)),x92222))
% 191.21/191.75 [9170]~P1(f773(f773(f233(a1),f773(f773(f82(a1),f773(f773(f83(a1),x91705),x91701)),x91706)),f2(a1)))+~E(f773(f773(f82(a1),f773(f773(f83(a1),x91703),x91702)),x91704),f773(f773(f82(a1),f773(f773(f83(a1),x91705),x91701)),x91706))+~P1(f773(f773(f233(a1),f2(a1)),x91705))+~P1(f773(f773(f232(a1),f2(a1)),x91706))+~P1(f773(f773(f233(a1),x91704),x91703))+~P1(f773(f773(f232(a1),x91705),x91703))+P1(f773(f773(f232(a1),x91701),x91702))
% 191.21/191.75 [8961]~E(f773(f773(f82(a1),f773(f773(f83(a1),x89613),x89611)),x89614),f773(f773(f82(a1),f773(f773(f83(a1),x89615),x89612)),x89616))+~P1(f773(f773(f233(a1),f2(a1)),x89615))+~P1(f773(f773(f232(a1),f2(a1)),x89614))+~P1(f773(f773(f233(a1),x89616),x89615))+~P1(f773(f773(f232(a1),x89615),x89613))+P1(f773(f773(f232(a1),x89611),x89612))+~P1(f773(f773(f232(a1),f2(a1)),f773(f773(f82(a1),f773(f773(f83(a1),x89615),x89612)),x89616)))
% 191.21/191.75 [9126]~P124(x91261)+~E(f773(f773(f82(x91261),x91262),x91264),f80(x91261))+~P1(f773(f773(f232(x91261),f2(x91261)),x91264))+~P1(f773(f773(f232(x91261),f2(x91261)),x91262))+~P1(f773(f773(f233(x91261),x91265),x91266))+~P1(f773(f773(f233(x91261),x91263),x91266))+P1(f773(f773(f233(x91261),f773(f773(f82(x91261),f773(f773(f83(x91261),x91262),x91263)),f773(f773(f83(x91261),x91264),x91265))),x91266))
% 191.21/191.75 [9127]~P126(x91271)+~E(f773(f773(f82(x91271),x91272),x91274),f80(x91271))+~P1(f773(f773(f232(x91271),x91275),x91276))+~P1(f773(f773(f232(x91271),x91273),x91276))+~P1(f773(f773(f232(x91271),f2(x91271)),x91274))+~P1(f773(f773(f232(x91271),f2(x91271)),x91272))+P1(f773(f773(f232(x91271),f773(f773(f82(x91271),f773(f773(f83(x91271),x91272),x91273)),f773(f773(f83(x91271),x91274),x91275))),x91276))
% 191.21/191.75 [9908]~P12(x99087,x99086,x99085)+E(x99081,x99082)+~P16(x99087,f855(x99084,a841),x99085,x99083)+E(f773(x99083,f499(x99081,x99082,x99083,x99084,x99085,x99086,x99087)),f773(x99083,f500(x99081,x99082,x99083,x99084,x99085,x99086,x99087)))+~E(f773(f773(f46(x99087,f855(x99084,a841)),x99081),x99083),f773(f773(f46(x99087,f855(x99084,a841)),x99082),x99083))+~P1(f773(f773(f334(f855(x99087,a841)),x99082),f773(f773(f61(x99087),x99086),x99085)))+~P1(f773(f773(f334(f855(x99087,a841)),x99081),f773(f773(f61(x99087),x99086),x99085)))
% 191.21/191.75 [9948]~P12(x99483,x99487,x99486)+E(x99481,x99482)+~P16(x99483,f855(x99485,a841),x99486,x99484)+~E(f773(f773(f46(x99483,f855(x99485,a841)),x99481),x99484),f773(f773(f46(x99483,f855(x99485,a841)),x99482),x99484))+P1(f773(f773(f334(x99483),f500(x99481,x99482,x99484,x99485,x99486,x99487,x99483)),x99487))+~P1(f773(f773(f334(f855(x99483,a841)),x99482),f773(f773(f61(x99483),x99487),x99486)))+~P1(f773(f773(f334(f855(x99483,a841)),x99481),f773(f773(f61(x99483),x99487),x99486)))
% 191.21/191.75 [9949]~P12(x99493,x99497,x99496)+E(x99491,x99492)+~P16(x99493,f855(x99495,a841),x99496,x99494)+~E(f773(f773(f46(x99493,f855(x99495,a841)),x99491),x99494),f773(f773(f46(x99493,f855(x99495,a841)),x99492),x99494))+P1(f773(f773(f334(x99493),f499(x99491,x99492,x99494,x99495,x99496,x99497,x99493)),x99497))+~P1(f773(f773(f334(f855(x99493,a841)),x99492),f773(f773(f61(x99493),x99497),x99496)))+~P1(f773(f773(f334(f855(x99493,a841)),x99491),f773(f773(f61(x99493),x99497),x99496)))
% 191.21/191.75 [10015]E(x100151,x100152)+~P12(x100153,x100156,x100157)+~P16(x100153,f855(x100154,a841),x100157,x100155)+~E(f773(f773(f46(x100153,f855(x100154,a841)),x100151),x100155),f773(f773(f46(x100153,f855(x100154,a841)),x100152),x100155))+~P1(f773(f773(f334(f854(x100153,x100153)),f773(f773(f241(x100153,x100153),f500(x100151,x100152,x100155,x100154,x100157,x100156,x100153)),f499(x100151,x100152,x100155,x100154,x100157,x100156,x100153))),x100157))+~P1(f773(f773(f334(f855(x100153,a841)),x100152),f773(f773(f61(x100153),x100156),x100157)))+~P1(f773(f773(f334(f855(x100153,a841)),x100151),f773(f773(f61(x100153),x100156),x100157)))
% 191.21/191.75 [8960]~P12(x89601,x89607,x89604)+~E(x89605,x89606)+~P1(f773(f773(f334(x89601),x89603),x89606))+~P1(f773(f773(f334(x89601),x89602),x89605))+~P1(f773(f773(f334(f855(x89601,a841)),x89606),f773(f773(f61(x89601),x89607),x89604)))+~P1(f773(f773(f334(f855(x89601,a841)),x89605),f773(f773(f61(x89601),x89607),x89604)))+P1(f773(f773(f334(f854(x89601,x89601)),f773(f773(f241(x89601,x89601),x89602),x89603)),x89604))
% 191.21/191.75 [9091]E(x90911,x90912)+~P12(x90913,x90914,x90915)+~P1(f773(f773(f334(x90913),x90916),x90912))+~P1(f773(f773(f334(x90913),x90917),x90911))+~P1(f773(f773(f334(f855(x90913,a841)),x90912),f773(f773(f61(x90913),x90914),x90915)))+~P1(f773(f773(f334(f855(x90913,a841)),x90911),f773(f773(f61(x90913),x90914),x90915)))+~P1(f773(f773(f334(f854(x90913,x90913)),f773(f773(f241(x90913,x90913),x90917),x90916)),x90915))
% 191.21/191.75 [10032]~P12(x100329,x100328,x100327)+~P12(x100321,x1003211,x1003210)+~P17(x100321,x100329,f855(x100326,a841),x1003210,x100327,x100325)+P1(f773(f773(f334(x100321),f501(x100322,x100323,x100324,x100325,x100326,x100327,x100328,x100329,x1003210,x1003211,x100321)),x1003211))+~P1(f773(f773(f334(f855(x100329,a841)),x100323),f773(f773(f61(x100329),x100328),x100327)))+~P1(f773(f773(f334(f855(x100321,a841)),x100324),f773(f773(f61(x100321),x1003211),x1003210)))+P1(f773(f773(f334(f855(x100326,a841)),f773(f773(f46(x100321,f855(x100326,a841)),x100324),f773(f773(f10(f855(x100329,f855(x100326,a841)),f855(x100326,a841),x100321),f773(f46(x100329,f855(x100326,a841)),x100323)),x100325))),x100322))
% 191.21/191.75 [10033]~P12(x1003311,x1003310,x100339)+~P12(x100331,x100338,x100337)+~P17(x1003311,x100331,f855(x100336,a841),x100339,x100337,x100335)+P1(f773(f773(f334(x100331),f502(x100332,x100333,x100334,x100335,x100336,x100337,x100338,x100331,x100339,x1003310,x1003311)),x100338))+~P1(f773(f773(f334(f855(x1003311,a841)),x100334),f773(f773(f61(x1003311),x1003310),x100339)))+~P1(f773(f773(f334(f855(x100331,a841)),x100333),f773(f773(f61(x100331),x100338),x100337)))+P1(f773(f773(f334(f855(x100336,a841)),f773(f773(f46(x1003311,f855(x100336,a841)),x100334),f773(f773(f10(f855(x100331,f855(x100336,a841)),f855(x100336,a841),x1003311),f773(f46(x100331,f855(x100336,a841)),x100333)),x100335))),x100332))
% 191.21/191.75 [10036]~P12(x100362,x100368,x100369)+~P12(x100364,x1003610,x1003611)+~P17(x100362,x100364,f855(x100361,a841),x100369,x1003611,x100366)+~P1(f773(f773(f334(f855(x100362,a841)),x100363),f773(f773(f61(x100362),x100368),x100369)))+~P1(f773(f773(f334(f855(x100364,a841)),x100365),f773(f773(f61(x100364),x1003610),x1003611)))+~P1(f773(f773(f334(f855(x100361,a841)),f773(f773(x100366,f501(x100367,x100365,x100363,x100366,x100361,x1003611,x1003610,x100364,x100369,x100368,x100362)),f502(x100367,x100365,x100363,x100366,x100361,x1003611,x1003610,x100364,x100369,x100368,x100362))),x100367))+P1(f773(f773(f334(f855(x100361,a841)),f773(f773(f46(x100362,f855(x100361,a841)),x100363),f773(f773(f10(f855(x100364,f855(x100361,a841)),f855(x100361,a841),x100362),f773(f46(x100364,f855(x100361,a841)),x100365)),x100366))),x100367))
% 191.21/191.75 [9003]E(x90031,x90032)+~P100(x90034)+~P29(x90033,x90034,x90035,f773(f773(f103(f855(x90033,a841)),f773(f158(x90033),x90031)),f773(f158(x90033),x90032)))+~E(f773(f158(x90033),x90031),f773(f158(x90033),x90032))+~P18(x90034,f773(f773(f143(x90033,x90034),x90035),x90032))+~P18(x90034,f773(f773(f143(x90033,x90034),x90035),x90031))+~P1(f773(f127(x90034),f773(f773(f143(x90033,x90034),x90035),x90032)))+~P1(f773(f127(x90034),f773(f773(f143(x90033,x90034),x90035),x90031)))
% 191.21/191.75 %EqnAxiom
% 191.21/191.75 [1]E(x11,x11)
% 191.21/191.75 [2]E(x22,x21)+~E(x21,x22)
% 191.21/191.75 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 191.21/191.75 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 191.21/191.75 [5]~E(x51,x52)+E(f3(x51),f3(x52))
% 191.21/191.75 [6]~E(x61,x62)+E(f102(x61),f102(x62))
% 191.21/191.75 [7]~E(x71,x72)+E(f34(x71),f34(x72))
% 191.21/191.75 [8]~E(x81,x82)+E(f773(x81,x83),f773(x82,x83))
% 191.21/191.75 [9]~E(x91,x92)+E(f773(x93,x91),f773(x93,x92))
% 191.21/191.75 [10]~E(x101,x102)+E(f86(x101),f86(x102))
% 191.21/191.75 [11]~E(x111,x112)+E(f586(x111,x113,x114,x115,x116,x117),f586(x112,x113,x114,x115,x116,x117))
% 191.21/191.75 [12]~E(x121,x122)+E(f586(x123,x121,x124,x125,x126,x127),f586(x123,x122,x124,x125,x126,x127))
% 191.21/191.75 [13]~E(x131,x132)+E(f586(x133,x134,x131,x135,x136,x137),f586(x133,x134,x132,x135,x136,x137))
% 191.21/191.75 [14]~E(x141,x142)+E(f586(x143,x144,x145,x141,x146,x147),f586(x143,x144,x145,x142,x146,x147))
% 191.21/191.75 [15]~E(x151,x152)+E(f586(x153,x154,x155,x156,x151,x157),f586(x153,x154,x155,x156,x152,x157))
% 191.21/191.75 [16]~E(x161,x162)+E(f586(x163,x164,x165,x166,x167,x161),f586(x163,x164,x165,x166,x167,x162))
% 191.21/191.75 [17]~E(x171,x172)+E(f170(x171,x173,x174,x175),f170(x172,x173,x174,x175))
% 191.21/191.75 [18]~E(x181,x182)+E(f170(x183,x181,x184,x185),f170(x183,x182,x184,x185))
% 191.21/191.75 [19]~E(x191,x192)+E(f170(x193,x194,x191,x195),f170(x193,x194,x192,x195))
% 191.21/191.75 [20]~E(x201,x202)+E(f170(x203,x204,x205,x201),f170(x203,x204,x205,x202))
% 191.21/191.75 [21]~E(x211,x212)+E(f9(x211,x213,x214),f9(x212,x213,x214))
% 191.21/191.75 [22]~E(x221,x222)+E(f9(x223,x221,x224),f9(x223,x222,x224))
% 191.21/191.75 [23]~E(x231,x232)+E(f9(x233,x234,x231),f9(x233,x234,x232))
% 191.21/191.75 [24]~E(x241,x242)+E(f179(x241),f179(x242))
% 191.21/191.75 [25]~E(x251,x252)+E(f103(x251),f103(x252))
% 191.21/191.75 [26]~E(x261,x262)+E(f180(x261),f180(x262))
% 191.21/191.75 [27]~E(x271,x272)+E(f502(x271,x273,x274,x275,x276,x277,x278,x279,x2710,x2711,x2712),f502(x272,x273,x274,x275,x276,x277,x278,x279,x2710,x2711,x2712))
% 191.21/191.75 [28]~E(x281,x282)+E(f502(x283,x281,x284,x285,x286,x287,x288,x289,x2810,x2811,x2812),f502(x283,x282,x284,x285,x286,x287,x288,x289,x2810,x2811,x2812))
% 191.21/191.75 [29]~E(x291,x292)+E(f502(x293,x294,x291,x295,x296,x297,x298,x299,x2910,x2911,x2912),f502(x293,x294,x292,x295,x296,x297,x298,x299,x2910,x2911,x2912))
% 191.21/191.75 [30]~E(x301,x302)+E(f502(x303,x304,x305,x301,x306,x307,x308,x309,x3010,x3011,x3012),f502(x303,x304,x305,x302,x306,x307,x308,x309,x3010,x3011,x3012))
% 191.21/191.75 [31]~E(x311,x312)+E(f502(x313,x314,x315,x316,x311,x317,x318,x319,x3110,x3111,x3112),f502(x313,x314,x315,x316,x312,x317,x318,x319,x3110,x3111,x3112))
% 191.21/191.75 [32]~E(x321,x322)+E(f502(x323,x324,x325,x326,x327,x321,x328,x329,x3210,x3211,x3212),f502(x323,x324,x325,x326,x327,x322,x328,x329,x3210,x3211,x3212))
% 191.21/191.75 [33]~E(x331,x332)+E(f502(x333,x334,x335,x336,x337,x338,x331,x339,x3310,x3311,x3312),f502(x333,x334,x335,x336,x337,x338,x332,x339,x3310,x3311,x3312))
% 191.21/191.75 [34]~E(x341,x342)+E(f502(x343,x344,x345,x346,x347,x348,x349,x341,x3410,x3411,x3412),f502(x343,x344,x345,x346,x347,x348,x349,x342,x3410,x3411,x3412))
% 191.21/191.75 [35]~E(x351,x352)+E(f502(x353,x354,x355,x356,x357,x358,x359,x3510,x351,x3511,x3512),f502(x353,x354,x355,x356,x357,x358,x359,x3510,x352,x3511,x3512))
% 191.21/191.75 [36]~E(x361,x362)+E(f502(x363,x364,x365,x366,x367,x368,x369,x3610,x3611,x361,x3612),f502(x363,x364,x365,x366,x367,x368,x369,x3610,x3611,x362,x3612))
% 191.21/191.75 [37]~E(x371,x372)+E(f502(x373,x374,x375,x376,x377,x378,x379,x3710,x3711,x3712,x371),f502(x373,x374,x375,x376,x377,x378,x379,x3710,x3711,x3712,x372))
% 191.21/191.75 [38]~E(x381,x382)+E(f236(x381),f236(x382))
% 191.21/191.75 [39]~E(x391,x392)+E(f104(x391),f104(x392))
% 191.21/191.75 [40]~E(x401,x402)+E(f105(x401),f105(x402))
% 191.21/191.75 [41]~E(x411,x412)+E(f39(x411),f39(x412))
% 191.21/191.75 [42]~E(x421,x422)+E(f334(x421),f334(x422))
% 191.21/191.75 [43]~E(x431,x432)+E(f80(x431),f80(x432))
% 191.21/191.75 [44]~E(x441,x442)+E(f501(x441,x443,x444,x445,x446,x447,x448,x449,x4410,x4411,x4412),f501(x442,x443,x444,x445,x446,x447,x448,x449,x4410,x4411,x4412))
% 191.21/191.75 [45]~E(x451,x452)+E(f501(x453,x451,x454,x455,x456,x457,x458,x459,x4510,x4511,x4512),f501(x453,x452,x454,x455,x456,x457,x458,x459,x4510,x4511,x4512))
% 191.21/191.75 [46]~E(x461,x462)+E(f501(x463,x464,x461,x465,x466,x467,x468,x469,x4610,x4611,x4612),f501(x463,x464,x462,x465,x466,x467,x468,x469,x4610,x4611,x4612))
% 191.21/191.75 [47]~E(x471,x472)+E(f501(x473,x474,x475,x471,x476,x477,x478,x479,x4710,x4711,x4712),f501(x473,x474,x475,x472,x476,x477,x478,x479,x4710,x4711,x4712))
% 191.21/191.75 [48]~E(x481,x482)+E(f501(x483,x484,x485,x486,x481,x487,x488,x489,x4810,x4811,x4812),f501(x483,x484,x485,x486,x482,x487,x488,x489,x4810,x4811,x4812))
% 191.21/191.75 [49]~E(x491,x492)+E(f501(x493,x494,x495,x496,x497,x491,x498,x499,x4910,x4911,x4912),f501(x493,x494,x495,x496,x497,x492,x498,x499,x4910,x4911,x4912))
% 191.21/191.75 [50]~E(x501,x502)+E(f501(x503,x504,x505,x506,x507,x508,x501,x509,x5010,x5011,x5012),f501(x503,x504,x505,x506,x507,x508,x502,x509,x5010,x5011,x5012))
% 191.21/191.75 [51]~E(x511,x512)+E(f501(x513,x514,x515,x516,x517,x518,x519,x511,x5110,x5111,x5112),f501(x513,x514,x515,x516,x517,x518,x519,x512,x5110,x5111,x5112))
% 191.21/191.75 [52]~E(x521,x522)+E(f501(x523,x524,x525,x526,x527,x528,x529,x5210,x521,x5211,x5212),f501(x523,x524,x525,x526,x527,x528,x529,x5210,x522,x5211,x5212))
% 191.21/191.75 [53]~E(x531,x532)+E(f501(x533,x534,x535,x536,x537,x538,x539,x5310,x5311,x531,x5312),f501(x533,x534,x535,x536,x537,x538,x539,x5310,x5311,x532,x5312))
% 191.21/191.75 [54]~E(x541,x542)+E(f501(x543,x544,x545,x546,x547,x548,x549,x5410,x5411,x5412,x541),f501(x543,x544,x545,x546,x547,x548,x549,x5410,x5411,x5412,x542))
% 191.21/191.75 [55]~E(x551,x552)+E(f113(x551),f113(x552))
% 191.21/191.75 [56]~E(x561,x562)+E(f44(x561,x563),f44(x562,x563))
% 191.21/191.75 [57]~E(x571,x572)+E(f44(x573,x571),f44(x573,x572))
% 191.21/191.75 [58]~E(x581,x582)+E(f855(x581,x583),f855(x582,x583))
% 191.21/191.75 [59]~E(x591,x592)+E(f855(x593,x591),f855(x593,x592))
% 191.21/191.75 [60]~E(x601,x602)+E(f6(x601),f6(x602))
% 191.21/191.75 [61]~E(x611,x612)+E(f82(x611),f82(x612))
% 191.21/191.75 [62]~E(x621,x622)+E(f35(x621,x623),f35(x622,x623))
% 191.21/191.75 [63]~E(x631,x632)+E(f35(x633,x631),f35(x633,x632))
% 191.21/191.75 [64]~E(x641,x642)+E(f81(x641),f81(x642))
% 191.21/191.75 [65]~E(x651,x652)+E(f63(x651),f63(x652))
% 191.21/191.75 [66]~E(x661,x662)+E(f181(x661),f181(x662))
% 191.21/191.75 [67]~E(x671,x672)+E(f10(x671,x673,x674),f10(x672,x673,x674))
% 191.21/191.75 [68]~E(x681,x682)+E(f10(x683,x681,x684),f10(x683,x682,x684))
% 191.21/191.75 [69]~E(x691,x692)+E(f10(x693,x694,x691),f10(x693,x694,x692))
% 191.21/191.75 [70]~E(x701,x702)+E(f106(x701),f106(x702))
% 191.21/191.75 [71]~E(x711,x712)+E(f854(x711,x713),f854(x712,x713))
% 191.21/191.75 [72]~E(x721,x722)+E(f854(x723,x721),f854(x723,x722))
% 191.21/191.75 [73]~E(x731,x732)+E(f20(x731,x733,x734),f20(x732,x733,x734))
% 191.21/191.75 [74]~E(x741,x742)+E(f20(x743,x741,x744),f20(x743,x742,x744))
% 191.21/191.75 [75]~E(x751,x752)+E(f20(x753,x754,x751),f20(x753,x754,x752))
% 191.21/191.75 [76]~E(x761,x762)+E(f256(x761),f256(x762))
% 191.21/191.75 [77]~E(x771,x772)+E(f42(x771),f42(x772))
% 191.21/191.75 [78]~E(x781,x782)+E(f61(x781),f61(x782))
% 191.21/191.75 [79]~E(x791,x792)+E(f409(x791,x793,x794,x795),f409(x792,x793,x794,x795))
% 191.21/191.75 [80]~E(x801,x802)+E(f409(x803,x801,x804,x805),f409(x803,x802,x804,x805))
% 191.21/191.75 [81]~E(x811,x812)+E(f409(x813,x814,x811,x815),f409(x813,x814,x812,x815))
% 191.21/191.75 [82]~E(x821,x822)+E(f409(x823,x824,x825,x821),f409(x823,x824,x825,x822))
% 191.21/191.75 [83]~E(x831,x832)+E(f83(x831),f83(x832))
% 191.21/191.75 [84]~E(x841,x842)+E(f305(x841,x843,x844),f305(x842,x843,x844))
% 191.21/191.75 [85]~E(x851,x852)+E(f305(x853,x851,x854),f305(x853,x852,x854))
% 191.21/191.75 [86]~E(x861,x862)+E(f305(x863,x864,x861),f305(x863,x864,x862))
% 191.21/191.75 [87]~E(x871,x872)+E(f405(x871,x873,x874),f405(x872,x873,x874))
% 191.21/191.75 [88]~E(x881,x882)+E(f405(x883,x881,x884),f405(x883,x882,x884))
% 191.21/191.75 [89]~E(x891,x892)+E(f405(x893,x894,x891),f405(x893,x894,x892))
% 191.21/191.75 [90]~E(x901,x902)+E(f115(x901),f115(x902))
% 191.21/191.75 [91]~E(x911,x912)+E(f466(x911,x913,x914),f466(x912,x913,x914))
% 191.21/191.75 [92]~E(x921,x922)+E(f466(x923,x921,x924),f466(x923,x922,x924))
% 191.21/191.75 [93]~E(x931,x932)+E(f466(x933,x934,x931),f466(x933,x934,x932))
% 191.21/191.75 [94]~E(x941,x942)+E(f233(x941),f233(x942))
% 191.21/191.75 [95]~E(x951,x952)+E(f294(x951,x953),f294(x952,x953))
% 191.21/191.75 [96]~E(x961,x962)+E(f294(x963,x961),f294(x963,x962))
% 191.21/191.75 [97]~E(x971,x972)+E(f467(x971,x973,x974),f467(x972,x973,x974))
% 191.21/191.75 [98]~E(x981,x982)+E(f467(x983,x981,x984),f467(x983,x982,x984))
% 191.21/191.75 [99]~E(x991,x992)+E(f467(x993,x994,x991),f467(x993,x994,x992))
% 191.21/191.75 [100]~E(x1001,x1002)+E(f232(x1001),f232(x1002))
% 191.21/191.75 [101]~E(x1011,x1012)+E(f130(x1011,x1013),f130(x1012,x1013))
% 191.21/191.75 [102]~E(x1021,x1022)+E(f130(x1023,x1021),f130(x1023,x1022))
% 191.21/191.75 [103]~E(x1031,x1032)+E(f164(x1031,x1033),f164(x1032,x1033))
% 191.21/191.75 [104]~E(x1041,x1042)+E(f164(x1043,x1041),f164(x1043,x1042))
% 191.21/191.75 [105]~E(x1051,x1052)+E(f848(x1051),f848(x1052))
% 191.21/191.75 [106]~E(x1061,x1062)+E(f33(x1061,x1063,x1064),f33(x1062,x1063,x1064))
% 191.21/191.75 [107]~E(x1071,x1072)+E(f33(x1073,x1071,x1074),f33(x1073,x1072,x1074))
% 191.21/191.75 [108]~E(x1081,x1082)+E(f33(x1083,x1084,x1081),f33(x1083,x1084,x1082))
% 191.21/191.75 [109]~E(x1091,x1092)+E(f126(x1091,x1093),f126(x1092,x1093))
% 191.21/191.75 [110]~E(x1101,x1102)+E(f126(x1103,x1101),f126(x1103,x1102))
% 191.21/191.75 [111]~E(x1111,x1112)+E(f187(x1111),f187(x1112))
% 191.21/191.75 [112]~E(x1121,x1122)+E(f52(x1121,x1123,x1124),f52(x1122,x1123,x1124))
% 191.21/191.75 [113]~E(x1131,x1132)+E(f52(x1133,x1131,x1134),f52(x1133,x1132,x1134))
% 191.21/191.75 [114]~E(x1141,x1142)+E(f52(x1143,x1144,x1141),f52(x1143,x1144,x1142))
% 191.21/191.75 [115]~E(x1151,x1152)+E(f239(x1151),f239(x1152))
% 191.21/191.75 [116]~E(x1161,x1162)+E(f11(x1161,x1163),f11(x1162,x1163))
% 191.21/191.75 [117]~E(x1171,x1172)+E(f11(x1173,x1171),f11(x1173,x1172))
% 191.21/191.75 [118]~E(x1181,x1182)+E(f159(x1181),f159(x1182))
% 191.21/191.75 [119]~E(x1191,x1192)+E(f8(x1191,x1193),f8(x1192,x1193))
% 191.21/191.75 [120]~E(x1201,x1202)+E(f8(x1203,x1201),f8(x1203,x1202))
% 191.21/191.75 [121]~E(x1211,x1212)+E(f84(x1211,x1213),f84(x1212,x1213))
% 191.21/191.75 [122]~E(x1221,x1222)+E(f84(x1223,x1221),f84(x1223,x1222))
% 191.21/191.75 [123]~E(x1231,x1232)+E(f241(x1231,x1233),f241(x1232,x1233))
% 191.21/191.75 [124]~E(x1241,x1242)+E(f241(x1243,x1241),f241(x1243,x1242))
% 191.21/191.75 [125]~E(x1251,x1252)+E(f279(x1251),f279(x1252))
% 191.21/191.75 [126]~E(x1261,x1262)+E(f283(x1261),f283(x1262))
% 191.21/191.75 [127]~E(x1271,x1272)+E(f250(x1271,x1273),f250(x1272,x1273))
% 191.21/191.75 [128]~E(x1281,x1282)+E(f250(x1283,x1281),f250(x1283,x1282))
% 191.21/191.75 [129]~E(x1291,x1292)+E(f127(x1291),f127(x1292))
% 191.21/191.75 [130]~E(x1301,x1302)+E(f43(x1301),f43(x1302))
% 191.21/191.75 [131]~E(x1311,x1312)+E(f484(x1311,x1313,x1314,x1315,x1316),f484(x1312,x1313,x1314,x1315,x1316))
% 191.21/191.75 [132]~E(x1321,x1322)+E(f484(x1323,x1321,x1324,x1325,x1326),f484(x1323,x1322,x1324,x1325,x1326))
% 191.21/191.75 [133]~E(x1331,x1332)+E(f484(x1333,x1334,x1331,x1335,x1336),f484(x1333,x1334,x1332,x1335,x1336))
% 191.21/191.75 [134]~E(x1341,x1342)+E(f484(x1343,x1344,x1345,x1341,x1346),f484(x1343,x1344,x1345,x1342,x1346))
% 191.21/191.75 [135]~E(x1351,x1352)+E(f484(x1353,x1354,x1355,x1356,x1351),f484(x1353,x1354,x1355,x1356,x1352))
% 191.21/191.75 [136]~E(x1361,x1362)+E(f259(x1361,x1363),f259(x1362,x1363))
% 191.21/191.75 [137]~E(x1371,x1372)+E(f259(x1373,x1371),f259(x1373,x1372))
% 191.21/191.75 [138]~E(x1381,x1382)+E(f132(x1381,x1383,x1384,x1385),f132(x1382,x1383,x1384,x1385))
% 191.21/191.75 [139]~E(x1391,x1392)+E(f132(x1393,x1391,x1394,x1395),f132(x1393,x1392,x1394,x1395))
% 191.21/191.75 [140]~E(x1401,x1402)+E(f132(x1403,x1404,x1401,x1405),f132(x1403,x1404,x1402,x1405))
% 191.21/191.75 [141]~E(x1411,x1412)+E(f132(x1413,x1414,x1415,x1411),f132(x1413,x1414,x1415,x1412))
% 191.21/191.75 [142]~E(x1421,x1422)+E(f371(x1421,x1423,x1424,x1425,x1426),f371(x1422,x1423,x1424,x1425,x1426))
% 191.21/191.75 [143]~E(x1431,x1432)+E(f371(x1433,x1431,x1434,x1435,x1436),f371(x1433,x1432,x1434,x1435,x1436))
% 191.21/191.75 [144]~E(x1441,x1442)+E(f371(x1443,x1444,x1441,x1445,x1446),f371(x1443,x1444,x1442,x1445,x1446))
% 191.21/191.75 [145]~E(x1451,x1452)+E(f371(x1453,x1454,x1455,x1451,x1456),f371(x1453,x1454,x1455,x1452,x1456))
% 191.21/191.75 [146]~E(x1461,x1462)+E(f371(x1463,x1464,x1465,x1466,x1461),f371(x1463,x1464,x1465,x1466,x1462))
% 191.21/191.75 [147]~E(x1471,x1472)+E(f158(x1471),f158(x1472))
% 191.21/191.75 [148]~E(x1481,x1482)+E(f303(x1481,x1483,x1484),f303(x1482,x1483,x1484))
% 191.21/191.75 [149]~E(x1491,x1492)+E(f303(x1493,x1491,x1494),f303(x1493,x1492,x1494))
% 191.21/191.75 [150]~E(x1501,x1502)+E(f303(x1503,x1504,x1501),f303(x1503,x1504,x1502))
% 191.21/191.75 [151]~E(x1511,x1512)+E(f300(x1511,x1513),f300(x1512,x1513))
% 191.21/191.75 [152]~E(x1521,x1522)+E(f300(x1523,x1521),f300(x1523,x1522))
% 191.21/191.75 [153]~E(x1531,x1532)+E(f108(x1531),f108(x1532))
% 191.21/191.75 [154]~E(x1541,x1542)+E(f110(x1541),f110(x1542))
% 191.21/191.75 [155]~E(x1551,x1552)+E(f333(x1551),f333(x1552))
% 191.21/191.75 [156]~E(x1561,x1562)+E(f140(x1561),f140(x1562))
% 191.21/191.75 [157]~E(x1571,x1572)+E(f146(x1571,x1573),f146(x1572,x1573))
% 191.21/191.75 [158]~E(x1581,x1582)+E(f146(x1583,x1581),f146(x1583,x1582))
% 191.21/191.75 [159]~E(x1591,x1592)+E(f238(x1591,x1593),f238(x1592,x1593))
% 191.21/191.75 [160]~E(x1601,x1602)+E(f238(x1603,x1601),f238(x1603,x1602))
% 191.21/191.75 [161]~E(x1611,x1612)+E(f65(x1611,x1613),f65(x1612,x1613))
% 191.21/191.75 [162]~E(x1621,x1622)+E(f65(x1623,x1621),f65(x1623,x1622))
% 191.21/191.75 [163]~E(x1631,x1632)+E(f183(x1631),f183(x1632))
% 191.21/191.75 [164]~E(x1641,x1642)+E(f248(x1641,x1643),f248(x1642,x1643))
% 191.21/191.75 [165]~E(x1651,x1652)+E(f248(x1653,x1651),f248(x1653,x1652))
% 191.21/191.75 [166]~E(x1661,x1662)+E(f454(x1661,x1663,x1664,x1665,x1666,x1667,x1668),f454(x1662,x1663,x1664,x1665,x1666,x1667,x1668))
% 191.21/191.75 [167]~E(x1671,x1672)+E(f454(x1673,x1671,x1674,x1675,x1676,x1677,x1678),f454(x1673,x1672,x1674,x1675,x1676,x1677,x1678))
% 191.21/191.75 [168]~E(x1681,x1682)+E(f454(x1683,x1684,x1681,x1685,x1686,x1687,x1688),f454(x1683,x1684,x1682,x1685,x1686,x1687,x1688))
% 191.21/191.75 [169]~E(x1691,x1692)+E(f454(x1693,x1694,x1695,x1691,x1696,x1697,x1698),f454(x1693,x1694,x1695,x1692,x1696,x1697,x1698))
% 191.21/191.75 [170]~E(x1701,x1702)+E(f454(x1703,x1704,x1705,x1706,x1701,x1707,x1708),f454(x1703,x1704,x1705,x1706,x1702,x1707,x1708))
% 191.21/191.75 [171]~E(x1711,x1712)+E(f454(x1713,x1714,x1715,x1716,x1717,x1711,x1718),f454(x1713,x1714,x1715,x1716,x1717,x1712,x1718))
% 191.21/191.75 [172]~E(x1721,x1722)+E(f454(x1723,x1724,x1725,x1726,x1727,x1728,x1721),f454(x1723,x1724,x1725,x1726,x1727,x1728,x1722))
% 191.21/191.75 [173]~E(x1731,x1732)+E(f79(x1731,x1733,x1734,x1735),f79(x1732,x1733,x1734,x1735))
% 191.21/191.75 [174]~E(x1741,x1742)+E(f79(x1743,x1741,x1744,x1745),f79(x1743,x1742,x1744,x1745))
% 191.21/191.75 [175]~E(x1751,x1752)+E(f79(x1753,x1754,x1751,x1755),f79(x1753,x1754,x1752,x1755))
% 191.21/191.75 [176]~E(x1761,x1762)+E(f79(x1763,x1764,x1765,x1761),f79(x1763,x1764,x1765,x1762))
% 191.21/191.75 [177]~E(x1771,x1772)+E(f7(x1771),f7(x1772))
% 191.21/191.75 [178]~E(x1781,x1782)+E(f301(x1781),f301(x1782))
% 191.21/191.75 [179]~E(x1791,x1792)+E(f171(x1791,x1793,x1794),f171(x1792,x1793,x1794))
% 191.21/191.75 [180]~E(x1801,x1802)+E(f171(x1803,x1801,x1804),f171(x1803,x1802,x1804))
% 191.21/191.75 [181]~E(x1811,x1812)+E(f171(x1813,x1814,x1811),f171(x1813,x1814,x1812))
% 191.21/191.75 [182]~E(x1821,x1822)+E(f281(x1821,x1823,x1824),f281(x1822,x1823,x1824))
% 191.21/191.75 [183]~E(x1831,x1832)+E(f281(x1833,x1831,x1834),f281(x1833,x1832,x1834))
% 191.21/191.75 [184]~E(x1841,x1842)+E(f281(x1843,x1844,x1841),f281(x1843,x1844,x1842))
% 191.21/191.75 [185]~E(x1851,x1852)+E(f505(x1851,x1853,x1854,x1855),f505(x1852,x1853,x1854,x1855))
% 191.21/191.75 [186]~E(x1861,x1862)+E(f505(x1863,x1861,x1864,x1865),f505(x1863,x1862,x1864,x1865))
% 191.21/191.75 [187]~E(x1871,x1872)+E(f505(x1873,x1874,x1871,x1875),f505(x1873,x1874,x1872,x1875))
% 191.21/191.75 [188]~E(x1881,x1882)+E(f505(x1883,x1884,x1885,x1881),f505(x1883,x1884,x1885,x1882))
% 191.21/191.75 [189]~E(x1891,x1892)+E(f148(x1891,x1893),f148(x1892,x1893))
% 191.21/191.75 [190]~E(x1901,x1902)+E(f148(x1903,x1901),f148(x1903,x1902))
% 191.21/191.75 [191]~E(x1911,x1912)+E(f143(x1911,x1913),f143(x1912,x1913))
% 191.21/191.75 [192]~E(x1921,x1922)+E(f143(x1923,x1921),f143(x1923,x1922))
% 191.21/191.75 [193]~E(x1931,x1932)+E(f240(x1931,x1933),f240(x1932,x1933))
% 191.21/191.75 [194]~E(x1941,x1942)+E(f240(x1943,x1941),f240(x1943,x1942))
% 191.21/191.75 [195]~E(x1951,x1952)+E(f141(x1951),f141(x1952))
% 191.21/191.75 [196]~E(x1961,x1962)+E(f207(x1961),f207(x1962))
% 191.21/191.75 [197]~E(x1971,x1972)+E(f75(x1971,x1973,x1974,x1975),f75(x1972,x1973,x1974,x1975))
% 191.21/191.75 [198]~E(x1981,x1982)+E(f75(x1983,x1981,x1984,x1985),f75(x1983,x1982,x1984,x1985))
% 191.21/191.75 [199]~E(x1991,x1992)+E(f75(x1993,x1994,x1991,x1995),f75(x1993,x1994,x1992,x1995))
% 191.21/191.75 [200]~E(x2001,x2002)+E(f75(x2003,x2004,x2005,x2001),f75(x2003,x2004,x2005,x2002))
% 191.21/191.75 [201]~E(x2011,x2012)+E(f142(x2011),f142(x2012))
% 191.21/191.75 [202]~E(x2021,x2022)+E(f242(x2021),f242(x2022))
% 191.21/191.75 [203]~E(x2031,x2032)+E(f137(x2031,x2033),f137(x2032,x2033))
% 191.21/191.75 [204]~E(x2041,x2042)+E(f137(x2043,x2041),f137(x2043,x2042))
% 191.21/191.75 [205]~E(x2051,x2052)+E(f14(x2051,x2053,x2054),f14(x2052,x2053,x2054))
% 191.21/191.75 [206]~E(x2061,x2062)+E(f14(x2063,x2061,x2064),f14(x2063,x2062,x2064))
% 191.21/191.75 [207]~E(x2071,x2072)+E(f14(x2073,x2074,x2071),f14(x2073,x2074,x2072))
% 191.21/191.75 [208]~E(x2081,x2082)+E(f175(x2081,x2083,x2084,x2085),f175(x2082,x2083,x2084,x2085))
% 191.21/191.75 [209]~E(x2091,x2092)+E(f175(x2093,x2091,x2094,x2095),f175(x2093,x2092,x2094,x2095))
% 191.21/191.75 [210]~E(x2101,x2102)+E(f175(x2103,x2104,x2101,x2105),f175(x2103,x2104,x2102,x2105))
% 191.21/191.75 [211]~E(x2111,x2112)+E(f175(x2113,x2114,x2115,x2111),f175(x2113,x2114,x2115,x2112))
% 191.21/191.75 [212]~E(x2121,x2122)+E(f429(x2121,x2123,x2124,x2125),f429(x2122,x2123,x2124,x2125))
% 191.21/191.75 [213]~E(x2131,x2132)+E(f429(x2133,x2131,x2134,x2135),f429(x2133,x2132,x2134,x2135))
% 191.21/191.75 [214]~E(x2141,x2142)+E(f429(x2143,x2144,x2141,x2145),f429(x2143,x2144,x2142,x2145))
% 191.21/191.75 [215]~E(x2151,x2152)+E(f429(x2153,x2154,x2155,x2151),f429(x2153,x2154,x2155,x2152))
% 191.21/191.75 [216]~E(x2161,x2162)+E(f304(x2161,x2163),f304(x2162,x2163))
% 191.21/191.75 [217]~E(x2171,x2172)+E(f304(x2173,x2171),f304(x2173,x2172))
% 191.21/191.75 [218]~E(x2181,x2182)+E(f47(x2181,x2183),f47(x2182,x2183))
% 191.21/191.75 [219]~E(x2191,x2192)+E(f47(x2193,x2191),f47(x2193,x2192))
% 191.21/191.75 [220]~E(x2201,x2202)+E(f169(x2201,x2203,x2204),f169(x2202,x2203,x2204))
% 191.21/191.75 [221]~E(x2211,x2212)+E(f169(x2213,x2211,x2214),f169(x2213,x2212,x2214))
% 191.21/191.75 [222]~E(x2221,x2222)+E(f169(x2223,x2224,x2221),f169(x2223,x2224,x2222))
% 191.21/191.75 [223]~E(x2231,x2232)+E(f851(x2231),f851(x2232))
% 191.21/191.75 [224]~E(x2241,x2242)+E(f46(x2241,x2243),f46(x2242,x2243))
% 191.21/191.75 [225]~E(x2251,x2252)+E(f46(x2253,x2251),f46(x2253,x2252))
% 191.21/191.75 [226]~E(x2261,x2262)+E(f302(x2261),f302(x2262))
% 191.21/191.75 [227]~E(x2271,x2272)+E(f227(x2271),f227(x2272))
% 191.21/191.75 [228]~E(x2281,x2282)+E(f74(x2281,x2283),f74(x2282,x2283))
% 191.21/191.75 [229]~E(x2291,x2292)+E(f74(x2293,x2291),f74(x2293,x2292))
% 191.21/191.75 [230]~E(x2301,x2302)+E(f496(x2301,x2303,x2304,x2305,x2306,x2307),f496(x2302,x2303,x2304,x2305,x2306,x2307))
% 191.21/191.75 [231]~E(x2311,x2312)+E(f496(x2313,x2311,x2314,x2315,x2316,x2317),f496(x2313,x2312,x2314,x2315,x2316,x2317))
% 191.21/191.75 [232]~E(x2321,x2322)+E(f496(x2323,x2324,x2321,x2325,x2326,x2327),f496(x2323,x2324,x2322,x2325,x2326,x2327))
% 191.21/191.75 [233]~E(x2331,x2332)+E(f496(x2333,x2334,x2335,x2331,x2336,x2337),f496(x2333,x2334,x2335,x2332,x2336,x2337))
% 191.21/191.75 [234]~E(x2341,x2342)+E(f496(x2343,x2344,x2345,x2346,x2341,x2347),f496(x2343,x2344,x2345,x2346,x2342,x2347))
% 191.21/191.75 [235]~E(x2351,x2352)+E(f496(x2353,x2354,x2355,x2356,x2357,x2351),f496(x2353,x2354,x2355,x2356,x2357,x2352))
% 191.21/191.75 [236]~E(x2361,x2362)+E(f77(x2361),f77(x2362))
% 191.21/191.75 [237]~E(x2371,x2372)+E(f686(x2371,x2373,x2374),f686(x2372,x2373,x2374))
% 191.21/191.75 [238]~E(x2381,x2382)+E(f686(x2383,x2381,x2384),f686(x2383,x2382,x2384))
% 191.21/191.75 [239]~E(x2391,x2392)+E(f686(x2393,x2394,x2391),f686(x2393,x2394,x2392))
% 191.21/191.75 [240]~E(x2401,x2402)+E(f36(x2401,x2403),f36(x2402,x2403))
% 191.21/191.75 [241]~E(x2411,x2412)+E(f36(x2413,x2411),f36(x2413,x2412))
% 191.21/191.75 [242]~E(x2421,x2422)+E(f92(x2421,x2423),f92(x2422,x2423))
% 191.21/191.75 [243]~E(x2431,x2432)+E(f92(x2433,x2431),f92(x2433,x2432))
% 191.21/191.75 [244]~E(x2441,x2442)+E(f138(x2441,x2443,x2444),f138(x2442,x2443,x2444))
% 191.21/191.75 [245]~E(x2451,x2452)+E(f138(x2453,x2451,x2454),f138(x2453,x2452,x2454))
% 191.21/191.75 [246]~E(x2461,x2462)+E(f138(x2463,x2464,x2461),f138(x2463,x2464,x2462))
% 191.21/191.75 [247]~E(x2471,x2472)+E(f230(x2471,x2473,x2474,x2475,x2476),f230(x2472,x2473,x2474,x2475,x2476))
% 191.21/191.75 [248]~E(x2481,x2482)+E(f230(x2483,x2481,x2484,x2485,x2486),f230(x2483,x2482,x2484,x2485,x2486))
% 191.21/191.75 [249]~E(x2491,x2492)+E(f230(x2493,x2494,x2491,x2495,x2496),f230(x2493,x2494,x2492,x2495,x2496))
% 191.21/191.75 [250]~E(x2501,x2502)+E(f230(x2503,x2504,x2505,x2501,x2506),f230(x2503,x2504,x2505,x2502,x2506))
% 191.21/191.75 [251]~E(x2511,x2512)+E(f230(x2513,x2514,x2515,x2516,x2511),f230(x2513,x2514,x2515,x2516,x2512))
% 191.21/191.75 [252]~E(x2521,x2522)+E(f781(x2521,x2523,x2524),f781(x2522,x2523,x2524))
% 191.21/191.75 [253]~E(x2531,x2532)+E(f781(x2533,x2531,x2534),f781(x2533,x2532,x2534))
% 191.21/191.75 [254]~E(x2541,x2542)+E(f781(x2543,x2544,x2541),f781(x2543,x2544,x2542))
% 191.21/191.75 [255]~E(x2551,x2552)+E(f653(x2551,x2553),f653(x2552,x2553))
% 191.21/191.75 [256]~E(x2561,x2562)+E(f653(x2563,x2561),f653(x2563,x2562))
% 191.21/191.75 [257]~E(x2571,x2572)+E(f711(x2571,x2573,x2574,x2575),f711(x2572,x2573,x2574,x2575))
% 191.21/191.75 [258]~E(x2581,x2582)+E(f711(x2583,x2581,x2584,x2585),f711(x2583,x2582,x2584,x2585))
% 191.21/191.75 [259]~E(x2591,x2592)+E(f711(x2593,x2594,x2591,x2595),f711(x2593,x2594,x2592,x2595))
% 191.21/191.75 [260]~E(x2601,x2602)+E(f711(x2603,x2604,x2605,x2601),f711(x2603,x2604,x2605,x2602))
% 191.21/191.75 [261]~E(x2611,x2612)+E(f163(x2611,x2613),f163(x2612,x2613))
% 191.21/191.75 [262]~E(x2621,x2622)+E(f163(x2623,x2621),f163(x2623,x2622))
% 191.21/191.75 [263]~E(x2631,x2632)+E(f135(x2631,x2633),f135(x2632,x2633))
% 191.21/191.75 [264]~E(x2641,x2642)+E(f135(x2643,x2641),f135(x2643,x2642))
% 191.21/191.75 [265]~E(x2651,x2652)+E(f116(x2651,x2653),f116(x2652,x2653))
% 191.21/191.75 [266]~E(x2661,x2662)+E(f116(x2663,x2661),f116(x2663,x2662))
% 191.21/191.75 [267]~E(x2671,x2672)+E(f278(x2671,x2673),f278(x2672,x2673))
% 191.21/191.75 [268]~E(x2681,x2682)+E(f278(x2683,x2681),f278(x2683,x2682))
% 191.21/191.75 [269]~E(x2691,x2692)+E(f184(x2691),f184(x2692))
% 191.21/191.75 [270]~E(x2701,x2702)+E(f153(x2701),f153(x2702))
% 191.21/191.75 [271]~E(x2711,x2712)+E(f117(x2711),f117(x2712))
% 191.21/191.75 [272]~E(x2721,x2722)+E(f196(x2721,x2723),f196(x2722,x2723))
% 191.21/191.75 [273]~E(x2731,x2732)+E(f196(x2733,x2731),f196(x2733,x2732))
% 191.21/191.75 [274]~E(x2741,x2742)+E(f12(x2741,x2743),f12(x2742,x2743))
% 191.21/191.75 [275]~E(x2751,x2752)+E(f12(x2753,x2751),f12(x2753,x2752))
% 191.21/191.75 [276]~E(x2761,x2762)+E(f638(x2761,x2763,x2764),f638(x2762,x2763,x2764))
% 191.21/191.75 [277]~E(x2771,x2772)+E(f638(x2773,x2771,x2774),f638(x2773,x2772,x2774))
% 191.21/191.75 [278]~E(x2781,x2782)+E(f638(x2783,x2784,x2781),f638(x2783,x2784,x2782))
% 191.21/191.75 [279]~E(x2791,x2792)+E(f799(x2791,x2793,x2794),f799(x2792,x2793,x2794))
% 191.21/191.75 [280]~E(x2801,x2802)+E(f799(x2803,x2801,x2804),f799(x2803,x2802,x2804))
% 191.21/191.75 [281]~E(x2811,x2812)+E(f799(x2813,x2814,x2811),f799(x2813,x2814,x2812))
% 191.21/191.75 [282]~E(x2821,x2822)+E(f18(x2821,x2823),f18(x2822,x2823))
% 191.21/191.75 [283]~E(x2831,x2832)+E(f18(x2833,x2831),f18(x2833,x2832))
% 191.21/191.75 [284]~E(x2841,x2842)+E(f251(x2841,x2843,x2844),f251(x2842,x2843,x2844))
% 191.21/191.75 [285]~E(x2851,x2852)+E(f251(x2853,x2851,x2854),f251(x2853,x2852,x2854))
% 191.21/191.75 [286]~E(x2861,x2862)+E(f251(x2863,x2864,x2861),f251(x2863,x2864,x2862))
% 191.21/191.75 [287]~E(x2871,x2872)+E(f38(x2871,x2873,x2874,x2875,x2876,x2877,x2878,x2879,x28710,x28711),f38(x2872,x2873,x2874,x2875,x2876,x2877,x2878,x2879,x28710,x28711))
% 191.21/191.75 [288]~E(x2881,x2882)+E(f38(x2883,x2881,x2884,x2885,x2886,x2887,x2888,x2889,x28810,x28811),f38(x2883,x2882,x2884,x2885,x2886,x2887,x2888,x2889,x28810,x28811))
% 191.21/191.75 [289]~E(x2891,x2892)+E(f38(x2893,x2894,x2891,x2895,x2896,x2897,x2898,x2899,x28910,x28911),f38(x2893,x2894,x2892,x2895,x2896,x2897,x2898,x2899,x28910,x28911))
% 191.21/191.75 [290]~E(x2901,x2902)+E(f38(x2903,x2904,x2905,x2901,x2906,x2907,x2908,x2909,x29010,x29011),f38(x2903,x2904,x2905,x2902,x2906,x2907,x2908,x2909,x29010,x29011))
% 191.21/191.75 [291]~E(x2911,x2912)+E(f38(x2913,x2914,x2915,x2916,x2911,x2917,x2918,x2919,x29110,x29111),f38(x2913,x2914,x2915,x2916,x2912,x2917,x2918,x2919,x29110,x29111))
% 191.21/191.75 [292]~E(x2921,x2922)+E(f38(x2923,x2924,x2925,x2926,x2927,x2921,x2928,x2929,x29210,x29211),f38(x2923,x2924,x2925,x2926,x2927,x2922,x2928,x2929,x29210,x29211))
% 191.21/191.75 [293]~E(x2931,x2932)+E(f38(x2933,x2934,x2935,x2936,x2937,x2938,x2931,x2939,x29310,x29311),f38(x2933,x2934,x2935,x2936,x2937,x2938,x2932,x2939,x29310,x29311))
% 191.21/191.75 [294]~E(x2941,x2942)+E(f38(x2943,x2944,x2945,x2946,x2947,x2948,x2949,x2941,x29410,x29411),f38(x2943,x2944,x2945,x2946,x2947,x2948,x2949,x2942,x29410,x29411))
% 191.21/191.75 [295]~E(x2951,x2952)+E(f38(x2953,x2954,x2955,x2956,x2957,x2958,x2959,x29510,x2951,x29511),f38(x2953,x2954,x2955,x2956,x2957,x2958,x2959,x29510,x2952,x29511))
% 191.21/191.75 [296]~E(x2961,x2962)+E(f38(x2963,x2964,x2965,x2966,x2967,x2968,x2969,x29610,x29611,x2961),f38(x2963,x2964,x2965,x2966,x2967,x2968,x2969,x29610,x29611,x2962))
% 191.21/191.75 [297]~E(x2971,x2972)+E(f167(x2971,x2973),f167(x2972,x2973))
% 191.21/191.75 [298]~E(x2981,x2982)+E(f167(x2983,x2981),f167(x2983,x2982))
% 191.21/191.75 [299]~E(x2991,x2992)+E(f16(x2991,x2993),f16(x2992,x2993))
% 191.21/191.75 [300]~E(x3001,x3002)+E(f16(x3003,x3001),f16(x3003,x3002))
% 191.21/191.75 [301]~E(x3011,x3012)+E(f157(x3011),f157(x3012))
% 191.21/191.75 [302]~E(x3021,x3022)+E(f15(x3021,x3023),f15(x3022,x3023))
% 191.21/191.75 [303]~E(x3031,x3032)+E(f15(x3033,x3031),f15(x3033,x3032))
% 191.21/191.75 [304]~E(x3041,x3042)+E(f666(x3041,x3043,x3044,x3045,x3046),f666(x3042,x3043,x3044,x3045,x3046))
% 191.21/191.75 [305]~E(x3051,x3052)+E(f666(x3053,x3051,x3054,x3055,x3056),f666(x3053,x3052,x3054,x3055,x3056))
% 191.21/191.75 [306]~E(x3061,x3062)+E(f666(x3063,x3064,x3061,x3065,x3066),f666(x3063,x3064,x3062,x3065,x3066))
% 191.21/191.75 [307]~E(x3071,x3072)+E(f666(x3073,x3074,x3075,x3071,x3076),f666(x3073,x3074,x3075,x3072,x3076))
% 191.21/191.75 [308]~E(x3081,x3082)+E(f666(x3083,x3084,x3085,x3086,x3081),f666(x3083,x3084,x3085,x3086,x3082))
% 191.21/191.75 [309]~E(x3091,x3092)+E(f53(x3091,x3093),f53(x3092,x3093))
% 191.21/191.75 [310]~E(x3101,x3102)+E(f53(x3103,x3101),f53(x3103,x3102))
% 191.21/191.75 [311]~E(x3111,x3112)+E(f291(x3111,x3113,x3114,x3115),f291(x3112,x3113,x3114,x3115))
% 191.21/191.75 [312]~E(x3121,x3122)+E(f291(x3123,x3121,x3124,x3125),f291(x3123,x3122,x3124,x3125))
% 191.21/191.75 [313]~E(x3131,x3132)+E(f291(x3133,x3134,x3131,x3135),f291(x3133,x3134,x3132,x3135))
% 191.21/191.75 [314]~E(x3141,x3142)+E(f291(x3143,x3144,x3145,x3141),f291(x3143,x3144,x3145,x3142))
% 191.21/191.75 [315]~E(x3151,x3152)+E(f64(x3151,x3153,x3154),f64(x3152,x3153,x3154))
% 191.21/191.75 [316]~E(x3161,x3162)+E(f64(x3163,x3161,x3164),f64(x3163,x3162,x3164))
% 191.21/191.75 [317]~E(x3171,x3172)+E(f64(x3173,x3174,x3171),f64(x3173,x3174,x3172))
% 191.21/191.75 [318]~E(x3181,x3182)+E(f66(x3181,x3183,x3184),f66(x3182,x3183,x3184))
% 191.21/191.75 [319]~E(x3191,x3192)+E(f66(x3193,x3191,x3194),f66(x3193,x3192,x3194))
% 191.21/191.75 [320]~E(x3201,x3202)+E(f66(x3203,x3204,x3201),f66(x3203,x3204,x3202))
% 191.21/191.75 [321]~E(x3211,x3212)+E(f257(x3211),f257(x3212))
% 191.21/191.75 [322]~E(x3221,x3222)+E(f60(x3221,x3223),f60(x3222,x3223))
% 191.21/191.75 [323]~E(x3231,x3232)+E(f60(x3233,x3231),f60(x3233,x3232))
% 191.21/191.75 [324]~E(x3241,x3242)+E(f359(x3241,x3243,x3244,x3245,x3246),f359(x3242,x3243,x3244,x3245,x3246))
% 191.21/191.75 [325]~E(x3251,x3252)+E(f359(x3253,x3251,x3254,x3255,x3256),f359(x3253,x3252,x3254,x3255,x3256))
% 191.21/191.75 [326]~E(x3261,x3262)+E(f359(x3263,x3264,x3261,x3265,x3266),f359(x3263,x3264,x3262,x3265,x3266))
% 191.21/191.75 [327]~E(x3271,x3272)+E(f359(x3273,x3274,x3275,x3271,x3276),f359(x3273,x3274,x3275,x3272,x3276))
% 191.21/191.75 [328]~E(x3281,x3282)+E(f359(x3283,x3284,x3285,x3286,x3281),f359(x3283,x3284,x3285,x3286,x3282))
% 191.21/191.75 [329]~E(x3291,x3292)+E(f825(x3291,x3293,x3294),f825(x3292,x3293,x3294))
% 191.21/191.75 [330]~E(x3301,x3302)+E(f825(x3303,x3301,x3304),f825(x3303,x3302,x3304))
% 191.21/191.75 [331]~E(x3311,x3312)+E(f825(x3313,x3314,x3311),f825(x3313,x3314,x3312))
% 191.21/191.75 [332]~E(x3321,x3322)+E(f17(x3321,x3323),f17(x3322,x3323))
% 191.21/191.75 [333]~E(x3331,x3332)+E(f17(x3333,x3331),f17(x3333,x3332))
% 191.21/191.75 [334]~E(x3341,x3342)+E(f28(x3341,x3343),f28(x3342,x3343))
% 191.21/191.75 [335]~E(x3351,x3352)+E(f28(x3353,x3351),f28(x3353,x3352))
% 191.21/191.75 [336]~E(x3361,x3362)+E(f172(x3361,x3363,x3364,x3365),f172(x3362,x3363,x3364,x3365))
% 191.21/191.75 [337]~E(x3371,x3372)+E(f172(x3373,x3371,x3374,x3375),f172(x3373,x3372,x3374,x3375))
% 191.21/191.75 [338]~E(x3381,x3382)+E(f172(x3383,x3384,x3381,x3385),f172(x3383,x3384,x3382,x3385))
% 191.21/191.75 [339]~E(x3391,x3392)+E(f172(x3393,x3394,x3395,x3391),f172(x3393,x3394,x3395,x3392))
% 191.21/191.75 [340]~E(x3401,x3402)+E(f162(x3401,x3403,x3404),f162(x3402,x3403,x3404))
% 191.21/191.75 [341]~E(x3411,x3412)+E(f162(x3413,x3411,x3414),f162(x3413,x3412,x3414))
% 191.21/191.75 [342]~E(x3421,x3422)+E(f162(x3423,x3424,x3421),f162(x3423,x3424,x3422))
% 191.21/191.75 [343]~E(x3431,x3432)+E(f784(x3431,x3433,x3434),f784(x3432,x3433,x3434))
% 191.21/191.75 [344]~E(x3441,x3442)+E(f784(x3443,x3441,x3444),f784(x3443,x3442,x3444))
% 191.21/191.75 [345]~E(x3451,x3452)+E(f784(x3453,x3454,x3451),f784(x3453,x3454,x3452))
% 191.21/191.75 [346]~E(x3461,x3462)+E(f324(x3461,x3463),f324(x3462,x3463))
% 191.21/191.75 [347]~E(x3471,x3472)+E(f324(x3473,x3471),f324(x3473,x3472))
% 191.21/191.75 [348]~E(x3481,x3482)+E(f698(x3481,x3483),f698(x3482,x3483))
% 191.21/191.75 [349]~E(x3491,x3492)+E(f698(x3493,x3491),f698(x3493,x3492))
% 191.21/191.75 [350]~E(x3501,x3502)+E(f326(x3501,x3503),f326(x3502,x3503))
% 191.21/191.75 [351]~E(x3511,x3512)+E(f326(x3513,x3511),f326(x3513,x3512))
% 191.21/191.75 [352]~E(x3521,x3522)+E(f383(x3521,x3523,x3524,x3525,x3526),f383(x3522,x3523,x3524,x3525,x3526))
% 191.21/191.75 [353]~E(x3531,x3532)+E(f383(x3533,x3531,x3534,x3535,x3536),f383(x3533,x3532,x3534,x3535,x3536))
% 191.21/191.75 [354]~E(x3541,x3542)+E(f383(x3543,x3544,x3541,x3545,x3546),f383(x3543,x3544,x3542,x3545,x3546))
% 191.21/191.75 [355]~E(x3551,x3552)+E(f383(x3553,x3554,x3555,x3551,x3556),f383(x3553,x3554,x3555,x3552,x3556))
% 191.21/191.75 [356]~E(x3561,x3562)+E(f383(x3563,x3564,x3565,x3566,x3561),f383(x3563,x3564,x3565,x3566,x3562))
% 191.21/191.75 [357]~E(x3571,x3572)+E(f468(x3571,x3573,x3574),f468(x3572,x3573,x3574))
% 191.21/191.75 [358]~E(x3581,x3582)+E(f468(x3583,x3581,x3584),f468(x3583,x3582,x3584))
% 191.21/191.75 [359]~E(x3591,x3592)+E(f468(x3593,x3594,x3591),f468(x3593,x3594,x3592))
% 191.21/191.75 [360]~E(x3601,x3602)+E(f765(x3601,x3603,x3604),f765(x3602,x3603,x3604))
% 191.21/191.75 [361]~E(x3611,x3612)+E(f765(x3613,x3611,x3614),f765(x3613,x3612,x3614))
% 191.21/191.75 [362]~E(x3621,x3622)+E(f765(x3623,x3624,x3621),f765(x3623,x3624,x3622))
% 191.21/191.75 [363]~E(x3631,x3632)+E(f145(x3631,x3633,x3634,x3635),f145(x3632,x3633,x3634,x3635))
% 191.21/191.75 [364]~E(x3641,x3642)+E(f145(x3643,x3641,x3644,x3645),f145(x3643,x3642,x3644,x3645))
% 191.21/191.75 [365]~E(x3651,x3652)+E(f145(x3653,x3654,x3651,x3655),f145(x3653,x3654,x3652,x3655))
% 191.21/191.75 [366]~E(x3661,x3662)+E(f145(x3663,x3664,x3665,x3661),f145(x3663,x3664,x3665,x3662))
% 191.21/191.75 [367]~E(x3671,x3672)+E(f282(x3671,x3673,x3674,x3675),f282(x3672,x3673,x3674,x3675))
% 191.21/191.75 [368]~E(x3681,x3682)+E(f282(x3683,x3681,x3684,x3685),f282(x3683,x3682,x3684,x3685))
% 191.21/191.75 [369]~E(x3691,x3692)+E(f282(x3693,x3694,x3691,x3695),f282(x3693,x3694,x3692,x3695))
% 191.21/191.75 [370]~E(x3701,x3702)+E(f282(x3703,x3704,x3705,x3701),f282(x3703,x3704,x3705,x3702))
% 191.21/191.75 [371]~E(x3711,x3712)+E(f469(x3711,x3713,x3714),f469(x3712,x3713,x3714))
% 191.21/191.75 [372]~E(x3721,x3722)+E(f469(x3723,x3721,x3724),f469(x3723,x3722,x3724))
% 191.21/191.75 [373]~E(x3731,x3732)+E(f469(x3733,x3734,x3731),f469(x3733,x3734,x3732))
% 191.21/191.75 [374]~E(x3741,x3742)+E(f173(x3741,x3743),f173(x3742,x3743))
% 191.21/191.75 [375]~E(x3751,x3752)+E(f173(x3753,x3751),f173(x3753,x3752))
% 191.21/191.75 [376]~E(x3761,x3762)+E(f277(x3761,x3763,x3764),f277(x3762,x3763,x3764))
% 191.21/191.75 [377]~E(x3771,x3772)+E(f277(x3773,x3771,x3774),f277(x3773,x3772,x3774))
% 191.21/191.75 [378]~E(x3781,x3782)+E(f277(x3783,x3784,x3781),f277(x3783,x3784,x3782))
% 191.21/191.75 [379]~E(x3791,x3792)+E(f605(x3791,x3793),f605(x3792,x3793))
% 191.21/191.75 [380]~E(x3801,x3802)+E(f605(x3803,x3801),f605(x3803,x3802))
% 191.21/191.75 [381]~E(x3811,x3812)+E(f295(x3811,x3813,x3814),f295(x3812,x3813,x3814))
% 191.21/191.75 [382]~E(x3821,x3822)+E(f295(x3823,x3821,x3824),f295(x3823,x3822,x3824))
% 191.21/191.75 [383]~E(x3831,x3832)+E(f295(x3833,x3834,x3831),f295(x3833,x3834,x3832))
% 191.21/191.75 [384]~E(x3841,x3842)+E(f166(x3841,x3843,x3844),f166(x3842,x3843,x3844))
% 191.21/191.75 [385]~E(x3851,x3852)+E(f166(x3853,x3851,x3854),f166(x3853,x3852,x3854))
% 191.21/191.75 [386]~E(x3861,x3862)+E(f166(x3863,x3864,x3861),f166(x3863,x3864,x3862))
% 191.21/191.75 [387]~E(x3871,x3872)+E(f125(x3871),f125(x3872))
% 191.21/191.75 [388]~E(x3881,x3882)+E(f538(x3881,x3883,x3884,x3885,x3886),f538(x3882,x3883,x3884,x3885,x3886))
% 191.21/191.75 [389]~E(x3891,x3892)+E(f538(x3893,x3891,x3894,x3895,x3896),f538(x3893,x3892,x3894,x3895,x3896))
% 191.21/191.75 [390]~E(x3901,x3902)+E(f538(x3903,x3904,x3901,x3905,x3906),f538(x3903,x3904,x3902,x3905,x3906))
% 191.21/191.75 [391]~E(x3911,x3912)+E(f538(x3913,x3914,x3915,x3911,x3916),f538(x3913,x3914,x3915,x3912,x3916))
% 191.21/191.75 [392]~E(x3921,x3922)+E(f538(x3923,x3924,x3925,x3926,x3921),f538(x3923,x3924,x3925,x3926,x3922))
% 191.21/191.75 [393]~E(x3931,x3932)+E(f846(x3931),f846(x3932))
% 191.21/191.75 [394]~E(x3941,x3942)+E(f128(x3941),f128(x3942))
% 191.21/191.75 [395]~E(x3951,x3952)+E(f149(x3951,x3953),f149(x3952,x3953))
% 191.21/191.75 [396]~E(x3961,x3962)+E(f149(x3963,x3961),f149(x3963,x3962))
% 191.21/191.75 [397]~E(x3971,x3972)+E(f87(x3971,x3973),f87(x3972,x3973))
% 191.21/191.75 [398]~E(x3981,x3982)+E(f87(x3983,x3981),f87(x3983,x3982))
% 191.21/191.75 [399]~E(x3991,x3992)+E(f816(x3991,x3993,x3994,x3995),f816(x3992,x3993,x3994,x3995))
% 191.21/191.75 [400]~E(x4001,x4002)+E(f816(x4003,x4001,x4004,x4005),f816(x4003,x4002,x4004,x4005))
% 191.21/191.75 [401]~E(x4011,x4012)+E(f816(x4013,x4014,x4011,x4015),f816(x4013,x4014,x4012,x4015))
% 191.21/191.75 [402]~E(x4021,x4022)+E(f816(x4023,x4024,x4025,x4021),f816(x4023,x4024,x4025,x4022))
% 191.21/191.75 [403]~E(x4031,x4032)+E(f122(x4031),f122(x4032))
% 191.21/191.75 [404]~E(x4041,x4042)+E(f210(x4041,x4043),f210(x4042,x4043))
% 191.21/191.75 [405]~E(x4051,x4052)+E(f210(x4053,x4051),f210(x4053,x4052))
% 191.21/191.75 [406]~E(x4061,x4062)+E(f274(x4061,x4063,x4064,x4065),f274(x4062,x4063,x4064,x4065))
% 191.21/191.75 [407]~E(x4071,x4072)+E(f274(x4073,x4071,x4074,x4075),f274(x4073,x4072,x4074,x4075))
% 191.21/191.75 [408]~E(x4081,x4082)+E(f274(x4083,x4084,x4081,x4085),f274(x4083,x4084,x4082,x4085))
% 191.21/191.75 [409]~E(x4091,x4092)+E(f274(x4093,x4094,x4095,x4091),f274(x4093,x4094,x4095,x4092))
% 191.21/191.75 [410]~E(x4101,x4102)+E(f722(x4101,x4103),f722(x4102,x4103))
% 191.21/191.75 [411]~E(x4111,x4112)+E(f722(x4113,x4111),f722(x4113,x4112))
% 191.21/191.75 [412]~E(x4121,x4122)+E(f518(x4121,x4123),f518(x4122,x4123))
% 191.21/191.75 [413]~E(x4131,x4132)+E(f518(x4133,x4131),f518(x4133,x4132))
% 191.21/191.75 [414]~E(x4141,x4142)+E(f419(x4141,x4143,x4144),f419(x4142,x4143,x4144))
% 191.21/191.75 [415]~E(x4151,x4152)+E(f419(x4153,x4151,x4154),f419(x4153,x4152,x4154))
% 191.21/191.75 [416]~E(x4161,x4162)+E(f419(x4163,x4164,x4161),f419(x4163,x4164,x4162))
% 191.21/191.75 [417]~E(x4171,x4172)+E(f139(x4171,x4173,x4174,x4175,x4176),f139(x4172,x4173,x4174,x4175,x4176))
% 191.21/191.75 [418]~E(x4181,x4182)+E(f139(x4183,x4181,x4184,x4185,x4186),f139(x4183,x4182,x4184,x4185,x4186))
% 191.21/191.75 [419]~E(x4191,x4192)+E(f139(x4193,x4194,x4191,x4195,x4196),f139(x4193,x4194,x4192,x4195,x4196))
% 191.21/191.75 [420]~E(x4201,x4202)+E(f139(x4203,x4204,x4205,x4201,x4206),f139(x4203,x4204,x4205,x4202,x4206))
% 191.21/191.75 [421]~E(x4211,x4212)+E(f139(x4213,x4214,x4215,x4216,x4211),f139(x4213,x4214,x4215,x4216,x4212))
% 191.21/191.75 [422]~E(x4221,x4222)+E(f313(x4221,x4223),f313(x4222,x4223))
% 191.21/191.76 [423]~E(x4231,x4232)+E(f313(x4233,x4231),f313(x4233,x4232))
% 191.21/191.76 [424]~E(x4241,x4242)+E(f507(x4241,x4243,x4244),f507(x4242,x4243,x4244))
% 191.21/191.76 [425]~E(x4251,x4252)+E(f507(x4253,x4251,x4254),f507(x4253,x4252,x4254))
% 191.21/191.76 [426]~E(x4261,x4262)+E(f507(x4263,x4264,x4261),f507(x4263,x4264,x4262))
% 191.21/191.76 [427]~E(x4271,x4272)+E(f260(x4271,x4273),f260(x4272,x4273))
% 191.21/191.76 [428]~E(x4281,x4282)+E(f260(x4283,x4281),f260(x4283,x4282))
% 191.21/191.76 [429]~E(x4291,x4292)+E(f783(x4291,x4293,x4294),f783(x4292,x4293,x4294))
% 191.21/191.76 [430]~E(x4301,x4302)+E(f783(x4303,x4301,x4304),f783(x4303,x4302,x4304))
% 191.21/191.76 [431]~E(x4311,x4312)+E(f783(x4313,x4314,x4311),f783(x4313,x4314,x4312))
% 191.21/191.76 [432]~E(x4321,x4322)+E(f856(x4321,x4323),f856(x4322,x4323))
% 191.21/191.76 [433]~E(x4331,x4332)+E(f856(x4333,x4331),f856(x4333,x4332))
% 191.21/191.76 [434]~E(x4341,x4342)+E(f88(x4341,x4343),f88(x4342,x4343))
% 191.21/191.76 [435]~E(x4351,x4352)+E(f88(x4353,x4351),f88(x4353,x4352))
% 191.21/191.76 [436]~E(x4361,x4362)+E(f550(x4361,x4363,x4364),f550(x4362,x4363,x4364))
% 191.21/191.76 [437]~E(x4371,x4372)+E(f550(x4373,x4371,x4374),f550(x4373,x4372,x4374))
% 191.21/191.76 [438]~E(x4381,x4382)+E(f550(x4383,x4384,x4381),f550(x4383,x4384,x4382))
% 191.21/191.76 [439]~E(x4391,x4392)+E(f755(x4391,x4393,x4394),f755(x4392,x4393,x4394))
% 191.21/191.76 [440]~E(x4401,x4402)+E(f755(x4403,x4401,x4404),f755(x4403,x4402,x4404))
% 191.21/191.76 [441]~E(x4411,x4412)+E(f755(x4413,x4414,x4411),f755(x4413,x4414,x4412))
% 191.21/191.76 [442]~E(x4421,x4422)+E(f413(x4421,x4423,x4424,x4425,x4426),f413(x4422,x4423,x4424,x4425,x4426))
% 191.21/191.76 [443]~E(x4431,x4432)+E(f413(x4433,x4431,x4434,x4435,x4436),f413(x4433,x4432,x4434,x4435,x4436))
% 191.21/191.76 [444]~E(x4441,x4442)+E(f413(x4443,x4444,x4441,x4445,x4446),f413(x4443,x4444,x4442,x4445,x4446))
% 191.21/191.76 [445]~E(x4451,x4452)+E(f413(x4453,x4454,x4455,x4451,x4456),f413(x4453,x4454,x4455,x4452,x4456))
% 191.21/191.76 [446]~E(x4461,x4462)+E(f413(x4463,x4464,x4465,x4466,x4461),f413(x4463,x4464,x4465,x4466,x4462))
% 191.21/191.76 [447]~E(x4471,x4472)+E(f782(x4471,x4473,x4474),f782(x4472,x4473,x4474))
% 191.21/191.76 [448]~E(x4481,x4482)+E(f782(x4483,x4481,x4484),f782(x4483,x4482,x4484))
% 191.21/191.76 [449]~E(x4491,x4492)+E(f782(x4493,x4494,x4491),f782(x4493,x4494,x4492))
% 191.21/191.76 [450]~E(x4501,x4502)+E(f78(x4501,x4503,x4504,x4505,x4506),f78(x4502,x4503,x4504,x4505,x4506))
% 191.29/191.76 [451]~E(x4511,x4512)+E(f78(x4513,x4511,x4514,x4515,x4516),f78(x4513,x4512,x4514,x4515,x4516))
% 191.29/191.76 [452]~E(x4521,x4522)+E(f78(x4523,x4524,x4521,x4525,x4526),f78(x4523,x4524,x4522,x4525,x4526))
% 191.29/191.76 [453]~E(x4531,x4532)+E(f78(x4533,x4534,x4535,x4531,x4536),f78(x4533,x4534,x4535,x4532,x4536))
% 191.29/191.76 [454]~E(x4541,x4542)+E(f78(x4543,x4544,x4545,x4546,x4541),f78(x4543,x4544,x4545,x4546,x4542))
% 191.29/191.76 [455]~E(x4551,x4552)+E(f800(x4551,x4553,x4554),f800(x4552,x4553,x4554))
% 191.29/191.76 [456]~E(x4561,x4562)+E(f800(x4563,x4561,x4564),f800(x4563,x4562,x4564))
% 191.29/191.76 [457]~E(x4571,x4572)+E(f800(x4573,x4574,x4571),f800(x4573,x4574,x4572))
% 191.29/191.76 [458]~E(x4581,x4582)+E(f144(x4581,x4583,x4584),f144(x4582,x4583,x4584))
% 191.29/191.76 [459]~E(x4591,x4592)+E(f144(x4593,x4591,x4594),f144(x4593,x4592,x4594))
% 191.29/191.76 [460]~E(x4601,x4602)+E(f144(x4603,x4604,x4601),f144(x4603,x4604,x4602))
% 191.29/191.76 [461]~E(x4611,x4612)+E(f637(x4611,x4613,x4614,x4615,x4616),f637(x4612,x4613,x4614,x4615,x4616))
% 191.29/191.76 [462]~E(x4621,x4622)+E(f637(x4623,x4621,x4624,x4625,x4626),f637(x4623,x4622,x4624,x4625,x4626))
% 191.29/191.76 [463]~E(x4631,x4632)+E(f637(x4633,x4634,x4631,x4635,x4636),f637(x4633,x4634,x4632,x4635,x4636))
% 191.29/191.76 [464]~E(x4641,x4642)+E(f637(x4643,x4644,x4645,x4641,x4646),f637(x4643,x4644,x4645,x4642,x4646))
% 191.29/191.76 [465]~E(x4651,x4652)+E(f637(x4653,x4654,x4655,x4656,x4651),f637(x4653,x4654,x4655,x4656,x4652))
% 191.29/191.76 [466]~E(x4661,x4662)+E(f320(x4661,x4663,x4664,x4665,x4666,x4667),f320(x4662,x4663,x4664,x4665,x4666,x4667))
% 191.29/191.76 [467]~E(x4671,x4672)+E(f320(x4673,x4671,x4674,x4675,x4676,x4677),f320(x4673,x4672,x4674,x4675,x4676,x4677))
% 191.29/191.76 [468]~E(x4681,x4682)+E(f320(x4683,x4684,x4681,x4685,x4686,x4687),f320(x4683,x4684,x4682,x4685,x4686,x4687))
% 191.29/191.76 [469]~E(x4691,x4692)+E(f320(x4693,x4694,x4695,x4691,x4696,x4697),f320(x4693,x4694,x4695,x4692,x4696,x4697))
% 191.29/191.76 [470]~E(x4701,x4702)+E(f320(x4703,x4704,x4705,x4706,x4701,x4707),f320(x4703,x4704,x4705,x4706,x4702,x4707))
% 191.29/191.76 [471]~E(x4711,x4712)+E(f320(x4713,x4714,x4715,x4716,x4717,x4711),f320(x4713,x4714,x4715,x4716,x4717,x4712))
% 191.29/191.76 [472]~E(x4721,x4722)+E(f357(x4721,x4723,x4724,x4725),f357(x4722,x4723,x4724,x4725))
% 191.29/191.76 [473]~E(x4731,x4732)+E(f357(x4733,x4731,x4734,x4735),f357(x4733,x4732,x4734,x4735))
% 191.29/191.76 [474]~E(x4741,x4742)+E(f357(x4743,x4744,x4741,x4745),f357(x4743,x4744,x4742,x4745))
% 191.29/191.76 [475]~E(x4751,x4752)+E(f357(x4753,x4754,x4755,x4751),f357(x4753,x4754,x4755,x4752))
% 191.29/191.76 [476]~E(x4761,x4762)+E(f830(x4761,x4763,x4764),f830(x4762,x4763,x4764))
% 191.29/191.76 [477]~E(x4771,x4772)+E(f830(x4773,x4771,x4774),f830(x4773,x4772,x4774))
% 191.29/191.76 [478]~E(x4781,x4782)+E(f830(x4783,x4784,x4781),f830(x4783,x4784,x4782))
% 191.29/191.76 [479]~E(x4791,x4792)+E(f307(x4791,x4793,x4794),f307(x4792,x4793,x4794))
% 191.29/191.76 [480]~E(x4801,x4802)+E(f307(x4803,x4801,x4804),f307(x4803,x4802,x4804))
% 191.29/191.76 [481]~E(x4811,x4812)+E(f307(x4813,x4814,x4811),f307(x4813,x4814,x4812))
% 191.29/191.76 [482]~E(x4821,x4822)+E(f49(x4821),f49(x4822))
% 191.29/191.76 [483]~E(x4831,x4832)+E(f321(x4831,x4833),f321(x4832,x4833))
% 191.29/191.76 [484]~E(x4841,x4842)+E(f321(x4843,x4841),f321(x4843,x4842))
% 191.29/191.76 [485]~E(x4851,x4852)+E(f258(x4851),f258(x4852))
% 191.29/191.76 [486]~E(x4861,x4862)+E(f559(x4861,x4863),f559(x4862,x4863))
% 191.29/191.76 [487]~E(x4871,x4872)+E(f559(x4873,x4871),f559(x4873,x4872))
% 191.29/191.76 [488]~E(x4881,x4882)+E(f650(x4881,x4883,x4884),f650(x4882,x4883,x4884))
% 191.29/191.76 [489]~E(x4891,x4892)+E(f650(x4893,x4891,x4894),f650(x4893,x4892,x4894))
% 191.29/191.76 [490]~E(x4901,x4902)+E(f650(x4903,x4904,x4901),f650(x4903,x4904,x4902))
% 191.29/191.76 [491]~E(x4911,x4912)+E(f421(x4911,x4913,x4914),f421(x4912,x4913,x4914))
% 191.29/191.76 [492]~E(x4921,x4922)+E(f421(x4923,x4921,x4924),f421(x4923,x4922,x4924))
% 191.29/191.76 [493]~E(x4931,x4932)+E(f421(x4933,x4934,x4931),f421(x4933,x4934,x4932))
% 191.29/191.76 [494]~E(x4941,x4942)+E(f299(x4941),f299(x4942))
% 191.29/191.76 [495]~E(x4951,x4952)+E(f459(x4951,x4953,x4954,x4955),f459(x4952,x4953,x4954,x4955))
% 191.29/191.76 [496]~E(x4961,x4962)+E(f459(x4963,x4961,x4964,x4965),f459(x4963,x4962,x4964,x4965))
% 191.29/191.76 [497]~E(x4971,x4972)+E(f459(x4973,x4974,x4971,x4975),f459(x4973,x4974,x4972,x4975))
% 191.29/191.76 [498]~E(x4981,x4982)+E(f459(x4983,x4984,x4985,x4981),f459(x4983,x4984,x4985,x4982))
% 191.29/191.76 [499]~E(x4991,x4992)+E(f687(x4991,x4993,x4994,x4995),f687(x4992,x4993,x4994,x4995))
% 191.29/191.76 [500]~E(x5001,x5002)+E(f687(x5003,x5001,x5004,x5005),f687(x5003,x5002,x5004,x5005))
% 191.29/191.76 [501]~E(x5011,x5012)+E(f687(x5013,x5014,x5011,x5015),f687(x5013,x5014,x5012,x5015))
% 191.29/191.76 [502]~E(x5021,x5022)+E(f687(x5023,x5024,x5025,x5021),f687(x5023,x5024,x5025,x5022))
% 191.29/191.76 [503]~E(x5031,x5032)+E(f147(x5031,x5033),f147(x5032,x5033))
% 191.29/191.76 [504]~E(x5041,x5042)+E(f147(x5043,x5041),f147(x5043,x5042))
% 191.29/191.76 [505]~E(x5051,x5052)+E(f67(x5051,x5053,x5054),f67(x5052,x5053,x5054))
% 191.29/191.76 [506]~E(x5061,x5062)+E(f67(x5063,x5061,x5064),f67(x5063,x5062,x5064))
% 191.29/191.76 [507]~E(x5071,x5072)+E(f67(x5073,x5074,x5071),f67(x5073,x5074,x5072))
% 191.29/191.76 [508]~E(x5081,x5082)+E(f89(x5081),f89(x5082))
% 191.29/191.76 [509]~E(x5091,x5092)+E(f748(x5091,x5093,x5094),f748(x5092,x5093,x5094))
% 191.29/191.76 [510]~E(x5101,x5102)+E(f748(x5103,x5101,x5104),f748(x5103,x5102,x5104))
% 191.29/191.76 [511]~E(x5111,x5112)+E(f748(x5113,x5114,x5111),f748(x5113,x5114,x5112))
% 191.29/191.76 [512]~E(x5121,x5122)+E(f452(x5121,x5123),f452(x5122,x5123))
% 191.29/191.76 [513]~E(x5131,x5132)+E(f452(x5133,x5131),f452(x5133,x5132))
% 191.29/191.76 [514]~E(x5141,x5142)+E(f55(x5141,x5143),f55(x5142,x5143))
% 191.29/191.76 [515]~E(x5151,x5152)+E(f55(x5153,x5151),f55(x5153,x5152))
% 191.29/191.76 [516]~E(x5161,x5162)+E(f151(x5161,x5163,x5164),f151(x5162,x5163,x5164))
% 191.29/191.76 [517]~E(x5171,x5172)+E(f151(x5173,x5171,x5174),f151(x5173,x5172,x5174))
% 191.29/191.76 [518]~E(x5181,x5182)+E(f151(x5183,x5184,x5181),f151(x5183,x5184,x5182))
% 191.29/191.76 [519]~E(x5191,x5192)+E(f32(x5191,x5193,x5194),f32(x5192,x5193,x5194))
% 191.29/191.76 [520]~E(x5201,x5202)+E(f32(x5203,x5201,x5204),f32(x5203,x5202,x5204))
% 191.29/191.76 [521]~E(x5211,x5212)+E(f32(x5213,x5214,x5211),f32(x5213,x5214,x5212))
% 191.29/191.76 [522]~E(x5221,x5222)+E(f155(x5221),f155(x5222))
% 191.29/191.76 [523]~E(x5231,x5232)+E(f136(x5231,x5233),f136(x5232,x5233))
% 191.29/191.76 [524]~E(x5241,x5242)+E(f136(x5243,x5241),f136(x5243,x5242))
% 191.29/191.76 [525]~E(x5251,x5252)+E(f13(x5251,x5253,x5254),f13(x5252,x5253,x5254))
% 191.29/191.76 [526]~E(x5261,x5262)+E(f13(x5263,x5261,x5264),f13(x5263,x5262,x5264))
% 191.29/191.76 [527]~E(x5271,x5272)+E(f13(x5273,x5274,x5271),f13(x5273,x5274,x5272))
% 191.29/191.76 [528]~E(x5281,x5282)+E(f93(x5281),f93(x5282))
% 191.29/191.76 [529]~E(x5291,x5292)+E(f787(x5291,x5293),f787(x5292,x5293))
% 191.29/191.76 [530]~E(x5301,x5302)+E(f787(x5303,x5301),f787(x5303,x5302))
% 191.29/191.76 [531]~E(x5311,x5312)+E(f420(x5311,x5313,x5314),f420(x5312,x5313,x5314))
% 191.29/191.76 [532]~E(x5321,x5322)+E(f420(x5323,x5321,x5324),f420(x5323,x5322,x5324))
% 191.29/191.76 [533]~E(x5331,x5332)+E(f420(x5333,x5334,x5331),f420(x5333,x5334,x5332))
% 191.29/191.76 [534]~E(x5341,x5342)+E(f718(x5341,x5343,x5344,x5345,x5346),f718(x5342,x5343,x5344,x5345,x5346))
% 191.29/191.76 [535]~E(x5351,x5352)+E(f718(x5353,x5351,x5354,x5355,x5356),f718(x5353,x5352,x5354,x5355,x5356))
% 191.29/191.76 [536]~E(x5361,x5362)+E(f718(x5363,x5364,x5361,x5365,x5366),f718(x5363,x5364,x5362,x5365,x5366))
% 191.29/191.76 [537]~E(x5371,x5372)+E(f718(x5373,x5374,x5375,x5371,x5376),f718(x5373,x5374,x5375,x5372,x5376))
% 191.29/191.76 [538]~E(x5381,x5382)+E(f718(x5383,x5384,x5385,x5386,x5381),f718(x5383,x5384,x5385,x5386,x5382))
% 191.29/191.76 [539]~E(x5391,x5392)+E(f375(x5391,x5393),f375(x5392,x5393))
% 191.29/191.76 [540]~E(x5401,x5402)+E(f375(x5403,x5401),f375(x5403,x5402))
% 191.29/191.76 [541]~E(x5411,x5412)+E(f648(x5411,x5413,x5414,x5415,x5416),f648(x5412,x5413,x5414,x5415,x5416))
% 191.29/191.76 [542]~E(x5421,x5422)+E(f648(x5423,x5421,x5424,x5425,x5426),f648(x5423,x5422,x5424,x5425,x5426))
% 191.29/191.76 [543]~E(x5431,x5432)+E(f648(x5433,x5434,x5431,x5435,x5436),f648(x5433,x5434,x5432,x5435,x5436))
% 191.29/191.76 [544]~E(x5441,x5442)+E(f648(x5443,x5444,x5445,x5441,x5446),f648(x5443,x5444,x5445,x5442,x5446))
% 191.29/191.76 [545]~E(x5451,x5452)+E(f648(x5453,x5454,x5455,x5456,x5451),f648(x5453,x5454,x5455,x5456,x5452))
% 191.29/191.76 [546]~E(x5461,x5462)+E(f832(x5461,x5463,x5464),f832(x5462,x5463,x5464))
% 191.29/191.76 [547]~E(x5471,x5472)+E(f832(x5473,x5471,x5474),f832(x5473,x5472,x5474))
% 191.29/191.76 [548]~E(x5481,x5482)+E(f832(x5483,x5484,x5481),f832(x5483,x5484,x5482))
% 191.29/191.76 [549]~E(x5491,x5492)+E(f708(x5491,x5493,x5494,x5495,x5496,x5497),f708(x5492,x5493,x5494,x5495,x5496,x5497))
% 191.29/191.76 [550]~E(x5501,x5502)+E(f708(x5503,x5501,x5504,x5505,x5506,x5507),f708(x5503,x5502,x5504,x5505,x5506,x5507))
% 191.29/191.76 [551]~E(x5511,x5512)+E(f708(x5513,x5514,x5511,x5515,x5516,x5517),f708(x5513,x5514,x5512,x5515,x5516,x5517))
% 191.29/191.76 [552]~E(x5521,x5522)+E(f708(x5523,x5524,x5525,x5521,x5526,x5527),f708(x5523,x5524,x5525,x5522,x5526,x5527))
% 191.29/191.76 [553]~E(x5531,x5532)+E(f708(x5533,x5534,x5535,x5536,x5531,x5537),f708(x5533,x5534,x5535,x5536,x5532,x5537))
% 191.29/191.76 [554]~E(x5541,x5542)+E(f708(x5543,x5544,x5545,x5546,x5547,x5541),f708(x5543,x5544,x5545,x5546,x5547,x5542))
% 191.29/191.76 [555]~E(x5551,x5552)+E(f709(x5551,x5553,x5554,x5555,x5556,x5557),f709(x5552,x5553,x5554,x5555,x5556,x5557))
% 191.29/191.76 [556]~E(x5561,x5562)+E(f709(x5563,x5561,x5564,x5565,x5566,x5567),f709(x5563,x5562,x5564,x5565,x5566,x5567))
% 191.29/191.76 [557]~E(x5571,x5572)+E(f709(x5573,x5574,x5571,x5575,x5576,x5577),f709(x5573,x5574,x5572,x5575,x5576,x5577))
% 191.29/191.76 [558]~E(x5581,x5582)+E(f709(x5583,x5584,x5585,x5581,x5586,x5587),f709(x5583,x5584,x5585,x5582,x5586,x5587))
% 191.29/191.76 [559]~E(x5591,x5592)+E(f709(x5593,x5594,x5595,x5596,x5591,x5597),f709(x5593,x5594,x5595,x5596,x5592,x5597))
% 191.29/191.76 [560]~E(x5601,x5602)+E(f709(x5603,x5604,x5605,x5606,x5607,x5601),f709(x5603,x5604,x5605,x5606,x5607,x5602))
% 191.29/191.76 [561]~E(x5611,x5612)+E(f68(x5611,x5613,x5614,x5615,x5616),f68(x5612,x5613,x5614,x5615,x5616))
% 191.29/191.76 [562]~E(x5621,x5622)+E(f68(x5623,x5621,x5624,x5625,x5626),f68(x5623,x5622,x5624,x5625,x5626))
% 191.29/191.76 [563]~E(x5631,x5632)+E(f68(x5633,x5634,x5631,x5635,x5636),f68(x5633,x5634,x5632,x5635,x5636))
% 191.29/191.76 [564]~E(x5641,x5642)+E(f68(x5643,x5644,x5645,x5641,x5646),f68(x5643,x5644,x5645,x5642,x5646))
% 191.29/191.76 [565]~E(x5651,x5652)+E(f68(x5653,x5654,x5655,x5656,x5651),f68(x5653,x5654,x5655,x5656,x5652))
% 191.29/191.76 [566]~E(x5661,x5662)+E(f297(x5661,x5663,x5664),f297(x5662,x5663,x5664))
% 191.29/191.76 [567]~E(x5671,x5672)+E(f297(x5673,x5671,x5674),f297(x5673,x5672,x5674))
% 191.29/191.76 [568]~E(x5681,x5682)+E(f297(x5683,x5684,x5681),f297(x5683,x5684,x5682))
% 191.29/191.76 [569]~E(x5691,x5692)+E(f50(x5691),f50(x5692))
% 191.29/191.76 [570]~E(x5701,x5702)+E(f613(x5701,x5703,x5704,x5705,x5706,x5707),f613(x5702,x5703,x5704,x5705,x5706,x5707))
% 191.29/191.76 [571]~E(x5711,x5712)+E(f613(x5713,x5711,x5714,x5715,x5716,x5717),f613(x5713,x5712,x5714,x5715,x5716,x5717))
% 191.29/191.76 [572]~E(x5721,x5722)+E(f613(x5723,x5724,x5721,x5725,x5726,x5727),f613(x5723,x5724,x5722,x5725,x5726,x5727))
% 191.29/191.76 [573]~E(x5731,x5732)+E(f613(x5733,x5734,x5735,x5731,x5736,x5737),f613(x5733,x5734,x5735,x5732,x5736,x5737))
% 191.29/191.76 [574]~E(x5741,x5742)+E(f613(x5743,x5744,x5745,x5746,x5741,x5747),f613(x5743,x5744,x5745,x5746,x5742,x5747))
% 191.29/191.76 [575]~E(x5751,x5752)+E(f613(x5753,x5754,x5755,x5756,x5757,x5751),f613(x5753,x5754,x5755,x5756,x5757,x5752))
% 191.29/191.76 [576]~E(x5761,x5762)+E(f772(x5761),f772(x5762))
% 191.29/191.76 [577]~E(x5771,x5772)+E(f453(x5771,x5773,x5774,x5775,x5776,x5777,x5778),f453(x5772,x5773,x5774,x5775,x5776,x5777,x5778))
% 191.29/191.76 [578]~E(x5781,x5782)+E(f453(x5783,x5781,x5784,x5785,x5786,x5787,x5788),f453(x5783,x5782,x5784,x5785,x5786,x5787,x5788))
% 191.29/191.76 [579]~E(x5791,x5792)+E(f453(x5793,x5794,x5791,x5795,x5796,x5797,x5798),f453(x5793,x5794,x5792,x5795,x5796,x5797,x5798))
% 191.29/191.76 [580]~E(x5801,x5802)+E(f453(x5803,x5804,x5805,x5801,x5806,x5807,x5808),f453(x5803,x5804,x5805,x5802,x5806,x5807,x5808))
% 191.29/191.76 [581]~E(x5811,x5812)+E(f453(x5813,x5814,x5815,x5816,x5811,x5817,x5818),f453(x5813,x5814,x5815,x5816,x5812,x5817,x5818))
% 191.29/191.76 [582]~E(x5821,x5822)+E(f453(x5823,x5824,x5825,x5826,x5827,x5821,x5828),f453(x5823,x5824,x5825,x5826,x5827,x5822,x5828))
% 191.29/191.76 [583]~E(x5831,x5832)+E(f453(x5833,x5834,x5835,x5836,x5837,x5838,x5831),f453(x5833,x5834,x5835,x5836,x5837,x5838,x5832))
% 191.29/191.76 [584]~E(x5841,x5842)+E(f587(x5841,x5843,x5844,x5845,x5846,x5847),f587(x5842,x5843,x5844,x5845,x5846,x5847))
% 191.29/191.76 [585]~E(x5851,x5852)+E(f587(x5853,x5851,x5854,x5855,x5856,x5857),f587(x5853,x5852,x5854,x5855,x5856,x5857))
% 191.29/191.76 [586]~E(x5861,x5862)+E(f587(x5863,x5864,x5861,x5865,x5866,x5867),f587(x5863,x5864,x5862,x5865,x5866,x5867))
% 191.29/191.76 [587]~E(x5871,x5872)+E(f587(x5873,x5874,x5875,x5871,x5876,x5877),f587(x5873,x5874,x5875,x5872,x5876,x5877))
% 191.29/191.76 [588]~E(x5881,x5882)+E(f587(x5883,x5884,x5885,x5886,x5881,x5887),f587(x5883,x5884,x5885,x5886,x5882,x5887))
% 191.29/191.76 [589]~E(x5891,x5892)+E(f587(x5893,x5894,x5895,x5896,x5897,x5891),f587(x5893,x5894,x5895,x5896,x5897,x5892))
% 191.29/191.76 [590]~E(x5901,x5902)+E(f432(x5901,x5903,x5904,x5905),f432(x5902,x5903,x5904,x5905))
% 191.29/191.76 [591]~E(x5911,x5912)+E(f432(x5913,x5911,x5914,x5915),f432(x5913,x5912,x5914,x5915))
% 191.29/191.76 [592]~E(x5921,x5922)+E(f432(x5923,x5924,x5921,x5925),f432(x5923,x5924,x5922,x5925))
% 191.29/191.76 [593]~E(x5931,x5932)+E(f432(x5933,x5934,x5935,x5931),f432(x5933,x5934,x5935,x5932))
% 191.29/191.76 [594]~E(x5941,x5942)+E(f226(x5941,x5943),f226(x5942,x5943))
% 191.29/191.76 [595]~E(x5951,x5952)+E(f226(x5953,x5951),f226(x5953,x5952))
% 191.29/191.76 [596]~E(x5961,x5962)+E(f339(x5961,x5963),f339(x5962,x5963))
% 191.29/191.76 [597]~E(x5971,x5972)+E(f339(x5973,x5971),f339(x5973,x5972))
% 191.29/191.76 [598]~E(x5981,x5982)+E(f176(x5981),f176(x5982))
% 191.29/191.76 [599]~E(x5991,x5992)+E(f404(x5991,x5993,x5994),f404(x5992,x5993,x5994))
% 191.29/191.76 [600]~E(x6001,x6002)+E(f404(x6003,x6001,x6004),f404(x6003,x6002,x6004))
% 191.29/191.76 [601]~E(x6011,x6012)+E(f404(x6013,x6014,x6011),f404(x6013,x6014,x6012))
% 191.29/191.76 [602]~E(x6021,x6022)+E(f397(x6021,x6023,x6024),f397(x6022,x6023,x6024))
% 191.29/191.76 [603]~E(x6031,x6032)+E(f397(x6033,x6031,x6034),f397(x6033,x6032,x6034))
% 191.29/191.76 [604]~E(x6041,x6042)+E(f397(x6043,x6044,x6041),f397(x6043,x6044,x6042))
% 191.29/191.76 [605]~E(x6051,x6052)+E(f358(x6051,x6053,x6054,x6055),f358(x6052,x6053,x6054,x6055))
% 191.29/191.76 [606]~E(x6061,x6062)+E(f358(x6063,x6061,x6064,x6065),f358(x6063,x6062,x6064,x6065))
% 191.29/191.76 [607]~E(x6071,x6072)+E(f358(x6073,x6074,x6071,x6075),f358(x6073,x6074,x6072,x6075))
% 191.29/191.76 [608]~E(x6081,x6082)+E(f358(x6083,x6084,x6085,x6081),f358(x6083,x6084,x6085,x6082))
% 191.29/191.76 [609]~E(x6091,x6092)+E(f705(x6091,x6093,x6094,x6095,x6096,x6097),f705(x6092,x6093,x6094,x6095,x6096,x6097))
% 191.29/191.76 [610]~E(x6101,x6102)+E(f705(x6103,x6101,x6104,x6105,x6106,x6107),f705(x6103,x6102,x6104,x6105,x6106,x6107))
% 191.29/191.76 [611]~E(x6111,x6112)+E(f705(x6113,x6114,x6111,x6115,x6116,x6117),f705(x6113,x6114,x6112,x6115,x6116,x6117))
% 191.29/191.76 [612]~E(x6121,x6122)+E(f705(x6123,x6124,x6125,x6121,x6126,x6127),f705(x6123,x6124,x6125,x6122,x6126,x6127))
% 191.29/191.76 [613]~E(x6131,x6132)+E(f705(x6133,x6134,x6135,x6136,x6131,x6137),f705(x6133,x6134,x6135,x6136,x6132,x6137))
% 191.29/191.76 [614]~E(x6141,x6142)+E(f705(x6143,x6144,x6145,x6146,x6147,x6141),f705(x6143,x6144,x6145,x6146,x6147,x6142))
% 191.29/191.76 [615]~E(x6151,x6152)+E(f276(x6151),f276(x6152))
% 191.29/191.76 [616]~E(x6161,x6162)+E(f45(x6161,x6163),f45(x6162,x6163))
% 191.29/191.76 [617]~E(x6171,x6172)+E(f45(x6173,x6171),f45(x6173,x6172))
% 191.29/191.76 [618]~E(x6181,x6182)+E(f679(x6181,x6183,x6184),f679(x6182,x6183,x6184))
% 191.29/191.76 [619]~E(x6191,x6192)+E(f679(x6193,x6191,x6194),f679(x6193,x6192,x6194))
% 191.29/191.76 [620]~E(x6201,x6202)+E(f679(x6203,x6204,x6201),f679(x6203,x6204,x6202))
% 191.29/191.76 [621]~E(x6211,x6212)+E(f647(x6211,x6213,x6214,x6215,x6216),f647(x6212,x6213,x6214,x6215,x6216))
% 191.29/191.76 [622]~E(x6221,x6222)+E(f647(x6223,x6221,x6224,x6225,x6226),f647(x6223,x6222,x6224,x6225,x6226))
% 191.29/191.76 [623]~E(x6231,x6232)+E(f647(x6233,x6234,x6231,x6235,x6236),f647(x6233,x6234,x6232,x6235,x6236))
% 191.29/191.76 [624]~E(x6241,x6242)+E(f647(x6243,x6244,x6245,x6241,x6246),f647(x6243,x6244,x6245,x6242,x6246))
% 191.29/191.76 [625]~E(x6251,x6252)+E(f647(x6253,x6254,x6255,x6256,x6251),f647(x6253,x6254,x6255,x6256,x6252))
% 191.29/191.76 [626]~E(x6261,x6262)+E(f614(x6261,x6263,x6264,x6265,x6266,x6267),f614(x6262,x6263,x6264,x6265,x6266,x6267))
% 191.29/191.76 [627]~E(x6271,x6272)+E(f614(x6273,x6271,x6274,x6275,x6276,x6277),f614(x6273,x6272,x6274,x6275,x6276,x6277))
% 191.29/191.76 [628]~E(x6281,x6282)+E(f614(x6283,x6284,x6281,x6285,x6286,x6287),f614(x6283,x6284,x6282,x6285,x6286,x6287))
% 191.29/191.76 [629]~E(x6291,x6292)+E(f614(x6293,x6294,x6295,x6291,x6296,x6297),f614(x6293,x6294,x6295,x6292,x6296,x6297))
% 191.29/191.76 [630]~E(x6301,x6302)+E(f614(x6303,x6304,x6305,x6306,x6301,x6307),f614(x6303,x6304,x6305,x6306,x6302,x6307))
% 191.29/191.76 [631]~E(x6311,x6312)+E(f614(x6313,x6314,x6315,x6316,x6317,x6311),f614(x6313,x6314,x6315,x6316,x6317,x6312))
% 191.29/191.76 [632]~E(x6321,x6322)+E(f565(x6321,x6323),f565(x6322,x6323))
% 191.29/191.76 [633]~E(x6331,x6332)+E(f565(x6333,x6331),f565(x6333,x6332))
% 191.29/191.76 [634]~E(x6341,x6342)+E(f56(x6341,x6343),f56(x6342,x6343))
% 191.29/191.76 [635]~E(x6351,x6352)+E(f56(x6353,x6351),f56(x6353,x6352))
% 191.29/191.76 [636]~E(x6361,x6362)+E(f778(x6361,x6363,x6364),f778(x6362,x6363,x6364))
% 191.29/191.76 [637]~E(x6371,x6372)+E(f778(x6373,x6371,x6374),f778(x6373,x6372,x6374))
% 191.29/191.76 [638]~E(x6381,x6382)+E(f778(x6383,x6384,x6381),f778(x6383,x6384,x6382))
% 191.29/191.76 [639]~E(x6391,x6392)+E(f366(x6391,x6393,x6394,x6395,x6396),f366(x6392,x6393,x6394,x6395,x6396))
% 191.29/191.76 [640]~E(x6401,x6402)+E(f366(x6403,x6401,x6404,x6405,x6406),f366(x6403,x6402,x6404,x6405,x6406))
% 191.29/191.76 [641]~E(x6411,x6412)+E(f366(x6413,x6414,x6411,x6415,x6416),f366(x6413,x6414,x6412,x6415,x6416))
% 191.29/191.76 [642]~E(x6421,x6422)+E(f366(x6423,x6424,x6425,x6421,x6426),f366(x6423,x6424,x6425,x6422,x6426))
% 191.29/191.76 [643]~E(x6431,x6432)+E(f366(x6433,x6434,x6435,x6436,x6431),f366(x6433,x6434,x6435,x6436,x6432))
% 191.29/191.76 [644]~E(x6441,x6442)+E(f296(x6441),f296(x6442))
% 191.29/191.76 [645]~E(x6451,x6452)+E(f271(x6451,x6453,x6454,x6455),f271(x6452,x6453,x6454,x6455))
% 191.29/191.76 [646]~E(x6461,x6462)+E(f271(x6463,x6461,x6464,x6465),f271(x6463,x6462,x6464,x6465))
% 191.29/191.76 [647]~E(x6471,x6472)+E(f271(x6473,x6474,x6471,x6475),f271(x6473,x6474,x6472,x6475))
% 191.29/191.76 [648]~E(x6481,x6482)+E(f271(x6483,x6484,x6485,x6481),f271(x6483,x6484,x6485,x6482))
% 191.29/191.76 [649]~E(x6491,x6492)+E(f742(x6491,x6493,x6494,x6495),f742(x6492,x6493,x6494,x6495))
% 191.29/191.76 [650]~E(x6501,x6502)+E(f742(x6503,x6501,x6504,x6505),f742(x6503,x6502,x6504,x6505))
% 191.29/191.76 [651]~E(x6511,x6512)+E(f742(x6513,x6514,x6511,x6515),f742(x6513,x6514,x6512,x6515))
% 191.29/191.76 [652]~E(x6521,x6522)+E(f742(x6523,x6524,x6525,x6521),f742(x6523,x6524,x6525,x6522))
% 191.29/191.76 [653]~E(x6531,x6532)+E(f252(x6531,x6533,x6534,x6535,x6536,x6537),f252(x6532,x6533,x6534,x6535,x6536,x6537))
% 191.29/191.76 [654]~E(x6541,x6542)+E(f252(x6543,x6541,x6544,x6545,x6546,x6547),f252(x6543,x6542,x6544,x6545,x6546,x6547))
% 191.29/191.76 [655]~E(x6551,x6552)+E(f252(x6553,x6554,x6551,x6555,x6556,x6557),f252(x6553,x6554,x6552,x6555,x6556,x6557))
% 191.29/191.76 [656]~E(x6561,x6562)+E(f252(x6563,x6564,x6565,x6561,x6566,x6567),f252(x6563,x6564,x6565,x6562,x6566,x6567))
% 191.29/191.76 [657]~E(x6571,x6572)+E(f252(x6573,x6574,x6575,x6576,x6571,x6577),f252(x6573,x6574,x6575,x6576,x6572,x6577))
% 191.29/191.76 [658]~E(x6581,x6582)+E(f252(x6583,x6584,x6585,x6586,x6587,x6581),f252(x6583,x6584,x6585,x6586,x6587,x6582))
% 191.29/191.76 [659]~E(x6591,x6592)+E(f54(x6591,x6593),f54(x6592,x6593))
% 191.29/191.76 [660]~E(x6601,x6602)+E(f54(x6603,x6601),f54(x6603,x6602))
% 191.29/191.76 [661]~E(x6611,x6612)+E(f188(x6611,x6613),f188(x6612,x6613))
% 191.29/191.76 [662]~E(x6621,x6622)+E(f188(x6623,x6621),f188(x6623,x6622))
% 191.29/191.76 [663]~E(x6631,x6632)+E(f675(x6631,x6633,x6634),f675(x6632,x6633,x6634))
% 191.29/191.76 [664]~E(x6641,x6642)+E(f675(x6643,x6641,x6644),f675(x6643,x6642,x6644))
% 191.29/191.76 [665]~E(x6651,x6652)+E(f675(x6653,x6654,x6651),f675(x6653,x6654,x6652))
% 191.29/191.76 [666]~E(x6661,x6662)+E(f229(x6661,x6663,x6664,x6665),f229(x6662,x6663,x6664,x6665))
% 191.29/191.76 [667]~E(x6671,x6672)+E(f229(x6673,x6671,x6674,x6675),f229(x6673,x6672,x6674,x6675))
% 191.29/191.76 [668]~E(x6681,x6682)+E(f229(x6683,x6684,x6681,x6685),f229(x6683,x6684,x6682,x6685))
% 191.29/191.76 [669]~E(x6691,x6692)+E(f229(x6693,x6694,x6695,x6691),f229(x6693,x6694,x6695,x6692))
% 191.29/191.76 [670]~E(x6701,x6702)+E(f751(x6701,x6703,x6704,x6705),f751(x6702,x6703,x6704,x6705))
% 191.29/191.76 [671]~E(x6711,x6712)+E(f751(x6713,x6711,x6714,x6715),f751(x6713,x6712,x6714,x6715))
% 191.29/191.76 [672]~E(x6721,x6722)+E(f751(x6723,x6724,x6721,x6725),f751(x6723,x6724,x6722,x6725))
% 191.29/191.76 [673]~E(x6731,x6732)+E(f751(x6733,x6734,x6735,x6731),f751(x6733,x6734,x6735,x6732))
% 191.29/191.76 [674]~E(x6741,x6742)+E(f759(x6741),f759(x6742))
% 191.29/191.76 [675]~E(x6751,x6752)+E(f119(x6751,x6753,x6754,x6755),f119(x6752,x6753,x6754,x6755))
% 191.29/191.76 [676]~E(x6761,x6762)+E(f119(x6763,x6761,x6764,x6765),f119(x6763,x6762,x6764,x6765))
% 191.29/191.76 [677]~E(x6771,x6772)+E(f119(x6773,x6774,x6771,x6775),f119(x6773,x6774,x6772,x6775))
% 191.29/191.76 [678]~E(x6781,x6782)+E(f119(x6783,x6784,x6785,x6781),f119(x6783,x6784,x6785,x6782))
% 191.29/191.76 [679]~E(x6791,x6792)+E(f790(x6791,x6793,x6794),f790(x6792,x6793,x6794))
% 191.29/191.76 [680]~E(x6801,x6802)+E(f790(x6803,x6801,x6804),f790(x6803,x6802,x6804))
% 191.29/191.76 [681]~E(x6811,x6812)+E(f790(x6813,x6814,x6811),f790(x6813,x6814,x6812))
% 191.29/191.76 [682]~E(x6821,x6822)+E(f777(x6821,x6823,x6824),f777(x6822,x6823,x6824))
% 191.29/191.76 [683]~E(x6831,x6832)+E(f777(x6833,x6831,x6834),f777(x6833,x6832,x6834))
% 191.29/191.76 [684]~E(x6841,x6842)+E(f777(x6843,x6844,x6841),f777(x6843,x6844,x6842))
% 191.29/191.76 [685]~E(x6851,x6852)+E(f98(x6851),f98(x6852))
% 191.29/191.76 [686]~E(x6861,x6862)+E(f425(x6861,x6863,x6864),f425(x6862,x6863,x6864))
% 191.29/191.76 [687]~E(x6871,x6872)+E(f425(x6873,x6871,x6874),f425(x6873,x6872,x6874))
% 191.29/191.76 [688]~E(x6881,x6882)+E(f425(x6883,x6884,x6881),f425(x6883,x6884,x6882))
% 191.29/191.76 [689]~E(x6891,x6892)+E(f57(x6891,x6893),f57(x6892,x6893))
% 191.29/191.76 [690]~E(x6901,x6902)+E(f57(x6903,x6901),f57(x6903,x6902))
% 191.29/191.76 [691]~E(x6911,x6912)+E(f197(x6911),f197(x6912))
% 191.29/191.76 [692]~E(x6921,x6922)+E(f577(x6921,x6923,x6924,x6925,x6926),f577(x6922,x6923,x6924,x6925,x6926))
% 191.29/191.76 [693]~E(x6931,x6932)+E(f577(x6933,x6931,x6934,x6935,x6936),f577(x6933,x6932,x6934,x6935,x6936))
% 191.29/191.76 [694]~E(x6941,x6942)+E(f577(x6943,x6944,x6941,x6945,x6946),f577(x6943,x6944,x6942,x6945,x6946))
% 191.29/191.76 [695]~E(x6951,x6952)+E(f577(x6953,x6954,x6955,x6951,x6956),f577(x6953,x6954,x6955,x6952,x6956))
% 191.29/191.76 [696]~E(x6961,x6962)+E(f577(x6963,x6964,x6965,x6966,x6961),f577(x6963,x6964,x6965,x6966,x6962))
% 191.29/191.76 [697]~E(x6971,x6972)+E(f298(x6971,x6973,x6974),f298(x6972,x6973,x6974))
% 191.29/191.76 [698]~E(x6981,x6982)+E(f298(x6983,x6981,x6984),f298(x6983,x6982,x6984))
% 191.29/191.76 [699]~E(x6991,x6992)+E(f298(x6993,x6994,x6991),f298(x6993,x6994,x6992))
% 191.29/191.76 [700]~E(x7001,x7002)+E(f573(x7001,x7003,x7004,x7005,x7006,x7007,x7008,x7009),f573(x7002,x7003,x7004,x7005,x7006,x7007,x7008,x7009))
% 191.29/191.76 [701]~E(x7011,x7012)+E(f573(x7013,x7011,x7014,x7015,x7016,x7017,x7018,x7019),f573(x7013,x7012,x7014,x7015,x7016,x7017,x7018,x7019))
% 191.29/191.76 [702]~E(x7021,x7022)+E(f573(x7023,x7024,x7021,x7025,x7026,x7027,x7028,x7029),f573(x7023,x7024,x7022,x7025,x7026,x7027,x7028,x7029))
% 191.29/191.76 [703]~E(x7031,x7032)+E(f573(x7033,x7034,x7035,x7031,x7036,x7037,x7038,x7039),f573(x7033,x7034,x7035,x7032,x7036,x7037,x7038,x7039))
% 191.29/191.76 [704]~E(x7041,x7042)+E(f573(x7043,x7044,x7045,x7046,x7041,x7047,x7048,x7049),f573(x7043,x7044,x7045,x7046,x7042,x7047,x7048,x7049))
% 191.29/191.76 [705]~E(x7051,x7052)+E(f573(x7053,x7054,x7055,x7056,x7057,x7051,x7058,x7059),f573(x7053,x7054,x7055,x7056,x7057,x7052,x7058,x7059))
% 191.29/191.76 [706]~E(x7061,x7062)+E(f573(x7063,x7064,x7065,x7066,x7067,x7068,x7061,x7069),f573(x7063,x7064,x7065,x7066,x7067,x7068,x7062,x7069))
% 191.29/191.76 [707]~E(x7071,x7072)+E(f573(x7073,x7074,x7075,x7076,x7077,x7078,x7079,x7071),f573(x7073,x7074,x7075,x7076,x7077,x7078,x7079,x7072))
% 191.29/191.76 [708]~E(x7081,x7082)+E(f719(x7081,x7083,x7084,x7085,x7086),f719(x7082,x7083,x7084,x7085,x7086))
% 191.29/191.76 [709]~E(x7091,x7092)+E(f719(x7093,x7091,x7094,x7095,x7096),f719(x7093,x7092,x7094,x7095,x7096))
% 191.29/191.76 [710]~E(x7101,x7102)+E(f719(x7103,x7104,x7101,x7105,x7106),f719(x7103,x7104,x7102,x7105,x7106))
% 191.29/191.76 [711]~E(x7111,x7112)+E(f719(x7113,x7114,x7115,x7111,x7116),f719(x7113,x7114,x7115,x7112,x7116))
% 191.29/191.76 [712]~E(x7121,x7122)+E(f719(x7123,x7124,x7125,x7126,x7121),f719(x7123,x7124,x7125,x7126,x7122))
% 191.29/191.76 [713]~E(x7131,x7132)+E(f211(x7131,x7133),f211(x7132,x7133))
% 191.29/191.76 [714]~E(x7141,x7142)+E(f211(x7143,x7141),f211(x7143,x7142))
% 191.29/191.76 [715]~E(x7151,x7152)+E(f31(x7151,x7153,x7154),f31(x7152,x7153,x7154))
% 191.29/191.76 [716]~E(x7161,x7162)+E(f31(x7163,x7161,x7164),f31(x7163,x7162,x7164))
% 191.29/191.76 [717]~E(x7171,x7172)+E(f31(x7173,x7174,x7171),f31(x7173,x7174,x7172))
% 191.29/191.76 [718]~E(x7181,x7182)+E(f327(x7181,x7183,x7184),f327(x7182,x7183,x7184))
% 191.29/191.76 [719]~E(x7191,x7192)+E(f327(x7193,x7191,x7194),f327(x7193,x7192,x7194))
% 191.29/191.76 [720]~E(x7201,x7202)+E(f327(x7203,x7204,x7201),f327(x7203,x7204,x7202))
% 191.29/191.76 [721]~E(x7211,x7212)+E(f823(x7211,x7213,x7214),f823(x7212,x7213,x7214))
% 191.29/191.76 [722]~E(x7221,x7222)+E(f823(x7223,x7221,x7224),f823(x7223,x7222,x7224))
% 191.29/191.76 [723]~E(x7231,x7232)+E(f823(x7233,x7234,x7231),f823(x7233,x7234,x7232))
% 191.29/191.76 [724]~E(x7241,x7242)+E(f736(x7241,x7243),f736(x7242,x7243))
% 191.29/191.76 [725]~E(x7251,x7252)+E(f736(x7253,x7251),f736(x7253,x7252))
% 191.29/191.76 [726]~E(x7261,x7262)+E(f805(x7261,x7263,x7264),f805(x7262,x7263,x7264))
% 191.29/191.76 [727]~E(x7271,x7272)+E(f805(x7273,x7271,x7274),f805(x7273,x7272,x7274))
% 191.29/191.76 [728]~E(x7281,x7282)+E(f805(x7283,x7284,x7281),f805(x7283,x7284,x7282))
% 191.29/191.76 [729]~E(x7291,x7292)+E(f292(x7291,x7293,x7294,x7295,x7296),f292(x7292,x7293,x7294,x7295,x7296))
% 191.29/191.76 [730]~E(x7301,x7302)+E(f292(x7303,x7301,x7304,x7305,x7306),f292(x7303,x7302,x7304,x7305,x7306))
% 191.29/191.76 [731]~E(x7311,x7312)+E(f292(x7313,x7314,x7311,x7315,x7316),f292(x7313,x7314,x7312,x7315,x7316))
% 191.29/191.76 [732]~E(x7321,x7322)+E(f292(x7323,x7324,x7325,x7321,x7326),f292(x7323,x7324,x7325,x7322,x7326))
% 191.29/191.76 [733]~E(x7331,x7332)+E(f292(x7333,x7334,x7335,x7336,x7331),f292(x7333,x7334,x7335,x7336,x7332))
% 191.29/191.76 [734]~E(x7341,x7342)+E(f286(x7341,x7343,x7344),f286(x7342,x7343,x7344))
% 191.29/191.76 [735]~E(x7351,x7352)+E(f286(x7353,x7351,x7354),f286(x7353,x7352,x7354))
% 191.29/191.76 [736]~E(x7361,x7362)+E(f286(x7363,x7364,x7361),f286(x7363,x7364,x7362))
% 191.29/191.76 [737]~E(x7371,x7372)+E(f389(x7371,x7373,x7374,x7375,x7376),f389(x7372,x7373,x7374,x7375,x7376))
% 191.29/191.76 [738]~E(x7381,x7382)+E(f389(x7383,x7381,x7384,x7385,x7386),f389(x7383,x7382,x7384,x7385,x7386))
% 191.29/191.76 [739]~E(x7391,x7392)+E(f389(x7393,x7394,x7391,x7395,x7396),f389(x7393,x7394,x7392,x7395,x7396))
% 191.29/191.76 [740]~E(x7401,x7402)+E(f389(x7403,x7404,x7405,x7401,x7406),f389(x7403,x7404,x7405,x7402,x7406))
% 191.29/191.76 [741]~E(x7411,x7412)+E(f389(x7413,x7414,x7415,x7416,x7411),f389(x7413,x7414,x7415,x7416,x7412))
% 191.29/191.76 [742]~E(x7421,x7422)+E(f532(x7421,x7423,x7424),f532(x7422,x7423,x7424))
% 191.29/191.76 [743]~E(x7431,x7432)+E(f532(x7433,x7431,x7434),f532(x7433,x7432,x7434))
% 191.29/191.76 [744]~E(x7441,x7442)+E(f532(x7443,x7444,x7441),f532(x7443,x7444,x7442))
% 191.29/191.76 [745]~E(x7451,x7452)+E(f317(x7451,x7453,x7454,x7455),f317(x7452,x7453,x7454,x7455))
% 191.29/191.76 [746]~E(x7461,x7462)+E(f317(x7463,x7461,x7464,x7465),f317(x7463,x7462,x7464,x7465))
% 191.29/191.76 [747]~E(x7471,x7472)+E(f317(x7473,x7474,x7471,x7475),f317(x7473,x7474,x7472,x7475))
% 191.29/191.76 [748]~E(x7481,x7482)+E(f317(x7483,x7484,x7485,x7481),f317(x7483,x7484,x7485,x7482))
% 191.29/191.76 [749]~E(x7491,x7492)+E(f213(x7491,x7493),f213(x7492,x7493))
% 191.29/191.76 [750]~E(x7501,x7502)+E(f213(x7503,x7501),f213(x7503,x7502))
% 191.29/191.76 [751]~E(x7511,x7512)+E(f350(x7511,x7513),f350(x7512,x7513))
% 191.29/191.76 [752]~E(x7521,x7522)+E(f350(x7523,x7521),f350(x7523,x7522))
% 191.29/191.76 [753]~E(x7531,x7532)+E(f472(x7531,x7533,x7534),f472(x7532,x7533,x7534))
% 191.29/191.76 [754]~E(x7541,x7542)+E(f472(x7543,x7541,x7544),f472(x7543,x7542,x7544))
% 191.29/191.76 [755]~E(x7551,x7552)+E(f472(x7553,x7554,x7551),f472(x7553,x7554,x7552))
% 191.29/191.76 [756]~E(x7561,x7562)+E(f156(x7561,x7563,x7564),f156(x7562,x7563,x7564))
% 191.29/191.76 [757]~E(x7571,x7572)+E(f156(x7573,x7571,x7574),f156(x7573,x7572,x7574))
% 191.29/191.76 [758]~E(x7581,x7582)+E(f156(x7583,x7584,x7581),f156(x7583,x7584,x7582))
% 191.29/191.76 [759]~E(x7591,x7592)+E(f604(x7591,x7593),f604(x7592,x7593))
% 191.29/191.76 [760]~E(x7601,x7602)+E(f604(x7603,x7601),f604(x7603,x7602))
% 191.29/191.76 [761]~E(x7611,x7612)+E(f552(x7611,x7613,x7614),f552(x7612,x7613,x7614))
% 191.29/191.76 [762]~E(x7621,x7622)+E(f552(x7623,x7621,x7624),f552(x7623,x7622,x7624))
% 191.29/191.76 [763]~E(x7631,x7632)+E(f552(x7633,x7634,x7631),f552(x7633,x7634,x7632))
% 191.29/191.76 [764]~E(x7641,x7642)+E(f112(x7641),f112(x7642))
% 191.29/191.76 [765]~E(x7651,x7652)+E(f739(x7651,x7653,x7654,x7655),f739(x7652,x7653,x7654,x7655))
% 191.29/191.76 [766]~E(x7661,x7662)+E(f739(x7663,x7661,x7664,x7665),f739(x7663,x7662,x7664,x7665))
% 191.29/191.76 [767]~E(x7671,x7672)+E(f739(x7673,x7674,x7671,x7675),f739(x7673,x7674,x7672,x7675))
% 191.29/191.76 [768]~E(x7681,x7682)+E(f739(x7683,x7684,x7685,x7681),f739(x7683,x7684,x7685,x7682))
% 191.29/191.76 [769]~E(x7691,x7692)+E(f160(x7691,x7693,x7694),f160(x7692,x7693,x7694))
% 191.29/191.76 [770]~E(x7701,x7702)+E(f160(x7703,x7701,x7704),f160(x7703,x7702,x7704))
% 191.29/191.76 [771]~E(x7711,x7712)+E(f160(x7713,x7714,x7711),f160(x7713,x7714,x7712))
% 191.29/191.76 [772]~E(x7721,x7722)+E(f198(x7721,x7723),f198(x7722,x7723))
% 191.29/191.76 [773]~E(x7731,x7732)+E(f198(x7733,x7731),f198(x7733,x7732))
% 191.29/191.76 [774]~E(x7741,x7742)+E(f314(x7741,x7743,x7744,x7745),f314(x7742,x7743,x7744,x7745))
% 191.29/191.76 [775]~E(x7751,x7752)+E(f314(x7753,x7751,x7754,x7755),f314(x7753,x7752,x7754,x7755))
% 191.29/191.76 [776]~E(x7761,x7762)+E(f314(x7763,x7764,x7761,x7765),f314(x7763,x7764,x7762,x7765))
% 191.29/191.76 [777]~E(x7771,x7772)+E(f314(x7773,x7774,x7775,x7771),f314(x7773,x7774,x7775,x7772))
% 191.29/191.76 [778]~E(x7781,x7782)+E(f556(x7781,x7783,x7784,x7785,x7786,x7787),f556(x7782,x7783,x7784,x7785,x7786,x7787))
% 191.29/191.76 [779]~E(x7791,x7792)+E(f556(x7793,x7791,x7794,x7795,x7796,x7797),f556(x7793,x7792,x7794,x7795,x7796,x7797))
% 191.29/191.76 [780]~E(x7801,x7802)+E(f556(x7803,x7804,x7801,x7805,x7806,x7807),f556(x7803,x7804,x7802,x7805,x7806,x7807))
% 191.29/191.76 [781]~E(x7811,x7812)+E(f556(x7813,x7814,x7815,x7811,x7816,x7817),f556(x7813,x7814,x7815,x7812,x7816,x7817))
% 191.29/191.76 [782]~E(x7821,x7822)+E(f556(x7823,x7824,x7825,x7826,x7821,x7827),f556(x7823,x7824,x7825,x7826,x7822,x7827))
% 191.29/191.76 [783]~E(x7831,x7832)+E(f556(x7833,x7834,x7835,x7836,x7837,x7831),f556(x7833,x7834,x7835,x7836,x7837,x7832))
% 191.29/191.76 [784]~E(x7841,x7842)+E(f319(x7841,x7843,x7844,x7845,x7846),f319(x7842,x7843,x7844,x7845,x7846))
% 191.29/191.76 [785]~E(x7851,x7852)+E(f319(x7853,x7851,x7854,x7855,x7856),f319(x7853,x7852,x7854,x7855,x7856))
% 191.29/191.76 [786]~E(x7861,x7862)+E(f319(x7863,x7864,x7861,x7865,x7866),f319(x7863,x7864,x7862,x7865,x7866))
% 191.29/191.76 [787]~E(x7871,x7872)+E(f319(x7873,x7874,x7875,x7871,x7876),f319(x7873,x7874,x7875,x7872,x7876))
% 191.29/191.76 [788]~E(x7881,x7882)+E(f319(x7883,x7884,x7885,x7886,x7881),f319(x7883,x7884,x7885,x7886,x7882))
% 191.29/191.76 [789]~E(x7891,x7892)+E(f270(x7891,x7893),f270(x7892,x7893))
% 191.29/191.76 [790]~E(x7901,x7902)+E(f270(x7903,x7901),f270(x7903,x7902))
% 191.29/191.76 [791]~E(x7911,x7912)+E(f564(x7911,x7913,x7914,x7915,x7916,x7917),f564(x7912,x7913,x7914,x7915,x7916,x7917))
% 191.29/191.76 [792]~E(x7921,x7922)+E(f564(x7923,x7921,x7924,x7925,x7926,x7927),f564(x7923,x7922,x7924,x7925,x7926,x7927))
% 191.29/191.76 [793]~E(x7931,x7932)+E(f564(x7933,x7934,x7931,x7935,x7936,x7937),f564(x7933,x7934,x7932,x7935,x7936,x7937))
% 191.29/191.76 [794]~E(x7941,x7942)+E(f564(x7943,x7944,x7945,x7941,x7946,x7947),f564(x7943,x7944,x7945,x7942,x7946,x7947))
% 191.29/191.76 [795]~E(x7951,x7952)+E(f564(x7953,x7954,x7955,x7956,x7951,x7957),f564(x7953,x7954,x7955,x7956,x7952,x7957))
% 191.29/191.76 [796]~E(x7961,x7962)+E(f564(x7963,x7964,x7965,x7966,x7967,x7961),f564(x7963,x7964,x7965,x7966,x7967,x7962))
% 191.29/191.76 [797]~E(x7971,x7972)+E(f753(x7971,x7973,x7974,x7975),f753(x7972,x7973,x7974,x7975))
% 191.29/191.76 [798]~E(x7981,x7982)+E(f753(x7983,x7981,x7984,x7985),f753(x7983,x7982,x7984,x7985))
% 191.29/191.76 [799]~E(x7991,x7992)+E(f753(x7993,x7994,x7991,x7995),f753(x7993,x7994,x7992,x7995))
% 191.29/191.76 [800]~E(x8001,x8002)+E(f753(x8003,x8004,x8005,x8001),f753(x8003,x8004,x8005,x8002))
% 191.29/191.76 [801]~E(x8011,x8012)+E(f90(x8011),f90(x8012))
% 191.29/191.76 [802]~E(x8021,x8022)+E(f798(x8021,x8023,x8024),f798(x8022,x8023,x8024))
% 191.29/191.76 [803]~E(x8031,x8032)+E(f798(x8033,x8031,x8034),f798(x8033,x8032,x8034))
% 191.29/191.76 [804]~E(x8041,x8042)+E(f798(x8043,x8044,x8041),f798(x8043,x8044,x8042))
% 191.29/191.76 [805]~E(x8051,x8052)+E(f815(x8051,x8053,x8054,x8055),f815(x8052,x8053,x8054,x8055))
% 191.29/191.76 [806]~E(x8061,x8062)+E(f815(x8063,x8061,x8064,x8065),f815(x8063,x8062,x8064,x8065))
% 191.29/191.76 [807]~E(x8071,x8072)+E(f815(x8073,x8074,x8071,x8075),f815(x8073,x8074,x8072,x8075))
% 191.29/191.76 [808]~E(x8081,x8082)+E(f815(x8083,x8084,x8085,x8081),f815(x8083,x8084,x8085,x8082))
% 191.29/191.76 [809]~E(x8091,x8092)+E(f418(x8091,x8093,x8094),f418(x8092,x8093,x8094))
% 191.29/191.76 [810]~E(x8101,x8102)+E(f418(x8103,x8101,x8104),f418(x8103,x8102,x8104))
% 191.29/191.76 [811]~E(x8111,x8112)+E(f418(x8113,x8114,x8111),f418(x8113,x8114,x8112))
% 191.29/191.76 [812]~E(x8121,x8122)+E(f673(x8121,x8123,x8124),f673(x8122,x8123,x8124))
% 191.29/191.76 [813]~E(x8131,x8132)+E(f673(x8133,x8131,x8134),f673(x8133,x8132,x8134))
% 191.29/191.76 [814]~E(x8141,x8142)+E(f673(x8143,x8144,x8141),f673(x8143,x8144,x8142))
% 191.29/191.76 [815]~E(x8151,x8152)+E(f234(x8151,x8153),f234(x8152,x8153))
% 191.29/191.76 [816]~E(x8161,x8162)+E(f234(x8163,x8161),f234(x8163,x8162))
% 191.29/191.76 [817]~E(x8171,x8172)+E(f134(x8171,x8173),f134(x8172,x8173))
% 191.29/191.76 [818]~E(x8181,x8182)+E(f134(x8183,x8181),f134(x8183,x8182))
% 191.29/191.76 [819]~E(x8191,x8192)+E(f414(x8191,x8193,x8194),f414(x8192,x8193,x8194))
% 191.29/191.76 [820]~E(x8201,x8202)+E(f414(x8203,x8201,x8204),f414(x8203,x8202,x8204))
% 191.29/191.76 [821]~E(x8211,x8212)+E(f414(x8213,x8214,x8211),f414(x8213,x8214,x8212))
% 191.29/191.76 [822]~E(x8221,x8222)+E(f265(x8221,x8223),f265(x8222,x8223))
% 191.29/191.76 [823]~E(x8231,x8232)+E(f265(x8233,x8231),f265(x8233,x8232))
% 191.29/191.76 [824]~E(x8241,x8242)+E(f689(x8241,x8243,x8244,x8245),f689(x8242,x8243,x8244,x8245))
% 191.29/191.76 [825]~E(x8251,x8252)+E(f689(x8253,x8251,x8254,x8255),f689(x8253,x8252,x8254,x8255))
% 191.29/191.76 [826]~E(x8261,x8262)+E(f689(x8263,x8264,x8261,x8265),f689(x8263,x8264,x8262,x8265))
% 191.29/191.76 [827]~E(x8271,x8272)+E(f689(x8273,x8274,x8275,x8271),f689(x8273,x8274,x8275,x8272))
% 191.29/191.76 [828]~E(x8281,x8282)+E(f351(x8281,x8283),f351(x8282,x8283))
% 191.29/191.76 [829]~E(x8291,x8292)+E(f351(x8293,x8291),f351(x8293,x8292))
% 191.29/191.76 [830]~E(x8301,x8302)+E(f510(x8301,x8303,x8304,x8305,x8306),f510(x8302,x8303,x8304,x8305,x8306))
% 191.29/191.76 [831]~E(x8311,x8312)+E(f510(x8313,x8311,x8314,x8315,x8316),f510(x8313,x8312,x8314,x8315,x8316))
% 191.29/191.76 [832]~E(x8321,x8322)+E(f510(x8323,x8324,x8321,x8325,x8326),f510(x8323,x8324,x8322,x8325,x8326))
% 191.29/191.76 [833]~E(x8331,x8332)+E(f510(x8333,x8334,x8335,x8331,x8336),f510(x8333,x8334,x8335,x8332,x8336))
% 191.29/191.76 [834]~E(x8341,x8342)+E(f510(x8343,x8344,x8345,x8346,x8341),f510(x8343,x8344,x8345,x8346,x8342))
% 191.29/191.76 [835]~E(x8351,x8352)+E(f658(x8351,x8353,x8354,x8355,x8356),f658(x8352,x8353,x8354,x8355,x8356))
% 191.29/191.76 [836]~E(x8361,x8362)+E(f658(x8363,x8361,x8364,x8365,x8366),f658(x8363,x8362,x8364,x8365,x8366))
% 191.29/191.76 [837]~E(x8371,x8372)+E(f658(x8373,x8374,x8371,x8375,x8376),f658(x8373,x8374,x8372,x8375,x8376))
% 191.29/191.76 [838]~E(x8381,x8382)+E(f658(x8383,x8384,x8385,x8381,x8386),f658(x8383,x8384,x8385,x8382,x8386))
% 191.29/191.76 [839]~E(x8391,x8392)+E(f658(x8393,x8394,x8395,x8396,x8391),f658(x8393,x8394,x8395,x8396,x8392))
% 191.29/191.76 [840]~E(x8401,x8402)+E(f261(x8401,x8403),f261(x8402,x8403))
% 191.29/191.76 [841]~E(x8411,x8412)+E(f261(x8413,x8411),f261(x8413,x8412))
% 191.29/191.76 [842]~E(x8421,x8422)+E(f780(x8421,x8423,x8424),f780(x8422,x8423,x8424))
% 191.29/191.76 [843]~E(x8431,x8432)+E(f780(x8433,x8431,x8434),f780(x8433,x8432,x8434))
% 191.29/191.76 [844]~E(x8441,x8442)+E(f780(x8443,x8444,x8441),f780(x8443,x8444,x8442))
% 191.29/191.76 [845]~E(x8451,x8452)+E(f849(x8451),f849(x8452))
% 191.29/191.76 [846]~E(x8461,x8462)+E(f154(x8461,x8463,x8464,x8465),f154(x8462,x8463,x8464,x8465))
% 191.29/191.76 [847]~E(x8471,x8472)+E(f154(x8473,x8471,x8474,x8475),f154(x8473,x8472,x8474,x8475))
% 191.29/191.76 [848]~E(x8481,x8482)+E(f154(x8483,x8484,x8481,x8485),f154(x8483,x8484,x8482,x8485))
% 191.29/191.76 [849]~E(x8491,x8492)+E(f154(x8493,x8494,x8495,x8491),f154(x8493,x8494,x8495,x8492))
% 191.29/191.76 [850]~E(x8501,x8502)+E(f504(x8501),f504(x8502))
% 191.29/191.76 [851]~E(x8511,x8512)+E(f763(x8511,x8513,x8514),f763(x8512,x8513,x8514))
% 191.29/191.76 [852]~E(x8521,x8522)+E(f763(x8523,x8521,x8524),f763(x8523,x8522,x8524))
% 191.29/191.76 [853]~E(x8531,x8532)+E(f763(x8533,x8534,x8531),f763(x8533,x8534,x8532))
% 191.29/191.76 [854]~E(x8541,x8542)+E(f322(x8541,x8543),f322(x8542,x8543))
% 191.29/191.76 [855]~E(x8551,x8552)+E(f322(x8553,x8551),f322(x8553,x8552))
% 191.29/191.76 [856]~E(x8561,x8562)+E(f764(x8561,x8563,x8564),f764(x8562,x8563,x8564))
% 191.29/191.76 [857]~E(x8571,x8572)+E(f764(x8573,x8571,x8574),f764(x8573,x8572,x8574))
% 191.29/191.76 [858]~E(x8581,x8582)+E(f764(x8583,x8584,x8581),f764(x8583,x8584,x8582))
% 191.29/191.76 [859]~E(x8591,x8592)+E(f775(x8591),f775(x8592))
% 191.29/191.76 [860]~E(x8601,x8602)+E(f263(x8601,x8603),f263(x8602,x8603))
% 191.29/191.76 [861]~E(x8611,x8612)+E(f263(x8613,x8611),f263(x8613,x8612))
% 191.29/191.76 [862]~E(x8621,x8622)+E(f636(x8621,x8623,x8624,x8625,x8626,x8627,x8628,x8629),f636(x8622,x8623,x8624,x8625,x8626,x8627,x8628,x8629))
% 191.29/191.76 [863]~E(x8631,x8632)+E(f636(x8633,x8631,x8634,x8635,x8636,x8637,x8638,x8639),f636(x8633,x8632,x8634,x8635,x8636,x8637,x8638,x8639))
% 191.29/191.76 [864]~E(x8641,x8642)+E(f636(x8643,x8644,x8641,x8645,x8646,x8647,x8648,x8649),f636(x8643,x8644,x8642,x8645,x8646,x8647,x8648,x8649))
% 191.29/191.76 [865]~E(x8651,x8652)+E(f636(x8653,x8654,x8655,x8651,x8656,x8657,x8658,x8659),f636(x8653,x8654,x8655,x8652,x8656,x8657,x8658,x8659))
% 191.29/191.76 [866]~E(x8661,x8662)+E(f636(x8663,x8664,x8665,x8666,x8661,x8667,x8668,x8669),f636(x8663,x8664,x8665,x8666,x8662,x8667,x8668,x8669))
% 191.29/191.76 [867]~E(x8671,x8672)+E(f636(x8673,x8674,x8675,x8676,x8677,x8671,x8678,x8679),f636(x8673,x8674,x8675,x8676,x8677,x8672,x8678,x8679))
% 191.29/191.76 [868]~E(x8681,x8682)+E(f636(x8683,x8684,x8685,x8686,x8687,x8688,x8681,x8689),f636(x8683,x8684,x8685,x8686,x8687,x8688,x8682,x8689))
% 191.29/191.76 [869]~E(x8691,x8692)+E(f636(x8693,x8694,x8695,x8696,x8697,x8698,x8699,x8691),f636(x8693,x8694,x8695,x8696,x8697,x8698,x8699,x8692))
% 191.29/191.76 [870]~E(x8701,x8702)+E(f571(x8701),f571(x8702))
% 191.29/191.76 [871]~E(x8711,x8712)+E(f692(x8711,x8713,x8714,x8715),f692(x8712,x8713,x8714,x8715))
% 191.29/191.76 [872]~E(x8721,x8722)+E(f692(x8723,x8721,x8724,x8725),f692(x8723,x8722,x8724,x8725))
% 191.29/191.76 [873]~E(x8731,x8732)+E(f692(x8733,x8734,x8731,x8735),f692(x8733,x8734,x8732,x8735))
% 191.29/191.76 [874]~E(x8741,x8742)+E(f692(x8743,x8744,x8745,x8741),f692(x8743,x8744,x8745,x8742))
% 191.29/191.76 [875]~E(x8751,x8752)+E(f615(x8751,x8753,x8754,x8755,x8756,x8757),f615(x8752,x8753,x8754,x8755,x8756,x8757))
% 191.29/191.76 [876]~E(x8761,x8762)+E(f615(x8763,x8761,x8764,x8765,x8766,x8767),f615(x8763,x8762,x8764,x8765,x8766,x8767))
% 191.29/191.76 [877]~E(x8771,x8772)+E(f615(x8773,x8774,x8771,x8775,x8776,x8777),f615(x8773,x8774,x8772,x8775,x8776,x8777))
% 191.29/191.76 [878]~E(x8781,x8782)+E(f615(x8783,x8784,x8785,x8781,x8786,x8787),f615(x8783,x8784,x8785,x8782,x8786,x8787))
% 191.29/191.76 [879]~E(x8791,x8792)+E(f615(x8793,x8794,x8795,x8796,x8791,x8797),f615(x8793,x8794,x8795,x8796,x8792,x8797))
% 191.29/191.76 [880]~E(x8801,x8802)+E(f615(x8803,x8804,x8805,x8806,x8807,x8801),f615(x8803,x8804,x8805,x8806,x8807,x8802))
% 191.29/191.76 [881]~E(x8811,x8812)+E(f254(x8811,x8813,x8814,x8815,x8816),f254(x8812,x8813,x8814,x8815,x8816))
% 191.29/191.76 [882]~E(x8821,x8822)+E(f254(x8823,x8821,x8824,x8825,x8826),f254(x8823,x8822,x8824,x8825,x8826))
% 191.29/191.76 [883]~E(x8831,x8832)+E(f254(x8833,x8834,x8831,x8835,x8836),f254(x8833,x8834,x8832,x8835,x8836))
% 191.29/191.76 [884]~E(x8841,x8842)+E(f254(x8843,x8844,x8845,x8841,x8846),f254(x8843,x8844,x8845,x8842,x8846))
% 191.29/191.76 [885]~E(x8851,x8852)+E(f254(x8853,x8854,x8855,x8856,x8851),f254(x8853,x8854,x8855,x8856,x8852))
% 191.29/191.76 [886]~E(x8861,x8862)+E(f367(x8861,x8863,x8864,x8865,x8866),f367(x8862,x8863,x8864,x8865,x8866))
% 191.29/191.76 [887]~E(x8871,x8872)+E(f367(x8873,x8871,x8874,x8875,x8876),f367(x8873,x8872,x8874,x8875,x8876))
% 191.29/191.76 [888]~E(x8881,x8882)+E(f367(x8883,x8884,x8881,x8885,x8886),f367(x8883,x8884,x8882,x8885,x8886))
% 191.29/191.76 [889]~E(x8891,x8892)+E(f367(x8893,x8894,x8895,x8891,x8896),f367(x8893,x8894,x8895,x8892,x8896))
% 191.29/191.76 [890]~E(x8901,x8902)+E(f367(x8903,x8904,x8905,x8906,x8901),f367(x8903,x8904,x8905,x8906,x8902))
% 191.29/191.76 [891]~E(x8911,x8912)+E(f601(x8911,x8913),f601(x8912,x8913))
% 191.29/191.76 [892]~E(x8921,x8922)+E(f601(x8923,x8921),f601(x8923,x8922))
% 191.29/191.76 [893]~E(x8931,x8932)+E(f185(x8931,x8933),f185(x8932,x8933))
% 191.29/191.76 [894]~E(x8941,x8942)+E(f185(x8943,x8941),f185(x8943,x8942))
% 191.29/191.76 [895]~E(x8951,x8952)+E(f827(x8951,x8953,x8954),f827(x8952,x8953,x8954))
% 191.29/191.76 [896]~E(x8961,x8962)+E(f827(x8963,x8961,x8964),f827(x8963,x8962,x8964))
% 191.29/191.76 [897]~E(x8971,x8972)+E(f827(x8973,x8974,x8971),f827(x8973,x8974,x8972))
% 191.29/191.76 [898]~E(x8981,x8982)+E(f120(x8981,x8983),f120(x8982,x8983))
% 191.29/191.76 [899]~E(x8991,x8992)+E(f120(x8993,x8991),f120(x8993,x8992))
% 191.29/191.76 [900]~E(x9001,x9002)+E(f194(x9001,x9003),f194(x9002,x9003))
% 191.29/191.76 [901]~E(x9011,x9012)+E(f194(x9013,x9011),f194(x9013,x9012))
% 191.29/191.76 [902]~E(x9021,x9022)+E(f131(x9021),f131(x9022))
% 191.29/191.76 [903]~E(x9031,x9032)+E(f123(x9031,x9033),f123(x9032,x9033))
% 191.29/191.76 [904]~E(x9041,x9042)+E(f123(x9043,x9041),f123(x9043,x9042))
% 191.29/191.76 [905]~E(x9051,x9052)+E(f497(x9051,x9053,x9054),f497(x9052,x9053,x9054))
% 191.29/191.76 [906]~E(x9061,x9062)+E(f497(x9063,x9061,x9064),f497(x9063,x9062,x9064))
% 191.29/191.76 [907]~E(x9071,x9072)+E(f497(x9073,x9074,x9071),f497(x9073,x9074,x9072))
% 191.29/191.76 [908]~E(x9081,x9082)+E(f733(x9081,x9083,x9084,x9085,x9086),f733(x9082,x9083,x9084,x9085,x9086))
% 191.29/191.76 [909]~E(x9091,x9092)+E(f733(x9093,x9091,x9094,x9095,x9096),f733(x9093,x9092,x9094,x9095,x9096))
% 191.29/191.76 [910]~E(x9101,x9102)+E(f733(x9103,x9104,x9101,x9105,x9106),f733(x9103,x9104,x9102,x9105,x9106))
% 191.29/191.76 [911]~E(x9111,x9112)+E(f733(x9113,x9114,x9115,x9111,x9116),f733(x9113,x9114,x9115,x9112,x9116))
% 191.29/191.76 [912]~E(x9121,x9122)+E(f733(x9123,x9124,x9125,x9126,x9121),f733(x9123,x9124,x9125,x9126,x9122))
% 191.29/191.76 [913]~E(x9131,x9132)+E(f720(x9131,x9133,x9134,x9135,x9136),f720(x9132,x9133,x9134,x9135,x9136))
% 191.29/191.76 [914]~E(x9141,x9142)+E(f720(x9143,x9141,x9144,x9145,x9146),f720(x9143,x9142,x9144,x9145,x9146))
% 191.29/191.76 [915]~E(x9151,x9152)+E(f720(x9153,x9154,x9151,x9155,x9156),f720(x9153,x9154,x9152,x9155,x9156))
% 191.29/191.76 [916]~E(x9161,x9162)+E(f720(x9163,x9164,x9165,x9161,x9166),f720(x9163,x9164,x9165,x9162,x9166))
% 191.29/191.76 [917]~E(x9171,x9172)+E(f720(x9173,x9174,x9175,x9176,x9171),f720(x9173,x9174,x9175,x9176,x9172))
% 191.29/191.76 [918]~E(x9181,x9182)+E(f245(x9181,x9183),f245(x9182,x9183))
% 191.29/191.76 [919]~E(x9191,x9192)+E(f245(x9193,x9191),f245(x9193,x9192))
% 191.29/191.76 [920]~E(x9201,x9202)+E(f682(x9201,x9203),f682(x9202,x9203))
% 191.29/191.76 [921]~E(x9211,x9212)+E(f682(x9213,x9211),f682(x9213,x9212))
% 191.29/191.76 [922]~E(x9221,x9222)+E(f435(x9221,x9223,x9224,x9225),f435(x9222,x9223,x9224,x9225))
% 191.29/191.76 [923]~E(x9231,x9232)+E(f435(x9233,x9231,x9234,x9235),f435(x9233,x9232,x9234,x9235))
% 191.29/191.76 [924]~E(x9241,x9242)+E(f435(x9243,x9244,x9241,x9245),f435(x9243,x9244,x9242,x9245))
% 191.29/191.76 [925]~E(x9251,x9252)+E(f435(x9253,x9254,x9255,x9251),f435(x9253,x9254,x9255,x9252))
% 191.29/191.76 [926]~E(x9261,x9262)+E(f464(x9261,x9263,x9264,x9265,x9266,x9267),f464(x9262,x9263,x9264,x9265,x9266,x9267))
% 191.29/191.76 [927]~E(x9271,x9272)+E(f464(x9273,x9271,x9274,x9275,x9276,x9277),f464(x9273,x9272,x9274,x9275,x9276,x9277))
% 191.29/191.76 [928]~E(x9281,x9282)+E(f464(x9283,x9284,x9281,x9285,x9286,x9287),f464(x9283,x9284,x9282,x9285,x9286,x9287))
% 191.29/191.76 [929]~E(x9291,x9292)+E(f464(x9293,x9294,x9295,x9291,x9296,x9297),f464(x9293,x9294,x9295,x9292,x9296,x9297))
% 191.29/191.76 [930]~E(x9301,x9302)+E(f464(x9303,x9304,x9305,x9306,x9301,x9307),f464(x9303,x9304,x9305,x9306,x9302,x9307))
% 191.29/191.76 [931]~E(x9311,x9312)+E(f464(x9313,x9314,x9315,x9316,x9317,x9311),f464(x9313,x9314,x9315,x9316,x9317,x9312))
% 191.29/191.76 [932]~E(x9321,x9322)+E(f649(x9321,x9323,x9324,x9325),f649(x9322,x9323,x9324,x9325))
% 191.29/191.76 [933]~E(x9331,x9332)+E(f649(x9333,x9331,x9334,x9335),f649(x9333,x9332,x9334,x9335))
% 191.29/191.76 [934]~E(x9341,x9342)+E(f649(x9343,x9344,x9341,x9345),f649(x9343,x9344,x9342,x9345))
% 191.29/191.76 [935]~E(x9351,x9352)+E(f649(x9353,x9354,x9355,x9351),f649(x9353,x9354,x9355,x9352))
% 191.29/191.76 [936]~E(x9361,x9362)+E(f192(x9361,x9363,x9364,x9365),f192(x9362,x9363,x9364,x9365))
% 191.29/191.76 [937]~E(x9371,x9372)+E(f192(x9373,x9371,x9374,x9375),f192(x9373,x9372,x9374,x9375))
% 191.29/191.76 [938]~E(x9381,x9382)+E(f192(x9383,x9384,x9381,x9385),f192(x9383,x9384,x9382,x9385))
% 191.29/191.76 [939]~E(x9391,x9392)+E(f192(x9393,x9394,x9395,x9391),f192(x9393,x9394,x9395,x9392))
% 191.29/191.76 [940]~E(x9401,x9402)+E(f506(x9401,x9403,x9404),f506(x9402,x9403,x9404))
% 191.29/191.76 [941]~E(x9411,x9412)+E(f506(x9413,x9411,x9414),f506(x9413,x9412,x9414))
% 191.29/191.76 [942]~E(x9421,x9422)+E(f506(x9423,x9424,x9421),f506(x9423,x9424,x9422))
% 191.29/191.76 [943]~E(x9431,x9432)+E(f833(x9431,x9433,x9434,x9435,x9436,x9437,x9438),f833(x9432,x9433,x9434,x9435,x9436,x9437,x9438))
% 191.29/191.76 [944]~E(x9441,x9442)+E(f833(x9443,x9441,x9444,x9445,x9446,x9447,x9448),f833(x9443,x9442,x9444,x9445,x9446,x9447,x9448))
% 191.29/191.76 [945]~E(x9451,x9452)+E(f833(x9453,x9454,x9451,x9455,x9456,x9457,x9458),f833(x9453,x9454,x9452,x9455,x9456,x9457,x9458))
% 191.29/191.76 [946]~E(x9461,x9462)+E(f833(x9463,x9464,x9465,x9461,x9466,x9467,x9468),f833(x9463,x9464,x9465,x9462,x9466,x9467,x9468))
% 191.29/191.76 [947]~E(x9471,x9472)+E(f833(x9473,x9474,x9475,x9476,x9471,x9477,x9478),f833(x9473,x9474,x9475,x9476,x9472,x9477,x9478))
% 191.29/191.76 [948]~E(x9481,x9482)+E(f833(x9483,x9484,x9485,x9486,x9487,x9481,x9488),f833(x9483,x9484,x9485,x9486,x9487,x9482,x9488))
% 191.29/191.76 [949]~E(x9491,x9492)+E(f833(x9493,x9494,x9495,x9496,x9497,x9498,x9491),f833(x9493,x9494,x9495,x9496,x9497,x9498,x9492))
% 191.29/191.76 [950]~E(x9501,x9502)+E(f410(x9501,x9503,x9504,x9505),f410(x9502,x9503,x9504,x9505))
% 191.29/191.76 [951]~E(x9511,x9512)+E(f410(x9513,x9511,x9514,x9515),f410(x9513,x9512,x9514,x9515))
% 191.29/191.76 [952]~E(x9521,x9522)+E(f410(x9523,x9524,x9521,x9525),f410(x9523,x9524,x9522,x9525))
% 191.29/191.76 [953]~E(x9531,x9532)+E(f410(x9533,x9534,x9535,x9531),f410(x9533,x9534,x9535,x9532))
% 191.29/191.76 [954]~E(x9541,x9542)+E(f364(x9541,x9543,x9544,x9545,x9546),f364(x9542,x9543,x9544,x9545,x9546))
% 191.29/191.76 [955]~E(x9551,x9552)+E(f364(x9553,x9551,x9554,x9555,x9556),f364(x9553,x9552,x9554,x9555,x9556))
% 191.29/191.76 [956]~E(x9561,x9562)+E(f364(x9563,x9564,x9561,x9565,x9566),f364(x9563,x9564,x9562,x9565,x9566))
% 191.29/191.76 [957]~E(x9571,x9572)+E(f364(x9573,x9574,x9575,x9571,x9576),f364(x9573,x9574,x9575,x9572,x9576))
% 191.29/191.76 [958]~E(x9581,x9582)+E(f364(x9583,x9584,x9585,x9586,x9581),f364(x9583,x9584,x9585,x9586,x9582))
% 191.29/191.76 [959]~E(x9591,x9592)+E(f531(x9591,x9593,x9594,x9595,x9596),f531(x9592,x9593,x9594,x9595,x9596))
% 191.29/191.76 [960]~E(x9601,x9602)+E(f531(x9603,x9601,x9604,x9605,x9606),f531(x9603,x9602,x9604,x9605,x9606))
% 191.29/191.76 [961]~E(x9611,x9612)+E(f531(x9613,x9614,x9611,x9615,x9616),f531(x9613,x9614,x9612,x9615,x9616))
% 191.29/191.76 [962]~E(x9621,x9622)+E(f531(x9623,x9624,x9625,x9621,x9626),f531(x9623,x9624,x9625,x9622,x9626))
% 191.29/191.76 [963]~E(x9631,x9632)+E(f531(x9633,x9634,x9635,x9636,x9631),f531(x9633,x9634,x9635,x9636,x9632))
% 191.29/191.76 [964]~E(x9641,x9642)+E(f838(x9641,x9643,x9644,x9645),f838(x9642,x9643,x9644,x9645))
% 191.29/191.76 [965]~E(x9651,x9652)+E(f838(x9653,x9651,x9654,x9655),f838(x9653,x9652,x9654,x9655))
% 191.29/191.76 [966]~E(x9661,x9662)+E(f838(x9663,x9664,x9661,x9665),f838(x9663,x9664,x9662,x9665))
% 191.29/191.76 [967]~E(x9671,x9672)+E(f838(x9673,x9674,x9675,x9671),f838(x9673,x9674,x9675,x9672))
% 191.29/191.76 [968]~E(x9681,x9682)+E(f289(x9681,x9683,x9684,x9685,x9686),f289(x9682,x9683,x9684,x9685,x9686))
% 191.29/191.76 [969]~E(x9691,x9692)+E(f289(x9693,x9691,x9694,x9695,x9696),f289(x9693,x9692,x9694,x9695,x9696))
% 191.29/191.76 [970]~E(x9701,x9702)+E(f289(x9703,x9704,x9701,x9705,x9706),f289(x9703,x9704,x9702,x9705,x9706))
% 191.29/191.76 [971]~E(x9711,x9712)+E(f289(x9713,x9714,x9715,x9711,x9716),f289(x9713,x9714,x9715,x9712,x9716))
% 191.29/191.76 [972]~E(x9721,x9722)+E(f289(x9723,x9724,x9725,x9726,x9721),f289(x9723,x9724,x9725,x9726,x9722))
% 191.29/191.76 [973]~E(x9731,x9732)+E(f202(x9731,x9733,x9734,x9735,x9736,x9737,x9738),f202(x9732,x9733,x9734,x9735,x9736,x9737,x9738))
% 191.29/191.76 [974]~E(x9741,x9742)+E(f202(x9743,x9741,x9744,x9745,x9746,x9747,x9748),f202(x9743,x9742,x9744,x9745,x9746,x9747,x9748))
% 191.29/191.76 [975]~E(x9751,x9752)+E(f202(x9753,x9754,x9751,x9755,x9756,x9757,x9758),f202(x9753,x9754,x9752,x9755,x9756,x9757,x9758))
% 191.29/191.76 [976]~E(x9761,x9762)+E(f202(x9763,x9764,x9765,x9761,x9766,x9767,x9768),f202(x9763,x9764,x9765,x9762,x9766,x9767,x9768))
% 191.29/191.76 [977]~E(x9771,x9772)+E(f202(x9773,x9774,x9775,x9776,x9771,x9777,x9778),f202(x9773,x9774,x9775,x9776,x9772,x9777,x9778))
% 191.29/191.76 [978]~E(x9781,x9782)+E(f202(x9783,x9784,x9785,x9786,x9787,x9781,x9788),f202(x9783,x9784,x9785,x9786,x9787,x9782,x9788))
% 191.29/191.76 [979]~E(x9791,x9792)+E(f202(x9793,x9794,x9795,x9796,x9797,x9798,x9791),f202(x9793,x9794,x9795,x9796,x9797,x9798,x9792))
% 191.29/191.76 [980]~E(x9801,x9802)+E(f769(x9801,x9803),f769(x9802,x9803))
% 191.29/191.76 [981]~E(x9811,x9812)+E(f769(x9813,x9811),f769(x9813,x9812))
% 191.29/191.76 [982]~E(x9821,x9822)+E(f620(x9821,x9823,x9824,x9825,x9826,x9827),f620(x9822,x9823,x9824,x9825,x9826,x9827))
% 191.29/191.76 [983]~E(x9831,x9832)+E(f620(x9833,x9831,x9834,x9835,x9836,x9837),f620(x9833,x9832,x9834,x9835,x9836,x9837))
% 191.29/191.76 [984]~E(x9841,x9842)+E(f620(x9843,x9844,x9841,x9845,x9846,x9847),f620(x9843,x9844,x9842,x9845,x9846,x9847))
% 191.29/191.76 [985]~E(x9851,x9852)+E(f620(x9853,x9854,x9855,x9851,x9856,x9857),f620(x9853,x9854,x9855,x9852,x9856,x9857))
% 191.29/191.76 [986]~E(x9861,x9862)+E(f620(x9863,x9864,x9865,x9866,x9861,x9867),f620(x9863,x9864,x9865,x9866,x9862,x9867))
% 191.29/191.76 [987]~E(x9871,x9872)+E(f620(x9873,x9874,x9875,x9876,x9877,x9871),f620(x9873,x9874,x9875,x9876,x9877,x9872))
% 191.29/191.76 [988]~E(x9881,x9882)+E(f191(x9881,x9883,x9884,x9885),f191(x9882,x9883,x9884,x9885))
% 191.29/191.76 [989]~E(x9891,x9892)+E(f191(x9893,x9891,x9894,x9895),f191(x9893,x9892,x9894,x9895))
% 191.29/191.76 [990]~E(x9901,x9902)+E(f191(x9903,x9904,x9901,x9905),f191(x9903,x9904,x9902,x9905))
% 191.29/191.76 [991]~E(x9911,x9912)+E(f191(x9913,x9914,x9915,x9911),f191(x9913,x9914,x9915,x9912))
% 191.29/191.76 [992]~E(x9921,x9922)+E(f643(x9921,x9923,x9924,x9925,x9926),f643(x9922,x9923,x9924,x9925,x9926))
% 191.29/191.76 [993]~E(x9931,x9932)+E(f643(x9933,x9931,x9934,x9935,x9936),f643(x9933,x9932,x9934,x9935,x9936))
% 191.29/191.76 [994]~E(x9941,x9942)+E(f643(x9943,x9944,x9941,x9945,x9946),f643(x9943,x9944,x9942,x9945,x9946))
% 191.29/191.76 [995]~E(x9951,x9952)+E(f643(x9953,x9954,x9955,x9951,x9956),f643(x9953,x9954,x9955,x9952,x9956))
% 191.29/191.76 [996]~E(x9961,x9962)+E(f643(x9963,x9964,x9965,x9966,x9961),f643(x9963,x9964,x9965,x9966,x9962))
% 191.29/191.76 [997]~E(x9971,x9972)+E(f735(x9971,x9973,x9974,x9975,x9976),f735(x9972,x9973,x9974,x9975,x9976))
% 191.29/191.76 [998]~E(x9981,x9982)+E(f735(x9983,x9981,x9984,x9985,x9986),f735(x9983,x9982,x9984,x9985,x9986))
% 191.29/191.76 [999]~E(x9991,x9992)+E(f735(x9993,x9994,x9991,x9995,x9996),f735(x9993,x9994,x9992,x9995,x9996))
% 191.29/191.76 [1000]~E(x10001,x10002)+E(f735(x10003,x10004,x10005,x10001,x10006),f735(x10003,x10004,x10005,x10002,x10006))
% 191.29/191.76 [1001]~E(x10011,x10012)+E(f735(x10013,x10014,x10015,x10016,x10011),f735(x10013,x10014,x10015,x10016,x10012))
% 191.29/191.76 [1002]~E(x10021,x10022)+E(f677(x10021,x10023,x10024),f677(x10022,x10023,x10024))
% 191.29/191.76 [1003]~E(x10031,x10032)+E(f677(x10033,x10031,x10034),f677(x10033,x10032,x10034))
% 191.29/191.76 [1004]~E(x10041,x10042)+E(f677(x10043,x10044,x10041),f677(x10043,x10044,x10042))
% 191.29/191.76 [1005]~E(x10051,x10052)+E(f814(x10051,x10053,x10054),f814(x10052,x10053,x10054))
% 191.29/191.76 [1006]~E(x10061,x10062)+E(f814(x10063,x10061,x10064),f814(x10063,x10062,x10064))
% 191.29/191.76 [1007]~E(x10071,x10072)+E(f814(x10073,x10074,x10071),f814(x10073,x10074,x10072))
% 191.29/191.76 [1008]~E(x10081,x10082)+E(f423(x10081,x10083,x10084,x10085),f423(x10082,x10083,x10084,x10085))
% 191.29/191.76 [1009]~E(x10091,x10092)+E(f423(x10093,x10091,x10094,x10095),f423(x10093,x10092,x10094,x10095))
% 191.29/191.76 [1010]~E(x10101,x10102)+E(f423(x10103,x10104,x10101,x10105),f423(x10103,x10104,x10102,x10105))
% 191.29/191.76 [1011]~E(x10111,x10112)+E(f423(x10113,x10114,x10115,x10111),f423(x10113,x10114,x10115,x10112))
% 191.29/191.76 [1012]~E(x10121,x10122)+E(f512(x10121,x10123,x10124,x10125,x10126),f512(x10122,x10123,x10124,x10125,x10126))
% 191.29/191.76 [1013]~E(x10131,x10132)+E(f512(x10133,x10131,x10134,x10135,x10136),f512(x10133,x10132,x10134,x10135,x10136))
% 191.29/191.76 [1014]~E(x10141,x10142)+E(f512(x10143,x10144,x10141,x10145,x10146),f512(x10143,x10144,x10142,x10145,x10146))
% 191.29/191.76 [1015]~E(x10151,x10152)+E(f512(x10153,x10154,x10155,x10151,x10156),f512(x10153,x10154,x10155,x10152,x10156))
% 191.29/191.76 [1016]~E(x10161,x10162)+E(f512(x10163,x10164,x10165,x10166,x10161),f512(x10163,x10164,x10165,x10166,x10162))
% 191.29/191.76 [1017]~E(x10171,x10172)+E(f662(x10171,x10173,x10174,x10175),f662(x10172,x10173,x10174,x10175))
% 191.29/191.76 [1018]~E(x10181,x10182)+E(f662(x10183,x10181,x10184,x10185),f662(x10183,x10182,x10184,x10185))
% 191.29/191.76 [1019]~E(x10191,x10192)+E(f662(x10193,x10194,x10191,x10195),f662(x10193,x10194,x10192,x10195))
% 191.29/191.76 [1020]~E(x10201,x10202)+E(f662(x10203,x10204,x10205,x10201),f662(x10203,x10204,x10205,x10202))
% 191.29/191.76 [1021]~E(x10211,x10212)+E(f734(x10211,x10213,x10214,x10215,x10216),f734(x10212,x10213,x10214,x10215,x10216))
% 191.29/191.76 [1022]~E(x10221,x10222)+E(f734(x10223,x10221,x10224,x10225,x10226),f734(x10223,x10222,x10224,x10225,x10226))
% 191.29/191.76 [1023]~E(x10231,x10232)+E(f734(x10233,x10234,x10231,x10235,x10236),f734(x10233,x10234,x10232,x10235,x10236))
% 191.29/191.76 [1024]~E(x10241,x10242)+E(f734(x10243,x10244,x10245,x10241,x10246),f734(x10243,x10244,x10245,x10242,x10246))
% 191.29/191.76 [1025]~E(x10251,x10252)+E(f734(x10253,x10254,x10255,x10256,x10251),f734(x10253,x10254,x10255,x10256,x10252))
% 191.29/191.76 [1026]~E(x10261,x10262)+E(f408(x10261,x10263,x10264,x10265),f408(x10262,x10263,x10264,x10265))
% 191.29/191.76 [1027]~E(x10271,x10272)+E(f408(x10273,x10271,x10274,x10275),f408(x10273,x10272,x10274,x10275))
% 191.29/191.76 [1028]~E(x10281,x10282)+E(f408(x10283,x10284,x10281,x10285),f408(x10283,x10284,x10282,x10285))
% 191.29/191.76 [1029]~E(x10291,x10292)+E(f408(x10293,x10294,x10295,x10291),f408(x10293,x10294,x10295,x10292))
% 191.29/191.76 [1030]~E(x10301,x10302)+E(f388(x10301,x10303,x10304,x10305,x10306),f388(x10302,x10303,x10304,x10305,x10306))
% 191.29/191.76 [1031]~E(x10311,x10312)+E(f388(x10313,x10311,x10314,x10315,x10316),f388(x10313,x10312,x10314,x10315,x10316))
% 191.29/191.76 [1032]~E(x10321,x10322)+E(f388(x10323,x10324,x10321,x10325,x10326),f388(x10323,x10324,x10322,x10325,x10326))
% 191.29/191.76 [1033]~E(x10331,x10332)+E(f388(x10333,x10334,x10335,x10331,x10336),f388(x10333,x10334,x10335,x10332,x10336))
% 191.29/191.76 [1034]~E(x10341,x10342)+E(f388(x10343,x10344,x10345,x10346,x10341),f388(x10343,x10344,x10345,x10346,x10342))
% 191.29/191.76 [1035]~E(x10351,x10352)+E(f651(x10351,x10353,x10354,x10355),f651(x10352,x10353,x10354,x10355))
% 191.29/191.76 [1036]~E(x10361,x10362)+E(f651(x10363,x10361,x10364,x10365),f651(x10363,x10362,x10364,x10365))
% 191.29/191.76 [1037]~E(x10371,x10372)+E(f651(x10373,x10374,x10371,x10375),f651(x10373,x10374,x10372,x10375))
% 191.29/191.76 [1038]~E(x10381,x10382)+E(f651(x10383,x10384,x10385,x10381),f651(x10383,x10384,x10385,x10382))
% 191.29/191.76 [1039]~E(x10391,x10392)+E(f519(x10391,x10393,x10394,x10395),f519(x10392,x10393,x10394,x10395))
% 191.29/191.76 [1040]~E(x10401,x10402)+E(f519(x10403,x10401,x10404,x10405),f519(x10403,x10402,x10404,x10405))
% 191.29/191.76 [1041]~E(x10411,x10412)+E(f519(x10413,x10414,x10411,x10415),f519(x10413,x10414,x10412,x10415))
% 191.29/191.76 [1042]~E(x10421,x10422)+E(f519(x10423,x10424,x10425,x10421),f519(x10423,x10424,x10425,x10422))
% 191.29/191.76 [1043]~E(x10431,x10432)+E(f379(x10431,x10433,x10434,x10435),f379(x10432,x10433,x10434,x10435))
% 191.29/191.76 [1044]~E(x10441,x10442)+E(f379(x10443,x10441,x10444,x10445),f379(x10443,x10442,x10444,x10445))
% 191.29/191.76 [1045]~E(x10451,x10452)+E(f379(x10453,x10454,x10451,x10455),f379(x10453,x10454,x10452,x10455))
% 191.29/191.76 [1046]~E(x10461,x10462)+E(f379(x10463,x10464,x10465,x10461),f379(x10463,x10464,x10465,x10462))
% 191.29/191.76 [1047]~E(x10471,x10472)+E(f536(x10471,x10473,x10474,x10475,x10476),f536(x10472,x10473,x10474,x10475,x10476))
% 191.29/191.76 [1048]~E(x10481,x10482)+E(f536(x10483,x10481,x10484,x10485,x10486),f536(x10483,x10482,x10484,x10485,x10486))
% 191.29/191.76 [1049]~E(x10491,x10492)+E(f536(x10493,x10494,x10491,x10495,x10496),f536(x10493,x10494,x10492,x10495,x10496))
% 191.29/191.76 [1050]~E(x10501,x10502)+E(f536(x10503,x10504,x10505,x10501,x10506),f536(x10503,x10504,x10505,x10502,x10506))
% 191.29/191.76 [1051]~E(x10511,x10512)+E(f536(x10513,x10514,x10515,x10516,x10511),f536(x10513,x10514,x10515,x10516,x10512))
% 191.29/191.76 [1052]~E(x10521,x10522)+E(f624(x10521,x10523,x10524,x10525,x10526),f624(x10522,x10523,x10524,x10525,x10526))
% 191.29/191.76 [1053]~E(x10531,x10532)+E(f624(x10533,x10531,x10534,x10535,x10536),f624(x10533,x10532,x10534,x10535,x10536))
% 191.29/191.76 [1054]~E(x10541,x10542)+E(f624(x10543,x10544,x10541,x10545,x10546),f624(x10543,x10544,x10542,x10545,x10546))
% 191.29/191.76 [1055]~E(x10551,x10552)+E(f624(x10553,x10554,x10555,x10551,x10556),f624(x10553,x10554,x10555,x10552,x10556))
% 191.29/191.76 [1056]~E(x10561,x10562)+E(f624(x10563,x10564,x10565,x10566,x10561),f624(x10563,x10564,x10565,x10566,x10562))
% 191.29/191.76 [1057]~E(x10571,x10572)+E(f811(x10571,x10573,x10574),f811(x10572,x10573,x10574))
% 191.29/191.76 [1058]~E(x10581,x10582)+E(f811(x10583,x10581,x10584),f811(x10583,x10582,x10584))
% 191.29/191.76 [1059]~E(x10591,x10592)+E(f811(x10593,x10594,x10591),f811(x10593,x10594,x10592))
% 191.29/191.76 [1060]~E(x10601,x10602)+E(f393(x10601,x10603),f393(x10602,x10603))
% 191.29/191.76 [1061]~E(x10611,x10612)+E(f393(x10613,x10611),f393(x10613,x10612))
% 191.29/191.76 [1062]~E(x10621,x10622)+E(f340(x10621,x10623),f340(x10622,x10623))
% 191.29/191.76 [1063]~E(x10631,x10632)+E(f340(x10633,x10631),f340(x10633,x10632))
% 191.29/191.76 [1064]~E(x10641,x10642)+E(f94(x10641,x10643,x10644),f94(x10642,x10643,x10644))
% 191.29/191.76 [1065]~E(x10651,x10652)+E(f94(x10653,x10651,x10654),f94(x10653,x10652,x10654))
% 191.29/191.76 [1066]~E(x10661,x10662)+E(f94(x10663,x10664,x10661),f94(x10663,x10664,x10662))
% 191.29/191.76 [1067]~E(x10671,x10672)+E(f288(x10671,x10673,x10674),f288(x10672,x10673,x10674))
% 191.29/191.76 [1068]~E(x10681,x10682)+E(f288(x10683,x10681,x10684),f288(x10683,x10682,x10684))
% 191.29/191.76 [1069]~E(x10691,x10692)+E(f288(x10693,x10694,x10691),f288(x10693,x10694,x10692))
% 191.29/191.76 [1070]~E(x10701,x10702)+E(f268(x10701,x10703,x10704,x10705),f268(x10702,x10703,x10704,x10705))
% 191.29/191.76 [1071]~E(x10711,x10712)+E(f268(x10713,x10711,x10714,x10715),f268(x10713,x10712,x10714,x10715))
% 191.29/191.76 [1072]~E(x10721,x10722)+E(f268(x10723,x10724,x10721,x10725),f268(x10723,x10724,x10722,x10725))
% 191.29/191.76 [1073]~E(x10731,x10732)+E(f268(x10733,x10734,x10735,x10731),f268(x10733,x10734,x10735,x10732))
% 191.29/191.76 [1074]~E(x10741,x10742)+E(f584(x10741,x10743),f584(x10742,x10743))
% 191.29/191.76 [1075]~E(x10751,x10752)+E(f584(x10753,x10751),f584(x10753,x10752))
% 191.29/191.76 [1076]~E(x10761,x10762)+E(f394(x10761,x10763,x10764),f394(x10762,x10763,x10764))
% 191.29/191.76 [1077]~E(x10771,x10772)+E(f394(x10773,x10771,x10774),f394(x10773,x10772,x10774))
% 191.29/191.76 [1078]~E(x10781,x10782)+E(f394(x10783,x10784,x10781),f394(x10783,x10784,x10782))
% 191.29/191.76 [1079]~E(x10791,x10792)+E(f503(x10791,x10793),f503(x10792,x10793))
% 191.29/191.76 [1080]~E(x10801,x10802)+E(f503(x10803,x10801),f503(x10803,x10802))
% 191.29/191.76 [1081]~E(x10811,x10812)+E(f701(x10811,x10813,x10814,x10815),f701(x10812,x10813,x10814,x10815))
% 191.29/191.76 [1082]~E(x10821,x10822)+E(f701(x10823,x10821,x10824,x10825),f701(x10823,x10822,x10824,x10825))
% 191.29/191.76 [1083]~E(x10831,x10832)+E(f701(x10833,x10834,x10831,x10835),f701(x10833,x10834,x10832,x10835))
% 191.29/191.76 [1084]~E(x10841,x10842)+E(f701(x10843,x10844,x10845,x10841),f701(x10843,x10844,x10845,x10842))
% 191.29/191.76 [1085]~E(x10851,x10852)+E(f500(x10851,x10853,x10854,x10855,x10856,x10857,x10858),f500(x10852,x10853,x10854,x10855,x10856,x10857,x10858))
% 191.29/191.76 [1086]~E(x10861,x10862)+E(f500(x10863,x10861,x10864,x10865,x10866,x10867,x10868),f500(x10863,x10862,x10864,x10865,x10866,x10867,x10868))
% 191.29/191.76 [1087]~E(x10871,x10872)+E(f500(x10873,x10874,x10871,x10875,x10876,x10877,x10878),f500(x10873,x10874,x10872,x10875,x10876,x10877,x10878))
% 191.29/191.76 [1088]~E(x10881,x10882)+E(f500(x10883,x10884,x10885,x10881,x10886,x10887,x10888),f500(x10883,x10884,x10885,x10882,x10886,x10887,x10888))
% 191.29/191.76 [1089]~E(x10891,x10892)+E(f500(x10893,x10894,x10895,x10896,x10891,x10897,x10898),f500(x10893,x10894,x10895,x10896,x10892,x10897,x10898))
% 191.29/191.76 [1090]~E(x10901,x10902)+E(f500(x10903,x10904,x10905,x10906,x10907,x10901,x10908),f500(x10903,x10904,x10905,x10906,x10907,x10902,x10908))
% 191.29/191.76 [1091]~E(x10911,x10912)+E(f500(x10913,x10914,x10915,x10916,x10917,x10918,x10911),f500(x10913,x10914,x10915,x10916,x10917,x10918,x10912))
% 191.29/191.76 [1092]~E(x10921,x10922)+E(f582(x10921,x10923),f582(x10922,x10923))
% 191.29/191.76 [1093]~E(x10931,x10932)+E(f582(x10933,x10931),f582(x10933,x10932))
% 191.29/191.76 [1094]~E(x10941,x10942)+E(f280(x10941,x10943),f280(x10942,x10943))
% 191.29/191.76 [1095]~E(x10951,x10952)+E(f280(x10953,x10951),f280(x10953,x10952))
% 191.29/191.76 [1096]~E(x10961,x10962)+E(f249(x10961,x10963,x10964,x10965),f249(x10962,x10963,x10964,x10965))
% 191.29/191.76 [1097]~E(x10971,x10972)+E(f249(x10973,x10971,x10974,x10975),f249(x10973,x10972,x10974,x10975))
% 191.29/191.76 [1098]~E(x10981,x10982)+E(f249(x10983,x10984,x10981,x10985),f249(x10983,x10984,x10982,x10985))
% 191.29/191.76 [1099]~E(x10991,x10992)+E(f249(x10993,x10994,x10995,x10991),f249(x10993,x10994,x10995,x10992))
% 191.29/191.76 [1100]~E(x11001,x11002)+E(f161(x11001,x11003,x11004),f161(x11002,x11003,x11004))
% 191.29/191.76 [1101]~E(x11011,x11012)+E(f161(x11013,x11011,x11014),f161(x11013,x11012,x11014))
% 191.29/191.76 [1102]~E(x11021,x11022)+E(f161(x11023,x11024,x11021),f161(x11023,x11024,x11022))
% 191.29/191.76 [1103]~E(x11031,x11032)+E(f395(x11031,x11033,x11034),f395(x11032,x11033,x11034))
% 191.29/191.76 [1104]~E(x11041,x11042)+E(f395(x11043,x11041,x11044),f395(x11043,x11042,x11044))
% 191.29/191.76 [1105]~E(x11051,x11052)+E(f395(x11053,x11054,x11051),f395(x11053,x11054,x11052))
% 191.29/191.76 [1106]~E(x11061,x11062)+E(f246(x11061,x11063,x11064),f246(x11062,x11063,x11064))
% 191.29/191.76 [1107]~E(x11071,x11072)+E(f246(x11073,x11071,x11074),f246(x11073,x11072,x11074))
% 191.29/191.76 [1108]~E(x11081,x11082)+E(f246(x11083,x11084,x11081),f246(x11083,x11084,x11082))
% 191.29/191.76 [1109]~E(x11091,x11092)+E(f730(x11091,x11093,x11094),f730(x11092,x11093,x11094))
% 191.29/191.76 [1110]~E(x11101,x11102)+E(f730(x11103,x11101,x11104),f730(x11103,x11102,x11104))
% 191.29/191.76 [1111]~E(x11111,x11112)+E(f730(x11113,x11114,x11111),f730(x11113,x11114,x11112))
% 191.29/191.76 [1112]~E(x11121,x11122)+E(f657(x11121,x11123,x11124,x11125,x11126),f657(x11122,x11123,x11124,x11125,x11126))
% 191.29/191.76 [1113]~E(x11131,x11132)+E(f657(x11133,x11131,x11134,x11135,x11136),f657(x11133,x11132,x11134,x11135,x11136))
% 191.29/191.76 [1114]~E(x11141,x11142)+E(f657(x11143,x11144,x11141,x11145,x11146),f657(x11143,x11144,x11142,x11145,x11146))
% 191.29/191.76 [1115]~E(x11151,x11152)+E(f657(x11153,x11154,x11155,x11151,x11156),f657(x11153,x11154,x11155,x11152,x11156))
% 191.29/191.76 [1116]~E(x11161,x11162)+E(f657(x11163,x11164,x11165,x11166,x11161),f657(x11163,x11164,x11165,x11166,x11162))
% 191.29/191.76 [1117]~E(x11171,x11172)+E(f723(x11171),f723(x11172))
% 191.29/191.76 [1118]~E(x11181,x11182)+E(f293(x11181),f293(x11182))
% 191.29/191.76 [1119]~E(x11191,x11192)+E(f231(x11191),f231(x11192))
% 191.29/191.76 [1120]~E(x11201,x11202)+E(f174(x11201,x11203,x11204),f174(x11202,x11203,x11204))
% 191.29/191.76 [1121]~E(x11211,x11212)+E(f174(x11213,x11211,x11214),f174(x11213,x11212,x11214))
% 191.29/191.76 [1122]~E(x11221,x11222)+E(f174(x11223,x11224,x11221),f174(x11223,x11224,x11222))
% 191.29/191.76 [1123]~E(x11231,x11232)+E(f670(x11231,x11233),f670(x11232,x11233))
% 191.29/191.76 [1124]~E(x11241,x11242)+E(f670(x11243,x11241),f670(x11243,x11242))
% 191.29/191.76 [1125]~E(x11251,x11252)+E(f563(x11251,x11253,x11254,x11255,x11256,x11257),f563(x11252,x11253,x11254,x11255,x11256,x11257))
% 191.29/191.76 [1126]~E(x11261,x11262)+E(f563(x11263,x11261,x11264,x11265,x11266,x11267),f563(x11263,x11262,x11264,x11265,x11266,x11267))
% 191.29/191.76 [1127]~E(x11271,x11272)+E(f563(x11273,x11274,x11271,x11275,x11276,x11277),f563(x11273,x11274,x11272,x11275,x11276,x11277))
% 191.29/191.76 [1128]~E(x11281,x11282)+E(f563(x11283,x11284,x11285,x11281,x11286,x11287),f563(x11283,x11284,x11285,x11282,x11286,x11287))
% 191.29/191.76 [1129]~E(x11291,x11292)+E(f563(x11293,x11294,x11295,x11296,x11291,x11297),f563(x11293,x11294,x11295,x11296,x11292,x11297))
% 191.29/191.76 [1130]~E(x11301,x11302)+E(f563(x11303,x11304,x11305,x11306,x11307,x11301),f563(x11303,x11304,x11305,x11306,x11307,x11302))
% 191.29/191.76 [1131]~E(x11311,x11312)+E(f785(x11311,x11313,x11314),f785(x11312,x11313,x11314))
% 191.29/191.76 [1132]~E(x11321,x11322)+E(f785(x11323,x11321,x11324),f785(x11323,x11322,x11324))
% 191.29/191.76 [1133]~E(x11331,x11332)+E(f785(x11333,x11334,x11331),f785(x11333,x11334,x11332))
% 191.29/191.76 [1134]~E(x11341,x11342)+E(f474(x11341,x11343,x11344),f474(x11342,x11343,x11344))
% 191.29/191.76 [1135]~E(x11351,x11352)+E(f474(x11353,x11351,x11354),f474(x11353,x11352,x11354))
% 191.29/191.76 [1136]~E(x11361,x11362)+E(f474(x11363,x11364,x11361),f474(x11363,x11364,x11362))
% 191.29/191.76 [1137]~E(x11371,x11372)+E(f710(x11371,x11373,x11374,x11375),f710(x11372,x11373,x11374,x11375))
% 191.29/191.76 [1138]~E(x11381,x11382)+E(f710(x11383,x11381,x11384,x11385),f710(x11383,x11382,x11384,x11385))
% 191.29/191.76 [1139]~E(x11391,x11392)+E(f710(x11393,x11394,x11391,x11395),f710(x11393,x11394,x11392,x11395))
% 191.29/191.76 [1140]~E(x11401,x11402)+E(f710(x11403,x11404,x11405,x11401),f710(x11403,x11404,x11405,x11402))
% 191.29/191.76 [1141]~E(x11411,x11412)+E(f634(x11411,x11413),f634(x11412,x11413))
% 191.29/191.76 [1142]~E(x11421,x11422)+E(f634(x11423,x11421),f634(x11423,x11422))
% 191.29/191.76 [1143]~E(x11431,x11432)+E(f526(x11431,x11433,x11434),f526(x11432,x11433,x11434))
% 191.29/191.76 [1144]~E(x11441,x11442)+E(f526(x11443,x11441,x11444),f526(x11443,x11442,x11444))
% 191.29/191.76 [1145]~E(x11451,x11452)+E(f526(x11453,x11454,x11451),f526(x11453,x11454,x11452))
% 191.29/191.76 [1146]~E(x11461,x11462)+E(f343(x11461,x11463),f343(x11462,x11463))
% 191.29/191.76 [1147]~E(x11471,x11472)+E(f343(x11473,x11471),f343(x11473,x11472))
% 191.29/191.76 [1148]~E(x11481,x11482)+E(f609(x11481,x11483,x11484),f609(x11482,x11483,x11484))
% 191.29/191.76 [1149]~E(x11491,x11492)+E(f609(x11493,x11491,x11494),f609(x11493,x11492,x11494))
% 191.29/191.76 [1150]~E(x11501,x11502)+E(f609(x11503,x11504,x11501),f609(x11503,x11504,x11502))
% 191.29/191.76 [1151]~E(x11511,x11512)+E(f622(x11511,x11513,x11514,x11515),f622(x11512,x11513,x11514,x11515))
% 191.29/191.76 [1152]~E(x11521,x11522)+E(f622(x11523,x11521,x11524,x11525),f622(x11523,x11522,x11524,x11525))
% 191.29/191.76 [1153]~E(x11531,x11532)+E(f622(x11533,x11534,x11531,x11535),f622(x11533,x11534,x11532,x11535))
% 191.29/191.76 [1154]~E(x11541,x11542)+E(f622(x11543,x11544,x11545,x11541),f622(x11543,x11544,x11545,x11542))
% 191.29/191.76 [1155]~E(x11551,x11552)+E(f600(x11551),f600(x11552))
% 191.29/191.76 [1156]~E(x11561,x11562)+E(f639(x11561,x11563,x11564),f639(x11562,x11563,x11564))
% 191.29/191.76 [1157]~E(x11571,x11572)+E(f639(x11573,x11571,x11574),f639(x11573,x11572,x11574))
% 191.29/191.76 [1158]~E(x11581,x11582)+E(f639(x11583,x11584,x11581),f639(x11583,x11584,x11582))
% 191.29/191.76 [1159]~E(x11591,x11592)+E(f771(x11591,x11593,x11594),f771(x11592,x11593,x11594))
% 191.29/191.76 [1160]~E(x11601,x11602)+E(f771(x11603,x11601,x11604),f771(x11603,x11602,x11604))
% 191.29/191.76 [1161]~E(x11611,x11612)+E(f771(x11613,x11614,x11611),f771(x11613,x11614,x11612))
% 191.29/191.76 [1162]~E(x11621,x11622)+E(f537(x11621,x11623,x11624,x11625),f537(x11622,x11623,x11624,x11625))
% 191.29/191.76 [1163]~E(x11631,x11632)+E(f537(x11633,x11631,x11634,x11635),f537(x11633,x11632,x11634,x11635))
% 191.29/191.76 [1164]~E(x11641,x11642)+E(f537(x11643,x11644,x11641,x11645),f537(x11643,x11644,x11642,x11645))
% 191.29/191.76 [1165]~E(x11651,x11652)+E(f537(x11653,x11654,x11655,x11651),f537(x11653,x11654,x11655,x11652))
% 191.29/191.76 [1166]~E(x11661,x11662)+E(f817(x11661,x11663,x11664),f817(x11662,x11663,x11664))
% 191.29/191.76 [1167]~E(x11671,x11672)+E(f817(x11673,x11671,x11674),f817(x11673,x11672,x11674))
% 191.29/191.76 [1168]~E(x11681,x11682)+E(f817(x11683,x11684,x11681),f817(x11683,x11684,x11682))
% 191.29/191.76 [1169]~E(x11691,x11692)+E(f150(x11691,x11693),f150(x11692,x11693))
% 191.29/191.76 [1170]~E(x11701,x11702)+E(f150(x11703,x11701),f150(x11703,x11702))
% 191.29/191.76 [1171]~E(x11711,x11712)+E(f574(x11711,x11713,x11714,x11715,x11716,x11717,x11718,x11719),f574(x11712,x11713,x11714,x11715,x11716,x11717,x11718,x11719))
% 191.29/191.76 [1172]~E(x11721,x11722)+E(f574(x11723,x11721,x11724,x11725,x11726,x11727,x11728,x11729),f574(x11723,x11722,x11724,x11725,x11726,x11727,x11728,x11729))
% 191.29/191.76 [1173]~E(x11731,x11732)+E(f574(x11733,x11734,x11731,x11735,x11736,x11737,x11738,x11739),f574(x11733,x11734,x11732,x11735,x11736,x11737,x11738,x11739))
% 191.29/191.76 [1174]~E(x11741,x11742)+E(f574(x11743,x11744,x11745,x11741,x11746,x11747,x11748,x11749),f574(x11743,x11744,x11745,x11742,x11746,x11747,x11748,x11749))
% 191.29/191.76 [1175]~E(x11751,x11752)+E(f574(x11753,x11754,x11755,x11756,x11751,x11757,x11758,x11759),f574(x11753,x11754,x11755,x11756,x11752,x11757,x11758,x11759))
% 191.29/191.76 [1176]~E(x11761,x11762)+E(f574(x11763,x11764,x11765,x11766,x11767,x11761,x11768,x11769),f574(x11763,x11764,x11765,x11766,x11767,x11762,x11768,x11769))
% 191.29/191.76 [1177]~E(x11771,x11772)+E(f574(x11773,x11774,x11775,x11776,x11777,x11778,x11771,x11779),f574(x11773,x11774,x11775,x11776,x11777,x11778,x11772,x11779))
% 191.29/191.76 [1178]~E(x11781,x11782)+E(f574(x11783,x11784,x11785,x11786,x11787,x11788,x11789,x11781),f574(x11783,x11784,x11785,x11786,x11787,x11788,x11789,x11782))
% 191.29/191.76 [1179]~E(x11791,x11792)+E(f247(x11791,x11793,x11794),f247(x11792,x11793,x11794))
% 191.29/191.76 [1180]~E(x11801,x11802)+E(f247(x11803,x11801,x11804),f247(x11803,x11802,x11804))
% 191.29/191.76 [1181]~E(x11811,x11812)+E(f247(x11813,x11814,x11811),f247(x11813,x11814,x11812))
% 191.29/191.76 [1182]~E(x11821,x11822)+E(f767(x11821,x11823,x11824),f767(x11822,x11823,x11824))
% 191.29/191.76 [1183]~E(x11831,x11832)+E(f767(x11833,x11831,x11834),f767(x11833,x11832,x11834))
% 191.29/191.76 [1184]~E(x11841,x11842)+E(f767(x11843,x11844,x11841),f767(x11843,x11844,x11842))
% 191.29/191.76 [1185]~E(x11851,x11852)+E(f309(x11851,x11853,x11854),f309(x11852,x11853,x11854))
% 191.29/191.76 [1186]~E(x11861,x11862)+E(f309(x11863,x11861,x11864),f309(x11863,x11862,x11864))
% 191.29/191.76 [1187]~E(x11871,x11872)+E(f309(x11873,x11874,x11871),f309(x11873,x11874,x11872))
% 191.29/191.76 [1188]~E(x11881,x11882)+E(f640(x11881,x11883,x11884),f640(x11882,x11883,x11884))
% 191.29/191.76 [1189]~E(x11891,x11892)+E(f640(x11893,x11891,x11894),f640(x11893,x11892,x11894))
% 191.29/191.76 [1190]~E(x11901,x11902)+E(f640(x11903,x11904,x11901),f640(x11903,x11904,x11902))
% 191.29/191.76 [1191]~E(x11911,x11912)+E(f465(x11911,x11913,x11914),f465(x11912,x11913,x11914))
% 191.29/191.76 [1192]~E(x11921,x11922)+E(f465(x11923,x11921,x11924),f465(x11923,x11922,x11924))
% 191.29/191.76 [1193]~E(x11931,x11932)+E(f465(x11933,x11934,x11931),f465(x11933,x11934,x11932))
% 191.29/191.76 [1194]~E(x11941,x11942)+E(f355(x11941,x11943,x11944,x11945),f355(x11942,x11943,x11944,x11945))
% 191.29/191.76 [1195]~E(x11951,x11952)+E(f355(x11953,x11951,x11954,x11955),f355(x11953,x11952,x11954,x11955))
% 191.29/191.76 [1196]~E(x11961,x11962)+E(f355(x11963,x11964,x11961,x11965),f355(x11963,x11964,x11962,x11965))
% 191.29/191.76 [1197]~E(x11971,x11972)+E(f355(x11973,x11974,x11975,x11971),f355(x11973,x11974,x11975,x11972))
% 191.29/191.76 [1198]~E(x11981,x11982)+E(f272(x11981,x11983,x11984,x11985),f272(x11982,x11983,x11984,x11985))
% 191.29/191.76 [1199]~E(x11991,x11992)+E(f272(x11993,x11991,x11994,x11995),f272(x11993,x11992,x11994,x11995))
% 191.29/191.76 [1200]~E(x12001,x12002)+E(f272(x12003,x12004,x12001,x12005),f272(x12003,x12004,x12002,x12005))
% 191.29/191.76 [1201]~E(x12011,x12012)+E(f272(x12013,x12014,x12015,x12011),f272(x12013,x12014,x12015,x12012))
% 191.29/191.76 [1202]~E(x12021,x12022)+E(f757(x12021,x12023,x12024,x12025),f757(x12022,x12023,x12024,x12025))
% 191.29/191.76 [1203]~E(x12031,x12032)+E(f757(x12033,x12031,x12034,x12035),f757(x12033,x12032,x12034,x12035))
% 191.29/191.76 [1204]~E(x12041,x12042)+E(f757(x12043,x12044,x12041,x12045),f757(x12043,x12044,x12042,x12045))
% 191.29/191.76 [1205]~E(x12051,x12052)+E(f757(x12053,x12054,x12055,x12051),f757(x12053,x12054,x12055,x12052))
% 191.29/191.76 [1206]~E(x12061,x12062)+E(f535(x12061,x12063,x12064,x12065,x12066,x12067,x12068,x12069),f535(x12062,x12063,x12064,x12065,x12066,x12067,x12068,x12069))
% 191.29/191.76 [1207]~E(x12071,x12072)+E(f535(x12073,x12071,x12074,x12075,x12076,x12077,x12078,x12079),f535(x12073,x12072,x12074,x12075,x12076,x12077,x12078,x12079))
% 191.29/191.76 [1208]~E(x12081,x12082)+E(f535(x12083,x12084,x12081,x12085,x12086,x12087,x12088,x12089),f535(x12083,x12084,x12082,x12085,x12086,x12087,x12088,x12089))
% 191.29/191.76 [1209]~E(x12091,x12092)+E(f535(x12093,x12094,x12095,x12091,x12096,x12097,x12098,x12099),f535(x12093,x12094,x12095,x12092,x12096,x12097,x12098,x12099))
% 191.29/191.76 [1210]~E(x12101,x12102)+E(f535(x12103,x12104,x12105,x12106,x12101,x12107,x12108,x12109),f535(x12103,x12104,x12105,x12106,x12102,x12107,x12108,x12109))
% 191.29/191.76 [1211]~E(x12111,x12112)+E(f535(x12113,x12114,x12115,x12116,x12117,x12111,x12118,x12119),f535(x12113,x12114,x12115,x12116,x12117,x12112,x12118,x12119))
% 191.29/191.76 [1212]~E(x12121,x12122)+E(f535(x12123,x12124,x12125,x12126,x12127,x12128,x12121,x12129),f535(x12123,x12124,x12125,x12126,x12127,x12128,x12122,x12129))
% 191.29/191.76 [1213]~E(x12131,x12132)+E(f535(x12133,x12134,x12135,x12136,x12137,x12138,x12139,x12131),f535(x12133,x12134,x12135,x12136,x12137,x12138,x12139,x12132))
% 191.29/191.76 [1214]~E(x12141,x12142)+E(f628(x12141,x12143),f628(x12142,x12143))
% 191.29/191.76 [1215]~E(x12151,x12152)+E(f628(x12153,x12151),f628(x12153,x12152))
% 191.29/191.76 [1216]~E(x12161,x12162)+E(f551(x12161,x12163,x12164,x12165,x12166),f551(x12162,x12163,x12164,x12165,x12166))
% 191.29/191.76 [1217]~E(x12171,x12172)+E(f551(x12173,x12171,x12174,x12175,x12176),f551(x12173,x12172,x12174,x12175,x12176))
% 191.29/191.76 [1218]~E(x12181,x12182)+E(f551(x12183,x12184,x12181,x12185,x12186),f551(x12183,x12184,x12182,x12185,x12186))
% 191.29/191.76 [1219]~E(x12191,x12192)+E(f551(x12193,x12194,x12195,x12191,x12196),f551(x12193,x12194,x12195,x12192,x12196))
% 191.29/191.76 [1220]~E(x12201,x12202)+E(f551(x12203,x12204,x12205,x12206,x12201),f551(x12203,x12204,x12205,x12206,x12202))
% 191.29/191.76 [1221]~E(x12211,x12212)+E(f182(x12211,x12213,x12214,x12215),f182(x12212,x12213,x12214,x12215))
% 191.29/191.76 [1222]~E(x12221,x12222)+E(f182(x12223,x12221,x12224,x12225),f182(x12223,x12222,x12224,x12225))
% 191.29/191.76 [1223]~E(x12231,x12232)+E(f182(x12233,x12234,x12231,x12235),f182(x12233,x12234,x12232,x12235))
% 191.29/191.76 [1224]~E(x12241,x12242)+E(f182(x12243,x12244,x12245,x12241),f182(x12243,x12244,x12245,x12242))
% 191.29/191.76 [1225]~E(x12251,x12252)+E(f426(x12251,x12253,x12254,x12255,x12256,x12257,x12258,x12259,x122510),f426(x12252,x12253,x12254,x12255,x12256,x12257,x12258,x12259,x122510))
% 191.29/191.76 [1226]~E(x12261,x12262)+E(f426(x12263,x12261,x12264,x12265,x12266,x12267,x12268,x12269,x122610),f426(x12263,x12262,x12264,x12265,x12266,x12267,x12268,x12269,x122610))
% 191.29/191.76 [1227]~E(x12271,x12272)+E(f426(x12273,x12274,x12271,x12275,x12276,x12277,x12278,x12279,x122710),f426(x12273,x12274,x12272,x12275,x12276,x12277,x12278,x12279,x122710))
% 191.29/191.76 [1228]~E(x12281,x12282)+E(f426(x12283,x12284,x12285,x12281,x12286,x12287,x12288,x12289,x122810),f426(x12283,x12284,x12285,x12282,x12286,x12287,x12288,x12289,x122810))
% 191.29/191.76 [1229]~E(x12291,x12292)+E(f426(x12293,x12294,x12295,x12296,x12291,x12297,x12298,x12299,x122910),f426(x12293,x12294,x12295,x12296,x12292,x12297,x12298,x12299,x122910))
% 191.29/191.76 [1230]~E(x12301,x12302)+E(f426(x12303,x12304,x12305,x12306,x12307,x12301,x12308,x12309,x123010),f426(x12303,x12304,x12305,x12306,x12307,x12302,x12308,x12309,x123010))
% 191.29/191.76 [1231]~E(x12311,x12312)+E(f426(x12313,x12314,x12315,x12316,x12317,x12318,x12311,x12319,x123110),f426(x12313,x12314,x12315,x12316,x12317,x12318,x12312,x12319,x123110))
% 191.29/191.76 [1232]~E(x12321,x12322)+E(f426(x12323,x12324,x12325,x12326,x12327,x12328,x12329,x12321,x123210),f426(x12323,x12324,x12325,x12326,x12327,x12328,x12329,x12322,x123210))
% 191.29/191.76 [1233]~E(x12331,x12332)+E(f426(x12333,x12334,x12335,x12336,x12337,x12338,x12339,x123310,x12331),f426(x12333,x12334,x12335,x12336,x12337,x12338,x12339,x123310,x12332))
% 191.29/191.76 [1234]~E(x12341,x12342)+E(f190(x12341,x12343,x12344,x12345),f190(x12342,x12343,x12344,x12345))
% 191.29/191.76 [1235]~E(x12351,x12352)+E(f190(x12353,x12351,x12354,x12355),f190(x12353,x12352,x12354,x12355))
% 191.29/191.76 [1236]~E(x12361,x12362)+E(f190(x12363,x12364,x12361,x12365),f190(x12363,x12364,x12362,x12365))
% 191.29/191.76 [1237]~E(x12371,x12372)+E(f190(x12373,x12374,x12375,x12371),f190(x12373,x12374,x12375,x12372))
% 191.29/191.76 [1238]~E(x12381,x12382)+E(f445(x12381,x12383),f445(x12382,x12383))
% 191.29/191.76 [1239]~E(x12391,x12392)+E(f445(x12393,x12391),f445(x12393,x12392))
% 191.29/191.76 [1240]~E(x12401,x12402)+E(f697(x12401,x12403,x12404),f697(x12402,x12403,x12404))
% 191.29/191.76 [1241]~E(x12411,x12412)+E(f697(x12413,x12411,x12414),f697(x12413,x12412,x12414))
% 191.29/191.76 [1242]~E(x12421,x12422)+E(f697(x12423,x12424,x12421),f697(x12423,x12424,x12422))
% 191.29/191.76 [1243]~E(x12431,x12432)+E(f566(x12431,x12433),f566(x12432,x12433))
% 191.29/191.76 [1244]~E(x12441,x12442)+E(f566(x12443,x12441),f566(x12443,x12442))
% 191.29/191.76 [1245]~E(x12451,x12452)+E(f338(x12451),f338(x12452))
% 191.29/191.76 [1246]~E(x12461,x12462)+E(f121(x12461,x12463,x12464,x12465),f121(x12462,x12463,x12464,x12465))
% 191.29/191.76 [1247]~E(x12471,x12472)+E(f121(x12473,x12471,x12474,x12475),f121(x12473,x12472,x12474,x12475))
% 191.29/191.76 [1248]~E(x12481,x12482)+E(f121(x12483,x12484,x12481,x12485),f121(x12483,x12484,x12482,x12485))
% 191.29/191.76 [1249]~E(x12491,x12492)+E(f121(x12493,x12494,x12495,x12491),f121(x12493,x12494,x12495,x12492))
% 191.29/191.76 [1250]~E(x12501,x12502)+E(f676(x12501,x12503,x12504),f676(x12502,x12503,x12504))
% 191.29/191.76 [1251]~E(x12511,x12512)+E(f676(x12513,x12511,x12514),f676(x12513,x12512,x12514))
% 191.29/191.76 [1252]~E(x12521,x12522)+E(f676(x12523,x12524,x12521),f676(x12523,x12524,x12522))
% 191.29/191.76 [1253]~E(x12531,x12532)+E(f661(x12531,x12533,x12534,x12535,x12536),f661(x12532,x12533,x12534,x12535,x12536))
% 191.29/191.76 [1254]~E(x12541,x12542)+E(f661(x12543,x12541,x12544,x12545,x12546),f661(x12543,x12542,x12544,x12545,x12546))
% 191.29/191.76 [1255]~E(x12551,x12552)+E(f661(x12553,x12554,x12551,x12555,x12556),f661(x12553,x12554,x12552,x12555,x12556))
% 191.29/191.76 [1256]~E(x12561,x12562)+E(f661(x12563,x12564,x12565,x12561,x12566),f661(x12563,x12564,x12565,x12562,x12566))
% 191.29/191.76 [1257]~E(x12571,x12572)+E(f661(x12573,x12574,x12575,x12576,x12571),f661(x12573,x12574,x12575,x12576,x12572))
% 191.29/191.76 [1258]~E(x12581,x12582)+E(f433(x12581,x12583,x12584,x12585),f433(x12582,x12583,x12584,x12585))
% 191.29/191.76 [1259]~E(x12591,x12592)+E(f433(x12593,x12591,x12594,x12595),f433(x12593,x12592,x12594,x12595))
% 191.29/191.76 [1260]~E(x12601,x12602)+E(f433(x12603,x12604,x12601,x12605),f433(x12603,x12604,x12602,x12605))
% 191.29/191.76 [1261]~E(x12611,x12612)+E(f433(x12613,x12614,x12615,x12611),f433(x12613,x12614,x12615,x12612))
% 191.29/191.76 [1262]~E(x12621,x12622)+E(f377(x12621,x12623),f377(x12622,x12623))
% 191.29/191.76 [1263]~E(x12631,x12632)+E(f377(x12633,x12631),f377(x12633,x12632))
% 191.29/191.76 [1264]~E(x12641,x12642)+E(f810(x12641,x12643,x12644,x12645,x12646),f810(x12642,x12643,x12644,x12645,x12646))
% 191.29/191.76 [1265]~E(x12651,x12652)+E(f810(x12653,x12651,x12654,x12655,x12656),f810(x12653,x12652,x12654,x12655,x12656))
% 191.29/191.76 [1266]~E(x12661,x12662)+E(f810(x12663,x12664,x12661,x12665,x12666),f810(x12663,x12664,x12662,x12665,x12666))
% 191.29/191.76 [1267]~E(x12671,x12672)+E(f810(x12673,x12674,x12675,x12671,x12676),f810(x12673,x12674,x12675,x12672,x12676))
% 191.29/191.76 [1268]~E(x12681,x12682)+E(f810(x12683,x12684,x12685,x12686,x12681),f810(x12683,x12684,x12685,x12686,x12682))
% 191.29/191.76 [1269]~E(x12691,x12692)+E(f415(x12691,x12693,x12694),f415(x12692,x12693,x12694))
% 191.29/191.76 [1270]~E(x12701,x12702)+E(f415(x12703,x12701,x12704),f415(x12703,x12702,x12704))
% 191.29/191.76 [1271]~E(x12711,x12712)+E(f415(x12713,x12714,x12711),f415(x12713,x12714,x12712))
% 191.29/191.76 [1272]~E(x12721,x12722)+E(f346(x12721,x12723,x12724,x12725),f346(x12722,x12723,x12724,x12725))
% 191.29/191.76 [1273]~E(x12731,x12732)+E(f346(x12733,x12731,x12734,x12735),f346(x12733,x12732,x12734,x12735))
% 191.29/191.76 [1274]~E(x12741,x12742)+E(f346(x12743,x12744,x12741,x12745),f346(x12743,x12744,x12742,x12745))
% 191.29/191.76 [1275]~E(x12751,x12752)+E(f346(x12753,x12754,x12755,x12751),f346(x12753,x12754,x12755,x12752))
% 191.29/191.76 [1276]~E(x12761,x12762)+E(f607(x12761,x12763),f607(x12762,x12763))
% 191.29/191.76 [1277]~E(x12771,x12772)+E(f607(x12773,x12771),f607(x12773,x12772))
% 191.29/191.76 [1278]~E(x12781,x12782)+E(f344(x12781,x12783),f344(x12782,x12783))
% 191.29/191.76 [1279]~E(x12791,x12792)+E(f344(x12793,x12791),f344(x12793,x12792))
% 191.29/191.76 [1280]~E(x12801,x12802)+E(f456(x12801,x12803),f456(x12802,x12803))
% 191.29/191.76 [1281]~E(x12811,x12812)+E(f456(x12813,x12811),f456(x12813,x12812))
% 191.29/191.76 [1282]~E(x12821,x12822)+E(f481(x12821,x12823,x12824,x12825,x12826),f481(x12822,x12823,x12824,x12825,x12826))
% 191.29/191.76 [1283]~E(x12831,x12832)+E(f481(x12833,x12831,x12834,x12835,x12836),f481(x12833,x12832,x12834,x12835,x12836))
% 191.29/191.76 [1284]~E(x12841,x12842)+E(f481(x12843,x12844,x12841,x12845,x12846),f481(x12843,x12844,x12842,x12845,x12846))
% 191.29/191.76 [1285]~E(x12851,x12852)+E(f481(x12853,x12854,x12855,x12851,x12856),f481(x12853,x12854,x12855,x12852,x12856))
% 191.29/191.76 [1286]~E(x12861,x12862)+E(f481(x12863,x12864,x12865,x12866,x12861),f481(x12863,x12864,x12865,x12866,x12862))
% 191.29/191.76 [1287]~E(x12871,x12872)+E(f325(x12871,x12873,x12874,x12875),f325(x12872,x12873,x12874,x12875))
% 191.29/191.76 [1288]~E(x12881,x12882)+E(f325(x12883,x12881,x12884,x12885),f325(x12883,x12882,x12884,x12885))
% 191.29/191.76 [1289]~E(x12891,x12892)+E(f325(x12893,x12894,x12891,x12895),f325(x12893,x12894,x12892,x12895))
% 191.29/191.76 [1290]~E(x12901,x12902)+E(f325(x12903,x12904,x12905,x12901),f325(x12903,x12904,x12905,x12902))
% 191.29/191.76 [1291]~E(x12911,x12912)+E(f336(x12911,x12913,x12914,x12915),f336(x12912,x12913,x12914,x12915))
% 191.29/191.76 [1292]~E(x12921,x12922)+E(f336(x12923,x12921,x12924,x12925),f336(x12923,x12922,x12924,x12925))
% 191.29/191.76 [1293]~E(x12931,x12932)+E(f336(x12933,x12934,x12931,x12935),f336(x12933,x12934,x12932,x12935))
% 191.29/191.76 [1294]~E(x12941,x12942)+E(f336(x12943,x12944,x12945,x12941),f336(x12943,x12944,x12945,x12942))
% 191.29/191.76 [1295]~E(x12951,x12952)+E(f354(x12951,x12953,x12954,x12955),f354(x12952,x12953,x12954,x12955))
% 191.29/191.76 [1296]~E(x12961,x12962)+E(f354(x12963,x12961,x12964,x12965),f354(x12963,x12962,x12964,x12965))
% 191.29/191.76 [1297]~E(x12971,x12972)+E(f354(x12973,x12974,x12971,x12975),f354(x12973,x12974,x12972,x12975))
% 191.29/191.76 [1298]~E(x12981,x12982)+E(f354(x12983,x12984,x12985,x12981),f354(x12983,x12984,x12985,x12982))
% 191.29/191.76 [1299]~E(x12991,x12992)+E(f731(x12991,x12993,x12994,x12995,x12996),f731(x12992,x12993,x12994,x12995,x12996))
% 191.29/191.76 [1300]~E(x13001,x13002)+E(f731(x13003,x13001,x13004,x13005,x13006),f731(x13003,x13002,x13004,x13005,x13006))
% 191.29/191.76 [1301]~E(x13011,x13012)+E(f731(x13013,x13014,x13011,x13015,x13016),f731(x13013,x13014,x13012,x13015,x13016))
% 191.29/191.76 [1302]~E(x13021,x13022)+E(f731(x13023,x13024,x13025,x13021,x13026),f731(x13023,x13024,x13025,x13022,x13026))
% 191.29/191.76 [1303]~E(x13031,x13032)+E(f731(x13033,x13034,x13035,x13036,x13031),f731(x13033,x13034,x13035,x13036,x13032))
% 191.29/191.76 [1304]~E(x13041,x13042)+E(f702(x13041,x13043,x13044,x13045,x13046),f702(x13042,x13043,x13044,x13045,x13046))
% 191.29/191.76 [1305]~E(x13051,x13052)+E(f702(x13053,x13051,x13054,x13055,x13056),f702(x13053,x13052,x13054,x13055,x13056))
% 191.29/191.76 [1306]~E(x13061,x13062)+E(f702(x13063,x13064,x13061,x13065,x13066),f702(x13063,x13064,x13062,x13065,x13066))
% 191.29/191.76 [1307]~E(x13071,x13072)+E(f702(x13073,x13074,x13075,x13071,x13076),f702(x13073,x13074,x13075,x13072,x13076))
% 191.29/191.76 [1308]~E(x13081,x13082)+E(f702(x13083,x13084,x13085,x13086,x13081),f702(x13083,x13084,x13085,x13086,x13082))
% 191.29/191.76 [1309]~E(x13091,x13092)+E(f508(x13091,x13093,x13094),f508(x13092,x13093,x13094))
% 191.29/191.76 [1310]~E(x13101,x13102)+E(f508(x13103,x13101,x13104),f508(x13103,x13102,x13104))
% 191.29/191.76 [1311]~E(x13111,x13112)+E(f508(x13113,x13114,x13111),f508(x13113,x13114,x13112))
% 191.29/191.76 [1312]~E(x13121,x13122)+E(f19(x13121,x13123,x13124,x13125),f19(x13122,x13123,x13124,x13125))
% 191.29/191.76 [1313]~E(x13131,x13132)+E(f19(x13133,x13131,x13134,x13135),f19(x13133,x13132,x13134,x13135))
% 191.29/191.76 [1314]~E(x13141,x13142)+E(f19(x13143,x13144,x13141,x13145),f19(x13143,x13144,x13142,x13145))
% 191.29/191.76 [1315]~E(x13151,x13152)+E(f19(x13153,x13154,x13155,x13151),f19(x13153,x13154,x13155,x13152))
% 191.29/191.76 [1316]~E(x13161,x13162)+E(f514(x13161,x13163,x13164,x13165,x13166),f514(x13162,x13163,x13164,x13165,x13166))
% 191.29/191.76 [1317]~E(x13171,x13172)+E(f514(x13173,x13171,x13174,x13175,x13176),f514(x13173,x13172,x13174,x13175,x13176))
% 191.29/191.76 [1318]~E(x13181,x13182)+E(f514(x13183,x13184,x13181,x13185,x13186),f514(x13183,x13184,x13182,x13185,x13186))
% 191.29/191.76 [1319]~E(x13191,x13192)+E(f514(x13193,x13194,x13195,x13191,x13196),f514(x13193,x13194,x13195,x13192,x13196))
% 191.29/191.76 [1320]~E(x13201,x13202)+E(f514(x13203,x13204,x13205,x13206,x13201),f514(x13203,x13204,x13205,x13206,x13202))
% 191.29/191.76 [1321]~E(x13211,x13212)+E(f740(x13211,x13213,x13214,x13215,x13216),f740(x13212,x13213,x13214,x13215,x13216))
% 191.29/191.76 [1322]~E(x13221,x13222)+E(f740(x13223,x13221,x13224,x13225,x13226),f740(x13223,x13222,x13224,x13225,x13226))
% 191.29/191.76 [1323]~E(x13231,x13232)+E(f740(x13233,x13234,x13231,x13235,x13236),f740(x13233,x13234,x13232,x13235,x13236))
% 191.29/191.76 [1324]~E(x13241,x13242)+E(f740(x13243,x13244,x13245,x13241,x13246),f740(x13243,x13244,x13245,x13242,x13246))
% 191.29/191.76 [1325]~E(x13251,x13252)+E(f740(x13253,x13254,x13255,x13256,x13251),f740(x13253,x13254,x13255,x13256,x13252))
% 191.29/191.76 [1326]~E(x13261,x13262)+E(f386(x13261,x13263,x13264,x13265,x13266),f386(x13262,x13263,x13264,x13265,x13266))
% 191.29/191.76 [1327]~E(x13271,x13272)+E(f386(x13273,x13271,x13274,x13275,x13276),f386(x13273,x13272,x13274,x13275,x13276))
% 191.29/191.76 [1328]~E(x13281,x13282)+E(f386(x13283,x13284,x13281,x13285,x13286),f386(x13283,x13284,x13282,x13285,x13286))
% 191.29/191.76 [1329]~E(x13291,x13292)+E(f386(x13293,x13294,x13295,x13291,x13296),f386(x13293,x13294,x13295,x13292,x13296))
% 191.29/191.76 [1330]~E(x13301,x13302)+E(f386(x13303,x13304,x13305,x13306,x13301),f386(x13303,x13304,x13305,x13306,x13302))
% 191.29/191.76 [1331]~E(x13311,x13312)+E(f728(x13311),f728(x13312))
% 191.29/191.76 [1332]~E(x13321,x13322)+E(f436(x13321,x13323,x13324,x13325),f436(x13322,x13323,x13324,x13325))
% 191.29/191.76 [1333]~E(x13331,x13332)+E(f436(x13333,x13331,x13334,x13335),f436(x13333,x13332,x13334,x13335))
% 191.29/191.76 [1334]~E(x13341,x13342)+E(f436(x13343,x13344,x13341,x13345),f436(x13343,x13344,x13342,x13345))
% 191.29/191.76 [1335]~E(x13351,x13352)+E(f436(x13353,x13354,x13355,x13351),f436(x13353,x13354,x13355,x13352))
% 191.29/191.76 [1336]~E(x13361,x13362)+E(f384(x13361,x13363,x13364,x13365),f384(x13362,x13363,x13364,x13365))
% 191.29/191.76 [1337]~E(x13371,x13372)+E(f384(x13373,x13371,x13374,x13375),f384(x13373,x13372,x13374,x13375))
% 191.29/191.76 [1338]~E(x13381,x13382)+E(f384(x13383,x13384,x13381,x13385),f384(x13383,x13384,x13382,x13385))
% 191.29/191.76 [1339]~E(x13391,x13392)+E(f384(x13393,x13394,x13395,x13391),f384(x13393,x13394,x13395,x13392))
% 191.29/191.76 [1340]~E(x13401,x13402)+E(f836(x13401,x13403),f836(x13402,x13403))
% 191.29/191.76 [1341]~E(x13411,x13412)+E(f836(x13413,x13411),f836(x13413,x13412))
% 191.29/191.76 [1342]~E(x13421,x13422)+E(f381(x13421,x13423,x13424,x13425),f381(x13422,x13423,x13424,x13425))
% 191.29/191.76 [1343]~E(x13431,x13432)+E(f381(x13433,x13431,x13434,x13435),f381(x13433,x13432,x13434,x13435))
% 191.29/191.76 [1344]~E(x13441,x13442)+E(f381(x13443,x13444,x13441,x13445),f381(x13443,x13444,x13442,x13445))
% 191.29/191.76 [1345]~E(x13451,x13452)+E(f381(x13453,x13454,x13455,x13451),f381(x13453,x13454,x13455,x13452))
% 191.29/191.76 [1346]~E(x13461,x13462)+E(f700(x13461,x13463,x13464,x13465),f700(x13462,x13463,x13464,x13465))
% 191.29/191.76 [1347]~E(x13471,x13472)+E(f700(x13473,x13471,x13474,x13475),f700(x13473,x13472,x13474,x13475))
% 191.29/191.76 [1348]~E(x13481,x13482)+E(f700(x13483,x13484,x13481,x13485),f700(x13483,x13484,x13482,x13485))
% 191.29/191.76 [1349]~E(x13491,x13492)+E(f700(x13493,x13494,x13495,x13491),f700(x13493,x13494,x13495,x13492))
% 191.29/191.76 [1350]~E(x13501,x13502)+E(f215(x13501,x13503,x13504,x13505),f215(x13502,x13503,x13504,x13505))
% 191.29/191.76 [1351]~E(x13511,x13512)+E(f215(x13513,x13511,x13514,x13515),f215(x13513,x13512,x13514,x13515))
% 191.29/191.76 [1352]~E(x13521,x13522)+E(f215(x13523,x13524,x13521,x13525),f215(x13523,x13524,x13522,x13525))
% 191.29/191.76 [1353]~E(x13531,x13532)+E(f215(x13533,x13534,x13535,x13531),f215(x13533,x13534,x13535,x13532))
% 191.29/191.76 [1354]~E(x13541,x13542)+E(f253(x13541,x13543,x13544,x13545),f253(x13542,x13543,x13544,x13545))
% 191.29/191.76 [1355]~E(x13551,x13552)+E(f253(x13553,x13551,x13554,x13555),f253(x13553,x13552,x13554,x13555))
% 191.29/191.76 [1356]~E(x13561,x13562)+E(f253(x13563,x13564,x13561,x13565),f253(x13563,x13564,x13562,x13565))
% 191.29/191.76 [1357]~E(x13571,x13572)+E(f253(x13573,x13574,x13575,x13571),f253(x13573,x13574,x13575,x13572))
% 191.29/191.76 [1358]~E(x13581,x13582)+E(f760(x13581,x13583),f760(x13582,x13583))
% 191.29/191.76 [1359]~E(x13591,x13592)+E(f760(x13593,x13591),f760(x13593,x13592))
% 191.29/191.76 [1360]~E(x13601,x13602)+E(f644(x13601,x13603,x13604,x13605,x13606),f644(x13602,x13603,x13604,x13605,x13606))
% 191.29/191.76 [1361]~E(x13611,x13612)+E(f644(x13613,x13611,x13614,x13615,x13616),f644(x13613,x13612,x13614,x13615,x13616))
% 191.29/191.76 [1362]~E(x13621,x13622)+E(f644(x13623,x13624,x13621,x13625,x13626),f644(x13623,x13624,x13622,x13625,x13626))
% 191.29/191.76 [1363]~E(x13631,x13632)+E(f644(x13633,x13634,x13635,x13631,x13636),f644(x13633,x13634,x13635,x13632,x13636))
% 191.29/191.76 [1364]~E(x13641,x13642)+E(f644(x13643,x13644,x13645,x13646,x13641),f644(x13643,x13644,x13645,x13646,x13642))
% 191.29/191.76 [1365]~E(x13651,x13652)+E(f570(x13651,x13653,x13654,x13655,x13656),f570(x13652,x13653,x13654,x13655,x13656))
% 191.29/191.76 [1366]~E(x13661,x13662)+E(f570(x13663,x13661,x13664,x13665,x13666),f570(x13663,x13662,x13664,x13665,x13666))
% 191.29/191.76 [1367]~E(x13671,x13672)+E(f570(x13673,x13674,x13671,x13675,x13676),f570(x13673,x13674,x13672,x13675,x13676))
% 191.29/191.76 [1368]~E(x13681,x13682)+E(f570(x13683,x13684,x13685,x13681,x13686),f570(x13683,x13684,x13685,x13682,x13686))
% 191.29/191.76 [1369]~E(x13691,x13692)+E(f570(x13693,x13694,x13695,x13696,x13691),f570(x13693,x13694,x13695,x13696,x13692))
% 191.29/191.76 [1370]~E(x13701,x13702)+E(f243(x13701,x13703,x13704),f243(x13702,x13703,x13704))
% 191.29/191.76 [1371]~E(x13711,x13712)+E(f243(x13713,x13711,x13714),f243(x13713,x13712,x13714))
% 191.29/191.76 [1372]~E(x13721,x13722)+E(f243(x13723,x13724,x13721),f243(x13723,x13724,x13722))
% 191.29/191.76 [1373]~E(x13731,x13732)+E(f546(x13731,x13733,x13734,x13735,x13736),f546(x13732,x13733,x13734,x13735,x13736))
% 191.29/191.76 [1374]~E(x13741,x13742)+E(f546(x13743,x13741,x13744,x13745,x13746),f546(x13743,x13742,x13744,x13745,x13746))
% 191.29/191.76 [1375]~E(x13751,x13752)+E(f546(x13753,x13754,x13751,x13755,x13756),f546(x13753,x13754,x13752,x13755,x13756))
% 191.29/191.76 [1376]~E(x13761,x13762)+E(f546(x13763,x13764,x13765,x13761,x13766),f546(x13763,x13764,x13765,x13762,x13766))
% 191.29/191.76 [1377]~E(x13771,x13772)+E(f546(x13773,x13774,x13775,x13776,x13771),f546(x13773,x13774,x13775,x13776,x13772))
% 191.29/191.76 [1378]~E(x13781,x13782)+E(f267(x13781,x13783),f267(x13782,x13783))
% 191.29/191.76 [1379]~E(x13791,x13792)+E(f267(x13793,x13791),f267(x13793,x13792))
% 191.29/191.76 [1380]~E(x13801,x13802)+E(f812(x13801,x13803,x13804),f812(x13802,x13803,x13804))
% 191.29/191.76 [1381]~E(x13811,x13812)+E(f812(x13813,x13811,x13814),f812(x13813,x13812,x13814))
% 191.29/191.76 [1382]~E(x13821,x13822)+E(f812(x13823,x13824,x13821),f812(x13823,x13824,x13822))
% 191.29/191.76 [1383]~E(x13831,x13832)+E(f671(x13831,x13833,x13834),f671(x13832,x13833,x13834))
% 191.29/191.76 [1384]~E(x13841,x13842)+E(f671(x13843,x13841,x13844),f671(x13843,x13842,x13844))
% 191.29/191.76 [1385]~E(x13851,x13852)+E(f671(x13853,x13854,x13851),f671(x13853,x13854,x13852))
% 191.29/191.76 [1386]~E(x13861,x13862)+E(f627(x13861,x13863,x13864),f627(x13862,x13863,x13864))
% 191.29/191.76 [1387]~E(x13871,x13872)+E(f627(x13873,x13871,x13874),f627(x13873,x13872,x13874))
% 191.29/191.76 [1388]~E(x13881,x13882)+E(f627(x13883,x13884,x13881),f627(x13883,x13884,x13882))
% 191.29/191.76 [1389]~E(x13891,x13892)+E(f712(x13891,x13893,x13894,x13895,x13896,x13897,x13898),f712(x13892,x13893,x13894,x13895,x13896,x13897,x13898))
% 191.29/191.76 [1390]~E(x13901,x13902)+E(f712(x13903,x13901,x13904,x13905,x13906,x13907,x13908),f712(x13903,x13902,x13904,x13905,x13906,x13907,x13908))
% 191.29/191.76 [1391]~E(x13911,x13912)+E(f712(x13913,x13914,x13911,x13915,x13916,x13917,x13918),f712(x13913,x13914,x13912,x13915,x13916,x13917,x13918))
% 191.29/191.76 [1392]~E(x13921,x13922)+E(f712(x13923,x13924,x13925,x13921,x13926,x13927,x13928),f712(x13923,x13924,x13925,x13922,x13926,x13927,x13928))
% 191.29/191.76 [1393]~E(x13931,x13932)+E(f712(x13933,x13934,x13935,x13936,x13931,x13937,x13938),f712(x13933,x13934,x13935,x13936,x13932,x13937,x13938))
% 191.29/191.76 [1394]~E(x13941,x13942)+E(f712(x13943,x13944,x13945,x13946,x13947,x13941,x13948),f712(x13943,x13944,x13945,x13946,x13947,x13942,x13948))
% 191.29/191.76 [1395]~E(x13951,x13952)+E(f712(x13953,x13954,x13955,x13956,x13957,x13958,x13951),f712(x13953,x13954,x13955,x13956,x13957,x13958,x13952))
% 191.29/191.76 [1396]~E(x13961,x13962)+E(f385(x13961,x13963,x13964,x13965),f385(x13962,x13963,x13964,x13965))
% 191.29/191.76 [1397]~E(x13971,x13972)+E(f385(x13973,x13971,x13974,x13975),f385(x13973,x13972,x13974,x13975))
% 191.29/191.76 [1398]~E(x13981,x13982)+E(f385(x13983,x13984,x13981,x13985),f385(x13983,x13984,x13982,x13985))
% 191.29/191.76 [1399]~E(x13991,x13992)+E(f385(x13993,x13994,x13995,x13991),f385(x13993,x13994,x13995,x13992))
% 191.29/191.76 [1400]~E(x14001,x14002)+E(f235(x14001,x14003),f235(x14002,x14003))
% 191.29/191.76 [1401]~E(x14011,x14012)+E(f235(x14013,x14011),f235(x14013,x14012))
% 191.29/191.76 [1402]~E(x14021,x14022)+E(f793(x14021,x14023,x14024),f793(x14022,x14023,x14024))
% 191.29/191.76 [1403]~E(x14031,x14032)+E(f793(x14033,x14031,x14034),f793(x14033,x14032,x14034))
% 191.29/191.76 [1404]~E(x14041,x14042)+E(f793(x14043,x14044,x14041),f793(x14043,x14044,x14042))
% 191.29/191.76 [1405]~E(x14051,x14052)+E(f599(x14051,x14053,x14054,x14055),f599(x14052,x14053,x14054,x14055))
% 191.29/191.76 [1406]~E(x14061,x14062)+E(f599(x14063,x14061,x14064,x14065),f599(x14063,x14062,x14064,x14065))
% 191.29/191.76 [1407]~E(x14071,x14072)+E(f599(x14073,x14074,x14071,x14075),f599(x14073,x14074,x14072,x14075))
% 191.29/191.76 [1408]~E(x14081,x14082)+E(f599(x14083,x14084,x14085,x14081),f599(x14083,x14084,x14085,x14082))
% 191.29/191.76 [1409]~E(x14091,x14092)+E(f533(x14091,x14093,x14094,x14095,x14096),f533(x14092,x14093,x14094,x14095,x14096))
% 191.29/191.76 [1410]~E(x14101,x14102)+E(f533(x14103,x14101,x14104,x14105,x14106),f533(x14103,x14102,x14104,x14105,x14106))
% 191.29/191.76 [1411]~E(x14111,x14112)+E(f533(x14113,x14114,x14111,x14115,x14116),f533(x14113,x14114,x14112,x14115,x14116))
% 191.29/191.76 [1412]~E(x14121,x14122)+E(f533(x14123,x14124,x14125,x14121,x14126),f533(x14123,x14124,x14125,x14122,x14126))
% 191.29/191.76 [1413]~E(x14131,x14132)+E(f533(x14133,x14134,x14135,x14136,x14131),f533(x14133,x14134,x14135,x14136,x14132))
% 191.29/191.76 [1414]~E(x14141,x14142)+E(f228(x14141,x14143,x14144),f228(x14142,x14143,x14144))
% 191.29/191.76 [1415]~E(x14151,x14152)+E(f228(x14153,x14151,x14154),f228(x14153,x14152,x14154))
% 191.29/191.76 [1416]~E(x14161,x14162)+E(f228(x14163,x14164,x14161),f228(x14163,x14164,x14162))
% 191.29/191.76 [1417]~E(x14171,x14172)+E(f392(x14171,x14173,x14174,x14175,x14176),f392(x14172,x14173,x14174,x14175,x14176))
% 191.29/191.76 [1418]~E(x14181,x14182)+E(f392(x14183,x14181,x14184,x14185,x14186),f392(x14183,x14182,x14184,x14185,x14186))
% 191.29/191.76 [1419]~E(x14191,x14192)+E(f392(x14193,x14194,x14191,x14195,x14196),f392(x14193,x14194,x14192,x14195,x14196))
% 191.29/191.76 [1420]~E(x14201,x14202)+E(f392(x14203,x14204,x14205,x14201,x14206),f392(x14203,x14204,x14205,x14202,x14206))
% 191.29/191.76 [1421]~E(x14211,x14212)+E(f392(x14213,x14214,x14215,x14216,x14211),f392(x14213,x14214,x14215,x14216,x14212))
% 191.29/191.76 [1422]~E(x14221,x14222)+E(f342(x14221,x14223),f342(x14222,x14223))
% 191.29/191.76 [1423]~E(x14231,x14232)+E(f342(x14233,x14231),f342(x14233,x14232))
% 191.29/191.76 [1424]~E(x14241,x14242)+E(f547(x14241,x14243,x14244),f547(x14242,x14243,x14244))
% 191.29/191.76 [1425]~E(x14251,x14252)+E(f547(x14253,x14251,x14254),f547(x14253,x14252,x14254))
% 191.29/191.76 [1426]~E(x14261,x14262)+E(f547(x14263,x14264,x14261),f547(x14263,x14264,x14262))
% 191.29/191.76 [1427]~E(x14271,x14272)+E(f766(x14271,x14273,x14274),f766(x14272,x14273,x14274))
% 191.29/191.76 [1428]~E(x14281,x14282)+E(f766(x14283,x14281,x14284),f766(x14283,x14282,x14284))
% 191.29/191.76 [1429]~E(x14291,x14292)+E(f766(x14293,x14294,x14291),f766(x14293,x14294,x14292))
% 191.29/191.76 [1430]~E(x14301,x14302)+E(f373(x14301,x14303),f373(x14302,x14303))
% 191.29/191.76 [1431]~E(x14311,x14312)+E(f373(x14313,x14311),f373(x14313,x14312))
% 191.29/191.76 [1432]~E(x14321,x14322)+E(f204(x14321,x14323,x14324,x14325),f204(x14322,x14323,x14324,x14325))
% 191.29/191.76 [1433]~E(x14331,x14332)+E(f204(x14333,x14331,x14334,x14335),f204(x14333,x14332,x14334,x14335))
% 191.29/191.76 [1434]~E(x14341,x14342)+E(f204(x14343,x14344,x14341,x14345),f204(x14343,x14344,x14342,x14345))
% 191.29/191.76 [1435]~E(x14351,x14352)+E(f204(x14353,x14354,x14355,x14351),f204(x14353,x14354,x14355,x14352))
% 191.29/191.76 [1436]~E(x14361,x14362)+E(f362(x14361,x14363,x14364,x14365,x14366),f362(x14362,x14363,x14364,x14365,x14366))
% 191.29/191.76 [1437]~E(x14371,x14372)+E(f362(x14373,x14371,x14374,x14375,x14376),f362(x14373,x14372,x14374,x14375,x14376))
% 191.29/191.76 [1438]~E(x14381,x14382)+E(f362(x14383,x14384,x14381,x14385,x14386),f362(x14383,x14384,x14382,x14385,x14386))
% 191.29/191.76 [1439]~E(x14391,x14392)+E(f362(x14393,x14394,x14395,x14391,x14396),f362(x14393,x14394,x14395,x14392,x14396))
% 191.29/191.76 [1440]~E(x14401,x14402)+E(f362(x14403,x14404,x14405,x14406,x14401),f362(x14403,x14404,x14405,x14406,x14402))
% 191.29/191.76 [1441]~E(x14411,x14412)+E(f542(x14411,x14413,x14414,x14415,x14416,x14417),f542(x14412,x14413,x14414,x14415,x14416,x14417))
% 191.29/191.76 [1442]~E(x14421,x14422)+E(f542(x14423,x14421,x14424,x14425,x14426,x14427),f542(x14423,x14422,x14424,x14425,x14426,x14427))
% 191.29/191.76 [1443]~E(x14431,x14432)+E(f542(x14433,x14434,x14431,x14435,x14436,x14437),f542(x14433,x14434,x14432,x14435,x14436,x14437))
% 191.29/191.76 [1444]~E(x14441,x14442)+E(f542(x14443,x14444,x14445,x14441,x14446,x14447),f542(x14443,x14444,x14445,x14442,x14446,x14447))
% 191.29/191.76 [1445]~E(x14451,x14452)+E(f542(x14453,x14454,x14455,x14456,x14451,x14457),f542(x14453,x14454,x14455,x14456,x14452,x14457))
% 191.29/191.76 [1446]~E(x14461,x14462)+E(f542(x14463,x14464,x14465,x14466,x14467,x14461),f542(x14463,x14464,x14465,x14466,x14467,x14462))
% 191.29/191.76 [1447]~E(x14471,x14472)+E(f752(x14471,x14473,x14474,x14475,x14476),f752(x14472,x14473,x14474,x14475,x14476))
% 191.29/191.76 [1448]~E(x14481,x14482)+E(f752(x14483,x14481,x14484,x14485,x14486),f752(x14483,x14482,x14484,x14485,x14486))
% 191.29/191.76 [1449]~E(x14491,x14492)+E(f752(x14493,x14494,x14491,x14495,x14496),f752(x14493,x14494,x14492,x14495,x14496))
% 191.29/191.76 [1450]~E(x14501,x14502)+E(f752(x14503,x14504,x14505,x14501,x14506),f752(x14503,x14504,x14505,x14502,x14506))
% 191.29/191.76 [1451]~E(x14511,x14512)+E(f752(x14513,x14514,x14515,x14516,x14511),f752(x14513,x14514,x14515,x14516,x14512))
% 191.29/191.76 [1452]~E(x14521,x14522)+E(f318(x14521,x14523,x14524,x14525,x14526),f318(x14522,x14523,x14524,x14525,x14526))
% 191.29/191.76 [1453]~E(x14531,x14532)+E(f318(x14533,x14531,x14534,x14535,x14536),f318(x14533,x14532,x14534,x14535,x14536))
% 191.29/191.76 [1454]~E(x14541,x14542)+E(f318(x14543,x14544,x14541,x14545,x14546),f318(x14543,x14544,x14542,x14545,x14546))
% 191.29/191.76 [1455]~E(x14551,x14552)+E(f318(x14553,x14554,x14555,x14551,x14556),f318(x14553,x14554,x14555,x14552,x14556))
% 191.29/191.76 [1456]~E(x14561,x14562)+E(f318(x14563,x14564,x14565,x14566,x14561),f318(x14563,x14564,x14565,x14566,x14562))
% 191.29/191.76 [1457]~E(x14571,x14572)+E(f440(x14571,x14573,x14574,x14575,x14576),f440(x14572,x14573,x14574,x14575,x14576))
% 191.29/191.76 [1458]~E(x14581,x14582)+E(f440(x14583,x14581,x14584,x14585,x14586),f440(x14583,x14582,x14584,x14585,x14586))
% 191.29/191.76 [1459]~E(x14591,x14592)+E(f440(x14593,x14594,x14591,x14595,x14596),f440(x14593,x14594,x14592,x14595,x14596))
% 191.29/191.76 [1460]~E(x14601,x14602)+E(f440(x14603,x14604,x14605,x14601,x14606),f440(x14603,x14604,x14605,x14602,x14606))
% 191.29/191.76 [1461]~E(x14611,x14612)+E(f440(x14613,x14614,x14615,x14616,x14611),f440(x14613,x14614,x14615,x14616,x14612))
% 191.29/191.76 [1462]~E(x14621,x14622)+E(f525(x14621,x14623,x14624,x14625),f525(x14622,x14623,x14624,x14625))
% 191.29/191.76 [1463]~E(x14631,x14632)+E(f525(x14633,x14631,x14634,x14635),f525(x14633,x14632,x14634,x14635))
% 191.29/191.76 [1464]~E(x14641,x14642)+E(f525(x14643,x14644,x14641,x14645),f525(x14643,x14644,x14642,x14645))
% 191.29/191.76 [1465]~E(x14651,x14652)+E(f525(x14653,x14654,x14655,x14651),f525(x14653,x14654,x14655,x14652))
% 191.29/191.76 [1466]~E(x14661,x14662)+E(f451(x14661,x14663,x14664,x14665),f451(x14662,x14663,x14664,x14665))
% 191.29/191.76 [1467]~E(x14671,x14672)+E(f451(x14673,x14671,x14674,x14675),f451(x14673,x14672,x14674,x14675))
% 191.29/191.76 [1468]~E(x14681,x14682)+E(f451(x14683,x14684,x14681,x14685),f451(x14683,x14684,x14682,x14685))
% 191.29/191.76 [1469]~E(x14691,x14692)+E(f451(x14693,x14694,x14695,x14691),f451(x14693,x14694,x14695,x14692))
% 191.29/191.76 [1470]~E(x14701,x14702)+E(f717(x14701,x14703,x14704,x14705,x14706),f717(x14702,x14703,x14704,x14705,x14706))
% 191.29/191.76 [1471]~E(x14711,x14712)+E(f717(x14713,x14711,x14714,x14715,x14716),f717(x14713,x14712,x14714,x14715,x14716))
% 191.29/191.76 [1472]~E(x14721,x14722)+E(f717(x14723,x14724,x14721,x14725,x14726),f717(x14723,x14724,x14722,x14725,x14726))
% 191.29/191.76 [1473]~E(x14731,x14732)+E(f717(x14733,x14734,x14735,x14731,x14736),f717(x14733,x14734,x14735,x14732,x14736))
% 191.29/191.76 [1474]~E(x14741,x14742)+E(f717(x14743,x14744,x14745,x14746,x14741),f717(x14743,x14744,x14745,x14746,x14742))
% 191.29/191.76 [1475]~E(x14751,x14752)+E(f482(x14751,x14753,x14754),f482(x14752,x14753,x14754))
% 191.29/191.76 [1476]~E(x14761,x14762)+E(f482(x14763,x14761,x14764),f482(x14763,x14762,x14764))
% 191.29/191.76 [1477]~E(x14771,x14772)+E(f482(x14773,x14774,x14771),f482(x14773,x14774,x14772))
% 191.29/191.76 [1478]~E(x14781,x14782)+E(f593(x14781,x14783,x14784,x14785),f593(x14782,x14783,x14784,x14785))
% 191.29/191.76 [1479]~E(x14791,x14792)+E(f593(x14793,x14791,x14794,x14795),f593(x14793,x14792,x14794,x14795))
% 191.29/191.76 [1480]~E(x14801,x14802)+E(f593(x14803,x14804,x14801,x14805),f593(x14803,x14804,x14802,x14805))
% 191.29/191.76 [1481]~E(x14811,x14812)+E(f593(x14813,x14814,x14815,x14811),f593(x14813,x14814,x14815,x14812))
% 191.29/191.76 [1482]~E(x14821,x14822)+E(f826(x14821,x14823,x14824),f826(x14822,x14823,x14824))
% 191.29/191.76 [1483]~E(x14831,x14832)+E(f826(x14833,x14831,x14834),f826(x14833,x14832,x14834))
% 191.29/191.76 [1484]~E(x14841,x14842)+E(f826(x14843,x14844,x14841),f826(x14843,x14844,x14842))
% 191.29/191.76 [1485]~E(x14851,x14852)+E(f273(x14851),f273(x14852))
% 191.29/191.76 [1486]~E(x14861,x14862)+E(f431(x14861,x14863,x14864,x14865),f431(x14862,x14863,x14864,x14865))
% 191.29/191.76 [1487]~E(x14871,x14872)+E(f431(x14873,x14871,x14874,x14875),f431(x14873,x14872,x14874,x14875))
% 191.29/191.76 [1488]~E(x14881,x14882)+E(f431(x14883,x14884,x14881,x14885),f431(x14883,x14884,x14882,x14885))
% 191.29/191.76 [1489]~E(x14891,x14892)+E(f431(x14893,x14894,x14895,x14891),f431(x14893,x14894,x14895,x14892))
% 191.29/191.76 [1490]~E(x14901,x14902)+E(f581(x14901,x14903),f581(x14902,x14903))
% 191.29/191.76 [1491]~E(x14911,x14912)+E(f581(x14913,x14911),f581(x14913,x14912))
% 191.29/191.76 [1492]~E(x14921,x14922)+E(f450(x14921,x14923,x14924),f450(x14922,x14923,x14924))
% 191.29/191.76 [1493]~E(x14931,x14932)+E(f450(x14933,x14931,x14934),f450(x14933,x14932,x14934))
% 191.29/191.76 [1494]~E(x14941,x14942)+E(f450(x14943,x14944,x14941),f450(x14943,x14944,x14942))
% 191.29/191.76 [1495]~E(x14951,x14952)+E(f652(x14951,x14953,x14954,x14955),f652(x14952,x14953,x14954,x14955))
% 191.29/191.76 [1496]~E(x14961,x14962)+E(f652(x14963,x14961,x14964,x14965),f652(x14963,x14962,x14964,x14965))
% 191.29/191.76 [1497]~E(x14971,x14972)+E(f652(x14973,x14974,x14971,x14975),f652(x14973,x14974,x14972,x14975))
% 191.29/191.76 [1498]~E(x14981,x14982)+E(f652(x14983,x14984,x14985,x14981),f652(x14983,x14984,x14985,x14982))
% 191.29/191.76 [1499]~E(x14991,x14992)+E(f745(x14991,x14993,x14994),f745(x14992,x14993,x14994))
% 191.29/191.76 [1500]~E(x15001,x15002)+E(f745(x15003,x15001,x15004),f745(x15003,x15002,x15004))
% 191.29/191.76 [1501]~E(x15011,x15012)+E(f745(x15013,x15014,x15011),f745(x15013,x15014,x15012))
% 191.29/191.76 [1502]~E(x15021,x15022)+E(f540(x15021,x15023,x15024,x15025,x15026),f540(x15022,x15023,x15024,x15025,x15026))
% 191.29/191.76 [1503]~E(x15031,x15032)+E(f540(x15033,x15031,x15034,x15035,x15036),f540(x15033,x15032,x15034,x15035,x15036))
% 191.29/191.76 [1504]~E(x15041,x15042)+E(f540(x15043,x15044,x15041,x15045,x15046),f540(x15043,x15044,x15042,x15045,x15046))
% 191.29/191.76 [1505]~E(x15051,x15052)+E(f540(x15053,x15054,x15055,x15051,x15056),f540(x15053,x15054,x15055,x15052,x15056))
% 191.29/191.76 [1506]~E(x15061,x15062)+E(f540(x15063,x15064,x15065,x15066,x15061),f540(x15063,x15064,x15065,x15066,x15062))
% 191.29/191.76 [1507]~E(x15071,x15072)+E(f603(x15071,x15073),f603(x15072,x15073))
% 191.29/191.76 [1508]~E(x15081,x15082)+E(f603(x15083,x15081),f603(x15083,x15082))
% 191.29/191.76 [1509]~E(x15091,x15092)+E(f590(x15091,x15093,x15094),f590(x15092,x15093,x15094))
% 191.29/191.76 [1510]~E(x15101,x15102)+E(f590(x15103,x15101,x15104),f590(x15103,x15102,x15104))
% 191.29/191.76 [1511]~E(x15111,x15112)+E(f590(x15113,x15114,x15111),f590(x15113,x15114,x15112))
% 191.29/191.76 [1512]~E(x15121,x15122)+E(f813(x15121,x15123,x15124),f813(x15122,x15123,x15124))
% 191.29/191.76 [1513]~E(x15131,x15132)+E(f813(x15133,x15131,x15134),f813(x15133,x15132,x15134))
% 191.29/191.76 [1514]~E(x15141,x15142)+E(f813(x15143,x15144,x15141),f813(x15143,x15144,x15142))
% 191.29/191.76 [1515]~E(x15151,x15152)+E(f470(x15151,x15153,x15154),f470(x15152,x15153,x15154))
% 191.29/191.76 [1516]~E(x15161,x15162)+E(f470(x15163,x15161,x15164),f470(x15163,x15162,x15164))
% 191.29/191.76 [1517]~E(x15171,x15172)+E(f470(x15173,x15174,x15171),f470(x15173,x15174,x15172))
% 191.29/191.76 [1518]~E(x15181,x15182)+E(f779(x15181,x15183,x15184),f779(x15182,x15183,x15184))
% 191.29/191.76 [1519]~E(x15191,x15192)+E(f779(x15193,x15191,x15194),f779(x15193,x15192,x15194))
% 191.29/191.76 [1520]~E(x15201,x15202)+E(f779(x15203,x15204,x15201),f779(x15203,x15204,x15202))
% 191.29/191.76 [1521]~E(x15211,x15212)+E(f461(x15211,x15213,x15214,x15215),f461(x15212,x15213,x15214,x15215))
% 191.29/191.76 [1522]~E(x15221,x15222)+E(f461(x15223,x15221,x15224,x15225),f461(x15223,x15222,x15224,x15225))
% 191.29/191.76 [1523]~E(x15231,x15232)+E(f461(x15233,x15234,x15231,x15235),f461(x15233,x15234,x15232,x15235))
% 191.29/191.76 [1524]~E(x15241,x15242)+E(f461(x15243,x15244,x15245,x15241),f461(x15243,x15244,x15245,x15242))
% 191.29/191.76 [1525]~E(x15251,x15252)+E(f625(x15251),f625(x15252))
% 191.29/191.76 [1526]~E(x15261,x15262)+E(f690(x15261,x15263,x15264,x15265,x15266,x15267),f690(x15262,x15263,x15264,x15265,x15266,x15267))
% 191.29/191.76 [1527]~E(x15271,x15272)+E(f690(x15273,x15271,x15274,x15275,x15276,x15277),f690(x15273,x15272,x15274,x15275,x15276,x15277))
% 191.29/191.76 [1528]~E(x15281,x15282)+E(f690(x15283,x15284,x15281,x15285,x15286,x15287),f690(x15283,x15284,x15282,x15285,x15286,x15287))
% 191.29/191.76 [1529]~E(x15291,x15292)+E(f690(x15293,x15294,x15295,x15291,x15296,x15297),f690(x15293,x15294,x15295,x15292,x15296,x15297))
% 191.29/191.76 [1530]~E(x15301,x15302)+E(f690(x15303,x15304,x15305,x15306,x15301,x15307),f690(x15303,x15304,x15305,x15306,x15302,x15307))
% 191.29/191.76 [1531]~E(x15311,x15312)+E(f690(x15313,x15314,x15315,x15316,x15317,x15311),f690(x15313,x15314,x15315,x15316,x15317,x15312))
% 191.29/191.76 [1532]~E(x15321,x15322)+E(f791(x15321,x15323,x15324),f791(x15322,x15323,x15324))
% 191.29/191.76 [1533]~E(x15331,x15332)+E(f791(x15333,x15331,x15334),f791(x15333,x15332,x15334))
% 191.29/191.76 [1534]~E(x15341,x15342)+E(f791(x15343,x15344,x15341),f791(x15343,x15344,x15342))
% 191.29/191.76 [1535]~E(x15351,x15352)+E(f209(x15351,x15353),f209(x15352,x15353))
% 191.29/191.76 [1536]~E(x15361,x15362)+E(f209(x15363,x15361),f209(x15363,x15362))
% 191.29/191.76 [1537]~E(x15371,x15372)+E(f569(x15371,x15373,x15374,x15375,x15376),f569(x15372,x15373,x15374,x15375,x15376))
% 191.29/191.76 [1538]~E(x15381,x15382)+E(f569(x15383,x15381,x15384,x15385,x15386),f569(x15383,x15382,x15384,x15385,x15386))
% 191.29/191.76 [1539]~E(x15391,x15392)+E(f569(x15393,x15394,x15391,x15395,x15396),f569(x15393,x15394,x15392,x15395,x15396))
% 191.29/191.76 [1540]~E(x15401,x15402)+E(f569(x15403,x15404,x15405,x15401,x15406),f569(x15403,x15404,x15405,x15402,x15406))
% 191.29/191.76 [1541]~E(x15411,x15412)+E(f569(x15413,x15414,x15415,x15416,x15411),f569(x15413,x15414,x15415,x15416,x15412))
% 191.29/191.76 [1542]~E(x15421,x15422)+E(f422(x15421,x15423,x15424,x15425),f422(x15422,x15423,x15424,x15425))
% 191.29/191.76 [1543]~E(x15431,x15432)+E(f422(x15433,x15431,x15434,x15435),f422(x15433,x15432,x15434,x15435))
% 191.29/191.76 [1544]~E(x15441,x15442)+E(f422(x15443,x15444,x15441,x15445),f422(x15443,x15444,x15442,x15445))
% 191.29/191.76 [1545]~E(x15451,x15452)+E(f422(x15453,x15454,x15455,x15451),f422(x15453,x15454,x15455,x15452))
% 191.29/191.76 [1546]~E(x15461,x15462)+E(f402(x15461,x15463),f402(x15462,x15463))
% 191.29/191.76 [1547]~E(x15471,x15472)+E(f402(x15473,x15471),f402(x15473,x15472))
% 191.29/191.76 [1548]~E(x15481,x15482)+E(f133(x15481,x15483),f133(x15482,x15483))
% 191.29/191.76 [1549]~E(x15491,x15492)+E(f133(x15493,x15491),f133(x15493,x15492))
% 191.29/191.76 [1550]~E(x15501,x15502)+E(f585(x15501,x15503,x15504,x15505),f585(x15502,x15503,x15504,x15505))
% 191.29/191.76 [1551]~E(x15511,x15512)+E(f585(x15513,x15511,x15514,x15515),f585(x15513,x15512,x15514,x15515))
% 191.29/191.76 [1552]~E(x15521,x15522)+E(f585(x15523,x15524,x15521,x15525),f585(x15523,x15524,x15522,x15525))
% 191.29/191.76 [1553]~E(x15531,x15532)+E(f585(x15533,x15534,x15535,x15531),f585(x15533,x15534,x15535,x15532))
% 191.29/191.76 [1554]~E(x15541,x15542)+E(f611(x15541,x15543,x15544),f611(x15542,x15543,x15544))
% 191.29/191.76 [1555]~E(x15551,x15552)+E(f611(x15553,x15551,x15554),f611(x15553,x15552,x15554))
% 191.29/191.76 [1556]~E(x15561,x15562)+E(f611(x15563,x15564,x15561),f611(x15563,x15564,x15562))
% 191.29/191.76 [1557]~E(x15571,x15572)+E(f76(x15571,x15573),f76(x15572,x15573))
% 191.29/191.76 [1558]~E(x15581,x15582)+E(f76(x15583,x15581),f76(x15583,x15582))
% 191.29/191.76 [1559]~E(x15591,x15592)+E(f494(x15591,x15593,x15594,x15595),f494(x15592,x15593,x15594,x15595))
% 191.29/191.76 [1560]~E(x15601,x15602)+E(f494(x15603,x15601,x15604,x15605),f494(x15603,x15602,x15604,x15605))
% 191.29/191.76 [1561]~E(x15611,x15612)+E(f494(x15613,x15614,x15611,x15615),f494(x15613,x15614,x15612,x15615))
% 191.29/191.76 [1562]~E(x15621,x15622)+E(f494(x15623,x15624,x15625,x15621),f494(x15623,x15624,x15625,x15622))
% 191.29/191.76 [1563]~E(x15631,x15632)+E(f623(x15631,x15633,x15634,x15635),f623(x15632,x15633,x15634,x15635))
% 191.29/191.76 [1564]~E(x15641,x15642)+E(f623(x15643,x15641,x15644,x15645),f623(x15643,x15642,x15644,x15645))
% 191.29/191.76 [1565]~E(x15651,x15652)+E(f623(x15653,x15654,x15651,x15655),f623(x15653,x15654,x15652,x15655))
% 191.29/191.76 [1566]~E(x15661,x15662)+E(f623(x15663,x15664,x15665,x15661),f623(x15663,x15664,x15665,x15662))
% 191.29/191.76 [1567]~E(x15671,x15672)+E(f530(x15671,x15673,x15674),f530(x15672,x15673,x15674))
% 191.29/191.76 [1568]~E(x15681,x15682)+E(f530(x15683,x15681,x15684),f530(x15683,x15682,x15684))
% 191.29/191.76 [1569]~E(x15691,x15692)+E(f530(x15693,x15694,x15691),f530(x15693,x15694,x15692))
% 191.29/191.76 [1570]~E(x15701,x15702)+E(f684(x15701,x15703,x15704),f684(x15702,x15703,x15704))
% 191.29/191.76 [1571]~E(x15711,x15712)+E(f684(x15713,x15711,x15714),f684(x15713,x15712,x15714))
% 191.29/191.76 [1572]~E(x15721,x15722)+E(f684(x15723,x15724,x15721),f684(x15723,x15724,x15722))
% 191.29/191.76 [1573]~E(x15731,x15732)+E(f372(x15731,x15733,x15734,x15735,x15736,x15737,x15738,x15739),f372(x15732,x15733,x15734,x15735,x15736,x15737,x15738,x15739))
% 191.29/191.76 [1574]~E(x15741,x15742)+E(f372(x15743,x15741,x15744,x15745,x15746,x15747,x15748,x15749),f372(x15743,x15742,x15744,x15745,x15746,x15747,x15748,x15749))
% 191.29/191.76 [1575]~E(x15751,x15752)+E(f372(x15753,x15754,x15751,x15755,x15756,x15757,x15758,x15759),f372(x15753,x15754,x15752,x15755,x15756,x15757,x15758,x15759))
% 191.29/191.76 [1576]~E(x15761,x15762)+E(f372(x15763,x15764,x15765,x15761,x15766,x15767,x15768,x15769),f372(x15763,x15764,x15765,x15762,x15766,x15767,x15768,x15769))
% 191.29/191.76 [1577]~E(x15771,x15772)+E(f372(x15773,x15774,x15775,x15776,x15771,x15777,x15778,x15779),f372(x15773,x15774,x15775,x15776,x15772,x15777,x15778,x15779))
% 191.29/191.76 [1578]~E(x15781,x15782)+E(f372(x15783,x15784,x15785,x15786,x15787,x15781,x15788,x15789),f372(x15783,x15784,x15785,x15786,x15787,x15782,x15788,x15789))
% 191.29/191.76 [1579]~E(x15791,x15792)+E(f372(x15793,x15794,x15795,x15796,x15797,x15798,x15791,x15799),f372(x15793,x15794,x15795,x15796,x15797,x15798,x15792,x15799))
% 191.29/191.76 [1580]~E(x15801,x15802)+E(f372(x15803,x15804,x15805,x15806,x15807,x15808,x15809,x15801),f372(x15803,x15804,x15805,x15806,x15807,x15808,x15809,x15802))
% 191.29/191.76 [1581]~E(x15811,x15812)+E(f400(x15811,x15813),f400(x15812,x15813))
% 191.29/191.76 [1582]~E(x15821,x15822)+E(f400(x15823,x15821),f400(x15823,x15822))
% 191.29/191.76 [1583]~E(x15831,x15832)+E(f768(x15831,x15833),f768(x15832,x15833))
% 191.29/191.76 [1584]~E(x15841,x15842)+E(f768(x15843,x15841),f768(x15843,x15842))
% 191.29/191.76 [1585]~E(x15851,x15852)+E(f486(x15851,x15853,x15854,x15855),f486(x15852,x15853,x15854,x15855))
% 191.29/191.76 [1586]~E(x15861,x15862)+E(f486(x15863,x15861,x15864,x15865),f486(x15863,x15862,x15864,x15865))
% 191.29/191.76 [1587]~E(x15871,x15872)+E(f486(x15873,x15874,x15871,x15875),f486(x15873,x15874,x15872,x15875))
% 191.29/191.76 [1588]~E(x15881,x15882)+E(f486(x15883,x15884,x15885,x15881),f486(x15883,x15884,x15885,x15882))
% 191.29/191.76 [1589]~E(x15891,x15892)+E(f455(x15891,x15893),f455(x15892,x15893))
% 191.29/191.76 [1590]~E(x15901,x15902)+E(f455(x15903,x15901),f455(x15903,x15902))
% 191.29/191.76 [1591]~E(x15911,x15912)+E(f553(x15911,x15913,x15914),f553(x15912,x15913,x15914))
% 191.29/191.76 [1592]~E(x15921,x15922)+E(f553(x15923,x15921,x15924),f553(x15923,x15922,x15924))
% 191.29/191.76 [1593]~E(x15931,x15932)+E(f553(x15933,x15934,x15931),f553(x15933,x15934,x15932))
% 191.29/191.76 [1594]~E(x15941,x15942)+E(f568(x15941,x15943,x15944),f568(x15942,x15943,x15944))
% 191.29/191.76 [1595]~E(x15951,x15952)+E(f568(x15953,x15951,x15954),f568(x15953,x15952,x15954))
% 191.29/191.76 [1596]~E(x15961,x15962)+E(f568(x15963,x15964,x15961),f568(x15963,x15964,x15962))
% 191.29/191.76 [1597]~E(x15971,x15972)+E(f491(x15971,x15973),f491(x15972,x15973))
% 191.29/191.76 [1598]~E(x15981,x15982)+E(f491(x15983,x15981),f491(x15983,x15982))
% 191.29/191.76 [1599]~E(x15991,x15992)+E(f437(x15991,x15993,x15994,x15995),f437(x15992,x15993,x15994,x15995))
% 191.29/191.76 [1600]~E(x16001,x16002)+E(f437(x16003,x16001,x16004,x16005),f437(x16003,x16002,x16004,x16005))
% 191.29/191.76 [1601]~E(x16011,x16012)+E(f437(x16013,x16014,x16011,x16015),f437(x16013,x16014,x16012,x16015))
% 191.29/191.76 [1602]~E(x16021,x16022)+E(f437(x16023,x16024,x16025,x16021),f437(x16023,x16024,x16025,x16022))
% 191.29/191.76 [1603]~E(x16031,x16032)+E(f588(x16031,x16033,x16034,x16035),f588(x16032,x16033,x16034,x16035))
% 191.29/191.76 [1604]~E(x16041,x16042)+E(f588(x16043,x16041,x16044,x16045),f588(x16043,x16042,x16044,x16045))
% 191.29/191.76 [1605]~E(x16051,x16052)+E(f588(x16053,x16054,x16051,x16055),f588(x16053,x16054,x16052,x16055))
% 191.29/191.76 [1606]~E(x16061,x16062)+E(f588(x16063,x16064,x16065,x16061),f588(x16063,x16064,x16065,x16062))
% 191.29/191.76 [1607]~E(x16071,x16072)+E(f463(x16071,x16073,x16074,x16075,x16076),f463(x16072,x16073,x16074,x16075,x16076))
% 191.29/191.76 [1608]~E(x16081,x16082)+E(f463(x16083,x16081,x16084,x16085,x16086),f463(x16083,x16082,x16084,x16085,x16086))
% 191.29/191.76 [1609]~E(x16091,x16092)+E(f463(x16093,x16094,x16091,x16095,x16096),f463(x16093,x16094,x16092,x16095,x16096))
% 191.29/191.76 [1610]~E(x16101,x16102)+E(f463(x16103,x16104,x16105,x16101,x16106),f463(x16103,x16104,x16105,x16102,x16106))
% 191.29/191.76 [1611]~E(x16111,x16112)+E(f463(x16113,x16114,x16115,x16116,x16111),f463(x16113,x16114,x16115,x16116,x16112))
% 191.29/191.76 [1612]~E(x16121,x16122)+E(f434(x16121,x16123,x16124,x16125),f434(x16122,x16123,x16124,x16125))
% 191.29/191.76 [1613]~E(x16131,x16132)+E(f434(x16133,x16131,x16134,x16135),f434(x16133,x16132,x16134,x16135))
% 191.29/191.76 [1614]~E(x16141,x16142)+E(f434(x16143,x16144,x16141,x16145),f434(x16143,x16144,x16142,x16145))
% 191.29/191.76 [1615]~E(x16151,x16152)+E(f434(x16153,x16154,x16155,x16151),f434(x16153,x16154,x16155,x16152))
% 191.29/191.76 [1616]~E(x16161,x16162)+E(f688(x16161,x16163,x16164,x16165),f688(x16162,x16163,x16164,x16165))
% 191.29/191.76 [1617]~E(x16171,x16172)+E(f688(x16173,x16171,x16174,x16175),f688(x16173,x16172,x16174,x16175))
% 191.29/191.76 [1618]~E(x16181,x16182)+E(f688(x16183,x16184,x16181,x16185),f688(x16183,x16184,x16182,x16185))
% 191.29/191.76 [1619]~E(x16191,x16192)+E(f688(x16193,x16194,x16195,x16191),f688(x16193,x16194,x16195,x16192))
% 191.29/191.76 [1620]~E(x16201,x16202)+E(f806(x16201,x16203,x16204),f806(x16202,x16203,x16204))
% 191.29/191.76 [1621]~E(x16211,x16212)+E(f806(x16213,x16211,x16214),f806(x16213,x16212,x16214))
% 191.29/191.76 [1622]~E(x16221,x16222)+E(f806(x16223,x16224,x16221),f806(x16223,x16224,x16222))
% 191.29/191.76 [1623]~E(x16231,x16232)+E(f696(x16231,x16233,x16234),f696(x16232,x16233,x16234))
% 191.29/191.76 [1624]~E(x16241,x16242)+E(f696(x16243,x16241,x16244),f696(x16243,x16242,x16244))
% 191.29/191.76 [1625]~E(x16251,x16252)+E(f696(x16253,x16254,x16251),f696(x16253,x16254,x16252))
% 191.29/191.76 [1626]~E(x16261,x16262)+E(f264(x16261),f264(x16262))
% 191.29/191.76 [1627]~E(x16271,x16272)+E(f219(x16271,x16273,x16274,x16275,x16276),f219(x16272,x16273,x16274,x16275,x16276))
% 191.29/191.76 [1628]~E(x16281,x16282)+E(f219(x16283,x16281,x16284,x16285,x16286),f219(x16283,x16282,x16284,x16285,x16286))
% 191.29/191.76 [1629]~E(x16291,x16292)+E(f219(x16293,x16294,x16291,x16295,x16296),f219(x16293,x16294,x16292,x16295,x16296))
% 191.29/191.76 [1630]~E(x16301,x16302)+E(f219(x16303,x16304,x16305,x16301,x16306),f219(x16303,x16304,x16305,x16302,x16306))
% 191.29/191.76 [1631]~E(x16311,x16312)+E(f219(x16313,x16314,x16315,x16316,x16311),f219(x16313,x16314,x16315,x16316,x16312))
% 191.29/191.76 [1632]~E(x16321,x16322)+E(f287(x16321,x16323,x16324),f287(x16322,x16323,x16324))
% 191.29/191.76 [1633]~E(x16331,x16332)+E(f287(x16333,x16331,x16334),f287(x16333,x16332,x16334))
% 191.29/191.76 [1634]~E(x16341,x16342)+E(f287(x16343,x16344,x16341),f287(x16343,x16344,x16342))
% 191.29/191.76 [1635]~E(x16351,x16352)+E(f118(x16351,x16353,x16354,x16355),f118(x16352,x16353,x16354,x16355))
% 191.29/191.76 [1636]~E(x16361,x16362)+E(f118(x16363,x16361,x16364,x16365),f118(x16363,x16362,x16364,x16365))
% 191.29/191.76 [1637]~E(x16371,x16372)+E(f118(x16373,x16374,x16371,x16375),f118(x16373,x16374,x16372,x16375))
% 191.29/191.76 [1638]~E(x16381,x16382)+E(f118(x16383,x16384,x16385,x16381),f118(x16383,x16384,x16385,x16382))
% 191.29/191.76 [1639]~E(x16391,x16392)+E(f352(x16391,x16393),f352(x16392,x16393))
% 191.29/191.76 [1640]~E(x16401,x16402)+E(f352(x16403,x16401),f352(x16403,x16402))
% 191.29/191.76 [1641]~E(x16411,x16412)+E(f284(x16411,x16413),f284(x16412,x16413))
% 191.29/191.76 [1642]~E(x16421,x16422)+E(f284(x16423,x16421),f284(x16423,x16422))
% 191.29/191.76 [1643]~E(x16431,x16432)+E(f310(x16431),f310(x16432))
% 191.29/191.76 [1644]~E(x16441,x16442)+E(f664(x16441,x16443,x16444,x16445,x16446),f664(x16442,x16443,x16444,x16445,x16446))
% 191.29/191.76 [1645]~E(x16451,x16452)+E(f664(x16453,x16451,x16454,x16455,x16456),f664(x16453,x16452,x16454,x16455,x16456))
% 191.29/191.76 [1646]~E(x16461,x16462)+E(f664(x16463,x16464,x16461,x16465,x16466),f664(x16463,x16464,x16462,x16465,x16466))
% 191.29/191.76 [1647]~E(x16471,x16472)+E(f664(x16473,x16474,x16475,x16471,x16476),f664(x16473,x16474,x16475,x16472,x16476))
% 191.29/191.76 [1648]~E(x16481,x16482)+E(f664(x16483,x16484,x16485,x16486,x16481),f664(x16483,x16484,x16485,x16486,x16482))
% 191.29/191.76 [1649]~E(x16491,x16492)+E(f548(x16491,x16493,x16494),f548(x16492,x16493,x16494))
% 191.29/191.76 [1650]~E(x16501,x16502)+E(f548(x16503,x16501,x16504),f548(x16503,x16502,x16504))
% 191.29/191.76 [1651]~E(x16511,x16512)+E(f548(x16513,x16514,x16511),f548(x16513,x16514,x16512))
% 191.29/191.76 [1652]~E(x16521,x16522)+E(f741(x16521,x16523,x16524,x16525),f741(x16522,x16523,x16524,x16525))
% 191.29/191.76 [1653]~E(x16531,x16532)+E(f741(x16533,x16531,x16534,x16535),f741(x16533,x16532,x16534,x16535))
% 191.29/191.76 [1654]~E(x16541,x16542)+E(f741(x16543,x16544,x16541,x16545),f741(x16543,x16544,x16542,x16545))
% 191.29/191.76 [1655]~E(x16551,x16552)+E(f741(x16553,x16554,x16555,x16551),f741(x16553,x16554,x16555,x16552))
% 191.29/191.76 [1656]~E(x16561,x16562)+E(f678(x16561,x16563,x16564,x16565,x16566,x16567,x16568,x16569),f678(x16562,x16563,x16564,x16565,x16566,x16567,x16568,x16569))
% 191.29/191.76 [1657]~E(x16571,x16572)+E(f678(x16573,x16571,x16574,x16575,x16576,x16577,x16578,x16579),f678(x16573,x16572,x16574,x16575,x16576,x16577,x16578,x16579))
% 191.29/191.76 [1658]~E(x16581,x16582)+E(f678(x16583,x16584,x16581,x16585,x16586,x16587,x16588,x16589),f678(x16583,x16584,x16582,x16585,x16586,x16587,x16588,x16589))
% 191.29/191.76 [1659]~E(x16591,x16592)+E(f678(x16593,x16594,x16595,x16591,x16596,x16597,x16598,x16599),f678(x16593,x16594,x16595,x16592,x16596,x16597,x16598,x16599))
% 191.29/191.76 [1660]~E(x16601,x16602)+E(f678(x16603,x16604,x16605,x16606,x16601,x16607,x16608,x16609),f678(x16603,x16604,x16605,x16606,x16602,x16607,x16608,x16609))
% 191.29/191.76 [1661]~E(x16611,x16612)+E(f678(x16613,x16614,x16615,x16616,x16617,x16611,x16618,x16619),f678(x16613,x16614,x16615,x16616,x16617,x16612,x16618,x16619))
% 191.29/191.76 [1662]~E(x16621,x16622)+E(f678(x16623,x16624,x16625,x16626,x16627,x16628,x16621,x16629),f678(x16623,x16624,x16625,x16626,x16627,x16628,x16622,x16629))
% 191.29/191.76 [1663]~E(x16631,x16632)+E(f678(x16633,x16634,x16635,x16636,x16637,x16638,x16639,x16631),f678(x16633,x16634,x16635,x16636,x16637,x16638,x16639,x16632))
% 191.29/191.76 [1664]~E(x16641,x16642)+E(f713(x16641,x16643,x16644),f713(x16642,x16643,x16644))
% 191.29/191.76 [1665]~E(x16651,x16652)+E(f713(x16653,x16651,x16654),f713(x16653,x16652,x16654))
% 191.29/191.76 [1666]~E(x16661,x16662)+E(f713(x16663,x16664,x16661),f713(x16663,x16664,x16662))
% 191.29/191.76 [1667]~E(x16671,x16672)+E(f699(x16671,x16673,x16674,x16675,x16676),f699(x16672,x16673,x16674,x16675,x16676))
% 191.29/191.76 [1668]~E(x16681,x16682)+E(f699(x16683,x16681,x16684,x16685,x16686),f699(x16683,x16682,x16684,x16685,x16686))
% 191.29/191.76 [1669]~E(x16691,x16692)+E(f699(x16693,x16694,x16691,x16695,x16696),f699(x16693,x16694,x16692,x16695,x16696))
% 191.29/191.76 [1670]~E(x16701,x16702)+E(f699(x16703,x16704,x16705,x16701,x16706),f699(x16703,x16704,x16705,x16702,x16706))
% 191.29/191.76 [1671]~E(x16711,x16712)+E(f699(x16713,x16714,x16715,x16716,x16711),f699(x16713,x16714,x16715,x16716,x16712))
% 191.29/191.76 [1672]~E(x16721,x16722)+E(f738(x16721,x16723,x16724,x16725),f738(x16722,x16723,x16724,x16725))
% 191.29/191.76 [1673]~E(x16731,x16732)+E(f738(x16733,x16731,x16734,x16735),f738(x16733,x16732,x16734,x16735))
% 191.29/191.76 [1674]~E(x16741,x16742)+E(f738(x16743,x16744,x16741,x16745),f738(x16743,x16744,x16742,x16745))
% 191.29/191.76 [1675]~E(x16751,x16752)+E(f738(x16753,x16754,x16755,x16751),f738(x16753,x16754,x16755,x16752))
% 191.29/191.76 [1676]~E(x16761,x16762)+E(f667(x16761,x16763,x16764,x16765,x16766),f667(x16762,x16763,x16764,x16765,x16766))
% 191.29/191.76 [1677]~E(x16771,x16772)+E(f667(x16773,x16771,x16774,x16775,x16776),f667(x16773,x16772,x16774,x16775,x16776))
% 191.29/191.76 [1678]~E(x16781,x16782)+E(f667(x16783,x16784,x16781,x16785,x16786),f667(x16783,x16784,x16782,x16785,x16786))
% 191.29/191.76 [1679]~E(x16791,x16792)+E(f667(x16793,x16794,x16795,x16791,x16796),f667(x16793,x16794,x16795,x16792,x16796))
% 191.29/191.76 [1680]~E(x16801,x16802)+E(f667(x16803,x16804,x16805,x16806,x16801),f667(x16803,x16804,x16805,x16806,x16802))
% 191.29/191.76 [1681]~E(x16811,x16812)+E(f663(x16811,x16813,x16814,x16815,x16816,x16817,x16818),f663(x16812,x16813,x16814,x16815,x16816,x16817,x16818))
% 191.29/191.76 [1682]~E(x16821,x16822)+E(f663(x16823,x16821,x16824,x16825,x16826,x16827,x16828),f663(x16823,x16822,x16824,x16825,x16826,x16827,x16828))
% 191.29/191.76 [1683]~E(x16831,x16832)+E(f663(x16833,x16834,x16831,x16835,x16836,x16837,x16838),f663(x16833,x16834,x16832,x16835,x16836,x16837,x16838))
% 191.29/191.76 [1684]~E(x16841,x16842)+E(f663(x16843,x16844,x16845,x16841,x16846,x16847,x16848),f663(x16843,x16844,x16845,x16842,x16846,x16847,x16848))
% 191.29/191.76 [1685]~E(x16851,x16852)+E(f663(x16853,x16854,x16855,x16856,x16851,x16857,x16858),f663(x16853,x16854,x16855,x16856,x16852,x16857,x16858))
% 191.29/191.76 [1686]~E(x16861,x16862)+E(f663(x16863,x16864,x16865,x16866,x16867,x16861,x16868),f663(x16863,x16864,x16865,x16866,x16867,x16862,x16868))
% 191.29/191.76 [1687]~E(x16871,x16872)+E(f663(x16873,x16874,x16875,x16876,x16877,x16878,x16871),f663(x16873,x16874,x16875,x16876,x16877,x16878,x16872))
% 191.29/191.76 [1688]~E(x16881,x16882)+E(f513(x16881,x16883,x16884,x16885,x16886),f513(x16882,x16883,x16884,x16885,x16886))
% 191.29/191.76 [1689]~E(x16891,x16892)+E(f513(x16893,x16891,x16894,x16895,x16896),f513(x16893,x16892,x16894,x16895,x16896))
% 191.29/191.76 [1690]~E(x16901,x16902)+E(f513(x16903,x16904,x16901,x16905,x16906),f513(x16903,x16904,x16902,x16905,x16906))
% 191.29/191.76 [1691]~E(x16911,x16912)+E(f513(x16913,x16914,x16915,x16911,x16916),f513(x16913,x16914,x16915,x16912,x16916))
% 191.29/191.76 [1692]~E(x16921,x16922)+E(f513(x16923,x16924,x16925,x16926,x16921),f513(x16923,x16924,x16925,x16926,x16922))
% 191.29/191.76 [1693]~E(x16931,x16932)+E(f221(x16931,x16933),f221(x16932,x16933))
% 191.29/191.76 [1694]~E(x16941,x16942)+E(f221(x16943,x16941),f221(x16943,x16942))
% 191.29/191.76 [1695]~E(x16951,x16952)+E(f275(x16951,x16953,x16954,x16955),f275(x16952,x16953,x16954,x16955))
% 191.29/191.76 [1696]~E(x16961,x16962)+E(f275(x16963,x16961,x16964,x16965),f275(x16963,x16962,x16964,x16965))
% 191.29/191.76 [1697]~E(x16971,x16972)+E(f275(x16973,x16974,x16971,x16975),f275(x16973,x16974,x16972,x16975))
% 191.29/191.76 [1698]~E(x16981,x16982)+E(f275(x16983,x16984,x16985,x16981),f275(x16983,x16984,x16985,x16982))
% 191.29/191.76 [1699]~E(x16991,x16992)+E(f789(x16991,x16993),f789(x16992,x16993))
% 191.29/191.76 [1700]~E(x17001,x17002)+E(f789(x17003,x17001),f789(x17003,x17002))
% 191.29/191.76 [1701]~E(x17011,x17012)+E(f203(x17011),f203(x17012))
% 191.29/191.76 [1702]~E(x17021,x17022)+E(f458(x17021,x17023,x17024,x17025),f458(x17022,x17023,x17024,x17025))
% 191.29/191.76 [1703]~E(x17031,x17032)+E(f458(x17033,x17031,x17034,x17035),f458(x17033,x17032,x17034,x17035))
% 191.29/191.76 [1704]~E(x17041,x17042)+E(f458(x17043,x17044,x17041,x17045),f458(x17043,x17044,x17042,x17045))
% 191.29/191.76 [1705]~E(x17051,x17052)+E(f458(x17053,x17054,x17055,x17051),f458(x17053,x17054,x17055,x17052))
% 191.29/191.76 [1706]~E(x17061,x17062)+E(f629(x17061,x17063,x17064),f629(x17062,x17063,x17064))
% 191.29/191.76 [1707]~E(x17071,x17072)+E(f629(x17073,x17071,x17074),f629(x17073,x17072,x17074))
% 191.29/191.76 [1708]~E(x17081,x17082)+E(f629(x17083,x17084,x17081),f629(x17083,x17084,x17082))
% 191.29/191.76 [1709]~E(x17091,x17092)+E(f348(x17091,x17093,x17094,x17095),f348(x17092,x17093,x17094,x17095))
% 191.29/191.76 [1710]~E(x17101,x17102)+E(f348(x17103,x17101,x17104,x17105),f348(x17103,x17102,x17104,x17105))
% 191.29/191.76 [1711]~E(x17111,x17112)+E(f348(x17113,x17114,x17111,x17115),f348(x17113,x17114,x17112,x17115))
% 191.29/191.76 [1712]~E(x17121,x17122)+E(f348(x17123,x17124,x17125,x17121),f348(x17123,x17124,x17125,x17122))
% 191.29/191.76 [1713]~E(x17131,x17132)+E(f534(x17131,x17133,x17134,x17135,x17136),f534(x17132,x17133,x17134,x17135,x17136))
% 191.29/191.76 [1714]~E(x17141,x17142)+E(f534(x17143,x17141,x17144,x17145,x17146),f534(x17143,x17142,x17144,x17145,x17146))
% 191.29/191.76 [1715]~E(x17151,x17152)+E(f534(x17153,x17154,x17151,x17155,x17156),f534(x17153,x17154,x17152,x17155,x17156))
% 191.29/191.76 [1716]~E(x17161,x17162)+E(f534(x17163,x17164,x17165,x17161,x17166),f534(x17163,x17164,x17165,x17162,x17166))
% 191.29/191.76 [1717]~E(x17171,x17172)+E(f534(x17173,x17174,x17175,x17176,x17171),f534(x17173,x17174,x17175,x17176,x17172))
% 191.29/191.76 [1718]~E(x17181,x17182)+E(f363(x17181,x17183,x17184,x17185,x17186),f363(x17182,x17183,x17184,x17185,x17186))
% 191.29/191.76 [1719]~E(x17191,x17192)+E(f363(x17193,x17191,x17194,x17195,x17196),f363(x17193,x17192,x17194,x17195,x17196))
% 191.29/191.76 [1720]~E(x17201,x17202)+E(f363(x17203,x17204,x17201,x17205,x17206),f363(x17203,x17204,x17202,x17205,x17206))
% 191.29/191.76 [1721]~E(x17211,x17212)+E(f363(x17213,x17214,x17215,x17211,x17216),f363(x17213,x17214,x17215,x17212,x17216))
% 191.29/191.76 [1722]~E(x17221,x17222)+E(f363(x17223,x17224,x17225,x17226,x17221),f363(x17223,x17224,x17225,x17226,x17222))
% 191.29/191.76 [1723]~E(x17231,x17232)+E(f562(x17231,x17233,x17234,x17235),f562(x17232,x17233,x17234,x17235))
% 191.29/191.76 [1724]~E(x17241,x17242)+E(f562(x17243,x17241,x17244,x17245),f562(x17243,x17242,x17244,x17245))
% 191.29/191.76 [1725]~E(x17251,x17252)+E(f562(x17253,x17254,x17251,x17255),f562(x17253,x17254,x17252,x17255))
% 191.29/191.76 [1726]~E(x17261,x17262)+E(f562(x17263,x17264,x17265,x17261),f562(x17263,x17264,x17265,x17262))
% 191.29/191.76 [1727]~E(x17271,x17272)+E(f727(x17271),f727(x17272))
% 191.29/191.76 [1728]~E(x17281,x17282)+E(f487(x17281,x17283,x17284,x17285),f487(x17282,x17283,x17284,x17285))
% 191.29/191.76 [1729]~E(x17291,x17292)+E(f487(x17293,x17291,x17294,x17295),f487(x17293,x17292,x17294,x17295))
% 191.29/191.76 [1730]~E(x17301,x17302)+E(f487(x17303,x17304,x17301,x17305),f487(x17303,x17304,x17302,x17305))
% 191.29/191.76 [1731]~E(x17311,x17312)+E(f487(x17313,x17314,x17315,x17311),f487(x17313,x17314,x17315,x17312))
% 191.29/191.76 [1732]~E(x17321,x17322)+E(f595(x17321,x17323,x17324,x17325),f595(x17322,x17323,x17324,x17325))
% 191.29/191.76 [1733]~E(x17331,x17332)+E(f595(x17333,x17331,x17334,x17335),f595(x17333,x17332,x17334,x17335))
% 191.29/191.76 [1734]~E(x17341,x17342)+E(f595(x17343,x17344,x17341,x17345),f595(x17343,x17344,x17342,x17345))
% 191.29/191.76 [1735]~E(x17351,x17352)+E(f595(x17353,x17354,x17355,x17351),f595(x17353,x17354,x17355,x17352))
% 191.29/191.76 [1736]~E(x17361,x17362)+E(f370(x17361,x17363),f370(x17362,x17363))
% 191.29/191.76 [1737]~E(x17371,x17372)+E(f370(x17373,x17371),f370(x17373,x17372))
% 191.29/191.76 [1738]~E(x17381,x17382)+E(f659(x17381,x17383,x17384,x17385,x17386),f659(x17382,x17383,x17384,x17385,x17386))
% 191.29/191.76 [1739]~E(x17391,x17392)+E(f659(x17393,x17391,x17394,x17395,x17396),f659(x17393,x17392,x17394,x17395,x17396))
% 191.29/191.76 [1740]~E(x17401,x17402)+E(f659(x17403,x17404,x17401,x17405,x17406),f659(x17403,x17404,x17402,x17405,x17406))
% 191.29/191.76 [1741]~E(x17411,x17412)+E(f659(x17413,x17414,x17415,x17411,x17416),f659(x17413,x17414,x17415,x17412,x17416))
% 191.29/191.76 [1742]~E(x17421,x17422)+E(f659(x17423,x17424,x17425,x17426,x17421),f659(x17423,x17424,x17425,x17426,x17422))
% 191.29/191.76 [1743]~E(x17431,x17432)+E(f483(x17431,x17433,x17434),f483(x17432,x17433,x17434))
% 191.29/191.76 [1744]~E(x17441,x17442)+E(f483(x17443,x17441,x17444),f483(x17443,x17442,x17444))
% 191.29/191.76 [1745]~E(x17451,x17452)+E(f483(x17453,x17454,x17451),f483(x17453,x17454,x17452))
% 191.29/191.76 [1746]~E(x17461,x17462)+E(f555(x17461,x17463,x17464),f555(x17462,x17463,x17464))
% 191.29/191.76 [1747]~E(x17471,x17472)+E(f555(x17473,x17471,x17474),f555(x17473,x17472,x17474))
% 191.29/191.76 [1748]~E(x17481,x17482)+E(f555(x17483,x17484,x17481),f555(x17483,x17484,x17482))
% 191.29/191.76 [1749]~E(x17491,x17492)+E(f567(x17491,x17493,x17494),f567(x17492,x17493,x17494))
% 191.29/191.76 [1750]~E(x17501,x17502)+E(f567(x17503,x17501,x17504),f567(x17503,x17502,x17504))
% 191.29/191.76 [1751]~E(x17511,x17512)+E(f567(x17513,x17514,x17511),f567(x17513,x17514,x17512))
% 191.29/191.76 [1752]~E(x17521,x17522)+E(f285(x17521,x17523),f285(x17522,x17523))
% 191.29/191.76 [1753]~E(x17531,x17532)+E(f285(x17533,x17531),f285(x17533,x17532))
% 191.29/191.76 [1754]~E(x17541,x17542)+E(f703(x17541,x17543,x17544,x17545,x17546),f703(x17542,x17543,x17544,x17545,x17546))
% 191.29/191.76 [1755]~E(x17551,x17552)+E(f703(x17553,x17551,x17554,x17555,x17556),f703(x17553,x17552,x17554,x17555,x17556))
% 191.29/191.76 [1756]~E(x17561,x17562)+E(f703(x17563,x17564,x17561,x17565,x17566),f703(x17563,x17564,x17562,x17565,x17566))
% 191.29/191.76 [1757]~E(x17571,x17572)+E(f703(x17573,x17574,x17575,x17571,x17576),f703(x17573,x17574,x17575,x17572,x17576))
% 191.29/191.76 [1758]~E(x17581,x17582)+E(f703(x17583,x17584,x17585,x17586,x17581),f703(x17583,x17584,x17585,x17586,x17582))
% 191.29/191.76 [1759]~E(x17591,x17592)+E(f443(x17591,x17593),f443(x17592,x17593))
% 191.29/191.76 [1760]~E(x17601,x17602)+E(f443(x17603,x17601),f443(x17603,x17602))
% 191.29/191.76 [1761]~E(x17611,x17612)+E(f427(x17611,x17613),f427(x17612,x17613))
% 191.29/191.76 [1762]~E(x17621,x17622)+E(f427(x17623,x17621),f427(x17623,x17622))
% 191.29/191.76 [1763]~E(x17631,x17632)+E(f545(x17631,x17633,x17634,x17635,x17636),f545(x17632,x17633,x17634,x17635,x17636))
% 191.29/191.76 [1764]~E(x17641,x17642)+E(f545(x17643,x17641,x17644,x17645,x17646),f545(x17643,x17642,x17644,x17645,x17646))
% 191.29/191.76 [1765]~E(x17651,x17652)+E(f545(x17653,x17654,x17651,x17655,x17656),f545(x17653,x17654,x17652,x17655,x17656))
% 191.29/191.76 [1766]~E(x17661,x17662)+E(f545(x17663,x17664,x17665,x17661,x17666),f545(x17663,x17664,x17665,x17662,x17666))
% 191.29/191.76 [1767]~E(x17671,x17672)+E(f545(x17673,x17674,x17675,x17676,x17671),f545(x17673,x17674,x17675,x17676,x17672))
% 191.29/191.76 [1768]~E(x17681,x17682)+E(f796(x17681,x17683),f796(x17682,x17683))
% 191.29/191.76 [1769]~E(x17691,x17692)+E(f796(x17693,x17691),f796(x17693,x17692))
% 191.29/191.76 [1770]~E(x17701,x17702)+E(f539(x17701,x17703,x17704,x17705),f539(x17702,x17703,x17704,x17705))
% 191.29/191.76 [1771]~E(x17711,x17712)+E(f539(x17713,x17711,x17714,x17715),f539(x17713,x17712,x17714,x17715))
% 191.29/191.76 [1772]~E(x17721,x17722)+E(f539(x17723,x17724,x17721,x17725),f539(x17723,x17724,x17722,x17725))
% 191.29/191.76 [1773]~E(x17731,x17732)+E(f539(x17733,x17734,x17735,x17731),f539(x17733,x17734,x17735,x17732))
% 191.29/191.76 [1774]~E(x17741,x17742)+E(f498(x17741,x17743,x17744,x17745),f498(x17742,x17743,x17744,x17745))
% 191.29/191.76 [1775]~E(x17751,x17752)+E(f498(x17753,x17751,x17754,x17755),f498(x17753,x17752,x17754,x17755))
% 191.29/191.76 [1776]~E(x17761,x17762)+E(f498(x17763,x17764,x17761,x17765),f498(x17763,x17764,x17762,x17765))
% 191.29/191.76 [1777]~E(x17771,x17772)+E(f498(x17773,x17774,x17775,x17771),f498(x17773,x17774,x17775,x17772))
% 191.29/191.76 [1778]~E(x17781,x17782)+E(f578(x17781,x17783,x17784,x17785,x17786,x17787,x17788),f578(x17782,x17783,x17784,x17785,x17786,x17787,x17788))
% 191.29/191.76 [1779]~E(x17791,x17792)+E(f578(x17793,x17791,x17794,x17795,x17796,x17797,x17798),f578(x17793,x17792,x17794,x17795,x17796,x17797,x17798))
% 191.29/191.76 [1780]~E(x17801,x17802)+E(f578(x17803,x17804,x17801,x17805,x17806,x17807,x17808),f578(x17803,x17804,x17802,x17805,x17806,x17807,x17808))
% 191.29/191.76 [1781]~E(x17811,x17812)+E(f578(x17813,x17814,x17815,x17811,x17816,x17817,x17818),f578(x17813,x17814,x17815,x17812,x17816,x17817,x17818))
% 191.29/191.76 [1782]~E(x17821,x17822)+E(f578(x17823,x17824,x17825,x17826,x17821,x17827,x17828),f578(x17823,x17824,x17825,x17826,x17822,x17827,x17828))
% 191.29/191.76 [1783]~E(x17831,x17832)+E(f578(x17833,x17834,x17835,x17836,x17837,x17831,x17838),f578(x17833,x17834,x17835,x17836,x17837,x17832,x17838))
% 191.29/191.76 [1784]~E(x17841,x17842)+E(f578(x17843,x17844,x17845,x17846,x17847,x17848,x17841),f578(x17843,x17844,x17845,x17846,x17847,x17848,x17842))
% 191.29/191.76 [1785]~E(x17851,x17852)+E(f819(x17851,x17853,x17854),f819(x17852,x17853,x17854))
% 191.29/191.76 [1786]~E(x17861,x17862)+E(f819(x17863,x17861,x17864),f819(x17863,x17862,x17864))
% 191.29/191.76 [1787]~E(x17871,x17872)+E(f819(x17873,x17874,x17871),f819(x17873,x17874,x17872))
% 191.29/191.76 [1788]~E(x17881,x17882)+E(f834(x17881,x17883,x17884,x17885,x17886,x17887,x17888),f834(x17882,x17883,x17884,x17885,x17886,x17887,x17888))
% 191.29/191.76 [1789]~E(x17891,x17892)+E(f834(x17893,x17891,x17894,x17895,x17896,x17897,x17898),f834(x17893,x17892,x17894,x17895,x17896,x17897,x17898))
% 191.29/191.76 [1790]~E(x17901,x17902)+E(f834(x17903,x17904,x17901,x17905,x17906,x17907,x17908),f834(x17903,x17904,x17902,x17905,x17906,x17907,x17908))
% 191.29/191.76 [1791]~E(x17911,x17912)+E(f834(x17913,x17914,x17915,x17911,x17916,x17917,x17918),f834(x17913,x17914,x17915,x17912,x17916,x17917,x17918))
% 191.29/191.76 [1792]~E(x17921,x17922)+E(f834(x17923,x17924,x17925,x17926,x17921,x17927,x17928),f834(x17923,x17924,x17925,x17926,x17922,x17927,x17928))
% 191.29/191.76 [1793]~E(x17931,x17932)+E(f834(x17933,x17934,x17935,x17936,x17937,x17931,x17938),f834(x17933,x17934,x17935,x17936,x17937,x17932,x17938))
% 191.29/191.76 [1794]~E(x17941,x17942)+E(f834(x17943,x17944,x17945,x17946,x17947,x17948,x17941),f834(x17943,x17944,x17945,x17946,x17947,x17948,x17942))
% 191.29/191.76 [1795]~E(x17951,x17952)+E(f707(x17951,x17953,x17954,x17955),f707(x17952,x17953,x17954,x17955))
% 191.29/191.76 [1796]~E(x17961,x17962)+E(f707(x17963,x17961,x17964,x17965),f707(x17963,x17962,x17964,x17965))
% 191.29/191.76 [1797]~E(x17971,x17972)+E(f707(x17973,x17974,x17971,x17975),f707(x17973,x17974,x17972,x17975))
% 191.29/191.76 [1798]~E(x17981,x17982)+E(f707(x17983,x17984,x17985,x17981),f707(x17983,x17984,x17985,x17982))
% 191.29/191.76 [1799]~E(x17991,x17992)+E(f691(x17991,x17993,x17994,x17995,x17996,x17997,x17998),f691(x17992,x17993,x17994,x17995,x17996,x17997,x17998))
% 191.29/191.76 [1800]~E(x18001,x18002)+E(f691(x18003,x18001,x18004,x18005,x18006,x18007,x18008),f691(x18003,x18002,x18004,x18005,x18006,x18007,x18008))
% 191.29/191.76 [1801]~E(x18011,x18012)+E(f691(x18013,x18014,x18011,x18015,x18016,x18017,x18018),f691(x18013,x18014,x18012,x18015,x18016,x18017,x18018))
% 191.29/191.76 [1802]~E(x18021,x18022)+E(f691(x18023,x18024,x18025,x18021,x18026,x18027,x18028),f691(x18023,x18024,x18025,x18022,x18026,x18027,x18028))
% 191.29/191.76 [1803]~E(x18031,x18032)+E(f691(x18033,x18034,x18035,x18036,x18031,x18037,x18038),f691(x18033,x18034,x18035,x18036,x18032,x18037,x18038))
% 191.29/191.76 [1804]~E(x18041,x18042)+E(f691(x18043,x18044,x18045,x18046,x18047,x18041,x18048),f691(x18043,x18044,x18045,x18046,x18047,x18042,x18048))
% 191.29/191.76 [1805]~E(x18051,x18052)+E(f691(x18053,x18054,x18055,x18056,x18057,x18058,x18051),f691(x18053,x18054,x18055,x18056,x18057,x18058,x18052))
% 191.29/191.76 [1806]~E(x18061,x18062)+E(f549(x18061,x18063,x18064),f549(x18062,x18063,x18064))
% 191.29/191.76 [1807]~E(x18071,x18072)+E(f549(x18073,x18071,x18074),f549(x18073,x18072,x18074))
% 191.29/191.76 [1808]~E(x18081,x18082)+E(f549(x18083,x18084,x18081),f549(x18083,x18084,x18082))
% 191.29/191.76 [1809]~E(x18091,x18092)+E(f829(x18091,x18093,x18094),f829(x18092,x18093,x18094))
% 191.29/191.76 [1810]~E(x18101,x18102)+E(f829(x18103,x18101,x18104),f829(x18103,x18102,x18104))
% 191.29/191.76 [1811]~E(x18111,x18112)+E(f829(x18113,x18114,x18111),f829(x18113,x18114,x18112))
% 191.29/191.76 [1812]~E(x18121,x18122)+E(f852(x18121,x18123),f852(x18122,x18123))
% 191.29/191.76 [1813]~E(x18131,x18132)+E(f852(x18133,x18131),f852(x18133,x18132))
% 191.29/191.76 [1814]~E(x18141,x18142)+E(f591(x18141,x18143,x18144,x18145),f591(x18142,x18143,x18144,x18145))
% 191.29/191.76 [1815]~E(x18151,x18152)+E(f591(x18153,x18151,x18154,x18155),f591(x18153,x18152,x18154,x18155))
% 191.29/191.76 [1816]~E(x18161,x18162)+E(f591(x18163,x18164,x18161,x18165),f591(x18163,x18164,x18162,x18165))
% 191.29/191.76 [1817]~E(x18171,x18172)+E(f591(x18173,x18174,x18175,x18171),f591(x18173,x18174,x18175,x18172))
% 191.29/191.76 [1818]~E(x18181,x18182)+E(f704(x18181,x18183,x18184,x18185),f704(x18182,x18183,x18184,x18185))
% 191.29/191.76 [1819]~E(x18191,x18192)+E(f704(x18193,x18191,x18194,x18195),f704(x18193,x18192,x18194,x18195))
% 191.29/191.76 [1820]~E(x18201,x18202)+E(f704(x18203,x18204,x18201,x18205),f704(x18203,x18204,x18202,x18205))
% 191.29/191.76 [1821]~E(x18211,x18212)+E(f704(x18213,x18214,x18215,x18211),f704(x18213,x18214,x18215,x18212))
% 191.29/191.76 [1822]~E(x18221,x18222)+E(f824(x18221,x18223,x18224),f824(x18222,x18223,x18224))
% 191.29/191.76 [1823]~E(x18231,x18232)+E(f824(x18233,x18231,x18234),f824(x18233,x18232,x18234))
% 191.29/191.76 [1824]~E(x18241,x18242)+E(f824(x18243,x18244,x18241),f824(x18243,x18244,x18242))
% 191.29/191.76 [1825]~E(x18251,x18252)+E(f369(x18251,x18253),f369(x18252,x18253))
% 191.29/191.76 [1826]~E(x18261,x18262)+E(f369(x18263,x18261),f369(x18263,x18262))
% 191.29/191.76 [1827]~E(x18271,x18272)+E(f597(x18271,x18273,x18274,x18275),f597(x18272,x18273,x18274,x18275))
% 191.29/191.76 [1828]~E(x18281,x18282)+E(f597(x18283,x18281,x18284,x18285),f597(x18283,x18282,x18284,x18285))
% 191.29/191.76 [1829]~E(x18291,x18292)+E(f597(x18293,x18294,x18291,x18295),f597(x18293,x18294,x18292,x18295))
% 191.29/191.76 [1830]~E(x18301,x18302)+E(f597(x18303,x18304,x18305,x18301),f597(x18303,x18304,x18305,x18302))
% 191.29/191.76 [1831]~E(x18311,x18312)+E(f726(x18311,x18313),f726(x18312,x18313))
% 191.29/191.76 [1832]~E(x18321,x18322)+E(f726(x18323,x18321),f726(x18323,x18322))
% 191.29/191.76 [1833]~E(x18331,x18332)+E(f499(x18331,x18333,x18334,x18335,x18336,x18337,x18338),f499(x18332,x18333,x18334,x18335,x18336,x18337,x18338))
% 191.29/191.76 [1834]~E(x18341,x18342)+E(f499(x18343,x18341,x18344,x18345,x18346,x18347,x18348),f499(x18343,x18342,x18344,x18345,x18346,x18347,x18348))
% 191.29/191.76 [1835]~E(x18351,x18352)+E(f499(x18353,x18354,x18351,x18355,x18356,x18357,x18358),f499(x18353,x18354,x18352,x18355,x18356,x18357,x18358))
% 191.29/191.76 [1836]~E(x18361,x18362)+E(f499(x18363,x18364,x18365,x18361,x18366,x18367,x18368),f499(x18363,x18364,x18365,x18362,x18366,x18367,x18368))
% 191.29/191.76 [1837]~E(x18371,x18372)+E(f499(x18373,x18374,x18375,x18376,x18371,x18377,x18378),f499(x18373,x18374,x18375,x18376,x18372,x18377,x18378))
% 191.29/191.76 [1838]~E(x18381,x18382)+E(f499(x18383,x18384,x18385,x18386,x18387,x18381,x18388),f499(x18383,x18384,x18385,x18386,x18387,x18382,x18388))
% 191.29/191.76 [1839]~E(x18391,x18392)+E(f499(x18393,x18394,x18395,x18396,x18397,x18398,x18391),f499(x18393,x18394,x18395,x18396,x18397,x18398,x18392))
% 191.29/191.76 [1840]~E(x18401,x18402)+E(f511(x18401,x18403,x18404,x18405,x18406),f511(x18402,x18403,x18404,x18405,x18406))
% 191.29/191.76 [1841]~E(x18411,x18412)+E(f511(x18413,x18411,x18414,x18415,x18416),f511(x18413,x18412,x18414,x18415,x18416))
% 191.29/191.76 [1842]~E(x18421,x18422)+E(f511(x18423,x18424,x18421,x18425,x18426),f511(x18423,x18424,x18422,x18425,x18426))
% 191.29/191.76 [1843]~E(x18431,x18432)+E(f511(x18433,x18434,x18435,x18431,x18436),f511(x18433,x18434,x18435,x18432,x18436))
% 191.29/191.76 [1844]~E(x18441,x18442)+E(f511(x18443,x18444,x18445,x18446,x18441),f511(x18443,x18444,x18445,x18446,x18442))
% 191.29/191.76 [1845]~E(x18451,x18452)+E(f642(x18451,x18453,x18454,x18455,x18456),f642(x18452,x18453,x18454,x18455,x18456))
% 191.29/191.76 [1846]~E(x18461,x18462)+E(f642(x18463,x18461,x18464,x18465,x18466),f642(x18463,x18462,x18464,x18465,x18466))
% 191.29/191.76 [1847]~E(x18471,x18472)+E(f642(x18473,x18474,x18471,x18475,x18476),f642(x18473,x18474,x18472,x18475,x18476))
% 191.29/191.76 [1848]~E(x18481,x18482)+E(f642(x18483,x18484,x18485,x18481,x18486),f642(x18483,x18484,x18485,x18482,x18486))
% 191.29/191.76 [1849]~E(x18491,x18492)+E(f642(x18493,x18494,x18495,x18496,x18491),f642(x18493,x18494,x18495,x18496,x18492))
% 191.29/191.76 [1850]~E(x18501,x18502)+E(f818(x18501,x18503,x18504),f818(x18502,x18503,x18504))
% 191.29/191.76 [1851]~E(x18511,x18512)+E(f818(x18513,x18511,x18514),f818(x18513,x18512,x18514))
% 191.29/191.76 [1852]~E(x18521,x18522)+E(f818(x18523,x18524,x18521),f818(x18523,x18524,x18522))
% 191.29/191.76 [1853]~E(x18531,x18532)+E(f616(x18531,x18533),f616(x18532,x18533))
% 191.29/191.76 [1854]~E(x18541,x18542)+E(f616(x18543,x18541),f616(x18543,x18542))
% 191.29/191.76 [1855]~E(x18551,x18552)+E(f380(x18551,x18553,x18554,x18555,x18556),f380(x18552,x18553,x18554,x18555,x18556))
% 191.29/191.76 [1856]~E(x18561,x18562)+E(f380(x18563,x18561,x18564,x18565,x18566),f380(x18563,x18562,x18564,x18565,x18566))
% 191.29/191.76 [1857]~E(x18571,x18572)+E(f380(x18573,x18574,x18571,x18575,x18576),f380(x18573,x18574,x18572,x18575,x18576))
% 191.29/191.76 [1858]~E(x18581,x18582)+E(f380(x18583,x18584,x18585,x18581,x18586),f380(x18583,x18584,x18585,x18582,x18586))
% 191.29/191.76 [1859]~E(x18591,x18592)+E(f380(x18593,x18594,x18595,x18596,x18591),f380(x18593,x18594,x18595,x18596,x18592))
% 191.29/191.76 [1860]~E(x18601,x18602)+E(f416(x18601,x18603,x18604,x18605),f416(x18602,x18603,x18604,x18605))
% 191.29/191.76 [1861]~E(x18611,x18612)+E(f416(x18613,x18611,x18614,x18615),f416(x18613,x18612,x18614,x18615))
% 191.29/191.76 [1862]~E(x18621,x18622)+E(f416(x18623,x18624,x18621,x18625),f416(x18623,x18624,x18622,x18625))
% 191.29/191.76 [1863]~E(x18631,x18632)+E(f416(x18633,x18634,x18635,x18631),f416(x18633,x18634,x18635,x18632))
% 191.29/191.76 [1864]~E(x18641,x18642)+E(f447(x18641,x18643),f447(x18642,x18643))
% 191.29/191.76 [1865]~E(x18651,x18652)+E(f447(x18653,x18651),f447(x18653,x18652))
% 191.29/191.76 [1866]~E(x18661,x18662)+E(f96(x18661,x18663,x18664,x18665),f96(x18662,x18663,x18664,x18665))
% 191.29/191.76 [1867]~E(x18671,x18672)+E(f96(x18673,x18671,x18674,x18675),f96(x18673,x18672,x18674,x18675))
% 191.29/191.76 [1868]~E(x18681,x18682)+E(f96(x18683,x18684,x18681,x18685),f96(x18683,x18684,x18682,x18685))
% 191.29/191.76 [1869]~E(x18691,x18692)+E(f96(x18693,x18694,x18695,x18691),f96(x18693,x18694,x18695,x18692))
% 191.29/191.76 [1870]~E(x18701,x18702)+E(f774(x18701),f774(x18702))
% 191.29/191.76 [1871]~E(x18711,x18712)+E(f430(x18711,x18713,x18714,x18715,x18716,x18717,x18718),f430(x18712,x18713,x18714,x18715,x18716,x18717,x18718))
% 191.29/191.76 [1872]~E(x18721,x18722)+E(f430(x18723,x18721,x18724,x18725,x18726,x18727,x18728),f430(x18723,x18722,x18724,x18725,x18726,x18727,x18728))
% 191.29/191.76 [1873]~E(x18731,x18732)+E(f430(x18733,x18734,x18731,x18735,x18736,x18737,x18738),f430(x18733,x18734,x18732,x18735,x18736,x18737,x18738))
% 191.29/191.76 [1874]~E(x18741,x18742)+E(f430(x18743,x18744,x18745,x18741,x18746,x18747,x18748),f430(x18743,x18744,x18745,x18742,x18746,x18747,x18748))
% 191.29/191.76 [1875]~E(x18751,x18752)+E(f430(x18753,x18754,x18755,x18756,x18751,x18757,x18758),f430(x18753,x18754,x18755,x18756,x18752,x18757,x18758))
% 191.29/191.76 [1876]~E(x18761,x18762)+E(f430(x18763,x18764,x18765,x18766,x18767,x18761,x18768),f430(x18763,x18764,x18765,x18766,x18767,x18762,x18768))
% 191.29/191.76 [1877]~E(x18771,x18772)+E(f430(x18773,x18774,x18775,x18776,x18777,x18778,x18771),f430(x18773,x18774,x18775,x18776,x18777,x18778,x18772))
% 191.29/191.76 [1878]~E(x18781,x18782)+E(f341(x18781,x18783,x18784),f341(x18782,x18783,x18784))
% 191.29/191.76 [1879]~E(x18791,x18792)+E(f341(x18793,x18791,x18794),f341(x18793,x18792,x18794))
% 191.29/191.76 [1880]~E(x18801,x18802)+E(f341(x18803,x18804,x18801),f341(x18803,x18804,x18802))
% 191.29/191.76 [1881]~E(x18811,x18812)+E(f438(x18811,x18813,x18814,x18815),f438(x18812,x18813,x18814,x18815))
% 191.29/191.76 [1882]~E(x18821,x18822)+E(f438(x18823,x18821,x18824,x18825),f438(x18823,x18822,x18824,x18825))
% 191.29/191.76 [1883]~E(x18831,x18832)+E(f438(x18833,x18834,x18831,x18835),f438(x18833,x18834,x18832,x18835))
% 191.29/191.76 [1884]~E(x18841,x18842)+E(f438(x18843,x18844,x18845,x18841),f438(x18843,x18844,x18845,x18842))
% 191.29/191.76 [1885]~E(x18851,x18852)+E(f449(x18851),f449(x18852))
% 191.29/191.76 [1886]~E(x18861,x18862)+E(f428(x18861,x18863,x18864,x18865),f428(x18862,x18863,x18864,x18865))
% 191.29/191.76 [1887]~E(x18871,x18872)+E(f428(x18873,x18871,x18874,x18875),f428(x18873,x18872,x18874,x18875))
% 191.29/191.76 [1888]~E(x18881,x18882)+E(f428(x18883,x18884,x18881,x18885),f428(x18883,x18884,x18882,x18885))
% 191.29/191.76 [1889]~E(x18891,x18892)+E(f428(x18893,x18894,x18895,x18891),f428(x18893,x18894,x18895,x18892))
% 191.29/191.76 [1890]~E(x18901,x18902)+E(f809(x18901,x18903,x18904),f809(x18902,x18903,x18904))
% 191.29/191.76 [1891]~E(x18911,x18912)+E(f809(x18913,x18911,x18914),f809(x18913,x18912,x18914))
% 191.29/191.76 [1892]~E(x18921,x18922)+E(f809(x18923,x18924,x18921),f809(x18923,x18924,x18922))
% 191.29/191.76 [1893]~E(x18931,x18932)+E(f152(x18931,x18933),f152(x18932,x18933))
% 191.29/191.76 [1894]~E(x18941,x18942)+E(f152(x18943,x18941),f152(x18943,x18942))
% 191.29/191.76 [1895]~E(x18951,x18952)+E(f387(x18951,x18953,x18954,x18955,x18956),f387(x18952,x18953,x18954,x18955,x18956))
% 191.29/191.76 [1896]~E(x18961,x18962)+E(f387(x18963,x18961,x18964,x18965,x18966),f387(x18963,x18962,x18964,x18965,x18966))
% 191.29/191.76 [1897]~E(x18971,x18972)+E(f387(x18973,x18974,x18971,x18975,x18976),f387(x18973,x18974,x18972,x18975,x18976))
% 191.29/191.76 [1898]~E(x18981,x18982)+E(f387(x18983,x18984,x18985,x18981,x18986),f387(x18983,x18984,x18985,x18982,x18986))
% 191.29/191.76 [1899]~E(x18991,x18992)+E(f387(x18993,x18994,x18995,x18996,x18991),f387(x18993,x18994,x18995,x18996,x18992))
% 191.29/191.76 [1900]~E(x19001,x19002)+E(f442(x19001,x19003,x19004,x19005),f442(x19002,x19003,x19004,x19005))
% 191.29/191.76 [1901]~E(x19011,x19012)+E(f442(x19013,x19011,x19014,x19015),f442(x19013,x19012,x19014,x19015))
% 191.29/191.76 [1902]~E(x19021,x19022)+E(f442(x19023,x19024,x19021,x19025),f442(x19023,x19024,x19022,x19025))
% 191.29/191.76 [1903]~E(x19031,x19032)+E(f442(x19033,x19034,x19035,x19031),f442(x19033,x19034,x19035,x19032))
% 191.29/191.76 [1904]~E(x19041,x19042)+E(f516(x19041,x19043),f516(x19042,x19043))
% 191.29/191.76 [1905]~E(x19051,x19052)+E(f516(x19053,x19051),f516(x19053,x19052))
% 191.29/191.76 [1906]~E(x19061,x19062)+E(f831(x19061,x19063,x19064,x19065),f831(x19062,x19063,x19064,x19065))
% 191.29/191.76 [1907]~E(x19071,x19072)+E(f831(x19073,x19071,x19074,x19075),f831(x19073,x19072,x19074,x19075))
% 191.29/191.76 [1908]~E(x19081,x19082)+E(f831(x19083,x19084,x19081,x19085),f831(x19083,x19084,x19082,x19085))
% 191.29/191.76 [1909]~E(x19091,x19092)+E(f831(x19093,x19094,x19095,x19091),f831(x19093,x19094,x19095,x19092))
% 191.29/191.76 [1910]~E(x19101,x19102)+E(f347(x19101,x19103,x19104,x19105),f347(x19102,x19103,x19104,x19105))
% 191.29/191.76 [1911]~E(x19111,x19112)+E(f347(x19113,x19111,x19114,x19115),f347(x19113,x19112,x19114,x19115))
% 191.29/191.76 [1912]~E(x19121,x19122)+E(f347(x19123,x19124,x19121,x19125),f347(x19123,x19124,x19122,x19125))
% 191.29/191.76 [1913]~E(x19131,x19132)+E(f347(x19133,x19134,x19135,x19131),f347(x19133,x19134,x19135,x19132))
% 191.29/191.76 [1914]~E(x19141,x19142)+E(f69(x19141,x19143,x19144),f69(x19142,x19143,x19144))
% 191.29/191.76 [1915]~E(x19151,x19152)+E(f69(x19153,x19151,x19154),f69(x19153,x19152,x19154))
% 191.29/191.76 [1916]~E(x19161,x19162)+E(f69(x19163,x19164,x19161),f69(x19163,x19164,x19162))
% 191.29/191.76 [1917]~E(x19171,x19172)+E(f668(x19171,x19173,x19174,x19175,x19176,x19177,x19178),f668(x19172,x19173,x19174,x19175,x19176,x19177,x19178))
% 191.29/191.76 [1918]~E(x19181,x19182)+E(f668(x19183,x19181,x19184,x19185,x19186,x19187,x19188),f668(x19183,x19182,x19184,x19185,x19186,x19187,x19188))
% 191.29/191.76 [1919]~E(x19191,x19192)+E(f668(x19193,x19194,x19191,x19195,x19196,x19197,x19198),f668(x19193,x19194,x19192,x19195,x19196,x19197,x19198))
% 191.29/191.76 [1920]~E(x19201,x19202)+E(f668(x19203,x19204,x19205,x19201,x19206,x19207,x19208),f668(x19203,x19204,x19205,x19202,x19206,x19207,x19208))
% 191.29/191.76 [1921]~E(x19211,x19212)+E(f668(x19213,x19214,x19215,x19216,x19211,x19217,x19218),f668(x19213,x19214,x19215,x19216,x19212,x19217,x19218))
% 191.29/191.76 [1922]~E(x19221,x19222)+E(f668(x19223,x19224,x19225,x19226,x19227,x19221,x19228),f668(x19223,x19224,x19225,x19226,x19227,x19222,x19228))
% 191.29/191.76 [1923]~E(x19231,x19232)+E(f668(x19233,x19234,x19235,x19236,x19237,x19238,x19231),f668(x19233,x19234,x19235,x19236,x19237,x19238,x19232))
% 191.29/191.76 [1924]~E(x19241,x19242)+E(f316(x19241,x19243,x19244,x19245),f316(x19242,x19243,x19244,x19245))
% 191.29/191.76 [1925]~E(x19251,x19252)+E(f316(x19253,x19251,x19254,x19255),f316(x19253,x19252,x19254,x19255))
% 191.29/191.76 [1926]~E(x19261,x19262)+E(f316(x19263,x19264,x19261,x19265),f316(x19263,x19264,x19262,x19265))
% 191.29/191.76 [1927]~E(x19271,x19272)+E(f316(x19273,x19274,x19275,x19271),f316(x19273,x19274,x19275,x19272))
% 191.29/191.76 [1928]~E(x19281,x19282)+E(f222(x19281,x19283,x19284),f222(x19282,x19283,x19284))
% 191.29/191.76 [1929]~E(x19291,x19292)+E(f222(x19293,x19291,x19294),f222(x19293,x19292,x19294))
% 191.29/191.76 [1930]~E(x19301,x19302)+E(f222(x19303,x19304,x19301),f222(x19303,x19304,x19302))
% 191.29/191.76 [1931]~E(x19311,x19312)+E(f732(x19311,x19313,x19314,x19315),f732(x19312,x19313,x19314,x19315))
% 191.29/191.76 [1932]~E(x19321,x19322)+E(f732(x19323,x19321,x19324,x19325),f732(x19323,x19322,x19324,x19325))
% 191.29/191.76 [1933]~E(x19331,x19332)+E(f732(x19333,x19334,x19331,x19335),f732(x19333,x19334,x19332,x19335))
% 191.29/191.76 [1934]~E(x19341,x19342)+E(f732(x19343,x19344,x19345,x19341),f732(x19343,x19344,x19345,x19342))
% 191.29/191.76 [1935]~E(x19351,x19352)+E(f368(x19351,x19353,x19354,x19355,x19356),f368(x19352,x19353,x19354,x19355,x19356))
% 191.29/191.76 [1936]~E(x19361,x19362)+E(f368(x19363,x19361,x19364,x19365,x19366),f368(x19363,x19362,x19364,x19365,x19366))
% 191.29/191.76 [1937]~E(x19371,x19372)+E(f368(x19373,x19374,x19371,x19375,x19376),f368(x19373,x19374,x19372,x19375,x19376))
% 191.29/191.76 [1938]~E(x19381,x19382)+E(f368(x19383,x19384,x19385,x19381,x19386),f368(x19383,x19384,x19385,x19382,x19386))
% 191.29/191.76 [1939]~E(x19391,x19392)+E(f368(x19393,x19394,x19395,x19396,x19391),f368(x19393,x19394,x19395,x19396,x19392))
% 191.29/191.76 [1940]~E(x19401,x19402)+E(f808(x19401,x19403,x19404),f808(x19402,x19403,x19404))
% 191.29/191.76 [1941]~E(x19411,x19412)+E(f808(x19413,x19411,x19414),f808(x19413,x19412,x19414))
% 191.29/191.76 [1942]~E(x19421,x19422)+E(f808(x19423,x19424,x19421),f808(x19423,x19424,x19422))
% 191.29/191.76 [1943]~E(x19431,x19432)+E(f473(x19431,x19433),f473(x19432,x19433))
% 191.29/191.76 [1944]~E(x19441,x19442)+E(f473(x19443,x19441),f473(x19443,x19442))
% 191.29/191.76 [1945]~E(x19451,x19452)+E(f685(x19451,x19453,x19454),f685(x19452,x19453,x19454))
% 191.29/191.76 [1946]~E(x19461,x19462)+E(f685(x19463,x19461,x19464),f685(x19463,x19462,x19464))
% 191.29/191.76 [1947]~E(x19471,x19472)+E(f685(x19473,x19474,x19471),f685(x19473,x19474,x19472))
% 191.29/191.76 [1948]~E(x19481,x19482)+E(f576(x19481,x19483,x19484,x19485,x19486),f576(x19482,x19483,x19484,x19485,x19486))
% 191.29/191.76 [1949]~E(x19491,x19492)+E(f576(x19493,x19491,x19494,x19495,x19496),f576(x19493,x19492,x19494,x19495,x19496))
% 191.29/191.76 [1950]~E(x19501,x19502)+E(f576(x19503,x19504,x19501,x19505,x19506),f576(x19503,x19504,x19502,x19505,x19506))
% 191.29/191.76 [1951]~E(x19511,x19512)+E(f576(x19513,x19514,x19515,x19511,x19516),f576(x19513,x19514,x19515,x19512,x19516))
% 191.29/191.76 [1952]~E(x19521,x19522)+E(f576(x19523,x19524,x19525,x19526,x19521),f576(x19523,x19524,x19525,x19526,x19522))
% 191.29/191.76 [1953]~E(x19531,x19532)+E(f770(x19531,x19533,x19534),f770(x19532,x19533,x19534))
% 191.29/191.76 [1954]~E(x19541,x19542)+E(f770(x19543,x19541,x19544),f770(x19543,x19542,x19544))
% 191.29/191.76 [1955]~E(x19551,x19552)+E(f770(x19553,x19554,x19551),f770(x19553,x19554,x19552))
% 191.29/191.76 [1956]~E(x19561,x19562)+E(f645(x19561,x19563,x19564,x19565,x19566),f645(x19562,x19563,x19564,x19565,x19566))
% 191.29/191.76 [1957]~E(x19571,x19572)+E(f645(x19573,x19571,x19574,x19575,x19576),f645(x19573,x19572,x19574,x19575,x19576))
% 191.29/191.76 [1958]~E(x19581,x19582)+E(f645(x19583,x19584,x19581,x19585,x19586),f645(x19583,x19584,x19582,x19585,x19586))
% 191.29/191.76 [1959]~E(x19591,x19592)+E(f645(x19593,x19594,x19595,x19591,x19596),f645(x19593,x19594,x19595,x19592,x19596))
% 191.29/191.76 [1960]~E(x19601,x19602)+E(f645(x19603,x19604,x19605,x19606,x19601),f645(x19603,x19604,x19605,x19606,x19602))
% 191.29/191.76 [1961]~E(x19611,x19612)+E(f492(x19611,x19613),f492(x19612,x19613))
% 191.29/191.76 [1962]~E(x19621,x19622)+E(f492(x19623,x19621),f492(x19623,x19622))
% 191.29/191.76 [1963]~E(x19631,x19632)+E(f630(x19631,x19633,x19634,x19635,x19636,x19637),f630(x19632,x19633,x19634,x19635,x19636,x19637))
% 191.29/191.76 [1964]~E(x19641,x19642)+E(f630(x19643,x19641,x19644,x19645,x19646,x19647),f630(x19643,x19642,x19644,x19645,x19646,x19647))
% 191.29/191.76 [1965]~E(x19651,x19652)+E(f630(x19653,x19654,x19651,x19655,x19656,x19657),f630(x19653,x19654,x19652,x19655,x19656,x19657))
% 191.29/191.76 [1966]~E(x19661,x19662)+E(f630(x19663,x19664,x19665,x19661,x19666,x19667),f630(x19663,x19664,x19665,x19662,x19666,x19667))
% 191.29/191.76 [1967]~E(x19671,x19672)+E(f630(x19673,x19674,x19675,x19676,x19671,x19677),f630(x19673,x19674,x19675,x19676,x19672,x19677))
% 191.29/191.76 [1968]~E(x19681,x19682)+E(f630(x19683,x19684,x19685,x19686,x19687,x19681),f630(x19683,x19684,x19685,x19686,x19687,x19682))
% 191.29/191.76 [1969]~E(x19691,x19692)+E(f37(x19691,x19693,x19694,x19695,x19696,x19697,x19698,x19699,x196910,x196911),f37(x19692,x19693,x19694,x19695,x19696,x19697,x19698,x19699,x196910,x196911))
% 191.29/191.76 [1970]~E(x19701,x19702)+E(f37(x19703,x19701,x19704,x19705,x19706,x19707,x19708,x19709,x197010,x197011),f37(x19703,x19702,x19704,x19705,x19706,x19707,x19708,x19709,x197010,x197011))
% 191.29/191.76 [1971]~E(x19711,x19712)+E(f37(x19713,x19714,x19711,x19715,x19716,x19717,x19718,x19719,x197110,x197111),f37(x19713,x19714,x19712,x19715,x19716,x19717,x19718,x19719,x197110,x197111))
% 191.29/191.76 [1972]~E(x19721,x19722)+E(f37(x19723,x19724,x19725,x19721,x19726,x19727,x19728,x19729,x197210,x197211),f37(x19723,x19724,x19725,x19722,x19726,x19727,x19728,x19729,x197210,x197211))
% 191.29/191.76 [1973]~E(x19731,x19732)+E(f37(x19733,x19734,x19735,x19736,x19731,x19737,x19738,x19739,x197310,x197311),f37(x19733,x19734,x19735,x19736,x19732,x19737,x19738,x19739,x197310,x197311))
% 191.29/191.76 [1974]~E(x19741,x19742)+E(f37(x19743,x19744,x19745,x19746,x19747,x19741,x19748,x19749,x197410,x197411),f37(x19743,x19744,x19745,x19746,x19747,x19742,x19748,x19749,x197410,x197411))
% 191.29/191.76 [1975]~E(x19751,x19752)+E(f37(x19753,x19754,x19755,x19756,x19757,x19758,x19751,x19759,x197510,x197511),f37(x19753,x19754,x19755,x19756,x19757,x19758,x19752,x19759,x197510,x197511))
% 191.29/191.76 [1976]~E(x19761,x19762)+E(f37(x19763,x19764,x19765,x19766,x19767,x19768,x19769,x19761,x197610,x197611),f37(x19763,x19764,x19765,x19766,x19767,x19768,x19769,x19762,x197610,x197611))
% 191.29/191.76 [1977]~E(x19771,x19772)+E(f37(x19773,x19774,x19775,x19776,x19777,x19778,x19779,x197710,x19771,x197711),f37(x19773,x19774,x19775,x19776,x19777,x19778,x19779,x197710,x19772,x197711))
% 191.29/191.76 [1978]~E(x19781,x19782)+E(f37(x19783,x19784,x19785,x19786,x19787,x19788,x19789,x197810,x197811,x19781),f37(x19783,x19784,x19785,x19786,x19787,x19788,x19789,x197810,x197811,x19782))
% 191.29/191.76 [1979]~E(x19791,x19792)+E(f596(x19791,x19793),f596(x19792,x19793))
% 191.29/191.76 [1980]~E(x19801,x19802)+E(f596(x19803,x19801),f596(x19803,x19802))
% 191.29/191.76 [1981]~E(x19811,x19812)+E(f398(x19811,x19813,x19814,x19815),f398(x19812,x19813,x19814,x19815))
% 191.29/191.76 [1982]~E(x19821,x19822)+E(f398(x19823,x19821,x19824,x19825),f398(x19823,x19822,x19824,x19825))
% 191.29/191.76 [1983]~E(x19831,x19832)+E(f398(x19833,x19834,x19831,x19835),f398(x19833,x19834,x19832,x19835))
% 191.29/191.76 [1984]~E(x19841,x19842)+E(f398(x19843,x19844,x19845,x19841),f398(x19843,x19844,x19845,x19842))
% 191.29/191.76 [1985]~E(x19851,x19852)+E(f382(x19851,x19853,x19854,x19855),f382(x19852,x19853,x19854,x19855))
% 191.29/191.76 [1986]~E(x19861,x19862)+E(f382(x19863,x19861,x19864,x19865),f382(x19863,x19862,x19864,x19865))
% 191.29/191.76 [1987]~E(x19871,x19872)+E(f382(x19873,x19874,x19871,x19875),f382(x19873,x19874,x19872,x19875))
% 191.29/191.76 [1988]~E(x19881,x19882)+E(f382(x19883,x19884,x19885,x19881),f382(x19883,x19884,x19885,x19882))
% 191.29/191.76 [1989]~E(x19891,x19892)+E(f820(x19891,x19893,x19894),f820(x19892,x19893,x19894))
% 191.29/191.76 [1990]~E(x19901,x19902)+E(f820(x19903,x19901,x19904),f820(x19903,x19902,x19904))
% 191.29/191.76 [1991]~E(x19911,x19912)+E(f820(x19913,x19914,x19911),f820(x19913,x19914,x19912))
% 191.29/191.76 [1992]~E(x19921,x19922)+E(f509(x19921,x19923,x19924,x19925,x19926,x19927,x19928),f509(x19922,x19923,x19924,x19925,x19926,x19927,x19928))
% 191.29/191.76 [1993]~E(x19931,x19932)+E(f509(x19933,x19931,x19934,x19935,x19936,x19937,x19938),f509(x19933,x19932,x19934,x19935,x19936,x19937,x19938))
% 191.29/191.76 [1994]~E(x19941,x19942)+E(f509(x19943,x19944,x19941,x19945,x19946,x19947,x19948),f509(x19943,x19944,x19942,x19945,x19946,x19947,x19948))
% 191.29/191.76 [1995]~E(x19951,x19952)+E(f509(x19953,x19954,x19955,x19951,x19956,x19957,x19958),f509(x19953,x19954,x19955,x19952,x19956,x19957,x19958))
% 191.29/191.76 [1996]~E(x19961,x19962)+E(f509(x19963,x19964,x19965,x19966,x19961,x19967,x19968),f509(x19963,x19964,x19965,x19966,x19962,x19967,x19968))
% 191.29/191.76 [1997]~E(x19971,x19972)+E(f509(x19973,x19974,x19975,x19976,x19977,x19971,x19978),f509(x19973,x19974,x19975,x19976,x19977,x19972,x19978))
% 191.29/191.76 [1998]~E(x19981,x19982)+E(f509(x19983,x19984,x19985,x19986,x19987,x19988,x19981),f509(x19983,x19984,x19985,x19986,x19987,x19988,x19982))
% 191.29/191.76 [1999]~E(x19991,x19992)+E(f654(x19991,x19993,x19994,x19995),f654(x19992,x19993,x19994,x19995))
% 191.29/191.76 [2000]~E(x20001,x20002)+E(f654(x20003,x20001,x20004,x20005),f654(x20003,x20002,x20004,x20005))
% 191.29/191.76 [2001]~E(x20011,x20012)+E(f654(x20013,x20014,x20011,x20015),f654(x20013,x20014,x20012,x20015))
% 191.29/191.76 [2002]~E(x20021,x20022)+E(f654(x20023,x20024,x20025,x20021),f654(x20023,x20024,x20025,x20022))
% 191.29/191.76 [2003]~E(x20031,x20032)+E(f407(x20031,x20033,x20034),f407(x20032,x20033,x20034))
% 191.29/191.76 [2004]~E(x20041,x20042)+E(f407(x20043,x20041,x20044),f407(x20043,x20042,x20044))
% 191.29/191.76 [2005]~E(x20051,x20052)+E(f407(x20053,x20054,x20051),f407(x20053,x20054,x20052))
% 191.29/191.76 [2006]~E(x20061,x20062)+E(f21(x20061,x20063,x20064,x20065),f21(x20062,x20063,x20064,x20065))
% 191.29/191.76 [2007]~E(x20071,x20072)+E(f21(x20073,x20071,x20074,x20075),f21(x20073,x20072,x20074,x20075))
% 191.29/191.76 [2008]~E(x20081,x20082)+E(f21(x20083,x20084,x20081,x20085),f21(x20083,x20084,x20082,x20085))
% 191.29/191.76 [2009]~E(x20091,x20092)+E(f21(x20093,x20094,x20095,x20091),f21(x20093,x20094,x20095,x20092))
% 191.29/191.76 [2010]~E(x20101,x20102)+E(f515(x20101,x20103,x20104,x20105),f515(x20102,x20103,x20104,x20105))
% 191.29/191.76 [2011]~E(x20111,x20112)+E(f515(x20113,x20111,x20114,x20115),f515(x20113,x20112,x20114,x20115))
% 191.29/191.76 [2012]~E(x20121,x20122)+E(f515(x20123,x20124,x20121,x20125),f515(x20123,x20124,x20122,x20125))
% 191.29/191.76 [2013]~E(x20131,x20132)+E(f515(x20133,x20134,x20135,x20131),f515(x20133,x20134,x20135,x20132))
% 191.29/191.76 [2014]~E(x20141,x20142)+E(f269(x20141,x20143,x20144),f269(x20142,x20143,x20144))
% 191.29/191.76 [2015]~E(x20151,x20152)+E(f269(x20153,x20151,x20154),f269(x20153,x20152,x20154))
% 191.29/191.76 [2016]~E(x20161,x20162)+E(f269(x20163,x20164,x20161),f269(x20163,x20164,x20162))
% 191.29/191.76 [2017]~E(x20171,x20172)+E(f193(x20171,x20173,x20174,x20175),f193(x20172,x20173,x20174,x20175))
% 191.29/191.76 [2018]~E(x20181,x20182)+E(f193(x20183,x20181,x20184,x20185),f193(x20183,x20182,x20184,x20185))
% 191.29/191.76 [2019]~E(x20191,x20192)+E(f193(x20193,x20194,x20191,x20195),f193(x20193,x20194,x20192,x20195))
% 191.29/191.76 [2020]~E(x20201,x20202)+E(f193(x20203,x20204,x20205,x20201),f193(x20203,x20204,x20205,x20202))
% 191.29/191.76 [2021]~E(x20211,x20212)+E(f528(x20211,x20213,x20214,x20215),f528(x20212,x20213,x20214,x20215))
% 191.29/191.76 [2022]~E(x20221,x20222)+E(f528(x20223,x20221,x20224,x20225),f528(x20223,x20222,x20224,x20225))
% 191.29/191.76 [2023]~E(x20231,x20232)+E(f528(x20233,x20234,x20231,x20235),f528(x20233,x20234,x20232,x20235))
% 191.29/191.76 [2024]~E(x20241,x20242)+E(f528(x20243,x20244,x20245,x20241),f528(x20243,x20244,x20245,x20242))
% 191.29/191.76 [2025]~E(x20251,x20252)+E(f424(x20251,x20253,x20254,x20255),f424(x20252,x20253,x20254,x20255))
% 191.29/191.76 [2026]~E(x20261,x20262)+E(f424(x20263,x20261,x20264,x20265),f424(x20263,x20262,x20264,x20265))
% 191.29/191.76 [2027]~E(x20271,x20272)+E(f424(x20273,x20274,x20271,x20275),f424(x20273,x20274,x20272,x20275))
% 191.29/191.76 [2028]~E(x20281,x20282)+E(f424(x20283,x20284,x20285,x20281),f424(x20283,x20284,x20285,x20282))
% 191.29/191.76 [2029]~E(x20291,x20292)+E(f417(x20291,x20293,x20294,x20295,x20296),f417(x20292,x20293,x20294,x20295,x20296))
% 191.29/191.76 [2030]~E(x20301,x20302)+E(f417(x20303,x20301,x20304,x20305,x20306),f417(x20303,x20302,x20304,x20305,x20306))
% 191.29/191.76 [2031]~E(x20311,x20312)+E(f417(x20313,x20314,x20311,x20315,x20316),f417(x20313,x20314,x20312,x20315,x20316))
% 191.29/191.76 [2032]~E(x20321,x20322)+E(f417(x20323,x20324,x20325,x20321,x20326),f417(x20323,x20324,x20325,x20322,x20326))
% 191.29/191.76 [2033]~E(x20331,x20332)+E(f417(x20333,x20334,x20335,x20336,x20331),f417(x20333,x20334,x20335,x20336,x20332))
% 191.29/191.76 [2034]~E(x20341,x20342)+E(f714(x20341,x20343,x20344,x20345,x20346),f714(x20342,x20343,x20344,x20345,x20346))
% 191.29/191.76 [2035]~E(x20351,x20352)+E(f714(x20353,x20351,x20354,x20355,x20356),f714(x20353,x20352,x20354,x20355,x20356))
% 191.29/191.76 [2036]~E(x20361,x20362)+E(f714(x20363,x20364,x20361,x20365,x20366),f714(x20363,x20364,x20362,x20365,x20366))
% 191.29/191.76 [2037]~E(x20371,x20372)+E(f714(x20373,x20374,x20375,x20371,x20376),f714(x20373,x20374,x20375,x20372,x20376))
% 191.29/191.76 [2038]~E(x20381,x20382)+E(f714(x20383,x20384,x20385,x20386,x20381),f714(x20383,x20384,x20385,x20386,x20382))
% 191.29/191.76 [2039]~E(x20391,x20392)+E(f575(x20391,x20393),f575(x20392,x20393))
% 191.29/191.76 [2040]~E(x20401,x20402)+E(f575(x20403,x20401),f575(x20403,x20402))
% 191.29/191.76 [2041]~E(x20411,x20412)+E(f626(x20411,x20413,x20414),f626(x20412,x20413,x20414))
% 191.29/191.76 [2042]~E(x20421,x20422)+E(f626(x20423,x20421,x20424),f626(x20423,x20422,x20424))
% 191.29/191.76 [2043]~E(x20431,x20432)+E(f626(x20433,x20434,x20431),f626(x20433,x20434,x20432))
% 191.29/191.76 [2044]~E(x20441,x20442)+E(f724(x20441,x20443,x20444),f724(x20442,x20443,x20444))
% 191.29/191.76 [2045]~E(x20451,x20452)+E(f724(x20453,x20451,x20454),f724(x20453,x20452,x20454))
% 191.29/191.76 [2046]~E(x20461,x20462)+E(f724(x20463,x20464,x20461),f724(x20463,x20464,x20462))
% 191.29/191.76 [2047]~E(x20471,x20472)+E(f337(x20471),f337(x20472))
% 191.29/191.76 [2048]~E(x20481,x20482)+E(f610(x20481,x20483,x20484),f610(x20482,x20483,x20484))
% 191.29/191.76 [2049]~E(x20491,x20492)+E(f610(x20493,x20491,x20494),f610(x20493,x20492,x20494))
% 191.29/191.76 [2050]~E(x20501,x20502)+E(f610(x20503,x20504,x20501),f610(x20503,x20504,x20502))
% 191.29/191.76 [2051]~E(x20511,x20512)+E(f729(x20511,x20513,x20514),f729(x20512,x20513,x20514))
% 191.29/191.76 [2052]~E(x20521,x20522)+E(f729(x20523,x20521,x20524),f729(x20523,x20522,x20524))
% 191.29/191.76 [2053]~E(x20531,x20532)+E(f729(x20533,x20534,x20531),f729(x20533,x20534,x20532))
% 191.29/191.76 [2054]~E(x20541,x20542)+E(f477(x20541,x20543,x20544),f477(x20542,x20543,x20544))
% 191.29/191.76 [2055]~E(x20551,x20552)+E(f477(x20553,x20551,x20554),f477(x20553,x20552,x20554))
% 191.29/191.76 [2056]~E(x20561,x20562)+E(f477(x20563,x20564,x20561),f477(x20563,x20564,x20562))
% 191.29/191.76 [2057]~E(x20571,x20572)+E(f165(x20571),f165(x20572))
% 191.29/191.76 [2058]~E(x20581,x20582)+E(f378(x20581,x20583,x20584,x20585),f378(x20582,x20583,x20584,x20585))
% 191.29/191.76 [2059]~E(x20591,x20592)+E(f378(x20593,x20591,x20594,x20595),f378(x20593,x20592,x20594,x20595))
% 191.29/191.76 [2060]~E(x20601,x20602)+E(f378(x20603,x20604,x20601,x20605),f378(x20603,x20604,x20602,x20605))
% 191.29/191.76 [2061]~E(x20611,x20612)+E(f378(x20613,x20614,x20615,x20611),f378(x20613,x20614,x20615,x20612))
% 191.29/191.76 [2062]~E(x20621,x20622)+E(f349(x20621,x20623,x20624,x20625),f349(x20622,x20623,x20624,x20625))
% 191.29/191.76 [2063]~E(x20631,x20632)+E(f349(x20633,x20631,x20634,x20635),f349(x20633,x20632,x20634,x20635))
% 191.29/191.76 [2064]~E(x20641,x20642)+E(f349(x20643,x20644,x20641,x20645),f349(x20643,x20644,x20642,x20645))
% 191.29/191.76 [2065]~E(x20651,x20652)+E(f349(x20653,x20654,x20655,x20651),f349(x20653,x20654,x20655,x20652))
% 191.29/191.76 [2066]~E(x20661,x20662)+E(f488(x20661,x20663,x20664,x20665,x20666),f488(x20662,x20663,x20664,x20665,x20666))
% 191.29/191.76 [2067]~E(x20671,x20672)+E(f488(x20673,x20671,x20674,x20675,x20676),f488(x20673,x20672,x20674,x20675,x20676))
% 191.29/191.76 [2068]~E(x20681,x20682)+E(f488(x20683,x20684,x20681,x20685,x20686),f488(x20683,x20684,x20682,x20685,x20686))
% 191.29/191.76 [2069]~E(x20691,x20692)+E(f488(x20693,x20694,x20695,x20691,x20696),f488(x20693,x20694,x20695,x20692,x20696))
% 191.29/191.76 [2070]~E(x20701,x20702)+E(f488(x20703,x20704,x20705,x20706,x20701),f488(x20703,x20704,x20705,x20706,x20702))
% 191.29/191.76 [2071]~E(x20711,x20712)+E(f520(x20711),f520(x20712))
% 191.29/191.76 [2072]~E(x20721,x20722)+E(f411(x20721,x20723,x20724,x20725),f411(x20722,x20723,x20724,x20725))
% 191.29/191.76 [2073]~E(x20731,x20732)+E(f411(x20733,x20731,x20734,x20735),f411(x20733,x20732,x20734,x20735))
% 191.29/191.76 [2074]~E(x20741,x20742)+E(f411(x20743,x20744,x20741,x20745),f411(x20743,x20744,x20742,x20745))
% 191.29/191.76 [2075]~E(x20751,x20752)+E(f411(x20753,x20754,x20755,x20751),f411(x20753,x20754,x20755,x20752))
% 191.29/191.76 [2076]~E(x20761,x20762)+E(f262(x20761,x20763,x20764),f262(x20762,x20763,x20764))
% 191.29/191.76 [2077]~E(x20771,x20772)+E(f262(x20773,x20771,x20774),f262(x20773,x20772,x20774))
% 191.29/191.76 [2078]~E(x20781,x20782)+E(f262(x20783,x20784,x20781),f262(x20783,x20784,x20782))
% 191.29/191.76 [2079]~E(x20791,x20792)+E(f290(x20791,x20793,x20794),f290(x20792,x20793,x20794))
% 191.29/191.76 [2080]~E(x20801,x20802)+E(f290(x20803,x20801,x20804),f290(x20803,x20802,x20804))
% 191.29/191.76 [2081]~E(x20811,x20812)+E(f290(x20813,x20814,x20811),f290(x20813,x20814,x20812))
% 191.29/191.76 [2082]~E(x20821,x20822)+E(f446(x20821,x20823),f446(x20822,x20823))
% 191.29/191.76 [2083]~E(x20831,x20832)+E(f446(x20833,x20831),f446(x20833,x20832))
% 191.29/191.76 [2084]~E(x20841,x20842)+E(f460(x20841,x20843,x20844),f460(x20842,x20843,x20844))
% 191.29/191.76 [2085]~E(x20851,x20852)+E(f460(x20853,x20851,x20854),f460(x20853,x20852,x20854))
% 191.29/191.76 [2086]~E(x20861,x20862)+E(f460(x20863,x20864,x20861),f460(x20863,x20864,x20862))
% 191.29/191.76 [2087]~E(x20871,x20872)+E(f201(x20871,x20873,x20874,x20875),f201(x20872,x20873,x20874,x20875))
% 191.29/191.76 [2088]~E(x20881,x20882)+E(f201(x20883,x20881,x20884,x20885),f201(x20883,x20882,x20884,x20885))
% 191.29/191.76 [2089]~E(x20891,x20892)+E(f201(x20893,x20894,x20891,x20895),f201(x20893,x20894,x20892,x20895))
% 191.29/191.76 [2090]~E(x20901,x20902)+E(f201(x20903,x20904,x20905,x20901),f201(x20903,x20904,x20905,x20902))
% 191.29/191.76 [2091]~E(x20911,x20912)+E(f485(x20911,x20913,x20914,x20915,x20916),f485(x20912,x20913,x20914,x20915,x20916))
% 191.29/191.76 [2092]~E(x20921,x20922)+E(f485(x20923,x20921,x20924,x20925,x20926),f485(x20923,x20922,x20924,x20925,x20926))
% 191.29/191.76 [2093]~E(x20931,x20932)+E(f485(x20933,x20934,x20931,x20935,x20936),f485(x20933,x20934,x20932,x20935,x20936))
% 191.29/191.76 [2094]~E(x20941,x20942)+E(f485(x20943,x20944,x20945,x20941,x20946),f485(x20943,x20944,x20945,x20942,x20946))
% 191.29/191.76 [2095]~E(x20951,x20952)+E(f485(x20953,x20954,x20955,x20956,x20951),f485(x20953,x20954,x20955,x20956,x20952))
% 191.29/191.76 [2096]~E(x20961,x20962)+E(f802(x20961,x20963,x20964),f802(x20962,x20963,x20964))
% 191.29/191.76 [2097]~E(x20971,x20972)+E(f802(x20973,x20971,x20974),f802(x20973,x20972,x20974))
% 191.29/191.76 [2098]~E(x20981,x20982)+E(f802(x20983,x20984,x20981),f802(x20983,x20984,x20982))
% 191.29/191.76 [2099]~E(x20991,x20992)+E(f306(x20991,x20993),f306(x20992,x20993))
% 191.29/191.76 [2100]~E(x21001,x21002)+E(f306(x21003,x21001),f306(x21003,x21002))
% 191.29/191.76 [2101]~E(x21011,x21012)+E(f478(x21011,x21013,x21014,x21015,x21016),f478(x21012,x21013,x21014,x21015,x21016))
% 191.29/191.76 [2102]~E(x21021,x21022)+E(f478(x21023,x21021,x21024,x21025,x21026),f478(x21023,x21022,x21024,x21025,x21026))
% 191.29/191.76 [2103]~E(x21031,x21032)+E(f478(x21033,x21034,x21031,x21035,x21036),f478(x21033,x21034,x21032,x21035,x21036))
% 191.29/191.76 [2104]~E(x21041,x21042)+E(f478(x21043,x21044,x21045,x21041,x21046),f478(x21043,x21044,x21045,x21042,x21046))
% 191.29/191.76 [2105]~E(x21051,x21052)+E(f478(x21053,x21054,x21055,x21056,x21051),f478(x21053,x21054,x21055,x21056,x21052))
% 191.29/191.76 [2106]~E(x21061,x21062)+E(f412(x21061,x21063,x21064,x21065),f412(x21062,x21063,x21064,x21065))
% 191.29/191.76 [2107]~E(x21071,x21072)+E(f412(x21073,x21071,x21074,x21075),f412(x21073,x21072,x21074,x21075))
% 191.29/191.76 [2108]~E(x21081,x21082)+E(f412(x21083,x21084,x21081,x21085),f412(x21083,x21084,x21082,x21085))
% 191.29/191.76 [2109]~E(x21091,x21092)+E(f412(x21093,x21094,x21095,x21091),f412(x21093,x21094,x21095,x21092))
% 191.29/191.76 [2110]~E(x21101,x21102)+E(f706(x21101,x21103,x21104,x21105,x21106,x21107),f706(x21102,x21103,x21104,x21105,x21106,x21107))
% 191.29/191.76 [2111]~E(x21111,x21112)+E(f706(x21113,x21111,x21114,x21115,x21116,x21117),f706(x21113,x21112,x21114,x21115,x21116,x21117))
% 191.29/191.76 [2112]~E(x21121,x21122)+E(f706(x21123,x21124,x21121,x21125,x21126,x21127),f706(x21123,x21124,x21122,x21125,x21126,x21127))
% 191.29/191.76 [2113]~E(x21131,x21132)+E(f706(x21133,x21134,x21135,x21131,x21136,x21137),f706(x21133,x21134,x21135,x21132,x21136,x21137))
% 191.29/191.76 [2114]~E(x21141,x21142)+E(f706(x21143,x21144,x21145,x21146,x21141,x21147),f706(x21143,x21144,x21145,x21146,x21142,x21147))
% 191.29/191.76 [2115]~E(x21151,x21152)+E(f706(x21153,x21154,x21155,x21156,x21157,x21151),f706(x21153,x21154,x21155,x21156,x21157,x21152))
% 191.29/191.76 [2116]~E(x21161,x21162)+E(f837(x21161,x21163,x21164),f837(x21162,x21163,x21164))
% 191.29/191.76 [2117]~E(x21171,x21172)+E(f837(x21173,x21171,x21174),f837(x21173,x21172,x21174))
% 191.29/191.76 [2118]~E(x21181,x21182)+E(f837(x21183,x21184,x21181),f837(x21183,x21184,x21182))
% 191.29/191.76 [2119]~E(x21191,x21192)+E(f390(x21191,x21193,x21194,x21195,x21196),f390(x21192,x21193,x21194,x21195,x21196))
% 191.29/191.76 [2120]~E(x21201,x21202)+E(f390(x21203,x21201,x21204,x21205,x21206),f390(x21203,x21202,x21204,x21205,x21206))
% 191.29/191.76 [2121]~E(x21211,x21212)+E(f390(x21213,x21214,x21211,x21215,x21216),f390(x21213,x21214,x21212,x21215,x21216))
% 191.29/191.76 [2122]~E(x21221,x21222)+E(f390(x21223,x21224,x21225,x21221,x21226),f390(x21223,x21224,x21225,x21222,x21226))
% 191.29/191.76 [2123]~E(x21231,x21232)+E(f390(x21233,x21234,x21235,x21236,x21231),f390(x21233,x21234,x21235,x21236,x21232))
% 191.29/191.76 [2124]~E(x21241,x21242)+E(f24(x21241,x21243),f24(x21242,x21243))
% 191.29/191.76 [2125]~E(x21251,x21252)+E(f24(x21253,x21251),f24(x21253,x21252))
% 191.29/191.76 [2126]~E(x21261,x21262)+E(f617(x21261),f617(x21262))
% 191.29/191.76 [2127]~E(x21271,x21272)+E(f656(x21271,x21273,x21274,x21275,x21276),f656(x21272,x21273,x21274,x21275,x21276))
% 191.29/191.76 [2128]~E(x21281,x21282)+E(f656(x21283,x21281,x21284,x21285,x21286),f656(x21283,x21282,x21284,x21285,x21286))
% 191.29/191.76 [2129]~E(x21291,x21292)+E(f656(x21293,x21294,x21291,x21295,x21296),f656(x21293,x21294,x21292,x21295,x21296))
% 191.29/191.76 [2130]~E(x21301,x21302)+E(f656(x21303,x21304,x21305,x21301,x21306),f656(x21303,x21304,x21305,x21302,x21306))
% 191.29/191.76 [2131]~E(x21311,x21312)+E(f656(x21313,x21314,x21315,x21316,x21311),f656(x21313,x21314,x21315,x21316,x21312))
% 191.29/191.76 [2132]~E(x21321,x21322)+E(f822(x21321,x21323,x21324),f822(x21322,x21323,x21324))
% 191.29/191.76 [2133]~E(x21331,x21332)+E(f822(x21333,x21331,x21334),f822(x21333,x21332,x21334))
% 191.29/191.76 [2134]~E(x21341,x21342)+E(f822(x21343,x21344,x21341),f822(x21343,x21344,x21342))
% 191.29/191.76 [2135]~E(x21351,x21352)+E(f758(x21351,x21353,x21354),f758(x21352,x21353,x21354))
% 191.29/191.76 [2136]~E(x21361,x21362)+E(f758(x21363,x21361,x21364),f758(x21363,x21362,x21364))
% 191.29/191.76 [2137]~E(x21371,x21372)+E(f758(x21373,x21374,x21371),f758(x21373,x21374,x21372))
% 191.29/191.76 [2138]~E(x21381,x21382)+E(f795(x21381,x21383,x21384,x21385),f795(x21382,x21383,x21384,x21385))
% 191.29/191.76 [2139]~E(x21391,x21392)+E(f795(x21393,x21391,x21394,x21395),f795(x21393,x21392,x21394,x21395))
% 191.29/191.76 [2140]~E(x21401,x21402)+E(f795(x21403,x21404,x21401,x21405),f795(x21403,x21404,x21402,x21405))
% 191.29/191.76 [2141]~E(x21411,x21412)+E(f795(x21413,x21414,x21415,x21411),f795(x21413,x21414,x21415,x21412))
% 191.29/191.76 [2142]~E(x21421,x21422)+E(f737(x21421,x21423,x21424,x21425),f737(x21422,x21423,x21424,x21425))
% 191.29/191.76 [2143]~E(x21431,x21432)+E(f737(x21433,x21431,x21434,x21435),f737(x21433,x21432,x21434,x21435))
% 191.29/191.76 [2144]~E(x21441,x21442)+E(f737(x21443,x21444,x21441,x21445),f737(x21443,x21444,x21442,x21445))
% 191.29/191.76 [2145]~E(x21451,x21452)+E(f737(x21453,x21454,x21455,x21451),f737(x21453,x21454,x21455,x21452))
% 191.29/191.76 [2146]~E(x21461,x21462)+E(f754(x21461,x21463,x21464),f754(x21462,x21463,x21464))
% 191.29/191.76 [2147]~E(x21471,x21472)+E(f754(x21473,x21471,x21474),f754(x21473,x21472,x21474))
% 191.29/191.76 [2148]~E(x21481,x21482)+E(f754(x21483,x21484,x21481),f754(x21483,x21484,x21482))
% 191.29/191.76 [2149]~E(x21491,x21492)+E(f558(x21491),f558(x21492))
% 191.29/191.76 [2150]~E(x21501,x21502)+E(f361(x21501,x21503,x21504,x21505,x21506),f361(x21502,x21503,x21504,x21505,x21506))
% 191.29/191.76 [2151]~E(x21511,x21512)+E(f361(x21513,x21511,x21514,x21515,x21516),f361(x21513,x21512,x21514,x21515,x21516))
% 191.29/191.76 [2152]~E(x21521,x21522)+E(f361(x21523,x21524,x21521,x21525,x21526),f361(x21523,x21524,x21522,x21525,x21526))
% 191.29/191.76 [2153]~E(x21531,x21532)+E(f361(x21533,x21534,x21535,x21531,x21536),f361(x21533,x21534,x21535,x21532,x21536))
% 191.29/191.76 [2154]~E(x21541,x21542)+E(f361(x21543,x21544,x21545,x21546,x21541),f361(x21543,x21544,x21545,x21546,x21542))
% 191.29/191.76 [2155]~E(x21551,x21552)+E(f665(x21551,x21553,x21554,x21555,x21556),f665(x21552,x21553,x21554,x21555,x21556))
% 191.29/191.76 [2156]~E(x21561,x21562)+E(f665(x21563,x21561,x21564,x21565,x21566),f665(x21563,x21562,x21564,x21565,x21566))
% 191.29/191.76 [2157]~E(x21571,x21572)+E(f665(x21573,x21574,x21571,x21575,x21576),f665(x21573,x21574,x21572,x21575,x21576))
% 191.29/191.76 [2158]~E(x21581,x21582)+E(f665(x21583,x21584,x21585,x21581,x21586),f665(x21583,x21584,x21585,x21582,x21586))
% 191.29/191.76 [2159]~E(x21591,x21592)+E(f665(x21593,x21594,x21595,x21596,x21591),f665(x21593,x21594,x21595,x21596,x21592))
% 191.29/191.76 [2160]~E(x21601,x21602)+E(f788(x21601,x21603),f788(x21602,x21603))
% 191.29/191.76 [2161]~E(x21611,x21612)+E(f788(x21613,x21611),f788(x21613,x21612))
% 191.29/191.76 [2162]~E(x21621,x21622)+E(f621(x21621,x21623,x21624),f621(x21622,x21623,x21624))
% 191.29/191.76 [2163]~E(x21631,x21632)+E(f621(x21633,x21631,x21634),f621(x21633,x21632,x21634))
% 191.29/191.76 [2164]~E(x21641,x21642)+E(f621(x21643,x21644,x21641),f621(x21643,x21644,x21642))
% 191.29/191.76 [2165]~E(x21651,x21652)+E(f580(x21651,x21653),f580(x21652,x21653))
% 191.29/191.76 [2166]~E(x21661,x21662)+E(f580(x21663,x21661),f580(x21663,x21662))
% 191.29/191.76 [2167]~E(x21671,x21672)+E(f641(x21671,x21673),f641(x21672,x21673))
% 191.29/191.76 [2168]~E(x21681,x21682)+E(f641(x21683,x21681),f641(x21683,x21682))
% 191.29/191.76 [2169]~E(x21691,x21692)+E(f462(x21691,x21693,x21694),f462(x21692,x21693,x21694))
% 191.29/191.76 [2170]~E(x21701,x21702)+E(f462(x21703,x21701,x21704),f462(x21703,x21702,x21704))
% 191.29/191.76 [2171]~E(x21711,x21712)+E(f462(x21713,x21714,x21711),f462(x21713,x21714,x21712))
% 191.29/191.76 [2172]~E(x21721,x21722)+E(f353(x21721,x21723),f353(x21722,x21723))
% 191.29/191.76 [2173]~E(x21731,x21732)+E(f353(x21733,x21731),f353(x21733,x21732))
% 191.29/191.76 [2174]~E(x21741,x21742)+E(f490(x21741),f490(x21742))
% 191.29/191.76 [2175]~E(x21751,x21752)+E(f801(x21751,x21753,x21754),f801(x21752,x21753,x21754))
% 191.29/191.76 [2176]~E(x21761,x21762)+E(f801(x21763,x21761,x21764),f801(x21763,x21762,x21764))
% 191.29/191.76 [2177]~E(x21771,x21772)+E(f801(x21773,x21774,x21771),f801(x21773,x21774,x21772))
% 191.29/191.76 [2178]~E(x21781,x21782)+E(f608(x21781,x21783,x21784,x21785),f608(x21782,x21783,x21784,x21785))
% 191.29/191.76 [2179]~E(x21791,x21792)+E(f608(x21793,x21791,x21794,x21795),f608(x21793,x21792,x21794,x21795))
% 191.29/191.76 [2180]~E(x21801,x21802)+E(f608(x21803,x21804,x21801,x21805),f608(x21803,x21804,x21802,x21805))
% 191.29/191.76 [2181]~E(x21811,x21812)+E(f608(x21813,x21814,x21815,x21811),f608(x21813,x21814,x21815,x21812))
% 191.29/191.76 [2182]~E(x21821,x21822)+E(f97(x21821,x21823,x21824,x21825),f97(x21822,x21823,x21824,x21825))
% 191.29/191.76 [2183]~E(x21831,x21832)+E(f97(x21833,x21831,x21834,x21835),f97(x21833,x21832,x21834,x21835))
% 191.29/191.76 [2184]~E(x21841,x21842)+E(f97(x21843,x21844,x21841,x21845),f97(x21843,x21844,x21842,x21845))
% 191.29/191.76 [2185]~E(x21851,x21852)+E(f97(x21853,x21854,x21855,x21851),f97(x21853,x21854,x21855,x21852))
% 191.29/191.76 [2186]~E(x21861,x21862)+E(f794(x21861,x21863,x21864),f794(x21862,x21863,x21864))
% 191.29/191.76 [2187]~E(x21871,x21872)+E(f794(x21873,x21871,x21874),f794(x21873,x21872,x21874))
% 191.29/191.76 [2188]~E(x21881,x21882)+E(f794(x21883,x21884,x21881),f794(x21883,x21884,x21882))
% 191.29/191.76 [2189]~E(x21891,x21892)+E(f403(x21891,x21893),f403(x21892,x21893))
% 191.29/191.76 [2190]~E(x21901,x21902)+E(f403(x21903,x21901),f403(x21903,x21902))
% 191.29/191.76 [2191]~E(x21911,x21912)+E(f660(x21911,x21913,x21914,x21915,x21916),f660(x21912,x21913,x21914,x21915,x21916))
% 191.29/191.76 [2192]~E(x21921,x21922)+E(f660(x21923,x21921,x21924,x21925,x21926),f660(x21923,x21922,x21924,x21925,x21926))
% 191.29/191.76 [2193]~E(x21931,x21932)+E(f660(x21933,x21934,x21931,x21935,x21936),f660(x21933,x21934,x21932,x21935,x21936))
% 191.29/191.76 [2194]~E(x21941,x21942)+E(f660(x21943,x21944,x21945,x21941,x21946),f660(x21943,x21944,x21945,x21942,x21946))
% 191.29/191.76 [2195]~E(x21951,x21952)+E(f660(x21953,x21954,x21955,x21956,x21951),f660(x21953,x21954,x21955,x21956,x21952))
% 191.29/191.76 [2196]~E(x21961,x21962)+E(f448(x21961,x21963),f448(x21962,x21963))
% 191.29/191.76 [2197]~E(x21971,x21972)+E(f448(x21973,x21971),f448(x21973,x21972))
% 191.29/191.76 [2198]~E(x21981,x21982)+E(f792(x21981,x21983,x21984),f792(x21982,x21983,x21984))
% 191.29/191.76 [2199]~E(x21991,x21992)+E(f792(x21993,x21991,x21994),f792(x21993,x21992,x21994))
% 191.29/191.76 [2200]~E(x22001,x22002)+E(f792(x22003,x22004,x22001),f792(x22003,x22004,x22002))
% 191.29/191.76 [2201]~E(x22011,x22012)+E(f218(x22011,x22013,x22014,x22015,x22016),f218(x22012,x22013,x22014,x22015,x22016))
% 191.29/191.76 [2202]~E(x22021,x22022)+E(f218(x22023,x22021,x22024,x22025,x22026),f218(x22023,x22022,x22024,x22025,x22026))
% 191.29/191.76 [2203]~E(x22031,x22032)+E(f218(x22033,x22034,x22031,x22035,x22036),f218(x22033,x22034,x22032,x22035,x22036))
% 191.29/191.76 [2204]~E(x22041,x22042)+E(f218(x22043,x22044,x22045,x22041,x22046),f218(x22043,x22044,x22045,x22042,x22046))
% 191.29/191.76 [2205]~E(x22051,x22052)+E(f218(x22053,x22054,x22055,x22056,x22051),f218(x22053,x22054,x22055,x22056,x22052))
% 191.29/191.76 [2206]~E(x22061,x22062)+E(f749(x22061,x22063,x22064),f749(x22062,x22063,x22064))
% 191.29/191.76 [2207]~E(x22071,x22072)+E(f749(x22073,x22071,x22074),f749(x22073,x22072,x22074))
% 191.29/191.76 [2208]~E(x22081,x22082)+E(f749(x22083,x22084,x22081),f749(x22083,x22084,x22082))
% 191.29/191.76 [2209]~E(x22091,x22092)+E(f631(x22091,x22093,x22094,x22095,x22096,x22097),f631(x22092,x22093,x22094,x22095,x22096,x22097))
% 191.29/191.76 [2210]~E(x22101,x22102)+E(f631(x22103,x22101,x22104,x22105,x22106,x22107),f631(x22103,x22102,x22104,x22105,x22106,x22107))
% 191.29/191.76 [2211]~E(x22111,x22112)+E(f631(x22113,x22114,x22111,x22115,x22116,x22117),f631(x22113,x22114,x22112,x22115,x22116,x22117))
% 191.29/191.76 [2212]~E(x22121,x22122)+E(f631(x22123,x22124,x22125,x22121,x22126,x22127),f631(x22123,x22124,x22125,x22122,x22126,x22127))
% 191.29/191.76 [2213]~E(x22131,x22132)+E(f631(x22133,x22134,x22135,x22136,x22131,x22137),f631(x22133,x22134,x22135,x22136,x22132,x22137))
% 191.29/191.76 [2214]~E(x22141,x22142)+E(f631(x22143,x22144,x22145,x22146,x22147,x22141),f631(x22143,x22144,x22145,x22146,x22147,x22142))
% 191.29/191.76 [2215]~E(x22151,x22152)+E(f561(x22151,x22153,x22154,x22155),f561(x22152,x22153,x22154,x22155))
% 191.29/191.76 [2216]~E(x22161,x22162)+E(f561(x22163,x22161,x22164,x22165),f561(x22163,x22162,x22164,x22165))
% 191.29/191.76 [2217]~E(x22171,x22172)+E(f561(x22173,x22174,x22171,x22175),f561(x22173,x22174,x22172,x22175))
% 191.29/191.76 [2218]~E(x22181,x22182)+E(f561(x22183,x22184,x22185,x22181),f561(x22183,x22184,x22185,x22182))
% 191.29/191.76 [2219]~E(x22191,x22192)+E(f619(x22191,x22193,x22194),f619(x22192,x22193,x22194))
% 191.29/191.76 [2220]~E(x22201,x22202)+E(f619(x22203,x22201,x22204),f619(x22203,x22202,x22204))
% 191.29/191.76 [2221]~E(x22211,x22212)+E(f619(x22213,x22214,x22211),f619(x22213,x22214,x22212))
% 191.29/191.76 [2222]~E(x22221,x22222)+E(f756(x22221,x22223,x22224,x22225),f756(x22222,x22223,x22224,x22225))
% 191.29/191.76 [2223]~E(x22231,x22232)+E(f756(x22233,x22231,x22234,x22235),f756(x22233,x22232,x22234,x22235))
% 191.29/191.76 [2224]~E(x22241,x22242)+E(f756(x22243,x22244,x22241,x22245),f756(x22243,x22244,x22242,x22245))
% 191.29/191.76 [2225]~E(x22251,x22252)+E(f756(x22253,x22254,x22255,x22251),f756(x22253,x22254,x22255,x22252))
% 191.29/191.76 [2226]~E(x22261,x22262)+E(f522(x22261,x22263,x22264,x22265),f522(x22262,x22263,x22264,x22265))
% 191.29/191.76 [2227]~E(x22271,x22272)+E(f522(x22273,x22271,x22274,x22275),f522(x22273,x22272,x22274,x22275))
% 191.29/191.76 [2228]~E(x22281,x22282)+E(f522(x22283,x22284,x22281,x22285),f522(x22283,x22284,x22282,x22285))
% 191.29/191.76 [2229]~E(x22291,x22292)+E(f522(x22293,x22294,x22295,x22291),f522(x22293,x22294,x22295,x22292))
% 191.29/191.76 [2230]~E(x22301,x22302)+E(f803(x22301,x22303,x22304),f803(x22302,x22303,x22304))
% 191.29/191.76 [2231]~E(x22311,x22312)+E(f803(x22313,x22311,x22314),f803(x22313,x22312,x22314))
% 191.29/191.76 [2232]~E(x22321,x22322)+E(f803(x22323,x22324,x22321),f803(x22323,x22324,x22322))
% 191.29/191.76 [2233]~E(x22331,x22332)+E(f406(x22331,x22333,x22334),f406(x22332,x22333,x22334))
% 191.29/191.76 [2234]~E(x22341,x22342)+E(f406(x22343,x22341,x22344),f406(x22343,x22342,x22344))
% 191.29/191.76 [2235]~E(x22351,x22352)+E(f406(x22353,x22354,x22351),f406(x22353,x22354,x22352))
% 191.29/191.76 [2236]~E(x22361,x22362)+E(f199(x22361),f199(x22362))
% 191.29/191.76 [2237]~E(x22371,x22372)+E(f543(x22371,x22373,x22374,x22375,x22376,x22377),f543(x22372,x22373,x22374,x22375,x22376,x22377))
% 191.29/191.76 [2238]~E(x22381,x22382)+E(f543(x22383,x22381,x22384,x22385,x22386,x22387),f543(x22383,x22382,x22384,x22385,x22386,x22387))
% 191.29/191.76 [2239]~E(x22391,x22392)+E(f543(x22393,x22394,x22391,x22395,x22396,x22397),f543(x22393,x22394,x22392,x22395,x22396,x22397))
% 191.29/191.76 [2240]~E(x22401,x22402)+E(f543(x22403,x22404,x22405,x22401,x22406,x22407),f543(x22403,x22404,x22405,x22402,x22406,x22407))
% 191.29/191.76 [2241]~E(x22411,x22412)+E(f543(x22413,x22414,x22415,x22416,x22411,x22417),f543(x22413,x22414,x22415,x22416,x22412,x22417))
% 191.29/191.76 [2242]~E(x22421,x22422)+E(f543(x22423,x22424,x22425,x22426,x22427,x22421),f543(x22423,x22424,x22425,x22426,x22427,x22422))
% 191.29/191.76 [2243]~E(x22431,x22432)+E(f612(x22431,x22433,x22434,x22435,x22436,x22437),f612(x22432,x22433,x22434,x22435,x22436,x22437))
% 191.29/191.76 [2244]~E(x22441,x22442)+E(f612(x22443,x22441,x22444,x22445,x22446,x22447),f612(x22443,x22442,x22444,x22445,x22446,x22447))
% 191.29/191.76 [2245]~E(x22451,x22452)+E(f612(x22453,x22454,x22451,x22455,x22456,x22457),f612(x22453,x22454,x22452,x22455,x22456,x22457))
% 191.29/191.76 [2246]~E(x22461,x22462)+E(f612(x22463,x22464,x22465,x22461,x22466,x22467),f612(x22463,x22464,x22465,x22462,x22466,x22467))
% 191.29/191.76 [2247]~E(x22471,x22472)+E(f612(x22473,x22474,x22475,x22476,x22471,x22477),f612(x22473,x22474,x22475,x22476,x22472,x22477))
% 191.29/191.76 [2248]~E(x22481,x22482)+E(f612(x22483,x22484,x22485,x22486,x22487,x22481),f612(x22483,x22484,x22485,x22486,x22487,x22482))
% 191.29/191.76 [2249]~E(x22491,x22492)+E(f444(x22491,x22493),f444(x22492,x22493))
% 191.29/191.76 [2250]~E(x22501,x22502)+E(f444(x22503,x22501),f444(x22503,x22502))
% 191.29/191.76 [2251]~E(x22511,x22512)+E(f225(x22511,x22513,x22514,x22515),f225(x22512,x22513,x22514,x22515))
% 191.29/191.76 [2252]~E(x22521,x22522)+E(f225(x22523,x22521,x22524,x22525),f225(x22523,x22522,x22524,x22525))
% 191.29/191.76 [2253]~E(x22531,x22532)+E(f225(x22533,x22534,x22531,x22535),f225(x22533,x22534,x22532,x22535))
% 191.29/191.76 [2254]~E(x22541,x22542)+E(f225(x22543,x22544,x22545,x22541),f225(x22543,x22544,x22545,x22542))
% 191.29/191.76 [2255]~E(x22551,x22552)+E(f266(x22551,x22553),f266(x22552,x22553))
% 191.29/191.76 [2256]~E(x22561,x22562)+E(f266(x22563,x22561),f266(x22563,x22562))
% 191.29/191.76 [2257]~E(x22571,x22572)+E(f674(x22571,x22573,x22574),f674(x22572,x22573,x22574))
% 191.29/191.76 [2258]~E(x22581,x22582)+E(f674(x22583,x22581,x22584),f674(x22583,x22582,x22584))
% 191.29/191.76 [2259]~E(x22591,x22592)+E(f674(x22593,x22594,x22591),f674(x22593,x22594,x22592))
% 191.29/191.76 [2260]~E(x22601,x22602)+E(f475(x22601,x22603,x22604),f475(x22602,x22603,x22604))
% 191.29/191.76 [2261]~E(x22611,x22612)+E(f475(x22613,x22611,x22614),f475(x22613,x22612,x22614))
% 191.29/191.76 [2262]~E(x22621,x22622)+E(f475(x22623,x22624,x22621),f475(x22623,x22624,x22622))
% 191.29/191.76 [2263]~E(x22631,x22632)+E(f529(x22631,x22633,x22634,x22635),f529(x22632,x22633,x22634,x22635))
% 191.29/191.76 [2264]~E(x22641,x22642)+E(f529(x22643,x22641,x22644,x22645),f529(x22643,x22642,x22644,x22645))
% 191.29/191.76 [2265]~E(x22651,x22652)+E(f529(x22653,x22654,x22651,x22655),f529(x22653,x22654,x22652,x22655))
% 191.29/191.76 [2266]~E(x22661,x22662)+E(f529(x22663,x22664,x22665,x22661),f529(x22663,x22664,x22665,x22662))
% 191.29/191.76 [2267]~E(x22671,x22672)+E(f725(x22671,x22673,x22674),f725(x22672,x22673,x22674))
% 191.29/191.76 [2268]~E(x22681,x22682)+E(f725(x22683,x22681,x22684),f725(x22683,x22682,x22684))
% 191.29/191.76 [2269]~E(x22691,x22692)+E(f725(x22693,x22694,x22691),f725(x22693,x22694,x22692))
% 191.29/191.76 [2270]~E(x22701,x22702)+E(f489(x22701,x22703,x22704,x22705,x22706),f489(x22702,x22703,x22704,x22705,x22706))
% 191.29/191.76 [2271]~E(x22711,x22712)+E(f489(x22713,x22711,x22714,x22715,x22716),f489(x22713,x22712,x22714,x22715,x22716))
% 191.29/191.76 [2272]~E(x22721,x22722)+E(f489(x22723,x22724,x22721,x22725,x22726),f489(x22723,x22724,x22722,x22725,x22726))
% 191.29/191.76 [2273]~E(x22731,x22732)+E(f489(x22733,x22734,x22735,x22731,x22736),f489(x22733,x22734,x22735,x22732,x22736))
% 191.29/191.76 [2274]~E(x22741,x22742)+E(f489(x22743,x22744,x22745,x22746,x22741),f489(x22743,x22744,x22745,x22746,x22742))
% 191.29/191.76 [2275]~E(x22751,x22752)+E(f541(x22751,x22753,x22754,x22755,x22756,x22757),f541(x22752,x22753,x22754,x22755,x22756,x22757))
% 191.29/191.76 [2276]~E(x22761,x22762)+E(f541(x22763,x22761,x22764,x22765,x22766,x22767),f541(x22763,x22762,x22764,x22765,x22766,x22767))
% 191.29/191.76 [2277]~E(x22771,x22772)+E(f541(x22773,x22774,x22771,x22775,x22776,x22777),f541(x22773,x22774,x22772,x22775,x22776,x22777))
% 191.29/191.76 [2278]~E(x22781,x22782)+E(f541(x22783,x22784,x22785,x22781,x22786,x22787),f541(x22783,x22784,x22785,x22782,x22786,x22787))
% 191.29/191.76 [2279]~E(x22791,x22792)+E(f541(x22793,x22794,x22795,x22796,x22791,x22797),f541(x22793,x22794,x22795,x22796,x22792,x22797))
% 191.29/191.76 [2280]~E(x22801,x22802)+E(f541(x22803,x22804,x22805,x22806,x22807,x22801),f541(x22803,x22804,x22805,x22806,x22807,x22802))
% 191.29/191.76 [2281]~E(x22811,x22812)+E(f391(x22811,x22813,x22814,x22815,x22816),f391(x22812,x22813,x22814,x22815,x22816))
% 191.29/191.76 [2282]~E(x22821,x22822)+E(f391(x22823,x22821,x22824,x22825,x22826),f391(x22823,x22822,x22824,x22825,x22826))
% 191.29/191.76 [2283]~E(x22831,x22832)+E(f391(x22833,x22834,x22831,x22835,x22836),f391(x22833,x22834,x22832,x22835,x22836))
% 191.29/191.76 [2284]~E(x22841,x22842)+E(f391(x22843,x22844,x22845,x22841,x22846),f391(x22843,x22844,x22845,x22842,x22846))
% 191.29/191.76 [2285]~E(x22851,x22852)+E(f391(x22853,x22854,x22855,x22856,x22851),f391(x22853,x22854,x22855,x22856,x22852))
% 191.29/191.76 [2286]~E(x22861,x22862)+E(f471(x22861),f471(x22862))
% 191.29/191.76 [2287]~E(x22871,x22872)+E(f835(x22871,x22873,x22874),f835(x22872,x22873,x22874))
% 191.29/191.76 [2288]~E(x22881,x22882)+E(f835(x22883,x22881,x22884),f835(x22883,x22882,x22884))
% 191.29/191.76 [2289]~E(x22891,x22892)+E(f835(x22893,x22894,x22891),f835(x22893,x22894,x22892))
% 191.29/191.76 [2290]~E(x22901,x22902)+E(f797(x22901,x22903),f797(x22902,x22903))
% 191.29/191.76 [2291]~E(x22911,x22912)+E(f797(x22913,x22911),f797(x22913,x22912))
% 191.29/191.76 [2292]~E(x22921,x22922)+E(f572(x22921,x22923,x22924),f572(x22922,x22923,x22924))
% 191.29/191.76 [2293]~E(x22931,x22932)+E(f572(x22933,x22931,x22934),f572(x22933,x22932,x22934))
% 191.29/191.76 [2294]~E(x22941,x22942)+E(f572(x22943,x22944,x22941),f572(x22943,x22944,x22942))
% 191.29/191.76 [2295]~E(x22951,x22952)+E(f721(x22951,x22953),f721(x22952,x22953))
% 191.29/191.76 [2296]~E(x22961,x22962)+E(f721(x22963,x22961),f721(x22963,x22962))
% 191.29/191.76 [2297]~E(x22971,x22972)+E(f807(x22971,x22973,x22974),f807(x22972,x22973,x22974))
% 191.29/191.76 [2298]~E(x22981,x22982)+E(f807(x22983,x22981,x22984),f807(x22983,x22982,x22984))
% 191.29/191.76 [2299]~E(x22991,x22992)+E(f807(x22993,x22994,x22991),f807(x22993,x22994,x22992))
% 191.29/191.76 [2300]~E(x23001,x23002)+E(f356(x23001,x23003,x23004,x23005),f356(x23002,x23003,x23004,x23005))
% 191.29/191.76 [2301]~E(x23011,x23012)+E(f356(x23013,x23011,x23014,x23015),f356(x23013,x23012,x23014,x23015))
% 191.29/191.76 [2302]~E(x23021,x23022)+E(f356(x23023,x23024,x23021,x23025),f356(x23023,x23024,x23022,x23025))
% 191.29/191.76 [2303]~E(x23031,x23032)+E(f356(x23033,x23034,x23035,x23031),f356(x23033,x23034,x23035,x23032))
% 191.29/191.76 [2304]~E(x23041,x23042)+E(f746(x23041,x23043,x23044),f746(x23042,x23043,x23044))
% 191.29/191.76 [2305]~E(x23051,x23052)+E(f746(x23053,x23051,x23054),f746(x23053,x23052,x23054))
% 191.29/191.76 [2306]~E(x23061,x23062)+E(f746(x23063,x23064,x23061),f746(x23063,x23064,x23062))
% 191.29/191.76 [2307]~E(x23071,x23072)+E(f124(x23071),f124(x23072))
% 191.29/191.76 [2308]~E(x23081,x23082)+E(f524(x23081,x23083,x23084,x23085,x23086),f524(x23082,x23083,x23084,x23085,x23086))
% 191.29/191.76 [2309]~E(x23091,x23092)+E(f524(x23093,x23091,x23094,x23095,x23096),f524(x23093,x23092,x23094,x23095,x23096))
% 191.29/191.76 [2310]~E(x23101,x23102)+E(f524(x23103,x23104,x23101,x23105,x23106),f524(x23103,x23104,x23102,x23105,x23106))
% 191.29/191.76 [2311]~E(x23111,x23112)+E(f524(x23113,x23114,x23115,x23111,x23116),f524(x23113,x23114,x23115,x23112,x23116))
% 191.29/191.76 [2312]~E(x23121,x23122)+E(f524(x23123,x23124,x23125,x23126,x23121),f524(x23123,x23124,x23125,x23126,x23122))
% 191.29/191.76 [2313]~E(x23131,x23132)+E(f495(x23131,x23133,x23134,x23135,x23136,x23137),f495(x23132,x23133,x23134,x23135,x23136,x23137))
% 191.29/191.76 [2314]~E(x23141,x23142)+E(f495(x23143,x23141,x23144,x23145,x23146,x23147),f495(x23143,x23142,x23144,x23145,x23146,x23147))
% 191.29/191.76 [2315]~E(x23151,x23152)+E(f495(x23153,x23154,x23151,x23155,x23156,x23157),f495(x23153,x23154,x23152,x23155,x23156,x23157))
% 191.29/191.76 [2316]~E(x23161,x23162)+E(f495(x23163,x23164,x23165,x23161,x23166,x23167),f495(x23163,x23164,x23165,x23162,x23166,x23167))
% 191.29/191.76 [2317]~E(x23171,x23172)+E(f495(x23173,x23174,x23175,x23176,x23171,x23177),f495(x23173,x23174,x23175,x23176,x23172,x23177))
% 191.29/191.76 [2318]~E(x23181,x23182)+E(f495(x23183,x23184,x23185,x23186,x23187,x23181),f495(x23183,x23184,x23185,x23186,x23187,x23182))
% 191.29/191.76 [2319]~E(x23191,x23192)+E(f672(x23191,x23193,x23194),f672(x23192,x23193,x23194))
% 191.29/191.76 [2320]~E(x23201,x23202)+E(f672(x23203,x23201,x23204),f672(x23203,x23202,x23204))
% 191.29/191.76 [2321]~E(x23211,x23212)+E(f672(x23213,x23214,x23211),f672(x23213,x23214,x23212))
% 191.29/191.76 [2322]~E(x23221,x23222)+E(f95(x23221,x23223,x23224),f95(x23222,x23223,x23224))
% 191.29/191.76 [2323]~E(x23231,x23232)+E(f95(x23233,x23231,x23234),f95(x23233,x23232,x23234))
% 191.29/191.76 [2324]~E(x23241,x23242)+E(f95(x23243,x23244,x23241),f95(x23243,x23244,x23242))
% 191.29/191.76 [2325]~E(x23251,x23252)+E(f396(x23251,x23253,x23254,x23255,x23256),f396(x23252,x23253,x23254,x23255,x23256))
% 191.29/191.76 [2326]~E(x23261,x23262)+E(f396(x23263,x23261,x23264,x23265,x23266),f396(x23263,x23262,x23264,x23265,x23266))
% 191.29/191.76 [2327]~E(x23271,x23272)+E(f396(x23273,x23274,x23271,x23275,x23276),f396(x23273,x23274,x23272,x23275,x23276))
% 191.29/191.76 [2328]~E(x23281,x23282)+E(f396(x23283,x23284,x23285,x23281,x23286),f396(x23283,x23284,x23285,x23282,x23286))
% 191.29/191.76 [2329]~E(x23291,x23292)+E(f396(x23293,x23294,x23295,x23296,x23291),f396(x23293,x23294,x23295,x23296,x23292))
% 191.29/191.76 [2330]~E(x23301,x23302)+E(f374(x23301,x23303,x23304),f374(x23302,x23303,x23304))
% 191.29/191.76 [2331]~E(x23311,x23312)+E(f374(x23313,x23311,x23314),f374(x23313,x23312,x23314))
% 191.29/191.76 [2332]~E(x23321,x23322)+E(f374(x23323,x23324,x23321),f374(x23323,x23324,x23322))
% 191.29/191.76 [2333]~E(x23331,x23332)+E(f557(x23331),f557(x23332))
% 191.29/191.76 [2334]~E(x23341,x23342)+E(f762(x23341,x23343,x23344),f762(x23342,x23343,x23344))
% 191.29/191.76 [2335]~E(x23351,x23352)+E(f762(x23353,x23351,x23354),f762(x23353,x23352,x23354))
% 191.29/191.76 [2336]~E(x23361,x23362)+E(f762(x23363,x23364,x23361),f762(x23363,x23364,x23362))
% 191.29/191.76 [2337]~E(x23371,x23372)+E(f635(x23371,x23373,x23374),f635(x23372,x23373,x23374))
% 191.29/191.76 [2338]~E(x23381,x23382)+E(f635(x23383,x23381,x23384),f635(x23383,x23382,x23384))
% 191.29/191.76 [2339]~E(x23391,x23392)+E(f635(x23393,x23394,x23391),f635(x23393,x23394,x23392))
% 191.29/191.76 [2340]~E(x23401,x23402)+E(f598(x23401,x23403,x23404,x23405),f598(x23402,x23403,x23404,x23405))
% 191.29/191.76 [2341]~E(x23411,x23412)+E(f598(x23413,x23411,x23414,x23415),f598(x23413,x23412,x23414,x23415))
% 191.29/191.76 [2342]~E(x23421,x23422)+E(f598(x23423,x23424,x23421,x23425),f598(x23423,x23424,x23422,x23425))
% 191.29/191.76 [2343]~E(x23431,x23432)+E(f598(x23433,x23434,x23435,x23431),f598(x23433,x23434,x23435,x23432))
% 191.29/191.76 [2344]~E(x23441,x23442)+E(f517(x23441,x23443,x23444,x23445),f517(x23442,x23443,x23444,x23445))
% 191.29/191.76 [2345]~E(x23451,x23452)+E(f517(x23453,x23451,x23454,x23455),f517(x23453,x23452,x23454,x23455))
% 191.29/191.76 [2346]~E(x23461,x23462)+E(f517(x23463,x23464,x23461,x23465),f517(x23463,x23464,x23462,x23465))
% 191.29/191.76 [2347]~E(x23471,x23472)+E(f517(x23473,x23474,x23475,x23471),f517(x23473,x23474,x23475,x23472))
% 191.29/191.76 [2348]~E(x23481,x23482)+E(f761(x23481,x23483),f761(x23482,x23483))
% 191.29/191.76 [2349]~E(x23491,x23492)+E(f761(x23493,x23491),f761(x23493,x23492))
% 191.29/191.76 [2350]~E(x23501,x23502)+E(f681(x23501,x23503),f681(x23502,x23503))
% 191.29/191.76 [2351]~E(x23511,x23512)+E(f681(x23513,x23511),f681(x23513,x23512))
% 191.29/191.76 [2352]~E(x23521,x23522)+E(f360(x23521,x23523,x23524,x23525,x23526),f360(x23522,x23523,x23524,x23525,x23526))
% 191.29/191.76 [2353]~E(x23531,x23532)+E(f360(x23533,x23531,x23534,x23535,x23536),f360(x23533,x23532,x23534,x23535,x23536))
% 191.29/191.76 [2354]~E(x23541,x23542)+E(f360(x23543,x23544,x23541,x23545,x23546),f360(x23543,x23544,x23542,x23545,x23546))
% 191.29/191.76 [2355]~E(x23551,x23552)+E(f360(x23553,x23554,x23555,x23551,x23556),f360(x23553,x23554,x23555,x23552,x23556))
% 191.29/191.76 [2356]~E(x23561,x23562)+E(f360(x23563,x23564,x23565,x23566,x23561),f360(x23563,x23564,x23565,x23566,x23562))
% 191.29/191.76 [2357]~E(x23571,x23572)+E(f646(x23571,x23573,x23574),f646(x23572,x23573,x23574))
% 191.29/191.76 [2358]~E(x23581,x23582)+E(f646(x23583,x23581,x23584),f646(x23583,x23582,x23584))
% 191.29/191.76 [2359]~E(x23591,x23592)+E(f646(x23593,x23594,x23591),f646(x23593,x23594,x23592))
% 191.29/191.76 [2360]~E(x23601,x23602)+E(f523(x23601,x23603,x23604,x23605),f523(x23602,x23603,x23604,x23605))
% 191.29/191.76 [2361]~E(x23611,x23612)+E(f523(x23613,x23611,x23614,x23615),f523(x23613,x23612,x23614,x23615))
% 191.29/191.76 [2362]~E(x23621,x23622)+E(f523(x23623,x23624,x23621,x23625),f523(x23623,x23624,x23622,x23625))
% 191.29/191.76 [2363]~E(x23631,x23632)+E(f523(x23633,x23634,x23635,x23631),f523(x23633,x23634,x23635,x23632))
% 191.29/191.76 [2364]~E(x23641,x23642)+E(f592(x23641,x23643),f592(x23642,x23643))
% 191.29/191.76 [2365]~E(x23651,x23652)+E(f592(x23653,x23651),f592(x23653,x23652))
% 191.29/191.76 [2366]~E(x23661,x23662)+E(f560(x23661,x23663,x23664,x23665),f560(x23662,x23663,x23664,x23665))
% 191.29/191.76 [2367]~E(x23671,x23672)+E(f560(x23673,x23671,x23674,x23675),f560(x23673,x23672,x23674,x23675))
% 191.29/191.76 [2368]~E(x23681,x23682)+E(f560(x23683,x23684,x23681,x23685),f560(x23683,x23684,x23682,x23685))
% 191.29/191.76 [2369]~E(x23691,x23692)+E(f560(x23693,x23694,x23695,x23691),f560(x23693,x23694,x23695,x23692))
% 191.29/191.76 [2370]~E(x23701,x23702)+E(f441(x23701,x23703,x23704,x23705,x23706),f441(x23702,x23703,x23704,x23705,x23706))
% 191.29/191.76 [2371]~E(x23711,x23712)+E(f441(x23713,x23711,x23714,x23715,x23716),f441(x23713,x23712,x23714,x23715,x23716))
% 191.29/191.76 [2372]~E(x23721,x23722)+E(f441(x23723,x23724,x23721,x23725,x23726),f441(x23723,x23724,x23722,x23725,x23726))
% 191.29/191.76 [2373]~E(x23731,x23732)+E(f441(x23733,x23734,x23735,x23731,x23736),f441(x23733,x23734,x23735,x23732,x23736))
% 191.29/191.76 [2374]~E(x23741,x23742)+E(f441(x23743,x23744,x23745,x23746,x23741),f441(x23743,x23744,x23745,x23746,x23742))
% 191.29/191.76 [2375]~E(x23751,x23752)+E(f476(x23751,x23753,x23754),f476(x23752,x23753,x23754))
% 191.29/191.76 [2376]~E(x23761,x23762)+E(f476(x23763,x23761,x23764),f476(x23763,x23762,x23764))
% 191.29/191.76 [2377]~E(x23771,x23772)+E(f476(x23773,x23774,x23771),f476(x23773,x23774,x23772))
% 191.29/191.76 [2378]~E(x23781,x23782)+E(f554(x23781),f554(x23782))
% 191.29/191.76 [2379]~E(x23791,x23792)+E(f51(x23791),f51(x23792))
% 191.29/191.76 [2380]~E(x23801,x23802)+E(f633(x23801,x23803,x23804),f633(x23802,x23803,x23804))
% 191.29/191.76 [2381]~E(x23811,x23812)+E(f633(x23813,x23811,x23814),f633(x23813,x23812,x23814))
% 191.29/191.76 [2382]~E(x23821,x23822)+E(f633(x23823,x23824,x23821),f633(x23823,x23824,x23822))
% 191.29/191.76 [2383]~E(x23831,x23832)+E(f457(x23831,x23833),f457(x23832,x23833))
% 191.29/191.76 [2384]~E(x23841,x23842)+E(f457(x23843,x23841),f457(x23843,x23842))
% 191.29/191.76 [2385]~E(x23851,x23852)+E(f399(x23851,x23853,x23854,x23855),f399(x23852,x23853,x23854,x23855))
% 191.29/191.76 [2386]~E(x23861,x23862)+E(f399(x23863,x23861,x23864,x23865),f399(x23863,x23862,x23864,x23865))
% 191.29/191.76 [2387]~E(x23871,x23872)+E(f399(x23873,x23874,x23871,x23875),f399(x23873,x23874,x23872,x23875))
% 191.29/191.76 [2388]~E(x23881,x23882)+E(f399(x23883,x23884,x23885,x23881),f399(x23883,x23884,x23885,x23882))
% 191.29/191.76 [2389]~E(x23891,x23892)+E(f694(x23891,x23893,x23894),f694(x23892,x23893,x23894))
% 191.29/191.76 [2390]~E(x23901,x23902)+E(f694(x23903,x23901,x23904),f694(x23903,x23902,x23904))
% 191.29/191.76 [2391]~E(x23911,x23912)+E(f694(x23913,x23914,x23911),f694(x23913,x23914,x23912))
% 191.29/191.76 [2392]~E(x23921,x23922)+E(f224(x23921,x23923,x23924),f224(x23922,x23923,x23924))
% 191.29/191.76 [2393]~E(x23931,x23932)+E(f224(x23933,x23931,x23934),f224(x23933,x23932,x23934))
% 191.29/191.76 [2394]~E(x23941,x23942)+E(f224(x23943,x23944,x23941),f224(x23943,x23944,x23942))
% 191.29/191.76 [2395]~E(x23951,x23952)+E(f439(x23951,x23953,x23954,x23955),f439(x23952,x23953,x23954,x23955))
% 191.29/191.76 [2396]~E(x23961,x23962)+E(f439(x23963,x23961,x23964,x23965),f439(x23963,x23962,x23964,x23965))
% 191.29/191.76 [2397]~E(x23971,x23972)+E(f439(x23973,x23974,x23971,x23975),f439(x23973,x23974,x23972,x23975))
% 191.29/191.76 [2398]~E(x23981,x23982)+E(f439(x23983,x23984,x23985,x23981),f439(x23983,x23984,x23985,x23982))
% 191.29/191.76 [2399]~E(x23991,x23992)+E(f693(x23991,x23993,x23994,x23995),f693(x23992,x23993,x23994,x23995))
% 191.29/191.76 [2400]~E(x24001,x24002)+E(f693(x24003,x24001,x24004,x24005),f693(x24003,x24002,x24004,x24005))
% 191.29/191.76 [2401]~E(x24011,x24012)+E(f693(x24013,x24014,x24011,x24015),f693(x24013,x24014,x24012,x24015))
% 191.29/191.76 [2402]~E(x24021,x24022)+E(f693(x24023,x24024,x24025,x24021),f693(x24023,x24024,x24025,x24022))
% 191.29/191.76 [2403]~E(x24031,x24032)+E(f493(x24031,x24033,x24034),f493(x24032,x24033,x24034))
% 191.29/191.76 [2404]~E(x24041,x24042)+E(f493(x24043,x24041,x24044),f493(x24043,x24042,x24044))
% 191.29/191.76 [2405]~E(x24051,x24052)+E(f493(x24053,x24054,x24051),f493(x24053,x24054,x24052))
% 191.29/191.76 [2406]~E(x24061,x24062)+E(f632(x24061,x24063,x24064),f632(x24062,x24063,x24064))
% 191.29/191.76 [2407]~E(x24071,x24072)+E(f632(x24073,x24071,x24074),f632(x24073,x24072,x24074))
% 191.29/191.76 [2408]~E(x24081,x24082)+E(f632(x24083,x24084,x24081),f632(x24083,x24084,x24082))
% 191.29/191.76 [2409]~E(x24091,x24092)+E(f315(x24091,x24093,x24094),f315(x24092,x24093,x24094))
% 191.29/191.76 [2410]~E(x24101,x24102)+E(f315(x24103,x24101,x24104),f315(x24103,x24102,x24104))
% 191.29/191.76 [2411]~E(x24111,x24112)+E(f315(x24113,x24114,x24111),f315(x24113,x24114,x24112))
% 191.29/191.76 [2412]~E(x24121,x24122)+E(f716(x24121,x24123,x24124,x24125),f716(x24122,x24123,x24124,x24125))
% 191.29/191.76 [2413]~E(x24131,x24132)+E(f716(x24133,x24131,x24134,x24135),f716(x24133,x24132,x24134,x24135))
% 191.29/191.76 [2414]~E(x24141,x24142)+E(f716(x24143,x24144,x24141,x24145),f716(x24143,x24144,x24142,x24145))
% 191.29/191.76 [2415]~E(x24151,x24152)+E(f716(x24153,x24154,x24155,x24151),f716(x24153,x24154,x24155,x24152))
% 191.29/191.76 [2416]~E(x24161,x24162)+E(f594(x24161,x24163,x24164,x24165),f594(x24162,x24163,x24164,x24165))
% 191.29/191.76 [2417]~E(x24171,x24172)+E(f594(x24173,x24171,x24174,x24175),f594(x24173,x24172,x24174,x24175))
% 191.29/191.76 [2418]~E(x24181,x24182)+E(f594(x24183,x24184,x24181,x24185),f594(x24183,x24184,x24182,x24185))
% 191.29/191.76 [2419]~E(x24191,x24192)+E(f594(x24193,x24194,x24195,x24191),f594(x24193,x24194,x24195,x24192))
% 191.29/191.76 [2420]~E(x24201,x24202)+E(f743(x24201,x24203,x24204,x24205),f743(x24202,x24203,x24204,x24205))
% 191.29/191.76 [2421]~E(x24211,x24212)+E(f743(x24213,x24211,x24214,x24215),f743(x24213,x24212,x24214,x24215))
% 191.29/191.76 [2422]~E(x24221,x24222)+E(f743(x24223,x24224,x24221,x24225),f743(x24223,x24224,x24222,x24225))
% 191.29/191.76 [2423]~E(x24231,x24232)+E(f743(x24233,x24234,x24235,x24231),f743(x24233,x24234,x24235,x24232))
% 191.29/191.76 [2424]~E(x24241,x24242)+E(f683(x24241),f683(x24242))
% 191.29/191.76 [2425]~E(x24251,x24252)+E(f480(x24251,x24253,x24254,x24255,x24256),f480(x24252,x24253,x24254,x24255,x24256))
% 191.29/191.76 [2426]~E(x24261,x24262)+E(f480(x24263,x24261,x24264,x24265,x24266),f480(x24263,x24262,x24264,x24265,x24266))
% 191.29/191.76 [2427]~E(x24271,x24272)+E(f480(x24273,x24274,x24271,x24275,x24276),f480(x24273,x24274,x24272,x24275,x24276))
% 191.29/191.76 [2428]~E(x24281,x24282)+E(f480(x24283,x24284,x24285,x24281,x24286),f480(x24283,x24284,x24285,x24282,x24286))
% 191.29/191.76 [2429]~E(x24291,x24292)+E(f480(x24293,x24294,x24295,x24296,x24291),f480(x24293,x24294,x24295,x24296,x24292))
% 191.29/191.76 [2430]~E(x24301,x24302)+E(f345(x24301,x24303,x24304,x24305),f345(x24302,x24303,x24304,x24305))
% 191.29/191.76 [2431]~E(x24311,x24312)+E(f345(x24313,x24311,x24314,x24315),f345(x24313,x24312,x24314,x24315))
% 191.29/191.76 [2432]~E(x24321,x24322)+E(f345(x24323,x24324,x24321,x24325),f345(x24323,x24324,x24322,x24325))
% 191.29/191.76 [2433]~E(x24331,x24332)+E(f345(x24333,x24334,x24335,x24331),f345(x24333,x24334,x24335,x24332))
% 191.29/191.76 [2434]~E(x24341,x24342)+E(f544(x24341,x24343,x24344,x24345,x24346,x24347),f544(x24342,x24343,x24344,x24345,x24346,x24347))
% 191.29/191.76 [2435]~E(x24351,x24352)+E(f544(x24353,x24351,x24354,x24355,x24356,x24357),f544(x24353,x24352,x24354,x24355,x24356,x24357))
% 191.29/191.76 [2436]~E(x24361,x24362)+E(f544(x24363,x24364,x24361,x24365,x24366,x24367),f544(x24363,x24364,x24362,x24365,x24366,x24367))
% 191.29/191.76 [2437]~E(x24371,x24372)+E(f544(x24373,x24374,x24375,x24371,x24376,x24377),f544(x24373,x24374,x24375,x24372,x24376,x24377))
% 191.29/191.76 [2438]~E(x24381,x24382)+E(f544(x24383,x24384,x24385,x24386,x24381,x24387),f544(x24383,x24384,x24385,x24386,x24382,x24387))
% 191.29/191.76 [2439]~E(x24391,x24392)+E(f544(x24393,x24394,x24395,x24396,x24397,x24391),f544(x24393,x24394,x24395,x24396,x24397,x24392))
% 191.29/191.76 [2440]~E(x24401,x24402)+E(f312(x24401,x24403,x24404),f312(x24402,x24403,x24404))
% 191.29/191.76 [2441]~E(x24411,x24412)+E(f312(x24413,x24411,x24414),f312(x24413,x24412,x24414))
% 191.29/191.76 [2442]~E(x24421,x24422)+E(f312(x24423,x24424,x24421),f312(x24423,x24424,x24422))
% 191.29/191.76 [2443]~E(x24431,x24432)+E(f655(x24431,x24433,x24434,x24435),f655(x24432,x24433,x24434,x24435))
% 191.29/191.76 [2444]~E(x24441,x24442)+E(f655(x24443,x24441,x24444,x24445),f655(x24443,x24442,x24444,x24445))
% 191.29/191.76 [2445]~E(x24451,x24452)+E(f655(x24453,x24454,x24451,x24455),f655(x24453,x24454,x24452,x24455))
% 191.29/191.76 [2446]~E(x24461,x24462)+E(f655(x24463,x24464,x24465,x24461),f655(x24463,x24464,x24465,x24462))
% 191.29/191.76 [2447]~E(x24471,x24472)+E(f195(x24471),f195(x24472))
% 191.29/191.76 [2448]~E(x24481,x24482)+E(f821(x24481,x24483,x24484),f821(x24482,x24483,x24484))
% 191.29/191.76 [2449]~E(x24491,x24492)+E(f821(x24493,x24491,x24494),f821(x24493,x24492,x24494))
% 191.29/191.76 [2450]~E(x24501,x24502)+E(f821(x24503,x24504,x24501),f821(x24503,x24504,x24502))
% 191.29/191.76 [2451]~E(x24511,x24512)+E(f715(x24511,x24513,x24514,x24515,x24516),f715(x24512,x24513,x24514,x24515,x24516))
% 191.29/191.76 [2452]~E(x24521,x24522)+E(f715(x24523,x24521,x24524,x24525,x24526),f715(x24523,x24522,x24524,x24525,x24526))
% 191.29/191.76 [2453]~E(x24531,x24532)+E(f715(x24533,x24534,x24531,x24535,x24536),f715(x24533,x24534,x24532,x24535,x24536))
% 191.29/191.76 [2454]~E(x24541,x24542)+E(f715(x24543,x24544,x24545,x24541,x24546),f715(x24543,x24544,x24545,x24542,x24546))
% 191.29/191.76 [2455]~E(x24551,x24552)+E(f715(x24553,x24554,x24555,x24556,x24551),f715(x24553,x24554,x24555,x24556,x24552))
% 191.29/191.76 [2456]~E(x24561,x24562)+E(f602(x24561,x24563),f602(x24562,x24563))
% 191.29/191.76 [2457]~E(x24571,x24572)+E(f602(x24573,x24571),f602(x24573,x24572))
% 191.29/191.76 [2458]~E(x24581,x24582)+E(f220(x24581,x24583,x24584,x24585,x24586),f220(x24582,x24583,x24584,x24585,x24586))
% 191.29/191.76 [2459]~E(x24591,x24592)+E(f220(x24593,x24591,x24594,x24595,x24596),f220(x24593,x24592,x24594,x24595,x24596))
% 191.29/191.76 [2460]~E(x24601,x24602)+E(f220(x24603,x24604,x24601,x24605,x24606),f220(x24603,x24604,x24602,x24605,x24606))
% 191.29/191.76 [2461]~E(x24611,x24612)+E(f220(x24613,x24614,x24615,x24611,x24616),f220(x24613,x24614,x24615,x24612,x24616))
% 191.29/191.76 [2462]~E(x24621,x24622)+E(f220(x24623,x24624,x24625,x24626,x24621),f220(x24623,x24624,x24625,x24626,x24622))
% 191.29/191.76 [2463]~E(x24631,x24632)+E(f308(x24631,x24633,x24634),f308(x24632,x24633,x24634))
% 191.29/191.76 [2464]~E(x24641,x24642)+E(f308(x24643,x24641,x24644),f308(x24643,x24642,x24644))
% 191.29/191.76 [2465]~E(x24651,x24652)+E(f308(x24653,x24654,x24651),f308(x24653,x24654,x24652))
% 191.29/191.76 [2466]~E(x24661,x24662)+E(f200(x24661,x24663,x24664,x24665),f200(x24662,x24663,x24664,x24665))
% 191.29/191.76 [2467]~E(x24671,x24672)+E(f200(x24673,x24671,x24674,x24675),f200(x24673,x24672,x24674,x24675))
% 191.29/191.76 [2468]~E(x24681,x24682)+E(f200(x24683,x24684,x24681,x24685),f200(x24683,x24684,x24682,x24685))
% 191.29/191.76 [2469]~E(x24691,x24692)+E(f200(x24693,x24694,x24695,x24691),f200(x24693,x24694,x24695,x24692))
% 191.29/191.76 [2470]~E(x24701,x24702)+E(f244(x24701,x24703,x24704),f244(x24702,x24703,x24704))
% 191.29/191.76 [2471]~E(x24711,x24712)+E(f244(x24713,x24711,x24714),f244(x24713,x24712,x24714))
% 191.29/191.76 [2472]~E(x24721,x24722)+E(f244(x24723,x24724,x24721),f244(x24723,x24724,x24722))
% 191.29/191.76 [2473]~E(x24731,x24732)+E(f828(x24731,x24733,x24734),f828(x24732,x24733,x24734))
% 191.29/191.76 [2474]~E(x24741,x24742)+E(f828(x24743,x24741,x24744),f828(x24743,x24742,x24744))
% 191.29/191.76 [2475]~E(x24751,x24752)+E(f828(x24753,x24754,x24751),f828(x24753,x24754,x24752))
% 191.29/191.76 [2476]~E(x24761,x24762)+E(f206(x24761,x24763,x24764,x24765,x24766,x24767,x24768),f206(x24762,x24763,x24764,x24765,x24766,x24767,x24768))
% 191.29/191.76 [2477]~E(x24771,x24772)+E(f206(x24773,x24771,x24774,x24775,x24776,x24777,x24778),f206(x24773,x24772,x24774,x24775,x24776,x24777,x24778))
% 191.29/191.76 [2478]~E(x24781,x24782)+E(f206(x24783,x24784,x24781,x24785,x24786,x24787,x24788),f206(x24783,x24784,x24782,x24785,x24786,x24787,x24788))
% 191.29/191.76 [2479]~E(x24791,x24792)+E(f206(x24793,x24794,x24795,x24791,x24796,x24797,x24798),f206(x24793,x24794,x24795,x24792,x24796,x24797,x24798))
% 191.29/191.76 [2480]~E(x24801,x24802)+E(f206(x24803,x24804,x24805,x24806,x24801,x24807,x24808),f206(x24803,x24804,x24805,x24806,x24802,x24807,x24808))
% 191.29/191.76 [2481]~E(x24811,x24812)+E(f206(x24813,x24814,x24815,x24816,x24817,x24811,x24818),f206(x24813,x24814,x24815,x24816,x24817,x24812,x24818))
% 191.29/191.76 [2482]~E(x24821,x24822)+E(f206(x24823,x24824,x24825,x24826,x24827,x24828,x24821),f206(x24823,x24824,x24825,x24826,x24827,x24828,x24822))
% 191.29/191.76 [2483]~E(x24831,x24832)+E(f376(x24831),f376(x24832))
% 191.29/191.76 [2484]~E(x24841,x24842)+E(f401(x24841),f401(x24842))
% 191.29/191.76 [2485]~E(x24851,x24852)+E(f479(x24851,x24853,x24854,x24855,x24856),f479(x24852,x24853,x24854,x24855,x24856))
% 191.29/191.76 [2486]~E(x24861,x24862)+E(f479(x24863,x24861,x24864,x24865,x24866),f479(x24863,x24862,x24864,x24865,x24866))
% 191.29/191.76 [2487]~E(x24871,x24872)+E(f479(x24873,x24874,x24871,x24875,x24876),f479(x24873,x24874,x24872,x24875,x24876))
% 191.29/191.76 [2488]~E(x24881,x24882)+E(f479(x24883,x24884,x24885,x24881,x24886),f479(x24883,x24884,x24885,x24882,x24886))
% 191.29/191.76 [2489]~E(x24891,x24892)+E(f479(x24893,x24894,x24895,x24896,x24891),f479(x24893,x24894,x24895,x24896,x24892))
% 191.29/191.76 [2490]~E(x24901,x24902)+E(f579(x24901),f579(x24902))
% 191.29/191.76 [2491]~E(x24911,x24912)+E(f48(x24911),f48(x24912))
% 191.29/191.76 [2492]~E(x24921,x24922)+E(f669(x24921,x24923,x24924),f669(x24922,x24923,x24924))
% 191.29/191.76 [2493]~E(x24931,x24932)+E(f669(x24933,x24931,x24934),f669(x24933,x24932,x24934))
% 191.29/191.76 [2494]~E(x24941,x24942)+E(f669(x24943,x24944,x24941),f669(x24943,x24944,x24942))
% 191.29/191.76 [2495]~E(x24951,x24952)+E(f129(x24951),f129(x24952))
% 191.29/191.76 [2496]~E(x24961,x24962)+E(f217(x24961,x24963,x24964),f217(x24962,x24963,x24964))
% 191.29/191.76 [2497]~E(x24971,x24972)+E(f217(x24973,x24971,x24974),f217(x24973,x24972,x24974))
% 191.29/191.76 [2498]~E(x24981,x24982)+E(f217(x24983,x24984,x24981),f217(x24983,x24984,x24982))
% 191.29/191.76 [2499]~E(x24991,x24992)+E(f776(x24991),f776(x24992))
% 191.29/191.76 [2500]~E(x25001,x25002)+E(f223(x25001,x25003,x25004,x25005),f223(x25002,x25003,x25004,x25005))
% 191.29/191.76 [2501]~E(x25011,x25012)+E(f223(x25013,x25011,x25014,x25015),f223(x25013,x25012,x25014,x25015))
% 191.29/191.76 [2502]~E(x25021,x25022)+E(f223(x25023,x25024,x25021,x25025),f223(x25023,x25024,x25022,x25025))
% 191.29/191.76 [2503]~E(x25031,x25032)+E(f223(x25033,x25034,x25035,x25031),f223(x25033,x25034,x25035,x25032))
% 191.29/191.76 [2504]~E(x25041,x25042)+E(f527(x25041,x25043,x25044,x25045),f527(x25042,x25043,x25044,x25045))
% 191.29/191.76 [2505]~E(x25051,x25052)+E(f527(x25053,x25051,x25054,x25055),f527(x25053,x25052,x25054,x25055))
% 191.29/191.76 [2506]~E(x25061,x25062)+E(f527(x25063,x25064,x25061,x25065),f527(x25063,x25064,x25062,x25065))
% 191.29/191.76 [2507]~E(x25071,x25072)+E(f527(x25073,x25074,x25075,x25071),f527(x25073,x25074,x25075,x25072))
% 191.29/191.76 [2508]~E(x25081,x25082)+E(f804(x25081,x25083,x25084),f804(x25082,x25083,x25084))
% 191.29/191.76 [2509]~E(x25091,x25092)+E(f804(x25093,x25091,x25094),f804(x25093,x25092,x25094))
% 191.29/191.76 [2510]~E(x25101,x25102)+E(f804(x25103,x25104,x25101),f804(x25103,x25104,x25102))
% 191.29/191.76 [2511]~E(x25111,x25112)+E(f606(x25111,x25113,x25114),f606(x25112,x25113,x25114))
% 191.29/191.76 [2512]~E(x25121,x25122)+E(f606(x25123,x25121,x25124),f606(x25123,x25122,x25124))
% 191.29/191.76 [2513]~E(x25131,x25132)+E(f606(x25133,x25134,x25131),f606(x25133,x25134,x25132))
% 191.29/191.76 [2514]~E(x25141,x25142)+E(f521(x25141,x25143,x25144),f521(x25142,x25143,x25144))
% 191.29/191.76 [2515]~E(x25151,x25152)+E(f521(x25153,x25151,x25154),f521(x25153,x25152,x25154))
% 191.29/191.76 [2516]~E(x25161,x25162)+E(f521(x25163,x25164,x25161),f521(x25163,x25164,x25162))
% 191.29/191.76 [2517]~E(x25171,x25172)+E(f365(x25171,x25173,x25174,x25175,x25176),f365(x25172,x25173,x25174,x25175,x25176))
% 191.29/191.76 [2518]~E(x25181,x25182)+E(f365(x25183,x25181,x25184,x25185,x25186),f365(x25183,x25182,x25184,x25185,x25186))
% 191.29/191.76 [2519]~E(x25191,x25192)+E(f365(x25193,x25194,x25191,x25195,x25196),f365(x25193,x25194,x25192,x25195,x25196))
% 191.29/191.76 [2520]~E(x25201,x25202)+E(f365(x25203,x25204,x25205,x25201,x25206),f365(x25203,x25204,x25205,x25202,x25206))
% 191.29/191.76 [2521]~E(x25211,x25212)+E(f365(x25213,x25214,x25215,x25216,x25211),f365(x25213,x25214,x25215,x25216,x25212))
% 191.29/191.76 [2522]~E(x25221,x25222)+E(f589(x25221,x25223),f589(x25222,x25223))
% 191.29/191.76 [2523]~E(x25231,x25232)+E(f589(x25233,x25231),f589(x25233,x25232))
% 191.29/191.76 [2524]~E(x25241,x25242)+E(f744(x25241,x25243,x25244,x25245),f744(x25242,x25243,x25244,x25245))
% 191.29/191.76 [2525]~E(x25251,x25252)+E(f744(x25253,x25251,x25254,x25255),f744(x25253,x25252,x25254,x25255))
% 191.29/191.76 [2526]~E(x25261,x25262)+E(f744(x25263,x25264,x25261,x25265),f744(x25263,x25264,x25262,x25265))
% 191.29/191.76 [2527]~E(x25271,x25272)+E(f744(x25273,x25274,x25275,x25271),f744(x25273,x25274,x25275,x25272))
% 191.29/191.76 [2528]~E(x25281,x25282)+E(f747(x25281),f747(x25282))
% 191.29/191.76 [2529]~E(x25291,x25292)+E(f205(x25291,x25293,x25294,x25295),f205(x25292,x25293,x25294,x25295))
% 191.29/191.76 [2530]~E(x25301,x25302)+E(f205(x25303,x25301,x25304,x25305),f205(x25303,x25302,x25304,x25305))
% 191.29/191.76 [2531]~E(x25311,x25312)+E(f205(x25313,x25314,x25311,x25315),f205(x25313,x25314,x25312,x25315))
% 191.29/191.76 [2532]~E(x25321,x25322)+E(f205(x25323,x25324,x25325,x25321),f205(x25323,x25324,x25325,x25322))
% 191.29/191.76 [2533]~E(x25331,x25332)+E(f618(x25331,x25333),f618(x25332,x25333))
% 191.29/191.76 [2534]~E(x25341,x25342)+E(f618(x25343,x25341),f618(x25343,x25342))
% 191.29/191.76 [2535]~E(x25351,x25352)+E(f680(x25351,x25353),f680(x25352,x25353))
% 191.29/191.76 [2536]~E(x25361,x25362)+E(f680(x25363,x25361),f680(x25363,x25362))
% 191.29/191.76 [2537]~E(x25371,x25372)+E(f255(x25371,x25373,x25374,x25375,x25376),f255(x25372,x25373,x25374,x25375,x25376))
% 191.29/191.76 [2538]~E(x25381,x25382)+E(f255(x25383,x25381,x25384,x25385,x25386),f255(x25383,x25382,x25384,x25385,x25386))
% 191.29/191.76 [2539]~E(x25391,x25392)+E(f255(x25393,x25394,x25391,x25395,x25396),f255(x25393,x25394,x25392,x25395,x25396))
% 191.29/191.76 [2540]~E(x25401,x25402)+E(f255(x25403,x25404,x25405,x25401,x25406),f255(x25403,x25404,x25405,x25402,x25406))
% 191.29/191.76 [2541]~E(x25411,x25412)+E(f255(x25413,x25414,x25415,x25416,x25411),f255(x25413,x25414,x25415,x25416,x25412))
% 191.29/191.76 [2542]~E(x25421,x25422)+E(f583(x25421,x25423),f583(x25422,x25423))
% 191.29/191.76 [2543]~E(x25431,x25432)+E(f583(x25433,x25431),f583(x25433,x25432))
% 191.29/191.76 [2544]~E(x25441,x25442)+E(f786(x25441,x25443),f786(x25442,x25443))
% 191.29/191.76 [2545]~E(x25451,x25452)+E(f786(x25453,x25451),f786(x25453,x25452))
% 191.29/191.76 [2546]~E(x25461,x25462)+E(f750(x25461,x25463,x25464),f750(x25462,x25463,x25464))
% 191.29/191.76 [2547]~E(x25471,x25472)+E(f750(x25473,x25471,x25474),f750(x25473,x25472,x25474))
% 191.29/191.76 [2548]~E(x25481,x25482)+E(f750(x25483,x25484,x25481),f750(x25483,x25484,x25482))
% 191.29/191.76 [2549]~P1(x25491)+P1(x25492)+~E(x25491,x25492)
% 191.29/191.76 [2550]~P2(x25501)+P2(x25502)+~E(x25501,x25502)
% 191.29/191.76 [2551]~P100(x25511)+P100(x25512)+~E(x25511,x25512)
% 191.29/191.76 [2552]~P9(x25521)+P9(x25522)+~E(x25521,x25522)
% 191.29/191.76 [2553]~P3(x25531)+P3(x25532)+~E(x25531,x25532)
% 191.29/191.76 [2554]~P102(x25541)+P102(x25542)+~E(x25541,x25542)
% 191.29/191.76 [2555]~P7(x25551)+P7(x25552)+~E(x25551,x25552)
% 191.29/191.76 [2556]~P4(x25561)+P4(x25562)+~E(x25561,x25562)
% 191.29/191.76 [2557]P50(x25572,x25573,x25574,x25575)+~E(x25571,x25572)+~P50(x25571,x25573,x25574,x25575)
% 191.29/191.76 [2558]P50(x25583,x25582,x25584,x25585)+~E(x25581,x25582)+~P50(x25583,x25581,x25584,x25585)
% 191.29/191.76 [2559]P50(x25593,x25594,x25592,x25595)+~E(x25591,x25592)+~P50(x25593,x25594,x25591,x25595)
% 191.29/191.76 [2560]P50(x25603,x25604,x25605,x25602)+~E(x25601,x25602)+~P50(x25603,x25604,x25605,x25601)
% 191.29/191.76 [2561]~P93(x25611)+P93(x25612)+~E(x25611,x25612)
% 191.29/191.76 [2562]~P5(x25621)+P5(x25622)+~E(x25621,x25622)
% 191.29/191.76 [2563]P28(x25632,x25633,x25634)+~E(x25631,x25632)+~P28(x25631,x25633,x25634)
% 191.29/191.76 [2564]P28(x25643,x25642,x25644)+~E(x25641,x25642)+~P28(x25643,x25641,x25644)
% 191.29/191.76 [2565]P28(x25653,x25654,x25652)+~E(x25651,x25652)+~P28(x25653,x25654,x25651)
% 191.29/191.76 [2566]~P137(x25661)+P137(x25662)+~E(x25661,x25662)
% 191.29/191.76 [2567]~P66(x25671)+P66(x25672)+~E(x25671,x25672)
% 191.29/191.76 [2568]~P78(x25681)+P78(x25682)+~E(x25681,x25682)
% 191.29/191.76 [2569]~P111(x25691)+P111(x25692)+~E(x25691,x25692)
% 191.29/191.76 [2570]~P67(x25701)+P67(x25702)+~E(x25701,x25702)
% 191.29/191.76 [2571]P39(x25712,x25713,x25714,x25715)+~E(x25711,x25712)+~P39(x25711,x25713,x25714,x25715)
% 191.29/191.76 [2572]P39(x25723,x25722,x25724,x25725)+~E(x25721,x25722)+~P39(x25723,x25721,x25724,x25725)
% 191.29/191.76 [2573]P39(x25733,x25734,x25732,x25735)+~E(x25731,x25732)+~P39(x25733,x25734,x25731,x25735)
% 191.29/191.76 [2574]P39(x25743,x25744,x25745,x25742)+~E(x25741,x25742)+~P39(x25743,x25744,x25745,x25741)
% 191.29/191.76 [2575]~P110(x25751)+P110(x25752)+~E(x25751,x25752)
% 191.29/191.76 [2576]~P68(x25761)+P68(x25762)+~E(x25761,x25762)
% 191.29/191.76 [2577]~P73(x25771)+P73(x25772)+~E(x25771,x25772)
% 191.29/191.76 [2578]~P62(x25781)+P62(x25782)+~E(x25781,x25782)
% 191.29/191.76 [2579]~P119(x25791)+P119(x25792)+~E(x25791,x25792)
% 191.29/191.76 [2580]~P91(x25801)+P91(x25802)+~E(x25801,x25802)
% 191.29/191.76 [2581]~P74(x25811)+P74(x25812)+~E(x25811,x25812)
% 191.29/191.76 [2582]~P85(x25821)+P85(x25822)+~E(x25821,x25822)
% 191.29/191.76 [2583]P140(x25832,x25833,x25834)+~E(x25831,x25832)+~P140(x25831,x25833,x25834)
% 191.29/191.76 [2584]P140(x25843,x25842,x25844)+~E(x25841,x25842)+~P140(x25843,x25841,x25844)
% 191.29/191.76 [2585]P140(x25853,x25854,x25852)+~E(x25851,x25852)+~P140(x25853,x25854,x25851)
% 191.29/191.76 [2586]~P133(x25861)+P133(x25862)+~E(x25861,x25862)
% 191.29/191.76 [2587]P18(x25872,x25873)+~E(x25871,x25872)+~P18(x25871,x25873)
% 191.29/191.76 [2588]P18(x25883,x25882)+~E(x25881,x25882)+~P18(x25883,x25881)
% 191.29/191.76 [2589]~P99(x25891)+P99(x25892)+~E(x25891,x25892)
% 191.29/191.76 [2590]~P63(x25901)+P63(x25902)+~E(x25901,x25902)
% 191.29/191.76 [2591]~P80(x25911)+P80(x25912)+~E(x25911,x25912)
% 191.29/191.76 [2592]~P38(x25921)+P38(x25922)+~E(x25921,x25922)
% 191.29/191.76 [2593]~P117(x25931)+P117(x25932)+~E(x25931,x25932)
% 191.29/191.76 [2594]P141(x25942,x25943,x25944)+~E(x25941,x25942)+~P141(x25941,x25943,x25944)
% 191.29/191.76 [2595]P141(x25953,x25952,x25954)+~E(x25951,x25952)+~P141(x25953,x25951,x25954)
% 191.29/191.76 [2596]P141(x25963,x25964,x25962)+~E(x25961,x25962)+~P141(x25963,x25964,x25961)
% 191.29/191.76 [2597]~P81(x25971)+P81(x25972)+~E(x25971,x25972)
% 191.29/191.76 [2598]~P132(x25981)+P132(x25982)+~E(x25981,x25982)
% 191.29/191.76 [2599]P29(x25992,x25993,x25994,x25995)+~E(x25991,x25992)+~P29(x25991,x25993,x25994,x25995)
% 191.29/191.76 [2600]P29(x26003,x26002,x26004,x26005)+~E(x26001,x26002)+~P29(x26003,x26001,x26004,x26005)
% 191.29/191.76 [2601]P29(x26013,x26014,x26012,x26015)+~E(x26011,x26012)+~P29(x26013,x26014,x26011,x26015)
% 191.29/191.76 [2602]P29(x26023,x26024,x26025,x26022)+~E(x26021,x26022)+~P29(x26023,x26024,x26025,x26021)
% 191.29/191.76 [2603]~P89(x26031)+P89(x26032)+~E(x26031,x26032)
% 191.29/191.76 [2604]~P88(x26041)+P88(x26042)+~E(x26041,x26042)
% 191.29/191.76 [2605]P55(x26052,x26053,x26054,x26055,x26056)+~E(x26051,x26052)+~P55(x26051,x26053,x26054,x26055,x26056)
% 191.29/191.76 [2606]P55(x26063,x26062,x26064,x26065,x26066)+~E(x26061,x26062)+~P55(x26063,x26061,x26064,x26065,x26066)
% 191.29/191.76 [2607]P55(x26073,x26074,x26072,x26075,x26076)+~E(x26071,x26072)+~P55(x26073,x26074,x26071,x26075,x26076)
% 191.29/191.76 [2608]P55(x26083,x26084,x26085,x26082,x26086)+~E(x26081,x26082)+~P55(x26083,x26084,x26085,x26081,x26086)
% 191.29/191.76 [2609]P55(x26093,x26094,x26095,x26096,x26092)+~E(x26091,x26092)+~P55(x26093,x26094,x26095,x26096,x26091)
% 191.29/191.76 [2610]~P86(x26101)+P86(x26102)+~E(x26101,x26102)
% 191.29/191.76 [2611]~P103(x26111)+P103(x26112)+~E(x26111,x26112)
% 191.29/191.76 [2612]P36(x26122,x26123)+~E(x26121,x26122)+~P36(x26121,x26123)
% 191.29/191.76 [2613]P36(x26133,x26132)+~E(x26131,x26132)+~P36(x26133,x26131)
% 191.29/191.76 [2614]~P61(x26141)+P61(x26142)+~E(x26141,x26142)
% 191.29/191.76 [2615]~P77(x26151)+P77(x26152)+~E(x26151,x26152)
% 191.29/191.76 [2616]P22(x26162,x26163,x26164)+~E(x26161,x26162)+~P22(x26161,x26163,x26164)
% 191.29/191.76 [2617]P22(x26173,x26172,x26174)+~E(x26171,x26172)+~P22(x26173,x26171,x26174)
% 191.29/191.76 [2618]P22(x26183,x26184,x26182)+~E(x26181,x26182)+~P22(x26183,x26184,x26181)
% 191.29/191.76 [2619]P23(x26192,x26193,x26194,x26195)+~E(x26191,x26192)+~P23(x26191,x26193,x26194,x26195)
% 191.29/191.76 [2620]P23(x26203,x26202,x26204,x26205)+~E(x26201,x26202)+~P23(x26203,x26201,x26204,x26205)
% 191.29/191.76 [2621]P23(x26213,x26214,x26212,x26215)+~E(x26211,x26212)+~P23(x26213,x26214,x26211,x26215)
% 191.29/191.76 [2622]P23(x26223,x26224,x26225,x26222)+~E(x26221,x26222)+~P23(x26223,x26224,x26225,x26221)
% 191.29/191.76 [2623]~P90(x26231)+P90(x26232)+~E(x26231,x26232)
% 191.29/191.76 [2624]~P79(x26241)+P79(x26242)+~E(x26241,x26242)
% 191.29/191.76 [2625]P53(x26252,x26253,x26254)+~E(x26251,x26252)+~P53(x26251,x26253,x26254)
% 191.29/191.76 [2626]P53(x26263,x26262,x26264)+~E(x26261,x26262)+~P53(x26263,x26261,x26264)
% 191.29/191.76 [2627]P53(x26273,x26274,x26272)+~E(x26271,x26272)+~P53(x26273,x26274,x26271)
% 191.29/191.76 [2628]~P60(x26281)+P60(x26282)+~E(x26281,x26282)
% 191.29/191.76 [2629]~P75(x26291)+P75(x26292)+~E(x26291,x26292)
% 191.29/191.76 [2630]P47(x26302,x26303,x26304)+~E(x26301,x26302)+~P47(x26301,x26303,x26304)
% 191.29/191.76 [2631]P47(x26313,x26312,x26314)+~E(x26311,x26312)+~P47(x26313,x26311,x26314)
% 191.29/191.76 [2632]P47(x26323,x26324,x26322)+~E(x26321,x26322)+~P47(x26323,x26324,x26321)
% 191.29/191.76 [2633]P56(x26332,x26333)+~E(x26331,x26332)+~P56(x26331,x26333)
% 191.29/191.76 [2634]P56(x26343,x26342)+~E(x26341,x26342)+~P56(x26343,x26341)
% 191.29/191.76 [2635]P12(x26352,x26353,x26354)+~E(x26351,x26352)+~P12(x26351,x26353,x26354)
% 191.29/191.76 [2636]P12(x26363,x26362,x26364)+~E(x26361,x26362)+~P12(x26363,x26361,x26364)
% 191.29/191.76 [2637]P12(x26373,x26374,x26372)+~E(x26371,x26372)+~P12(x26373,x26374,x26371)
% 191.29/191.76 [2638]~P65(x26381)+P65(x26382)+~E(x26381,x26382)
% 191.29/191.76 [2639]~P129(x26391)+P129(x26392)+~E(x26391,x26392)
% 191.29/191.76 [2640]P20(x26402,x26403,x26404)+~E(x26401,x26402)+~P20(x26401,x26403,x26404)
% 191.29/191.76 [2641]P20(x26413,x26412,x26414)+~E(x26411,x26412)+~P20(x26413,x26411,x26414)
% 191.29/191.76 [2642]P20(x26423,x26424,x26422)+~E(x26421,x26422)+~P20(x26423,x26424,x26421)
% 191.29/191.76 [2643]~P92(x26431)+P92(x26432)+~E(x26431,x26432)
% 191.29/191.76 [2644]~P120(x26441)+P120(x26442)+~E(x26441,x26442)
% 191.29/191.76 [2645]~P121(x26451)+P121(x26452)+~E(x26451,x26452)
% 191.29/191.76 [2646]~P64(x26461)+P64(x26462)+~E(x26461,x26462)
% 191.29/191.76 [2647]~P112(x26471)+P112(x26472)+~E(x26471,x26472)
% 191.29/191.76 [2648]P32(x26482,x26483,x26484)+~E(x26481,x26482)+~P32(x26481,x26483,x26484)
% 191.29/191.76 [2649]P32(x26493,x26492,x26494)+~E(x26491,x26492)+~P32(x26493,x26491,x26494)
% 191.29/191.76 [2650]P32(x26503,x26504,x26502)+~E(x26501,x26502)+~P32(x26503,x26504,x26501)
% 191.29/191.76 [2651]~P69(x26511)+P69(x26512)+~E(x26511,x26512)
% 191.29/191.76 [2652]~P70(x26521)+P70(x26522)+~E(x26521,x26522)
% 191.29/191.76 [2653]~P105(x26531)+P105(x26532)+~E(x26531,x26532)
% 191.29/191.76 [2654]P27(x26542,x26543,x26544,x26545,x26546,x26547)+~E(x26541,x26542)+~P27(x26541,x26543,x26544,x26545,x26546,x26547)
% 191.29/191.76 [2655]P27(x26553,x26552,x26554,x26555,x26556,x26557)+~E(x26551,x26552)+~P27(x26553,x26551,x26554,x26555,x26556,x26557)
% 191.29/191.76 [2656]P27(x26563,x26564,x26562,x26565,x26566,x26567)+~E(x26561,x26562)+~P27(x26563,x26564,x26561,x26565,x26566,x26567)
% 191.29/191.76 [2657]P27(x26573,x26574,x26575,x26572,x26576,x26577)+~E(x26571,x26572)+~P27(x26573,x26574,x26575,x26571,x26576,x26577)
% 191.29/191.76 [2658]P27(x26583,x26584,x26585,x26586,x26582,x26587)+~E(x26581,x26582)+~P27(x26583,x26584,x26585,x26586,x26581,x26587)
% 191.29/191.76 [2659]P27(x26593,x26594,x26595,x26596,x26597,x26592)+~E(x26591,x26592)+~P27(x26593,x26594,x26595,x26596,x26597,x26591)
% 191.29/191.76 [2660]~P59(x26601)+P59(x26602)+~E(x26601,x26602)
% 191.29/191.76 [2661]P57(x26612,x26613,x26614,x26615)+~E(x26611,x26612)+~P57(x26611,x26613,x26614,x26615)
% 191.29/191.76 [2662]P57(x26623,x26622,x26624,x26625)+~E(x26621,x26622)+~P57(x26623,x26621,x26624,x26625)
% 191.29/191.76 [2663]P57(x26633,x26634,x26632,x26635)+~E(x26631,x26632)+~P57(x26633,x26634,x26631,x26635)
% 191.29/191.76 [2664]P57(x26643,x26644,x26645,x26642)+~E(x26641,x26642)+~P57(x26643,x26644,x26645,x26641)
% 191.29/191.76 [2665]P26(x26652,x26653,x26654,x26655,x26656,x26657)+~E(x26651,x26652)+~P26(x26651,x26653,x26654,x26655,x26656,x26657)
% 191.29/191.76 [2666]P26(x26663,x26662,x26664,x26665,x26666,x26667)+~E(x26661,x26662)+~P26(x26663,x26661,x26664,x26665,x26666,x26667)
% 191.29/191.76 [2667]P26(x26673,x26674,x26672,x26675,x26676,x26677)+~E(x26671,x26672)+~P26(x26673,x26674,x26671,x26675,x26676,x26677)
% 191.29/191.76 [2668]P26(x26683,x26684,x26685,x26682,x26686,x26687)+~E(x26681,x26682)+~P26(x26683,x26684,x26685,x26681,x26686,x26687)
% 191.29/191.76 [2669]P26(x26693,x26694,x26695,x26696,x26692,x26697)+~E(x26691,x26692)+~P26(x26693,x26694,x26695,x26696,x26691,x26697)
% 191.29/191.76 [2670]P26(x26703,x26704,x26705,x26706,x26707,x26702)+~E(x26701,x26702)+~P26(x26703,x26704,x26705,x26706,x26707,x26701)
% 191.29/191.76 [2671]~P76(x26711)+P76(x26712)+~E(x26711,x26712)
% 191.29/191.76 [2672]~P98(x26721)+P98(x26722)+~E(x26721,x26722)
% 191.29/191.76 [2673]~P136(x26731)+P136(x26732)+~E(x26731,x26732)
% 191.29/191.76 [2674]~P87(x26741)+P87(x26742)+~E(x26741,x26742)
% 191.29/191.76 [2675]~P10(x26751)+P10(x26752)+~E(x26751,x26752)
% 191.29/191.76 [2676]~P104(x26761)+P104(x26762)+~E(x26761,x26762)
% 191.29/191.76 [2677]P58(x26772,x26773)+~E(x26771,x26772)+~P58(x26771,x26773)
% 191.29/191.76 [2678]P58(x26783,x26782)+~E(x26781,x26782)+~P58(x26783,x26781)
% 191.29/191.76 [2679]~P6(x26791)+P6(x26792)+~E(x26791,x26792)
% 191.29/191.76 [2680]~P122(x26801)+P122(x26802)+~E(x26801,x26802)
% 191.29/191.76 [2681]P31(x26812,x26813,x26814)+~E(x26811,x26812)+~P31(x26811,x26813,x26814)
% 191.29/191.76 [2682]P31(x26823,x26822,x26824)+~E(x26821,x26822)+~P31(x26823,x26821,x26824)
% 191.29/191.76 [2683]P31(x26833,x26834,x26832)+~E(x26831,x26832)+~P31(x26833,x26834,x26831)
% 191.29/191.76 [2684]P33(x26842,x26843)+~E(x26841,x26842)+~P33(x26841,x26843)
% 191.29/191.76 [2685]P33(x26853,x26852)+~E(x26851,x26852)+~P33(x26853,x26851)
% 191.29/191.76 [2686]~P134(x26861)+P134(x26862)+~E(x26861,x26862)
% 191.29/191.76 [2687]~P127(x26871)+P127(x26872)+~E(x26871,x26872)
% 191.29/191.76 [2688]P42(x26882,x26883)+~E(x26881,x26882)+~P42(x26881,x26883)
% 191.29/191.76 [2689]P42(x26893,x26892)+~E(x26891,x26892)+~P42(x26893,x26891)
% 191.29/191.76 [2690]P25(x26902,x26903,x26904,x26905,x26906)+~E(x26901,x26902)+~P25(x26901,x26903,x26904,x26905,x26906)
% 191.29/191.76 [2691]P25(x26913,x26912,x26914,x26915,x26916)+~E(x26911,x26912)+~P25(x26913,x26911,x26914,x26915,x26916)
% 191.29/191.76 [2692]P25(x26923,x26924,x26922,x26925,x26926)+~E(x26921,x26922)+~P25(x26923,x26924,x26921,x26925,x26926)
% 191.29/191.76 [2693]P25(x26933,x26934,x26935,x26932,x26936)+~E(x26931,x26932)+~P25(x26933,x26934,x26935,x26931,x26936)
% 191.29/191.76 [2694]P25(x26943,x26944,x26945,x26946,x26942)+~E(x26941,x26942)+~P25(x26943,x26944,x26945,x26946,x26941)
% 191.29/191.76 [2695]~P138(x26951)+P138(x26952)+~E(x26951,x26952)
% 191.29/191.76 [2696]P45(x26962,x26963,x26964)+~E(x26961,x26962)+~P45(x26961,x26963,x26964)
% 191.29/191.76 [2697]P45(x26973,x26972,x26974)+~E(x26971,x26972)+~P45(x26973,x26971,x26974)
% 191.29/191.76 [2698]P45(x26983,x26984,x26982)+~E(x26981,x26982)+~P45(x26983,x26984,x26981)
% 191.29/191.76 [2699]P37(x26992,x26993)+~E(x26991,x26992)+~P37(x26991,x26993)
% 191.29/191.76 [2700]P37(x27003,x27002)+~E(x27001,x27002)+~P37(x27003,x27001)
% 191.29/191.76 [2701]~P109(x27011)+P109(x27012)+~E(x27011,x27012)
% 191.29/191.76 [2702]P52(x27022,x27023,x27024,x27025)+~E(x27021,x27022)+~P52(x27021,x27023,x27024,x27025)
% 191.29/191.76 [2703]P52(x27033,x27032,x27034,x27035)+~E(x27031,x27032)+~P52(x27033,x27031,x27034,x27035)
% 191.29/191.76 [2704]P52(x27043,x27044,x27042,x27045)+~E(x27041,x27042)+~P52(x27043,x27044,x27041,x27045)
% 191.29/191.76 [2705]P52(x27053,x27054,x27055,x27052)+~E(x27051,x27052)+~P52(x27053,x27054,x27055,x27051)
% 191.29/191.76 [2706]~P123(x27061)+P123(x27062)+~E(x27061,x27062)
% 191.29/191.76 [2707]~P135(x27071)+P135(x27072)+~E(x27071,x27072)
% 191.29/191.76 [2708]~P43(x27081)+P43(x27082)+~E(x27081,x27082)
% 191.29/191.76 [2709]~P139(x27091)+P139(x27092)+~E(x27091,x27092)
% 191.29/191.76 [2710]~P118(x27101)+P118(x27102)+~E(x27101,x27102)
% 191.29/191.76 [2711]~P94(x27111)+P94(x27112)+~E(x27111,x27112)
% 191.29/191.76 [2712]~P113(x27121)+P113(x27122)+~E(x27121,x27122)
% 191.29/191.76 [2713]P51(x27132,x27133,x27134,x27135,x27136,x27137,x27138)+~E(x27131,x27132)+~P51(x27131,x27133,x27134,x27135,x27136,x27137,x27138)
% 191.29/191.76 [2714]P51(x27143,x27142,x27144,x27145,x27146,x27147,x27148)+~E(x27141,x27142)+~P51(x27143,x27141,x27144,x27145,x27146,x27147,x27148)
% 191.29/191.76 [2715]P51(x27153,x27154,x27152,x27155,x27156,x27157,x27158)+~E(x27151,x27152)+~P51(x27153,x27154,x27151,x27155,x27156,x27157,x27158)
% 191.29/191.76 [2716]P51(x27163,x27164,x27165,x27162,x27166,x27167,x27168)+~E(x27161,x27162)+~P51(x27163,x27164,x27165,x27161,x27166,x27167,x27168)
% 191.29/191.76 [2717]P51(x27173,x27174,x27175,x27176,x27172,x27177,x27178)+~E(x27171,x27172)+~P51(x27173,x27174,x27175,x27176,x27171,x27177,x27178)
% 191.29/191.76 [2718]P51(x27183,x27184,x27185,x27186,x27187,x27182,x27188)+~E(x27181,x27182)+~P51(x27183,x27184,x27185,x27186,x27187,x27181,x27188)
% 191.29/191.76 [2719]P51(x27193,x27194,x27195,x27196,x27197,x27198,x27192)+~E(x27191,x27192)+~P51(x27193,x27194,x27195,x27196,x27197,x27198,x27191)
% 191.29/191.76 [2720]~P82(x27201)+P82(x27202)+~E(x27201,x27202)
% 191.29/191.76 [2721]~P115(x27211)+P115(x27212)+~E(x27211,x27212)
% 191.29/191.76 [2722]P14(x27222,x27223,x27224)+~E(x27221,x27222)+~P14(x27221,x27223,x27224)
% 191.29/191.76 [2723]P14(x27233,x27232,x27234)+~E(x27231,x27232)+~P14(x27233,x27231,x27234)
% 191.29/191.76 [2724]P14(x27243,x27244,x27242)+~E(x27241,x27242)+~P14(x27243,x27244,x27241)
% 191.29/191.76 [2725]~P130(x27251)+P130(x27252)+~E(x27251,x27252)
% 191.29/191.76 [2726]P34(x27262,x27263,x27264,x27265)+~E(x27261,x27262)+~P34(x27261,x27263,x27264,x27265)
% 191.29/191.76 [2727]P34(x27273,x27272,x27274,x27275)+~E(x27271,x27272)+~P34(x27273,x27271,x27274,x27275)
% 191.29/191.76 [2728]P34(x27283,x27284,x27282,x27285)+~E(x27281,x27282)+~P34(x27283,x27284,x27281,x27285)
% 191.29/191.76 [2729]P34(x27293,x27294,x27295,x27292)+~E(x27291,x27292)+~P34(x27293,x27294,x27295,x27291)
% 191.29/191.76 [2730]~P124(x27301)+P124(x27302)+~E(x27301,x27302)
% 191.29/191.76 [2731]P19(x27312,x27313,x27314)+~E(x27311,x27312)+~P19(x27311,x27313,x27314)
% 191.29/191.76 [2732]P19(x27323,x27322,x27324)+~E(x27321,x27322)+~P19(x27323,x27321,x27324)
% 191.29/191.76 [2733]P19(x27333,x27334,x27332)+~E(x27331,x27332)+~P19(x27333,x27334,x27331)
% 191.29/191.76 [2734]~P128(x27341)+P128(x27342)+~E(x27341,x27342)
% 191.29/191.76 [2735]~P131(x27351)+P131(x27352)+~E(x27351,x27352)
% 191.29/191.76 [2736]P46(x27362,x27363,x27364)+~E(x27361,x27362)+~P46(x27361,x27363,x27364)
% 191.29/191.76 [2737]P46(x27373,x27372,x27374)+~E(x27371,x27372)+~P46(x27373,x27371,x27374)
% 191.29/191.76 [2738]P46(x27383,x27384,x27382)+~E(x27381,x27382)+~P46(x27383,x27384,x27381)
% 191.29/191.76 [2739]P17(x27392,x27393,x27394,x27395,x27396,x27397)+~E(x27391,x27392)+~P17(x27391,x27393,x27394,x27395,x27396,x27397)
% 191.29/191.76 [2740]P17(x27403,x27402,x27404,x27405,x27406,x27407)+~E(x27401,x27402)+~P17(x27403,x27401,x27404,x27405,x27406,x27407)
% 191.29/191.76 [2741]P17(x27413,x27414,x27412,x27415,x27416,x27417)+~E(x27411,x27412)+~P17(x27413,x27414,x27411,x27415,x27416,x27417)
% 191.29/191.76 [2742]P17(x27423,x27424,x27425,x27422,x27426,x27427)+~E(x27421,x27422)+~P17(x27423,x27424,x27425,x27421,x27426,x27427)
% 191.29/191.76 [2743]P17(x27433,x27434,x27435,x27436,x27432,x27437)+~E(x27431,x27432)+~P17(x27433,x27434,x27435,x27436,x27431,x27437)
% 191.29/191.76 [2744]P17(x27443,x27444,x27445,x27446,x27447,x27442)+~E(x27441,x27442)+~P17(x27443,x27444,x27445,x27446,x27447,x27441)
% 191.29/191.76 [2745]P41(x27452,x27453,x27454,x27455,x27456,x27457)+~E(x27451,x27452)+~P41(x27451,x27453,x27454,x27455,x27456,x27457)
% 191.29/191.76 [2746]P41(x27463,x27462,x27464,x27465,x27466,x27467)+~E(x27461,x27462)+~P41(x27463,x27461,x27464,x27465,x27466,x27467)
% 191.29/191.76 [2747]P41(x27473,x27474,x27472,x27475,x27476,x27477)+~E(x27471,x27472)+~P41(x27473,x27474,x27471,x27475,x27476,x27477)
% 191.29/191.76 [2748]P41(x27483,x27484,x27485,x27482,x27486,x27487)+~E(x27481,x27482)+~P41(x27483,x27484,x27485,x27481,x27486,x27487)
% 191.29/191.76 [2749]P41(x27493,x27494,x27495,x27496,x27492,x27497)+~E(x27491,x27492)+~P41(x27493,x27494,x27495,x27496,x27491,x27497)
% 191.29/191.76 [2750]P41(x27503,x27504,x27505,x27506,x27507,x27502)+~E(x27501,x27502)+~P41(x27503,x27504,x27505,x27506,x27507,x27501)
% 191.29/191.76 [2751]P24(x27512,x27513,x27514,x27515)+~E(x27511,x27512)+~P24(x27511,x27513,x27514,x27515)
% 191.29/191.76 [2752]P24(x27523,x27522,x27524,x27525)+~E(x27521,x27522)+~P24(x27523,x27521,x27524,x27525)
% 191.29/191.76 [2753]P24(x27533,x27534,x27532,x27535)+~E(x27531,x27532)+~P24(x27533,x27534,x27531,x27535)
% 191.29/191.76 [2754]P24(x27543,x27544,x27545,x27542)+~E(x27541,x27542)+~P24(x27543,x27544,x27545,x27541)
% 191.29/191.76 [2755]~P13(x27551)+P13(x27552)+~E(x27551,x27552)
% 191.29/191.76 [2756]P142(x27562,x27563)+~E(x27561,x27562)+~P142(x27561,x27563)
% 191.29/191.76 [2757]P142(x27573,x27572)+~E(x27571,x27572)+~P142(x27573,x27571)
% 191.29/191.76 [2758]~P114(x27581)+P114(x27582)+~E(x27581,x27582)
% 191.29/191.76 [2759]P30(x27592,x27593)+~E(x27591,x27592)+~P30(x27591,x27593)
% 191.29/191.76 [2760]P30(x27603,x27602)+~E(x27601,x27602)+~P30(x27603,x27601)
% 191.29/191.76 [2761]~P125(x27611)+P125(x27612)+~E(x27611,x27612)
% 191.29/191.76 [2762]~P8(x27621)+P8(x27622)+~E(x27621,x27622)
% 191.29/191.76 [2763]~P97(x27631)+P97(x27632)+~E(x27631,x27632)
% 191.29/191.76 [2764]~P108(x27641)+P108(x27642)+~E(x27641,x27642)
% 191.29/191.76 [2765]P16(x27652,x27653,x27654,x27655)+~E(x27651,x27652)+~P16(x27651,x27653,x27654,x27655)
% 191.29/191.76 [2766]P16(x27663,x27662,x27664,x27665)+~E(x27661,x27662)+~P16(x27663,x27661,x27664,x27665)
% 191.29/191.76 [2767]P16(x27673,x27674,x27672,x27675)+~E(x27671,x27672)+~P16(x27673,x27674,x27671,x27675)
% 191.29/191.76 [2768]P16(x27683,x27684,x27685,x27682)+~E(x27681,x27682)+~P16(x27683,x27684,x27685,x27681)
% 191.29/191.76 [2769]~P126(x27691)+P126(x27692)+~E(x27691,x27692)
% 191.29/191.76 [2770]P11(x27702,x27703)+~E(x27701,x27702)+~P11(x27701,x27703)
% 191.29/191.76 [2771]P11(x27713,x27712)+~E(x27711,x27712)+~P11(x27713,x27711)
% 191.29/191.76 [2772]~P95(x27721)+P95(x27722)+~E(x27721,x27722)
% 191.29/191.76 [2773]P54(x27732,x27733,x27734)+~E(x27731,x27732)+~P54(x27731,x27733,x27734)
% 191.29/191.76 [2774]P54(x27743,x27742,x27744)+~E(x27741,x27742)+~P54(x27743,x27741,x27744)
% 191.29/191.76 [2775]P54(x27753,x27754,x27752)+~E(x27751,x27752)+~P54(x27753,x27754,x27751)
% 191.29/191.76 [2776]~P101(x27761)+P101(x27762)+~E(x27761,x27762)
% 191.29/191.76 [2777]P21(x27772,x27773,x27774)+~E(x27771,x27772)+~P21(x27771,x27773,x27774)
% 191.29/191.76 [2778]P21(x27783,x27782,x27784)+~E(x27781,x27782)+~P21(x27783,x27781,x27784)
% 191.29/191.76 [2779]P21(x27793,x27794,x27792)+~E(x27791,x27792)+~P21(x27793,x27794,x27791)
% 191.29/191.76 [2780]~P84(x27801)+P84(x27802)+~E(x27801,x27802)
% 191.29/191.76 [2781]~P83(x27811)+P83(x27812)+~E(x27811,x27812)
% 191.29/191.76 [2782]~P71(x27821)+P71(x27822)+~E(x27821,x27822)
% 191.29/191.76 [2783]~P72(x27831)+P72(x27832)+~E(x27831,x27832)
% 191.29/191.76 [2784]~P96(x27841)+P96(x27842)+~E(x27841,x27842)
% 191.29/191.76 [2785]P15(x27852,x27853,x27854,x27855,x27856)+~E(x27851,x27852)+~P15(x27851,x27853,x27854,x27855,x27856)
% 191.29/191.76 [2786]P15(x27863,x27862,x27864,x27865,x27866)+~E(x27861,x27862)+~P15(x27863,x27861,x27864,x27865,x27866)
% 191.29/191.76 [2787]P15(x27873,x27874,x27872,x27875,x27876)+~E(x27871,x27872)+~P15(x27873,x27874,x27871,x27875,x27876)
% 191.29/191.76 [2788]P15(x27883,x27884,x27885,x27882,x27886)+~E(x27881,x27882)+~P15(x27883,x27884,x27885,x27881,x27886)
% 191.29/191.76 [2789]P15(x27893,x27894,x27895,x27896,x27892)+~E(x27891,x27892)+~P15(x27893,x27894,x27895,x27896,x27891)
% 191.29/191.76 [2790]P49(x27902,x27903)+~E(x27901,x27902)+~P49(x27901,x27903)
% 191.29/191.76 [2791]P49(x27913,x27912)+~E(x27911,x27912)+~P49(x27913,x27911)
% 191.29/191.76 [2792]~P106(x27921)+P106(x27922)+~E(x27921,x27922)
% 191.29/191.76 [2793]P40(x27932,x27933,x27934,x27935)+~E(x27931,x27932)+~P40(x27931,x27933,x27934,x27935)
% 191.29/191.76 [2794]P40(x27943,x27942,x27944,x27945)+~E(x27941,x27942)+~P40(x27943,x27941,x27944,x27945)
% 191.29/191.76 [2795]P40(x27953,x27954,x27952,x27955)+~E(x27951,x27952)+~P40(x27953,x27954,x27951,x27955)
% 191.29/191.76 [2796]P40(x27963,x27964,x27965,x27962)+~E(x27961,x27962)+~P40(x27963,x27964,x27965,x27961)
% 191.29/191.76 [2797]P48(x27972,x27973)+~E(x27971,x27972)+~P48(x27971,x27973)
% 191.29/191.76 [2798]P48(x27983,x27982)+~E(x27981,x27982)+~P48(x27983,x27981)
% 191.29/191.76 [2799]P44(x27992,x27993)+~E(x27991,x27992)+~P44(x27991,x27993)
% 191.29/191.76 [2800]P44(x28003,x28002)+~E(x28001,x28002)+~P44(x28003,x28001)
% 191.29/191.76 [2801]~P35(x28011)+P35(x28012)+~E(x28011,x28012)
% 191.29/191.76 [2802]~P107(x28021)+P107(x28022)+~E(x28021,x28022)
% 191.29/191.76 [2803]~P116(x28031)+P116(x28032)+~E(x28031,x28032)
% 191.29/191.76
% 191.29/191.76 %-------------------------------------------
% 191.32/191.79 cnf(10038,plain,
% 191.32/191.79 (E(f37(x100381,x100382,x100383,x100384,x100385,x100386,x100387,x100388,x100389,a25),x100382)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(10041,plain,
% 191.32/191.79 (E(f37(x100411,x100412,x100413,x100414,x100415,x100416,x100417,x100418,x100419,a25),x100412)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(10044,plain,
% 191.32/191.79 (~E(f773(a114,x100441),x100441)),
% 191.32/191.79 inference(rename_variables,[],[4364])).
% 191.32/191.79 cnf(10047,plain,
% 191.32/191.79 (E(f37(x100471,x100472,x100473,x100474,x100475,x100476,x100477,x100478,x100479,a25),x100472)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(10054,plain,
% 191.32/191.79 (~E(f773(a114,x100541),x100541)),
% 191.32/191.79 inference(rename_variables,[],[4364])).
% 191.32/191.79 cnf(10065,plain,
% 191.32/191.79 (~E(f773(a114,x100651),x100651)),
% 191.32/191.79 inference(rename_variables,[],[4364])).
% 191.32/191.79 cnf(10068,plain,
% 191.32/191.79 (~P1(f773(f64(x100681,x100682,f180(f855(x100681,a841))),x100683))),
% 191.32/191.79 inference(rename_variables,[],[4475])).
% 191.32/191.79 cnf(10071,plain,
% 191.32/191.79 (~P1(f773(f64(x100711,x100712,f180(f855(x100711,a841))),x100713))),
% 191.32/191.79 inference(rename_variables,[],[4475])).
% 191.32/191.79 cnf(10074,plain,
% 191.32/191.79 (~E(f773(a114,x100741),x100741)),
% 191.32/191.79 inference(rename_variables,[],[4364])).
% 191.32/191.79 cnf(10077,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x100771),f2(a847)))),
% 191.32/191.79 inference(rename_variables,[],[4452])).
% 191.32/191.79 cnf(10080,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x100801),f2(a847)))),
% 191.32/191.79 inference(rename_variables,[],[4452])).
% 191.32/191.79 cnf(10097,plain,
% 191.32/191.79 (~P1(f773(f773(f232(a847),f773(a114,x100971)),x100971))),
% 191.32/191.79 inference(rename_variables,[],[4461])).
% 191.32/191.79 cnf(10100,plain,
% 191.32/191.79 (~E(f773(f773(f140(x101001),x101002),x101003),x101003)),
% 191.32/191.79 inference(rename_variables,[],[4398])).
% 191.32/191.79 cnf(10106,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x101061),f2(a847)))),
% 191.32/191.79 inference(rename_variables,[],[4452])).
% 191.32/191.79 cnf(10109,plain,
% 191.32/191.79 (E(f37(x101091,x101092,x101093,x101094,x101095,x101096,x101097,x101098,x101099,a25),x101092)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(10112,plain,
% 191.32/191.79 (E(f37(x101121,x101122,x101123,x101124,x101125,x101126,x101127,x101128,x101129,a25),x101122)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(10119,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),f773(f773(f82(a847),x101191),x101192)),x101192))),
% 191.32/191.79 inference(rename_variables,[],[4476])).
% 191.32/191.79 cnf(10122,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),f773(f773(f82(a847),x101221),x101222)),x101222))),
% 191.32/191.79 inference(rename_variables,[],[4476])).
% 191.32/191.79 cnf(10143,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x101431),x101431))),
% 191.32/191.79 inference(rename_variables,[],[4448])).
% 191.32/191.79 cnf(10146,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),f52(a847,x101461,x101462)),x101461))),
% 191.32/191.79 inference(rename_variables,[],[3636])).
% 191.32/191.79 cnf(10165,plain,
% 191.32/191.79 (E(f773(f42(a847),f773(f257(a847),x101651)),x101651)),
% 191.32/191.79 inference(rename_variables,[],[3082])).
% 191.32/191.79 cnf(10173,plain,
% 191.32/191.79 (~E(f773(a114,x101731),x101731)),
% 191.32/191.79 inference(rename_variables,[],[4364])).
% 191.32/191.79 cnf(10176,plain,
% 191.32/191.79 (~E(f773(a114,x101761),x101761)),
% 191.32/191.79 inference(rename_variables,[],[4364])).
% 191.32/191.79 cnf(10179,plain,
% 191.32/191.79 (~E(f773(a114,x101791),x101791)),
% 191.32/191.79 inference(rename_variables,[],[4364])).
% 191.32/191.79 cnf(10184,plain,
% 191.32/191.79 (P1(f773(f773(f233(a847),x101841),f773(a114,x101841)))),
% 191.32/191.79 inference(rename_variables,[],[3253])).
% 191.32/191.79 cnf(10187,plain,
% 191.32/191.79 (P1(f773(f773(f233(a847),x101871),f773(a114,x101871)))),
% 191.32/191.79 inference(rename_variables,[],[3253])).
% 191.32/191.79 cnf(10189,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x101891),f773(a114,x101891)))),
% 191.32/191.79 inference(scs_inference,[],[4338,10038,10041,10047,10109,4364,10044,10054,10065,10074,10173,10176,3027,3085,3050,3034,3118,4398,3082,4480,3101,3253,10184,4452,10077,10080,3769,3187,4449,4392,4448,10143,3279,3700,3636,4461,10097,4006,4459,4440,3161,4444,4475,10068,4478,4476,10119,4489,4494,4500,4562,4565,4593,4611,4618,4619,4655,4684,4690,4794,4795,4832,4855,4856,4879,4881,4894,4898,4918,4924,4941,4945,4946,4951,4956,4957,4979,5003,5004,5014,5019,5025,5070,5071,5079,5088,5090,5091,5100,5102,5110,5115,5128,5134,5137,5138,5142,5175,5185,5192,5194,5195,5198,5199,5200,5208,5209,5212])).
% 191.32/191.79 cnf(10196,plain,
% 191.32/191.79 (P1(f773(f773(f187(a25),x101961),x101961))),
% 191.32/191.79 inference(rename_variables,[],[3183])).
% 191.32/191.79 cnf(10203,plain,
% 191.32/191.79 (E(f37(x102031,x102032,x102033,x102034,x102035,x102036,x102037,x102038,x102039,a25),x102032)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(10206,plain,
% 191.32/191.79 (E(f37(x102061,x102062,x102063,x102064,x102065,x102066,x102067,x102068,x102069,a25),x102062)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(10231,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x102311),x102311))),
% 191.32/191.79 inference(rename_variables,[],[4448])).
% 191.32/191.79 cnf(10236,plain,
% 191.32/191.79 (~E(f773(f773(f773(f74(x102361,f851(x102362)),x102363),x102364),f773(f227(x102362),x102365)),f773(f18(f851(x102362),x102361),f183(x102362)))),
% 191.32/191.79 inference(rename_variables,[],[4472])).
% 191.32/191.79 cnf(10265,plain,
% 191.32/191.79 (~E(f773(f773(f140(x102651),x102652),x102653),x102653)),
% 191.32/191.79 inference(rename_variables,[],[4398])).
% 191.32/191.79 cnf(10268,plain,
% 191.32/191.79 (~E(f773(a27,x102681),f35(x102682,x102683))),
% 191.32/191.79 inference(rename_variables,[],[4382])).
% 191.32/191.79 cnf(10281,plain,
% 191.32/191.79 (P1(f773(f773(f232(a1),x102811),x102811))),
% 191.32/191.79 inference(rename_variables,[],[3185])).
% 191.32/191.79 cnf(10284,plain,
% 191.32/191.79 (~E(f773(a114,x102841),x102841)),
% 191.32/191.79 inference(rename_variables,[],[4364])).
% 191.32/191.79 cnf(10291,plain,
% 191.32/191.79 (P1(f773(f773(f187(a25),x102911),x102911))),
% 191.32/191.79 inference(rename_variables,[],[3183])).
% 191.32/191.79 cnf(10300,plain,
% 191.32/191.79 (P1(f773(f773(f233(a847),x103001),f773(a114,x103001)))),
% 191.32/191.79 inference(rename_variables,[],[3253])).
% 191.32/191.79 cnf(10305,plain,
% 191.32/191.79 (E(f773(f773(f125(x103051),f115(x103051)),x103052),x103052)),
% 191.32/191.79 inference(rename_variables,[],[3138])).
% 191.32/191.79 cnf(10323,plain,
% 191.32/191.79 (~P1(f773(f64(x103231,x103232,f180(f855(x103231,a841))),x103233))),
% 191.32/191.79 inference(rename_variables,[],[4475])).
% 191.32/191.79 cnf(10342,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x103421),x103421))),
% 191.32/191.79 inference(rename_variables,[],[4448])).
% 191.32/191.79 cnf(10363,plain,
% 191.32/191.79 (~E(f773(a27,x103631),f35(x103632,x103633))),
% 191.32/191.79 inference(rename_variables,[],[4382])).
% 191.32/191.79 cnf(10372,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x103721),x103721))),
% 191.32/191.79 inference(rename_variables,[],[4448])).
% 191.32/191.79 cnf(10377,plain,
% 191.32/191.79 (P1(f773(f773(f233(a847),x103771),f773(a114,x103771)))),
% 191.32/191.79 inference(rename_variables,[],[3253])).
% 191.32/191.79 cnf(10390,plain,
% 191.32/191.79 (~E(f773(a114,x103901),x103901)),
% 191.32/191.79 inference(rename_variables,[],[4364])).
% 191.32/191.79 cnf(10415,plain,
% 191.32/191.79 (P1(f773(f773(f187(a25),x104151),x104151))),
% 191.32/191.79 inference(rename_variables,[],[3183])).
% 191.32/191.79 cnf(10418,plain,
% 191.32/191.79 (P1(f773(f773(f233(a847),x104181),f773(a114,f773(f773(f82(a847),x104182),x104181))))),
% 191.32/191.79 inference(rename_variables,[],[3629])).
% 191.32/191.79 cnf(10421,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x104211),f773(f773(f83(a847),x104211),x104211)))),
% 191.32/191.79 inference(rename_variables,[],[3453])).
% 191.32/191.79 cnf(10424,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x104241),f773(f773(f83(a847),x104241),x104241)))),
% 191.32/191.79 inference(rename_variables,[],[3453])).
% 191.32/191.79 cnf(10429,plain,
% 191.32/191.79 (P1(f773(f773(f233(a847),x104291),f773(a114,x104291)))),
% 191.32/191.79 inference(rename_variables,[],[3253])).
% 191.32/191.79 cnf(10432,plain,
% 191.32/191.79 (P1(f773(f773(f233(a847),x104321),f773(a114,x104321)))),
% 191.32/191.79 inference(rename_variables,[],[3253])).
% 191.32/191.79 cnf(10435,plain,
% 191.32/191.79 (P1(f773(f773(f334(x104351),x104352),f239(f855(x104351,a841))))),
% 191.32/191.79 inference(rename_variables,[],[3340])).
% 191.32/191.79 cnf(10448,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),f773(f773(f82(a847),x104481),x104482)),x104482))),
% 191.32/191.79 inference(rename_variables,[],[4476])).
% 191.32/191.79 cnf(10451,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),f773(f773(f82(a847),x104511),x104512)),x104512))),
% 191.32/191.79 inference(rename_variables,[],[4476])).
% 191.32/191.79 cnf(10454,plain,
% 191.32/191.79 (~P1(f773(f773(f232(a847),f773(a114,x104541)),x104541))),
% 191.32/191.79 inference(rename_variables,[],[4461])).
% 191.32/191.79 cnf(10457,plain,
% 191.32/191.79 (~P1(f773(f773(f232(a847),f773(a114,x104571)),x104571))),
% 191.32/191.79 inference(rename_variables,[],[4461])).
% 191.32/191.79 cnf(10460,plain,
% 191.32/191.79 (P1(f773(f239(f855(x104601,a841)),x104602))),
% 191.32/191.79 inference(rename_variables,[],[3247])).
% 191.32/191.79 cnf(10463,plain,
% 191.32/191.79 (E(f773(f42(a847),f773(f257(a847),x104631)),x104631)),
% 191.32/191.79 inference(rename_variables,[],[3082])).
% 191.32/191.79 cnf(10466,plain,
% 191.32/191.79 (P1(f773(f773(f233(a847),x104661),f773(a114,x104661)))),
% 191.32/191.79 inference(rename_variables,[],[3253])).
% 191.32/191.79 cnf(10473,plain,
% 191.32/191.79 (P1(f773(f773(f187(a25),x104731),x104731))),
% 191.32/191.79 inference(rename_variables,[],[3183])).
% 191.32/191.79 cnf(10478,plain,
% 191.32/191.79 (P1(f773(f773(f232(a1),x104781),x104781))),
% 191.32/191.79 inference(rename_variables,[],[3185])).
% 191.32/191.79 cnf(10487,plain,
% 191.32/191.79 (E(f37(x104871,x104872,x104873,x104874,x104875,x104876,x104877,x104878,x104879,a25),x104872)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(10490,plain,
% 191.32/191.79 (P1(f773(f239(f855(x104901,a841)),x104902))),
% 191.32/191.79 inference(rename_variables,[],[3247])).
% 191.32/191.79 cnf(10493,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x104931),f773(f773(f83(a847),x104931),x104931)))),
% 191.32/191.79 inference(rename_variables,[],[3453])).
% 191.32/191.79 cnf(10498,plain,
% 191.32/191.79 (E(f37(x104981,x104982,x104983,x104984,x104985,x104986,x104987,x104988,x104989,a25),x104982)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(10510,plain,
% 191.32/191.79 (~P1(f773(f773(f232(a847),f773(a114,f773(a114,f773(f773(f82(a847),x105101),x105102)))),f773(a114,x105102)))),
% 191.32/191.79 inference(scs_inference,[],[4338,10038,10041,10047,10109,10112,10203,10206,10487,4364,10044,10054,10065,10074,10173,10176,10179,10284,4382,10268,3027,3085,3050,3034,3118,3138,10305,4472,4398,10100,3082,10165,3961,4480,3101,3542,3488,3253,10184,10187,10300,10377,10429,10432,10466,3631,4452,10077,10080,10106,4468,3616,3393,3769,3212,3214,3187,4449,4392,3911,3183,10196,10291,10415,3184,3185,10281,4448,10143,10231,10342,3340,3247,10460,3279,3700,3636,10146,4461,10097,10454,4006,4459,4440,4443,3161,3162,4442,4444,4475,10068,10071,3453,10421,10424,4478,3659,4476,10119,10122,10448,3629,4489,4494,4500,4562,4565,4593,4611,4618,4619,4655,4684,4690,4794,4795,4832,4855,4856,4879,4881,4894,4898,4918,4924,4941,4945,4946,4951,4956,4957,4979,5003,5004,5014,5019,5025,5070,5071,5079,5088,5090,5091,5100,5102,5110,5115,5128,5134,5137,5138,5142,5175,5185,5192,5194,5195,5198,5199,5200,5208,5209,5212,5216,5217,5218,5225,5229,5230,5231,5239,5242,5244,5250,5261,5268,5281,5283,5291,5292,5296,5299,5324,5330,5340,5341,5342,5357,5369,5391,5397,5415,5416,5419,5438,5446,5447,5449,5450,5459,5460,5474,5478,5487,5488,5490,5505,5508,5519,5530,5537,5550,5556,5562,5563,5564,5567,5572,5609,5611,5614,5616,5619,5620,5621,5623,5625,5627,5630,5637,5651,5665,5671,5672,5691,5692,5697,5698,5700,5703,5706,5707,5712,5756,5770,5778,5782,5794,5804,5821,5839,5842,5852,5879,5894,5921,5941,5942,5945,5959,5961,5962,5964,5977,5978,5981,5983,5986,5987,6001,6007,6008,6009,6012,6014,6056,6066,6075,6110,6112,6114,6116,6126,6128,6131,6137,6139,6143,6146,6154,6161,6162,6163,6169,6195,6202,6209,6245,6246,6250,6251,6252,6253,6254])).
% 191.32/191.79 cnf(10533,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x105331),x105331))),
% 191.32/191.79 inference(rename_variables,[],[3184])).
% 191.32/191.79 cnf(10544,plain,
% 191.32/191.79 (~P1(f773(f773(f180(f855(x105441,f855(x105442,a841))),x105443),x105444))),
% 191.32/191.79 inference(rename_variables,[],[4479])).
% 191.32/191.79 cnf(10555,plain,
% 191.32/191.79 (P1(f773(f773(f233(a847),x105551),f773(a114,x105551)))),
% 191.32/191.79 inference(rename_variables,[],[3253])).
% 191.32/191.79 cnf(10558,plain,
% 191.32/191.79 (~E(f773(a114,x105581),x105581)),
% 191.32/191.79 inference(rename_variables,[],[4364])).
% 191.32/191.79 cnf(10560,plain,
% 191.32/191.79 (P1(f773(f773(f233(a1),f773(f773(f3(a1),x105601),f80(a1))),x105601))),
% 191.32/191.79 inference(scs_inference,[],[4338,10038,10041,10047,10109,10112,10203,10206,10487,4364,10044,10054,10065,10074,10173,10176,10179,10284,10390,4382,10268,3027,3085,3050,3034,3118,3138,10305,4472,4398,10100,3082,10165,3961,3815,4480,3101,3542,3488,3253,10184,10187,10300,10377,10429,10432,10466,3631,4452,10077,10080,10106,4468,3616,3393,3769,3212,3214,3187,4449,4392,3911,3183,10196,10291,10415,3184,10533,3185,10281,10478,4448,10143,10231,10342,3340,4464,3247,10460,3279,3700,3636,10146,4461,10097,10454,10457,4006,4459,4440,4443,3161,3162,4442,4444,4475,10068,10071,3453,10421,10424,4478,4479,3659,4476,10119,10122,10448,3629,4489,4494,4500,4562,4565,4593,4611,4618,4619,4655,4684,4690,4794,4795,4832,4855,4856,4879,4881,4894,4898,4918,4924,4941,4945,4946,4951,4956,4957,4979,5003,5004,5014,5019,5025,5070,5071,5079,5088,5090,5091,5100,5102,5110,5115,5128,5134,5137,5138,5142,5175,5185,5192,5194,5195,5198,5199,5200,5208,5209,5212,5216,5217,5218,5225,5229,5230,5231,5239,5242,5244,5250,5261,5268,5281,5283,5291,5292,5296,5299,5324,5330,5340,5341,5342,5357,5369,5391,5397,5415,5416,5419,5438,5446,5447,5449,5450,5459,5460,5474,5478,5487,5488,5490,5505,5508,5519,5530,5537,5550,5556,5562,5563,5564,5567,5572,5609,5611,5614,5616,5619,5620,5621,5623,5625,5627,5630,5637,5651,5665,5671,5672,5691,5692,5697,5698,5700,5703,5706,5707,5712,5756,5770,5778,5782,5794,5804,5821,5839,5842,5852,5879,5894,5921,5941,5942,5945,5959,5961,5962,5964,5977,5978,5981,5983,5986,5987,6001,6007,6008,6009,6012,6014,6056,6066,6075,6110,6112,6114,6116,6126,6128,6131,6137,6139,6143,6146,6154,6161,6162,6163,6169,6195,6202,6209,6245,6246,6250,6251,6252,6253,6254,6255,6256,6263,6300,6301,6310,6330,6331,6356,6360,6371,6372,6380,6411,6412,6427,6449,6450,6469,6472,6473,6519,6527])).
% 191.32/191.79 cnf(10561,plain,
% 191.32/191.79 (P1(f773(f773(f232(a1),x105611),x105611))),
% 191.32/191.79 inference(rename_variables,[],[3185])).
% 191.32/191.79 cnf(10566,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x105661),f2(a847)))),
% 191.32/191.79 inference(rename_variables,[],[4452])).
% 191.32/191.79 cnf(10581,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x105811),f2(a847)))),
% 191.32/191.79 inference(rename_variables,[],[4452])).
% 191.32/191.79 cnf(10584,plain,
% 191.32/191.79 (~P1(f773(f773(f233(f855(x105841,a841)),x105842),f180(f855(x105841,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4473])).
% 191.32/191.79 cnf(10587,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x105871),x105871))),
% 191.32/191.79 inference(rename_variables,[],[3184])).
% 191.32/191.79 cnf(10590,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x105901),x105901))),
% 191.32/191.79 inference(rename_variables,[],[3184])).
% 191.32/191.79 cnf(10605,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x106051),x106051))),
% 191.32/191.79 inference(rename_variables,[],[4448])).
% 191.32/191.79 cnf(10614,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x106141),x106142),f180(f855(x106141,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(10623,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x106231),x106231))),
% 191.32/191.79 inference(rename_variables,[],[3184])).
% 191.32/191.79 cnf(10626,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x106261),x106262),f180(f855(x106261,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(10629,plain,
% 191.32/191.79 (P1(f773(f773(f279(a847),x106291),x106291))),
% 191.32/191.79 inference(rename_variables,[],[3186])).
% 191.32/191.79 cnf(10632,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x106321,a841)),f773(f303(x106322,x106321,x106323),f773(f305(x106322,x106321,x106323),x106324))),x106324))),
% 191.32/191.79 inference(rename_variables,[],[4066])).
% 191.32/191.79 cnf(10639,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x106391,a841)),f773(f158(x106391),f773(f126(x106391,x106392),x106393))),f773(f158(x106391),x106393)))),
% 191.32/191.79 inference(rename_variables,[],[3825])).
% 191.32/191.79 cnf(10642,plain,
% 191.32/191.79 (E(f773(f303(x106421,x106421,f7(x106421)),x106422),x106422)),
% 191.32/191.79 inference(rename_variables,[],[3243])).
% 191.32/191.79 cnf(10647,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),f2(a847)),x106471))),
% 191.32/191.79 inference(rename_variables,[],[3206])).
% 191.32/191.79 cnf(10650,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x106501),x106501))),
% 191.32/191.79 inference(rename_variables,[],[3184])).
% 191.32/191.79 cnf(10653,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x106531),x106531))),
% 191.32/191.79 inference(rename_variables,[],[4448])).
% 191.32/191.79 cnf(10660,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x106601),x106601))),
% 191.32/191.79 inference(rename_variables,[],[4448])).
% 191.32/191.79 cnf(10671,plain,
% 191.32/191.79 (P1(f773(f773(f233(a847),x106711),f773(a114,f773(f773(f82(a847),x106712),x106711))))),
% 191.32/191.79 inference(rename_variables,[],[3629])).
% 191.32/191.79 cnf(10674,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x106741),f773(f773(f83(a847),x106741),x106741)))),
% 191.32/191.79 inference(rename_variables,[],[3453])).
% 191.32/191.79 cnf(10684,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x106841),x106841))),
% 191.32/191.79 inference(rename_variables,[],[3184])).
% 191.32/191.79 cnf(10687,plain,
% 191.32/191.79 (P1(f773(f773(f232(a1),x106871),x106871))),
% 191.32/191.79 inference(rename_variables,[],[3185])).
% 191.32/191.79 cnf(10690,plain,
% 191.32/191.79 (~E(f773(a114,x106901),x106901)),
% 191.32/191.79 inference(rename_variables,[],[4364])).
% 191.32/191.79 cnf(10695,plain,
% 191.32/191.79 (P1(f773(f773(f279(a847),x106951),x106951))),
% 191.32/191.79 inference(rename_variables,[],[3186])).
% 191.32/191.79 cnf(10698,plain,
% 191.32/191.79 (P1(f773(f773(f334(x106981),x106982),f239(f855(x106981,a841))))),
% 191.32/191.79 inference(rename_variables,[],[3340])).
% 191.32/191.79 cnf(10703,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x107031),f2(a847)))),
% 191.32/191.79 inference(rename_variables,[],[4452])).
% 191.32/191.79 cnf(10714,plain,
% 191.32/191.79 (~E(f773(a114,x107141),f2(a847))),
% 191.32/191.79 inference(rename_variables,[],[4376])).
% 191.32/191.79 cnf(10721,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),f2(a847)),x107211))),
% 191.32/191.79 inference(rename_variables,[],[3206])).
% 191.32/191.79 cnf(10728,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x107281),x107281))),
% 191.32/191.79 inference(rename_variables,[],[3184])).
% 191.32/191.79 cnf(10735,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x107351),x107352),f180(f855(x107351,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(10743,plain,
% 191.32/191.79 (P1(f773(f773(f334(x107431),x107432),f239(f855(x107431,a841))))),
% 191.32/191.79 inference(rename_variables,[],[3340])).
% 191.32/191.79 cnf(10746,plain,
% 191.32/191.79 (~P1(f773(f773(f334(f854(f848(x107461),f848(x107461))),f773(f773(f241(f848(x107461),f848(x107461)),x107462),f115(x107461))),f135(x107461,x107463)))),
% 191.32/191.79 inference(rename_variables,[],[4480])).
% 191.32/191.79 cnf(10753,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x107531),x107532),f180(f855(x107531,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(10756,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x107561),x107562),f180(f855(x107561,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(10759,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x107591,a841)),x107592),f773(f773(f302(x107591),x107593),x107592)))),
% 191.32/191.79 inference(rename_variables,[],[3624])).
% 191.32/191.79 cnf(10762,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x107621),x107621))),
% 191.32/191.79 inference(rename_variables,[],[3184])).
% 191.32/191.79 cnf(10765,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x107651,a841)),x107652),f773(f773(f302(x107651),x107653),x107652)))),
% 191.32/191.79 inference(rename_variables,[],[3624])).
% 191.32/191.79 cnf(10776,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x107761,a841)),x107762),f773(f773(f302(x107761),x107763),x107762)))),
% 191.32/191.79 inference(rename_variables,[],[3624])).
% 191.32/191.79 cnf(10781,plain,
% 191.32/191.79 (~P1(f773(f64(x107811,x107812,f180(f855(x107811,a841))),x107813))),
% 191.32/191.79 inference(rename_variables,[],[4475])).
% 191.32/191.79 cnf(10794,plain,
% 191.32/191.79 (P1(f773(f773(f233(a847),x107941),f773(a114,x107941)))),
% 191.32/191.79 inference(rename_variables,[],[3253])).
% 191.32/191.79 cnf(10804,plain,
% 191.32/191.79 (~E(f773(f313(x108041,x108042),x108043),f773(f304(x108042,x108041),x108044))),
% 191.32/191.79 inference(rename_variables,[],[4437])).
% 191.32/191.79 cnf(10807,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x108071),x108072),f180(f855(x108071,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(10810,plain,
% 191.32/191.79 (P1(f773(f773(f334(f854(x108101,x108101)),f773(f773(f241(x108101,x108101),x108102),x108102)),f300(x108101,x108103)))),
% 191.32/191.79 inference(rename_variables,[],[3815])).
% 191.32/191.79 cnf(10813,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x108131,a841)),f773(f158(x108131),f151(x108131,x108132,x108133))),f773(f158(x108131),x108133)))),
% 191.32/191.79 inference(rename_variables,[],[3873])).
% 191.32/191.79 cnf(10816,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x108161,a841)),x108162),f239(f855(x108161,a841))))),
% 191.32/191.79 inference(rename_variables,[],[3560])).
% 191.32/191.79 cnf(10823,plain,
% 191.32/191.79 (~E(f773(a114,x108231),x108231)),
% 191.32/191.79 inference(rename_variables,[],[4364])).
% 191.32/191.79 cnf(10839,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x108391,a841)),f180(f855(x108391,a841))),x108392))),
% 191.32/191.79 inference(rename_variables,[],[3628])).
% 191.32/191.79 cnf(10850,plain,
% 191.32/191.79 (~P1(f773(f773(f334(f854(f848(x108501),f848(x108501))),f773(f773(f241(f848(x108501),f848(x108501)),x108502),f115(x108501))),f137(x108501,x108503)))),
% 191.32/191.79 inference(rename_variables,[],[4481])).
% 191.32/191.79 cnf(10858,plain,
% 191.32/191.79 (P1(f773(f773(f334(f854(f848(x108581),f848(x108581))),f773(f773(f241(f848(x108581),f848(x108581)),f115(x108581)),f115(x108581))),f773(f773(f281(f848(x108581),f848(x108581),f848(x108581)),f147(x108581,x108582)),f300(f848(x108581),f147(x108581,x108582)))))),
% 191.32/191.79 inference(scs_inference,[],[4338,10038,10041,10047,10109,10112,10203,10206,10487,4364,10044,10054,10065,10074,10173,10176,10179,10284,10390,10558,10690,4382,10268,4376,3639,3027,4437,3085,3050,3034,3243,3118,3138,10305,4472,3814,4398,10100,3082,10165,3961,3815,10810,4480,10746,4481,3101,3382,3542,3488,3694,3253,10184,10187,10300,10377,10429,10432,10466,10555,3631,4452,10077,10080,10106,10566,10581,10703,4468,3616,3393,3769,3212,3214,3187,4449,4392,3922,3825,10639,3873,3543,3911,3560,4473,3183,10196,10291,10415,3184,10533,10587,10590,10623,10650,10684,10728,3185,10281,10478,10561,3186,10629,4448,10143,10231,10342,10372,10605,10653,3340,10435,10698,10743,4464,10614,10626,10735,10753,10756,3247,10460,3279,3700,3636,10146,4461,10097,10454,10457,3206,10647,4006,4459,3708,4440,4441,4443,3161,3162,4442,4444,4475,10068,10071,10323,3786,3624,10759,10765,3628,3453,10421,10424,10493,10674,4478,4479,4066,3659,4476,10119,10122,10448,3629,10418,3895,4489,4494,4500,4562,4565,4593,4611,4618,4619,4655,4684,4690,4794,4795,4832,4855,4856,4879,4881,4894,4898,4918,4924,4941,4945,4946,4951,4956,4957,4979,5003,5004,5014,5019,5025,5070,5071,5079,5088,5090,5091,5100,5102,5110,5115,5128,5134,5137,5138,5142,5175,5185,5192,5194,5195,5198,5199,5200,5208,5209,5212,5216,5217,5218,5225,5229,5230,5231,5239,5242,5244,5250,5261,5268,5281,5283,5291,5292,5296,5299,5324,5330,5340,5341,5342,5357,5369,5391,5397,5415,5416,5419,5438,5446,5447,5449,5450,5459,5460,5474,5478,5487,5488,5490,5505,5508,5519,5530,5537,5550,5556,5562,5563,5564,5567,5572,5609,5611,5614,5616,5619,5620,5621,5623,5625,5627,5630,5637,5651,5665,5671,5672,5691,5692,5697,5698,5700,5703,5706,5707,5712,5756,5770,5778,5782,5794,5804,5821,5839,5842,5852,5879,5894,5921,5941,5942,5945,5959,5961,5962,5964,5977,5978,5981,5983,5986,5987,6001,6007,6008,6009,6012,6014,6056,6066,6075,6110,6112,6114,6116,6126,6128,6131,6137,6139,6143,6146,6154,6161,6162,6163,6169,6195,6202,6209,6245,6246,6250,6251,6252,6253,6254,6255,6256,6263,6300,6301,6310,6330,6331,6356,6360,6371,6372,6380,6411,6412,6427,6449,6450,6469,6472,6473,6519,6527,6552,6593,6609,6618,6627,6628,6629,6630,6652,6653,6659,6671,6674,6677,6679,6680,6681,6683,6697,6710,6712,6713,6724,6727,6784,6797,6799,6805,6819,6822,6823,6860,6875,6903,6936,6986,7017,7074,7102,7105,7163,7175,7242,7244,7259,7269,7272,7273,7291,7297,7299,7352,7362,7368,7371,7384,7429,7432,7436,7483,7484,7502,7565,7572,7591,7615,7637,7651,7667,7676,7684,7713,7715,7717,7725,7769,7779,7804,7862,7894,7928,7973,7988,8076,8124,8143,8167,8186,8208,8307,8309,8315,8335,8339,8353,8374,8385,8387,8399,8405,8409,8433,8448,8449,8460,8461,8462,8468,8469,8474,8475,8476,8477,8478,8496,8497,8498,8506,8518,8520,8534,8536,8542])).
% 191.32/191.79 cnf(10868,plain,
% 191.32/191.79 (P29(x108681,x108681,f7(x108681),x108682)),
% 191.32/191.79 inference(rename_variables,[],[3426])).
% 191.32/191.79 cnf(10873,plain,
% 191.32/191.79 (~E(f773(f303(x108731,f855(x108731,a841),x108732),x108733),f773(f301(x108731),x108733))),
% 191.32/191.79 inference(rename_variables,[],[4462])).
% 191.32/191.79 cnf(10878,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x108781,a841)),x108782),f239(f855(x108781,a841))))),
% 191.32/191.79 inference(rename_variables,[],[3560])).
% 191.32/191.79 cnf(10885,plain,
% 191.32/191.79 (P36(x108851,f773(f773(f280(a847,x108851),a237),x108852))),
% 191.32/191.79 inference(rename_variables,[],[3289])).
% 191.32/191.79 cnf(10892,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x108921),x108922),f180(f855(x108921,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(10895,plain,
% 191.32/191.79 (~P1(f773(f773(f232(a847),f773(a114,x108951)),x108951))),
% 191.32/191.79 inference(rename_variables,[],[4461])).
% 191.32/191.79 cnf(10902,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x109021),x109022),f180(f855(x109021,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(10910,plain,
% 191.32/191.79 (~P1(f773(f773(f334(a847),f773(a114,f773(f132(a847,a847,f82(a847),f2(a847)),x109101))),f773(f158(a847),x109101)))),
% 191.32/191.79 inference(scs_inference,[],[3426,4338,10038,10041,10047,10109,10112,10203,10206,10487,4364,10044,10054,10065,10074,10173,10176,10179,10284,10390,10558,10690,4382,10268,10363,4376,3639,3027,4437,3085,3050,3034,3243,3118,3138,10305,4472,3814,4398,10100,4462,3289,3082,10165,3961,3815,10810,4480,10746,4481,3101,3382,3542,3488,3694,3253,10184,10187,10300,10377,10429,10432,10466,10555,10794,3631,4452,10077,10080,10106,10566,10581,10703,4468,3616,3393,3769,3212,3214,3187,4449,4392,3922,3825,10639,3873,3543,3911,3560,10816,4473,3183,10196,10291,10415,3184,10533,10587,10590,10623,10650,10684,10728,3185,10281,10478,10561,3186,10629,4448,10143,10231,10342,10372,10605,10653,3340,10435,10698,10743,4464,10614,10626,10735,10753,10756,10807,10892,3247,10460,3279,3700,3636,10146,4461,10097,10454,10457,10895,3206,10647,4006,4459,3708,4440,4441,4443,3161,3162,4442,4444,4475,10068,10071,10323,3786,3624,10759,10765,3628,3453,10421,10424,10493,10674,4478,4479,4066,3659,4476,10119,10122,10448,3629,10418,3895,4489,4494,4500,4562,4565,4593,4611,4618,4619,4655,4684,4690,4794,4795,4832,4855,4856,4879,4881,4894,4898,4918,4924,4941,4945,4946,4951,4956,4957,4979,5003,5004,5014,5019,5025,5070,5071,5079,5088,5090,5091,5100,5102,5110,5115,5128,5134,5137,5138,5142,5175,5185,5192,5194,5195,5198,5199,5200,5208,5209,5212,5216,5217,5218,5225,5229,5230,5231,5239,5242,5244,5250,5261,5268,5281,5283,5291,5292,5296,5299,5324,5330,5340,5341,5342,5357,5369,5391,5397,5415,5416,5419,5438,5446,5447,5449,5450,5459,5460,5474,5478,5487,5488,5490,5505,5508,5519,5530,5537,5550,5556,5562,5563,5564,5567,5572,5609,5611,5614,5616,5619,5620,5621,5623,5625,5627,5630,5637,5651,5665,5671,5672,5691,5692,5697,5698,5700,5703,5706,5707,5712,5756,5770,5778,5782,5794,5804,5821,5839,5842,5852,5879,5894,5921,5941,5942,5945,5959,5961,5962,5964,5977,5978,5981,5983,5986,5987,6001,6007,6008,6009,6012,6014,6056,6066,6075,6110,6112,6114,6116,6126,6128,6131,6137,6139,6143,6146,6154,6161,6162,6163,6169,6195,6202,6209,6245,6246,6250,6251,6252,6253,6254,6255,6256,6263,6300,6301,6310,6330,6331,6356,6360,6371,6372,6380,6411,6412,6427,6449,6450,6469,6472,6473,6519,6527,6552,6593,6609,6618,6627,6628,6629,6630,6652,6653,6659,6671,6674,6677,6679,6680,6681,6683,6697,6710,6712,6713,6724,6727,6784,6797,6799,6805,6819,6822,6823,6860,6875,6903,6936,6986,7017,7074,7102,7105,7163,7175,7242,7244,7259,7269,7272,7273,7291,7297,7299,7352,7362,7368,7371,7384,7429,7432,7436,7483,7484,7502,7565,7572,7591,7615,7637,7651,7667,7676,7684,7713,7715,7717,7725,7769,7779,7804,7862,7894,7928,7973,7988,8076,8124,8143,8167,8186,8208,8307,8309,8315,8335,8339,8353,8374,8385,8387,8399,8405,8409,8433,8448,8449,8460,8461,8462,8468,8469,8474,8475,8476,8477,8478,8496,8497,8498,8506,8518,8520,8534,8536,8542,8547,8568,8569,8598,8611,8615,8633,8654,8655,8657,8658,8668,8669,8691,8700,8707,8708,8709,8710,8733,8734,8745])).
% 191.32/191.79 cnf(10911,plain,
% 191.32/191.79 (~P1(f773(f773(f232(a847),f773(a114,x109111)),x109111))),
% 191.32/191.79 inference(rename_variables,[],[4461])).
% 191.32/191.79 cnf(10914,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x109141),x109142),f180(f855(x109141,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(10929,plain,
% 191.32/191.79 (P1(f773(f773(f334(f854(x109291,x109291)),f773(f773(f241(x109291,x109291),x109292),x109292)),f300(x109291,x109293)))),
% 191.32/191.79 inference(rename_variables,[],[3815])).
% 191.32/191.79 cnf(10936,plain,
% 191.32/191.79 (~P1(f773(f773(f334(f854(f848(x109361),f848(x109361))),f773(f773(f241(f848(x109361),f848(x109361)),x109362),f115(x109361))),f135(x109361,x109363)))),
% 191.32/191.79 inference(rename_variables,[],[4480])).
% 191.32/191.79 cnf(10939,plain,
% 191.32/191.79 (~P1(f773(f773(f334(f854(f848(x109391),f848(x109391))),f773(f773(f241(f848(x109391),f848(x109391)),x109392),f115(x109391))),f137(x109391,x109393)))),
% 191.32/191.79 inference(rename_variables,[],[4481])).
% 191.32/191.79 cnf(10942,plain,
% 191.32/191.79 (~P1(f773(f773(f334(f854(f848(x109421),f848(x109421))),f773(f773(f241(f848(x109421),f848(x109421)),x109422),f115(x109421))),f146(x109421,x109423)))),
% 191.32/191.79 inference(rename_variables,[],[4482])).
% 191.32/191.79 cnf(10947,plain,
% 191.32/191.79 (~P1(f773(f773(f233(f855(x109471,a841)),x109472),f180(f855(x109471,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4473])).
% 191.32/191.79 cnf(10950,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x109501),x109502),f180(f855(x109501,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(10963,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x109631,a841)),x109632),f239(f855(x109631,a841))))),
% 191.32/191.79 inference(rename_variables,[],[3560])).
% 191.32/191.79 cnf(10966,plain,
% 191.32/191.79 (~P1(f773(f773(f180(f855(x109661,f855(x109662,a841))),x109663),x109664))),
% 191.32/191.79 inference(rename_variables,[],[4479])).
% 191.32/191.79 cnf(10973,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x109731),x109731))),
% 191.32/191.79 inference(rename_variables,[],[4448])).
% 191.32/191.79 cnf(10978,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x109781),x109782),f180(f855(x109781,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(10981,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x109811,a841)),x109812),x109812))),
% 191.32/191.79 inference(rename_variables,[],[3482])).
% 191.32/191.79 cnf(10984,plain,
% 191.32/191.79 (E(f319(x109841,x109842,x109843,f773(f773(f10(f856(x109841,x109843),x109842,x109841),x109844),f304(x109841,x109843)),f773(f773(f10(f856(x109841,x109843),x109842,x109843),x109844),f313(x109843,x109841))),x109844)),
% 191.32/191.79 inference(rename_variables,[],[4046])).
% 191.32/191.79 cnf(10990,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x109901),x109902),f180(f855(x109901,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(10993,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x109931,a841)),f180(f855(x109931,a841))),x109932))),
% 191.32/191.79 inference(rename_variables,[],[3628])).
% 191.32/191.79 cnf(10996,plain,
% 191.32/191.79 (P1(f773(f773(f334(f854(x109961,x109961)),f773(f773(f241(x109961,x109961),x109962),x109962)),f300(x109961,x109963)))),
% 191.32/191.79 inference(rename_variables,[],[3815])).
% 191.32/191.79 cnf(10998,plain,
% 191.32/191.79 (~E(f773(f773(f104(f855(f854(f848(x109981),f848(x109981)),a841)),f773(f278(f848(x109981),f848(x109981)),f147(x109981,x109982))),f300(f848(x109981),f147(x109981,x109982))),f180(f855(f854(f848(x109981),f848(x109981)),a841)))),
% 191.32/191.79 inference(scs_inference,[],[3426,4338,10038,10041,10047,10109,10112,10203,10206,10487,4364,10044,10054,10065,10074,10173,10176,10179,10284,10390,10558,10690,4382,10268,10363,4376,3639,3027,4437,3085,3050,3034,4046,10984,3243,3118,3138,10305,3288,4472,3814,4398,10100,4462,3289,3082,10165,3961,3815,10810,10929,4480,10746,10936,4481,10850,4482,3101,3382,3542,3488,3694,3253,10184,10187,10300,10377,10429,10432,10466,10555,10794,3631,4452,10077,10080,10106,10566,10581,10703,4468,3616,3393,3769,3212,3214,3187,4449,4392,3922,3825,10639,3873,3543,3911,3560,10816,10878,4473,10584,3183,10196,10291,10415,3184,10533,10587,10590,10623,10650,10684,10728,3185,10281,10478,10561,3186,10629,4448,10143,10231,10342,10372,10605,10653,10660,3340,10435,10698,10743,4464,10614,10626,10735,10753,10756,10807,10892,10902,10914,10950,10978,3247,10460,3279,3700,3636,10146,4461,10097,10454,10457,10895,3206,10647,4006,4459,3708,4440,4441,4443,3161,3162,4442,4444,4475,10068,10071,10323,3786,3624,10759,10765,3482,3628,10839,3453,10421,10424,10493,10674,4478,4479,10544,4066,3659,4476,10119,10122,10448,3629,10418,3895,4489,4494,4500,4562,4565,4593,4611,4618,4619,4655,4684,4690,4794,4795,4832,4855,4856,4879,4881,4894,4898,4918,4924,4941,4945,4946,4951,4956,4957,4979,5003,5004,5014,5019,5025,5070,5071,5079,5088,5090,5091,5100,5102,5110,5115,5128,5134,5137,5138,5142,5175,5185,5192,5194,5195,5198,5199,5200,5208,5209,5212,5216,5217,5218,5225,5229,5230,5231,5239,5242,5244,5250,5261,5268,5281,5283,5291,5292,5296,5299,5324,5330,5340,5341,5342,5357,5369,5391,5397,5415,5416,5419,5438,5446,5447,5449,5450,5459,5460,5474,5478,5487,5488,5490,5505,5508,5519,5530,5537,5550,5556,5562,5563,5564,5567,5572,5609,5611,5614,5616,5619,5620,5621,5623,5625,5627,5630,5637,5651,5665,5671,5672,5691,5692,5697,5698,5700,5703,5706,5707,5712,5756,5770,5778,5782,5794,5804,5821,5839,5842,5852,5879,5894,5921,5941,5942,5945,5959,5961,5962,5964,5977,5978,5981,5983,5986,5987,6001,6007,6008,6009,6012,6014,6056,6066,6075,6110,6112,6114,6116,6126,6128,6131,6137,6139,6143,6146,6154,6161,6162,6163,6169,6195,6202,6209,6245,6246,6250,6251,6252,6253,6254,6255,6256,6263,6300,6301,6310,6330,6331,6356,6360,6371,6372,6380,6411,6412,6427,6449,6450,6469,6472,6473,6519,6527,6552,6593,6609,6618,6627,6628,6629,6630,6652,6653,6659,6671,6674,6677,6679,6680,6681,6683,6697,6710,6712,6713,6724,6727,6784,6797,6799,6805,6819,6822,6823,6860,6875,6903,6936,6986,7017,7074,7102,7105,7163,7175,7242,7244,7259,7269,7272,7273,7291,7297,7299,7352,7362,7368,7371,7384,7429,7432,7436,7483,7484,7502,7565,7572,7591,7615,7637,7651,7667,7676,7684,7713,7715,7717,7725,7769,7779,7804,7862,7894,7928,7973,7988,8076,8124,8143,8167,8186,8208,8307,8309,8315,8335,8339,8353,8374,8385,8387,8399,8405,8409,8433,8448,8449,8460,8461,8462,8468,8469,8474,8475,8476,8477,8478,8496,8497,8498,8506,8518,8520,8534,8536,8542,8547,8568,8569,8598,8611,8615,8633,8654,8655,8657,8658,8668,8669,8691,8700,8707,8708,8709,8710,8733,8734,8745,8781,8787,8791,8804,8807,8809,8810,8817,8826,8891,8920,8921,8922,8936,8950,8956,8983,8984,8985,8986,8987,8990,9027,9030,9054,9088,9098,9099,9109,9119,9120,9134,9144,9146,9165])).
% 191.32/191.79 cnf(11003,plain,
% 191.32/191.79 (~P1(f773(f773(f334(f854(f848(x110031),f848(x110031))),f773(f773(f241(f848(x110031),f848(x110031)),x110032),f115(x110031))),f146(x110031,x110033)))),
% 191.32/191.79 inference(rename_variables,[],[4482])).
% 191.32/191.79 cnf(11006,plain,
% 191.32/191.79 (~P1(f773(f773(f334(f854(f848(x110061),f848(x110061))),f773(f773(f241(f848(x110061),f848(x110061)),f115(x110061)),x110062)),f135(x110061,x110063)))),
% 191.32/191.79 inference(rename_variables,[],[4483])).
% 191.32/191.79 cnf(11014,plain,
% 191.32/191.79 (P1(f773(f773(f334(x110141),x110142),f239(f855(x110141,a841))))),
% 191.32/191.79 inference(rename_variables,[],[3340])).
% 191.32/191.79 cnf(11019,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x110191,a841)),f180(f855(x110191,a841))),x110192))),
% 191.32/191.79 inference(rename_variables,[],[3628])).
% 191.32/191.79 cnf(11022,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x110221),x110222),f180(f855(x110221,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(11025,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x110251,a841)),x110252),f239(f855(x110251,a841))))),
% 191.32/191.79 inference(rename_variables,[],[3560])).
% 191.32/191.79 cnf(11030,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x110301,a841)),f180(f855(x110301,a841))),x110302))),
% 191.32/191.79 inference(rename_variables,[],[3628])).
% 191.32/191.79 cnf(11050,plain,
% 191.32/191.79 (~P1(f773(f773(f334(f854(f848(x110501),f848(x110501))),f773(f773(f241(f848(x110501),f848(x110501)),x110502),f115(x110501))),f135(x110501,x110503)))),
% 191.32/191.79 inference(rename_variables,[],[4480])).
% 191.32/191.79 cnf(11053,plain,
% 191.32/191.79 (~P1(f773(f773(f334(f854(f848(x110531),f848(x110531))),f773(f773(f241(f848(x110531),f848(x110531)),x110532),f115(x110531))),f137(x110531,x110533)))),
% 191.32/191.79 inference(rename_variables,[],[4481])).
% 191.32/191.79 cnf(11056,plain,
% 191.32/191.79 (~E(f773(f773(f140(x110561),x110562),x110563),x110563)),
% 191.32/191.79 inference(rename_variables,[],[4398])).
% 191.32/191.79 cnf(11059,plain,
% 191.32/191.79 (~E(f773(a114,x110591),x110591)),
% 191.32/191.79 inference(rename_variables,[],[4364])).
% 191.32/191.79 cnf(11062,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x110621),x110622),f180(f855(x110621,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(11067,plain,
% 191.32/191.79 (P1(f773(f773(f334(f854(f848(x110671),f848(x110671))),f773(f773(f241(f848(x110671),f848(x110671)),x110672),x110672)),f147(x110671,f300(x110671,x110673))))),
% 191.32/191.79 inference(rename_variables,[],[3955])).
% 191.32/191.79 cnf(11070,plain,
% 191.32/191.79 (~P1(f773(f773(f334(f854(f848(x110701),f848(x110701))),f773(f773(f241(f848(x110701),f848(x110701)),x110702),f115(x110701))),f135(x110701,x110703)))),
% 191.32/191.79 inference(rename_variables,[],[4480])).
% 191.32/191.79 cnf(11078,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x110781),x110782),f180(f855(x110781,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(11081,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x110811),x110812),f180(f855(x110811,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(11084,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x110841),x110842),f180(f855(x110841,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(11087,plain,
% 191.32/191.79 (P1(f773(f773(f334(x110871),x110872),f239(f855(x110871,a841))))),
% 191.32/191.79 inference(rename_variables,[],[3340])).
% 191.32/191.79 cnf(11098,plain,
% 191.32/191.79 (~E(f773(f313(x110981,x110982),x110983),f773(f304(x110982,x110981),x110984))),
% 191.32/191.79 inference(rename_variables,[],[4437])).
% 191.32/191.79 cnf(11101,plain,
% 191.32/191.79 (~E(f773(f313(x111011,x111012),x111013),f773(f304(x111012,x111011),x111014))),
% 191.32/191.79 inference(rename_variables,[],[4437])).
% 191.32/191.79 cnf(11106,plain,
% 191.32/191.79 (~P1(f773(f773(f334(f854(f848(x111061),f848(x111061))),f773(f773(f241(f848(x111061),f848(x111061)),x111062),f115(x111061))),f135(x111061,x111063)))),
% 191.32/191.79 inference(rename_variables,[],[4480])).
% 191.32/191.79 cnf(11109,plain,
% 191.32/191.79 (~P1(f773(f773(f334(f854(f848(x111091),f848(x111091))),f773(f773(f241(f848(x111091),f848(x111091)),x111092),f115(x111091))),f137(x111091,x111093)))),
% 191.32/191.79 inference(rename_variables,[],[4481])).
% 191.32/191.79 cnf(11112,plain,
% 191.32/191.79 (~P1(f773(f773(f334(f854(f848(x111121),f848(x111121))),f773(f773(f241(f848(x111121),f848(x111121)),x111122),f115(x111121))),f135(x111121,x111123)))),
% 191.32/191.79 inference(rename_variables,[],[4480])).
% 191.32/191.79 cnf(11115,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x111151),x111152),f180(f855(x111151,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(11118,plain,
% 191.32/191.79 (~P1(f773(f773(f180(f855(x111181,f855(x111182,a841))),x111183),x111184))),
% 191.32/191.79 inference(rename_variables,[],[4479])).
% 191.32/191.79 cnf(11121,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x111211),f2(a847)))),
% 191.32/191.79 inference(rename_variables,[],[4452])).
% 191.32/191.79 cnf(11126,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x111261),x111262),f180(f855(x111261,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(11129,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x111291),x111292),f180(f855(x111291,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(11132,plain,
% 191.32/191.79 (P1(f773(f773(f334(x111321),f773(x111322,x111323)),f773(f303(x111324,x111321,x111322),f239(f855(x111324,a841)))))),
% 191.32/191.79 inference(rename_variables,[],[3786])).
% 191.32/191.79 cnf(11139,plain,
% 191.32/191.79 (E(f37(x111391,x111392,x111393,x111394,x111395,x111396,x111397,x111398,x111399,a25),x111392)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(11142,plain,
% 191.32/191.79 (~E(f773(a114,x111421),x111421)),
% 191.32/191.79 inference(rename_variables,[],[4364])).
% 191.32/191.79 cnf(11149,plain,
% 191.32/191.79 (~E(f773(a114,x111491),x111491)),
% 191.32/191.79 inference(rename_variables,[],[4364])).
% 191.32/191.79 cnf(11154,plain,
% 191.32/191.79 (E(f37(x111541,x111542,x111543,x111544,x111545,x111546,x111547,x111548,x111549,a25),x111542)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(11155,plain,
% 191.32/191.79 (E(f38(x111551,x111552,x111553,x111554,x111555,x111556,x111557,x111558,x111559,a25),x111552)),
% 191.32/191.79 inference(rename_variables,[],[4339])).
% 191.32/191.79 cnf(11158,plain,
% 191.32/191.79 (E(f37(x111581,x111582,x111583,x111584,x111585,x111586,x111587,x111588,x111589,a25),x111582)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(11165,plain,
% 191.32/191.79 (~E(f773(a114,x111651),x111651)),
% 191.32/191.79 inference(rename_variables,[],[4364])).
% 191.32/191.79 cnf(11170,plain,
% 191.32/191.79 (~E(f773(f773(f82(a1),x111701),x111701),a99)),
% 191.32/191.79 inference(rename_variables,[],[4395])).
% 191.32/191.79 cnf(11179,plain,
% 191.32/191.79 (E(f773(f773(f3(a847),f2(a847)),x111791),f2(a847))),
% 191.32/191.79 inference(rename_variables,[],[3104])).
% 191.32/191.79 cnf(11182,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x111821),f2(a847)))),
% 191.32/191.79 inference(rename_variables,[],[4452])).
% 191.32/191.79 cnf(11187,plain,
% 191.32/191.79 (E(f773(f773(f82(a1),f773(f773(f83(a1),x111871),f773(f773(f43(a1),x111872),x111871))),f52(a1,x111872,x111871)),x111872)),
% 191.32/191.79 inference(rename_variables,[],[3732])).
% 191.32/191.79 cnf(11199,plain,
% 191.32/191.79 (E(f37(x111991,x111992,x111993,x111994,x111995,x111996,x111997,x111998,x111999,a25),x111992)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(11202,plain,
% 191.32/191.79 (E(f37(x112021,x112022,x112023,x112024,x112025,x112026,x112027,x112028,x112029,a25),x112022)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(11205,plain,
% 191.32/191.79 (E(f37(x112051,x112052,x112053,x112054,x112055,x112056,x112057,x112058,x112059,a25),x112052)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(11208,plain,
% 191.32/191.79 (E(f37(x112081,x112082,x112083,x112084,x112085,x112086,x112087,x112088,x112089,a25),x112082)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(11213,plain,
% 191.32/191.79 (~E(f773(a114,x112131),x112131)),
% 191.32/191.79 inference(rename_variables,[],[4364])).
% 191.32/191.79 cnf(11216,plain,
% 191.32/191.79 (~E(f773(a114,x112161),x112161)),
% 191.32/191.79 inference(rename_variables,[],[4364])).
% 191.32/191.79 cnf(11220,plain,
% 191.32/191.79 (E(f37(x112201,x112202,x112203,x112204,x112205,x112206,x112207,x112208,x112209,a25),x112202)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(11243,plain,
% 191.32/191.79 (P1(f773(f773(f334(x112431),x112432),f239(f855(x112431,a841))))),
% 191.32/191.79 inference(rename_variables,[],[3340])).
% 191.32/191.79 cnf(11251,plain,
% 191.32/191.79 (E(f37(x112511,x112512,x112513,x112514,x112515,x112516,x112517,x112518,x112519,a25),x112512)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(11256,plain,
% 191.32/191.79 (P1(f773(f773(f187(a25),x112561),x112561))),
% 191.32/191.79 inference(rename_variables,[],[3183])).
% 191.32/191.79 cnf(11263,plain,
% 191.32/191.79 (P1(f773(f773(f187(a25),x112631),x112631))),
% 191.32/191.79 inference(rename_variables,[],[3183])).
% 191.32/191.79 cnf(11264,plain,
% 191.32/191.79 (E(f37(x112641,x112642,x112643,x112644,x112645,x112646,x112647,x112648,x112649,a25),x112642)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(11277,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),f773(f773(f82(a847),x112771),x112772)),x112772))),
% 191.32/191.79 inference(rename_variables,[],[4476])).
% 191.32/191.79 cnf(11280,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a1),f773(f102(a1),x112801)),f2(a1)))),
% 191.32/191.79 inference(rename_variables,[],[4468])).
% 191.32/191.79 cnf(11291,plain,
% 191.32/191.79 (E(f37(x112911,x112912,x112913,x112914,x112915,x112916,x112917,x112918,x112919,a25),x112912)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(11294,plain,
% 191.32/191.79 (E(f37(x112941,x112942,x112943,x112944,x112945,x112946,x112947,x112948,x112949,a25),x112942)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(11305,plain,
% 191.32/191.79 (E(f37(x113051,x113052,x113053,x113054,x113055,x113056,x113057,x113058,x113059,a25),x113052)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(11310,plain,
% 191.32/191.79 (E(f37(x113101,x113102,x113103,x113104,x113105,x113106,x113107,x113108,x113109,a25),x113102)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(11313,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a1),f773(f102(a1),x113131)),f2(a1)))),
% 191.32/191.79 inference(rename_variables,[],[4468])).
% 191.32/191.79 cnf(11316,plain,
% 191.32/191.79 (E(f37(x113161,x113162,x113163,x113164,x113165,x113166,x113167,x113168,x113169,a25),x113162)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(11319,plain,
% 191.32/191.79 (~E(f773(a114,x113191),x113191)),
% 191.32/191.79 inference(rename_variables,[],[4364])).
% 191.32/191.79 cnf(11330,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x113301),x113301))),
% 191.32/191.79 inference(rename_variables,[],[4448])).
% 191.32/191.79 cnf(11353,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a1),f773(f102(a1),x113531)),f2(a1)))),
% 191.32/191.79 inference(rename_variables,[],[4468])).
% 191.32/191.79 cnf(11366,plain,
% 191.32/191.79 (P1(f773(f773(f232(a1),x113661),x113661))),
% 191.32/191.79 inference(rename_variables,[],[3185])).
% 191.32/191.79 cnf(11369,plain,
% 191.32/191.79 (~P1(f773(f773(f232(a847),f773(a114,x113691)),x113691))),
% 191.32/191.79 inference(rename_variables,[],[4461])).
% 191.32/191.79 cnf(11370,plain,
% 191.32/191.79 (~E(f773(a114,x113701),x113701)),
% 191.32/191.79 inference(rename_variables,[],[4364])).
% 191.32/191.79 cnf(11380,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),f773(f773(f82(a847),x113801),x113802)),x113801))),
% 191.32/191.79 inference(rename_variables,[],[4477])).
% 191.32/191.79 cnf(11383,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a1),f773(f102(a1),x113831)),f2(a1)))),
% 191.32/191.79 inference(rename_variables,[],[4468])).
% 191.32/191.79 cnf(11386,plain,
% 191.32/191.79 (~E(f773(a114,x113861),x113861)),
% 191.32/191.79 inference(rename_variables,[],[4364])).
% 191.32/191.79 cnf(11399,plain,
% 191.32/191.79 (P1(f773(f773(f334(x113991),x113992),f773(f773(f302(x113991),x113992),x113993)))),
% 191.32/191.79 inference(rename_variables,[],[3497])).
% 191.32/191.79 cnf(11400,plain,
% 191.32/191.79 (~P1(f773(f773(f232(a1),f2(a1)),f773(f81(a1),f773(f102(a1),f773(a114,x114001)))))),
% 191.32/191.79 inference(rename_variables,[],[4478])).
% 191.32/191.79 cnf(11403,plain,
% 191.32/191.79 (P1(f773(f773(f233(a847),f773(f773(f3(a847),x114031),x114032)),f773(a114,x114031)))),
% 191.32/191.79 inference(rename_variables,[],[3631])).
% 191.32/191.79 cnf(11406,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),f52(a847,x114061,x114062)),x114061))),
% 191.32/191.79 inference(rename_variables,[],[3636])).
% 191.32/191.79 cnf(11412,plain,
% 191.32/191.79 (E(f773(f773(f125(x114121),x114122),f115(x114121)),x114122)),
% 191.32/191.79 inference(rename_variables,[],[3119])).
% 191.32/191.79 cnf(11415,plain,
% 191.32/191.79 (E(f37(x114151,x114152,x114153,x114154,x114155,x114156,x114157,x114158,x114159,a25),x114152)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(11418,plain,
% 191.32/191.79 (E(f37(x114181,x114182,x114183,x114184,x114185,x114186,x114187,x114188,x114189,a25),x114182)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(11422,plain,
% 191.32/191.79 (E(f37(x114221,x114222,x114223,x114224,x114225,x114226,x114227,x114228,x114229,a25),x114222)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(11425,plain,
% 191.32/191.79 (~P1(f773(f773(f232(a847),f773(a114,x114251)),x114251))),
% 191.32/191.79 inference(rename_variables,[],[4461])).
% 191.32/191.79 cnf(11426,plain,
% 191.32/191.79 (E(f37(x114261,x114262,x114263,x114264,x114265,x114266,x114267,x114268,x114269,a25),x114262)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(11435,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x114351),x114351))),
% 191.32/191.79 inference(rename_variables,[],[4448])).
% 191.32/191.79 cnf(11436,plain,
% 191.32/191.79 (E(f37(x114361,x114362,x114363,x114364,x114365,x114366,x114367,x114368,x114369,a25),x114362)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(11439,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),f52(a847,x114391,x114392)),x114391))),
% 191.32/191.79 inference(rename_variables,[],[3636])).
% 191.32/191.79 cnf(11440,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),f2(a847)),x114401))),
% 191.32/191.79 inference(rename_variables,[],[3206])).
% 191.32/191.79 cnf(11457,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x114571),x114571))),
% 191.32/191.79 inference(rename_variables,[],[4448])).
% 191.32/191.79 cnf(11460,plain,
% 191.32/191.79 (E(f37(x114601,x114602,x114603,x114604,x114605,x114606,x114607,x114608,x114609,a25),x114602)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(11463,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x114631),x114631))),
% 191.32/191.79 inference(rename_variables,[],[4448])).
% 191.32/191.79 cnf(11466,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x114661),x114661))),
% 191.32/191.79 inference(rename_variables,[],[4448])).
% 191.32/191.79 cnf(11469,plain,
% 191.32/191.79 (P1(f773(f773(f334(x114691),f773(x114692,x114693)),f773(f303(x114694,x114691,x114692),f239(f855(x114694,a841)))))),
% 191.32/191.79 inference(rename_variables,[],[3786])).
% 191.32/191.79 cnf(11470,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),f773(f773(f82(a847),x114701),x114702)),x114702))),
% 191.32/191.79 inference(rename_variables,[],[4476])).
% 191.32/191.79 cnf(11473,plain,
% 191.32/191.79 (P1(f773(f773(f334(x114731),f773(x114732,x114733)),f773(f303(x114734,x114731,x114732),f239(f855(x114734,a841)))))),
% 191.32/191.79 inference(rename_variables,[],[3786])).
% 191.32/191.79 cnf(11474,plain,
% 191.32/191.79 (~P1(f773(f773(f232(a847),f773(a114,x114741)),x114741))),
% 191.32/191.79 inference(rename_variables,[],[4461])).
% 191.32/191.79 cnf(11479,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),f773(f773(f82(a847),x114791),x114792)),x114791))),
% 191.32/191.79 inference(rename_variables,[],[4477])).
% 191.32/191.79 cnf(11482,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x114821),x114821))),
% 191.32/191.79 inference(rename_variables,[],[4448])).
% 191.32/191.79 cnf(11485,plain,
% 191.32/191.79 (P1(f773(f773(f187(a25),x114851),x114851))),
% 191.32/191.79 inference(rename_variables,[],[3183])).
% 191.32/191.79 cnf(11492,plain,
% 191.32/191.79 (P1(f773(f773(f334(x114921),x114922),f239(f855(x114921,a841))))),
% 191.32/191.79 inference(rename_variables,[],[3340])).
% 191.32/191.79 cnf(11493,plain,
% 191.32/191.79 (~P1(f773(f773(f232(a847),f773(a114,x114931)),x114931))),
% 191.32/191.79 inference(rename_variables,[],[4461])).
% 191.32/191.79 cnf(11496,plain,
% 191.32/191.79 (P1(f773(f773(f187(a25),x114961),x114961))),
% 191.32/191.79 inference(rename_variables,[],[3183])).
% 191.32/191.79 cnf(11509,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x115091),x115092),f180(f855(x115091,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(11512,plain,
% 191.32/191.79 (E(f773(f773(f18(x115121,x115122),x115123),x115124),x115123)),
% 191.32/191.79 inference(rename_variables,[],[3175])).
% 191.32/191.79 cnf(11515,plain,
% 191.32/191.79 (E(f773(f773(f18(x115151,x115152),x115153),x115154),x115153)),
% 191.32/191.79 inference(rename_variables,[],[3175])).
% 191.32/191.79 cnf(11526,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),f773(f773(f43(a847),x115261),x115262)),x115261))),
% 191.32/191.79 inference(rename_variables,[],[3603])).
% 191.32/191.79 cnf(11530,plain,
% 191.32/191.79 (P1(f773(f773(f187(a25),x115301),x115301))),
% 191.32/191.79 inference(rename_variables,[],[3183])).
% 191.32/191.79 cnf(11531,plain,
% 191.32/191.79 (E(f37(x115311,x115312,x115313,x115314,x115315,x115316,x115317,x115318,x115319,a25),x115312)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(11534,plain,
% 191.32/191.79 (P1(f773(f773(f334(x115341),f773(x115342,x115343)),f773(f303(x115344,x115341,x115342),f239(f855(x115344,a841)))))),
% 191.32/191.79 inference(rename_variables,[],[3786])).
% 191.32/191.79 cnf(11537,plain,
% 191.32/191.79 (P1(f773(f63(x115371),f169(x115371,x115372,f166(x115371,x115372,x115373))))),
% 191.32/191.79 inference(rename_variables,[],[3729])).
% 191.32/191.79 cnf(11540,plain,
% 191.32/191.79 (P1(f773(f63(x115401),f169(x115401,x115402,f166(x115401,x115402,x115403))))),
% 191.32/191.79 inference(rename_variables,[],[3729])).
% 191.32/191.79 cnf(11543,plain,
% 191.32/191.79 (P1(f773(f773(f232(a1),f773(f81(a1),f773(f102(a1),x115431))),f773(f102(a1),x115432)))),
% 191.32/191.79 inference(rename_variables,[],[3660])).
% 191.32/191.79 cnf(11546,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x115461),x115462),f180(f855(x115461,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(11567,plain,
% 191.32/191.79 (P1(f773(f773(f187(a25),x115671),x115671))),
% 191.32/191.79 inference(rename_variables,[],[3183])).
% 191.32/191.79 cnf(11568,plain,
% 191.32/191.79 (E(f37(x115681,x115682,x115683,x115684,x115685,x115686,x115687,x115688,x115689,a25),x115682)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(11571,plain,
% 191.32/191.79 (P1(f773(f773(f233(a847),x115711),f773(a114,x115711)))),
% 191.32/191.79 inference(rename_variables,[],[3253])).
% 191.32/191.79 cnf(11574,plain,
% 191.32/191.79 (P1(f773(f773(f232(a1),x115741),x115741))),
% 191.32/191.79 inference(rename_variables,[],[3185])).
% 191.32/191.79 cnf(11585,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x115851),f2(a847)))),
% 191.32/191.79 inference(rename_variables,[],[4452])).
% 191.32/191.79 cnf(11588,plain,
% 191.32/191.79 (P1(f773(f773(f232(a1),x115881),x115881))),
% 191.32/191.79 inference(rename_variables,[],[3185])).
% 191.32/191.79 cnf(11593,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x115931),f2(a847)))),
% 191.32/191.79 inference(rename_variables,[],[4452])).
% 191.32/191.79 cnf(11602,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),f2(a847)),x116021))),
% 191.32/191.79 inference(rename_variables,[],[3206])).
% 191.32/191.79 cnf(11603,plain,
% 191.32/191.79 (~P1(f773(f773(f232(a847),f773(a114,x116031)),x116031))),
% 191.32/191.79 inference(rename_variables,[],[4461])).
% 191.32/191.79 cnf(11606,plain,
% 191.32/191.79 (~P1(f773(f64(x116061,x116062,f180(f855(x116061,a841))),x116063))),
% 191.32/191.79 inference(rename_variables,[],[4475])).
% 191.32/191.79 cnf(11619,plain,
% 191.32/191.79 (P1(f773(f773(f233(a847),x116191),f773(a114,x116191)))),
% 191.32/191.79 inference(rename_variables,[],[3253])).
% 191.32/191.79 cnf(11634,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x116341),x116341))),
% 191.32/191.79 inference(rename_variables,[],[4448])).
% 191.32/191.79 cnf(11637,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x116371),x116371))),
% 191.32/191.79 inference(rename_variables,[],[4448])).
% 191.32/191.79 cnf(11640,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x116401),x116401))),
% 191.32/191.79 inference(rename_variables,[],[4448])).
% 191.32/191.79 cnf(11643,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x116431),x116431))),
% 191.32/191.79 inference(rename_variables,[],[4448])).
% 191.32/191.79 cnf(11646,plain,
% 191.32/191.79 (~P1(f773(f773(f232(a847),f773(a114,x116461)),x116461))),
% 191.32/191.79 inference(rename_variables,[],[4461])).
% 191.32/191.79 cnf(11649,plain,
% 191.32/191.79 (~P1(f773(f773(f232(a847),f773(a114,x116491)),x116491))),
% 191.32/191.79 inference(rename_variables,[],[4461])).
% 191.32/191.79 cnf(11652,plain,
% 191.32/191.79 (~P1(f773(f773(f232(a847),f773(a114,x116521)),x116521))),
% 191.32/191.79 inference(rename_variables,[],[4461])).
% 191.32/191.79 cnf(11655,plain,
% 191.32/191.79 (~P1(f773(f773(f232(a847),f773(a114,x116551)),x116551))),
% 191.32/191.79 inference(rename_variables,[],[4461])).
% 191.32/191.79 cnf(11673,plain,
% 191.32/191.79 (E(f773(f181(f848(x116731)),f773(f141(x116731),x116732)),f773(f181(f848(x116731)),x116732))),
% 191.32/191.79 inference(rename_variables,[],[3197])).
% 191.32/191.79 cnf(11676,plain,
% 191.32/191.79 (P1(f773(f773(f187(a25),x116761),x116761))),
% 191.32/191.79 inference(rename_variables,[],[3183])).
% 191.32/191.79 cnf(11682,plain,
% 191.32/191.79 (P1(f773(f773(f232(a1),x116821),x116821))),
% 191.32/191.79 inference(rename_variables,[],[3185])).
% 191.32/191.79 cnf(11693,plain,
% 191.32/191.79 (P1(f773(f773(f232(a1),x116931),x116931))),
% 191.32/191.79 inference(rename_variables,[],[3185])).
% 191.32/191.79 cnf(11696,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(f854(f848(x116961),f848(x116961)),a841)),f147(x116961,x116962)),f300(f848(x116961),f146(x116961,x116962))))),
% 191.32/191.79 inference(rename_variables,[],[3878])).
% 191.32/191.79 cnf(11703,plain,
% 191.32/191.79 (P1(f773(f773(f233(a847),x117031),f773(a114,x117031)))),
% 191.32/191.79 inference(rename_variables,[],[3253])).
% 191.32/191.79 cnf(11706,plain,
% 191.32/191.79 (P1(f773(f773(f334(f855(x117061,a841)),x117062),f773(f301(x117061),x117062)))),
% 191.32/191.79 inference(rename_variables,[],[3543])).
% 191.32/191.79 cnf(11707,plain,
% 191.32/191.79 (~E(f773(a114,x117071),x117071)),
% 191.32/191.79 inference(rename_variables,[],[4364])).
% 191.32/191.79 cnf(11714,plain,
% 191.32/191.79 (P1(f773(f773(f232(a1),x117141),x117141))),
% 191.32/191.79 inference(rename_variables,[],[3185])).
% 191.32/191.79 cnf(11719,plain,
% 191.32/191.79 (P1(f773(f773(f232(a1),x117191),x117191))),
% 191.32/191.79 inference(rename_variables,[],[3185])).
% 191.32/191.79 cnf(11728,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x117281,a841)),x117282),f773(f773(f302(x117281),x117283),x117282)))),
% 191.32/191.79 inference(rename_variables,[],[3624])).
% 191.32/191.79 cnf(11731,plain,
% 191.32/191.79 (P1(f773(f773(f187(a25),x117311),x117311))),
% 191.32/191.79 inference(rename_variables,[],[3183])).
% 191.32/191.79 cnf(11732,plain,
% 191.32/191.79 (~E(f773(a114,x117321),x117321)),
% 191.32/191.79 inference(rename_variables,[],[4364])).
% 191.32/191.79 cnf(11745,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x117451),x117451))),
% 191.32/191.79 inference(rename_variables,[],[4448])).
% 191.32/191.79 cnf(11746,plain,
% 191.32/191.79 (~E(f773(a114,x117461),x117461)),
% 191.32/191.79 inference(rename_variables,[],[4364])).
% 191.32/191.79 cnf(11749,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x117491),x117491))),
% 191.32/191.79 inference(rename_variables,[],[3184])).
% 191.32/191.79 cnf(11752,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x117521),x117521))),
% 191.32/191.79 inference(rename_variables,[],[3184])).
% 191.32/191.79 cnf(11755,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x117551),x117551))),
% 191.32/191.79 inference(rename_variables,[],[3184])).
% 191.32/191.79 cnf(11758,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x117581),x117581))),
% 191.32/191.79 inference(rename_variables,[],[3184])).
% 191.32/191.79 cnf(11761,plain,
% 191.32/191.79 (P1(f773(f773(f232(a1),x117611),x117611))),
% 191.32/191.79 inference(rename_variables,[],[3185])).
% 191.32/191.79 cnf(11764,plain,
% 191.32/191.79 (P1(f773(f773(f232(a1),x117641),x117641))),
% 191.32/191.79 inference(rename_variables,[],[3185])).
% 191.32/191.79 cnf(11767,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x117671),x117671))),
% 191.32/191.79 inference(rename_variables,[],[4448])).
% 191.32/191.79 cnf(11770,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x117701),x117701))),
% 191.32/191.79 inference(rename_variables,[],[4448])).
% 191.32/191.79 cnf(11771,plain,
% 191.32/191.79 (P1(f773(f773(f233(a847),x117711),f773(a114,x117711)))),
% 191.32/191.79 inference(rename_variables,[],[3253])).
% 191.32/191.79 cnf(11780,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x117801),x117801))),
% 191.32/191.79 inference(rename_variables,[],[4448])).
% 191.32/191.79 cnf(11781,plain,
% 191.32/191.79 (~E(f773(a114,x117811),x117811)),
% 191.32/191.79 inference(rename_variables,[],[4364])).
% 191.32/191.79 cnf(11786,plain,
% 191.32/191.79 (P1(f773(f773(f232(a1),x117861),x117861))),
% 191.32/191.79 inference(rename_variables,[],[3185])).
% 191.32/191.79 cnf(11801,plain,
% 191.32/191.79 (P1(f773(f773(f232(a1),x118011),x118011))),
% 191.32/191.79 inference(rename_variables,[],[3185])).
% 191.32/191.79 cnf(11806,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),f2(a847)),x118061))),
% 191.32/191.79 inference(rename_variables,[],[3206])).
% 191.32/191.79 cnf(11825,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x118251),f2(a847)))),
% 191.32/191.79 inference(rename_variables,[],[4452])).
% 191.32/191.79 cnf(11828,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x118281),f2(a847)))),
% 191.32/191.79 inference(rename_variables,[],[4452])).
% 191.32/191.79 cnf(11831,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x118311),x118312),f180(f855(x118311,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(11834,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x118341),x118342),f180(f855(x118341,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(11837,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x118371),x118371))),
% 191.32/191.79 inference(rename_variables,[],[4448])).
% 191.32/191.79 cnf(11840,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x118401),x118401))),
% 191.32/191.79 inference(rename_variables,[],[4448])).
% 191.32/191.79 cnf(11843,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x118431),x118431))),
% 191.32/191.79 inference(rename_variables,[],[4448])).
% 191.32/191.79 cnf(11846,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x118461),x118461))),
% 191.32/191.79 inference(rename_variables,[],[4448])).
% 191.32/191.79 cnf(11849,plain,
% 191.32/191.79 (P1(f773(f773(f233(a847),x118491),f773(a114,x118491)))),
% 191.32/191.79 inference(rename_variables,[],[3253])).
% 191.32/191.79 cnf(11856,plain,
% 191.32/191.79 (P1(f773(f773(f334(f855(x118561,a841)),x118562),f773(f301(x118561),x118562)))),
% 191.32/191.79 inference(rename_variables,[],[3543])).
% 191.32/191.79 cnf(11861,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x118611,a841)),f773(f158(x118611),f773(f126(x118611,x118612),x118613))),f773(f158(x118611),x118613)))),
% 191.32/191.79 inference(rename_variables,[],[3825])).
% 191.32/191.79 cnf(11868,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x118681),x118682),f180(f855(x118681,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(11877,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x118771,a841)),x118772),f239(f855(x118771,a841))))),
% 191.32/191.79 inference(rename_variables,[],[3560])).
% 191.32/191.79 cnf(11878,plain,
% 191.32/191.79 (~E(f773(a114,x118781),x118781)),
% 191.32/191.79 inference(rename_variables,[],[4364])).
% 191.32/191.79 cnf(11881,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x118811,a841)),f773(f158(x118811),f773(f126(x118811,x118812),x118813))),f773(f158(x118811),x118813)))),
% 191.32/191.79 inference(rename_variables,[],[3825])).
% 191.32/191.79 cnf(11887,plain,
% 191.32/191.79 (P1(f773(f773(f233(a847),x118871),f773(a114,x118871)))),
% 191.32/191.79 inference(rename_variables,[],[3253])).
% 191.32/191.79 cnf(11896,plain,
% 191.32/191.79 (E(f773(f181(f848(x118961)),f773(f141(x118961),x118962)),f773(f181(f848(x118961)),x118962))),
% 191.32/191.79 inference(rename_variables,[],[3197])).
% 191.32/191.79 cnf(11899,plain,
% 191.32/191.79 (P39(a25,x118991,x118992,x118991)),
% 191.32/191.79 inference(rename_variables,[],[3402])).
% 191.32/191.79 cnf(11912,plain,
% 191.32/191.79 (P1(f773(f63(x119121),f180(f855(x119121,a841))))),
% 191.32/191.79 inference(rename_variables,[],[3261])).
% 191.32/191.79 cnf(11913,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x119131),x119132),f180(f855(x119131,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(11916,plain,
% 191.32/191.79 (P39(a25,x119161,x119162,x119161)),
% 191.32/191.79 inference(rename_variables,[],[3402])).
% 191.32/191.79 cnf(11921,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x119211),f2(a847)))),
% 191.32/191.79 inference(rename_variables,[],[4452])).
% 191.32/191.79 cnf(11922,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x119221),x119221))),
% 191.32/191.79 inference(rename_variables,[],[4448])).
% 191.32/191.79 cnf(11929,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x119291,a841)),f773(f158(x119291),f151(x119291,x119292,x119293))),f773(f158(x119291),x119293)))),
% 191.32/191.79 inference(rename_variables,[],[3873])).
% 191.32/191.79 cnf(11934,plain,
% 191.32/191.79 (P29(x119341,x119341,f7(x119341),x119342)),
% 191.32/191.79 inference(rename_variables,[],[3426])).
% 191.32/191.79 cnf(11939,plain,
% 191.32/191.79 (P1(f773(f773(f334(f855(x119391,a841)),x119392),f773(f301(x119391),x119392)))),
% 191.32/191.79 inference(rename_variables,[],[3543])).
% 191.32/191.79 cnf(11946,plain,
% 191.32/191.79 (P1(f773(f773(f187(a25),x119461),x119461))),
% 191.32/191.79 inference(rename_variables,[],[3183])).
% 191.32/191.79 cnf(11949,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x119491),x119492),f180(f855(x119491,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(11952,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x119521,a841)),x119522),f773(f773(f302(x119521),x119523),x119522)))),
% 191.32/191.79 inference(rename_variables,[],[3624])).
% 191.32/191.79 cnf(11953,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x119531,a841)),x119532),f239(f855(x119531,a841))))),
% 191.32/191.79 inference(rename_variables,[],[3560])).
% 191.32/191.79 cnf(11960,plain,
% 191.32/191.79 (P1(f773(f773(f233(a847),x119601),f773(a114,x119601)))),
% 191.32/191.79 inference(rename_variables,[],[3253])).
% 191.32/191.79 cnf(11963,plain,
% 191.32/191.79 (P1(f773(f773(f233(a847),x119631),f773(a114,x119631)))),
% 191.32/191.79 inference(rename_variables,[],[3253])).
% 191.32/191.79 cnf(11966,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x119661),x119661))),
% 191.32/191.79 inference(rename_variables,[],[3184])).
% 191.32/191.79 cnf(11969,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x119691),x119691))),
% 191.32/191.79 inference(rename_variables,[],[3184])).
% 191.32/191.79 cnf(11972,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x119721),x119721))),
% 191.32/191.79 inference(rename_variables,[],[3184])).
% 191.32/191.79 cnf(11975,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x119751),x119751))),
% 191.32/191.79 inference(rename_variables,[],[3184])).
% 191.32/191.79 cnf(11978,plain,
% 191.32/191.79 (P1(f773(f773(f279(a847),x119781),x119781))),
% 191.32/191.79 inference(rename_variables,[],[3186])).
% 191.32/191.79 cnf(11981,plain,
% 191.32/191.79 (P1(f773(f773(f279(a847),x119811),x119811))),
% 191.32/191.79 inference(rename_variables,[],[3186])).
% 191.32/191.79 cnf(11988,plain,
% 191.32/191.79 (P1(f773(f773(f334(f855(x119881,a841)),x119882),f773(f301(x119881),x119882)))),
% 191.32/191.79 inference(rename_variables,[],[3543])).
% 191.32/191.79 cnf(11997,plain,
% 191.32/191.79 (~E(f773(a114,x119971),x119971)),
% 191.32/191.79 inference(rename_variables,[],[4364])).
% 191.32/191.79 cnf(11998,plain,
% 191.32/191.79 (E(f773(f303(x119981,x119981,f7(x119981)),x119982),x119982)),
% 191.32/191.79 inference(rename_variables,[],[3243])).
% 191.32/191.79 cnf(12001,plain,
% 191.32/191.79 (P34(x120011,x120012,f115(x120011),f115(x120011))),
% 191.32/191.79 inference(rename_variables,[],[3434])).
% 191.32/191.79 cnf(12004,plain,
% 191.32/191.79 (~E(f773(a114,x120041),x120041)),
% 191.32/191.79 inference(rename_variables,[],[4364])).
% 191.32/191.79 cnf(12007,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x120071,a841)),f773(f158(x120071),f151(x120071,x120072,x120073))),f773(f158(x120071),x120073)))),
% 191.32/191.79 inference(rename_variables,[],[3873])).
% 191.32/191.79 cnf(12008,plain,
% 191.32/191.79 (P1(f773(f63(x120081),f773(f158(x120081),x120082)))),
% 191.32/191.79 inference(rename_variables,[],[3225])).
% 191.32/191.79 cnf(12019,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x120191),x120191))),
% 191.32/191.79 inference(rename_variables,[],[4448])).
% 191.32/191.79 cnf(12022,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x120221),x120221))),
% 191.32/191.79 inference(rename_variables,[],[4448])).
% 191.32/191.79 cnf(12031,plain,
% 191.32/191.79 (E(f773(f181(f848(x120311)),f773(f141(x120311),x120312)),f773(f181(f848(x120311)),x120312))),
% 191.32/191.79 inference(rename_variables,[],[3197])).
% 191.32/191.79 cnf(12034,plain,
% 191.32/191.79 (P18(a847,f773(f142(a847),f773(f773(f143(f848(x120341),a847),f181(f848(x120341))),f164(x120341,x120342))))),
% 191.32/191.79 inference(rename_variables,[],[3742])).
% 191.32/191.79 cnf(12037,plain,
% 191.32/191.79 (P29(x120371,x120371,f7(x120371),x120372)),
% 191.32/191.79 inference(rename_variables,[],[3426])).
% 191.32/191.79 cnf(12040,plain,
% 191.32/191.79 (P1(f773(f773(f334(f848(x120401)),f115(x120401)),f149(x120401,x120402)))),
% 191.32/191.79 inference(rename_variables,[],[3382])).
% 191.32/191.79 cnf(12043,plain,
% 191.32/191.79 (~P1(f773(f773(f180(f855(x120431,f855(x120432,a841))),x120433),x120434))),
% 191.32/191.79 inference(rename_variables,[],[4479])).
% 191.32/191.79 cnf(12048,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x120481),x120481))),
% 191.32/191.79 inference(rename_variables,[],[3184])).
% 191.32/191.79 cnf(12049,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),f2(a847)),x120491))),
% 191.32/191.79 inference(rename_variables,[],[3206])).
% 191.32/191.79 cnf(12052,plain,
% 191.32/191.79 (~P1(f773(f773(f180(f855(x120521,f855(x120522,a841))),x120523),x120524))),
% 191.32/191.79 inference(rename_variables,[],[4479])).
% 191.32/191.79 cnf(12055,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(f854(f848(x120551),f848(x120551)),a841)),f147(x120551,x120552)),f300(f848(x120551),f146(x120551,x120552))))),
% 191.32/191.79 inference(rename_variables,[],[3878])).
% 191.32/191.79 cnf(12061,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x120611,a841)),f180(f855(x120611,a841))),x120612))),
% 191.32/191.79 inference(rename_variables,[],[3628])).
% 191.32/191.79 cnf(12064,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x120641,a841)),f773(f303(x120642,x120641,x120643),f773(f305(x120642,x120641,x120643),x120644))),x120644))),
% 191.32/191.79 inference(rename_variables,[],[4066])).
% 191.32/191.79 cnf(12067,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x120671,a841)),f773(f158(x120671),f151(x120671,x120672,x120673))),f773(f158(x120671),x120673)))),
% 191.32/191.79 inference(rename_variables,[],[3873])).
% 191.32/191.79 cnf(12068,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x120681,a841)),f773(f158(x120681),f773(f126(x120681,x120682),x120683))),f773(f158(x120681),x120683)))),
% 191.32/191.79 inference(rename_variables,[],[3825])).
% 191.32/191.79 cnf(12073,plain,
% 191.32/191.79 (P29(x120731,f851(x120731),f227(x120731),x120732)),
% 191.32/191.79 inference(rename_variables,[],[3435])).
% 191.32/191.79 cnf(12078,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x120781,a841)),f773(f303(x120782,x120781,x120783),f773(f305(x120782,x120781,x120783),x120784))),x120784))),
% 191.32/191.79 inference(rename_variables,[],[4066])).
% 191.32/191.79 cnf(12081,plain,
% 191.32/191.79 (P1(f773(f63(f851(x120811)),f773(f303(x120812,f851(x120811),f166(x120812,x120811,x120813)),f239(f855(x120812,a841)))))),
% 191.32/191.79 inference(rename_variables,[],[3935])).
% 191.32/191.79 cnf(12086,plain,
% 191.32/191.79 (P1(f773(f773(f334(f855(x120861,a841)),x120862),f773(f301(x120861),x120862)))),
% 191.32/191.79 inference(rename_variables,[],[3543])).
% 191.32/191.79 cnf(12089,plain,
% 191.32/191.79 (~P1(f773(f773(f334(f854(f848(x120891),f848(x120891))),f773(f773(f241(f848(x120891),f848(x120891)),x120892),f115(x120891))),f135(x120891,x120893)))),
% 191.32/191.79 inference(rename_variables,[],[4480])).
% 191.32/191.79 cnf(12092,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x120921),f2(a847)))),
% 191.32/191.79 inference(rename_variables,[],[4452])).
% 191.32/191.79 cnf(12094,plain,
% 191.32/191.79 (~P1(f773(f63(x120941),f239(f855(x120941,a841))))),
% 191.32/191.79 inference(scs_inference,[],[2999,3402,11899,3426,10868,11934,3434,3435,3485,3155,4386,4338,10038,10041,10047,10109,10112,10203,10206,10487,10498,11139,11154,11158,11199,11202,11205,11208,11220,11251,11264,11291,11294,11305,11310,11316,11415,11418,11422,11426,11436,11460,11531,4339,11155,3066,4364,10044,10054,10065,10074,10173,10176,10179,10284,10390,10558,10690,10823,11059,11142,11149,11165,11213,11216,11319,11370,11386,11707,11732,11746,11781,11878,11997,4382,10268,10363,4376,2808,2811,2820,2826,2830,2831,2832,2833,2835,2841,2845,2848,2851,2853,2855,2857,2859,2860,2862,2863,2872,2873,2883,2885,2931,2941,2942,2947,2958,2960,2961,2964,2975,2977,4360,3119,11412,3128,3236,3639,3948,3027,4437,10804,11098,11101,3732,11187,3085,3050,3045,3034,3040,4046,10984,3064,3197,11673,11896,3243,10642,3118,3138,10305,3288,4472,3814,4398,10100,10265,3175,11512,4462,3578,3289,3081,3082,10165,10463,3344,3004,3104,11179,3961,3815,10810,10929,10996,4480,10746,10936,11050,11070,11106,11112,4481,10850,10939,11053,11109,4482,10942,4483,11006,4484,3101,3382,12040,3542,4241,4242,4395,3488,3694,3742,3368,3619,3253,10184,10187,10300,10377,10429,10432,10466,10555,10794,11571,11619,11703,11771,11849,11887,11960,3631,11403,3267,3450,4452,10077,10080,10106,10566,10581,10703,11121,11182,11585,11593,11825,11828,11921,4468,11280,11313,11353,11383,3616,3393,3769,3212,3214,3187,4449,4392,3374,4469,3955,11067,3507,3729,11537,11540,3225,3922,3878,11696,12055,3825,10639,11861,11881,3873,10813,11929,12007,3543,11706,11856,11939,11988,3911,3560,10816,10878,10963,11025,11877,4473,10584,10947,3183,10196,10291,10415,10473,11256,11263,11485,11496,11530,11567,11676,11731,3184,10533,10587,10590,10623,10650,10684,10728,10762,11749,11752,11755,11758,11966,11969,11972,11975,3185,10281,10478,10561,10687,11366,11574,11588,11682,11693,11714,11719,11761,11764,11786,3186,10629,10695,11978,3261,11912,4448,10143,10231,10342,10372,10605,10653,10660,10973,11330,11435,11457,11463,11466,11482,11634,11637,11640,11643,11745,11767,11770,11780,11837,11840,11843,11846,11922,12019,3340,10435,10698,10743,11014,11087,11243,11492,4464,10614,10626,10735,10753,10756,10807,10892,10902,10914,10950,10978,10990,11022,11062,11078,11081,11084,11115,11126,11129,11509,11546,11831,11834,11868,11913,3247,10460,3284,3279,3700,3636,10146,11406,11439,4461,10097,10454,10457,10895,10911,11369,11425,11474,11493,11603,11646,11649,11652,11655,3206,10647,10721,11440,11602,11806,3660,4006,4459,3671,3708,4440,4441,4443,3161,3162,4442,4444,3497,4475,10068,10071,10323,10781,11606,3935,3786,11132,11469,11473,3624,10759,10765,10776,11728,3482,10981,3628,10839,10993,11019,11030,3453,10421,10424,10493,10674,4478,11400,4479,10544,10966,11118,12043,4066,10632,12064,3966,3659,3603,4476,10119,10122,10448,10451,11277,4477,11380,3629,10418,3630,3895,4489,4494,4500,4562,4565,4593,4611,4618,4619,4655,4684,4690,4794,4795,4832,4855,4856,4879,4881,4894,4898,4918,4924,4941,4945,4946,4951,4956,4957,4979,5003,5004,5014,5019,5025,5070,5071,5079,5088,5090,5091,5100,5102,5110,5115,5128,5134,5137,5138,5142,5175,5185,5192,5194,5195,5198,5199,5200,5208,5209,5212,5216,5217,5218,5225,5229,5230,5231,5239,5242,5244,5250,5261,5268,5281,5283,5291,5292,5296,5299,5324,5330,5340,5341,5342,5357,5369,5391,5397,5415,5416,5419,5438,5446,5447,5449,5450,5459,5460,5474,5478,5487,5488,5490,5505,5508,5519,5530,5537,5550,5556,5562,5563,5564,5567,5572,5609,5611,5614,5616,5619,5620,5621,5623,5625,5627,5630,5637,5651,5665,5671,5672,5691,5692,5697,5698,5700,5703,5706,5707,5712,5756,5770,5778,5782,5794,5804,5821,5839,5842,5852,5879,5894,5921,5941,5942,5945,5959,5961,5962,5964,5977,5978,5981,5983,5986,5987,6001,6007,6008,6009,6012,6014,6056,6066,6075,6110,6112,6114,6116,6126,6128,6131,6137,6139,6143,6146,6154,6161,6162,6163,6169,6195,6202,6209,6245,6246,6250,6251,6252,6253,6254,6255,6256,6263,6300,6301,6310,6330,6331,6356,6360,6371,6372,6380,6411,6412,6427,6449,6450,6469,6472,6473,6519,6527,6552,6593,6609,6618,6627,6628,6629,6630,6652,6653,6659,6671,6674,6677,6679,6680,6681,6683,6697,6710,6712,6713,6724,6727,6784,6797,6799,6805,6819,6822,6823,6860,6875,6903,6936,6986,7017,7074,7102,7105,7163,7175,7242,7244,7259,7269,7272,7273,7291,7297,7299,7352,7362,7368,7371,7384,7429,7432,7436,7483,7484,7502,7565,7572,7591,7615,7637,7651,7667,7676,7684,7713,7715,7717,7725,7769,7779,7804,7862,7894,7928,7973,7988,8076,8124,8143,8167,8186,8208,8307,8309,8315,8335,8339,8353,8374,8385,8387,8399,8405,8409,8433,8448,8449,8460,8461,8462,8468,8469,8474,8475,8476,8477,8478,8496,8497,8498,8506,8518,8520,8534,8536,8542,8547,8568,8569,8598,8611,8615,8633,8654,8655,8657,8658,8668,8669,8691,8700,8707,8708,8709,8710,8733,8734,8745,8781,8787,8791,8804,8807,8809,8810,8817,8826,8891,8920,8921,8922,8936,8950,8956,8983,8984,8985,8986,8987,8990,9027,9030,9054,9088,9098,9099,9109,9119,9120,9134,9144,9146,9165,9187,9248,9286,9287,9288,9314,9315,9332,9349,9356,9367,9390,9408,9418,9419,9420,9421,9422,9437,9442,9477,9478,9484,9485,9521,9522,9547,9571,9573,9574,9589,9595,9619,9648,9695,9732,9745,9747,9751,9752,9754,9763,9764,9784,9789,9810,9815,9886,9962,9963,10014,2,8,9,4503,4519,4550,4551,4553,4577,4585,4586,4597,4644,4646,4689,4717,4809,4810,4826,4845,4901,4904,4905,4908,4909,4921,4931,4943,4944,4954,4963,4974,4975,4993,4998,4999,5000,5001,5002,5010,5013,5020,5084,5094,5125,5135,5140,5156,5174,5181,5182,5184,5189,5204,5206,5207,5214,5221,5222,5235,5236,5237,5238,5240,5241,5246,5247,5248,5249,5277,5278,5279,5287,5288,5289,5290,5319,5335,5337,5339,5376,5378,5379,5381,5382,5384,5385,5387,5396,5401,5403,5405,5406,5407,5408,5409,5410,5417,5427,5430,5441,5453,5454,5457,5467,5470,5471,5472,5497,5507,5521,5522,5531,5532,5534,5536,5540,5574,5578,5580,5638,5673,5674,5687,5690,5693,5694,5695,5696,5704,5708,5718,5719,5721,5722,5730,5751,5786,5799,5800,5801,5805,5815,5829,5833,5834,5835,5838,5854,5865,5866,5896,5897,5901,5923,5927,5930,5948,5953,5954,5979,5982,5990,5997,5999,6006,6010,6018,6019,6020,6021,6059,6060,6076,6130,6164,6166,6167,6191,6192,6194,6198,6199,6205,6219,6238,6258,6259,6264,6276,6277,6280,6293,6314,6319,6321,6335,6336,6340,6342,6343,6344,6346,6348,6349,6350,6358,6365,6366,6367,6368,6374,6376,6383,6420,6426,6441,6444,6445,6446,6484,6486,6488,6493,6494,6505,6508,6523,6548,6549,6550,6551,6562,6566,6583,6587,6610,6631,6647,6648,6649,6654,6667,6689,6691,6693,6695,6698,6699,6706,6708,6721,6729,6769,6772,6773,6789,6790,6791,6792,6812,6813,6831,6858,6880,6890,6892,6893,6895,6897,6898,6932,6933,6934,6939,6940,6942,6944,6945,6946,6968,6976,6977,6989,6999,7041,7050,7056,7064,7075,7080,7082,7088,7096,7109,7126,7143,7145,7155,7161,7222,7224,7225,7226,7234,7235,7241,7243,7268,7313,7332,7349,7365,7366,7383,7411,7415,7440,7467,7485,7488,7489,7499,7517,7518,7520,7522,7524,7526,7527,7528,7580,7581,7614,7616,7617,7618,7624,7643,7652,7663,7668,7674,7675,7681,7691,7692,7694,7723,7750,7780,7817,7818,7865,7872,7873,7895,7896,7915,7916,7981,7982,7983,8003,8004,8038,8042,8046,8055,8069,8096,8100,8106])).
% 191.32/191.79 cnf(12095,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x120951,a841)),x120952),x120952))),
% 191.32/191.79 inference(rename_variables,[],[3482])).
% 191.32/191.79 cnf(12098,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x120981),x120982),f180(f855(x120981,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(12101,plain,
% 191.32/191.79 (~P1(f773(f773(f180(f855(x121011,f855(x121012,a841))),x121013),x121014))),
% 191.32/191.79 inference(rename_variables,[],[4479])).
% 191.32/191.79 cnf(12104,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x121041,a841)),f773(f303(x121042,x121041,x121043),f773(f305(x121042,x121041,x121043),x121044))),x121044))),
% 191.32/191.79 inference(rename_variables,[],[4066])).
% 191.32/191.79 cnf(12105,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x121051,a841)),x121052),x121052))),
% 191.32/191.79 inference(rename_variables,[],[3482])).
% 191.32/191.79 cnf(12110,plain,
% 191.32/191.79 (E(f37(x121101,x121102,x121103,x121104,x121105,x121106,x121107,x121108,x121109,a25),x121102)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(12113,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x121131,a841)),f773(f158(x121131),f151(x121131,x121132,x121133))),f773(f158(x121131),x121133)))),
% 191.32/191.79 inference(rename_variables,[],[3873])).
% 191.32/191.79 cnf(12114,plain,
% 191.32/191.79 (P1(f773(f63(x121141),f773(f158(x121141),x121142)))),
% 191.32/191.79 inference(rename_variables,[],[3225])).
% 191.32/191.79 cnf(12117,plain,
% 191.32/191.79 (P1(f773(f773(f187(a25),x121171),x121171))),
% 191.32/191.79 inference(rename_variables,[],[3183])).
% 191.32/191.79 cnf(12120,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x121201),x121201))),
% 191.32/191.79 inference(rename_variables,[],[4448])).
% 191.32/191.79 cnf(12123,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x121231),x121231))),
% 191.32/191.79 inference(rename_variables,[],[4448])).
% 191.32/191.79 cnf(12134,plain,
% 191.32/191.79 (P29(x121341,x121341,f7(x121341),x121342)),
% 191.32/191.79 inference(rename_variables,[],[3426])).
% 191.32/191.79 cnf(12141,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x121411),x121412),f180(f855(x121411,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(12144,plain,
% 191.32/191.79 (P1(f773(f773(f334(f854(x121441,x121441)),f773(f773(f241(x121441,x121441),x121442),x121442)),f300(x121441,x121443)))),
% 191.32/191.79 inference(rename_variables,[],[3815])).
% 191.32/191.79 cnf(12147,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x121471),x121472),f180(f855(x121471,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(12150,plain,
% 191.32/191.79 (P1(f773(f773(f334(f854(x121501,x121501)),f773(f773(f241(x121501,x121501),x121502),x121502)),f300(x121501,x121503)))),
% 191.32/191.79 inference(rename_variables,[],[3815])).
% 191.32/191.79 cnf(12160,plain,
% 191.32/191.79 (~E(f773(f773(f140(x121601),x121602),x121603),x121603)),
% 191.32/191.79 inference(rename_variables,[],[4398])).
% 191.32/191.79 cnf(12163,plain,
% 191.32/191.79 (P1(f773(f773(f334(x121631),x121632),f239(f855(x121631,a841))))),
% 191.32/191.79 inference(rename_variables,[],[3340])).
% 191.32/191.79 cnf(12164,plain,
% 191.32/191.79 (~E(f773(a114,x121641),x121641)),
% 191.32/191.79 inference(rename_variables,[],[4364])).
% 191.32/191.79 cnf(12167,plain,
% 191.32/191.79 (P1(f773(f773(f334(f848(x121671)),f115(x121671)),f149(x121671,x121672)))),
% 191.32/191.79 inference(rename_variables,[],[3382])).
% 191.32/191.79 cnf(12168,plain,
% 191.32/191.79 (~E(f773(f773(f140(x121681),x121682),x121683),f115(x121681))),
% 191.32/191.79 inference(rename_variables,[],[4407])).
% 191.32/191.79 cnf(12171,plain,
% 191.32/191.79 (P1(f773(f773(f334(x121711),f773(x121712,x121713)),f773(f303(x121714,x121711,x121712),f239(f855(x121714,a841)))))),
% 191.32/191.79 inference(rename_variables,[],[3786])).
% 191.32/191.79 cnf(12172,plain,
% 191.32/191.79 (P29(x121721,x121721,f7(x121721),x121722)),
% 191.32/191.79 inference(rename_variables,[],[3426])).
% 191.32/191.79 cnf(12175,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x121751,a841)),f180(f855(x121751,a841))),x121752))),
% 191.32/191.79 inference(rename_variables,[],[3628])).
% 191.32/191.79 cnf(12176,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x121761,a841)),x121762),x121762))),
% 191.32/191.79 inference(rename_variables,[],[3482])).
% 191.32/191.79 cnf(12179,plain,
% 191.32/191.79 (P1(f773(f773(f334(x121791),f773(x121792,x121793)),f773(f303(x121794,x121791,x121792),f239(f855(x121794,a841)))))),
% 191.32/191.79 inference(rename_variables,[],[3786])).
% 191.32/191.79 cnf(12180,plain,
% 191.32/191.79 (P29(x121801,x121801,f7(x121801),x121802)),
% 191.32/191.79 inference(rename_variables,[],[3426])).
% 191.32/191.79 cnf(12183,plain,
% 191.32/191.79 (P1(f773(f773(f334(f854(f848(x121831),f848(x121831))),f773(f773(f241(f848(x121831),f848(x121831)),f115(x121831)),f115(x121831))),f147(x121831,x121832)))),
% 191.32/191.79 inference(rename_variables,[],[3961])).
% 191.32/191.79 cnf(12189,plain,
% 191.32/191.79 (P29(x121891,x121891,f7(x121891),x121892)),
% 191.32/191.79 inference(rename_variables,[],[3426])).
% 191.32/191.79 cnf(12192,plain,
% 191.32/191.79 (E(f773(f773(f125(x121921),x121922),f115(x121921)),x121922)),
% 191.32/191.79 inference(rename_variables,[],[3119])).
% 191.32/191.79 cnf(12193,plain,
% 191.32/191.79 (~E(f773(f773(f140(x121931),x121932),x121933),x121933)),
% 191.32/191.79 inference(rename_variables,[],[4398])).
% 191.32/191.79 cnf(12196,plain,
% 191.32/191.79 (E(f773(f773(f125(x121961),x121962),f115(x121961)),x121962)),
% 191.32/191.79 inference(rename_variables,[],[3119])).
% 191.32/191.79 cnf(12197,plain,
% 191.32/191.79 (~E(f773(f773(f140(x121971),x121972),x121973),x121973)),
% 191.32/191.79 inference(rename_variables,[],[4398])).
% 191.32/191.79 cnf(12200,plain,
% 191.32/191.79 (E(f773(f773(f125(x122001),x122002),f115(x122001)),x122002)),
% 191.32/191.79 inference(rename_variables,[],[3119])).
% 191.32/191.79 cnf(12209,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x122091,a841)),x122092),f239(f855(x122091,a841))))),
% 191.32/191.79 inference(rename_variables,[],[3560])).
% 191.32/191.79 cnf(12213,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x122131),x122131))),
% 191.32/191.79 inference(rename_variables,[],[4448])).
% 191.32/191.79 cnf(12214,plain,
% 191.32/191.79 (~E(f773(a114,x122141),x122141)),
% 191.32/191.79 inference(rename_variables,[],[4364])).
% 191.32/191.79 cnf(12217,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x122171,a841)),f180(f855(x122171,a841))),x122172))),
% 191.32/191.79 inference(rename_variables,[],[3628])).
% 191.32/191.79 cnf(12220,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x122201),x122201))),
% 191.32/191.79 inference(rename_variables,[],[3184])).
% 191.32/191.79 cnf(12223,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x122231,a841)),x122232),x122232))),
% 191.32/191.79 inference(rename_variables,[],[3482])).
% 191.32/191.79 cnf(12228,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x122281,a841)),x122282),f773(f773(f302(x122281),x122283),x122282)))),
% 191.32/191.79 inference(rename_variables,[],[3624])).
% 191.32/191.79 cnf(12231,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x122311,a841)),x122312),x122312))),
% 191.32/191.79 inference(rename_variables,[],[3482])).
% 191.32/191.79 cnf(12232,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x122321),x122322),f180(f855(x122321,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(12235,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x122351),x122352),f180(f855(x122351,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(12242,plain,
% 191.32/191.79 (P29(x122421,x122421,f7(x122421),x122422)),
% 191.32/191.79 inference(rename_variables,[],[3426])).
% 191.32/191.79 cnf(12245,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x122451),x122452),f180(f855(x122451,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(12248,plain,
% 191.32/191.79 (P1(f773(f773(f334(x122481),f773(x122482,x122483)),f773(f303(x122484,x122481,x122482),f239(f855(x122484,a841)))))),
% 191.32/191.79 inference(rename_variables,[],[3786])).
% 191.32/191.79 cnf(12249,plain,
% 191.32/191.79 (P1(f773(f773(f334(f854(x122491,x122491)),f773(f773(f241(x122491,x122491),x122492),x122492)),f300(x122491,x122493)))),
% 191.32/191.79 inference(rename_variables,[],[3815])).
% 191.32/191.79 cnf(12252,plain,
% 191.32/191.79 (P1(f773(f773(f334(f854(x122521,x122521)),f773(f773(f241(x122521,x122521),x122522),x122522)),f300(x122521,x122523)))),
% 191.32/191.79 inference(rename_variables,[],[3815])).
% 191.32/191.79 cnf(12255,plain,
% 191.32/191.79 (P1(f773(f63(x122551),f773(f158(x122551),x122552)))),
% 191.32/191.79 inference(rename_variables,[],[3225])).
% 191.32/191.79 cnf(12262,plain,
% 191.32/191.79 (P1(f773(f773(f334(f854(x122621,x122621)),f773(f773(f241(x122621,x122621),x122622),x122622)),f773(f773(f281(x122621,x122621,x122621),f300(x122621,x122623)),f300(x122621,f300(x122621,x122623)))))),
% 191.32/191.79 inference(scs_inference,[],[2999,3402,11899,3426,10868,11934,12037,12134,12172,12180,12189,3434,3435,3485,3155,4386,4338,10038,10041,10047,10109,10112,10203,10206,10487,10498,11139,11154,11158,11199,11202,11205,11208,11220,11251,11264,11291,11294,11305,11310,11316,11415,11418,11422,11426,11436,11460,11531,11568,4339,11155,3066,4364,10044,10054,10065,10074,10173,10176,10179,10284,10390,10558,10690,10823,11059,11142,11149,11165,11213,11216,11319,11370,11386,11707,11732,11746,11781,11878,11997,12004,12164,4382,10268,10363,3240,4376,2808,2811,2820,2826,2830,2831,2832,2833,2835,2841,2845,2848,2851,2853,2855,2857,2859,2860,2862,2863,2868,2872,2873,2883,2885,2931,2941,2942,2947,2958,2960,2961,2964,2975,2977,4360,3119,11412,12192,12196,12200,3128,3236,3639,3948,3027,4378,4437,10804,11098,11101,3732,11187,3085,3050,3045,3034,3040,4046,10984,3064,3197,11673,11896,3243,10642,11998,3117,3118,3138,10305,3288,4472,3814,4398,10100,10265,11056,12160,12193,4407,12168,3175,11512,4462,3578,3289,3081,3082,10165,10463,3344,3004,3104,11179,3961,12183,3815,10810,10929,10996,12144,12150,12249,12252,4480,10746,10936,11050,11070,11106,11112,12089,4481,10850,10939,11053,11109,4482,10942,4483,11006,4484,3101,3382,12040,12167,3542,4241,4242,4395,11170,3488,3694,3742,3368,3619,3253,10184,10187,10300,10377,10429,10432,10466,10555,10794,11571,11619,11703,11771,11849,11887,11960,11963,3631,11403,3267,3450,4452,10077,10080,10106,10566,10581,10703,11121,11182,11585,11593,11825,11828,11921,12092,4468,11280,11313,11353,11383,3616,3393,3769,3212,3214,3187,4449,4392,3569,3374,4469,3955,11067,3507,3729,11537,11540,3225,12008,12114,3922,3878,11696,12055,3825,10639,11861,11881,3873,10813,11929,12007,12067,12113,3543,11706,11856,11939,11988,3911,3560,10816,10878,10963,11025,11877,11953,4473,10584,10947,3183,10196,10291,10415,10473,11256,11263,11485,11496,11530,11567,11676,11731,11946,3184,10533,10587,10590,10623,10650,10684,10728,10762,11749,11752,11755,11758,11966,11969,11972,11975,12048,3185,10281,10478,10561,10687,11366,11574,11588,11682,11693,11714,11719,11761,11764,11786,3186,10629,10695,11978,3261,11912,4448,10143,10231,10342,10372,10605,10653,10660,10973,11330,11435,11457,11463,11466,11482,11634,11637,11640,11643,11745,11767,11770,11780,11837,11840,11843,11846,11922,12019,12022,12120,12123,3340,10435,10698,10743,11014,11087,11243,11492,4464,10614,10626,10735,10753,10756,10807,10892,10902,10914,10950,10978,10990,11022,11062,11078,11081,11084,11115,11126,11129,11509,11546,11831,11834,11868,11913,11949,12098,12141,12147,12232,12235,3247,10460,3284,3279,3700,3636,10146,11406,11439,4461,10097,10454,10457,10895,10911,11369,11425,11474,11493,11603,11646,11649,11652,11655,3206,10647,10721,11440,11602,11806,3660,4006,4459,3671,3708,4440,4441,4443,3161,3162,4442,4444,3497,4475,10068,10071,10323,10781,11606,3935,3786,11132,11469,11473,11534,12171,12179,3624,10759,10765,10776,11728,11952,3482,10981,12095,12105,12176,12223,3628,10839,10993,11019,11030,12061,12175,3453,10421,10424,10493,10674,4478,11400,4479,10544,10966,11118,12043,12052,4066,10632,12064,12078,3966,3659,3603,4476,10119,10122,10448,10451,11277,4477,11380,3629,10418,3630,3895,4489,4494,4500,4562,4565,4593,4611,4618,4619,4655,4684,4690,4794,4795,4832,4855,4856,4879,4881,4894,4898,4918,4924,4941,4945,4946,4951,4956,4957,4979,5003,5004,5014,5019,5025,5070,5071,5079,5088,5090,5091,5100,5102,5110,5115,5128,5134,5137,5138,5142,5175,5185,5192,5194,5195,5198,5199,5200,5208,5209,5212,5216,5217,5218,5225,5229,5230,5231,5239,5242,5244,5250,5261,5268,5281,5283,5291,5292,5296,5299,5324,5330,5340,5341,5342,5357,5369,5391,5397,5415,5416,5419,5438,5446,5447,5449,5450,5459,5460,5474,5478,5487,5488,5490,5505,5508,5519,5530,5537,5550,5556,5562,5563,5564,5567,5572,5609,5611,5614,5616,5619,5620,5621,5623,5625,5627,5630,5637,5651,5665,5671,5672,5691,5692,5697,5698,5700,5703,5706,5707,5712,5756,5770,5778,5782,5794,5804,5821,5839,5842,5852,5879,5894,5921,5941,5942,5945,5959,5961,5962,5964,5977,5978,5981,5983,5986,5987,6001,6007,6008,6009,6012,6014,6056,6066,6075,6110,6112,6114,6116,6126,6128,6131,6137,6139,6143,6146,6154,6161,6162,6163,6169,6195,6202,6209,6245,6246,6250,6251,6252,6253,6254,6255,6256,6263,6300,6301,6310,6330,6331,6356,6360,6371,6372,6380,6411,6412,6427,6449,6450,6469,6472,6473,6519,6527,6552,6593,6609,6618,6627,6628,6629,6630,6652,6653,6659,6671,6674,6677,6679,6680,6681,6683,6697,6710,6712,6713,6724,6727,6784,6797,6799,6805,6819,6822,6823,6860,6875,6903,6936,6986,7017,7074,7102,7105,7163,7175,7242,7244,7259,7269,7272,7273,7291,7297,7299,7352,7362,7368,7371,7384,7429,7432,7436,7483,7484,7502,7565,7572,7591,7615,7637,7651,7667,7676,7684,7713,7715,7717,7725,7769,7779,7804,7862,7894,7928,7973,7988,8076,8124,8143,8167,8186,8208,8307,8309,8315,8335,8339,8353,8374,8385,8387,8399,8405,8409,8433,8448,8449,8460,8461,8462,8468,8469,8474,8475,8476,8477,8478,8496,8497,8498,8506,8518,8520,8534,8536,8542,8547,8568,8569,8598,8611,8615,8633,8654,8655,8657,8658,8668,8669,8691,8700,8707,8708,8709,8710,8733,8734,8745,8781,8787,8791,8804,8807,8809,8810,8817,8826,8891,8920,8921,8922,8936,8950,8956,8983,8984,8985,8986,8987,8990,9027,9030,9054,9088,9098,9099,9109,9119,9120,9134,9144,9146,9165,9187,9248,9286,9287,9288,9314,9315,9332,9349,9356,9367,9390,9408,9418,9419,9420,9421,9422,9437,9442,9477,9478,9484,9485,9521,9522,9547,9571,9573,9574,9589,9595,9619,9648,9695,9732,9745,9747,9751,9752,9754,9763,9764,9784,9789,9810,9815,9886,9962,9963,10014,2,8,9,4503,4519,4550,4551,4553,4577,4585,4586,4597,4644,4646,4689,4717,4809,4810,4826,4845,4901,4904,4905,4908,4909,4921,4931,4943,4944,4954,4963,4974,4975,4993,4998,4999,5000,5001,5002,5010,5013,5020,5084,5094,5125,5135,5140,5156,5174,5181,5182,5184,5189,5204,5206,5207,5214,5221,5222,5235,5236,5237,5238,5240,5241,5246,5247,5248,5249,5277,5278,5279,5287,5288,5289,5290,5319,5335,5337,5339,5376,5378,5379,5381,5382,5384,5385,5387,5396,5401,5403,5405,5406,5407,5408,5409,5410,5417,5427,5430,5441,5453,5454,5457,5467,5470,5471,5472,5497,5507,5521,5522,5531,5532,5534,5536,5540,5574,5578,5580,5638,5673,5674,5687,5690,5693,5694,5695,5696,5704,5708,5718,5719,5721,5722,5730,5751,5786,5799,5800,5801,5805,5815,5829,5833,5834,5835,5838,5854,5865,5866,5896,5897,5901,5923,5927,5930,5948,5953,5954,5979,5982,5990,5997,5999,6006,6010,6018,6019,6020,6021,6059,6060,6076,6130,6164,6166,6167,6191,6192,6194,6198,6199,6205,6219,6238,6258,6259,6264,6276,6277,6280,6293,6314,6319,6321,6335,6336,6340,6342,6343,6344,6346,6348,6349,6350,6358,6365,6366,6367,6368,6374,6376,6383,6420,6426,6441,6444,6445,6446,6484,6486,6488,6493,6494,6505,6508,6523,6548,6549,6550,6551,6562,6566,6583,6587,6610,6631,6647,6648,6649,6654,6667,6689,6691,6693,6695,6698,6699,6706,6708,6721,6729,6769,6772,6773,6789,6790,6791,6792,6812,6813,6831,6858,6880,6890,6892,6893,6895,6897,6898,6932,6933,6934,6939,6940,6942,6944,6945,6946,6968,6976,6977,6989,6999,7041,7050,7056,7064,7075,7080,7082,7088,7096,7109,7126,7143,7145,7155,7161,7222,7224,7225,7226,7234,7235,7241,7243,7268,7313,7332,7349,7365,7366,7383,7411,7415,7440,7467,7485,7488,7489,7499,7517,7518,7520,7522,7524,7526,7527,7528,7580,7581,7614,7616,7617,7618,7624,7643,7652,7663,7668,7674,7675,7681,7691,7692,7694,7723,7750,7780,7817,7818,7865,7872,7873,7895,7896,7915,7916,7981,7982,7983,8003,8004,8038,8042,8046,8055,8069,8096,8100,8106,8119,8138,8144,8166,8206,8236,8248,8265,8268,8297,8324,8388,8389,8392,8393,8410,8500,8501,8502,8503,8526,8550,8572,8614,8632,8685,8726,8729,8742,8779,8797,8813,8814,8829,8830,8958,8963,8981,8997,9017,9019,9022,9025,9028,9029,9041,9042,9065,9138,9173,9174,9239,9245,9279,9290])).
% 191.32/191.79 cnf(12265,plain,
% 191.32/191.79 (~P1(f773(f773(f180(f855(x122651,f855(x122652,a841))),x122653),x122654))),
% 191.32/191.79 inference(rename_variables,[],[4479])).
% 191.32/191.79 cnf(12268,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x122681,a841)),x122682),f239(f855(x122681,a841))))),
% 191.32/191.79 inference(rename_variables,[],[3560])).
% 191.32/191.79 cnf(12271,plain,
% 191.32/191.79 (P1(f773(f773(f334(f854(x122711,x122711)),f773(f773(f241(x122711,x122711),x122712),x122712)),f300(x122711,x122713)))),
% 191.32/191.79 inference(rename_variables,[],[3815])).
% 191.32/191.79 cnf(12274,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),f773(f773(f82(a847),x122741),x122742)),x122742))),
% 191.32/191.79 inference(rename_variables,[],[4476])).
% 191.32/191.79 cnf(12275,plain,
% 191.32/191.79 (P1(f773(f773(f233(a847),x122751),f773(a114,x122751)))),
% 191.32/191.79 inference(rename_variables,[],[3253])).
% 191.32/191.79 cnf(12278,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x122781,a841)),x122782),f239(f855(x122781,a841))))),
% 191.32/191.79 inference(rename_variables,[],[3560])).
% 191.32/191.79 cnf(12281,plain,
% 191.32/191.79 (E(f37(x122811,x122812,x122813,x122814,x122815,x122816,x122817,x122818,x122819,a25),x122812)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(12292,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x122921),x122922),f180(f855(x122921,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(12293,plain,
% 191.32/191.79 (P1(f773(f773(f334(f854(f848(x122931),f848(x122931))),f773(f773(f241(f848(x122931),f848(x122931)),f115(x122931)),f115(x122931))),f147(x122931,x122932)))),
% 191.32/191.79 inference(rename_variables,[],[3961])).
% 191.32/191.79 cnf(12298,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x122981),x122982),f180(f855(x122981,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(12301,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x123011),x123012),f180(f855(x123011,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(12304,plain,
% 191.32/191.79 (P1(f773(f773(f187(a25),x123041),x123041))),
% 191.32/191.79 inference(rename_variables,[],[3183])).
% 191.32/191.79 cnf(12307,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x123071),x123071))),
% 191.32/191.79 inference(rename_variables,[],[4448])).
% 191.32/191.79 cnf(12310,plain,
% 191.32/191.79 (P1(f773(f773(f334(x123101),x123102),f239(f855(x123101,a841))))),
% 191.32/191.79 inference(rename_variables,[],[3340])).
% 191.32/191.79 cnf(12320,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x123201),x123202),f180(f855(x123201,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(12323,plain,
% 191.32/191.79 (P1(f773(f773(f232(a1),f2(a1)),f773(f773(f242(a1),f773(f77(a1),x123231)),x123232)))),
% 191.32/191.79 inference(rename_variables,[],[3659])).
% 191.32/191.79 cnf(12326,plain,
% 191.32/191.79 (~E(f773(a114,x123261),x123261)),
% 191.32/191.79 inference(rename_variables,[],[4364])).
% 191.32/191.79 cnf(12328,plain,
% 191.32/191.79 (E(f37(x123281,x123282,x123283,x123284,x123285,x123286,x123287,x123288,x123289,a25),x123282)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(12330,plain,
% 191.32/191.79 (E(f37(x123301,x123302,x123303,x123304,x123305,x123306,x123307,x123308,x123309,a25),x123302)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(12332,plain,
% 191.32/191.79 (P28(x123321,x123322,f180(f855(f846(x123321),a841)))),
% 191.32/191.79 inference(rename_variables,[],[3239])).
% 191.32/191.79 cnf(12337,plain,
% 191.32/191.79 (P39(a25,x123371,x123372,x123371)),
% 191.32/191.79 inference(rename_variables,[],[3402])).
% 191.32/191.79 cnf(12339,plain,
% 191.32/191.79 (P39(a25,x123391,x123392,x123391)),
% 191.32/191.79 inference(rename_variables,[],[3402])).
% 191.32/191.79 cnf(12343,plain,
% 191.32/191.79 (E(f37(x123431,x123432,x123433,x123434,x123435,x123436,x123437,x123438,x123439,a25),x123432)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(12350,plain,
% 191.32/191.79 (E(f37(x123501,x123502,x123503,x123504,x123505,x123506,x123507,x123508,x123509,a25),x123502)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(12355,plain,
% 191.32/191.79 (P29(x123551,x123551,f7(x123551),x123552)),
% 191.32/191.79 inference(rename_variables,[],[3426])).
% 191.32/191.79 cnf(12357,plain,
% 191.32/191.79 (P29(x123571,x123571,f7(x123571),x123572)),
% 191.32/191.79 inference(rename_variables,[],[3426])).
% 191.32/191.79 cnf(12368,plain,
% 191.32/191.79 (E(f37(x123681,x123682,x123683,x123684,x123685,x123686,x123687,x123688,x123689,a25),x123682)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(12370,plain,
% 191.32/191.79 (P53(x123701,x123701,f260(x123701,x123702))),
% 191.32/191.79 inference(rename_variables,[],[3155])).
% 191.32/191.79 cnf(12376,plain,
% 191.32/191.79 (P47(x123761,x123762,f260(x123761,x123762))),
% 191.32/191.79 inference(rename_variables,[],[3154])).
% 191.32/191.79 cnf(12378,plain,
% 191.32/191.79 (P47(x123781,x123782,f260(x123781,x123782))),
% 191.32/191.79 inference(rename_variables,[],[3154])).
% 191.32/191.79 cnf(12383,plain,
% 191.32/191.79 (E(f180(f855(f854(x123831,x123831),a841)),f260(x123831,f180(f855(x123831,a841))))),
% 191.32/191.79 inference(rename_variables,[],[3256])).
% 191.32/191.79 cnf(12387,plain,
% 191.32/191.79 (E(f37(x123871,x123872,x123873,x123874,x123875,x123876,x123877,x123878,x123879,a25),x123872)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(12389,plain,
% 191.32/191.79 (E(f37(x123891,x123892,x123893,x123894,x123895,x123896,x123897,x123898,x123899,a25),x123892)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(12391,plain,
% 191.32/191.79 (E(f37(x123911,x123912,x123913,x123914,x123915,x123916,x123917,x123918,x123919,a25),x123912)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(12395,plain,
% 191.32/191.79 (E(f37(x123951,x123952,x123953,x123954,x123955,x123956,x123957,x123958,x123959,a25),x123952)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(12397,plain,
% 191.32/191.79 (P31(x123971,f2(a847),f773(f773(f773(f93(x123971),x123972),f773(a27,x123973)),x123974))),
% 191.32/191.79 inference(rename_variables,[],[3553])).
% 191.32/191.79 cnf(12404,plain,
% 191.32/191.79 (P37(x124041,f183(x124041))),
% 191.32/191.79 inference(rename_variables,[],[3024])).
% 191.32/191.79 cnf(12411,plain,
% 191.32/191.79 (P19(x124111,f855(x124111,a841),f302(x124111))),
% 191.32/191.79 inference(rename_variables,[],[3158])).
% 191.32/191.79 cnf(12415,plain,
% 191.32/191.79 (P41(x124151,x124152,x124153,x124154,f180(f855(x124151,a841)),x124154)),
% 191.32/191.79 inference(rename_variables,[],[4128])).
% 191.32/191.79 cnf(12418,plain,
% 191.32/191.79 (P41(x124181,x124182,x124183,x124184,f180(f855(x124181,a841)),x124184)),
% 191.32/191.79 inference(rename_variables,[],[4128])).
% 191.32/191.79 cnf(12426,plain,
% 191.32/191.79 (P54(x124261,f180(f855(x124261,a841)),x124262)),
% 191.32/191.79 inference(rename_variables,[],[3204])).
% 191.32/191.79 cnf(12430,plain,
% 191.32/191.79 (E(f37(x124301,x124302,x124303,x124304,x124305,x124306,x124307,x124308,x124309,a25),x124302)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(12441,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x124411),f2(a847)))),
% 191.32/191.79 inference(rename_variables,[],[4452])).
% 191.32/191.79 cnf(12450,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a1),f773(f102(a1),x124501)),f773(f81(a1),f773(f102(a1),x124502))))),
% 191.32/191.79 inference(rename_variables,[],[4474])).
% 191.32/191.79 cnf(12456,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),f773(f42(x124561),f773(f158(x124561),x124562))),f773(f181(f848(x124561)),x124562)))),
% 191.32/191.79 inference(rename_variables,[],[3725])).
% 191.32/191.79 cnf(12460,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x124601),f2(a847)))),
% 191.32/191.79 inference(rename_variables,[],[4452])).
% 191.32/191.79 cnf(12463,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x124631),f2(a847)))),
% 191.32/191.79 inference(rename_variables,[],[4452])).
% 191.32/191.79 cnf(12466,plain,
% 191.32/191.79 (P1(f773(f63(a847),f297(a847,x124661,x124662)))),
% 191.32/191.79 inference(rename_variables,[],[3394])).
% 191.32/191.79 cnf(12469,plain,
% 191.32/191.79 (P1(f773(f63(a847),f297(a847,x124691,x124692)))),
% 191.32/191.79 inference(rename_variables,[],[3394])).
% 191.32/191.79 cnf(12472,plain,
% 191.32/191.79 (P1(f773(f63(a847),f297(a847,x124721,x124722)))),
% 191.32/191.79 inference(rename_variables,[],[3394])).
% 191.32/191.79 cnf(12475,plain,
% 191.32/191.79 (P1(f773(f63(a847),f297(a847,x124751,x124752)))),
% 191.32/191.79 inference(rename_variables,[],[3394])).
% 191.32/191.79 cnf(12482,plain,
% 191.32/191.79 (P1(f773(f773(f232(a1),f773(f81(a1),f773(f102(a1),x124821))),f773(f102(a1),x124822)))),
% 191.32/191.79 inference(rename_variables,[],[3660])).
% 191.32/191.79 cnf(12485,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x124851),f2(a847)))),
% 191.32/191.79 inference(rename_variables,[],[4452])).
% 191.32/191.79 cnf(12486,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x124861),x124861))),
% 191.32/191.79 inference(rename_variables,[],[3184])).
% 191.32/191.79 cnf(12493,plain,
% 191.32/191.79 (P1(f773(f773(f233(a847),x124931),f773(a114,x124931)))),
% 191.32/191.79 inference(rename_variables,[],[3253])).
% 191.32/191.79 cnf(12499,plain,
% 191.32/191.79 (P1(f773(f773(f334(x124991),f773(x124992,x124993)),f773(f303(x124994,x124991,x124992),f239(f855(x124994,a841)))))),
% 191.32/191.79 inference(rename_variables,[],[3786])).
% 191.32/191.79 cnf(12502,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a1),f2(a1)),f773(f106(a1),f2(a1))))),
% 191.32/191.79 inference(scs_inference,[],[2999,3402,11899,11916,12337,12339,3426,10868,11934,12037,12134,12172,12180,12189,12242,12355,3434,12001,3435,12073,3485,3154,12376,12378,3155,12370,4128,12415,12418,3158,12411,3003,3024,12404,4386,4338,10038,10041,10047,10109,10112,10203,10206,10487,10498,11139,11154,11158,11199,11202,11205,11208,11220,11251,11264,11291,11294,11305,11310,11316,11415,11418,11422,11426,11436,11460,11531,11568,12110,12281,12328,12330,12343,12350,12368,12387,12389,12391,12395,4339,11155,3484,3066,4364,10044,10054,10065,10074,10173,10176,10179,10284,10390,10558,10690,10823,11059,11142,11149,11165,11213,11216,11319,11370,11386,11707,11732,11746,11781,11878,11997,12004,12164,12214,4382,10268,10363,3240,3204,12426,4376,10714,2808,2811,2820,2826,2830,2831,2832,2833,2835,2841,2845,2848,2851,2853,2855,2857,2859,2860,2862,2863,2868,2872,2873,2883,2885,2886,2911,2931,2941,2942,2947,2958,2960,2961,2964,2975,2977,4359,3058,4360,3519,3166,4351,3119,11412,12192,12196,12200,3128,3236,3639,3948,3027,4378,4396,4437,10804,11098,11101,3732,11187,3239,12332,3097,3085,3050,3553,12397,3045,3845,3558,4324,3034,3013,3040,4046,10984,3064,3197,11673,11896,12031,3243,10642,11998,3117,3118,3138,10305,3288,4472,10236,3814,4398,10100,10265,11056,12160,12193,4407,12168,3175,11512,4462,3578,3289,10885,3508,3256,12383,3081,3082,10165,10463,3344,3073,3004,3104,11179,3961,12183,12293,3815,10810,10929,10996,12144,12150,12249,12252,12271,4480,10746,10936,11050,11070,11106,11112,12089,4481,10850,10939,11053,11109,4482,10942,4483,11006,4484,3101,3382,12040,12167,3542,4241,4242,4395,11170,3488,3522,3694,3742,3368,3619,3253,10184,10187,10300,10377,10429,10432,10466,10555,10794,11571,11619,11703,11771,11849,11887,11960,11963,12275,3631,11403,3267,3450,4452,10077,10080,10106,10566,10581,10703,11121,11182,11585,11593,11825,11828,11921,12092,12441,12460,12463,4468,11280,11313,11353,11383,3616,3393,3394,12466,12469,12472,3769,3212,3214,3187,4449,3080,4392,3569,3880,3374,4469,3955,11067,3507,3729,11537,11540,3225,12008,12114,3922,3878,11696,12055,3825,10639,11861,11881,3873,10813,11929,12007,12067,12113,3543,11706,11856,11939,11988,3911,3560,10816,10878,10963,11025,11877,11953,12209,12268,12278,4473,10584,10947,3183,10196,10291,10415,10473,11256,11263,11485,11496,11530,11567,11676,11731,11946,12117,3184,10533,10587,10590,10623,10650,10684,10728,10762,11749,11752,11755,11758,11966,11969,11972,11975,12048,12220,3185,10281,10478,10561,10687,11366,11574,11588,11682,11693,11714,11719,11761,11764,11786,3186,10629,10695,11978,3261,11912,4448,10143,10231,10342,10372,10605,10653,10660,10973,11330,11435,11457,11463,11466,11482,11634,11637,11640,11643,11745,11767,11770,11780,11837,11840,11843,11846,11922,12019,12022,12120,12123,12213,3340,10435,10698,10743,11014,11087,11243,11492,12163,4464,10614,10626,10735,10753,10756,10807,10892,10902,10914,10950,10978,10990,11022,11062,11078,11081,11084,11115,11126,11129,11509,11546,11831,11834,11868,11913,11949,12098,12141,12147,12232,12235,12245,12292,12298,12301,3247,10460,3284,3279,3700,3636,10146,11406,11439,4461,10097,10454,10457,10895,10911,11369,11425,11474,11493,11603,11646,11649,11652,11655,3206,10647,10721,11440,11602,11806,3660,11543,4006,3399,4459,3671,3708,4440,4441,4443,3161,3162,4442,4444,3497,4102,4475,10068,10071,10323,10781,11606,3935,12081,3786,11132,11469,11473,11534,12171,12179,12248,3624,10759,10765,10776,11728,11952,3482,10981,12095,12105,12176,12223,12231,3959,3628,10839,10993,11019,11030,12061,12175,3725,12456,3453,10421,10424,10493,10674,4478,11400,4474,12450,4479,10544,10966,11118,12043,12052,12101,12265,4066,10632,12064,12078,3966,3659,3603,11526,4476,10119,10122,10448,10451,11277,11470,4477,11380,3629,10418,3630,3895,4489,4494,4500,4562,4565,4593,4611,4618,4619,4655,4684,4690,4794,4795,4832,4855,4856,4879,4881,4894,4898,4918,4924,4941,4945,4946,4951,4956,4957,4979,5003,5004,5014,5019,5025,5070,5071,5079,5088,5090,5091,5100,5102,5110,5115,5128,5134,5137,5138,5142,5175,5185,5192,5194,5195,5198,5199,5200,5208,5209,5212,5216,5217,5218,5225,5229,5230,5231,5239,5242,5244,5250,5261,5268,5281,5283,5291,5292,5296,5299,5324,5330,5340,5341,5342,5357,5369,5391,5397,5415,5416,5419,5438,5446,5447,5449,5450,5459,5460,5474,5478,5487,5488,5490,5505,5508,5519,5530,5537,5550,5556,5562,5563,5564,5567,5572,5609,5611,5614,5616,5619,5620,5621,5623,5625,5627,5630,5637,5651,5665,5671,5672,5691,5692,5697,5698,5700,5703,5706,5707,5712,5756,5770,5778,5782,5794,5804,5821,5839,5842,5852,5879,5894,5921,5941,5942,5945,5959,5961,5962,5964,5977,5978,5981,5983,5986,5987,6001,6007,6008,6009,6012,6014,6056,6066,6075,6110,6112,6114,6116,6126,6128,6131,6137,6139,6143,6146,6154,6161,6162,6163,6169,6195,6202,6209,6245,6246,6250,6251,6252,6253,6254,6255,6256,6263,6300,6301,6310,6330,6331,6356,6360,6371,6372,6380,6411,6412,6427,6449,6450,6469,6472,6473,6519,6527,6552,6593,6609,6618,6627,6628,6629,6630,6652,6653,6659,6671,6674,6677,6679,6680,6681,6683,6697,6710,6712,6713,6724,6727,6784,6797,6799,6805,6819,6822,6823,6860,6875,6903,69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% 191.32/191.79 cnf(12505,plain,
% 191.32/191.79 (P1(f773(f773(f232(a1),x125051),x125051))),
% 191.32/191.79 inference(rename_variables,[],[3185])).
% 191.32/191.79 cnf(12508,plain,
% 191.32/191.79 (P1(f773(f63(a847),f297(a847,x125081,x125082)))),
% 191.32/191.79 inference(rename_variables,[],[3394])).
% 191.32/191.79 cnf(12514,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x125141),x125141))),
% 191.32/191.79 inference(rename_variables,[],[3184])).
% 191.32/191.79 cnf(12527,plain,
% 191.32/191.79 (P1(f773(f773(f233(a847),x125271),f773(a114,x125271)))),
% 191.32/191.79 inference(rename_variables,[],[3253])).
% 191.32/191.79 cnf(12532,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),f52(a847,x125321,x125322)),x125321))),
% 191.32/191.79 inference(rename_variables,[],[3636])).
% 191.32/191.79 cnf(12541,plain,
% 191.32/191.79 (P1(f773(f773(f233(a847),x125411),f773(a114,x125411)))),
% 191.32/191.79 inference(rename_variables,[],[3253])).
% 191.32/191.79 cnf(12542,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x125421),f2(a847)))),
% 191.32/191.79 inference(rename_variables,[],[4452])).
% 191.32/191.79 cnf(12551,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a1),f773(f102(a1),x125511)),f2(a1)))),
% 191.32/191.79 inference(rename_variables,[],[4468])).
% 191.32/191.79 cnf(12552,plain,
% 191.32/191.79 (P1(f773(f239(f855(x125521,a841)),x125522))),
% 191.32/191.79 inference(rename_variables,[],[3247])).
% 191.32/191.79 cnf(12555,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a1),f773(f102(a1),x125551)),f2(a1)))),
% 191.32/191.79 inference(rename_variables,[],[4468])).
% 191.32/191.79 cnf(12556,plain,
% 191.32/191.79 (P1(f773(f239(f855(x125561,a841)),x125562))),
% 191.32/191.79 inference(rename_variables,[],[3247])).
% 191.32/191.79 cnf(12559,plain,
% 191.32/191.79 (P1(f773(f239(f855(x125591,a841)),x125592))),
% 191.32/191.79 inference(rename_variables,[],[3247])).
% 191.32/191.79 cnf(12562,plain,
% 191.32/191.79 (P1(f773(f239(f855(x125621,a841)),x125622))),
% 191.32/191.79 inference(rename_variables,[],[3247])).
% 191.32/191.79 cnf(12570,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x125701),x125702),f180(f855(x125701,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(12571,plain,
% 191.32/191.79 (P1(f773(f63(x125711),f180(f855(x125711,a841))))),
% 191.32/191.79 inference(rename_variables,[],[3261])).
% 191.32/191.79 cnf(12586,plain,
% 191.32/191.79 (P1(f773(f773(f233(a847),x125861),f773(a114,x125861)))),
% 191.32/191.79 inference(rename_variables,[],[3253])).
% 191.32/191.79 cnf(12587,plain,
% 191.32/191.79 (~E(f773(a114,x125871),x125871)),
% 191.32/191.79 inference(rename_variables,[],[4364])).
% 191.32/191.79 cnf(12590,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x125901),x125902),f180(f855(x125901,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(12593,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x125931),x125932),f180(f855(x125931,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(12595,plain,
% 191.32/191.79 (P1(f773(f773(f279(a847),x125951),f52(a847,x125951,x125951)))),
% 191.32/191.79 inference(scs_inference,[],[2999,3402,11899,11916,12337,12339,3426,10868,11934,12037,12134,12172,12180,12189,12242,12355,3434,12001,3435,12073,3485,3154,12376,12378,3155,12370,4128,12415,12418,3158,12411,3003,3024,12404,4386,4338,10038,10041,10047,10109,10112,10203,10206,10487,10498,11139,11154,11158,11199,11202,11205,11208,11220,11251,11264,11291,11294,11305,11310,11316,11415,11418,11422,11426,11436,11460,11531,11568,12110,12281,12328,12330,12343,12350,12368,12387,12389,12391,12395,4339,11155,3484,3066,4364,10044,10054,10065,10074,10173,10176,10179,10284,10390,10558,10690,10823,11059,11142,11149,11165,11213,11216,11319,11370,11386,11707,11732,11746,11781,11878,11997,12004,12164,12214,12326,4382,10268,10363,3240,3204,12426,4376,10714,2808,2811,2820,2826,2830,2831,2832,2833,2835,2841,2845,2848,2851,2853,2855,2857,2859,2860,2862,2863,2868,2869,2872,2873,2883,2885,2886,2911,2931,2941,2942,2947,2951,2954,2958,2960,2961,2964,2975,2977,4359,3058,4360,3519,3166,3509,4351,3119,11412,12192,12196,12200,3128,3236,3639,3948,3027,4378,4396,4437,10804,11098,11101,3732,11187,3239,12332,3097,3085,3050,3553,12397,3045,3845,3558,4324,3034,3013,3040,4046,10984,3064,3197,11673,11896,12031,3243,10642,11998,3117,3118,3138,10305,3288,4472,10236,3814,4398,10100,10265,11056,12160,12193,4407,12168,3175,11512,4462,3578,3289,10885,3508,3256,12383,3081,3082,10165,10463,3344,3073,3004,3104,11179,3961,12183,12293,3815,10810,10929,10996,12144,12150,12249,12252,12271,4480,10746,10936,11050,11070,11106,11112,12089,4481,10850,10939,11053,11109,4482,10942,4483,11006,4484,3101,3382,12040,12167,3542,4241,4242,4395,11170,3488,3522,3694,3742,12034,3368,3619,3253,10184,10187,10300,10377,10429,10432,10466,10555,10794,11571,11619,11703,11771,11849,11887,11960,11963,12275,12493,12527,12541,3631,11403,3267,3450,4452,10077,10080,10106,10566,10581,10703,11121,11182,11585,11593,11825,11828,11921,12092,12441,12460,12463,12485,4468,11280,11313,11353,11383,12551,12555,3616,3393,3394,12466,12469,12472,12475,12508,3769,3212,3214,3187,4449,3080,4392,3569,3880,3374,4469,3955,11067,3507,3729,11537,11540,3225,12008,12114,3922,3878,11696,12055,3825,10639,11861,11881,3873,10813,11929,12007,12067,12113,3543,11706,11856,11939,11988,12086,3911,3560,10816,10878,10963,11025,11877,11953,12209,12268,12278,4473,10584,10947,3183,10196,10291,10415,10473,11256,11263,11485,11496,11530,11567,11676,11731,11946,12117,12304,3184,10533,10587,10590,10623,10650,10684,10728,10762,11749,11752,11755,11758,11966,11969,11972,11975,12048,12220,12486,3185,10281,10478,10561,10687,11366,11574,11588,11682,11693,11714,11719,11761,11764,11786,11801,3186,10629,10695,11978,11981,3261,11912,12571,4448,10143,10231,10342,10372,10605,10653,10660,10973,11330,11435,11457,11463,11466,11482,11634,11637,11640,11643,11745,11767,11770,11780,11837,11840,11843,11846,11922,12019,12022,12120,12123,12213,3340,10435,10698,10743,11014,11087,11243,11492,12163,4464,10614,10626,10735,10753,10756,10807,10892,10902,10914,10950,10978,10990,11022,11062,11078,11081,11084,11115,11126,11129,11509,11546,11831,11834,11868,11913,11949,12098,12141,12147,12232,12235,12245,12292,12298,12301,12320,12570,12590,3247,10460,10490,12552,12556,12559,3284,3279,3700,3636,10146,11406,11439,4461,10097,10454,10457,10895,10911,11369,11425,11474,11493,11603,11646,11649,11652,11655,3206,10647,10721,11440,11602,11806,12049,3660,11543,4006,3399,4459,3671,3708,4440,4441,4443,3161,3162,4442,4444,3497,4102,4475,10068,10071,10323,10781,11606,3935,12081,3786,11132,11469,11473,11534,12171,12179,12248,3624,10759,10765,10776,11728,11952,3482,10981,12095,12105,12176,12223,12231,3959,3628,10839,10993,11019,11030,12061,12175,3725,12456,3453,10421,10424,10493,10674,4478,11400,4474,12450,4479,10544,10966,11118,12043,12052,12101,12265,4066,10632,12064,12078,3966,3659,12323,3603,11526,4476,10119,10122,10448,10451,11277,11470,4477,11380,3629,10418,3630,3895,4489,4494,4500,4562,4565,4593,4611,4618,4619,4655,4684,4690,4794,4795,4832,4855,4856,4879,4881,4894,4898,4918,4924,4941,4945,4946,4951,4956,4957,4979,5003,5004,5014,5019,5025,5070,5071,5079,5088,5090,5091,5100,5102,5110,5115,5128,5134,5137,5138,5142,5175,5185,5192,5194,5195,5198,5199,5200,5208,5209,5212,5216,5217,5218,5225,5229,5230,5231,5239,5242,5244,5250,5261,5268,5281,5283,5291,5292,5296,5299,5324,5330,5340,5341,5342,5357,5369,5391,5397,5415,5416,5419,5438,5446,5447,5449,5450,5459,5460,5474,5478,5487,5488,5490,5505,5508,5519,5530,5537,5550,5556,5562,5563,5564,5567,5572,5609,5611,5614,5616,5619,5620,5621,5623,5625,5627,5630,5637,5651,5665,5671,5672,5691,5692,5697,5698,5700,5703,5706,5707,5712,5756,5770,5778,5782,5794,5804,5821,5839,5842,5852,5879,5894,5921,5941,5942,5945,5959,5961,5962,5964,5977,5978,5981,5983,5986,5987,6001,6007,6008,6009,6012,6014,6056,6066,6075,6110,6112,6114,6116,6126,6128,6131,6137,6139,6143,6146,6154,6161,6162,6163,6169,6195,6202,6209,6245,6246,6250,6251,6252,6253,6254,6255,6256,6263,6300,6301,6310,6330,6331,6356,6360,6371,6372,6380,6411,6412,6427,6449,6450,6469,6472,6473,6519,6527,6552,6593,6609,6618,6627,6628,6629,6630,6652,6653,6659,6671,6674,6677,6679,6680,6681,6683,6697,6710,6712,6713,6724,6727,6784,6797,6799,6805,6819,6822,6823,6860,6875,6903,6936,6986,7017,7074,7102,7105,7163,7175,7242,7244,7259,7269,7272,7273,7291,7297,7299,7352,7362,7368,7371,7384,7429,7432,7436,7483,7484,7502,7565,7572,7591,7615,7637,7651,7667,7676,7684,7713,7715,7717,7725,7769,7779,7804,7862,7894,7928,7973,7988,8076,8124,8143,8167,8186,8208,8307,8309,8315,8335,8339,8353,8374,8385,8387,8399,8405,8409,8433,8448,8449,8460,8461,8462,8468,8469,8474,8475,8476,8477,8478,8496,8497,8498,8506,8518,8520,8534,8536,8542,8547,8568,8569,8598,8611,8615,8633,8654,8655,8657,8658,8668,8669,8691,8700,8707,8708,8709,8710,8733,8734,8745,8781,8787,8791,8804,8807,8809,8810,8817,8826,8891,8920,8921,8922,8936,8950,8956,8983,8984,8985,8986,8987,8990,9027,9030,9054,9088,9098,9099,9109,9119,9120,9134,9144,9146,9165,9187,9248,9286,9287,9288,9314,9315,9332,9349,9356,9367,9390,9408,9418,9419,9420,9421,9422,9437,9442,9477,9478,9484,9485,9521,9522,9547,9571,9573,9574,9589,9595,9619,9648,9695,9732,9745,9747,9751,9752,9754,9763,9764,9784,9789,9810,9815,9886,9962,9963,10014,2,8,9,4503,4519,4550,4551,4553,4577,4585,4586,4597,4644,4646,4689,4717,4809,4810,4826,4845,4901,4904,4905,4908,4909,4921,4931,4943,4944,4954,4963,4974,4975,4993,4998,4999,5000,5001,5002,5010,5013,5020,5084,5094,5125,5135,5140,5156,5174,5181,5182,5184,5189,5204,5206,5207,5214,5221,5222,5235,5236,5237,5238,5240,5241,5246,5247,5248,5249,5277,5278,5279,5287,5288,5289,5290,5319,5335,5337,5339,5376,5378,5379,5381,5382,5384,5385,5387,5396,5401,5403,5405,5406,5407,5408,5409,5410,5417,5427,5430,5441,5453,5454,5457,5467,5470,5471,5472,5497,5507,5521,5522,5531,5532,5534,5536,5540,5574,5578,5580,5638,5673,5674,5687,5690,5693,5694,5695,5696,5704,5708,5718,5719,5721,5722,5730,5751,5786,5799,5800,5801,5805,5815,5829,5833,5834,5835,5838,5854,5865,5866,5896,5897,5901,5923,5927,5930,5948,5953,5954,5979,5982,5990,5997,5999,6006,6010,6018,6019,6020,6021,6059,6060,6076,6130,6164,6166,6167,6191,6192,6194,6198,6199,6205,6219,6238,6258,6259,6264,6276,6277,6280,6293,6314,6319,6321,6335,6336,6340,6342,6343,6344,6346,6348,6349,6350,6358,6365,6366,6367,6368,6374,6376,6383,6420,6426,6441,6444,6445,6446,6484,6486,6488,6493,6494,6505,6508,6523,6548,6549,6550,6551,6562,6566,6583,6587,6610,6631,6647,6648,6649,6654,6667,6689,6691,6693,6695,6698,6699,6706,6708,6721,6729,6769,6772,6773,6789,6790,6791,6792,6812,6813,6831,6858,6880,6890,6892,6893,6895,6897,6898,6932,6933,6934,6939,6940,6942,6944,6945,6946,6968,6976,6977,6989,6999,7041,7050,7056,7064,7075,7080,7082,7088,7096,7109,7126,7143,7145,7155,7161,7222,7224,7225,7226,7234,7235,7241,7243,7268,7313,7332,7349,7365,7366,7383,7411,7415,7440,7467,7485,7488,7489,7499,7517,7518,7520,7522,7524,7526,7527,7528,7580,7581,7614,7616,7617,7618,7624,7643,7652,7663,7668,7674,7675,7681,7691,7692,7694,7723,7750,7780,7817,7818,7865,7872,7873,7895,7896,7915,7916,7981,7982,7983,8003,8004,8038,8042,8046,8055,8069,8096,8100,8106,8119,8138,8144,8166,8206,8236,8248,8265,8268,8297,8324,8388,8389,8392,8393,8410,8500,8501,8502,8503,8526,8550,8572,8614,8632,8685,8726,8729,8742,8779,8797,8813,8814,8829,8830,8958,8963,8981,8997,9017,9019,9022,9025,9028,9029,9041,9042,9065,9138,9173,9174,9239,9245,9279,9290,9294,9298,9299,9313,9337,9348,9357,9358,9360,9362,9389,9505,9584,9722,9723,9793,9863,9943,9954,9959,3,2549,2552,2563,2564,2565,2571,2572,2574,2575,2583,2584,2585,2588,2592,2594,2595,2596,2599,2600,2601,2602,2607,2608,2612,2613,2615,2625,2626,2627,2630,2631,2632,2635,2637,2648,2650,2651,2660,2675,2677,2679,2681,2682,2683,2685,2699,2700,2716,2726,2731,2733,2745,2748,2749,2750,2765,2767,2771,2773,2774,2792,2797,2798,2799,5171,5344,5350,5351,5428,5520,5549,5581,5597,5603,5605,5666,5667,5668,5669,5685,5720,5849,5895,5920,5956,5991,5995,6144,6151,6189,6190,6211,6213,6215,6221,6222,6223,6224,6225,6226,6227,6228,6229,6316,6390,6391,6482,6517,6518,6559,6560,6707,6720,6781,6802,6803,6807,6832,6856,6865,6867,6871])).
% 191.32/191.79 cnf(12598,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x125981),x125981))),
% 191.32/191.79 inference(rename_variables,[],[3184])).
% 191.32/191.79 cnf(12605,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x126051),x126051))),
% 191.32/191.79 inference(rename_variables,[],[3184])).
% 191.32/191.79 cnf(12609,plain,
% 191.32/191.79 (P1(f773(f773(f233(a847),x126091),f773(a114,x126091)))),
% 191.32/191.79 inference(rename_variables,[],[3253])).
% 191.32/191.79 cnf(12612,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x126121),x126121))),
% 191.32/191.79 inference(rename_variables,[],[3184])).
% 191.32/191.79 cnf(12617,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x126171),x126171))),
% 191.32/191.79 inference(rename_variables,[],[3184])).
% 191.32/191.79 cnf(12620,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x126201),x126201))),
% 191.32/191.79 inference(rename_variables,[],[3184])).
% 191.32/191.79 cnf(12623,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x126231),x126231))),
% 191.32/191.79 inference(rename_variables,[],[3184])).
% 191.32/191.79 cnf(12626,plain,
% 191.32/191.79 (E(f773(f773(f3(f855(x126261,a841)),f180(f855(x126261,a841))),x126262),f180(f855(x126261,a841)))),
% 191.32/191.79 inference(rename_variables,[],[3455])).
% 191.32/191.79 cnf(12627,plain,
% 191.32/191.79 (P1(f773(f63(x126271),f180(f855(x126271,a841))))),
% 191.32/191.79 inference(rename_variables,[],[3261])).
% 191.32/191.79 cnf(12630,plain,
% 191.32/191.79 (E(f773(f773(f3(f855(x126301,a841)),f180(f855(x126301,a841))),x126302),f180(f855(x126301,a841)))),
% 191.32/191.79 inference(rename_variables,[],[3455])).
% 191.32/191.79 cnf(12631,plain,
% 191.32/191.79 (P1(f773(f63(x126311),f180(f855(x126311,a841))))),
% 191.32/191.79 inference(rename_variables,[],[3261])).
% 191.32/191.79 cnf(12634,plain,
% 191.32/191.79 (E(f773(f773(f3(f855(x126341,a841)),f180(f855(x126341,a841))),x126342),f180(f855(x126341,a841)))),
% 191.32/191.79 inference(rename_variables,[],[3455])).
% 191.32/191.79 cnf(12635,plain,
% 191.32/191.79 (P1(f773(f63(x126351),f180(f855(x126351,a841))))),
% 191.32/191.79 inference(rename_variables,[],[3261])).
% 191.32/191.79 cnf(12638,plain,
% 191.32/191.79 (E(f773(f773(f3(f855(x126381,a841)),f180(f855(x126381,a841))),x126382),f180(f855(x126381,a841)))),
% 191.32/191.79 inference(rename_variables,[],[3455])).
% 191.32/191.79 cnf(12639,plain,
% 191.32/191.79 (P1(f773(f63(x126391),f180(f855(x126391,a841))))),
% 191.32/191.79 inference(rename_variables,[],[3261])).
% 191.32/191.79 cnf(12643,plain,
% 191.32/191.79 (E(f37(x126431,x126432,x126433,x126434,x126435,x126436,x126437,x126438,x126439,a25),x126432)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(12648,plain,
% 191.32/191.79 (P1(f773(f773(f279(a847),f773(a114,f2(a847))),x126481))),
% 191.32/191.79 inference(rename_variables,[],[3341])).
% 191.32/191.79 cnf(12649,plain,
% 191.32/191.79 (~P1(f773(f773(f232(a847),f773(a114,x126491)),x126491))),
% 191.32/191.79 inference(rename_variables,[],[4461])).
% 191.32/191.79 cnf(12652,plain,
% 191.32/191.79 (E(f773(f773(f3(f855(x126521,a841)),f180(f855(x126521,a841))),x126522),f180(f855(x126521,a841)))),
% 191.32/191.79 inference(rename_variables,[],[3455])).
% 191.32/191.79 cnf(12653,plain,
% 191.32/191.79 (P1(f773(f63(x126531),f180(f855(x126531,a841))))),
% 191.32/191.79 inference(rename_variables,[],[3261])).
% 191.32/191.79 cnf(12657,plain,
% 191.32/191.79 (P1(f773(f63(x126571),f180(f855(x126571,a841))))),
% 191.32/191.79 inference(rename_variables,[],[3261])).
% 191.32/191.79 cnf(12660,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x126601),x126601))),
% 191.32/191.79 inference(rename_variables,[],[3184])).
% 191.32/191.79 cnf(12666,plain,
% 191.32/191.79 (P1(f773(f773(f232(a1),x126661),x126661))),
% 191.32/191.79 inference(rename_variables,[],[3185])).
% 191.32/191.79 cnf(12669,plain,
% 191.32/191.79 (P1(f773(f773(f233(a847),x126691),f773(a114,x126691)))),
% 191.32/191.79 inference(rename_variables,[],[3253])).
% 191.32/191.79 cnf(12676,plain,
% 191.32/191.79 (P1(f773(f773(f233(a847),x126761),f773(a114,x126761)))),
% 191.32/191.79 inference(rename_variables,[],[3253])).
% 191.32/191.79 cnf(12679,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x126791),x126791))),
% 191.32/191.79 inference(rename_variables,[],[3184])).
% 191.32/191.79 cnf(12690,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x126901),x126901))),
% 191.32/191.79 inference(rename_variables,[],[3184])).
% 191.32/191.79 cnf(12693,plain,
% 191.32/191.79 (P1(f773(f773(f232(a1),x126931),x126931))),
% 191.32/191.79 inference(rename_variables,[],[3185])).
% 191.32/191.79 cnf(12700,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x127001),x127002),f180(f855(x127001,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(12711,plain,
% 191.32/191.79 (P1(f773(f773(f334(x127111),x127112),f239(f855(x127111,a841))))),
% 191.32/191.79 inference(rename_variables,[],[3340])).
% 191.32/191.79 cnf(12723,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x127231),f2(a847)))),
% 191.32/191.79 inference(rename_variables,[],[4452])).
% 191.32/191.79 cnf(12724,plain,
% 191.32/191.79 (P1(f773(f773(f232(a1),x127241),x127241))),
% 191.32/191.79 inference(rename_variables,[],[3185])).
% 191.32/191.79 cnf(12728,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x127281),f2(a847)))),
% 191.32/191.79 inference(rename_variables,[],[4452])).
% 191.32/191.79 cnf(12729,plain,
% 191.32/191.79 (P1(f773(f773(f232(a1),x127291),x127291))),
% 191.32/191.79 inference(rename_variables,[],[3185])).
% 191.32/191.79 cnf(12734,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x127341),x127341))),
% 191.32/191.79 inference(rename_variables,[],[3184])).
% 191.32/191.79 cnf(12741,plain,
% 191.32/191.79 (E(f773(f773(f18(x127411,x127412),x127413),x127414),x127413)),
% 191.32/191.79 inference(rename_variables,[],[3175])).
% 191.32/191.79 cnf(12751,plain,
% 191.32/191.79 (~P1(f773(f773(f233(a847),x127511),f2(a847)))),
% 191.32/191.79 inference(rename_variables,[],[4452])).
% 191.32/191.79 cnf(12752,plain,
% 191.32/191.79 (P1(f773(f773(f232(a1),x127521),x127521))),
% 191.32/191.79 inference(rename_variables,[],[3185])).
% 191.32/191.79 cnf(12760,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x127601),x127601))),
% 191.32/191.79 inference(rename_variables,[],[3184])).
% 191.32/191.79 cnf(12762,plain,
% 191.32/191.79 (~P1(f773(f773(f232(f855(a847,a841)),f295(a847,f773(a114,x127621),f773(a114,x127621))),f295(a847,x127622,x127621)))),
% 191.32/191.79 inference(scs_inference,[],[2999,3402,11899,11916,12337,12339,3426,10868,11934,12037,12134,12172,12180,12189,12242,12355,3434,12001,3435,12073,3485,3154,12376,12378,3155,12370,4128,12415,12418,3158,12411,3003,3024,12404,4386,4338,10038,10041,10047,10109,10112,10203,10206,10487,10498,11139,11154,11158,11199,11202,11205,11208,11220,11251,11264,11291,11294,11305,11310,11316,11415,11418,11422,11426,11436,11460,11531,11568,12110,12281,12328,12330,12343,12350,12368,12387,12389,12391,12395,12430,4339,11155,3484,3066,4364,10044,10054,10065,10074,10173,10176,10179,10284,10390,10558,10690,10823,11059,11142,11149,11165,11213,11216,11319,11370,11386,11707,11732,11746,11781,11878,11997,12004,12164,12214,12326,4382,10268,10363,3240,3204,12426,4376,10714,2808,2811,2820,2826,2830,2831,2832,2833,2835,2838,2841,2842,2845,2848,2851,2853,2855,2857,2859,2860,2862,2863,2868,2869,2872,2873,2883,2885,2886,2904,2906,2911,2916,2917,2931,2941,2942,2943,2946,2947,2951,2954,2958,2960,2961,2964,2975,2977,4359,3058,4360,3519,3166,3509,3759,4351,3119,11412,12192,12196,12200,3128,3236,3639,3948,3027,4378,4396,4437,10804,11098,11101,3732,11187,3239,12332,3097,3085,3050,3553,12397,3045,3845,3558,4324,3034,3013,3040,4046,10984,3064,3197,11673,11896,12031,3243,10642,11998,3117,3118,3138,10305,3288,4472,10236,3814,4398,10100,10265,11056,12160,12193,4407,12168,3175,11512,11515,4462,3578,3289,10885,3508,3256,12383,3081,3082,10165,10463,3344,3073,3004,3104,11179,3961,12183,12293,3815,10810,10929,10996,12144,12150,12249,12252,12271,4480,10746,10936,11050,11070,11106,11112,12089,4481,10850,10939,11053,11109,4482,10942,4483,11006,4484,3101,3382,12040,12167,3542,4241,4242,4395,11170,3488,3522,3694,3455,12626,12630,12634,12638,12652,3742,12034,3368,3619,3253,10184,10187,10300,10377,10429,10432,10466,10555,10794,11571,11619,11703,11771,11849,11887,11960,11963,12275,12493,12527,12541,12586,12609,12669,12676,3631,11403,3267,3450,4452,10077,10080,10106,10566,10581,10703,11121,11182,11585,11593,11825,11828,11921,12092,12441,12460,12463,12485,12542,12723,12728,12751,4468,11280,11313,11353,11383,12551,12555,3616,3393,3394,12466,12469,12472,12475,12508,3769,3212,3214,3187,4449,3080,4392,3569,3880,3374,4469,3955,11067,3507,3729,11537,11540,3225,12008,12114,12255,3922,3878,11696,12055,3825,10639,11861,11881,12068,3873,10813,11929,12007,12067,12113,3543,11706,11856,11939,11988,12086,3911,3560,10816,10878,10963,11025,11877,11953,12209,12268,12278,4473,10584,10947,3183,10196,10291,10415,10473,11256,11263,11485,11496,11530,11567,11676,11731,11946,12117,12304,3184,10533,10587,10590,10623,10650,10684,10728,10762,11749,11752,11755,11758,11966,11969,11972,11975,12048,12220,12486,12514,12598,12605,12612,12617,12620,12623,12660,12679,12690,12734,12760,3185,10281,10478,10561,10687,11366,11574,11588,11682,11693,11714,11719,11761,11764,11786,11801,12505,12666,12693,12724,12729,12752,3186,10629,10695,11978,11981,3261,11912,12571,12627,12631,12635,12639,12653,12657,4448,10143,10231,10342,10372,10605,10653,10660,10973,11330,11435,11457,11463,11466,11482,11634,11637,11640,11643,11745,11767,11770,11780,11837,11840,11843,11846,11922,12019,12022,12120,12123,12213,12307,3340,10435,10698,10743,11014,11087,11243,11492,12163,12310,4464,10614,10626,10735,10753,10756,10807,10892,10902,10914,10950,10978,10990,11022,11062,11078,11081,11084,11115,11126,11129,11509,11546,11831,11834,11868,11913,11949,12098,12141,12147,12232,12235,12245,12292,12298,12301,12320,12570,12590,12593,3247,10460,10490,12552,12556,12559,12562,3284,3279,3700,3636,10146,11406,11439,12532,4461,10097,10454,10457,10895,10911,11369,11425,11474,11493,11603,11646,11649,11652,11655,12649,3206,10647,10721,11440,11602,11806,12049,3660,11543,12482,4006,3399,4459,3671,3708,4440,4441,4443,3161,3162,4442,4444,3497,4102,4475,10068,10071,10323,10781,11606,3935,12081,3786,11132,11469,11473,11534,12171,12179,12248,3624,10759,10765,10776,11728,11952,3482,10981,12095,12105,12176,12223,12231,3959,3628,10839,10993,11019,11030,12061,12175,3725,12456,3341,3453,10421,10424,10493,10674,4478,11400,4474,12450,4479,10544,10966,11118,12043,12052,12101,12265,4066,10632,12064,12078,3966,3659,12323,3603,11526,4476,10119,10122,10448,10451,11277,11470,12274,4477,11380,11479,3629,10418,3630,3895,4489,4494,4500,4562,4565,4593,4611,4618,4619,4655,4684,4690,4794,4795,4832,4855,4856,4879,4881,4894,4898,4918,4924,4941,4945,4946,4951,4956,4957,4979,5003,5004,5014,5019,5025,5070,5071,5079,5088,5090,5091,5100,5102,5110,5115,5128,5134,5137,5138,5142,5175,5185,5192,5194,5195,5198,5199,5200,5208,5209,5212,5216,5217,5218,5225,5229,5230,5231,5239,5242,5244,5250,5261,5268,5281,5283,5291,5292,5296,5299,5324,5330,5340,5341,5342,5357,5369,5391,5397,5415,5416,5419,5438,5446,5447,5449,5450,5459,5460,5474,5478,5487,5488,5490,5505,5508,5519,5530,5537,5550,5556,5562,5563,5564,5567,5572,5609,5611,5614,5616,5619,5620,5621,5623,5625,5627,5630,5637,5651,5665,5671,5672,5691,5692,5697,5698,5700,5703,5706,5707,5712,5756,5770,5778,5782,5794,5804,5821,5839,5842,5852,5879,5894,5921,59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% 191.32/191.79 cnf(12763,plain,
% 191.32/191.79 (P1(f773(f773(f232(a847),x127631),x127631))),
% 191.32/191.79 inference(rename_variables,[],[3184])).
% 191.32/191.79 cnf(12766,plain,
% 191.32/191.79 (~P1(f773(f773(f232(a847),f773(a114,x127661)),x127661))),
% 191.32/191.79 inference(rename_variables,[],[4461])).
% 191.32/191.79 cnf(12772,plain,
% 191.32/191.79 (P1(f773(f773(f334(x127721),f773(x127722,x127723)),f773(f303(x127724,x127721,x127722),f239(f855(x127724,a841)))))),
% 191.32/191.79 inference(rename_variables,[],[3786])).
% 191.32/191.79 cnf(12773,plain,
% 191.32/191.79 (P29(x127731,x127731,f7(x127731),x127732)),
% 191.32/191.79 inference(rename_variables,[],[3426])).
% 191.32/191.79 cnf(12778,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x127781,a841)),x127782),f239(f855(x127781,a841))))),
% 191.32/191.79 inference(rename_variables,[],[3560])).
% 191.32/191.79 cnf(12779,plain,
% 191.32/191.79 (P29(x127791,x127791,f7(x127791),x127792)),
% 191.32/191.79 inference(rename_variables,[],[3426])).
% 191.32/191.79 cnf(12783,plain,
% 191.32/191.79 (P1(f773(f773(f232(f855(x127831,a841)),x127832),f239(f855(x127831,a841))))),
% 191.32/191.79 inference(rename_variables,[],[3560])).
% 191.32/191.79 cnf(12784,plain,
% 191.32/191.79 (P29(x127841,x127841,f7(x127841),x127842)),
% 191.32/191.79 inference(rename_variables,[],[3426])).
% 191.32/191.79 cnf(12788,plain,
% 191.32/191.79 (P29(x127881,x127881,f7(x127881),x127882)),
% 191.32/191.79 inference(rename_variables,[],[3426])).
% 191.32/191.79 cnf(12791,plain,
% 191.32/191.79 (~P1(f773(f773(f233(f855(x127911,a841)),x127912),f180(f855(x127911,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4473])).
% 191.32/191.79 cnf(12794,plain,
% 191.32/191.79 (P29(x127941,x127941,f7(x127941),x127942)),
% 191.32/191.79 inference(rename_variables,[],[3426])).
% 191.32/191.79 cnf(12797,plain,
% 191.32/191.79 (P29(x127971,x127971,f7(x127971),x127972)),
% 191.32/191.79 inference(rename_variables,[],[3426])).
% 191.32/191.79 cnf(12812,plain,
% 191.32/191.79 (E(f37(x128121,x128122,x128123,x128124,x128125,x128126,x128127,x128128,x128129,a25),x128122)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(12816,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x128161),x128162),f180(f855(x128161,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(12820,plain,
% 191.32/191.79 (P1(f773(f773(f334(x128201),f773(x128202,x128203)),f773(f303(x128204,x128201,x128202),f239(f855(x128204,a841)))))),
% 191.32/191.79 inference(rename_variables,[],[3786])).
% 191.32/191.79 cnf(12831,plain,
% 191.32/191.79 (~P1(f773(f773(f334(x128311),x128312),f180(f855(x128311,a841))))),
% 191.32/191.79 inference(rename_variables,[],[4464])).
% 191.32/191.79 cnf(12837,plain,
% 191.32/191.79 (E(f37(x128371,x128372,x128373,x128374,x128375,x128376,x128377,x128378,x128379,a25),x128372)),
% 191.32/191.79 inference(rename_variables,[],[4338])).
% 191.32/191.79 cnf(12839,plain,
% 191.32/191.79 (~E(f773(a114,x128391),x128391)),
% 191.32/191.79 inference(rename_variables,[],[4364])).
% 191.32/191.79 cnf(12844,plain,
% 191.32/191.79 (~E(f773(a114,x128441),x128441)),
% 191.32/191.79 inference(rename_variables,[],[4364])).
% 191.32/191.79 cnf(12849,plain,
% 191.32/191.79 (~E(f773(a114,x128491),x128491)),
% 191.32/191.79 inference(rename_variables,[],[4364])).
% 191.32/191.79 cnf(12856,plain,
% 191.32/191.79 (P1(f773(f773(f233(a847),x128561),f773(a114,x128561)))),
% 191.32/191.79 inference(rename_variables,[],[3253])).
% 191.32/191.79 cnf(12857,plain,
% 191.32/191.79 (~E(f773(a114,x128571),x128571)),
% 191.32/191.79 inference(rename_variables,[],[4364])).
% 191.32/191.79 cnf(12863,plain,
% 191.32/191.79 (~E(f773(f773(f83(a847),f773(a114,f2(a847))),f35(x128631,x128632)),f773(f773(f83(a847),f773(a114,f2(a847))),f36(x128633,x128634)))),
% 191.32/191.79 inference(scs_inference,[],[2999,3402,11899,11916,12337,12339,3426,10868,11934,12037,12134,12172,12180,12189,12242,12355,12357,12773,12779,12784,12788,12794,12797,3434,12001,3435,12073,3485,3154,12376,12378,3155,12370,4128,12415,12418,3158,12411,3003,3024,12404,4386,4338,10038,10041,10047,10109,10112,10203,10206,10487,10498,11139,11154,11158,11199,11202,11205,11208,11220,11251,11264,11291,11294,11305,11310,11316,11415,11418,11422,11426,11436,11460,11531,11568,12110,12281,12328,12330,12343,12350,12368,12387,12389,12391,12395,12430,12643,12812,12837,4339,11155,3484,3066,4364,10044,10054,10065,10074,10173,10176,10179,10284,10390,10558,10690,10823,11059,11142,11149,11165,11213,11216,11319,11370,11386,11707,11732,11746,11781,11878,11997,12004,12164,12214,12326,12587,12839,12844,12849,12857,4382,10268,10363,3240,3204,12426,4376,10714,2808,2811,2820,2826,2830,2831,2832,2833,2835,2838,2841,2842,2845,2848,2851,2853,2855,2857,2859,2860,2862,2863,2868,2869,2872,2873,2883,2885,2886,2904,2906,2911,2916,2917,2931,2941,2942,2943,2946,2947,2951,2954,2958,2960,2961,2964,2975,2977,4359,3058,4360,3519,3166,3509,3759,4351,3119,11412,12192,12196,12200,3128,3236,3639,3948,3026,3027,4378,4396,4437,10804,11098,11101,3732,11187,3239,12332,3097,3085,3050,3553,12397,3045,3845,3065,3558,4324,3034,3013,3040,4046,10984,3064,3197,11673,11896,12031,3243,10642,11998,3117,3118,3138,10305,3288,4472,10236,3814,4398,10100,10265,11056,12160,12193,12197,4407,12168,3175,11512,11515,12741,4462,10873,3148,3578,3170,3289,10885,3508,3256,12383,3081,3082,10165,10463,4446,3344,3073,3004,3127,3104,11179,3961,12183,12293,3815,10810,10929,10996,12144,12150,12249,12252,12271,4480,10746,10936,11050,11070,11106,11112,12089,4481,10850,10939,11053,11109,4482,10942,11003,4483,11006,4484,3101,3382,12040,12167,3542,4241,4242,4395,11170,3488,3522,3694,3455,12626,12630,12634,12638,12652,3742,12034,3368,3619,3253,10184,10187,10300,10377,10429,10432,10466,10555,10794,11571,11619,11703,11771,11849,11887,11960,11963,12275,12493,12527,12541,12586,12609,12669,12676,12856,3631,11403,3267,3450,4452,10077,10080,10106,10566,10581,10703,11121,11182,11585,11593,11825,11828,11921,12092,12441,12460,12463,12485,12542,12723,12728,12751,4468,11280,11313,11353,11383,12551,12555,3616,3393,3394,12466,12469,12472,12475,12508,3769,3212,3214,3187,4449,3080,4392,3569,3880,3374,4469,3955,11067,3507,3729,11537,11540,3225,12008,12114,12255,3922,3878,11696,12055,3825,10639,11861,11881,12068,3873,10813,11929,12007,12067,12113,3543,11706,11856,11939,11988,12086,3911,3560,10816,10878,10963,11025,11877,11953,12209,12268,12278,12778,12783,4473,10584,10947,12791,3183,10196,10291,10415,10473,11256,11263,11485,11496,11530,11567,11676,11731,11946,12117,12304,3184,10533,10587,10590,10623,10650,10684,10728,10762,11749,11752,11755,11758,11966,11969,11972,11975,12048,12220,12486,12514,12598,12605,12612,12617,12620,12623,12660,12679,12690,12734,12760,12763,3185,10281,10478,10561,10687,11366,11574,11588,11682,11693,11714,11719,11761,11764,11786,11801,12505,12666,12693,12724,12729,12752,3186,10629,10695,11978,11981,3261,11912,12571,12627,12631,12635,12639,12653,12657,4448,10143,10231,10342,10372,10605,10653,10660,10973,11330,11435,11457,11463,11466,11482,11634,11637,11640,11643,11745,11767,11770,11780,11837,11840,11843,11846,11922,12019,12022,12120,12123,12213,12307,3340,10435,10698,10743,11014,11087,11243,11492,12163,12310,12711,4464,10614,10626,10735,10753,10756,10807,10892,10902,10914,10950,10978,10990,11022,11062,11078,11081,11084,11115,11126,11129,11509,11546,11831,11834,11868,11913,11949,12098,12141,12147,12232,12235,12245,12292,12298,12301,12320,12570,12590,12593,12700,12816,12831,3247,10460,10490,12552,12556,12559,12562,3284,3279,3700,3636,10146,11406,11439,12532,4461,10097,10454,10457,10895,10911,11369,11425,11474,11493,11603,11646,11649,11652,11655,12649,12766,3206,10647,10721,11440,11602,11806,12049,3660,11543,12482,4006,3399,4459,3671,3708,4440,4441,4443,3161,3162,4442,4444,3497,11399,4102,4475,10068,10071,10323,10781,11606,3935,12081,3786,11132,11469,11473,11534,12171,12179,12248,12499,12772,12820,3624,10759,10765,10776,11728,11952,12228,3482,10981,12095,12105,12176,12223,12231,3959,3628,10839,10993,11019,11030,12061,12175,12217,3725,12456,3341,12648,3453,10421,10424,10493,10674,4478,11400,4474,12450,4479,10544,10966,11118,12043,12052,12101,12265,4066,10632,12064,12078,12104,3966,3659,12323,3603,11526,4476,10119,10122,10448,10451,11277,11470,12274,4477,11380,11479,3629,10418,10671,3630,3895,4489,4494,4500,4562,4565,4593,4611,4618,4619,4655,4684,4690,4794,4795,4832,4855,4856,4879,4881,4894,4898,4918,4924,4941,4945,4946,4951,4956,4957,4979,5003,5004,5014,5019,5025,5070,5071,5079,5088,5090,5091,5100,5102,5110,5115,5128,5134,5137,5138,5142,5175,5185,5192,5194,5195,5198,5199,5200,5208,5209,5212,5216,5217,5218,5225,5229,5230,5231,5239,5242,5244,5250,5261,5268,5281,5283,5291,5292,5296,5299,5324,5330,5340,5341,5342,5357,5369,5391,5397,5415,5416,5419,5438,5446,5447,5449,5450,5459,5460,5474,5478,5487,5488,5490,5505,5508,5519,5530,5537,5550,5556,5562,5563,5564,5567,5572,5609,5611,5614,5616,5619,5620,5621,5623,5625,5627,5630,5637,5651,5665,5671,5672,5691,5692,5697,5698,5700,5703,5706,5707,5712,5756,5770,5778,5782,5794,5804,5821,5839,5842,5852,5879,5894,5921,5941,5942,5945,5959,5961,5962,5964,5977,5978,5981,5983,5986,5987,6001,6007,6008,6009,6012,6014,6056,6066,6075,6110,6112,6114,6116,6126,6128,6131,6137,6139,6143,6146,6154,6161,6162,6163,6169,6195,6202,6209,6245,6246,6250,6251,6252,6253,6254,6255,6256,6263,6300,6301,6310,6330,6331,6356,6360,6371,6372,6380,6411,6412,6427,6449,6450,6469,6472,6473,6519,6527,6552,6593,6609,6618,6627,6628,6629,6630,6652,6653,6659,6671,6674,6677,6679,6680,6681,6683,6697,6710,6712,6713,6724,6727,6784,6797,6799,6805,6819,6822,6823,6860,6875,6903,6936,6986,7017,7074,7102,7105,7163,7175,7242,7244,7259,7269,7272,7273,7291,7297,7299,7352,7362,7368,7371,7384,7429,7432,7436,7483,7484,7502,7565,7572,7591,7615,7637,7651,7667,7676,7684,7713,7715,7717,7725,7769,7779,7804,7862,7894,7928,7973,7988,8076,8124,8143,8167,8186,8208,8307,8309,8315,8335,8339,8353,8374,8385,8387,8399,8405,8409,8433,8448,8449,8460,8461,8462,8468,8469,8474,8475,8476,8477,8478,8496,8497,8498,8506,8518,8520,8534,8536,8542,8547,8568,8569,8598,8611,8615,8633,8654,8655,8657,8658,8668,8669,8691,8700,8707,8708,8709,8710,8733,8734,8745,8781,8787,8791,8804,8807,8809,8810,8817,8826,8891,8920,8921,8922,8936,8950,8956,8983,8984,8985,8986,8987,8990,9027,9030,9054,9088,9098,9099,9109,9119,9120,9134,9144,9146,9165,9187,9248,9286,9287,9288,9314,9315,9332,9349,9356,9367,9390,9408,9418,9419,9420,9421,9422,9437,9442,9477,9478,9484,9485,9521,9522,9547,9571,9573,9574,9589,9595,9619,9648,9695,9732,9745,9747,9751,9752,9754,9763,9764,9784,9789,9810,9815,9886,9962,9963,10014,2,8,9,4503,4519,4550,4551,4553,4577,4585,4586,4597,4644,4646,4689,4717,4809,4810,4826,4845,4901,4904,4905,4908,4909,4921,4931,4943,4944,4954,4963,4974,4975,4993,4998,4999,5000,5001,5002,5010,5013,5020,5084,5094,5125,5135,5140,5156,5174,5181,5182,5184,5189,5204,5206,5207,5214,5221,5222,5235,5236,5237,5238,5240,5241,5246,5247,5248,5249,5277,5278,5279,5287,5288,5289,5290,5319,5335,5337,5339,5376,5378,5379,5381,5382,5384,5385,5387,5396,5401,5403,5405,5406,5407,5408,5409,5410,5417,5427,5430,5441,5453,5454,5457,5467,5470,5471,5472,5497,5507,5521,5522,5531,5532,5534,5536,5540,5574,5578,5580,5638,5673,5674,5687,5690,5693,5694,5695,5696,5704,5708,5718,5719,5721,5722,5730,5751,5786,5799,5800,5801,5805,5815,5829,5833,5834,5835,5838,5854,5865,5866,5896,5897,5901,5923,5927,5930,5948,5953,5954,5979,5982,5990,5997,5999,6006,6010,6018,6019,6020,6021,6059,6060,6076,6130,6164,6166,6167,6191,6192,6194,6198,6199,6205,6219,6238,6258,6259,6264,6276,6277,6280,6293,6314,6319,6321,6335,6336,6340,6342,6343,6344,6346,6348,6349,6350,6358,6365,6366,6367,6368,6374,6376,6383,6420,6426,6441,6444,6445,6446,6484,6486,6488,6493,6494,6505,6508,6523,6548,6549,6550,6551,6562,6566,6583,6587,6610,6631,6647,6648,6649,6654,6667,6689,6691,6693,6695,6698,6699,6706,6708,6721,6729,6769,6772,6773,6789,6790,6791,6792,6812,6813,6831,6858,6880,6890,6892,6893,6895,6897,6898,6932,6933,6934,6939,6940,6942,6944,6945,6946,6968,6976,6977,6989,6999,7041,7050,7056,7064,7075,7080,7082,7088,7096,7109,7126,7143,7145,7155,7161,7222,7224,7225,7226,7234,7235,7241,7243,7268,7313,7332,7349,7365,7366,7383,7411,7415,7440,7467,7485,7488,7489,7499,7517,7518,7520,7522,7524,7526,7527,7528,7580,7581,7614,7616,7617,7618,7624,7643,7652,7663,7668,7674,7675,7681,7691,7692,7694,7723,7750,7780,7817,7818,7865,7872,7873,7895,7896,7915,7916,7981,7982,7983,8003,8004,8038,8042,8046,8055,8069,8096,8100,8106,8119,8138,8144,8166,8206,8236,8248,8265,8268,8297,8324,8388,8389,8392,8393,8410,8500,8501,8502,8503,8526,8550,8572,8614,8632,8685,8726,8729,8742,8779,8797,8813,8814,8829,8830,8958,8963,8981,8997,9017,9019,9022,9025,9028,9029,9041,9042,9065,9138,9173,9174,9239,9245,9279,9290,9294,9298,9299,9313,9337,9348,9357,9358,9360,9362,9389,9505,9584,9722,9723,9793,9863,9943,9954,9959,3,2549,2552,2563,2564,2565,2571,2572,2574,2575,2583,2584,2585,2588,2592,2594,2595,2596,2599,2600,2601,2602,2607,2608,2612,2613,2615,2625,2626,2627,2630,2631,2632,2635,2637,2648,2650,2651,2660,2675,2677,2679,2681,2682,2683,2685,2699,2700,2716,2726,2731,2733,2745,2748,2749,2750,2765,2767,2771,2773,2774,2792,2797,2798,2799,5171,5344,5350,5351,5428,5520,5549,5581,5597,5603,5605,5666,5667,5668,5669,5685,5720,5849,5895,5920,5956,5991,5995,6144,6151,6189,6190,6211,6213,6215,6221,6222,6223,6224,6225,6226,6227,6228,6229,6316,6390,6391,6482,6517,6518,6559,6560,6707,6720,6781,6802,6803,6807,6832,6856,6865,6867,6871,6914,6937,6938,6954,6955,6957,6988,7035,7036,7132,7201,7202,7203,7204,7220,7260,7274,7318,7319,7328,7337,7339,7351,7386,7387,7388,7389,7534,7535,7541,7542,7544,7546,7622,7756,7759,7761,7762,7777,7815,7892,7936,7990,8009,8010,8082,8179,8246,8247,8249,8281,8320,8349,8350,8441,8442,8443,8444,8576,8793,8794,8854,8869,8923,8924,9038,9069,9092,9122,9153,9335,9579,9761,9818,9821,5491,5752,5753,5913,6298,6299,6393])).
% 191.32/191.79 cnf(13356,plain,
% 191.32/191.79 ($false),
% 191.32/191.79 inference(scs_inference,[],[3922,4478,3815,4464,3873,3013,4462,4395,3341,3542,4484,4474,12863,10998,12595,10189,10858,12262,10560,4273,12762,10510,12094,12502,10910,2967,9,2,8,5570,6552,7371,5563,5692,7769,8476,8449,5852,6424,8791,4945,6331,9732,9747,5564,9165,9745,5987,7429,7908,9248,4820,6252,8534,4593]),
% 191.32/191.79 ['proof']).
% 191.32/191.79 % SZS output end Proof
% 191.32/191.79 % Total time :162.710000s
%------------------------------------------------------------------------------